Hydrology Research sample issue by IWA Publishing

45.1

2014

Editorial: New category of Invited Papers

We are pleased to announce the launch of a new category of

will moderate the review process for Invited Papers

Hydrology Research paper – the Invited Paper. The Editors

accordingly.

encourage submission of manuscripts under this category

The Editors will contact potential authors of Invited

from experienced research hydrologists, especially those

Papers. However, authors not approached in this way with

with an international proﬁle. The aim is to establish a

an interest in submitting a manuscript under this new cat-

series of prestigious papers that will contribute to the conti-

egory should contact the Editors directly with an outline

nuing development of research and applied hydrology.

proposal. Ideas from third parties about topics for, and

An Invited Paper can cover a topic of the author’s

potential authors of, Invited Papers are welcome at any

choice and need not necessarily include new research. In

time. Jointly authored manuscripts are welcome (not more

this respect it will be different from a Research Paper. We

than three co-authors as a guideline).

are seeking substantial, well-written essays on topics of inter-

This issue of Hydrology Research launches the Invited

est to research and practising hydrologists. An Invited Paper

Paper series with ‘Reconciling hydrology with engineering’

should, of course, review published research and discussions

by Professor Demetris Koutsoyiannis of the National Techni-

of relevance to the topic being addressed. It will provide an

cal University of Athens, Greece (Koutsoyiannis ). It is an

opportunity for the author to present arguments in a way

excellent example of the sort of Invited Paper we are seeking.

that may not be acceptable in a Research Paper. It can include personal opinions, based on the arguments pre-

Ian G. Littlewood

sented, in a way that might stimulate further published

Editor (BHS)

discussion (in Hydrology Research or elsewhere).

Chong-Yu Xu

The manuscript will typically be sent to two highly

Editor (NHF)

experienced reviewers who will advise the Editors and the author in terms of it being attractive to readers of Hydrology

REFERENCE

Research and becoming a valuable contribution to the literature more generally. The author may express views and opinions different from those of the reviewers; the Editors

doi: 10.2166/nh.2013.201

Koutsoyiannis, D.  Reconciling hydrology with engineering. Hydrology Research 45 (1), 2–22.

Invited Paper

45.1

2014

Invited Paper Reconciling hydrology with engineering Demetris Koutsoyiannis

ABSTRACT Hydrology has played an important role in the birth of science. Yet practical hydrological knowledge, related to human needs for water storage, transfer and management, existed before the development of natural philosophy and science. In contemporary times, hydrology has had strong links with engineering as its development has been related to the needs of the design and

Demetris Koutsoyiannis Department of Water Resources and Environmental Engineering, Faculty of Civil Engineering, National Technical University of Athens, Greece E-mail: dk@itia.ntua.gr

management of water infrastructures. In the 1980s these links were questioned and it was suggested that separating hydrology from engineering would be beneficial for both. It is argued that, thereafter, hydrology, instead of becoming an autonomous science, developed new dependencies, particularly on politically driven agendas. This change of direction in effect demoted the role of hydrology, for example in studying hypothetical or projected climate-related threats. Revisiting past experiences suggests that re-establishing the relationship of hydrology with engineering could be beneficial. The study of change and the implied uncertainty and risk could constitute a field of mutual integration of hydrology and engineering. Engineering experience may help hydrology to appreciate that change is essential for progress and evolution, rather than only having adverse impacts. While the uncertainty and risk cannot be eliminated they can be dealt with in a quantitative and rigorous manner. Key words

| history and philosophy of science, hydraulics, hydrology, water resource engineering, water technology

‘The philosophers have only interpreted the world, in var-

natural philosophy and science), in addition to his scientiﬁc

ious ways; the point, however, is to change it’ (Karl Marx;

achievements on geometry, proposed an explanation of this

Theses on Feuerbach, 1845)

‘paradox’. The historian Herodotus (Histories, 2.20), who lived more than a century later (ca. 484–425

BC)

relates

this explanation and quotes additional ones by other

A BRIEF HISTORY OF HYDROLOGY AND ITS LINKS WITH ENGINEERING

Greek philosophers, including his own. Up to that time, all explanations were incorrect, but the important thing is that they were physical and thus scientiﬁc, contrary to the

Hydrology has played an important role in the birth of

tradition of attributing natural phenomena to divine action.

science as the ﬁrst scientiﬁc problems, put and studied as

Soon after Thales, the notion of what we call today the

such, were about hydrological phenomena. It appears that

hydrological cycle was established. Speciﬁcally, Anaximander

the ﬁrst geophysical problem formulated in scientiﬁc terms

(c. 610–547

was the explanation of the ﬂood regime of the Nile, then

evaporation, Xenophanes (570–480

BC)

understood that rainfall is generated from BC)

described the whole

regarded as a paradox, i.e. the fact that ﬂooding occurs in

hydrological cycle, while Aristotle (384–328

summer when rainfall in Egypt is very low to non-existent

Meteorologica recognized the principle of mass conservation

(Koutsoyiannis et al. , ). Thales of Miletus (640–

within the hydrological cycle (see the relevant extracts from

546

classical texts in Koutsoyiannis et al. ()). It is clear in

BC,

one of the Seven Sages of Greece and the father of

doi: 10.2166/nh.2013.092

BC)

in his book

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

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Meteorologica that the ancient Greek natural philosophers

accompanied by similar scientiﬁc progress. The latter had

formed a view of the hydrological cycle, which was generally

to wait until the Renaissance. Then, not only did the ancient

consistent with the modern one, but also included some incor-

scientiﬁc knowledge revive but it was further advanced by the

rect elements (as happens in the development of scientiﬁc

Italian Renaissance scientists Leonardo da Vinci (1452–

knowledge all the time). Aristotle himself incorrectly asserted

1519), Galileo Galilei (1564–1642) and Benedetto Castelli

that vapour condensation occurs not only in the atmosphere,

(1578–1643). The major breakthrough during the Renais-

but also underground. For this assertion (as well as a passage

sance was the recognition of the importance of the

from Plato’s dialogue Phaedo; Koutsoyiannis et al. ()) the

empirical basis in hydrological phenomena, acquired by

modern hydrological literature charges these philosophers

observation, measurement and experiment. Leonardo da

with vastly erroneous or fanciful views, providing a picture

Vinci, the great artist, scientist and engineer, was also a

that is opposite to what they actually proclaimed, sometimes

great experimentalist and gave particular focus to water

using ‘quotations’ that do not actually appear in the original

ﬂow, as testiﬁed by his book Del moto e misura dell’ acqua,

texts. The most signiﬁcant advances in the science of the anti-

written around 1500 (but published much later) and many

quity, as well as its marriage with technology, were made

of his manuscripts (see also Pfister et al. ). Also, Bene-

during the Hellenistic period (323–146

For example, it

detto Castelli in his book Della misura delle acque correnti,

was at that period that the ‘paradox’ of the Nile was resolved

published in 1628, explained how he installed a rain gauge

by Eratosthenes (ca. 276–195

who among other achieve-

in Perugia in order to provide a basis for estimating the vari-

ments also calculated the Earth’s circumference with an

ations in level of the Trasimeno Lake (Dooge ) and

error of less than 2%. During the same period, hydraulics

controlling the discharge of its outlet. Interestingly, similar

was founded on a scientiﬁc basis (hydrostatics by Archi-

knowledge had been developed even earlier in other places

BC)

BC).

pressurized ﬂow by Hero of

of the world. Thus, the Korean King Sejo is attributed to

Alexandria, ∼150 BC) and was able to support large-scale tech-

have invented a rain gauging device in 1442 (Arakawa )

nological applications (e.g. the 3 km long inverted siphon of

while it is thought that rainfall measurements were taken

the Pergamon aqueduct; Koutsoyiannis et al. (b)).

also in ancient times in China and India (Montanari et al.

medes, ca. 287–212

BC;

Yet practical hydrological knowledge existed before the

). Nonetheless, the oldest systematic and ofﬁcial rainfall

development of natural philosophy and science. This knowl-

measurements in the world were perhaps those made in

edge had its roots in human needs related to water storage,

Korea, in the ﬁfteenth century, from which the records

transfer and management. Thales’ achievements include

from the eighteenth century (namely after 1770) to date

hydraulic engineering as he accomplished the diversion of

have survived (Koutsoyiannis & Langousis ).

the River Halys for military purposes. Nonetheless, hydraulic

In the eighteenth century, Daniel Bernoulli (mostly

engineering achievements started in prehistory, in several civi-

known for the discovery of what we call Bernoulli’s law)

lizations in Mesopotamia, Egypt, India and Greece (Mays

understood that the study of the motion of ﬂuids needs

et al. ) and aimed to control the ﬂow of water, initially

advanced knowledge of mathematics and is very difﬁcult:

for agricultural needs (irrigation) and later for urban needs (water supply and sewerage). Remains of prehistoric irrigation

‘Admittedly, as useful a matter as the motion of ﬂuid and

canals, as well as urban water systems still exist. The historical

related sciences has always been an object of thought. Yet

fact that technological applications to solve practical prob-

until this day neither our knowledge of pure mathematics

lems preceded the development of scientiﬁc knowledge is

nor our command of the mathematical principles of

important to recognize and relevant when revisiting the cur-

nature have permitted a successful treatment’ (Bernoulli,

rent state of hydrology, as this paper attempts.

in a letter to J. D. Schöpﬂin, Sept. 1734).

Substantial progress in hydraulic engineering occurred during Roman times, as demonstrated by the famous

Despite spectacular progress in the next three centuries,

Roman aqueducts which advanced in scale and spread

there still remain issues for which the phrase ‘until this

through Europe and beyond. This however was not

day’ in this quotation could well represent present day.

D. Koutsoyiannis

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Hydrology Research

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The term hydraulic was used already in the Hellenistic

apparatus); (ii) Medical Hydrology (physiological and medi-

period (by Hero of Alexandria in his Pneumatica, and later

cal questions); and (iii) Climatology, Scientiﬁc and Medical.

by Pliny). However, it seems that the term hydrology did

One can then infer that the term Scientiﬁc Hydrology, which

not exist in the classical literature (neither a search in the

was used even in the name International Association of

archive of classical texts of www.perseus.tufts.edu, nor the

Scientiﬁc Hydrology of what is now called International

Liddell & Scott () Lexicon provide any related entry).

Association of Hydrological Sciences (IAHS) aimed to dis-

It only appeared towards the end of the eighteenth century,

tinguish it from Medical Hydrology (rather than distinguish

as a search on Google books testiﬁes (Figure 1). In its ﬁrst

it from charlatans’ and simpletons’ practices as generally

use, the term hydrology had a broad meaning and described

thought; cf. www.iahs.info/About-IAHS/History.do).

a body of knowledge related to water and its links to other

Other textbooks and manuals of the same period clearly

geophysical sciences, like geology, meteorology, climatology

manifest the link of hydrology with hydraulics and, through

and natural history, as well as to botany, zoology, anthropol-

this, with engineering:

ogy and health issues. Such links have been reﬂected in some of the ﬁrst books and papers, published in the late nineteenth

•

century, having the term hydrology in their titles:

Manual of Hydrology: containing I. Hydraulic and other tables. II. Rivers, ﬂow of water, springs, wells, and percolation. III. Tides, estuaries, and tidal rivers. IV. Rainfall and

•

A Treatise on Physical Geography: Comprising Hydrology, Geognosy, Geology, Meteorology, Botany, Zoology, and Anthropology (Barrington & Burdett ; see cover in

•

Figure 2, left); Atlas of Physical Geography: Illustrating in a Series of Original Designs the Elementary Facts of Chartography, Geology, Topography, Hydrology, Meteorology, and Natu-

•

ral History (Johnston ); On the Proceedings of the International Congress of Hydrology and Climatology at Biarritz, October 1886 (Symons ).

•

evaporation (Beardmore ; see cover in Figure 2, right); A Practical Treatise on Hydraulic and Water-supply Engineering: Relating to the Hydrology, Hydrodynamics, and Practical Construction of Water-works, in North America (Fanning ). These books contained hydraulic formulae and tables

(Figure 3, upper) along with observational hydrological information (Figure 3, lower). They indirectly indicate that the reasons leading to hydrology becoming a quantitative science are related to engineering needs. It was only in the 1960s that hydrology acquired a clear, elegant and practically unquestionable, deﬁnition as a

Interestingly, in the last source, the related subﬁelds (sec-

science:

tions) covered in the 1886 Congress of Hydrology, are listed as: (i) Scientiﬁc Hydrology (water analysis, micro-organisms,

‘Hydrology is the science which deals with the waters of

collection of mineral water, geological inﬂuences, bathing

the earth, their occurrence, circulation and distribution

Figure 1

Evolution of the frequency per year of the indicated words, as found in millions of books digitized by Google (data and visualization by Google books: books.google.com/ngrams/; see also Michel et al. (2011)).

D. Koutsoyiannis

Figure 2

Reconciling hydrology with engineering

Hydrology Research

45.1

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Covers of two of the earliest books whose title includes the term ‘hydrology’.

on the planet, their physical and chemical properties and

up to the 1970s, the developed world was investing in building

their interactions with the physical and biological

public infrastructures (Burges ), hydraulics was a domi-

environment, including their responses to human

nant and primary ﬁeld in engineering and supported the

activity’ (United Nations Educational, Scientific and

design of hydraulic structures such as dams, canals, pipelines

Cultural Organization (UNESCO) , ).

and ﬂood protection works. At those times, hydrology was regarded as an appendage of hydraulic engineering (Yevje-

This deﬁnition complemented an earlier one by the US Ad

vich ), again to support the design of hydraulic

Hoc Panel on Hydrology (), adding an essential

structures, especially in estimating their design discharges.

element, the interaction of water with human activity. Some-

The engineering aspect of hydrology was prominent also

times the term, hydrological science has been used as a

because it was part of the professional education in engineer-

synonym but it conceals the fact that hydrology is strongly

ing schools. It is because of this aspect that hydrology made

linked with engineering and technology. Besides, hydrologi-

signiﬁcant progress in developing a scientiﬁc approach to

cal sciences (plural), although in common use for several

study natural variability and the implied uncertainty.

decades, is ill-deﬁned as it has not been explained which

In other words, the close relationship of hydrology with

the constituent sciences are and perhaps indicates a misspe-

engineering advanced it as a modern quantitative scientiﬁc

ciﬁcation of scientiﬁc branches of hydrology as sciences.

discipline. Some of these advances are pertinent to both

The above deﬁnition, however, does not explicitly recog-

hydraulics and hydrology, such as those related to the ﬂow

nize the link of hydrology with hydraulics and, more

in aquifers and in unsaturated soils, as well as the transport

generally, with engineering. Because, in the twentieth century

phenomena and the movement of sediments. Other

D. Koutsoyiannis

Figure 3

Reconciling hydrology with engineering

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Images from pages of the book by Beardmore (1862) whose cover is shown in Figure 2, right; (upper) Du Buât’s formula for water pipes; (lower) observations of maximum water level of the Po River.

advances in hydrology were not connected to hydraulics, yet

unit hydrograph), the systems analysis techniques used for

they had a clear engineering orientation. These include the

assisting with water resources management, and the para-

probabilistic and stochastic modelling of hydrological pro-

meterization–optimization of the modelling of hydrological

cesses, the development of data processing methodologies,

processes.

algorithms and computer tools, as well as of Monte Carlo

The involvement of stochastics in hydrology enabled a

simulation techniques, the reliability theory of reservoir sto-

new type of prediction, the probabilistic prediction which

rage, the linear systems approximations to ﬂood routing (e.g.

replaces deterministic prediction when it becomes infeasible

D. Koutsoyiannis

Reconciling hydrology with engineering

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due to the very long prediction horizons in engineering planning and design. A basic premise in planning and design is that all engineering constructions are subject to uncertain loadings and are inescapably associated with risk.

SIMILARITIES, DIFFERENCES AND INTERACTION OF HYDROLOGY AND HYDRAULICS An informative analysis of the differences of hydrology from hydraulics has been made by Savenije (), who, inter alia, says: ‘Hydraulic engineers describe the behaviour of water within well-defined boundaries. There is nothing wrong with that. The problem appears when hydraulic engineers start to apply their ‘physical laws’ to hydrology.’ It could be added that, in hydraulics, the well-defined boundaries have also simple geometry, usually with rectangular, trapezoidal or circular cross sections, and uniform longitudinal slope (Figure 4, upper). Once the geometry of, say, a canal is defined, there is no difference in the hydraulic characteristics whether the canal is in the Nile Delta or in the Po Valley. For this reason, hydraulics can proceed to construct abstract objects, which are generalizations of the natural objects. Actually, the structural simplicity enables repeatability (multiple copies of the same element), which is desirable in engineering constructions as, by studying only one element, we can infer the behaviour of all identical elements. In contrast, with their complex geometry and structure (Figure 4, middle), the objects of hydrology are unique and non-repeatable (Koutsoyiannis et al. ). In hydrology, the Nile Delta and Po Valley are different entities, have different identities and, from a quantitative point of view, it looks impossible to devise an abstract concept that would generalize and unify both in one. In addition, hydrology deals with all three phases of water, solid, liquid, gaseous, and its domain includes the atmosphere, and the Earth’s surface and subsurface (Figure 4, lower). Hydrology is interrelated to hydraulics as well as to other disciplines that study flows including fluid mechanics

Figure 4

(Upper) An irrigation canal as a typical, simple and repeatable, object representative of hydraulics (Lugagnano, Verona, Italy; photo from www. panoramio.com/photo/40777649); (Middle) The Po River basin illustrating the complex and unique objects of hydrology (map from Wikipedia); (Lower) A satellite image of the same basin (from visibleearth.nasa.gov/view.php?id ¼

and physics, as depicted in Figure 5. The schematic on the

5,5161) suggestive of the fact that hydrology deals with all three phases of water, solid, liquid, gaseous, and its domain includes the atmosphere, and the

left shows the entire pyramid of knowledge and has been

Earth’s surface and subsurface.

D. Koutsoyiannis

Figure 5

Reconciling hydrology with engineering

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A schematic depiction of the domain of hydrology and some of its relatives, hydraulics, ﬂuid mechanics and physics, within the pyramid of knowledge as suggested by Gauch (2003).

adapted from a book by Gauch () on the scientiﬁc

power spectrum of turbulence indicates two scaling areas

method. The schematic on the right focusing on hydrology

with different slopes for high and low frequencies, as seen

and some of its relatives, tries to indicate that, on the one

in the Appendix. The frequencies most relevant to ﬂuid mech-

hand, the ﬂow of water is represented by two disciplines:

anics and hydraulics are the highest (the time scales are the

ﬂuid mechanics – the more theoretical – and hydraulics –

smallest), which deﬁne the turbulent (Reynolds) stresses.

the more technological. On the other hand, the circulation

These are characterized by the Kolmogorov’s 5/3 scaling

of water on Earth is represented by a single discipline,

law (spectrum slope ¼ 5/3). But hydrology is more con-

hydrology. This should necessarily cover both the scientiﬁc

cerned

domain and the technological domain. In addition, hydrol-

frequencies), in which the Hurst–Kolmogorov dynamics

ogy is associated with higher complexity in comparison to

applies, reﬂected in a milder slope (between 0 and 1; see

physics, ﬂuid mechanics and hydraulics.

Appendix). The different scales and scaling behaviours signify

Physics and ﬂuid mechanics often deal with complex phenomena, too. Among them, turbulence is the most charac-

about

the

largest

time

scales

(the

lowest

another dissimilarity between ﬂuid mechanics and hydraulics, on the one hand, and hydrology, on the other hand.

teristic that traverses all interrelated ﬁelds and is important

The stochastic behaviour of turbulence does not enable

also for hydrology, as exempliﬁed in Figure 6. Almost all

accurate microscopic descriptions, but helps to develop

ﬂows we deal with in practical problems are turbulent. Turbu-

good macroscopic descriptions for the temporal and spatial

lence is a phenomenon that resists a deterministic description

averages of the involved processes. In ﬂuid mechanics the

and its quantiﬁcation demands a stochastic approach.

5/3 law has helped the analytical and numerical modelling

Random ﬁelds of turbulent quantities, such as the ﬂow vel-

of turbulence. In hydraulics, this law can yield the cele-

ocity at a point and at a time, are much more complex than

brated Manning’s equation for rectangular cross sections

purely random ﬁelds. This more complex behaviour is mani-

(Gioia & Bombardelli ),

fested, inter alia, in the power spectrum of a turbulent time series, which is very different from the ﬂat power spectrum of white noise. More importantly, a logarithmic plot of the

V¼

1 2=3 1=2 R i n

(1)

D. Koutsoyiannis

Figure 6

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A photo of a junction of two branches of the Karpenisiotis river, tributary to Acheloos in SW Greece; suspended sediment transport, evident on the right branch, would not be possible without turbulence (photo by author).

where V is the mean velocity of the cross section, n is a

trapezoidal) cross sections (e.g. Papanicolaou ) and the

roughness coefﬁcient, R is the hydraulic radius and i is the

correction needed for meandering channels (Chow ).

energy slope. The simplicity of Manning’s equation is

Even the very notion of the velocity in the equation is

remarkable and it becomes more evident if we compare it

not strictly a deterministic physical quantity, whether we

with the purely empirical and engineering-oriented Du

use a Lagrangian or an Eulerian type of description. It is a

Buat’s equation of the eighteenth century, shown in Figure 3,

statistical quantity, a spatial and, simultaneously, a temporal

which in metric units is written:

average. In this respect, Manning’s equation is a statistical

pffiffiffiffi pffiffiffiffi 48:92( R 0:016) pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:05( R 0:016) V ¼ pffiffiffiffiffiffiffi 1=i ln 1=i þ 1:6

equation rather than a deterministic one. It does not (2)

describe the physics faithfully, yet it can perhaps be classiﬁed as a physical equation, if we accept that statistics is part of physics (the example of statistical thermophysics

We may notice that despite being more complicated and not

is characteristic of this type). It is a macroscopic equation,

consistent dimension-wise, the latter equation does not con-

because of the assumed integration of the ﬂow properties

tain a roughness coefﬁcient.

across the cross

Yet Manning’s equation is neither an exact, nor a general physical law. The fact that the formula is not exact

section,

thus

reducing

the actual

three-dimensional domain, where the ﬂow occurs, into a one-dimensional domain.

can be seen by inspecting its performance in open surface

It is useful to rethink how this equation is derived. His-

ﬂow in conduits with circular cross sections, where an

torically, it has not been established solely by theoretical

increase of n by up to 28% may be necessary to apply for

reasoning and deduction, but is a result of several laboratory

medium ﬂow depths (e.g. Koutsoyiannis b). The fact

and ﬁeld experiments. This is reasonable for a statistical

that it is not general can be inferred by inspecting the adap-

equation. Given its basis on experiments and data, we can

tation needed to describe the ﬂow in composite (e.g. double

also call it an empirical equation. Alternatively, it can be

D. Koutsoyiannis

Reconciling hydrology with engineering

derived as an approximation of the Darcy–Weisbach and

Hydrology Research

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THE MODERN CHANGE OF PERCEPTION

Colebrook–White equations, which in principle are more accurate (albeit again not exact and of empirical type).

An impressive result of the combined effort of hydrology

Indeed, for pipes with rough walls, these equations practi-

and hydraulics in an engineering frame is the transform-

cally switch to the Manning’s equation (Koutsoyiannis

ation, through large-scale constructions such as dams,

). In brief, measurement data, numerical methods and

reservoirs and hydropower plants, of highly varying and

theoretical reasoning (as in Gioia & Bombardelli (),

uncertain natural ﬂows into regular, often constant, outﬂows

mentioned above) are all useful approaches in this particular

that satisfy the water and energy demands of society (see

case, and in all other cases of complex phenomena.

also Koutsoyiannis a). Up to the 1980s the engineering

Obviously, among the three approaches, the one based on

efforts had provided the basic infrastructure for reliable,

data offers the most precious information and can be used

technology-enabled, water resources to the developed

either to derive the equation or to validate it if it was derived

world and allowed a high-quality hygienic lifestyle. As the

by a more theoretical approach.

infrastructures were completed to a large extent in the devel-

Can we retain anything from this analysis if we move

oped world, engineering started to lose importance and

from the typical domain of the Manning’s equation, i.e. a

hydraulics lost its primary role as a scientiﬁc and engineer-

simple prismatic channel, to a hydrological system, such

ing ﬁeld.

as a catchment with its unique characteristics? First of all,

Interestingly, at about the same time the link of

concerning the Manning equation per se, since it is a macro-

hydrology with engineering was questioned. This was

scopic equation, we may still use it for river channels. But

reﬂected in the discussions about the character of

we should have in mind that, as it is not exact even for pris-

IAHS. The then president Vít Klemeš deﬁned the focus

matic channels, it will result in even greater errors in the

of IAHS as

irregular and varying cross sections of the river, which have also irregularly varying roughness.

‘the development of hydrology as a strong geophysical

Second, it is even more useful in helping us perceive

(earth) science and the promotion of sound applications

some characteristics and limitations of hydrology. Speciﬁ-

of this science on solving practical problems’ (Klemeš

cally, hydrology, with its much more complex, unique (not

).

repeatable) objects, is:

• • •

However, despite recognizing the importance of solving macroscopic: it cannot (and need not) describe details;

practical problems, he also asserted that water resources

statistical/stochastic: it should use averages, standard

management is not a hydrological science and IAHS is

deviations and probability distributions;

not its professional home (Klemeš ()); see also Kout-

empirical: it necessarily relies on ﬁeld data, recognizing

soyiannis (e)). He did not clarify in this text his view

that deduction by theoretical reasoning is rather weak

about the relationship of hydrology with engineering but

and should be complemented by induction based on

this can be inferred from other texts, where he described

measurements (this is the philosophy behind, for

himself as

instance, establishing stage-discharge curves at river

• •

cross sections, based on hydrometric data, instead of rely-

‘trying to cut the umbilical cord between [hydrologists

ing on application of Manning’s equation or on three-

and engineers], which [he saw] as inevitable and

dimensional hydrodynamic modelling of the river);

eventually beneﬁcial to both’ (Klemeš ).

not exact: errors and uncertainty will never be eliminated;

A similar message was broadcast in a book by the US Com-

difﬁcult to generalize: different catchments may need

mittee on Opportunities in the Hydrological Sciences ()

different treatment as similarities may not be enough to

that has been regarded by some as the gospel of modern

allow accurate generalizations.

hydrology (and commonly referred to as the Blue Book).

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

This gave the emphasis on the understanding of hydrologi-

The most frequently appearing words in US Committee on

cal processes and asserted that:

Opportunities in the Hydrological Sciences () are

‘Development of hydrology as a science is vital to the current effort to understand the interactive behaviour of the earth system’

shown in Figure 7 (left) in comparison with the frequencies of some engineering-related words. Clearly, Figure 7 reveals depreciation of engineering-oriented aspects of hydrology. In fact, this trend did not concern merely hydrology.

as if hydrology was not a science until then and as if understand-

Rather it was part of a more general change of perspective,

ing was the primary goal of science. It also concluded that:

marked by a departure from a problem-solving approach that needs to be accompanied with engineering solutions.

‘graduate education in the hydrologic sciences should be

By deﬁnition, engineering deals with real-world problems

pursued independently of civil engineering’.

and aims to change, transform or control natural processes,

Figure 7

Most appearing words (top 20) and their frequencies in: (left) US Committee on Opportunities in the Hydrological Sciences (1992) and (right) its recent update, US Committee on Challenges & Opportunities in the Hydrologic Sciences (2012). In both graphs the frequencies of some engineering-related words are also shown for comparison. In the right panel (2012 book) the words losing frequency, by more than 50%, in comparison with the 1992 book, are printed in bold, while the words entering the top-20 list in the 2012 book or gaining frequency by more than 100% are printed in italics.

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

and to provide solutions to these problems. As manifest in

of greater duration due to climate change, as well as the

the history of water engineering, it does not demand full

need for adaptation to climate change. The soft path concept

understanding of the details of the processes and usually

has become popular in several countries and international

relies on a macroscopic view and an approximate descrip-

organizations (Brooks et al. ). Thus, it was argued that

tion of such processes, provided that the degree of

some ‘major shortcomings of conventional water manage-

approximation is satisfactory for the purposes of the study.

ment’ [are] avoided by using the ‘soft path’ (Wagner et al.

Engineering solutions were also opposed during the last

; a UNESCO publication) and that ‘the soft path

decades by the developing ‘green’ ideology as well as by poli-

opens new avenues for accessing capital’ (Leflaive ; an

tico-economic agendas related to the climate-change

OECD publication). On the other side, in one of the rare

movement (Klemeš ; Koutsoyiannis a). The latter

instances that the concept was criticized, Stakhiv ()

has been strong enough to determine the direction of

found it wholly inadequate for the needs of most of the

research funding of national and international (e.g. Euro-

developing world.

pean) bodies in a manner that hydrology would not have

As the new promoted soft path approach is weakly con-

any share except in assisting with subjects dictated by the

nected to the material world, it encouraged a new culture in

dominant political agendas (e.g. in studying hypothetical

research procedures, which could be exempliﬁed by the fol-

or projected climate-related threats and impacts). Thus,

lowing approach in developing a research programme fully

arguably, hydrology, instead of becoming an autonomous

consistent with the modern socio-economic emphasis on

science with a broader domain, as envisaged, developed

virtual reality: (a) we invent a problem that does not exist;

dependencies on politically driven agendas and this

(b) we coin a smart name to describe it; (c) we get plenty

demoted its role accordingly.

of money to study it; (d) we organize brain-storming meet-

The change of perspective was further supported by the notion of the so-called soft water path (Gleick , ;

ings to deﬁne the problem; (e) we produce deliverables and publications to justify the funding received.

Brooks ; Pahl-Wostl ; Pahl-Wostl et al. ; Brooks et al. ), which

While the soft path was developing as a new dominant doctrine, the scientiﬁc developments in hydrology did not contest it. In particular, the new emerging areas of interest

‘by investing in decentralized facilities, efﬁcient technol-

(in addition to the traditional branches such as hydrome-

ogies and policies, and human capital […] will seek to

teorology and hydrogeology) seem to comply with this

improve overall productivity rather than to ﬁnd new

doctrine. Some examples are:

sources of supply [and] will deliver water services that are matched to the needs of end users, on both local and community scales’ (Gleick ).

•

biohydrology: the study of the interactions between biological and hydrological systems (initially meant to be the study of catchment hydrology in conjunction with

This has been promoted as a contrasting alternative to

the micro-organisms which the living populations of the

engineering solutions to problems that rely on infrastructure

catchment introduce into the various water ﬂows;

development, which Gleick () calls the hard path and

Feachem );

criticizes for ‘spawning ecologically damaging, socially intrusive and capital-intensive projects that fail to deliver their promised beneﬁts’. Interestingly, the groups that discourage building new water projects and promote their soft path, at the same time highlight projections on threats like bigger ﬂoods and droughts

• • • •

ecohydrology: the study of the interactions between water and ecosystems within water bodies (Zalewski et al. ; Rodriguez-Iturbe ); hydropsychology: the study of the transactions between humans and water-related activities (Sivakumar ); hydrosociology: the study of human–water interactions (Falkenmark , ; Sivakumar ); sociohydrology: ‘the science of people and water, a new science that is aimed at understanding the dynamics

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

and co-evolution of coupled human-water systems’ (Siva-

alongside Chernobyls, Exxon Valdezes, ‘rape of the

palan et al. ).

environment’, AIDS, cancer and genocide.’

The importance of the new knowledge acquired by these

‘I shall close with a plea to all of you, hydrologists and

emerging ﬁelds should not be questioned. Particularly, eco-

other water professionals, to stand up for water, hydrol-

hydrology, by shedding light on the interactions and

ogy and water resource engineering, to restore their

feedbacks between hydrologic processes and terrestrial eco-

good name, unmask the demagoguery hiding behind

systems (Porporato & Rodriguez-Iturbe ; D’Odorico et al. ) has indeed offered useful knowledge. Also the importance of the interactions of humans with water,

the various ‘green’ slogans. As in any sphere of human activity, errors with adverse effects were and will be made in our profession as well […]. But, on the whole,

emphasized by hydropsychology, hydrosociology and socio-

our profession has nothing to be ashamed of – from the

hydrology, is not put in question. However, these

times of the ancient Mesopotamia, Greece and Rome to

interactions are already part of the domain of hydrology

the present, it has done more good for mankind than

even according to the UNESCO () deﬁnition, and thus

all its critics combined.’

introducing new labels and calling them new sciences is arguably pointless. In addition, the interaction of water and human societies can hardly be perceived without engin-

ON UNDERSTANDING, MISUNDERSTANDING AND OVERSTANDING

eering means. On the other hand, the mandate to make hydrology a

It is interesting to observe that the period of the emphasis on

science independent of engineering, combined with other

the

socio-economic developments of the last decades, impelled

coincided with a bewildering over-optimistic view that

scientiﬁc,

non-engineering,

aspect

hydrology

hydrology (or part of it) to a virtual reality nexus, which

data are not absolutely necessary in hydrological modelling,

deals with hypotheses, future projections and scenarios,

a view that is opposite to the above discourse. Speciﬁcally, it

and pays less attention to elements of reality. As stated in

was hoped that, by cutting the hydrological systems into

the beginning of this section, the late Vít Klemeš was one

small nearly-homogeneous pieces and by describing the

of the pioneers of this mandate. It is thus instructive to see

natural processes in each piece using differential equations,

his own view of the state of affairs that was gradually

it would be possible to fully model the system behaviour in

formed in the last decades. The following passages are

detail without the need for data. The differential equations

from one of his last talks (Klemeš ; emphasis added):

could be, in principle, solved numerically thanks to the ever increasing computer power.

‘[A] new infectious disease has sprung up – a WATER-

This reductionist philosophical view constituted the

BORN SCHIZOPHRENIA: on the one hand, we are

basis of the so-named ‘physically-based’ hydrological model-

daily inundated by the media with reports about water-

ling (e.g. Abbott et al. ) and was highly promoted in the

caused disasters, from destructive droughts to even

initial document of the decade-long IAHS initiative for Pre-

more destructive ﬂoods, and with complaints that ‘not

diction in Ungauged Basins. The idea was that a new

enough is done’ to mitigate them and, on the other

generation of models would not need calibration and,

hand, attempts to do so by any engineering means –

hence, data and, simultaneously, would radically reduce

and so far no other similarly effective means are

uncertainty (Sivapalan et al. ). However, pragmatism

usually available – are invariably denounced as ‘rape

and experience help us see that the more complex and

of nature’ (often by people with only the foggiest ideas

detailed an approach is, the more data it needs to calibrate.

about their functioning), and are opposed, prevented, or

Also, common sense helps us understand that it is infeasible

at least delayed by never ending ‘environmental assess-

to estimate the evapotranspiration of a forested area by

ments and reassessments’. In the present ‘green’

examining each tree separately and then by further model-

propaganda, all dams are evil by deﬁnition, ranking

ling the transpiration of each maple or pine leaf

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

individually. History of science teaches that feasible and

to the majority of scientists, it leaves out important targets

convenient macroscopic views can better be achieved

such as the understanding of uncertainty. And as it is used

using principles of probability theory like the law of large

to mean detailed views of phenomena, it may lead to failure

numbers and the principle of maximum entropy or even

in constructing the big picture; for the latter the term over-

by conceptual and systems approaches.

standing has been coined (Koutsoyiannis ) which

Parsimony in process description is paramount (Ros-

highlights the importance of macroscopic views of complex

bjerg & Madsen ). There are several examples where

phenomena. (Note that a literal translation of the Greek

simpler and more parsimonious models gave better ﬁts

word episteme would be overstanding.)

and better predictions in complex hydrological systems. It

A characteristic effect of this misleading approach

is worth mentioning just one, which refers to a karstic

(detailed physically-based modelling in a hopeless attempt

basin in Bosnia and Herzegovina with a complex system

to achieve a correct understanding and produce analytical

of surface poljes and underground natural conduits. Three

and insightful calculations of the detailed dynamics at the

different research teams modelled it, working independently

ﬁnest scales) is that most hydrological models are for natural

from each other and adopting different approaches. One of

(intact) conditions, while most of the catchments have been

those was of the type commonly referred to as ‘physically-

modiﬁed by humans. In modiﬁed catchments it is mislead-

based’, one was based on a detailed conceptual description

ing to study the hydrological behaviour independently of

of the processes and the third was a toy model, lumping

their management or even in a serial approach where a man-

similar elements of the system into a single substitute

agement model is fed by the outputs of a hydrological

element. Interestingly, the toy model performed best, while

model. A more consistent approach would admit a two-

the ‘physically-based’ model gave the worst predictions

way interaction of hydrological processes and management

(Makropoulos et al. ).

practices (Nalbantis et al. ).

One could say that, despite giving worse predictions, a

In an engineering approach, understanding is not

physically-based model by providing distributed information

necessarily of primary importance. Rather, the primary

across the entire basin may eventually be preferable. This

target depends on the pragmatic objectives of the problem

argument seems to have some merit, particularly if we

which we study (cf. Littlewood (), who compares utility

target at understanding the hydrological system. Under-

versus process understanding and Rosbjerg & Madsen

standing seems to have become the Holy Grail of modern

(), who suggest that the development or selection of a

science, not excluding hydrology, as testiﬁed by the frequent

model should reﬂect the actual needs for modelling results).

and emphatic use of this word in scientiﬁc papers. For

As history teaches, full understanding has not been a prere-

example, a Google Scholar search reveals that out of

quisite to act. Furthermore, the spatially distributed

31,200 papers published since 2009 that contain the word

information provided by such approaches may be mislead-

hydrologic (as of January 2013), 64% also contain the

ing or even wrong if it is not controlled through real world

word understanding. This is a negative development,

data, which provide the ﬁnal judge for the entire modelling

because understanding is a vague and obscure term. In par-

exercise.

ticular, understanding is a subjective cognitive procedure

Furthermore, contemplating the complexity, heterogen-

rather than anything objective. Perhaps a more relevant

eity, non-repeatability and uniqueness of hydrological

term is interpretation (cf. the motto in the beginning),

systems, one can easily conclude that a target of uncertainty

which is also subjective, but more honest in admitting the

elimination or radical reduction would be infeasible

subjectivity: while fans of the term understanding would pre-

(Koutsoyiannis ). Instead, a feasible target would be to

tend to target a unique type of understanding (characterizing

quantify uncertainty. Admitting this, we can extend the

other views as misunderstanding), they would be less reluc-

notion of a physically-based or conceptual model to incor-

tant to allow multiple interpretations of a phenomenon as

porate the estimation or description of uncertainty into the

legitimate. In addition, as understanding is typically used

model ( Jakeman et al. ). In this respect, Montanari &

within a deterministic point of view, which is more familiar

Koutsoyiannis () emphasize the need for uniﬁcation of

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

hydrological modelling and total uncertainty assessment,

As we are approaching the time of the so-called peak oil

and outline a blueprint for process-based modelling of

production (Hubbert ), the importance of the renewable

uncertain hydrological systems.

energy sources becomes increasingly higher. With the excep-

As noted above, uncertainty and risk have been funda-

tion of hydroelectric energy from large-scale infrastructures

mental notions in engineering as there cannot be risk-free

that include reservoirs, all other renewable energy forms are

human constructions. Also, in science, uncertainty is

highly variable, depending on hydrometeorological con-

increasingly appreciated as a fundamental, intrinsic feature

ditions, unpredictable and unavailable at the time of

of nature, which we have to study and accept, rather than

energy demand. Therefore regulation of energy production

try to eliminate.

through energy storage is necessary. The only available technology for large-scale storage of energy is provided by reversible hydropower plants, i.e. by pumping water to an

HYDROLOGY AND THE MAJOR PROBLEMS OF THE TWENTY-FIRST CENTURY

upstream reservoir in periods of excessive energy availability and recovering it by producing electric energy as the stored water is moved downstream. For large-scale plants, the efﬁ-

As already described, current dominant ideological views

ciency of the two-step cycle is extremely high, reaching 85%

have obscured real contemporary problems and their real

(Koutsoyiannis a). Again here engineering hydrology,

causes. For example, anthropogenic global warming

with its particular experience in studying and managing

cannot be regarded anything more than a symptom – and

natural variability can substantially help.

not the major one – of other changes. The real problems

With respect to natural hazards, hydrology and hydrau-

are related to the demographic change (overpopulation in

lics are the scientiﬁc ﬁelds most pertinent to the study and

developing countries, overconsumption and immigration

management of the ﬂood risk both in real time and in plan-

in developed countries), energy change (intense fossil fuel

ning and design time horizons. While soft-path low-cost

use) and environmental change (urbanization, deforestation,

means, like public awareness building and ﬂood warning

pollution) (Koutsoyiannis et al. ). In the current con-

systems, are pertinent for mitigation of the ﬂood risk (Di

ditions marked with these three historical changes, water

Baldassare et al. ), engineering means (including struc-

supply, food security, energy security, natural hazard pre-

tural solutions and urban planning) remain the most

vention and environmental recovery are among the major

powerful weapon in ﬂood protection.

real challenges of the twenty-ﬁrst century. All these ﬁve challenges are related to engineering hydrology.

Creation of technological infrastructure is inevitably accompanied by environmental problems. Modernizing

As urbanization increased, and big cities and megacities

management practices of traditional human activities (e.g.

were created, sometimes without proper water infrastruc-

agriculture) also create similar problems like pollution and

ture (in developing countries) and sometimes with old

degradation of ecosystems. Envisaging a regression and

infrastructure (in developed countries), it has become a big

recovery of the traditional conditions would be utopian,

challenge to create or modernize the urban water systems

unless it were combined with mass reduction of the popu-

to serve the needs of the population, while minimizing the

lation and return to the agrarian age – and hopefully no

damage to the environment. This challenge calls for engin-

one supports such vision. Therefore, technology and engin-

eering means and hydrology has certainly a big role to

eering solutions for existing pollution problems and for

play in this.

minimizing adverse effects in new infrastructures should

Food security is more vulnerable in areas with high evapotranspiration, which necessitates irrigated agriculture.

be the way forward. Engineering hydrology has again a role to play.

Population density, land availability, crop types, water

The above engineering challenges are particularly rel-

resources availability and irrigation efﬁciency are the con-

evant to the developing countries in South America, Asia

trolling factors for this challenge. Obviously, the last two

and, above all, Africa, where the level of infrastructure

are related to engineering hydrology.

development is lower. But this does not necessarily mean

D. Koutsoyiannis

Reconciling hydrology with engineering

Hydrology Research

45.1

2014

that there are no similar challenges in Europe and North

economic interests. However, it would be more beneﬁcial

America. While it is true that the level of infrastructure

for the future of hydrology:

development in the latter areas has been high since a few

•

if it revisited its strong technological and engineering

•

if it took advantage from the historical fact that hydrology

decades ago, human constructions have a limited life cycle and need good management, maintenance, adaptation to changing conditions and, at times, replacement. In this respect, planning and design of engineering infrastructures are not once-and-for-all actions but perpetual processes. Perhaps this has not been appreciated by the hydrologi-

•

roots; has studied natural uncertainty better and in greater depth than other disciplines; if it recognized again that change, uncertainty and risk are intrinsic and interrelated properties of this world

cal community, which, as described above, in the last

and are not eliminable, but are quantiﬁable and

decades seems to have proceeded to a divorce from engin-

manageable;

eering, which also led to divergence of hydrologists in academia from professional engineers. Certainly this is an

•

if it appreciated that, in studying catchment scale problems, parsimonious macroscopic descriptions are more

unfortunate development as both scientiﬁc and engineering

powerful than inﬂationary detailed ones and that holistic

aspects of hydrology are equally important if we wish to deal

approaches are more effective than reductionist ones;

with real-world problems.

and

At the same time, part of the hydrological community preferred, over the real-world problems, its engagement to

•

if it identiﬁed its role within the real and pressing problems of the contemporary world.

the virtual reality of climate models. Certainly, assisting in climate impact studies provides funding opportunities. The

In conclusion, reconciling hydrology with engineering

reasons are understandable as without the cooperation of

could help hydrology to come back from the virtual reality

hydrologists, without involving extreme ﬂoods and droughts,

into the real world, where data and facts are more important

the necessary prediction of future threats and catastrophes is

than model simulations, where predictions are tested against

not frightening enough. However, the entire endeavour may

empirical evidence, and where uncertainty and risk domi-

be in vain given the generally admitted, even by climate

nate. In the real world change is the rule rather than an

modellers, failure of climate models to simulate processes

adverse property that should be opposed (see also Kout-

relevant to hydrology (see Koutsoyiannis et al. a, ;

soyiannis

Anagnostopoulos et al. ; Kundzewicz & Stakhiv ; Stakhiv ). On the other hand, the irony is that anthropogenic effects other than CO2 emissions, for example land use

;

Montanari

al.

).

Therefore

engineering as a means of planned and sophisticated change is essential for progress and evolution. Thus, the study of change, natural and engineered, as well as the

changes, deforestation and urbanization, have major

implied uncertainty and risk, can constitute the ﬁeld of

impacts on hydrological processes and are more predictable

mutual integration of hydrology and engineering.

(e.g. Ranzi et al. ). Will hydrology keep on walking on those trails formed in the last three decades? It is very probable and an indi-

ACKNOWLEDGEMENTS

cation is already provided by a recent update of the 1992 document mentioned above by the US Committee on Chal-

I thank Baldassare Bacchi and Roberto Ranzi for inviting

lenges & Opportunities in the Hydrologic Sciences ().

me to deliver the opening lecture at the IDRA 2012

As shown in the right panel of Figure 7, the engineering-

(XXXIII

related words that had appeared infrequently in the 1992

Engineering, Brescia, Italy, 2012) and for their comments

document

on the script of this lecture, from which the current paper

have

almost

disappeared

from

the

2012

document.

Conference

Hydraulics

and

Hydraulic

grew. I also thank the Editor, Ian Littlewood, as well as

It can be speculated that the current trails are consistent

the eponymous reviewers Dan Rosbjerg and Tim Cohn for

with the targets of the classe politique and the related socio-

their detailed and very constructive comments on an

D. Koutsoyiannis

Reconciling hydrology with engineering

earlier version of this paper which resulted in substantial improvements.

REFERENCES Abbott, M. B., Bathurst, J. C., Cunge, J. A., O’Connell, P. E. & Rasmussen, J.  An introduction to the European Hydrological System – Systeme Hydrologique Europeen “SHE”, 1, History and philosophy of a physically-based, distributed modelling system. Journal of Hydrology 87 (1–2), 45–59. Anagnostopoulos, G. G., Koutsoyiannis, D., Christofides, A., Efstratiadis, A. & Mamassis, N.  A comparison of local and aggregated climate model outputs with observed data. Hydrological Sciences Journal 55 (7), 1094–1110. Arakawa, H.  On the secular variation of annual totals of rainfall at Seoul from 1770 to 1944. Theoretical and Applied Climatology 7 (2), 205–211. Barrington, A. & Burdett, C.  A Treatise on Physical Geography: Comprising Hydrology, Geognosy, Geology, Meteorology, Botany, Zoology, and Anthropology. Mark H. Newman & Co., New York, 420 pp. books.google.gr/ books?hl=en&lr=&id=7XYAAAAAMAAJ; subsequent editions 1855, 1857, 2009, 2010. Beardmore, N.  Manual of Hydrology. Waterlow and Sons, London, 384 pp. books.google.gr/books?id=szMDAAAAQ AAJ; subsequent editions 1872, 1906, 1914, 2011. Brooks, D. B.  Beyond greater efficiency: the concept of water soft path. Canadian Water Resources Journal 30 (1), 83–92. Brooks, D. B., Brandes, O. M. & Gurman, S. (eds)  Making the Most of the Water We Have: The Soft Path Approach to Water Management. Earthscan, London. Burges, S. J.  Water resource systems planning in USA: 1776– 1976. Journal of the Water Resources Planning and Management Division 105 (1), 91–111. Chow, V. T.  Open-Channel Hydraulics. McGraw-Hill, New York. Di Baldassarre, G., Montanari, A., Lins, H. F., Koutsoyiannis, D., Brandimarte, L. & Blöschl, G.  Flood fatalities in Africa: from diagnosis to mitigation. Geophysical Research Letters 37, L22402. D’Odorico, P., Laio, F., Porporato, A., Ridolfi, L., Rinaldo, A. & Rodriguez-Iturbe, I.  Ecohydrology of terrestrial ecosystems. BioScience 60 (11), 898–907. Dooge, J. C. I.  Background to modern hydrology, The Basis of Civilization –Water Science. In Proceedings of the UNESCO/IAHS /IWHA Symposium held in Rome, December 2003, IAHS Publ. 286, pp. 3–12. Falkenmark, M.  Main problems of water use and transfer of technology. Geo Journal 3 (5), 435–443. Falkenmark, M.  Society’s interaction with the water cycle: a conceptual framework for a more holistic approach. Hydrological Sciences Journal 42 (4), 451–466.

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Fanning, J. T.  A Practical Treatise on Hydraulic and Watersupply Engineering: Relating to the Hydrology, Hydrodynamics, and Practical Construction of Water-works, in North America. Van Nostrand, New York, 619 pp. books.google.gr/books? id=p7AOAAAAYAAJ; subsequent editions 1878, 1882, 1884, 1886, 1887, 1889, 1891, 1892, 1890, 1893, 1895, 1896, 1899, 1902, 1906, 1909, 1913, 2010, 2011, 2012. Feachem, R.  Faecal coliforms and faecal streptococci in streams in the New Guinea highlands. Water Research 8 (6), 367–374. Gauch Jr, H. G.  Scientific Method in Practice. Cambridge University Press, Cambridge. Gleick, P. H.  Soft water paths. Nature 418, 373. Gleick, P. H.  Global freshwater resources: soft-path solutions for the 21st century. Science 302 (5650), 1524–1528. Gioia, G. & Bombardelli, F. A.  Scaling and similarity in rough channel flows. Physical Review Letters 88 (1), 014501.1–4. Hubbert, M. K.  Techniques of prediction as applied to the production of oil and gas. In: Oil and Gas Supply Modeling (S.I. Gass, ed.), Spec. Publ. 631, Natl. Inst. of Stand. and Technol., Gaithersburg, MD, USA, pp. 16–141. Jakeman, A. J., Littlewood, I. G. & Whitehead, P. G.  Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments. Journal of Hydrology 117, 275–300. Johnston, W. A. K.  Atlas of Physical Geography: Illustrating in a Series of Original Designs the Elementary Facts of Chartography, Geology, Topography, Hydrology, Meteorology, and Natural History. William Blackwood and Sons, Edinburgh-London, 52 pp. books.google.gr/books? id=mMY_SQAACAAJ; subsequent edition, 1892; see also school versions in books.google.gr/books?id ¼ Di4BAAAA QAAJ and books.google.gr/books?id ¼ YXYNAQAAMAAJ. Kang, H. S., Chester, S. & Meneveau, C.  Decaying turbulence in an active-grid-generated flow and comparisons with largeeddy simulation. Journal of Fluid Mechanics 480, 129–160. Klemeš, V.  Dilettantism in hydrology: transition or destiny? Water Resources Research 22 (9S), 177S–188S. Klemeš, V.  President’s page. IAHS Newsletter 31, 5–6. http:// www.iahs.info/News/Newsletters.do. Klemeš, V.  20 years later: what has changed – and what hasn’t. In XXIV General Assembly of the International Union of Geodesy and Geophysics, International Union of Geodesy and Geophysics, International Association of Hydrological Sciences, Perugia. itia.ntua.gr/831/. Koutsoyiannis, D.  A power-law approximation of the turbulent flow friction factor useful for the design and simulation of urban water networks. Urban Water Journal 5 (2), 117–115. Koutsoyiannis, D.  HESS Opinions “A random walk on water”. Hydrology and Earth System Sciences 14, 585–601. Koutsoyiannis, D. a Scale of water resources development and sustainability: Small is beautiful, large is great. Hydrological Sciences Journal 56 (4), 553–575.

D. Koutsoyiannis

Reconciling hydrology with engineering

Koutsoyiannis, D. b Design of Urban Sewer Networks, 4th edn. National Technical University of Athens, Athens, 180 pp. (in Greek). itia.ntua.gr/123/. Koutsoyiannis, D. c Hurst-Kolmogorov dynamics as a result of extremal entropy production. Physica A: Statistical Mechanics and its Applications 390 (8), 1424–1432. Koutsoyiannis, D. d Hurst-Kolmogorov dynamics and uncertainty. Journal of the American Water Resources Association 47 (3), 481–495. Koutsoyiannis, D. e Prolegomena. In: Common Sense and Other Heresies, Selected Papers on Hydrology and Water Resources Engineering by Vít Klemeš (C.D. Sellars, ed.), 2nd edn. Canadian Water Resources Association, International Association of Hydrological Sciences, pp. xi–xv. Koutsoyiannis, D.  Hydrology and change. Hydrological Sciences Journal 58 (6), 1177–1197. Koutsoyiannis, D. & Langousis, A.  Precipitation, Treatise on Water Science (P. Wilderer & S. Uhlenbrook, eds). Vol. 2, Academic Press, Oxford, pp. 27–78. Koutsoyiannis, D., Mamassis, N. & Tegos, A.  Logical and illogical exegeses of hydrometeorological phenomena in ancient Greece. Water Science and Technology: Water Supply 7 (1), 13–22. Koutsoyiannis, D., Efstratiadis, A., Mamassis, N. & Christofides, A. a On the credibility of climate predictions. Hydrological Sciences Journal 53 (4), 671–684. Koutsoyiannis, D., Zarkadoulas, N., Angelakis, A. N. & Tchobanoglous, G. b Urban water management in Ancient Greece: Legacies and lessons. Journal of Water Resources Planning and Management – ASCE 134 (1), 45–54. Koutsoyiannis, D., Makropoulos, C., Langousis, A., Baki, S., Efstratiadis, A., Christofides, A., Karavokiros, G. & Mamassis, N.  Climate, hydrology, energy, water: recognizing uncertainty and seeking sustainability. Hydrology and Earth System Sciences 13, 247–257. Koutsoyiannis, D., Kundzewicz, Z. W., Watkins, F. & Gardner, C.  Something old, something new, something red, something blue. Hydrological Sciences Journal 55 (1), 1–3. Koutsoyiannis, D., Christofides, A., Efstratiadis, A., Anagnostopoulos, G. G. & Mamassis, N.  Scientific dialogue on climate: is it giving black eyes or opening closed eyes? Reply to ‘A black eye for the Hydrological Sciences Journal’ by D. Huard. Hydrological Sciences Journal 56 (7), 1334–1339. Kundzewicz, Z. W. & Stakhiv, E. Z.  Are climate models ‘ready for prime time’ in water resources management applications, or is more research needed? Editorial. Hydrological Sciences Journal 55 (7), 1085–1089. Leflaive, X.  Alternative Ways of Providing Water – Emerging Options and their Policy Implications, OECD, Paris. www. oecd.org/env/resources/42349741.pdf. Liddell, H. G. & Scott, R.  A Greek-English Lexicon (revised and augmented throughout by Sir Henry Stuart Jones, with the assistance of. Roderick McKenzie). Clarendon Press, Oxford.

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Littlewood, I. G.  Catchment-scale Rainfall-streamflow Modelling: Utility Versus Process Understanding. Vol. 336, IAHS-AISH Publication, pp. 257–263. Makropoulos, C., Koutsoyiannis, D., Stanic, M., Djordevic, S., Prodanovic, D., Dasic, T., Prohaska, S., Maksimovic, C. & Wheater, H. S.  A multi-model approach to the simulation of large scale karst flows. Journal of Hydrology 348 (3–4), 412–424. Mays, L. W., Koutsoyiannis, D. & Angelakis, A. N.  A brief history of urban water supply in antiquity. Water Science and Technology: Water Supply 7 (1), 1–12. Michel, J.-B., Shen, Y. K., Aiden, A. P., Veres, A., Gray, M. K., The Google Books Team, Pickett, J. P., Hoiberg, D., Clancy, D., Norvig, P., Orwant, J., Pinker, S., Nowak, M. A., Aiden, E. L.  Quantitative analysis of culture using millions of digitized books. Science 331 (6014), 176–182. Montanari, A. & Koutsoyiannis, D.  A blueprint for processbased modeling of uncertain hydrological systems. Water Resources Research 48, W09555, doi: 10.1029/ 2011WR011412. Montanari, A., Young, G., Savenije, H. H. G., Hughes, D., Wagener, T., Ren, L. L., Koutsoyiannis, D., Cudennec, C., Toth, E., Grimaldi, S., Blöschl, G., Sivapalan, M., Beven, K., Gupta, H., Hipsey, M., Schaefli, B., Arheimer, B., Boegh, E., Schymanski, S. J., Di Baldassarre, G., Yu, B., Hubert, P., Huang, Y., Schumann, A., Post, D., Srinivasan, V., Harman, C., Thompson, S., Rogger, M., Viglione, A., McMillan, H., Characklis, G., Pang, Z. & Belyaev, V.  “Panta Rhei – Everything flows”, change in hydrology and society – The IAHS scientific decade 2013–2022. Hydrological Sciences Journal 58 (6), 1256–1275. Nalbantis, I., Efstratiadis, A., Rozos, E., Kopsiafti, M. & Koutsoyiannis, D.  Holistic versus monomeric strategies for hydrological modelling of human-modified hydrosystems. Hydrology and Earth System Sciences 15, 743–758. Papanicolaou, P. N.  Open Channels, Lecture Notes. National Technical University of Athens, Athens, 122 pp. (in Greek). itia.ntua.gr/ ∼ panospap/EFARMOSMENH_YDRAULIKH/ SHMEIWSEIS_NOTES/OpenChannel_2008_Papanicolaou. pdf. Pahl-Wostl, C.  Transitions towards adaptive management of water facing climate and global change. Water Resources Management 21 (1), 49–62. Pahl-Wostl, C., Tabara, D., Bouwen, R., Craps, A., Mostert, E., Ridder, D. & Taillieu, T.  The importance of social learning and culture for sustainable water management. Ecological Economics 64 (3), 484–495. Pfister, L., Savenije, H. H. G. & Fenicia, F.  Leonardo da Vinci’s Water Theory. IAHS Special Publication no. 9, IAHS Press, Wallingford. Porporato, A. & Rodriguez-Iturbe, I.  Ecohydrology – a challenging multidisciplinary research perspective. Hydrological Sciences Journal 47 (5), 811–821. Ranzi, R., Bochicchio, M. & Bacchi, B.  Effects on floods of recent afforestation and urbanisation in the Mella River (Italian Alps). Hydrology and Earth System Sciences 6, 239–254.

D. Koutsoyiannis

Reconciling hydrology with engineering

Rodriguez-Iturbe, I.  Ecohydrology: a hydrologic perspective of climate-soil-vegetation dynamics. Water Resources Research 36 (1), 3–9. Rosbjerg, D. & Madsen, H.  Concepts of hydrologic modeling. In: Encyclopedia of Hydrological Sciences (M. G. Anderson, ed.), Vol. 1, Part 1, Chapter 10, John Wiley & Sons, Ltd., New Jersey, pp. 155–163. Savenije, H. H. G.  HESS Opinions “The art of hydrology”. Hydrology and Earth System Sciences 13, 157–161. Sivakumar, B.  Hydropsychology: the human side of water research. Hydrological Sciences Journal 56 (4), 719–732. Sivakumar, B.  Socio-hydrology: not a new science, but a recycled and re-worded Hydrosociology. Hydrological Processes 26 (24), 3788–3790. Sivapalan, M., Takeuchi, K., Franks, S. W., Gupta, V. K., Karambiri, H., Lakshmi, V., Liang, X., McDonnell, J. J., Mendiondo, E. M., O’Connell, P. E., Oki, T., Pomeroy, J. W., Schertzer, D., Uhlenbrook, S. & Zehe, E.  IAHS Decade on Predictions in Un-gauged Basins (PUB), 2003–2012: Shaping an exciting future for the hydrological sciences. Hydrological Sciences Journal 48 (6), 857–880. Sivapalan, M., Savenije, H. H. G. & Blöschl, G.  Sociohydrology: A new science of people and water. Hydrological Processes 26 (8), 1270–1276. Stakhiv, E. Z.  Pragmatic approaches for water management under climate change uncertainty. Journal of the American Water Resources Association 47 (6), 1183–1196. Symons, G. J.  On the Proceedings of the International Congress of Hydrology and Climatology at Biarritz, October 1886. Quarterly Journal of the Royal Meteorological Society 13 (61), 46–60.

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UNESCO (United Nations Educational, Scientific and Cultural Organization)  Report, Preparatory Meeting on the LongTerm Programme of Research in Scientific Hydrology. UNESCO/NS/181, UNESCO House, Paris. unesdoc.unesco. org/images/0001/000173/017325EB.pdf. UNESCO (United Nations Educational, Scientific and Cultural Organization)  Final Report, International Hydrological Decade, Intergovernmental Meeting of Experts, UNESCO/ NS/188, UNESCO House, Paris. unesdoc.unesco.org/ images/0001/000170/017099EB.pdf. US Ad Hoc Panel on Hydrology  Scientific Hydrology, US Federal Council for Science and Technology, Washington, DC, 37 pp. US Committee on Challenges and Opportunities in the Hydrologic Sciences  Challenges and Opportunities in the Hydrologic Sciences. National Academies Press, Washington, DC, USA. www.nap.edu/catalog.php? record_id=13293. US Committee on Opportunities in the Hydrologic Sciences  Opportunities in the Hydrologic Sciences (P. S. Eagleson ed.). National Academy Press, Washington, DC, USA. www.nap. edu/catalog.php?record_id=1543 and books.google.gr/ books?id=ADorAAAAYAAJ. Wagner, I., Marsalek, J. & Breil, P.  Aquatic Habitats in Sustainable Urban Water Management: Science. Policy and Practice, UNESCO, Paris. Yevjevich, V.  Misconceptions in hydrology and their consequences. Water Resources Research 4 (2), 225–232. Zalewski, M., Janauer, G. A. & Jolankai, G.  Ecohydrology, A new paradigm for the sustainable use of aquatic resources, UNESCO IHP Technical Document in Hydrology No. 7. IHP – V Projects 2.3/2.4, UNESCO, Paris, 60 pp.

First received 24 May 2013; accepted in revised form 17 September 2013. Available online 6 November 2013

APPENDIX

velocity time series is also plotted (lower panel). The differences become more visible on aggregate time scales (k ¼ 0.1 and 1 s in Figure A1).

TURBULENCE FROM FLUID MECHANICS TO HYDROLOGY: DIFFERENT SCALES AND SCALING BEHAVIOURS

In particular, it is visually recognizable that the variability at higher time scales is higher in the turbulent time series than in the random one. The variability is quantiﬁed by the statistical concept of standard deviation. We can

A high-resolution time series of turbulence is shown in

estimate the standard deviation σ(k) of the time-averaged

Figure A1. Speciﬁcally, the plot of the upper panel shows

process at any time scale k, from the initial time step of

velocity ﬂuctuations from a laboratory experiment in a

the time series to, say, one tenth of its total length. The

wind tunnel at a millisecond scale for a period of 30 s. For

(typically logarithmic) plot of σ(k) vs. k has been termed

comparison, purely random synthetic time series with

the climacogram (Koutsoyiannis ) and it is one-to-one

mean and standard deviation equal to those of the turbulent

related to the autocovariance function and the power

D. Koutsoyiannis

Figure A1

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(Upper) Laboratory measurements of velocity ﬂuctuations in nearly isotropic turbulence at a high Reynolds number; each data point represents the average velocity every 1.2 ms, while time averages at time scales of 0.1 and 1 s are also plotted (the original data, available online at www.me.jhu.edu/meneveau/datasets/Activegrid/M20/H1/m20h101.zip, are measurements by X-wire probes with sampling rate of 40 kHz, here aggregated at 0.833 kHz, from an experiment at the Corrsin Wind Tunnel; Kang et al. 2003). (Lower) A purely random synthetic time series with mean and standard deviation equal to those in the upper panel. (Reproduced from Koutsoyiannis (2013)).

spectrum. The climacogram of the time series of observed

1 and 2, which have climacograms, respectively,

turbulent velocities of Figure A1 is shown in Figure A2 (upper) along with the theoretical climacograms of four models. We can see that the turbulent velocity process dif-

σ 2 ðkÞ ¼

fers from random noise at all time scales. It also differs

λ1 2=3 k 1þ α1

(A2)

from the well-known Markov model, whose climacogram is given by (Koutsoyiannis c):

σ 2 ðkÞ ¼

λ0 1 e k=α0 1 k=α0 k=α0

σ 2 ðkÞ ¼ (A1)

λ2

2 2H 1 þ ðk=a2 Þ2=3 2=3

λ3 1 þ k=a3

(A3)

where α0 denotes a characteristic time scale, and λ0 ¼

The time scale parameters (in s) in the models ﬁtted to

σ 2(0)/2 (half the variance of the instantaneous process).

the empirical data are α0 ¼ 0.01347, α1 ¼ 0.03831; α2 ¼

Two more realistic models are additionally ﬁtted, Models

0.007346; α3 ¼ 0.03518; the variance parameters (in m2/s2)

D. Koutsoyiannis

Figure A2

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(Upper) Empirical climacogram of the turbulent velocity time series shown in Figure A1 upper, along with the four models (purely random, Markov, and Models 1 and 2) outlined in text, fitted to the empirical climacogram; statistical bias in standard deviation was accounted for in the fitting. (Lower) Theoretical power spectra of the four models; Models 1 and 2 on the left (low frequencies, most relevant to hydrology) indicate the Hurst–Kolmogorov behaviour and on the right (high frequencies, most relevant to fluid mechanics and hydraulics) are consistent with Kolmogorov’s 5/3 law of isotropic turbulence; the purely random and the Markov model fail to capture both behaviours.

are λ0 ¼ 6.776, λ1 ¼ 3.624, λ2 ¼ 1.283, λ3 ¼ 2.316; for Model

have the same asymptotic slope, –1/2, for large scales k

2 the dimensionless Hurst parameter H is 0.87.

(this can be proved by deduction) and this is inconsistent

A common characteristic of the purely random (white

with the empirical slope. Models 1 and 2 give milder slopes,

noise) and the Markov models is that their climacograms

–1/3 and –0.13, respectively, which suggest long-term

D. Koutsoyiannis

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persistence, else known as Hurst–Kolmogorov behaviour,

iour with slope –2 for the Markov model and –5/3 for

with Hurst parameter H ¼ 2/3 (Model 1) and 0.87 (Model

Models 1 and 2. The latter is consistent with the well-

2). We recall that the Hurst parameter indicates how strong

known Kolmogorov’s 5/3 law of turbulence combined

the long-term persistence is, or equivalently, how large the

with Taylor’s frozen turbulence hypothesis. Note that an

predictive uncertainty is at large time scales (Koutsoyiannis

asymptotic slope in the spectrum steeper than –1 is math-

c, d). The closer the Hurst coefﬁcient to the value 1

ematically

(which is the highest possible), the greater the uncertainty at

mathematically infeasible for frequency tending to zero.

large scales.

This results in the necessity of a break of scaling, which

At small time scales, the Markov model as well as

feasible

for

high

frequencies,

but

is evident in Figure A2. In some way, this break of scaling

Models 1 and 2 appear to have indistinguishable climaco-

indicates a rough border between ﬂuid mechanics and

grams. However, there are differences which can better

hydraulics, on the one hand, which focus on high frequen-

be seen in the power spectra of the three models shown

cies (small time scales) and hydrology, on the other hand,

in the lower panel of Figure A2. Small scales appear here

which is more interested in small frequencies (large time

as high frequencies, and indicate a different scaling behav-

scales).

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The effect of spatially uniform and non-uniform precipitation bias correction methods on improving NEXRAD rainfall accuracy for distributed hydrologic modeling Kwangmin Kang and Venkatesh Merwade

ABSTRACT In order to improve the accuracy of rainfall estimates from next generation radar (NEXRAD) uncertainties, data assimilation technique is performed by considering NEXRAD and available rain gauges which can be used to assimilate spatially uniform Multisensor Precipitation Estimator (MPE) scheme and non-uniform (based on rainfall interpolation and bias interpolation) NEXRAD bias estimations during a storm event by Kalman ﬁltering. Even though NEXRAD provides a better spatial representation of rainfall variability than rain gauge information, it suffers from uncertainties and biases due to Z–R (reﬂectivity–rainfall) conversion method and limitation of available rain gauge information for NEXRAD bias correction in a particular river basin. Analysis of correcting NEXRAD bias rainfall with three different bias correction schemes is described in this study. The prediction

Kwangmin Kang (corresponding author) APEC Climate Center, 12 Centum 7-ro, Haeundae-gu, Busan 612-020, Republic of Korea E-mail: hbkangkm@apcc21.org Venkatesh Merwade School of Civil Engineering, 550 Stadium Mall Drive, Purdue University, West Lafayette, IN 47907, USA

accuracy of the STORE DHM (Storage Released based Distributed Hydrologic Model) simulations is also evaluated by using three different NEXRAD bias corrected rainfall inputs. The Upper Wabash River (17,907 km2) and the Upper Cumberland River (38,160 km2) basins are selected as the study areas to evaluate rainfall input sensitivity on different spatial characteristics. Use of spatially non-uniform NEXRAD bias correction schemes results has better rainfall and prediction accuracy compared to that of spatially uniform NEXRAD bias correction rainfall. Key words

| bias correction, Kalman ﬁlter, NEXRAD, STORE DHM, Upper Cumberland River, Upper Wabash River

INTRODUCTION Representation of spatio-temporal rainfall variability is criti-

resolution rainfall information in space and time for the

cal for making accurate hydrologic predictions (Abedini

United States. Currently, the NEXRAD precipitation pro-

et al. ; Feiccabrino et al. ; Jeong et al. ). Numerous

ducts are categorized into four levels based on the extent of

studies in the past decades have investigated the sensitivity of

preprocessing, calibration, and quality control performed.

runoff hydrographs to rainfall data obtained from point

The StageI product is an hourly digital precipitation (HDP)

gauges. In addition to the accuracy of gauged rainfall input,

directly derived from reﬂectivity measurements using a Z–R

the predictability and sensitivity of hydrologic models is

(reﬂectivity–rainfall) relationship after the application of sev-

dependent on the spatio-temporal representation of rainfall

eral quality control algorithms (e.g., Fulton et al. ).

(Nicótina et al. ; Viglione et al. ; Zoccatelli et al.

StageII is the single radar site HDP product, which is

, ; Li et al. ), which can be obtained from radar

merged with surface rain gauge observations in order to cor-

rainfall data (Smith et al. ). The next generation radar

rect mean ﬁeld bias (MFB) using Kalman ﬁltering (Smith &

(NEXRAD) products available since 1992 provide high

Krajewski ; Anagnostou et al. ). In StageIII, the

doi: 10.2166/nh.2013.194

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

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StageII rainfall data from multiple weather radars covering a

procedures assume that the biases are spatially uniform over

River Forecast Center (RFC) region are combined (Fulton

the entire RFC region. These spatially uniform biases are

et al. ; Reed & Maidment ). Finally, StageIV is the

referred to as MFB (Smith & Krajewski ). However,

mosaicked StageIII rainfall product covering the entire Con-

recent studies have shown that the assumption of spatially uni-

tinental United States (CONUS).

form bias is not valid over particular regions (Li & Shao ).

The most commonly used NEXRAD product in hydro-

The NEXRAD rainfall bias over a small watershed in an RFC

meteorological applications is the NEXRAD StageIII data

region could be very different from the mean bias over the

(e.g., Young et al. ) because the radar rainfall rates are

entire RFC region. Looper et al. () concluded that even

corrected using multiple surface rain gauges and it undergoes

though MPE accounts for radar bias, the resulting precipi-

a signiﬁcant degree of meteorological quality control by

tation may not be accurate for a particular river basin,

trained personnel at individual RFCs (Fulton et al. ).

because adjustment is performed on the entire RFC region.

Since around 2002, Multisensor Precipitation Estimator

Consequently, hydrologic model simulations for a particular

(MPE), which is developed by the National Weather Service

watershed with MPE analysis data could be unrealistic. In

(NWS) Ofﬁce of Hydrology, is available for each RFC. The

addition, the effect of these spatially non-uniform local

MPE product is obtained by merging radar, gauge, and satel-

biases on hydrologic simulations is not well understood (Li

lite estimates of rainfall and is adjusted for MFBs. In spite of

& Shao ). Furthermore, a few methods that are available

better spatial representation of rainfall variability by radar,

in order to correct spatially non-uniform local biases (Seo &

there are limitations of radar estimates due to data contami-

Breidenbach ) have limitations such as insufﬁcient rain

nation and uncertainty issues (Smith et al. ; Legates

gauge and uneven rain gauge networks, and their sensitivity

; Xie et al. ). In particular, uncertainty in radar rain-

to hydrologic model simulations has not been tested.

fall is caused by Z–R conversion method, limitation of

Use of radar rainfall in hydrology is a challenge and further

available rain gauge information for MFB adjustment, and

work remains to be done on how to reﬁne radar rainfall for

spatially uniform bias correction for entire RFCs.

hydrology (Berne & Krajewski ). Dense and high quality

Schmid & Wuest () suggest that new decade research

rain gauge networks are one of the key factors in solving the

in hydrometeorology is minimizing radar precipitation

problem of radar-rainfall uncertainties (Krajewski et al. ;

errors. Smith & Krajewski () found that combining

Villarini & Krajewski ). Applying constant bias factor for

radar and gauge information produces improved precipi-

correcting radar rainfall to the entire radar-rainfall ﬁeld was

tation estimates, in terms of both quality and spatial

suggested by Anagnostou et al. (), Smith & Krajewski

resolution, in comparison with either radar or gauge esti-

(), and Seo et al. (). After that, Seo & Breidenbach

mates alone. Dinku et al. () investigated different radar

() investigated spatially varying radar rainfall biases

rainfall error correction schemes in mountainous areas.

which can be adjusted by using against rain gauge data. Conse-

These schemes included correction for terrain blocking,

quently, studying radar-rainfall error correction shifted to ﬁnd

adjustment for rain attenuation, interpolation of reﬂectivity

out spatially varying radar rainfall biases.

data, and Kalman ﬁltering-based mean ﬁeld radar bias correc-

Most research focus has already tried to ﬁnd the best way

tion scheme similar to that of Anagnostou et al. (). Dinku

of correcting spatial radar rainfall biases (Young et al. ;

et al. () found that adjustment of radar bias with the ﬁlter-

Jayakrishnan et al. ; Xie et al. ; Wang et al. ;

ing approach produced high accuracy radar rainfall. Despite

Habib et al. ). Seo & Breidenbach (), Haberlandt

several techniques available for merging radar data with rain-

(), and Li et al. () suggest that rain gauge data inter-

fall gauges, uncertainty persists in radar precipitation

polation

products because large portions of radar coverage areas do

precipitation, is the most common method to reduce spatially

not have rain gauge data to adjust biases in radar rainfall

varying radar rainfall biases. A more advanced attempt has

(Winchell et al. ; Habib et al. ).

been tried by Li et al. (), using a linear regression based

into

radar

rainfall,

especially

NEXRAD

In NEXRAD StageIII (MPE), analysis bias in radar rainfall

Kriging method to improve daily NEXRAD precipitation

is corrected using available rain gauges. The correction

using rain gauge data applied in Texas to estimate daily

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

spatial precipitation in 2003. Even though several research

on the sensitivity of a grid based distributed hydrologic model

results in which radar error correction was done by rain

simulation with two study areas (ﬂat and mountainous).

gauge data promise spatially better radar rainfall distributions, minimal research has been devoted to evaluate the accuracy in localized precipitation that is critical for accurate

STUDY AREAS AND DATA

hydrologic simulations (Xie et al. ; Parkes et al. ). The aim of this research is to provide better methods for

The Upper Wabash River (UWR) and the Upper Cumber-

correcting radar precipitation error by using available rain

land River (UCR) (Figure 1) basins were selected as the

gauges through a spatial grid based Kalman ﬁltering approach

test beds for this study. In addition to providing two distinct

instead of a MFB scheme. Those correcting radar precipitation

geographic locations, both study areas include a reasonable

data should improve the correct simulation prediction in

rain gauge network to compare bias correction schemes

hydrologic models. The literature shows that the availability

using NEXRAD data. The UWR basin (17,907 km2) is

of high-resolution precipitation data from different weather

located in north central Indiana and drains into the

radar platforms has led to improved understanding of rainfall

Wabash River. The elevation in UWR ranges from 149 to

uncertainty in hydrologic models, but few efforts have been

529 m. Normal annual precipitation of the UWR ranges

directed towards understanding the inﬂuence of NEXRAD

between 920 and 1,120 mm as computed by using data

precipitation and its bias correction on rainfall-runoff simu-

from 17 rain gauges in the region. The UCR basin

lations (Xie et al. ). Thus, results from this study will

(38,160 km2) is located in southeastern Kentucky bordering

provide insight into the performance of three different

with Virginia and Tennessee. The UCR is primarily mountai-

NEXRAD rainfall bias correction schemes and their inﬂuence

nous and forested, and it lies in the Eastern Coal Field

Figure 1

Study basin locations including rain and stream gauges (UWR – Upper Wabash River basin; UCR – Upper Cumberland River basin).

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

physiographic region. The elevation in the UCR ranges from

NEXRAD StageIII data are pre-processed by using the algor-

146 to 1,428 m. Normal annual precipitation of the UCR

ithm of Xie & Zhou (): (1) convert the XMRG (binary)

ranges from 950 to 1,300 mm as computed from 19 rain

ﬁle format to ASCII; and (2) create a desired coordinate

gauges in the region.

system by projecting the HRAP data which format is con-

The NEXRAD domain of the Ohio River Forecast

verted to GIS grid from ASCII. The streamﬂow data for

Center (OHRFC) encompasses both study areas. Hourly

the study sites were obtained from the United States Geo-

NEXRAD StageIII precipitation (4 km × 4 km resolution)

logical Survey’s (USGS) Instantaneous Data Archive (IDA)

estimates are obtained from the National Oceanic Atmos-

website (http://ida.water.usgs.gov/ida/). The straight line

pheric Administration’s (NOAA) Hydrologic Data System

base ﬂow separation method was used for retrieving surface

group website (http://dipper.nws.noaa.gov/hds/data/nexrad/

runoff hydrographs from streamﬂow. The study was con-

ohrfcmpe), and hourly gauge precipitation estimates are

ducted by selecting ﬁve storms for each study region. The

obtained from the National Climatic Data Center (NCDC)

details of these storm events are provided in Table 1.

website (http://gis.ncdc.noaa.gov/maps/). The NEXRAD rainfall dataset for the study area is available with the HRAP (Hydrologic Rainfall Analysis Project) geographic projec-

NEXRAD BIAS CORRECTION METHODS

tion. The HRAP or secant polar stereographic projection is an earth-centered datum coordinate system. Reed & Maid-

A statistical method should be used to remove the bias

ment () describe the HRAP projection and its

between NEXRAD estimates at the rain gauge locations,

transformations to other geodetic coordinate systems. The

and corresponding gauge rainfall measurements because

Table 1

Summary of storm events and calibrated Manning’s n values for each study site

(a) Upper Wabash River Upper Wabash River basin Land use calibration Start date and

Total precipitation

Total streamﬂow

Peak ﬂow:

PF/Mean

Time to

Event

time

(mm)

PF (m3/s)

annual PF

peak (hr)

Agricultural

Forest

Developed

Water

06-02-17, 01:00

3.864

0.558

37.37

1.41

0.023

0.013

0.011

0.006

06-04-16, 19:00

5.057

1.635

142.15

5.38

0.02

0.019

0.015

0.005

06-07-12, 03:00

4.884

1.515

197.14

7.46

0.019

0.014

0.011

0.006

06-10-27, 19:00

4.519

1.184

86.98

3.29

0.025

0.02

0.018

0.006

06-11-16, 08:00

4.995

1.865

147.41

5.58

0.018

0.015

0.013

0.005

(b) Upper Cumberland River Upper Cumberland River basin Land use calibration Start date and

Total precipitation

Total streamﬂow

Peak ﬂow:

PF/Mean

Time to

Event

time

(mm)

PF (m3/s)

annual PF

peak (hr)

Agricultural

Forest

Developed

Water

05-01-11, 12:00

9.108

1.076

160.55

4.73

0.051

0.035

0.033

0.016

05-02-13, 10:00

12.944

2.462

354.81

10.46

0.081

0.055

0.043

0.026

05-03-27, 23:00

10.548

1.531

252.3

7.44

0.061

0.036

0.023

0.02

05-04-01, 18:00

12.577

2.379

305.25

9.00

0.062

0.043

0.037

0.012

05-07-13, 08:00

6.579

0.486

76.54

2.26

0.054

0.037

0.035

0.015

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

The a priori estimate of β can be estimated using

NEXRAD rainfall estimates have errors from reﬂectivity measurement and the Z–R conversion. In order to test the

Equation (4):

sensitivity of NEXRAD bias correction on rainfall-runoff simulation, three methods based on Kalman ﬁltering are

β Δ ðtÞ ¼ ρβ × β Δ ðt 1Þ

(4)

used in this study which can be considered a time updated mechanism. The ﬁrst method is based on the application

where β Δ takes into account the new measurement that is

of spatially uniform bias correction as used in the MPE

observed and corrects for any errors that may be present

data. The second and third methods are based on the appli-

in the newly measured value. The process variance P ðtÞ is estimated using Equation

cation of spatially non-uniform bias correction. A brief description of the Kalman ﬁltering and its application for spatially and non-spatially uniform bias correction is presented below. Kalman ﬁlter

P ðtÞ ¼ ρ2β × Pðt 1Þ þ 1 ρ2β × σ 2β

(5)

where P(t 1) is the a posteriori estimate of error variance at

The Kalman ﬁltering equations have two steps in the form of time update and measurement update, in order to estimate the best possible bias. Projection of the current state to a forward time step is performed via time update, and the correction of a priori estimate at the current time step is performed via measurement update (Welch & Bishop ).

time t 1. The initial value of β0 and P0 are zero and σ 2β , respectively. Discrete Kalman ﬁlter measurement update In each time and measurement update, the process is repeated with the previous a posteriori estimates in order to project or predict the new a priori estimates. This recur-

Discrete Kalman ﬁlter time update

sive nature is one of the important features of the Kalman

According to Smith & Krajewski (), NEXRAD bias (β) is assumed as an autoregressive order one (AR1) process whose parameters are updated using a Kalman ﬁlter as given by Equation (1): β ðtÞ ¼ ρβ × β ðt 1Þ þ W ðtÞ; W ðtÞ ∼ N ð0, ν Þ

(5):

ﬁlter. Updating the a priori estimates of the logarithmic NEXRAD bias β Δ ðtÞ and its variance P ðtÞ based on the actual bias for the current time step t are performed in measurement update. The errors associated with the observed rain ﬁeld lead to a deviation between the observed

(1)

where β(t) is the NEXRAD bias for hour t, ρβ is lag-one correlation coefﬁcient of the logarithmic bias, and W(t) is a

and true values for βt. Observed logarithmic NEXRAD bias Y (t) is represented by using Equation (6): Y ðtÞ ¼ β ðtÞ þ MðtÞ; MðtÞ ∼ N 0, σ ½ηðtÞ 2

(6)

sequence of independent normally distributed random variables with zero mean and variance ν. The stationary process

where σ ðηÞ is a non-negative function representing the

variance ν and the stationary variance of the log bias process

observation error given that the number of gauges with measurable rainfall is η, and M (t) is a sequence of independent

σβ are given by Equations (2) and (3):

normally distributed random variable with zero mean and

ν ¼ 1 ρ2β × σ 2β

(2)

σ 2β ¼ Var½β ðtÞ ; t ¼ 0, . . . , T

(3)

where T is storm duration.

variance of σ ðηÞ2 , which is given by Equation (7) from Smith & Krajewski (): σ ðηÞ2 ¼ n 2 where n is the number of the rain gauge.

(7)

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

The measurement update of the Kalman ﬁlter allows

where G(t)i is hourly rain gauge rainfall at NEXRAD-gauge

estimation of β Δ ðtÞ and P(t) by Kalman gain K(t) and it is

paired cell i for hour t, R(t)i is hourly NEXRAD rainfall at

presented in Equations (8), (9), and (10).

NEXRAD-gauge paired cell i for hour t, and n is the number

1 KðtÞ ¼ P ðtÞ P ðtÞ þ σ ðηÞ2

of pairs of radar-gauge data. Spatially uniform bias corrected (8)

NEXRAD rainfall is then computed by using Equation (13): R ðtÞj ¼ BðtÞ RðtÞj

(13)

After this stage for time step t, the estimated logarithmic bias β Δ ðtÞ and its variance P(t) are calculated by Equations

where R*(t)j is bias corrected NEXRAD rainfall at cell j at time

(9) and (10).

t, and R(t)j is hourly NEXRAD rainfall at gauge cell j for hour t

β Δ ðtÞ ¼ β Δ ðtÞ þ KðtÞ Y ðtÞ β Δ ðtÞ

within and around the study area. (9) Spatially non-uniform NEXRAD precipitation bias

PðtÞ ¼ ð1 KðtÞÞ × P ðtÞ

(10)

Due to the bias model deﬁned in terms of the log bias process, Smith & Krajewski () suggest Equation (11) for the state expectation of the bias correction factor at the time t as shown below: Δ BðtÞ ¼ 10½β ðtÞþ0:5PðtÞ

correction using Kalman ﬁlter In the spatially uniform bias correction method, the radar rainfall bias (Equation (12)) over the cells with observed rain gauge data is assumed to be uniform for all NEXRAD cells. The assumption of uniform bias may or may not be true depending on the rainfall dynamics and the size of the watershed. For example, the bias may be higher for

(11)

NEXRAD cells that do not overlap with rain gauge locations. In order to minimize such ungauged NEXRAD

Spatially uniform NEXRAD precipitation bias correction using Kalman ﬁlter

form bias correction using the Kalman ﬁlter. Unlike the MFB (Equation (12)), the spatially non-uniform biases vary

According to Seo et al. () and Dinku et al. (), the MFB corrections and vertical profile of reflectivity adjustments are needed for correcting spatially uniform biases in NEXRAD data. The variance of the observed MFB should affect the magnitude of the Kalman filter observation error model. The timedependent variance of the observed MFB is estimated by using the variance of logarithmic bias proposed by Smith & Krajewski (). The correction procedures assume that the biases are spatially uniform over the entire study area. The logarithmic MFB between NEXRAD estimates at the rain gauge locations and the corresponding gauge rainfall amounts is computed by Equation (12): n 1X log10 GðtÞi n i¼1 β ðtÞ ¼ n 1X log10 RðtÞi n i¼1

cell bias, this study suggests application of spatially non-uni-

from pixel to pixel across the NEXRAD domain. Corrected NEXRAD rainfall at an ungauged NEXRAD pixel j for hour t, R*(t)j, is computed by multiplying spatially non-uniform bias correction factor (B(t)j) at each ungauged NEXRAD grid location j using Equation (14): R ðtÞj ¼ BðtÞj RðtÞj

(14)

There are two approaches for computing the spatially non-uniform bias. In the ﬁrst approach, the rain gauge data are interpolated using squared inversed distance weighting (Equation (15)) to yield rainfall estimates for ungauged NEXRAD pixels: n P

(12)

wi GðtÞi G ðtÞj ¼ i¼1 n P wi i¼1

(15)

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

where G*(t)j is interpolated gauge information at an un-

Hydrology Research

45.1

2014

HYDROLOGIC MODEL

gauged NEXRAD pixel j for hour t, and wi (Equation (16)) is the weight corresponding to each gauged point:

The sensitivity of bias correction methods for runoff prediction was tested by using the bias corrected rainfall data to

1=db wi ¼ n i P 1=dbi

(16)

run a storage release based distributed hydrologic model (STORE DHM) developed by Kang & Merwade (, ). The STORE DHM is a grid based conceptual model

i¼0

that involves computing excess rainfall, volumetric ﬂow where di is the distance between a radar pixel and the ith

rate, and travel time to the basin outlet by combining

rain gauge with b ¼ 2 for squared inverse distance weighting,

steady-state uniform ﬂow approximation with Manning’s

and n is the number of rain gauges. The spatially non-uni-

equation. After computing excess rainfall by using the SCS

form local NEXRAD biases can then be estimated and

curve number method, the direct runoff is routed by using

corrected by using the interpolated rainfall (Equation (17)):

a simple storage release approach. In this approach

log10 G ðtÞj β ðtÞj ¼ log10 RðtÞj

(Figure 2), water within a watershed or stream can be (17)

time step, each bucket stores the accumulated water of all upstream buckets that drain into it, and then releases the

where β ðtÞj is logarithmic local bias at an ungauged NEXRAD pixel j for hour t within the study area. In the second approach for applying non-uniform bias, the error of radar rainfall at each gauged location is computed using Equation (18): log10 GðtÞi eðtÞi ¼ log10 RðtÞi

assumed to ﬂow through a series of buckets. At any given

stored water to its next downstream bucket at the next time step, as shown in Figure 2. Following the conceptual model from Figure 2, storage at any given time in any given bucket (a raster cell in the model) is given by Equation (20): Si,t ¼ Qi,t Δt þ Si,t 1 Ri,t Δt þ

Ru,t Δt

(20)

(18) where Ri,t (given by Equation (21)) represents the release term from a cell i in the tth time step, and the difference

The errors of radar rainfall at each ith gauge are then

between S and R represents the storage in the cell. The sub-

interpolated in order to get errors at all ungauged

script u in Equation (20) represents the surrounding

NEXRAD pixels using squared inverse distance weighing.

upstream cells that are draining to cell i. In Figure 2, each

Ware () found that the interpolation errors associated

bucket or cell releases its stored water to a downstream

with this IDW are comparable to those obtained using the

cell depending on the residence or travel time of the water

multi-quadric interpolation (Nuss & Titley ) and ordinary kriging. An ungauged NEXRAD bias for spatially

within each cell. The connectivity of all raster cells is established from the ﬂow direction grid derived by using the eight

non-uniform bias correction is computed based on the

points pour model. Each release term in Equation (20) is

surrounding ratios of precipitation errors and the distance

computed by using Equation (21):

of each gauge from the selected grid cell (Equation (19)): n P

β ðtÞj ¼

i¼1

wi eðtÞi

n P

(19) wi

i¼1

Ri,t ¼

8 > S > < i,t 1 Δt

S Δt > > : i,t 1 × Ti,t 1 Δt

if Ti,t 1 < Δt

(21)

if Ti,t 1 > Δt

where β ðtÞj is logarithmic local precipitation bias at un-

where Ti,t is the travel time within each cell, and is estimated

gauged NEXRAD pixel j for hour t within the study area.

depending on the ﬂow conditions (overland ﬂow or channel

Figure 2

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

Storage release concept.

ﬂow). In Equation (21), all the water stored within a cell is

created by using spatially uniform and non-uniform bias cor-

released downstream if the travel time (Ti,t ) is smaller than

rection is presented.

the model time step (Δt), or a fraction (Δt=Ti,t ) of the water is released if the travel time is greater than the model time

Assessment of NEXRAD rainfall inputs

step. More details on computation of travel time for overland ﬂow and channel ﬂow, and selection of appropriate

The cross-validation of NEXRAD rainfall inputs created by

time step can be found in Kang & Merwade (). The

using MPE, SNU-R, and SNU-E is conducted by using a

data requirements for STORE DHM include DEM of the

total of 17 rain gauges in UWR and 19 rain gauges in

study area, rainfall data (gauged points or NEXRAD grid),

UCR basins for ﬁve different events (Table 1). From the com-

and land use. STORE DHM is selected in this study because

plete set of gauging stations, three stations are excluded for

of its simplicity involving only one calibration parameter

cross-validation. The scatter plot of NEXRAD bias corrected

(Manning’s n).

rainfall and cross-validated observed gauge rainfall for the UWR and the UCR are shown in Figure 3. The results presented in Figures 3(a) and 3(b) show that the NEXRAD

RESULTS

rainfall created using the MPE scheme has considerable scatter in comparison with data created by applying spatially

Results are presented in two sections. In the ﬁrst section, the

non-uniform bias correction schemes. The performance of

quality of NEXRAD data is assessed through cross-vali-

bias corrected NEXRAD is assessed by computing the root

dation with observed rainfall. The NEXRAD data used in

mean square error (RMSE), mean absolute percentage

cross-validation are prepared by using the spatially uniform

error (MAPE), and coefﬁcient of determination (R 2) as

bias correction method (MPE), spatially non-uniform bias

shown in Tables 2 and 3.

correction method by interpolating rainfall data (SNU-R),

The spatially non-uniform NEXRAD bias correction

and spatially non-uniform bias correction method by inter-

improves rainfall accuracy for the UWR events by reducing

polating errors (SNU-E). In the second section, the

error from 1.17 mm RMSE for MPE to 0.80 mm RMSE for

sensitivity of STORE DHM hydrograph outputs to rainfall

SNU-R and 0.94 mm RMSE for SNU-E. For the UCR

K. Kang & V. Merwade

Figure 3

Table 2

Spatially uniform and non-uniform NEXRAD bias correction

SNU-R scheme

RMSE (mm)

MAPE (%)

RMSE (mm)

0.80

12.06

0.74

0.59

1.73

48.13

0.57

1.63

30.72

0.62

0.38

22.00

1.30

Ave.

1.17

2014

SNU-E scheme R2

RMSE (mm)

8.05

0.87

0.71

9.98

0.80

0.76

18.76

0.92

1.09

31.07

0.82

1.46

14.40

0.70

1.44

17.56

0.70

0.89

0.13

10.28

0.98

0.26

17.73

0.93

93.41

0.53

1.05

19.04

0.67

1.21

66.79

0.57

41.26

0.67

0.80

14.11

0.83

0.94

28.63

0.76

MAPE (%)

2.08

30.27

0.93

MAPE (%)

NEXRAD bias corrected rainfall statistics in the UCR basin

MPE scheme Event

45.1

NEXRAD bias corrected rainfall statistics in the UWR basin

Event

Scatter plot of NEXRAD bias corrected rainfall and cross-validated observed gauge rainfall for (a) the UWR and (b) the UCR basins.

MPE scheme

Table 3

Hydrology Research

RMSE (mm)

SNU-R scheme MAPE (%)

SNU-E scheme MAPE (%)

1.02

15.45

0.88

RMSE (mm)

3.27

80.37

0.35

5.15

169.69

0.37

0.59

29.37

0.60

0.99

45.27

0.85

29.48

90.38

0.01

26.47

26.34

0.04

26.64

34.88

0.01

16.66

127.66

0.13

1.84

23.93

0.53

2.04

36.74

0.53

14.23

108.64

0.67

0.88

25.70

0.90

2.02

41.60

0.88

Ave.

13.76

115.35

0.30

6.16

24.16

0.58

6.75

37.75

0.64

events, the RMSE is reduced from 13.76 mm for MPE to

show similar results where the MAPE is reduced by more

6.16 mm for SNU-R and 6.75 mm for SNU-R. The reduction

than 65% for UWR with the SNU-R scheme, and is reduced

in RMSE from the MPE scheme to the non-uniform bias cor-

by 80% for UCR with the SNU-R scheme. The average R 2 in

rection method is more than 53% for the UCR, and more

the UWR (Table 2) is 0.67 for the MPE scheme, 0.83 for

than 25% for the UWR. Average values for MAPE also

SNU-R, and 0.76 for SNU-E. For the UCR dataset, the

K. Kang & V. Merwade

Figure 4

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

Time series plots of (a) standard deviation and (b) variance in rainfall for each NEXRAD cell.

average R 2 is 0.30 for the MPE scheme, 0.58 for the SNU-R

watersheds. The model was manually calibrated by using

scheme, and 0.64 in the SNU-E scheme (Table 3). Overall,

the Nash–Sutcliffe efﬁcient coefﬁcient (ENS; Equation

the most reduction in errors is achieved by SNU-R com-

(22)) for discharge and RMSE (Equation (23)) for the

pared to SNU-E for both watersheds. In addition, the

total runoff volume.

reduction in error is greater for UCR compared to UWR. The UCR basin has greater rainfall variability compared to the UWR basin (Figure 4). Thus, it can be hypothesized

n P

ENS ¼ 1 i¼1n P

that the reduction in error is greater in larger areas with more variable rainfall compared to smaller areas with a less variable rainfall pattern.

Qisim Qiobs

i¼1

Qisim Q

2 (22)

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX 2 RMSE ¼ t Qisim Qiobs

(23)

i¼1

Sensitivity of model hydrographs with different where Qsim is the simulated hourly streamﬂow, Qobs is the

NEXRAD bias correction schemes

observed hourly streamﬂow, and Q is the mean hourly To study the sensitivity of the model hydrograph to rainfall

observed streamﬂow. Calibration parameters used to

inputs obtained by using three different NEXRAD bias cor-

adjust the model and the corresponding parameter values

rection

are presented in Table 1. The results from calibration are

approaches,

the

STORE

DHM

model

was

calibrated with original NEXRAD for each event for both

Table 4

presented in Table 4 and Figure 5.

Calibrated simulation statistics for each study site

Upper Wabash River basin Calibration with NEXRAD input Event

ENS

0.98

0.97

0.94

0.98

0.95

Ave.

0.96

Upper Cumberland River basin Calibration with NEXRAD input RMSE (m3/s)

MAPE (%)

ENS

RMSE (m3/s)

MAPE (%)

2.21

14.58

0.97

0.96

10.24

10.48

0.97

9.13

19.56

0.94

0.86

43.97

23.77

0.93

13.49

37.59

0.98

0.96

16.50

16.94

0.97

4.70

27.45

0.97

0.94

24.36

16.57

0.93

12.83

33.89

0.95

0.90

7.54

40.81

0.95

8.47

26.62

0.96

0.93

20.52

21.72

Figure 5

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

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2014

Calibrated model results for every event using NEXRAD rainfall input (e.g. UWR1 represents event 1 for UWR basin). X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second. (a) UWR basin. (b) UCR basin.

Figure 6

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

Storm event 1 model hydrographs for both (a) the UWR basin and (b) the UCR basin. X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second.

Figure 7

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

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45.1

2014

Storm event 2 model hydrographs for both (a) the UWR basin and (b) the UCR basin. X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second.

Figure 8

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

Storm event 3 model hydrographs for both (a) the UWR basin and (b) the UCR basin. X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second.

Figure 9

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Hydrology Research

45.1

2014

Storm event 4 model hydrographs for both (a) the UWR basin and (b) the UCR basin. X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second.

K. Kang & V. Merwade

Figure 10

Spatially uniform and non-uniform NEXRAD bias correction

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45.1

2014

Storm event 5 model hydrographs for both (a) the UWR basin and (b) the UCR basin. X-axis represents time in hours and Y-axis represents ďŹ&#x201A;ow in cubic meters per second.

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

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45.1

2014

After calibration, each event is simulated with the

For the UCR basin (Figures 6(b)–10(b) and Table 6), the

STORE DHM using three variations of NEXRAD rainfall

calibrated R 2 of 0.96 decreased to 0.80 for MPE, and 0.94

created by applying uniform and non-uniform spatial bias

for both SNU-R and SNU-E. The calibrated ENS of 0.93

correction. The hydrographs from these simulations are pre-

decreased to 0.65 for MPE, 0.88 for SNU-R, and 0.94 for

sented in Figures 6–10, and the results are summarized in

SNU-E. The calibrated RMSE of 20.52 m3/s changed to

Tables 5 and 6. For the UWR basin (Figures 6(a)–10(a)

47.36 m3/s for MPE, 27.08 m3/s for SNU-R and 24.73 m3/s

and Table 5), the calibrated R of 0.96 decreased to 0.92

for SNU-E. Similarly, the calibrated MAPE of 21.72% chan-

for MPE, and 0.95 for both SNU-R and SNU-E. The cali-

ged to 54.75% for MPE, 26.99% for SNU-R, and 26.56% for

brated ENS of 0.95 decreased to 0.82 for MPE, but

SNU-E. Overall, SNU-R improved the RMSE by 75% and

remained unchanged for SNU-R and SNU-E. The calibrated

MAPE by 103% in the output hydrographs compared to

RMSE of 8.47 m3/s changed to 16.49 m3/s for MPE,

hydrographs from MPE rainfall input. SNU-E improved

9.86 m /s for SNU-R, and 11.20 m /s for SNU-E. Similarly,

the RMSE by 92% and MAPE by 106% in the output hydro-

the calibrated MAPE of 26.62% changed to 33.75% for

graphs compared to hydrographs from MPE rainfall input.

MPE, 27.98% for SNU-R, and 30.80% for SNU-E. Overall,

The rainfall input derived by applying a spatially uni-

SNU-R improved the RMSE by 67%, and MAPE by 21%

form

in the output hydrographs compared to hydrographs from

calibrated model prediction accuracy as evident from R 2,

MPE rainfall input. SNU-E improved the RMSE by 47%

ENS, RMSE, and MAPE values in comparison to input

and MAPE by 10% in the output hydrographs compared

derived by applying a spatially non-uniform bias correction

to hydrographs from MPE rainfall input.

scheme. The improvement in model results from the

Table 5

Event

ENS

0.96

0.92

0.90

0.72

0.86

0.84

0.96

0.85

0.94

Ave.

0.92

correction

NEXRAD

data

decreased

Details of simulation results with different NEXRAD bias corrected rainfall for the UWR basin

Simulation with MPE scheme

Table 6

bias

RMSE (m3/s)

Simulation with SNU-R scheme RMSE (m3/s)

Simulation with SNU-E scheme

MAPE (%)

ENS

3.51

21.48

0.97

0.96

2.56

18.18

0.97

0.96

2.53

18.19

25.83

30.30

0.97

0.93

13.13

19.59

0.96

0.86

18.38

28.24

20.43

41.58

0.91

15.54

40.42

0.91

0.90

16.24

41.26

10.63

29.46

0.98

0.97

4.94

27.48

0.97

0.96

5.35

28.63

0.79

22.08

45.95

0.95

0.93

13.12

34.22

0.94

0.92

13.49

37.66

0.82

16.49

33.75

0.95

0.94

9.86

27.98

0.95

0.92

11.20

30.80

MAPE (%)

ENS

RMSE (m3/s)

MAPE (%)

Details of simulation results with different NEXRAD bias corrected rainfall for the UCR basin

Simulation with MPE scheme Event

ENS

RMSE (m3/s)

0.88

0.81

23.24

0.92

0.60

0.36

0.19

0.89

0.95

Ave.

0.80

Simulation with SNU-R scheme R2

ENS

17.40

0.99

0.97

74.64

37.95

0.82

92.02

149.85

0.97

0.89

34.51

19.66

0.73

12.40

48.90

0.65

47.36

54.75

MAPE (%)

RMSE (m3/s)

Simulation with SNU-E scheme MAPE (%)

ENS

RMSE (m3/s)

MAPE (%)

9.42

10.81

0.96

11.42

12.69

0.70

65.16

32.74

0.89

0.75

59.06

31.22

0.95

19.48

30.89

0.97

0.95

18.25

26.69

0.96

0.89

33.74

18.51

0.94

0.93

27.27

18.76

0.95

0.90

7.59

42.00

0.94

0.90

7.64

43.42

0.94

0.88

27.08

26.99

0.94

0.90

24.73

26.56

K. Kang & V. Merwade

Figure 11

Spatially uniform and non-uniform NEXRAD bias correction

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2014

Storm events peak discharge (m3/s) scatter plots for (a) the UWR and (b) the UCR basins.

spatially non-uniform bias corrected input are better in

on hydrologic simulations. The following conclusions can

the UCR basin compared to the UWR basin because the

be drawn from this study:

NEXRAD values are more variable in time over the UCR basin compared to the UWR basin, as shown in Figure 4.

1. For the two basins used in this study, the cross-validation

Although the spatially non-uniform bias correction scheme

of rainfall estimates obtained by applying spatially non-

takes care of both spatial and temporal NEXRAD bias, the

uniform bias correction methods have better accuracy

results from this study show that the bias correction is

in terms of RMSE compared to spatially uniform bias cor-

more effective for the UCR basin, which has more spatio-

rection method.

temporal variability in rainfall compared to the UWR basin.

2. Between the two spatially non-uniform bias correction

Even though the NEXRAD input is adjusted by using

methods used in this study, the method that involves

gauged rainfall, some under-prediction or over-prediction

interpolation of rainfall before applying the bias correc-

of runoff volume and peak ﬂow is found for both study

tion (SNU-R) performed better in the hydrologic model

areas, as shown in Figures 6–10. Simulations with SNU-E

simulation than the method that involves interpolation

inputs performed the best with regard to the estimation of

of error (SNU-E).

peak ﬂow as shown in scatter plots in Figure 11. Similarly,

3. Hydrologic simulations performed using a grid based dis-

the input from both methods using spatially non-uniform

tributed hydrologic model show that the input rainfall

bias correction produced an overall better output compared

obtained by using spatially non-uniform bias correction

to input from spatially uniform bias correction method in

method produced output hydrographs that are more com-

terms of total runoff volume. Within the UCR basin, the pre-

parable with the calibrated model output compared to

diction accuracy with SNU inputs is considerably better

the output from the model using spatially uniform bias cor-

than the ﬂat elevation region such as the UWR basin.

rected rainfall input. Of the two spatially non-uniform bias correction methods, the SNU-R method produced better runoff hydrographs compared to the SNU-E method.

CONCLUSIONS

4. The improvement in rainfall estimates and hydrologic simulations from using spatially non-uniform bias correction

Three different NEXRAD bias correction schemes are

methods is consistent for both watersheds used in this

applied to two study basins (UWR and UCR) in order to

study. The overall improvement is greater in the UCR

evaluate the effects of each NEXRAD bias correction

basin compared to the UWR basin. This shows that the

scheme on the representation of the rainfall, and its effect

application of spatially non-uniform bias correction for

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

radar rainfall is more effective in larger areas with more variable rainfall (i.e., UCR) compared to smaller areas with less variable rainfall (i.e., UWR) basin. However, this conclusion is based on only the two watersheds used in this study, and in order to make it generally applicable it must be investigated further by including more watersheds. 5. Although SNU methods show better performance than MPE rainfall, there are still several issues that need investigating for correcting radar-rainfall error: limitation of rain gauge density (instead of making an interpolated rain gauge in a non-gauge grid), large scale of radar rainfall grid (4 km × 4 km is large to get spatially distributed rainfall dynamic), and many assumptions about the physical radar function (Z–R law). 6. Calibration in each event is needed to investigate simulation validity depending on the individual NEXRAD bias correction scheme. However, the aim of this research was to investigate three different NEXRAD bias correction schemes on hydrologic modeling performance. Thus, this research has focused more on sensitivity checks for rainfall inputs. 7. For further research, new interpolation methods to gain a robust rainfall input in hydrologic modeling are encouraging,

such

Parameter-elevation

Regression

Independent Slope Model (PRISM) which can be considered by temperature, elevation, distance from true value (observed rainfall data), and distance from coastline.

REFERENCES Abedini, M., Said, Md Azlin Md & Ahmad, F.  Integration of statistical and spatial methods for distributing precipitation in tropical areas. Hydrol. Res. 44 (6), 982–994. doi: 10.2166/nh. 2012.159. Anagnostou, E. N., Krajewski, K. F. & Smith, J.  Uncertainty quantiﬁcation of mean real radar-rainfall estimates. J. Atmos. Ocean Technol. 16, 206–215. Berne, A. & Krajewski, W. F.  Radar for hydrology: unfulﬁlled promise or unrecognized potential? Adv. Water Resour. 51, 357–366. Dinku, T., Ananostou, E. N. & Borga, M.  Improving radarbased estimation of rainfall over complex terrain. J. Appl. Meteorol. 41, 1163–1178. Feiccabrino, J., Gustafsson, G. & Lundberg, A.  Surface-based precipitation phase determination methods in hydrological models. Hydrol. Res. 44 (1), 44–57.

Hydrology Research

45.1

2014

Fulton, R. A., Breidenbach, J. P., Seo, D., Miller, D. A. & O’Bannon, T.  The WSR-88D rainfall algorithm. Weather Forecast. 13, 377–395. Haberlandt, U.  Geostatistical interpolation of hourly precipitation from rain gauges and radar for a large-scale extreme rainfall event. J. Hydrol. 332, 144–157. Habib, E., Larson, B. F. & Graschel, J.  Validation of NEXRAD multisensory precipitation estimates using an experimental dense rain gauge network in South Louisiana. J. Hydrol. 373 (3–4), 463–478. Jayakrishnan, R., Srinivasan, R. & Arnold, J. G.  Comparison of raingauge and WSR-88D stage III precipitation data over the Texas-Gulf River Basin. J. Hydrol. 292, 135–152. Jeong, D. L., St-Hilaire, A., Ouarda, T. B. M. J. & Gachon, P.  Projection of future daily precipitation series and extreme events by using a multi-site statistical downscaling model over the great Montréal area, Québec, Canada. Hydrol. Res. 44 (1), 147–168. Kang, K. & Merwade, V.  Effects of rain gage density on correcting radar precipitation and its inﬂuence on hydrologic model simulation. EOS Transactions AGU, 90(52), Fall meeting, San Francisco, CA, December 2009. Kang, K. & Merwade, V.  Development and application of a storage-release based distributed hydrologic modeling using GIS. J. Hydrol. 403 (1–2), 1–13. Krajewski, W. F., Villarini, G. & Smith, J. A.  Radar-rainfall uncertainties: where are we after thirty years of effort. Bull. Am. Meteorol. Soc. 91 (1), 87–94. Legates, D. R.  Real-time calibration of radar precipitation estimates. Prof. Geogr. 52 (2), 235–246. Li, B., Eriksson, M., Srinivasan, R. & Sherman, M.  A geostatistical method for Texas NexRad data calibration. Environmetrics 19 (1), 1–19. Li, L., Ngongondo, C. S., Xu, C. Y. & Gong, L.  Comparison of the global TRMM and WFD precipitation datasets in driving a large-scale hydrological model in Southern Africa. Hydrol. Res. 44 (5), 770–788. doi:10.2166/nh.2012.175. Li, M. & Shao, Q.  An improved statistical approach to merge satellite rainfall estimates and rain gauge data. J. Hydrol. 385 (1–4), 51–64. Looper, J., Vieux, B. & Moreno, M.  Assessing the impacts of precipitation bias on distributed hydrologic model calibration and prediction accuracy. J. Hydrol. 418–419, 110–122. Nicótina, L., Alessi Celegon, E., Rinaldo, A. & Marani, M.  On the impact of rainfall patterns on the hydrology response. Water Resour. Res. 44 (12), W12401. Nuss, W. A. & Titley, D. W.  Use of multiquadric interpolation for meteorological objective analysis. Month. Weather Rev. 122, 1611–1631. Parkes, B. L., Wetterhall, F., Pappenberger, F., He, Y., Malamud, B. D. & Cloke, H. L.  Assessment of a 1-hour gridded precipitation dataset to drive a hydrological model: a case study of the summer 2007 ﬂoods in the Upper Severn, UK. Hydrol. Res. 44 (1), 89–105.

K. Kang & V. Merwade

Spatially uniform and non-uniform NEXRAD bias correction

Reed, S. M. & Maidment, D. R.  Coordinate transformations for using NEXRAD data in GIS-based hydrologic modeling. J. Hydrol. Eng. 4, 174–182. Schmid, W. & Wuest, M.  Verifying warnings for point precipitation. Atmos. Res. 77, 347–353. Seo, D. J. & Breidenbach, J. P.  Real-time correction of spatially nonuniform bias in radar rainfall data using rain gauge measurements. J. Hydrometeorol. 2, 93–111. Seo, D. J., Breidenbach, J. P. & Johnson, E. R.  Real-time estimation of mean field bias in radar rainfall data. J. Hydrol. 223, 131–147. Smith, J. A. & Krajewski, W. F.  Estimation of the mean field bias of radar rainfall estimates. J. Appl. Meteorol. 30, 397–412. Smith, J. A., Seo, D. J., Baeck, M. L. & Hudlow, M. D.  An intercomparison study of NEXRAD precipitation estimates. Water Resour. Res. 31, 2035–2045. Smith, M. B., Seo, D. J. & Koren, V. I.  The distributed model intercomparison project (DMIP); an overview. J. Hydrol. 298 (1–4), 4–26. Viglione, A., Chirico, G. B., Woods, R. & Blöschl, G.  Generalised synthesis of space-time variability in flood response: an analytical framework. J. Hydrol. 394 (1), 198–212. Villarini, G. & Krajewski, W. F.  Review of the different sources of uncertainty in single polarization radar-based estimates of rainfall. Surv. Geophys. 31 (1), 107–129. Wang, X., Xie, H., Sharif, H. & Zeitler, J.  Validating NEXRAD MPE and stage III precipitation products for uniform rainfall on the Upper Guadalupe River Basin of the Texas Hill Country. J. Hydrol. 348 (1–2), 73–86. Ware, E. C.  Correction to Radar-estimated Precipitation using Observed Rain Gauge Data. MS Thesis, Cornell University, Ithaca, p. 87.

Hydrology Research

45.1

2014

Welch, G. & Bishop, G.  An Introduction to the Kalman Filter. SIGGRAPH 2001 course 8. In: Computer Graphics Annual Conference Graphics & Interactive Techniques, ACM Press, New York. Winchell, M., Gupta, H. V. & Sorooshian, S.  On the simulation of infiltration and saturation excess runoff using radar-based rainfall estimates: effects of algorithm uncertainty and pixel aggregation. Water Resour. Res. 34 (10), 2655–2670. Xie, H. & Zhou, X.  GIS-based NEXRAD Stage III precipitation database: automated approaches for data processing and visualization. Comput. Geosci. 31, 65–76. Xie, H., Zhou, X., Hendricks, J., Vivoni, E., Guan, H., Tian, Y. & Small, E.  Evaluation of NEXRAD Stage III precipitation data over semiarid region. J. Am. Water Resour. Assoc. 42 (1), 237–256. Xie, H., Zhou, X., Yu, B. & Sharif, H.  Performance evaluation of interpolation methods for incorporating rain gauge measurements into NEXRAD precipitation data: a case study in the Upper Guadalupe River Basin. Hydrol. Process. 25 (24), 3711–3720. Young, C. B., Bradley, A. A., Krajewski, W. F., Kruger, A. & Morrissey, M. L.  Evaluating NEXRAD multisensor precipitation estimates for operational hydrologic forecasting. J. Appl. Meteorol. 14, 1430–1436. Zoccatelli, D., Borga, M., Viglione, A., Chirico, G. B. & Bloschl, G.  Spatial moments of catchment rainfall: rainfall spatial organization, basin morphology, and flood response. Hydrol. Earth Syst. Sci. 15 (12), 3767–3783. Zoccatelli, D., Borga, M., Zanon, F., Antonescu, B. & Stancalie, G.  Which rainfall spatial information for flash flood response modeling? A numerical investigation based on data from the Carpathian range, Romania. J. Hydrol. 394 (1–2), 148–161.

First received 21 November 2012; accepted in revised form 14 May 2013. Available online 18 June 2013

45.1

2014

Analytical solution of a kinematic wave approximation for channel routing P. Reggiani, E. Todini and D. Meißner

ABSTRACT The kinematic wave approach is often used in hydrological models to describe channel and overland ﬂow. The kinematic wave is suitable for situations where the local and convective acceleration, as well as the pressure term in the dynamic wave model is negligible with respect to the friction and body forces. This is the case when describing runoff processes in the upper parts of catchments, where slopes are generally of the order of 10 3. In physical-based hydrological models, the point-scale conservation equations are integrated over model entities, such as grid pixels or control volumes. The integration leads to a set of ordinary differential governing equations, which can be solved numerically by methods such as the Runge–Kutta integrator. Here, we propose an analytical solution of a Taylor-series approximation of the kinematic wave equation, which is presented as nonlinear reservoir equation. We show that the analytical solution is numerically robust and third-order accurate. It is compared with the numerical solution and the solution of the complete dynamic wave model. The analytical solution proves to be computationally better performing and more accurate than the numerical solution. The proposed analytical solution can also be generalized to situations of leaking channels. Key words

P. Reggiani (corresponding author) Deltares, P.O. Box 177, 2600MH Delft, The Netherlands and Department of Physical Geography, and Climatology, RWTH Aachen University, 52056 Aachen, Germany E-mail: paolo.reggiani@deltares.nl E. Todini BiGeA, University of Bologna, Via Zamboni 67, 40126 Bologna, Italy D. Meißner Bundesanstalt für Gewässerkunde, Am Mainzer Tor 1, 56068 Koblenz, Germany

| analytical solution, channel routing, kinematic wave, representative elementary watershed model, River Mosel

NOTATION a, c, k hydraulic geometry coefﬁcients A

area of reach cross section

b, f, m hydraulic geometry exponents

volume of channel segment

channel top width

x-coordinate along channel axis

channel depth coordinate

channel maximum depth (Leopold & Maddock

gravity constant

Manning roughness

channel average depth (Leopold & Maddock )

wetted perimeter of channel segment

▵x

channel segment length

qlat

lateral inﬂow per unit channel length

truncation error

qgw

reach–groundwater exchange

ξ; ζ

generic integration variables

discharge

Qin

up-stream inﬂow into channel segment

Qout

down-stream outﬂow from channel segment

hydraulic radius

channel bed slope

Channel, overland (Hortonian and saturation excess) and sub-

friction slope

surface storm ﬂow are important runoff mechanisms that

time

characterize the hydrological response footprint of a water-

channel velocity Q/A

shed. A comprehensive hydrological model should include

doi: 10.2166/nh.2013.157

)

INTRODUCTION

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

separate descriptions of these mechanisms. Surface and subsur-

Whitham ; Dooge ). The parameters for the linear

face runoff are typical processes that are included in most

routing schemes can be derived either by direct physical

models in the literature. Channel ﬂow can be simulated by com-

interpretation or by matching hydrodynamic patterns (Kund-

bining a hydrological model with an external dynamic wave

zewicz ). Flow routing in hydrology can also be set aside

model, for which the hydrological model provides the lateral

completely and replaced by a cascade of linear reservoirs

inﬂow. The choice of modelling the channel separately is motiv-

(Nash ), in which the outﬂow of a storage element is

ated by the potential need to describe ﬂow propagation via a

assumed to be a linear function of storage, allowing for an

complete dynamic wave model (Chow ) instead of using

analytical solution. Kalinin & Miljukov () demonstrated

simpler approaches. A full dynamic representation becomes

that a river channel can be modelled as a succession of

necessary when modelling river ﬂow over very mild slopes (of

linear reaches of characteristic length, which, similar to the

the order of 0:5 × 10 3 or milder), where storage effects

Nash cascade model, leads to a gamma function response,

cannot be neglected and surface gradients as well as inertial

whose parameters can be derived from the physical proper-

terms (local and convective acceleration) become important.

ties instead of being estimated from input–output data as in

A commonly used alternative to the dynamic wave model is

the Nash modelling approach (Kalinin & Miljukov ;

the variable-parameter Muskingum–Cunge (MC) routing

Dooge ; Strupczewski & Kundzewicz ).

method. Cunge () modiﬁed the original ﬁxed-parameter

Similarly, the use of the mass balance equation, where

linear Muskingum approach introduced by McCarthy (),

closure schemes for ﬂuxes across storage elements bound-

which he interpreted as a ﬁrst-order kinematic approximation

aries (channel cross sections) are expressed in terms of

of a diffusion wave model. Cunge converted it into a parabolic

power laws, can also be used instead of linear relationships.

model by enabling variable parameters in time according to a

The model parameters are introduced ad hoc, and are

suitable estimation of the parameter values that matches the

usually not interpretable in terms of measurable quantities,

physical to the numerical diffusion. Todini () revised and

such as channel slope and geometry or bed friction, leaving

generalized the variable-parameter MC method, thus addres-

the effects of gravity unaccounted for. The power law par-

sing situations in which the original scheme is not mass

ameters need to be determined on the basis of calibration,

conservative (Ponce & Yevjevich ; Tang et al. ).

whereby historical time series of observed discharges are

Notably, the modiﬁed MC method can now adequately capture

needed. Examples include the HBV (Bergström ), the

non-linear effects of the dynamic wave such as the hysteresis

Sacramento (Crawford & Linsley ) or the Xinanjiang

loop of the stage–discharge curve.

(Zhao ) models. Important drawbacks are that readily

In watershed hydrology, the use of complex physical-

available information such as digital terrain elevation

based routing is often replaced by much simpler analogies,

remains unused, and an application to ungauged basins is

which still provide accurate ﬂow descriptions in situations

impossible in the absence of historical observations.

where second-order effects are negligible. This choice is

Owing to the rapid progress in space-borne data

mainly motivated by the comparatively modest input data

acquisition, recent research is oriented towards the develop-

requirement by the latter and the option not to use detailed

ment of process-based hydrological models, in which the

channel geometries, which are required in the complete

physical principles governing the ﬂow are explicitly included.

dynamic wave model, but which in practice are frequently

The underlying formulations start from the point-scale con-

coarsely described or not available (e.g. in ungauged

servation equations for mass and momentum and integrate

basins). Examples include several simpliﬁcations of the

these up to spatial scales, which are meaningful for hydrolo-

dynamic wave model, which yields a hyperbolic differential

gical applications. The spatial domain over which the point-

equation (Henderson ). Otherwise, ﬂood propagation

scale equations are integrated differs between approaches.

can be studied by a diffusion wave analogy formulated in

It can either consist of elements of a square lattice by a land-

terms of a parabolic differential equation, which is derived

scape discretization into a pixel grid, or of more general

from the dynamic wave model through linearization and neg-

shapes, such as generic control volumes deﬁned on the

ligence of acceleration terms (Hayami ; Lighthill &

basis

topographically

driven

subdivision.

The

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

topographic kinematic approximation and integration model

The paper is structured as follows: the background sec-

(Liu & Todini , ; Liu et al. ) introduces a series

tion revisits the theory, then the analytical solution is

of conservation equations at the spatial scale of a pixel,

presented, while the section on channel geometry describes

whereas the representative elementary watershed (REW) for-

the hydraulic representation of the cross sections. The section

mulation (Reggiani et al. ; Reggiani & Rientjes )

on numerical analysis examines the analytical solution, the

deﬁnes irregularly shaped control volumes for different

sections on applications and simulations describe the model

types of ﬂows and independently of spatial scale.

implementation, and then the results are discussed.

The integration of the point-scale conservation law of mass leads to a transformation of local gradients into fluxes across the boundaries of the storage elements. The fluxes need to be closed by appropriately combining mass and momentum conservation. The combination yields to a nonlinear ordinary differential equation (ODE) for a reach segment, whose analytical solution is only available for specific values of the exponent (as, for instance, when the exponent equals 1, namely in the linear reservoir case), but not in general. Therefore, this ODE can be solved analytically with linear approximations (Ostrowski ) or numerically with methods such as the Runge–Kutta (RK) integrator (Reggiani et al. ; Todini & Ciarapica ). In the interest of numerical efficiency, we demonstrate that under restrictive assumptions, such as time-invariant (averaged) lateral inflow into a channel segment over an integration timestep, and based on an approximation of the non-linear reservoir equation introduced by Liu & Todini (), it is possible to

BACKGROUND The dynamic wave model, known as the Saint-Venant (SV) equations, is derived by integrating the point-scale conservation equations of mass and momentum over the cross section of a channel slab of infinitesimal thickness. In this process, the SV assumptions (Chow ) are applied: (i) hydrostatic pressure, (ii) uni-dimensional flow, (iii) incompressible fluid, (iv) depth and velocity vary only in the longitudinal direction, (v) steady-state flow resistance, and (vi) small bed slope with a fixed channel bed. The mass conservation equation for the infinitesimal slab is: @A @Q þ ¼ qlat þ qgw @t @x

(1)

ﬁnd an analytical solution that is equivalent to the non-

where Q(x, t) is the discharge and A(x, t) is the cross-sec-

linear kinematic wave model (Liu & Todini ). Note

tional area at location x and time t. The terms qlat (x, t)

that the resulting non-linear reservoir equation model

and qgw (x, t) deﬁned per unit channel length are, respect-

highly differs from the previously cited approaches, such as

ively, the lateral inﬂow and a recharge/loss term

the Nash reservoirs cascade (Nash ) or the Kalinin & Mil-

representing the interaction between the channel and the

jukov () approach, in that it is the result of the

groundwater system. The latter term is positive in the

discretization at the scale of the reach of the non-linear kin-

case of groundwater discharge into the reach or negative

ematic model, as opposed to the mentioned approaches,

in the case of groundwater recharge from the channel.

which are discretizations of the linear kinematic model.

Direct input through precipitation and evaporation

The approximation of the original equation is obtained by

across the top surface are omitted. The momentum conser-

means of a second-order polynomial. Here, we revisit the

vation equation for the inﬁnitesimal slab reads:

theory and perform an error analysis of the approximated solution. Moreover, we extend the theory to include analytical solutions for the case of channel–aquifer exchange. The

@Q @ Q2 =A @y þ S0 þ gASf ¼ 0 þ gA @t @x @x

(2)

implementation of the analytical solution proves to be computationally efﬁcient with potential for a wide range of

In the kinematic wave model, the inertial term (ﬁrst

applications in hydrological models. The analytical solution

term on the left-hand side (l.h.s.)), the convective accelera-

should however be used by acknowledging the restrictive

tion term (second term on the l.h.s.) and the pressure term

assumptions of the kinematic wave model.

(@y=@x ≈ 0) are neglected, while the slope of the energy

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

line Sf is derived from Manning’s formula. Consequently,

for A ¼ 0; B ¼ 0; γ ¼ 0; γ ¼ 1; γ ¼ 2 shown in Appendix A

Equation (2) reduces to a steady-state ﬂow equation:

(available online at http://www.iwaponline.com/nh/045/157.

Q 1 2=3 1=2 ¼ R S A n h f

and A ≠ 0, we propose a Taylor-series approximation of V γ

pdf). In the case of kinematic ﬂood routing, where γ ¼ 5=3 (3)

where n is the Manning coefﬁcient and Rh is the hydraulic radius. Integration of Equation (1) over a channel segment of length Δx yields a time-dependent expression: dV(t) þ ðQout Qin Þ ¼ dt

ð Δx

described later. In principle, a least-squares polynomial could also be used in ﬁnding an analytical solution; however, this approach bears the potential for numerical drawbacks, and therefore we refrain from pursuing it further.

Taylor-series approximation (qlat þ qgw )dx

(4) In searching for an analytical solution, the second right-

The inﬂow Qin is provided by the outﬂow of the up-stream

hand side (r.h.s.) term in Equation (6) is expanded as a

reaches meeting at the segment’s inﬂow section. Under the

second-order Taylor polynomial around the centre point of

kinematic wave model assumption, the outﬂow Qout is pro-

the volume between time t and t þ Δt, denoted by VΔt ¼ Vt-

vided by Equation (3). By recalling that the hydraulic radius is deﬁned as Rh ¼ A=Pw , where Pw is the wetted perimeter, and for qlat and qgw constant over Δx, we obtain the nonlinear reservoir equation for a channel segment of length Δx:

þ(A B Vγt ) Δ t/2:

A B V γ ¼ fjΔt þ 2

f 0 jΔt 2

ðV VΔt Þ þ 2

f 00 jΔt 2

ðV VΔt Þ2 þ OðΔV 3 Þ 2

(7) 1=2 Sf

dV(t) ¼ Qin þ (qlat þ qgw )Δx dt n

Pw (Pw Δx)5=3

V(t)5=3

(5)

with ΔV ¼ V VΔt , and the ﬁrst- and second-order deriva2

tives are deﬁned as follows:

whereby Qin , Pw , qlat and qgw can still vary in time. Next, we proceed to deriving an analytical solution of Equation (5) for different values of Qin þ (qlat þ qgw ) Δx corresponding to net recharge or discharge situations of the channel segment. In particular the term qgw can switch sign depending on leakage

γ fjΔt ¼ A B VΔt 2

f jΔt ¼ B γ 2

γ 1 VΔt 2

γ 2 f 00 jΔt ¼ B γðγ 1ÞVΔt 2

from the channel towards the groundwater or vice versa.

(8)

After insertion and rearrangements, one can state the

ANALYTICAL SOLUTION

l.h.s. in Equation (6) as:

In the quest for an analytical solution for Equation (5),

i dV ΔV h ^ ^ þ O(ΔV 3 ) ^ V þ C) ¼ lim ¼ A (V 2 þ B Δt!0 Δt dt

rewrite

the

expression

assuming 1=2

term A ¼ Qin þ (qlat þ qgw ) Δx and B ¼ Sf

that

the

Pw =[n(PwΔx)5/3]

remains constant over a typical integration interval Δt: dV ¼ A B Vγ dt

(6)

Generically, an analytical solution for Equation (6) is not available. Analytical solutions for Equation (6) are only

known

limited

number

cases,

(9)

The Taylor-series polynomial coefﬁcients are deﬁned as: ^ ¼ 1 B γ(γ 1)V γ 2 A Δt 2 2 ^ ¼ 2 (γ 2) VΔt B (γ 1) 2 ^ ¼ A þ (γ 2) V 2 C Δt ^ γ A 2

(10)

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

Through the Taylor-series expansion, V γ in Equation (6) has effectively been substituted by a second-order polynomial. At this stage, we can perform an integration for cases with A ≠ 0, obtaining respective solutions in closed

45.1

2014

After setting:

(Vt p1 ) ^ et ¼ eA (p1 p2 ) Δt (Vt p2 )

(17)

form as shown next. Two cases need to be distinguished depending on the channel inflow and outflow terms, influen-

the analytical solution for VtþΔt becomes:

cing the sign and magnitude of A and C: VtþΔt ¼ ^ 0 ^ 2 4C Case 1 : A ≠ 0, B

p1 p2 et (1 et )

(18)

After we neglect the error term O(ΔV 3 ), an approximated

^ <0 ^ 2 4C Case 2 : A ≠ 0, B

integral solution can be found analytically by variable separ-

^ a different integration ^ 2 4C, For negative values of B

ation and integration of Equation (9): ð

1 ^ dV ¼ A ^ ^ V þC V2 þ B

approach needs to be adopted. First, we complete the quadratic in the denominator in Equation (11) in such a way that we

ð dt þ const:

(11)

can reduce it to an integrable expression. Adding and sub^ 2 yields: tracting 1 B 4

for which a primitive is available in closed form. The second-order polynomial at the denominator can be factorized:

1 1 ¼ ^ ^ (V p ) 1 (V p2 ) þBV þC

p1 ¼

p2 ¼

^ B

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ ^ 2 4C B 0 2

1 (V þ

1^ 2 2B)

^ ^ þC 14 B

and t þ Δt, one obtains: ð VtþΔt ð tþΔt 1 ^ dV ¼ A dξ 2 ^ ^ 2 1B ^ þC t Vt (V þ 1B) 2

(13)

(19)

The integral on the r.h.s. can be performed analytically

(14)

ð VtþΔt þ1B^ 2

Substitution into Equation (11) and integration ﬁnally

du u2

^ þD

^ Δt ¼A

(21)

^ is a known form: The indeﬁnite integral of du=(u2 þ D) ð

(15)

which can be re-arranged and evaluated between [t, Δt] and

(20)

leading to Δt; equally, the integral on the l.h.s can be performed ^ 1B ^ ¼C ^ 2 and u ¼ V þ 1B, ^ which leads to: by setting D

yield the following primitive: 1 (V p1 ) ln þ const: (p1 p2 ) (V p2 )

^ þC

After substitution into Equation (11) and by integrating

1^ Vt þ2B

^ Δt ¼ A

^2 14 B

the l.h.s. between Vt and Vt þ Δt and the r.h.s. between t

nomial: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ^ ^ 2 4C B 0 2

^Vþ V2 þ B

(12)

where p1 and p2 are real roots of the second-order poly-

^ þ B

1 1 ^2 4B

du ^ u2 þ D

^ 1=2 arctan ¼D

u ^ 1=2 D

! þ const:

(22)

which allows evaluation of Equation (21) as:

[Vt , VtþΔt ] as follows:

(V p1 ) VtþΔt ^ ¼ eA (p1 p2 ) Δt (V p2 ) Vt

" (16)

^ D

1=2

arctan

u ^ D

1=2

!#VtþΔt þ1B^ 2

1^ Vt þ2B

^ Δt ¼A

(23)

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

as follows: depth Y at-a-station depends on Y

The resulting analytical solution is ﬁnally:

VtþΔt

! " # ^ B ^ V þ 1=2 1=2 B t 2 ^ Δt ^ ^ ¼ þD tan arctan þD A 2 ^ 1=2 D

(24)

Y ¼ Y(b=f þ 1)

(26)

The at-a-station wetted perimeter Pw can be derived by which is deﬁned for values of the term between square brackets ½ ∈ Rn{kπ þ

1 2π,

integration over depth:

k ∈ Z}. In this way, the analytical

^ ^ 4C solution is fully generalized for all possible values of B 2

and A ≠ 0.

Pw ¼ 2

ðw ðY " 0

1þ

#0:5 1 dξ 2 dζdξ 4 dζ

(27)

where ξ and ζ are dummy variables integrated between 0 and w and 0 and Y. The integral cannot be obtained in

CHANNEL GEOMETRY

closed form and must be evaluated numerically. Details of the channel geometry formulation can be accessed in Snell

Solution of Equation (5) requires the knowledge of the

& Sivapalan ().

wetted perimeter Pw . In the absence of regional data, standard assumptions such as a rectangular, semicircular, triangular or trapezoidal cross section can be adopted. If

NUMERICAL ANALYSIS

observations of stream ﬂow and channel morphology are accessible, a regionalized approach for the estimation of

Properties of the approximated solution

channel geometry can be used (Naden et al. ). Snell & Sivapalan () proposed to estimate Pw using a combi-

At this stage, it is important to perform a numerical analysis

nation of empirical hydraulic geometry relationships by

of the approximated analytical solution to verify if it is accu-

Leopold & Maddock (). These power laws tie the aver-

rate, consistent, stable, convergent and conservative. We

age velocity, channel top width and average depth to

note that the analysis below is an error assessment of the

steady-state discharge under a gradually varying ﬂow

integral formulation of the initial-value problem:

regime and uniform roughness. Under reasonable assumptions, these relationships can be extrapolated to non-steady situations. For a reach, the top width w, average depth Y

V(t) V(t0 ) ¼

ðt t0

dV dζ ¼ dζ

ðt

F[V(ζ), ζ]dζ

(28)

and velocity v at a point in time (at-a-station) or along stream locations ﬁxed in time (down-stream) can be

whereby the differential and the integral formulation are

expressed as power laws of Q:

mutually linked via the fundamental theorem of calculus. Accuracy and consistency

w ¼ a (Q)b ¼ c (Q)f Y

(25)

An approximate solution of a differential equation is said to

v ¼ k (Q)m

be consistent, if the local truncation error between the

where the scaling coefﬁcients a, c and k are a combination

size decreases towards zero. The local truncation error at

of the at-a-station and down-stream coefﬁcients and can

time t is expressed as the difference between the volume

vary regionally. The exponents b, f and m remain indepen-

Vt given by the approximated solution of Equation (18) ~ t: and the exact one V

dent of space and time. The coefﬁcients and exponents of the hydraulic geometry relationships are established on the basis of ﬁeld surveys. It can be proven that the maximum

approximation and the exact solution vanishes as the step-

~t τ t ¼ Vt V

(29)

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

By exploiting the algebraic properties of the Landau

truncation error, then the global error is bounded by a

notation O( ), which quantiﬁes the higher order terms of

multiple of Δtm . Under the condition of local Lipschitz conti-

the approximation, Equation (11) is restated as: ð VtþΔt Vt

1 ^ dV ¼ A ^ 2 ^ V þBV þC

ð tþΔt

nuity of Vt given by Equation (18), we show in Appendix B (available online at http://www.iwaponline.com/nh/045/

dξ þ O(ΔV 4 )

(30)

157.pdf) that the following relationship holds:

En L n Δt þ K Δtm ; m 1

(32)

By invoking the analytical expression for VtþΔt in Equation (18), the local truncation error is stated as follows:

where L and K are constants. It follows that the global error is bounded and tends towards zero as Δt ! 0 and the approxi-

τ tþΔt ¼

p1 p2 et ~ V tþΔt ¼ O(ΔV 4 ) (1 et )

(31)

In other words, the local truncation error grows asymptotically no faster than ΔV 4 . By recognizing that ΔV scales like Δt and choosing progressively smaller timesteps, the error between the exact solution and the approximated analytical solution tends towards zero with the fourth power of the stepsize. As such, the approximated solution is, by deﬁnition, consistent. The approximated solution is also said to be third-order accurate, one order below the local truncation error. The same can be

mated solution converges to the exact solution. A similar proof can be obtained for the solution in the form of Equation (24). Conservation As a corollary of the previous analysis, it follows that the method is conservative. The mass outﬂow from a channel reach is given by Equation (9). It is obvious that for Δt ! 0, the Taylor-series approximation of the volume derivative tends towards the exact analytical expression (6), thus ensuring conservation.

shown to also hold for the solution in the form of Equation (24). Stability The approximate analytical solution given by Equation (18) remains defined and does not asymptotically blow up, if the denominator is different from zero, thus if et ≠ 1. This con^ ≠ 0. dition requires foremost that (i) p1 ≠ p2 and that (ii) A Conditions (i) and (ii) are always met due to the non-zero discriminant of the quadratic polynomial and the very defi^ For the case in which Δt ! 0, it can easily be nition of A. shown that VtþΔt ! Vt , thus the solution continues to remain stable. By analogy, the stability of the solution (24) can be proven for all values in which it is defined.

APPLICATION Study area and hydrology To test the analytical solution, we applied it to flood propagation in the River Mosel. The Mosel drains a 29,000 km2 basin and is one of the largest tributaries to the River Rhine. The lower catchment area includes mainly Germany, with parts of the upper basin situated in France and Luxembourg. The Mosel joins the Rhine at the city of Koblenz. The longterm average flow in the Mosel at Koblenz is about 330 m3/s. Peak discharges of approximately 4,200 m3/s have been recorded, making the Mosel a significant contributor to the

Convergence

Rhine. Therefore, accurate ﬂow forecasting in River Mosel is very relevant for ﬂow prediction on the Rhine, and attracts sta-

A numerical solution is said to be convergent, if the global

keholder interest to compare computational and forecasting

truncation error En at step n tends towards zero for a decreas-

performance of non-linear routing methods. A drawback of

ing timestep, thus the approximated solution converges

using the Mosel River system for the present study is the high

towards the exact one over the sum of all n integration

level of river training, as the Mosel also serves navigation and

steps. Under fairly general assumptions, such as when a func-

hydro-electric generation purposes. The engineering works

tion is locally Lipschitz continuous, it can be proven that if the

have a severe impact on low-ﬂow regimes, but their effect is

approximated solution is of order m as measured by the local

felt more during low-ﬂow periods and gradually disappears

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

during medium to high ﬂows, where the structures are operated in such a way as to allow ﬂoods to propagate undisturbed.

Hydrology Research

45.1

2014

The main objective here is to compare the proposed kinematic wave solution with a full dynamic wave solution in a

The Mosel has been selected as the study system because a

real setting. The ODEs governing the system of non-linear

pre-operational forecasting system based on the REW model

reservoir equations are formulated for individual stream chan-

(Reggiani & Rientjes ) is currently tested at the forecasting

nel segments and are resolved analytically as well as with a

ofﬁce at the Federal Institute of Hydrology in Koblenz (BFG).

ﬁfth-order RK ODE solver (Press et al. ). The results are

Meteorological forcing data over the 16 year period 1996–

compared with ﬂood propagation using the ﬁnite-difference

2011 are available at hourly intervals, including hourly

solution of the dynamic wave model with the SV equation

water-level observations transformed into discharges at several

solver SOBEK (Stelling & Duinmeijer ) used operation-

locations, including Cochem and Trier. These data were uti-

ally by the BFG. The SOBEK model contains a total of 455

lized to calibrate and validate the REW model, which is used

high-resolution cross-section proﬁles. Over a length of

to estimate lateral inﬂows into the Mosel and main tributaries.

240 km, this corresponds to circa one proﬁle every 500 m.

The Nash–Sutcliffe coefﬁcient was used as a performance indi-

The spatial resolution of the computation grid includes 726

cator by comparing simulated discharges against observations

nodes. The Manning roughness in the SOBEK model is vari-

at Cochem and Trier for daily average ﬂows. Channel routing is

able, with values ranging between 0.022 and 0.025.

performed using the integral kinematic wave approach as stated by Equation (6). The choice of the kinematic wave is jus-

Stream network characteristics

tiﬁed by the main channel bed slope, which is around 1:12 × 10 3 on average, and by the relatively low hydraulic

The channel network was extracted from a 75 × 75 m digi-

roughness. In fact, the Mosel is known to behave as a kin-

tal elevation model (DEM). Different spatial resolutions of

ematic system, by barely exhibiting any parabolic behaviour

the network can be deﬁned. If a single reach per REW is

and looped stage–discharge relationships anywhere in the

used, we obtain a network of 85 reaches, as shown in

river, which will also become clear from the results.

Figure 1. Alternatively a higher-resolution network with

Figure 1

The Mosel basin including 85 REW modelling elements.

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

a larger number of stream segments can be used, whereby

45.1

2014

SIMULATIONS

each link is subdivided into a number of stream segments with a Strahler order lower than a set cut-off order value.

We performed ﬂow simulations for the 1 January 1996 to 31

By lowering the cut-off value, the amount of segments

December 2001 period by using hourly forcing to generate

increases. Here, it is possible to work with a network

lateral inﬂow time series via the hydrological model. Exactly

including 501 segments (cut-off order 3), 951 segments

the same inﬂows are used for all channel routing simu-

(cut-off order 2) and 1,903 segments (cut-off order 1).

lations. We note that these lateral inﬂows are generated

We carried out different trials with all four resolution

using uncertain meteorological forcing on the REW

levels and concluded to use 501 reach elements, which

model. No data assimilation or input correction has been

proved to be a sound compromise between spatial resol-

applied to address the uncertainty in the forcing. The simu-

ution and computational effort. The bed slopes were

lated ﬂow is therefore an uncertain and suboptimal estimate

extracted from the DEM, whereby in the lower end, bed

of the hourly observed ﬂow. The main purpose of this exer-

slopes of the order of 10 5 or less were encountered.

cise, however, is to compare the routing methods.

No river–groundwater interaction is assumed to ensure

was assigned in case the slope was smaller. A uniform

that the amount of water routed through the network is the

For numerical reasons, a minimum value of 2:5 × 10

Manning coefﬁcient of 0.025 has been assigned to all

same for all simulations. The analytical solution (18) is com-

reaches in conformity with the values used in the oper-

pared against the solution of Equation (6) with the RK

ational model currently in use at BFG.

method and the solution of the SV equations with SOBEK.

Finally, the channel geometry for the kinematic wave

Figure 2 provides a schematic view of the interface between

formulation was determined using the Leopold & Mad-

the SOBEK and REW models. The stations Perl (Mosel),

dock

combined

the inﬂow point of the Sauer, and Fremersdorf (Saar) were

formulation. For the exponents, parameter values from

taken as upper model boundaries with concentrated inﬂows,

Leopold & Maddock () were employed. For the

while lateral inﬂows further down-stream were distributed

remaining parameters, values were applied that yielded a

uniformly along the main channel of River Mosel. Flow

channel geometry based on essentially triangular cross sec-

rates were compared at the measurement locations Cochem

tions. Table 1 summarizes the values assumed for the

and Trier. All computations, except SOBEK, were performed

hydraulic geometry.

in C þþ code on a 64 bit LINUX machine cluster.

()

down-stream

and

at-a-station

RESULTS AND DISCUSSION Table 1

Leopold & Maddock (1953) scaling coefﬁcients and exponents (Snell & Sivapalan 1995)

The results are presented against those obtained with

At-a-station depth scaling exponent

0.33

At-a-station width scaling exponent

0.33

At-a-station velocity scaling exponent

0.34

Down-stream depth scaling exponent

0.4

Down-stream width scaling exponent

0.5

Down-stream velocity scaling exponent

0.1

Down-stream depth scaling coefﬁcient

0.23

Down-stream width scaling coefﬁcient

7.09

Down-stream velocity scaling coefﬁcient

0.61

Discharge-area scaling coefﬁcient

2.0 × 10 6

Discharge-area scaling exponent

0.8

dynamic wave model SOBEK, which we consider as the reference case (SV0) because it involves the numerical solution of the complete SV equation set with the actual surveyed cross-section proﬁles. All other simulations are compared against the SV0 benchmark case. Table 2 summarizes the characteristics of each simulation run. We note that in the SV0 simulation, all relevant hydraulic structures, such as bridges and weirs, have been modelled. SOBEK performs regular mass balance checks. In case the mass balance error in a computation cell exceeds the order 1 × 10 7 , the code approximates the solution iteratively until the desired error tolerance is reached.

P. Reggiani et al.

Figure 2

Table 2

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

Coupling of the REW hydrological model and the SOBEK dynamic wave model.

Mass balance and CPU time analysis, Cochem, 1996–2001

Case

Run characteristics

Mass error (m3)

Cumulative outﬂow volume (mm)

CPU time

Observed

Measured discharge

N/A

2:3272 × 103

N/A 3 h ca.

SV0

726 nodes, 3,600 s

1:0 × 10

2:3768 × 10

AS0

85 elements, Δt ¼ 180 s

2:6209 × 10 6

2:4041 × 103

28 min 23 s

AS1

85 elements, Δt ¼ 900 s

5:0950 × 10

2:4060 × 10

4 min 47 s

AS2

85 elements, Δt ¼ 3,600 s

7:4340 × 10 7

2:4031 × 103

1 min 30 s

2:4031 × 10

29 min 9 s

2:4031 × 103

5 min 15 s

2:4044 × 10

2 min 28 s

AS3

501 elements, Δt ¼ 180 s

2:0209 × 10

AS4

501 elements, Δt ¼ 900 s

1:0437 × 10 6 7

AS5

501 elements, Δt ¼ 3,600 s

3:1804 × 10

RK0

85 elements, ε ¼ 10 7

4:9813 × 10 7

RK1

85 elements, ε ¼ 10

2:5167 × 10

RK2

501 elements, ε ¼ 10 5

8:5880 × 10 6

Analytical solution

2:4004 × 103

23 min 37 s

2:4040 × 10

11 min 56 s

2:4073 × 103

25 min 19 s

elements), but increase the timesteps to Δt ¼ 900 s and Δt ¼ 3, 600 s, respectively. In doing so, we accept a lower

Six simulations are performed with the analytical solution

accuracy of the solution as the local and total truncation

(18). In the ﬁrst case (AS0), we use a network with one

errors increase. Moreover the assumption of constant

reach element per REW, thus 85 elements in total. The maxi-

inﬂow and wetted perimeter in Equation (5) breaks down,

mum timestep Δt ¼ 180 s. In the second (AS1) and third

leading to progressively larger approximation errors over

cases (AS2), we use the same network resolution (85

longer timesteps due to poorer inﬂow and wetted perimeter

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

estimations. In the fourth case (AS3), we increase the number

sensitive to larger timesteps, whereby the solution starts to

of reach elements to 501, while the timestep Δt ¼ 180 s. In

deteriorate dramatically for Δt ! 3,600 s. The approximation

the ﬁfth (AS4) and sixth cases (AS5), we use 501 elements

error of the solution, mainly caused by the growing local trun-

and Δt ¼ 900 s and Δt ¼ 3,600 s, respectively. The total

cation error, is cumulative and therefore has a larger impact

mass computation error for all reach elements and the cumu-

on the solution for 501 links with respect to the 85 link case.

lative outﬂow volume per unit basin area for all cases are

Figure 3 shows a comparison of the AS0–AS5 solutions

summarized in columns three and four of Table 2, while

against the SV0 reference case and the observed discharge

the central processing unit (CPU) times are reported in

at Cochem for the triple ﬂood peak that occurred between

column ﬁve. The CPU times are a good indicator of the rela-

9 December 1999 and 6 January 2000. Overall, the analytical

tive computational economics of the different solutions,

solutions compare well with the SV0 reference case. We note

especially as the stepsize for the adaptive timestep method

the slightly higher peaks, which are due to the implicit

(RK) is controlled by the routing scheme. We note that

assumptions of the kinematic wave model to neglect

with the 85 link scheme, an increase of the timestep to

second-order effects, which are responsible for peak attenu-

Δt ¼ 3,600 s has very little impact on the accuracy of the sol-

ation. The consistency with the SV0 case shows (a) the

ution. This is different with the 501 links scheme, where the

validity of the kinematic wave model for the particular situ-

number of computational cells has been increased by a factor

ation, (b) the accuracy of the analytical solution for

of approximately six. As a result, the model becomes more

sufﬁciently small timesteps (up to 1 h for 85 reach elements)

Figure 3

Inter-comparison of the solutions SV0, AS0–5 and observations for the 9 December 1999 to 6 January 2000 event, Cochem.

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

and (c) the adequacy of the hydraulic geometry relationships

transited at Cochem, as listed in Table 2. In the third case

to describe the hydrodynamic properties of the channel.

(RK2), the network resolution is increased to 501 links and ε ¼ 10 5 . The solutions for the RK0, RK1 and RK2 cases

RK solution

are very similar and barely appreciable to ε. In summary,

Next, we compare the analytical solution of the kinematic

utions in terms of computation time economics. However,

wave with the results obtained by resolving Equation (6)

all RK solutions compare well to the SV0 and the AS0–2 sol-

with a ﬁfth-order variable-stepsize RK scheme and examine

utions during peak and low ﬂows, as visible in Figures 4–6.

the RK method performs much worse than the AS0–5 sol-

the sensitivity of method. Three cases were simulated. In the ﬁrst case (RK0), we use 85 reach elements and an accuracy tolerance ε ¼ 10 7 (see Press et al. ). The stepsize in

SUMMARY AND CONCLUSIONS

this case can drop below 60 s. In the second case (RK1), we accept an accuracy tolerance ε ¼ 10 5 , which results in com-

We have presented an analytical solution of the kinematic

putational efﬁciency gains by at least a factor two. The results

wave equation under a series of assumptions, which are

for the 9 December 1999 to 6 January 2000 events are com-

applicable in practical ﬂow routing. The method has been

pared in Figure 4. The impact of reducing ε by two orders

tested by simulating the hydraulics of the River Mosel chan-

of magnitude is minimal in terms of cumulative volume

nel over a 6 year continuous period and compared against

Figure 4

Inter-comparison of the solutions SV0, RK0–2 and observations for the 9 December 1999 to 6 January 2000 event, Cochem.

Figure 5

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Hydrology Research

45.1

2014

Inter-comparison of all solutions and observations for the 9 December 1999 to 6 January 2000 event, Cochem.

the solutions of a complete dynamic wave model and a

computational economics with respect to the numerical

numerical solution of the original non-linear reservoir

solution of (i) the ODE with a numerical integrator

equation by using the exact same lateral inﬂow series for

such as the RK method and (ii) the ﬁnite-difference sol-

all cases. The ﬁndings can be summarized as follows.

ution of the dynamic wave model.

•

• •

The integral and original form of the non-linear kin-

•

It has been shown that the kinematic wave equation in the form of a non-linear reservoir equation can be applied

ematic wave model for a reach element is obtained by

by using empirical relationships to represent the channel

combining the mass and energy conservation equations,

geometry. The approach has therefore signiﬁcant poten-

whereby lateral inﬂows are assumed constant over a time-

tial to be used for channel routing in ungauged basins,

step. The result is a non-linear reservoir equation in the

where detailed information on cross-sectional proﬁles,

form of an ODE.

as required by the dynamic wave model, is unavailable.

We have demonstrated that the analytical solution obtained by means of a second-order Taylor-series

•

A solution for situations, such as aquifer recharge in which water is lost through the channel bed, has been

approximation of the original equation is third-order

found that can be used for a whole range of recharge situ-

accurate, consistent, stable and conservative.

ations potentially encountered in practice.

The utilization of an analytical solution of the kinematic wave equation has a signiﬁcant advantage in terms of

•

The method has been applied to channel routing on River Mosel, and compared against the dynamic wave model

Figure 6

•

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

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2014

Inter-comparison of all solutions and observations for the 9 December 1999 to 6 January 2000 event, Trier.

SOBEK. The comparison shows that besides the known

We also acknowledge the International Commission for the

inherent limitations of the kinematic wave with respect

River Rhine (CHR) for providing the digital terrain model

to the dynamic wave model (absence of the convective

for the River Mosel basin. We would like to thank two

acceleration and surface slope terms), the wave solution

anonymous referees for their contributions, who have

performs well by requiring a signiﬁcantly inferior

signiﬁcantly contributed to improving the manuscript.

amount of input information. On bed slopes that have an order of magnitude equal or larger to 10 3 , where peak attenuations are minimal, the kinematic wave model provides an accurate approximation of ﬂood propagation and the solution of the dynamic wave model collapses onto the kinematic wave model.

ACKNOWLEDGEMENTS We acknowledge the E-OBS dataset from the EU-FP6 project ENSEMBLES and the data providers in the ECA&D project.

REFERENCES Bergström, S.  The HBV model. In: Computer Models of Watershed Hydrology (V. P. Singh, ed.). Water Resources Publications, Highlands Ranch, CO, pp. 443–476. Chow, V. T.  Handbook of Hydrology. McGraw-Hill, New York, NY. Crawford, N. H. & Linsley, R. K.  Digital simulation in hydrology: Stanford Watershed Model IV, Technical Report No. 39, Stanford University, Palo Alto, CA. Cunge, J. A.  On the subject of a ﬂood propagation computation method (Muskingum method), Delft, The Netherlands. J. Hydrol. Res. 7 (2), 205–230.

P. Reggiani et al.

Analytical approximation of a kinematic wave solution

Dooge, J. C. I.  Linear Theory of Hydrologic Systems, USDA Technical Bulletin 1468, US Department of Agriculture, Washington, DC. Henderson, F. M.  Open Channel Flow. Macmillan, New York, NY. Hayami, S.  On the propagation of flood waves, Bulletin no. 1, Disaster Prevention Research Institute, Kyoto University, Japan. Kalinin, G. P. & Miljukov, P. I.  O raschete neustanovivshegosya dvizheniya vody votkrytykh ruslakh (On the computation of unsteady flow in open channels). Meteorologiya i Gidrologiya Zhuzurnal, Leningrad 10, 10–18 (in Russian). Kundzewicz, Z.  Hydrodynamic determination of parameters of linear routing models. In: Scientific Procedures Applied to the Planning, Design and Management of Water Resources Systems (E. Plate & N. Buras, eds). IAHS, Oxford, IAHS Publication no. 147, pp. 149–160. Leopold, L. B. & Maddock Jr, T.  The hydraulic geometry of stream channels and some physiographic implications. U.S. Geological Survey Professional Paper 252, US Government Printing Office, Washington, DC. Lighthill, M. J. & Whitham, G. B.  On kinematic waves. I. Flood movement in long rivers. Proc. R. Soc. Lond. A 229, 281–316. Liu, Z., Martina, M. L. V. & Todini, E.  Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian catchment. Hydrol. Earth Syst. Sci. 9 (4), 347–364. Liu, Z. & Todini, E.  Towards a comprehensive physically-based rainfall runoff method. Hydrol. Earth Syst. Sci. 6 (5), 859–881. Liu, Z. & Todini, E.  Assessing the TOPKAPI nonlinear reservoir cascade approximation by means of a characteristic lines solution. Hydrol. Process. 19 (10), 1983–2006. McCarthy, G. T.  Flood routing. In: Flood Control, Chapter V. Engineer School, Fort Belvoir, VA, pp. 127–147. Naden, P., Broadhurst, P., Tauveron, N. & Walker, A.  River routing at the continental scale: use of globally available data and an a-priori method of parameter estimation. Hydrol. Earth Syst. Sci. 3 (1), 109–124. Nash, J. E.  The Form of the Instantaneous Unit Hydrograph. IUGG General Assembly of Toronto, vol. III, IAHS Publication, pp. 114–121.

Hydrology Research

45.1

2014

Ostrowski, M.  A universal module for the simulation of hydrological processes. Wasser und Boden 11, 755–760 (in German). Ponce, V. M. & Yevjevich, V.  Muskingum–Cunge method with variable parameters. J. Hydraulic Division, ASCE 104 (12), 1663–1667. Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T.  Numerical Recipes in C þ þ: The Art of Scientific Computing, 2nd edn. Cambridge University Press, New York, NY. Reggiani, P. & Rientjes, T. H. M.  Internal flux parameterisation in the representative elementary watershed (REW) approach: application to a natural basin. Water Resour. Res. 41, W04013. Reggiani, P., Sivapalan, M. & Hassanizadeh, S. M.  A unifying framework of watershed thermodynamics: balance equations for mass, momentum, energy and entropy and the second law of thermodynamics. Adv. Water Resour. 22 (4), 367–398. Reggiani, P., Sivapalan, M., Hassanizadeh, S. M. & Gray, W. G.  Coupled equations for mass and momentum balance in a stream network: theoretical derivation and computational experiments. Proc. R. Soc. A 457, 157–189. Snell, J. & Sivapalan, M.  Application of the meta-channel concept: construction of the meta-channel hydraulic geometry for a natural channel. Hydrol. Proc. 9, 485–495. Stelling, G. S. & Duinmeijer, S. P. A.  A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int. J. Numer. Meth. Fluids 43, 1329–1354. Strupczewski, W. G. & Kundzewicz, Z. W.  Analysis of physical interpretation of parameters of linear conceptual models by means of moment matching method. J. Hydrol. Sci. 6, 143–159. Tang, X., Knight, D. W. & Samuels, P. G.  Volume conservation in the Variable Parameter Muskingum–Cunge method. J. Hydraulic Eng. (ASCE) 125 (6), 610–620. Todini, E.  A mass conservative and water storage consistent variable parameter Muskingum–Cunge approach. Hydrol. Earth Syst. Sci. 11, 1645–1659. Todini, E. & Ciarapica, L.  The TOPKAPI model. In: Mathematical Models of Large Watershed Hydrology (V. P. Singh & D. K. Frevert, eds), chapter 12. Water Resources Publications, Littleton, CO. Zhao, R. J.  The Xinanjiang model applied in China. J. Hyrol. 135, 371–381.

First received 18 September 2012; accepted in revised form 16 March 2013. Available online 29 May 2013

45.1

2014

Overcoming the challenges of using a rainfall–runoff model to estimate the impacts of groundwater extraction on low ﬂows in an ephemeral stream K. M. Ivkovic, B. F. W. Croke and R. A. Kelly (née Letcher)

ABSTRACT Simple modelling approaches such as a spatially lumped, rainfall–runoff model offer a number of advantages in the management of water resources including the relative ease with which groundwater and surface water accounts can be evaluated at the river-reach scale in data-poor areas. However, rainfall–runoff models are generally not well suited for use in ephemeral river systems because of their inability to simulate abrupt transitions from flow to no-flow periods and the highly non-linear rainfall–runoff relationships that exist in low yielding catchments. This paper discusses some of the challenges of using a rainfall–runoff model to assess the impacts of groundwater extraction on low flows within an ephemeral river system and demonstrates how these challenges were overcome during the development of the IHACRES_GW (Identification of Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data – with Ground Water store) model. Details on the model algorithms, calibration, validation and objective function fits are provided. The performance of the IHACRES_GW model in Cox’s Creek (Namoi Valley, Australia), and 13 additional areas investigated, suggests that this simple modelling approach may be of considerable utility for water accounting, especially when attempting to evaluate the impacts of groundwater extraction on low flows in similar systems. Key words

K. M. Ivkovic (corresponding author) B. F. W. Croke R. A. Kelly The Fenner School of Environment and Society, The Australian National University, Canberra, Australia 0200 E-mail: karen.ivkovic@gmail.com; karen.ivkovic@anu.edu.au K. M. Ivkovic Naiades Geohydrology, Deakin ACT, Australia 2600 B. F. W. Croke Department of Mathematics, The Australian National University, Canberra, Australia 0200 R. A. Kelly isNRM Pty Ltd, PO Box 8017, Trevallyn, Tasmania, Australia 7250

| ephemeral stream, groundwater extraction, low ﬂows, rainfall–runoff, surface–groundwater interactions, water accounting

INTRODUCTION The importance of managing connected groundwater and sur-

catchment-scale water balance accounts. In the past, hydrolo-

face water resources as a single resource has been highlighted

gical models have tended to focus on estimating total river

in Australian and international water reform legislation, and

ﬂows, with little emphasis on modelling the groundwater

these requirements have necessitated a change to the way

component of river ﬂows (Fleckenstein et al. ). However,

that water systems have traditionally been managed. One chal-

the importance of considering groundwater exchanges in

lenging area is in the modelling of aquifer–river volumetric

rainfall–runoff models has increasingly been recognised

exchanges, and in particular, accounting for low ﬂows,

(Tan & O’Conner ; Croke et al. ; Moore & Bell

which are especially critical when considering resource sus-

; Le Moine et al. ; Herron & Croke a; Ivkovic

tainability and ecosystem health in anthropogenically

et al. a; Pushpalatha et al. ; Gilfedder et al. ).

modiﬁed basins (Rassam ; McCallum et al. ). A complementary approach to using complex, physically

There is clearly an ongoing need to continue to test and trial simple approaches that require limited data when assessing

based, surface–groundwater interaction models is to use a

groundwater contributions to river ﬂows in order to more efﬁ-

simpler, conceptual, rainfall–runoff model to consider

ciently meet water management policy objectives, particularly

doi: 10.2166/nh.2013.204

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

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2014

in data-poor areas (Larocque et al. ). Some of the main

previously discussed; however, rainfall–runoff models are

beneﬁts of using simple rainfall–runoff models for catchment-

generally not well suited to modelling low ﬂows within

scale water balance accounting are that they have relatively

ephemeral river systems. This is because: (1) rainfall–

low data requirements, are easy to use, and they often have

runoff modelled steamﬂows typically use exponentially

greater predictive certainty when simulating ﬂows. These

decaying stores in the formulation of the unit hydrograph,

models are also able to provide estimates of ﬂows on short time-

and therefore do not allow for the possibility of zero ﬂows;

scales (e.g., daily or shorter), and as a result, they potentially

and (2) rainfall–runoff relationships in semi-arid to arid

have a greater ability to simulate the baseﬂow discharges that

catchments are characterised by strong non-linearities that

can occur within these shorter time frames. This is especially

lead to considerable uncertainty when estimating effective

important when simulating the ﬂow of ephemeral streams

rainfall depths and predicting streamﬂow (Ye et al. ).

where surface–groundwater exchanges can be rapid.

In many cases, the uncertainty in estimating effective rain-

The utility of using a simple surface–groundwater model

fall using a non-linear module exceeds the volumes of

to inform water management policy was discussed by Ivko-

groundwater being extracted within the catchment, making

vic et al. (a), where the conceptual, spatially lumped

it difﬁcult – or even impossible – to assess the impacts of

IHACRES_GW model was introduced. The IHACRES_GW

groundwater extraction on low ﬂows using a rainfall–

model was used to quantify the historical impacts of ground-

runoff model in low yielding catchments.

water extraction on river ﬂows in the ephemeral Cox’s

In order for rainfall–runoff models to be successfully used

Creek subcatchment in Australia. They found that baseﬂow

for water accounting in low-yielding catchments, they must

discharges in the catchment had been reduced by approxi-

have the capacity to simulate ephemeral river ﬂows, which

mately 82% of the volume of groundwater extracted, and

often terminate abruptly, or else which may be sustained by

that an average of 5% of the total streamﬂow volume

baseﬂows for varying periods of time. To effectively simulate

(78.3 GL) had been lost to the river as a consequence of

these processes, a rainfall–runoff model must be able to

groundwater extractions over the 15-year simulation period.

account for the changes in groundwater storage that occur

While the considerable strengths of using a simple mod-

as a consequence of groundwater extractions and other catch-

elling approach were highlighted by Ivkovic et al. (a),

ment losses. In particular, it is important to maintain a water

they provided little information on the development of the

balance account of groundwater stores throughout no-ﬂow

IHACRES_GW model used in their study. Nor did they pro-

periods in order to be able to correctly simulate the resump-

vide the background on the model testing calibration and

tion to a ﬂow period. The transition between ﬂow and no-

validation. This paper discusses some of the challenges of

ﬂow periods is especially important to assess in catchments

using a rainfall–runoff model when assessing the impacts

where groundwater extractions may be impacting on low

of groundwater extraction on low ﬂows within an ephemeral

ﬂows and where extractions result in variable groundwater–

river system and shows how these challenges were over-

river connectivity (Ivkovic b).

come through the development of the IHACRES_GW model. Details on the model algorithms, calibration, validation and objective function ﬁts are provided using the same datasets used in the Ivkovic et al. (a) investigation.

OBJECTIVES In order for rainfall–runoff models to be able to provide

CHALLENGES OF USING RAINFALL–RUNOFF MODELS TO ASSESS LOW FLOWS WITHIN EPHEMERAL RIVER SYSTEMS

useful outputs in the study of low ﬂow behaviour within ephemeral streams they must be able to provide: 1. an accurate simulation of both high and low ﬂows, including the correct timing in the switch between base-

There are a number of advantages of using conceptual, rain-

ﬂow and no-ﬂow transitions at the river reach scale on

fall–runoff models for catchment-scale water accounting, as

a daily time-step; and

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

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2. an ongoing water balance account of the changes in

Namoi River is the Cox’s Creek, which was the case-study

groundwater storages arising from groundwater extrac-

area selected (Figure 2). The Cox’s Creek subcatchment rep-

tion and other losses, even during no-ﬂow periods, and

resents an area of 4,040 km2, and it has an average annual

the inﬂuences of these losses on low ﬂows on a daily

rainfall of 600 mm and an average potential evapotrans-

time-step. A primary research objective was to consider whether an existing rainfall–runoff model could be modiﬁed to meet these requirements, and then to rigorously test the modiﬁed model for its performance.

piration of 1,900 mm (Zhang et al. ). The rainfall distribution is highly variable, and this is reflected in the streamflow duration throughout the catchment. The Cox’s Creek river reach has been categorised by Ivkovic (b) as a variably connected–disconnected aquifer–river system that is variably gaining–losing (Figure 2). The Cox’s Creek is an ephemeral river system, with flows measured 37% of the time at the catchment outlet at Boggabri. The average flow

APPLICATION CASE-STUDY: NAMOI RIVER CATCHMENT, AUSTRALIA

over the streamflow record (1965–2003) is 254 ML/day, with baseflows contributing approximately 9% of flows (Ivkovic b). The Cox’s Creek alluvium sits within a

The Namoi River catchment is one of Australia’s most devel-

narrow, bedrock-contained alluvial valley about 10 km

oped irrigation areas where both river and alluvial

wide and 72 km in length. The maximum thickness of

groundwater resources are heavily utilised for irrigation

the alluvium is 140 m in the Boggabri area (Broughton

(Figure 1). One of the major unregulated tributaries to the

).

Figure 1

Namoi River catchment, New South Wales, Australia.

Figure 2

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

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Cox’s Creek subcatchment, gauging station and extraction bores (after Ivkovic et al. (2009a)).

Evaporation and Streamﬂow data) (Jakeman et al. ;

METHODS

Jakeman & Hornberger ) was ultimately selected for use in this investigation because it was among the models

Model selection

with the fewest parameters. The IHACRES model typically A number of existing rainfall–runoff models were reviewed

uses only three parameters for the linear unit hydrograph

with the speciﬁc purpose of meeting the two main model

routing module, suggesting that its linear module could be

output criteria previously outlined above. One of the main

more easily modiﬁed to meet the model output criteria. An

considerations for model selection was parsimony. This is

overview of the IHACRES model follows in some detail

because simple rainfall–runoff models tend to give more

below in order to show how the algorithm was later modi-

robust results than more complex models when simulating

ﬁed to include a groundwater store in the development of

ﬂows (Perrin et al. ; Nalbantis et al. ). There are

IHACRES_GW.

many examples of rainfall–runoff conceptual models that have been used to model storage–outﬂow relationships,

IHACRES model background

such as the Sacramento (Burnash et al. ), HBV (Bergström ) and SIMHYD (Chiew et al. ) to name a

The structure of the linear routing module of the IHACRES

few. However, the IHACRES model (Identiﬁcation of

model is based on transfer function theory that relates inputs

Hydrographs

And

Component

ﬂows

from

Rainfall,

to outputs through linear transformation equations (Young

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

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; Whitehead & Young ). Most applications of

The parameters αq and αs deﬁne the recession character-

IHACRES involve two stores arranged in parallel, one repre-

istics of the hydrographs, and they can also be expressed as

senting a quick ﬂow pathway, and the other a slow ﬂow

time constants, τq and τs for the quick and slow ﬂow com-

pathway (Figure 3).

ponents, respectively, of streamﬂow decay:

The quick flow pathway is used to infer the overland and shallow subsurface contributions to streamflow, and the slow flow pathway to infer the groundwater contri-

τq ¼

Δ In αq

(1)

τs ¼

Δ Inð αs Þ

(2)

butions to streamﬂow or baseﬂow. Refer to Figure 3, ðqÞ

where Qt

ðsÞ

and Qt

represent the modelled quick and

slow ﬂow volumes at time-step t, and Qt represents the modelled total streamﬂow. The parameters βq and βs govern the height of the unit hydrograph peaks of the

where Δ is the sampling interval. The derivation of τq and τs is

quick and slow ﬂow components, respectively, and Ut is

given in Jakeman et al. (). The time constants are estimated

the effective rainfall depth at time-step t. The A term rep-

for the sampling interval, and as a result the calibrated value is

resents the catchment area and is used to convert units

dependent upon the sampling interval and time-step as was

of effective rainfall in mm to units of streamﬂow in mega-

shown by Littlewood & Croke (, ), so care should be

litres (ML). The parameters αq and αs deﬁne the rates

taken in interpreting the time constants obtained as being

ðqÞ

ðsÞ

of quick and slow ﬂow recession. Qt 1 and Qt 1 are the

representative of the conditions being investigated.

modelled quick and slow ﬂow volumes from the previous time-step.

Introduction of a groundwater store

The partitioning of effective rainfall into its quick and slow ﬂow components is assumed to be linear and constant

The IHACRES model was modiﬁed to include a groundwater

in time. Thus, if vs represents the fraction of effective rainfall

store and the resultant model was entitled IHACRES_GW

that is partitioned as slow ﬂow, conservation of mass

(Ivkovic et al. a). The IHACRES_GW model is based

requires that the fraction partitioned as quick ﬂow vq is

on the IHACRES rainfall–runoff model, as outlined above.

1–vs. The depth of recharge to the slow ﬂow store is implicitly

However, in IHACRES_GW the slow transfer function com-

considered by vs, and its value is calibrated along with the

ponent of the IHACRES model, which makes no allowance

parameters representing the unit hydrograph.

conceptually for an aquifer, has been replaced with a store

Figure 3

IHACRES linear routing model structure.

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

that more explicitly accounts for the presence of groundwater

Hydrology Research

45.1

2014

Derivation of the IHACRES_GW model

(Figure 4). The conceptual model was derived from ideas initially developed in Croke et al. ().

The exponentially decaying slow ﬂow component in the

In the IHACRES_GW model, groundwater storage is con-

IHACRES model can be reformulated to consider the total

ceptualised as a single reservoir with its areal extent

volume of groundwater by adopting a linear relationship

represented by the catchment area above the stream gauging

between groundwater storage and baseﬂow (Boussinesq

station of interest. As one can see from Figure 4, the depth

; Maillet ; Chapman ):

of water that recharges the groundwater store is determined by the proportion of effective rainfall that is partitioned as slow ﬂow, which is a calibrated value. The remaining fraction

ðsÞ Qt

aGt if Gt > 0 0 otherwise

(3)

of effective rainfall is apportioned to quick flow. (Note that the methodology for estimating effective rainfall for input to IHACRES_GW is discussed later in this paper.) The volume of water released from groundwater storage to the river system is represented by the slow flow component of streamflow, and is assumed to be baseflow. Groundwater extraction and other losses behave as additional outflows from the groundwater store. The main assumptions of the IHACRES_GW model were provided in the Ivkovic et al. (a) paper. The details of the derivation of the IHACRES_GW

where: ðsÞ

Modelled slow ﬂow inferred as baseﬂow at time-step t

(ML/time-step). Gt Volume of groundwater (ML) stored above the catchment outlet at time-step t. a The value of this parameter gives the linear relationship between groundwater storage and the contribution of groundwater discharge to baseﬂow.

model algorithms follow, and it is important to note that

This representation of the baseﬂow results in an expo-

these changes could be made to any rainfall–runoff model

nentially decaying store (i.e., behaves identically to the

that uses exponentially decaying stores to represent the

formulation in IHACRES). Replacing the IHACRES slow

total unit hydrograph.

transfer function in this way allows the inclusion of

Figure 4

IHACRES_GW model structure.

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

extractions and other losses in the mass balance equation for groundwater storage:

β s ¼ vs

Hydrology Research

a 1þa

45.1

2014

(9)

Solving Equation (8) in terms of a yields:

ðsÞ

Gt ¼ Gt 1 Qt þ vs AUt Et Lt

(4)

where Et is the groundwater extraction at time-step t, and is

a¼

ðαs þ 1Þ αs

(10)

based on annual extraction data, converted to a daily rate and lumped for the catchment area. Lt represents any

The baseﬂow contribution at time-step t is then calcu-

losses from groundwater storage at time-step t, including

lated by solving Equation (6) for Gt, where Gt is greater

subsurface outﬂow below the level of the stream gauging

than zero, and then by multiplying through by a as shown

station, evapotranspiration and other losses (or gains if the

in Equation (3). If Gt is less than zero, then the baseﬂow is

loss term is negative such as would be the case with irriga-

zero. The parameter a is calculated with Equation (10)

tion returns and river inﬁltration) and is a calibrated term

using the calibrated τs parameter derived from running the

that remains constant at each time-step.

IHACRES_GW model over a number of years in which

ðsÞ

The Qt term in Equation (4) can be substituted with aG from Equation (3) yielding:

streamflow events demonstrate some baseflow components to flow, and solving for αs using Equation (2). To summarise, the IHACRES_GW model requires the

Gt ¼

calibration of four parameters, τq, τs, υs and Lt,. The cali-

Gt 1 aGt þ vs AUt Et Lt ; if Gt > 0 Gt 1 þ vs AUt Et Lt otherwise

(5)

bration process is discussed in more detail later in the paper as part of the model testing.

This can be arranged as: Estimating effective rainfall Gt ¼

8 <

1 ðGt 1 þ vs AUt Et Lt Þ if Gt > 0 1þa : Gt 1 þ vs AUt Et Lt otherwise

(6)

A non-linear loss module, such as the Catchment Moisture Deﬁcit (CMD) module (Croke & Jakeman ), is usually used to transform observed rainfall and temperature data

Solving for the above equations allows for a continuous accounting

groundwater

storage

volumes

maintained. be calculated by Equation (3), resulting in: 1 a ðs Þ Q þ ðv AUt Et Lt Þ if ¼ 1 þ a t 1 1 þ a s : 0 otherwise

ðsÞ

Thiessen polygon (Croke et al. ) approach in the Cox’s Creek catchment revealed mismatches between

Gt > 0

observed streamﬂow events and the occurrence of rainfall,

Equation (7) has a similar functional form to the equation for the slow transfer function shown in Figure 1, but without the added extraction and loss terms. It therefore follows that: 1 1þa

often tend to be non-uniform. An analysis of the input rainfall time-series generated using a standard weighted

(7)

αs ¼

ever, the spatial coverage of raingauges throughout many catchments in Australia is poor and the rainfall patterns

ðs Þ

Multiplying Equation (6) through by a allows for Qt to

8 <

to effective rainfall depth when using IHACRES. How-

which imposed major limits on model performance when using the CMD module with IHACRES_GW (Herron & Croke a). As previously mentioned, the highly nonlinear relationships between rainfall and runoff in low yielding catchments commonly result in poor estimates of effective rainfall depth when using non-linear models. In addition, ephemeral catchments have more zero ﬂow

(8)

days and typically fewer streamﬂow events, and therefore the streamﬂow series provides less information for

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Hydrology Research

45.1

2014

parameter estimation. Furthermore, there is no infor-

from the total ﬂow for each time-step. The effective rainfall

mation on the catchment’s soil moisture status during

was then calculated by: 8 ðqf Þ ðqÞ > < Qt þ αq Qt 1 Ut ¼ if βq A > : 0 otherwise

dry periods (Ye et al. ). In our assessments of ephemeral river catchments in the Namoi Catchment, it was noted that the consequent errors in estimating catchment average rainfall increased

Qt > Qt 1

(11)

the uncertainty in the non-linear loss module to the

where Ut is the effective rainfall and Qt(qf) is the ﬁltered

extent that the inﬂuence of groundwater extraction using

quick ﬂow at time-step t. αq is the quick ﬂow recession

the IHACRES_GW linear module was masked. Taking

rate, βq is the height of the unit hydrograph peak for

the Cox’s Creek catchment as an example, where the aver-

quick ﬂow, and A is the catchment area (Croke ).

age extraction rate during the irrigation season is on the

Assumptions in this formulation are: (i) that the ﬁltered

order of 7,390 ML/year, over a catchment area of

quick ﬂow volume provides the effective rainfall input to the

4,040 km2 this volume equates to less than 1.8 mm/year

model; (ii) that for effective rainfall to be generated there

of extraction. The estimated average effective rainfall

must be a measurable quick ﬂow (because of the way effec-

depth over the simulation period was 36.7 mm/year. It

tive rainfall is estimated in Equation (11)); and, furthermore,

would be expected that the uncertainty in effective rainfall

(iii) that the quick ﬂow signature has not changed over time

depth would be greater than 10% (i.e., greater than

in response to groundwater extraction. These assumptions

∼4 mm) when using a non-linear module. And yet, it is

render the calculation of effective rainfall in this way to be

important to note that the impacts of 1.8 mm/year extrac-

only suited to ephemeral river systems which are quick

tion within the Cox’s Creek catchment were shown by

ﬂow dominated and yet exhibit an intermittent baseﬂow

Ivkovic et al. (a) to have a considerable impact on

signal, such as the situation we are considering here.

low ﬂows.

A sensitivity analysis described by Ivkovic () showed

Given the high uncertainty of estimating catchment

that the calculated effective rainfall depth inﬂuenced the

yield using a non-linear module, a top-down modelling

modelled streamﬂow, and in turn, the choice of parameter

approach was employed that relied on the streamﬂow data

values selected when calibrating the IHACRES_GW model

to estimate effective rainfall. This involved ﬁltering the

inﬂuenced the effective rainfall depth. This is expected

observed streamﬂow series to generate its quick and slow

given the inter-relationships evident in Equation (11). Impor-

components using the box-car minimum baseﬂow ﬁlter tech-

tantly though, the errors were relatively small and found to be

nique described by Croke et al. ().

within the bounds of 0.5 to 2.3 ML/day ( 0.2 to 1% of

The mathematical box-car minimum baseflow filter method is applied in two steps. The first step involves running a filter using a width of 2w þ 1 time-steps (w ¼ 2),

mean ﬂows) for 10% perturbations relative to the optimal reference parameter values. Using Equation (11) to calculate effective rainfall for

where at each time-step t, the minimum of the observed

model input to IHACRES_GW had the critical beneﬁt of

ﬂows from time-step t w to t þ w is determined. In the

reducing the uncertainty in effective rainfall depth, which

next step, the resulting time series is smoothed using a

as previously stated, was greater than the inﬂuence of

box-car ﬁlter of the same width (i.e., ﬁve time-steps),

groundwater extractions on modelled streamﬂow. More-

which is the width also used by the Institute of Hydrology

over, employing this approach allowed for a more

Base Flow Index (BFI) ﬁlter (Gustard et al. ). The ﬁl-

thorough testing of the performance of the IHACRES_GW

tered stream ﬂow values were then used to estimate the

linear model structure, as will now be discussed.

baseﬂow volume contribution to the stream, and as discussed in Littlewood (, ), the ﬁltered value is

Model calibration and performance criteria

sensitive to the data interval assessed. The quick ﬂow contribution to streamﬂow was then estimated by subtracting

The calibration of the four parameters, τq, τs, υs and Lt, was

the ﬁltered baseﬂow, using the method outlined above,

performed through a manual trial-and-error process using

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Hydrology Research

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2014

visual inspection of the observed ﬂows and ﬂow duration.

The selection of the value 1 was somewhat arbitrary, and

Modelled versus observed ﬂows were visually assessed in

in this investigation represents about 1/400th of the mean

log space in order to focus on the low ﬂow component of

ﬂow to emphasise the behaviour of the model at the ﬂow

model ﬁts. The visual calibration was complemented by ana-

to no-ﬂow transition.

lysing ﬁve performance criteria, namely R 2, R 2slow, R 2inv,

The relative bias (RB) was also assessed, which is given by:

relative bias (RB) and RBslow (deﬁned below) during the manual calibration process. Confusion matrices (Dunham ), a type of contingency table, were also analysed to assess the timing in the switch between baseﬂow and no-

RB ¼

n 1X ðOt Mt Þ n t¼1

flow periods on a daily time-step; they provided an indicator of the proportions of correctly and incorrectly classified flows

RB measures are useful in assessing streamﬂow volumes

for the presence of baseﬂow (>0.1 ML/day). The objective

over the length of the modelled period. RB was calculated

functions utilised for this investigation are described below. R 2 is the coefﬁcient of efﬁciency described by Nash & Sutcliffe () as: n P

for both the modelled streamflow as well as for comparing the modelled slow flow relative to filter-generated slow flow volumes (RBslow) using the minima filter.

ðOt Mt Þ2

R2 ¼ 1 t¼1 n P

ðOt OÞ2

RESULTS

t¼1

where Ot is the observed value at time t, Mt is the predicted value at time t, O is the mean of the Ot and n is the number of daily time-steps in the record being simulated. The R 2 values were calculated for total streamflow and filtered baseflow (R 2slow) using the minima filter previously described. R 2 is biased towards reproducing high flows, not baseflow behaviour, so it was of limited interest in terms of calibrating the model except to ensure the overall acceptability of model performance. The R 2slow, however, was of particular interest because it gave an indication of how well the slow flow volumes modelled by IHACRES_GW compared with filter-derived slow flow values (based on observed streamflow) using the minima filter. A similar statistic to the coefficient of efficiency is the R 2inv which is calculated as:

R2inv

The IHACRES_GW model was calibrated to daily streamflow data for gauging station 419032 (Boggabri) at the outlet of the Cox’s Creek subcatchment (Figure 2). The period for calibration selected was 1 June 1965 to 30 June 1980 (15 years) using a continuous record of daily streamflow data, as was outlined by Ivkovic et al. (a). The river flows during this period of time were considered to be representative of pre-groundwater extraction conditions. The model calibration was commenced at the onset of a baseflow event when groundwater storage volumes would be expected to be close to the zero reference point. A 50day warm-up period was used. The order of the calibration was to first fit the τq par-

2 1 1 1 þ Qt 1 þ Mt ¼ 1 t¼1 2 n P 1 1 1þO t¼1 1 þ Qt

ameter, to which the model is most sensitive, with

R 2inv measures the ﬁt to mostly low ﬂows (Pushpalatha

model ﬁt are shown in Table 1.

n P

Model calibration

emphasis on fitting towards the end of a baseflow recession period. Second, υs was calibrated, followed by the τs parameter. The Lt parameter was fitted last, and had the overall effect of shortening the duration of the baseflow recession. The calibration parameters providing the best

et al. ). The addition of 1 to the observed and modelled

A visual inspection of the modelled output showed a

ﬂows enables the inclusion of time-steps with zero ﬂows.

good match to the stream hydrograph recession behaviour.

K. M. Ivkovic et al.

Table 1

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Hydrology Research

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2014

Calibration period parameter values and objective function ﬁts (1/6/1965 to

baseﬂow predicted over the 15-year calibration period is

30/6/1980)

about half the volume estimated from the ﬁltered

Parameters

Calibrated values

Objective functions

Fits

νs

0.09

0.89

τs

15 days

R 2slow

0.62

τq

0.9 days

R 2inv

0.79

6 ML/day

0.28

RBslow

0.48

streamflow. The underprediction of low flows is also evident in the flow duration curve (Figure 6). Some underprediction is due in part to the fact that low flow events below 8 ML/day were not reliably recorded at the gauging station between 1965 and 1980, which resulted in either no data, or else data infilling had been employed using a constant value of around 8 ML/day. This affected about 10% of the data (a

A typical streamﬂow record is shown in Figure 5 and high-

similar ﬁnding was noted for the other gauging stations

lights the inﬂuence of the loss term (Lt). Note that the

within the Namoi Catchment over this period of time).

reproduction of the high ﬂows is very good due to the

Because effective rainfall is calculated using Equation (11),

manner of estimating the effective rainfall, and is therefore

effective rainfall input to IHACRES_GW is constrained to

not a good indicator of the model ﬁt. Rather, it is the behav-

only those days where an increase in streamﬂow is observed,

iour of the model following the ﬂow peaks that is of primary

or else it is assumed to be zero. The data-inﬁlling with con-

interest in this case.

stant values had the effect of resulting in zero effective

The values for R 2 and RB for the 15-year calibration

rainfall input over those days (since no increases in stream-

period are very good, as would be expected, given that effec-

ﬂow were observed), and thus there is also zero groundwater

tive rainfall was calculated using a ﬁlter-derived quick ﬂow

recharge, further reducing low ﬂow contributions to mod-

value (refer to Equation (11)). However, the ﬁts to the

elled streamﬂow. An additional source of uncertainty

high ﬂows are not perfect due to having constrained effec-

includes sources of recharge to the aquifer from outside of

tive rainfall to only days with an increase in observed

the catchment, or at greater depth within the catchment.

ﬂow, as well as the non-stationarity in the unit hydrograph.

For example, Dyce & Richardson () reported that

R 2slow

R 2inv

statistics, which focus on low ﬂow behav-

some upward vertical leakage from the underlying basalt

iour, suggest that the model is capturing the recession

bedrock aquifer may be occurring in parts of the Cox’s

volumes of baseﬂows well on a daily time-step. The RBslow

Creek catchment, although these volumes have not been

statistics, however, indicate that the overall volume of

quantiﬁed.

The

Figure 5

and

Observed and modelled streamﬂow at Gauging Station 419032, Cox’s Creek at Boggabri for September 1973–1976 portion of the calibration period.

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Hydrology Research

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2014

daily average over the irrigation season) were available over the record. Simulations were run on a daily time-step using the calibrated model parameters (Table 1). Groundwater extraction data were used as an additional loss from groundwater storage (Et). The model was not calibrated to this period, so this simulation also serves as a test/validation of the calibrated model. Outside of the irrigation season groundwater extraction was set to zero, while the constant loss term (Lt) remained 6 ML/day based on the calibration period. The model ﬁts assessed by our ﬁve performance statistics for the simulation period are provided in Table 2. An Figure 6

improvement in R 2, R 2slow and RB is evident together with Flow exceedence percentages for observed and modelled streamﬂow for the 1/6/1965 to 30/6/1980 calibration period.

a slight decrease in R 2inv and RBslow in comparison to the calibration period (Table 1). The value of RBslow indicates

The evaluation of modelled and minima filtered low flows relative to the 0.01 ML/day threshold value indicated that the proportion of modelled flows with incorrect recession timings (e.g., filtered >0.01 ML/day and modelled <0.01 ML/day; and filtered <0.01 ML/day and modelled >0.01 ML/day) was 6.6%. The proportion of time where a minima filter-derived baseflow was estimated, but not modelled was 2.1%. These percentages suggest that the model performed well in terms of capturing the baseflow to noflow transitions. By contrast, if no groundwater losses were included in the model run (Figure 5), 49% of the total proportion of flows are incorrectly modelled. These data suggest that the IHACRES_GW model configuration is more capable of simulating the rapid transition from a flow to no-flow periods.

that the baseflow volumes over the simulation period are approximately one-third of those estimated by the minimaderived filter. The confusion matrix for flows greater than 0.01 ML/day gives the proportion of modelled flows with incorrect recession timings as 7.4%. The proportion where baseflow was estimated but not modelled was 5.9% (an increase from the 2.1% found for the calibration period). These performance measures indicate that the model still performed well in terms of capturing the behaviour of the baseflow recessions, as well as the transitions from flow to no-flow events over the simulation period, despite the fact that the model was not calibrated to this period. A plot of observed versus modelled streamflow for a representative portion of the simulation period is shown in Figure 7, and demonstrates that the model is representing the overall streamflow recession behaviour reasonably well. However, it is also apparent that the modelled flows

Model simulation

are underestimated for periods where observed ﬂows last for a couple of months or longer, e.g., the baseﬂow-

Model simulation in this investigation consisted of running

dominated periods, consistent with the value of the RBslow

the model forward with calibrated parameters using input

objective function ﬁt of 0.36. The residual differences reﬂect

data from a period that did not include any data from the calibration period. The term simulation, rather than validation, is used in this instance because groundwater extraction data were used for the simulation (and were not used in the preextraction calibration period). The period selected for model simulation using IHACRES_GW was 2 September 1988 to 9 December 2003 (15.3 years) as discussed by Ivkovic et al. (a). This period was selected because daily streamﬂow and yearly groundwater extraction data (converted to a

Table 2

Simulation period objective function ﬁts (2/9/1988 to 9/12/2003)

Evaluation criteria

Fits

0.96

R 2slow

0.75

R 2inv

0.70

0.10

RBslow

0.36

K. M. Ivkovic et al.

Figure 7

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Hydrology Research

45.1

2014

Observed and modelled stream ﬂow at Gauging Station 419032, Cox’s Creek at Boggabri for the September 1988–1993 portion of the simulation period.

an underestimation of very high ﬂows and a too rapid decay

parameter values derived during the calibration period

of baseﬂow recession.

(Table 1) were no longer applicable for the developed

The ﬂow exceedence percentages for streamﬂows below

period. This hypothesis was tested by a recalibration to the

100 ML are accordingly underpredicted between 2 and 14%

1988–2003 post-groundwater development period data.

(Figure 8). Despite the tendency of the model to underpre-

The recalibration showed an increase in the υs, τs and τq par-

dict low ﬂows, one would expect that the differences

ameters and a decrease in Lt, with slightly improved

between model outputs for a range of extraction scenarios,

objective function and visual ﬁts (Table 3). There were no

using the model as a base-case, would be much smaller

improvements noted in the model performance of switching

than the uncertainties in the predictions themselves as dis-

behaviour. The changes in parameter values suggest that

cussed by Reichert & Borsuk ().

groundwater extraction and irrigation have resulted in

A possible reason for the underestimation of baseﬂows

increased recharge, most likely from deep drainage and

over the simulation period may have been because the

induced and captured forms of recharge, which have resulted in a consequent slowing down in the baseﬂow recession rates. However, given that the IHACRES_GW model was calibrated to pre-development data, and yet managed to predict the overall streamﬂow behaviour well in a

Table 3

Calibration period parameter values and objective function ﬁts for post development period (2/9/1988 to 9/12/2003)

Parameters

Figure 8

Flow exceedence percentages for observed and modelled streamﬂow for the simulation period (2/91988 to 9/12/2003).

Calibrated values

Objective functions

Fits

0.94 0.72

νs

0.1

τs

25 days

R 2slow

τq

1.4 days

R 2inv

3 ML/day

0.1

RBslow

0.2

0.79

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

post-development state outside of the calibration period,

Hydrology Research

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2014

CONCLUSIONS

suggests a degree of robustness in the model structure. Two main challenges associated with using a rainfall–runoff model to estimate the impacts of groundwater extraction on low ﬂows in an ephemeral stream were investigated during

FURTHER TESTING OF IHACRES_GW

the development of the IHACRES_GW (Ivkovic et al. The IHACRES_GW model was subsequently tested in a

a) model.

further 13 semi-arid, narrow, semi-conﬁned alluvial aquifer

The ﬁrst challenge was to be able to correctly simulate

catchments in Australia (Zhu ). The IHACRES_GW

the transitions between baseﬂows and no-ﬂow periods

model was found to perform well in the seven variably con-

within an ephemeral stream, and to be able to correctly

nected gaining–losing and losing reaches (R 2inv values of

account for changes in groundwater storages arising from

(R 2inv

groundwater extraction and other losses. To address these

0.876–0.691). However, IHACRES_GW performed poorly

problems, the slow transfer function component of the

in the connected-gaining, permanently ﬂowing perennial

IHACRES model was replaced with a groundwater store.

river system (R 2inv ¼ 0.156), consistent with the fact that the

The derivation is fully described in this paper, and could

IHACRES_GW model is not suited to groundwater-domi-

be applied to any rainfall–runoff model that represents base-

nated (e.g., perennial) streams.

ﬂow as one or more exponentially decaying stores.

0.972–0.877) and the ﬁve connected gaining reaches

The IHACRES_GW model was also tested in the Mes-

The second challenge was to address the uncertainty in

sara Valley, Crete where it was coupled with the CMD non-

estimated effective rainfall depths when using a non-linear

linear module (Herron & Croke b). The ephemeral

module due to the highly non-linear rainfall–runoff relation-

river investigated was similarly situated within a narrow, con-

ships typically found in low yielding catchments. This

tained alluvial valley. No information was provided about the

problem was overcome by using streamﬂow data to estimate

hydrogeology of the Messara Valley in Herron & Croke’s

effective rainfall depth. Such an approach is best suited for

study (b), making it impossible to know whether the

use in areas where the error in the rainfall data is high as

aquifer conﬁguration was consistent with a two-store model

a consequence of poor spatial coverage of raingauges and

such as IHACRES_GW. Herron & Croke (b) reported

non-uniform rainfall patterns. Using streamﬂow data to esti-

they required the addition of a third store to represent a

mate effective rainfall depth has the beneﬁt of allowing for

perched aquifer system in order to calibrate their model.

greater certainty in the low ﬂow simulation of runoff-domi-

The resultant IHACRES_3S (3-storage) model was found to

nated catchments; however, this approach is not suitable

satisfactorily reproduce streamﬂow volumes and patterns

for use in groundwater-dominated (i.e., perennial) river

using the complete data record (i.e., no data remained for

systems.

validation). The IHACRES_3S model was subsequently

Model testing of IHACRES_GW demonstrated that it

used to investigate the impact of climate variability on catch-

was able to effectively simulate the transition between base-

ment hydrology in Australia by Kim et al. (). They found

ﬂow and no-ﬂow periods in rivers exhibiting variable

that the subcatchments located in the lower rainfall regimes

groundwater–river connection in low yielding catchments.

showed poor to average model performance using the

The model also demonstrated that baseﬂow volumes could

IHACRES_3S model. This ﬁnding is consistent with the

be simulated on a daily time-step, although, the model com-

problems IHACRES_GW attempted to overcome by using

monly underpredicted baseﬂow volumes by between 2 and

streamﬂow to calculate effective rainfall, as discussed in

14%.

this paper. Zhu () further reported that the additional

Ongoing research of the IHACRES_GW and IHA-

model complexity of the IHACRES_3S model was not war-

CRES_3S models is continuing in order to improve

ranted in the Australian catchments they investigated when

aspects of rainfall–runoff model performance in low yielding

streamﬂow data were used to calculate effective rainfall.

catchments. The IHACRES_GW model approach of using

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

streamflow to estimate effective rainfall depth requires further evaluation, including the possibility of generating effective rainfall when streamflow volumes are constant and decreasing, rather than only when there is an observed increase. Other research directions include modifying the linear module structure to have a variable partitioning between quick and slow flow components in order to capture any event-dependent variability present in the total unit hydrograph and the use of a variable loss parameter (Lt). Other considerations include modifying the non-linear CMD module so it produces a greater effective rainfall depth for large rainfall events in order to better represent the sharper form of the unit hydrograph peak observed with these types of events (Kim et al. ). A formal analysis of the predictive uncertainty (data, parameter and model structure) of the IHACRES model and its derivations is currently in progress (Blakers et al. ).

ACKNOWLEDGEMENTS This research was funded through an Australian Postgraduate Award with top-up scholarship funds from CSIRO Land & Water and

the

Cotton

Research

and

Development

Corporation. Data sets were supplied by the New South Wales Department of Water and Energy. Discussions with Prof. Tony Jakeman are also acknowledged. The authors are grateful to the Editor, Ian Littlewood, and the anonymous reviewers for their insightful comments and suggestions, which have resulted in a better paper.

REFERENCES Bergström, S.  Development and application of a conceptual runoff model for Scandinavian catchments. SMHI Report RHO 7, Norrköping, 134 pp. (PhD Thesis). Blakers, R. S., Croke, B. F. W. & Jakeman, A. J.  The inﬂuence of model simplicity on uncertainty in the context of surface– groundwater modelling and integrated assessment. MODSIM 2011 19th International Congress on Modelling and Simulation, Perth, Australia, 12–16 December 2011, pp. 3833–3839. Available at: http://mssanz.org.au/modsim2011. Boussinesq, J.  Essai sûr la théorie des eaux courantes. Mémories présentes par divers savants à l’Academie des Sciences de l’Institute National de France 23, 1–680.

Hydrology Research

45.1

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Broughton, A.  Cox’s Creek Catchment Hydrogeological Investigation and Dryland Salinity Studies. Volumes 1 & 2. TS94.082, Department of Water Resources, Barwon Region. Burnash, R. J. C., Ferral, R. L. & McGuire, R. A.  A generalized streamflow simulation system – Conceptual modeling for digital computers. Technical Report, Joint Federal and State River Forecast Center, US National Weather Service and California Department of Water Resources, Sacramento, pp. 204. Chapman, T. G.  Modelling stream recession flows. Environ. Modell. Softw. 18, 683–692. Chiew, F. H. S., Peel, M. C. & Western, A. W.  Application and testing of the simple rainfall-runoff model SIMHYD. In: Mathematical Models of Small Watershed Hydrology and Applications (V. P. Singh & D. K. Frevert, eds). Water Resources Publication, Littleton, CO, pp. 335–367. Croke, B. F. W.  A technique for deriving an average event unit hydrograph from streamflow-only data for ephemeral quick-flow-dominant catchments. Adv. Water Resour. 29, 493–502. Croke, B. F. W. & Jakeman, A. J.  A catchment moisture deficit module for the IHACRES rainfall-runoff model. Environ. Modell. Softw. 19, 1–5. Croke, B. F. W., Cleridou, N., Kolovos, A., Vardavas, I. & Papamastorakis, J.  Water resources in the desertificationthreatened Messara Valley of Crete: estimation of the annual water budget using a rainfall-runoff model. Environ. Modell. Softw. 15, 387–402. Croke, B. F. W., Evans, W. R., Schreider, S. Y. & Buller, C.  Recharge estimation for Jerrabomberra Creek Catchment, the Australian Capital Territory. MODSIM 2001, Modelling and Simulation Society of Australia and New Zealand, The Australian National University Canberra, Australia. Croke, B. F. W., Islam, A., Ghosh, J. & Khan, M. A.  Evaluation of approaches for estimation of rainfall and the Unit Hydrograph. Hydrol. Res. 42 (5), 372–385. Dunham, M. H.  Data Mining: Introductory and Advanced Topics. Prentice Hall, Upper Saddle River, NJ, pp. 315. Dyce, P. & Richardson, P.  Characterisation of subcatchment aquifers in the Liverpool Plains for the purpose of groundwater modelling. Technical Report 16/97, CSIRO Land and Water. Fleckenstein, J. H., Niswonger, R. G. & Fogg, G. E.  Riveraquifer interactions, geologic heterogeneity, and low-flow management. Ground Water 44 (6), 837–852. Gilfedder, M., Rassam, D. W., Stenson, M. P., Jolly, I. D., Walker, G. R. & Littleboy, M.  Incorporating land-use changes and surface–groundwater interactions in a simple catchment water yield model. Environ. Modell. Softw. 38, 62–73. Gustard, A., Bullock, A. & Dixon, J.  Low Flow Estimation in the United Kingdom. Institute of Hydrology Report 108, Institute of Hydrology, Wallingford, UK. Herron, N. & Croke, B. a Including the influence of groundwater exchanges in a lumped rainfall-runoff model. Math. Comput. Simulat. 79, 2689–2700.

K. M. Ivkovic et al.

Overcoming the challenges of using a rainfall–runoff model to simulate low ﬂows

Herron, N. F. & Croke, B. F. W. b IHACRES-3S – A 3-store formulation for modelling groundwater-surface water interactions. 18th World IMACS / MODSIM Congress, Cairns, Australia, 13–17 July 2009, pp. 3081–3087. Ivkovic, K. M.  Modelling Groundwater-river Interactions for Assessing Water Allocation Options. PhD Thesis, The Australian National University, Canberra, Australia. Ivkovic, K. M., Letcher, R. A. & Croke, B. F. W. a The use of a simple surface-groundwater interaction model to inform water management. Aust. J. Earth Sci. 56, 61–70. Ivkovic, K. M. b A top-down approach to characterise aquiferriver interaction processes. J. Hydrol. 365 (3–4), 145–155. Jakeman, A. J. & Hornberger, G. M.  How much complexity is warranted in a rainfall-runoff model? Water Resour. Res. 29, 2637–2649. Jakeman, A. J., Littlewood, I. G. & Whitehead, P. G.  Computation of the instantaneous unit hydrograph and identifiable component flows with application to two small upland catchments. J. Hydrol. 117, 275–300. Kim, H. S., Croke, B. F. W., Jakeman, A. J. & Chiew, F. H. S.  An assessment of modelling capacity to identify the impacts of climate variability on catchment hydrology. Math. Comput. Simulat. 81, 1419–1429. Larocque, M., Fortin, V., Pharand, M. C. & Rivard, C.  Groundwater contribution to river flows – using hydrograph separation, hydrological and hydrogeological models in a southern Quebec aquifer. Hydrol. Earth Syst. Sci. 17, 7809–7838. Le Moine, N., Andréassian, V., Perrin, C. & Michel, C.  How can rainfall-runoff models handle intercatchment groundwater flows? Theoretical study based on 1040 French catchments. Water Resour. Res. 43, W06428. Littlewood, I. G.  Characterisation of river flow regimes for environmental and engineering hydrology: unit hydrographs for rainfall-streamflow modelling. Folia Geographica ser Geographica-Physica XXXIX, 5–36. Littlewood, I. G.  Progress with unit hydrograph-based rainfallstreamflow models for engineering and environmental hydrology. In: Hydrological Extremes in Small Basins (W. Chelmicki & J. Siwek, eds). UNESCO IHP-VII Technical documents in hydrology series No. 84, Paris, pp. 117–122. Littlewood, I. G. & Croke, B. F. W.  Data time-step dependency of conceptual rainfall-streamflow model parameters: an empirical study with implications for regionalisation. Hydrol. Sci. J. 53 (4), 685–695. Littlewood, I. G. & Croke, B. F. W.  Effects of data time-step on the accuracy of calibrated rainfall-streamflow model parameters: practical aspects of uncertainty reduction. Hydrol. Res. 44 (3), 430–440. Maillet, E.  Essais d’hydraulique souterraine et fluviale. Hermann, Paris, pp. 218. McCallum, A. M., Andersen, M. S., Giambastiani, B. M. S., Kelly, B. F. J. & Acworth, R. I.  River-aquifer interactions in a

Hydrology Research

45.1

2014

semi-arid environment stressed by groundwater abstraction. Hydrol. Process. 27 (7), 1072–1085. Moore, R. J. & Bell, V. A.  Incorporation of groundwater losses and well level data in rainfall-runoff models illustrated using the PDM. Hydrol. Earth Syst. Sci. 6 (1), 25–38. Nalbantis, I., Efstratiadis, A., Rozos, E., Kopsiafti, M. & Koutsoyiannis, D.  Holistic versus monomeric strategies for hydrological modelling of human-modified hydrosystems. Hydrol. Earth Syst. Sci. 15, 743–758. Nash, J. E. & Sutcliffe, J. V.  River flow forecasting through conceptual models, Part 1-A discussion of principles. J. Hydrol. 10, 282–290. Perrin, C., Michel, C. & Andréassian, V.  Does a large number of parameters enhance model performance? Comparative assessment of common catchment model structures on 429 catchments. J. Hydrol. 242, 275–301. Pushpalatha, R., Perrin, C., Le Moine, N., Mathevet, T. & Andréassian, V.  A downward structural sensitivity analysis of hydrological models to improve low-flow simulation. J. Hydrol. 411, 66–76. Pushpalatha, R., Perrin, C., Moine, N. L. & Andréassian, V.  A review of efficiency criteria suitable for evaluating low-flow simulations. J. Hydrol. 420–421, 171–182. Rassam, D. W.  A conceptual framework for incorporating surface-groundwater interactions into a river operation-planning model. Environ. Modell. Softw. 26 (12), 1554–1567. Reichert, P. & Borsuk, M. E.  Does high forecast uncertainty preclude effective decision support? Environ. Modell. Softw. 20, 991–1001. Tan, B. Q. & O’Connor, K. M.  Application of an empirical infiltration equation in the SMAR conceptual model. J. Hydrol. 185, 275–295. Whitehead, P. G. & Young, P. C.  A recursive approach to time series analysis for multivariable systems. In: Modeling and Simulation of Water Resources Systems (G. C. Vansteenkiste, ed.). North Holland, Amsterdam, pp. 39–58. Ye, W., Bates, B. C., Viney, N. R., Sivapalan, M. & Jakeman, A. J.  Performance of conceptual rainfall-runoff models in low-yielding catchments. Water Resour. Res. 33, 153–166. Young, P. C.  Recursive approaches to time series analysis. Bull. Inst. Math. Appl. 10, 209–224. Zhang, L., Stauffacher, M., Walker, G. R. & Dyce, P.  Recharge estimation in the Liverpool Plains (NSW) for input groundwater models. Technical Report 10/97, Cooperative Research Centre for Catchment Hydrology. Zhu, Y.  An Investigation of the Relationship Between Surface Water-groundwater Connectivity and Hydrologic Model Structure for 13 Australian Catchments. Master of Environment, Fenner School of Environment and Society, The Australian National University, Canberra.

First received 28 November 2012; accepted in revised form 17 April 2013. Available online 29 May 2013

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2014

Reducing uncertainty in the calibration and validation of the INCA-N model by using soft data J. Randall Etheridge, Ahti Lepistö, Kirsti Granlund, Katri Rankinen, François Birgand and Michael R. Burchell II

ABSTRACT Process-based nutrient models are increasingly used to determine the impact of future changes in land use, agriculture production practices and climate on the quantity and timing of nutrients reaching surface waters. Calibration of catchment-scale models to observed conditions can be difﬁcult due to parameter uncertainty and the heterogeneity of catchment processes. Soft data, i.e. knowledge of processes gained through experimentation, have been suggested as one method of reducing uncertainty and producing a more accurate model of the processes that occur in a catchment. In this work, the Integrated Catchment model for Nitrogen was calibrated and validated for the Yläneenjoki catchment in south-western Finland by incorporating soft data. The calibration for 2003–2008 produced an adequate model of the in-stream nitrate concentrations (R 2 ¼ 0.45, NS ¼ 0.42). However, model validation using data from 1997–2002 showed that the simulated in-stream

J. Randall Etheridge (corresponding author) François Birgand Michael R. Burchell II Department of Biological and Agricultural Engineering, North Carolina State University, Raleigh, North Carolina, USA E-mail: jretheri@ncsu.edu Ahti Lepistö Kirsti Granlund Katri Rankinen Finnish Environment Institute, Helsinki, Finland

nitrate concentrations were above the observed concentrations throughout the entire period (R 2 ¼ 0.34, NS < 0). These results show that soft data can be used to constrain model parameters, resulting in a more accurate model of the catchment, but do not guarantee the best validation results as the simulated processes may not occur at the same time and rate as they did in the catchment. Key words

| catchment, modeling, nitrogen, soft data

INTRODUCTION Agricultural production has been identiﬁed as a major con-

climate change provide incentive to gain a better under-

tributor of non-point source pollution in catchments

standing

throughout the world (e.g. Howarth et al. ; Räike et al.

agriculture on the nitrogen cycle (Galloway et al. ).

nitrogen

processes

and

the

effects

; Cherry et al. ; HELCOM ). Although agricul-

Process-based models focused on hydrology and nutri-

tural land use in Finland covers only 7% of the total land

ent leaching are increasingly used to determine the impact

area, the losses of nutrients from agriculture are approxi-

of future changes in land use (agriculture, forestry, etc.)

mately 50% of the total nitrogen (N) loading (Vuorenmaa

and climate on the nutrients reaching surface waters. Such

et al. ). The diffuse pollution from agriculture is concen-

models have been developed and used for assessing water

trated in southern, south-western and western areas of

quality issues at the small catchment scale (Lunn et al.

Finland. The nutrient-rich waters leave the agricultural

; Heng & Nikolaidis ). However, as decision tools

land and enter streams, lakes and estuaries leading to eutro-

for planners and managers, the use of these models is

phication (Vitousek et al. ) and potentially make the

often limited due to high input data requirements, which

water supply unﬁt for consumption because of health risks

prevent the calibration of the models for large river systems.

(Ward et al. ; Townsend et al. ). The negative effects

At the catchment scale and in larger river-dominated basins,

of nitrogen-rich waters on human health, biodiversity and

advanced process-based semi-distributed dynamic nutrient

doi: 10.2166/nh.2013.039

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

45.1

2014

models such as the Integrated Catchment model for Nitro-

used directly in support of model calibration (Winsemius

gen (INCA-N) (Whitehead et al. a; Wade et al. )

et al. ). The uncertainty associated with soft data for

can be applied over a wide range of spatial and temporal

use in process-based modeling is partially due to the process

scales. INCA-N is a process-based model that uses a mass-

rates being measured at the ﬁeld scale and the processes

balance approach to track mineral nitrogen within a catch-

being simulated at the catchment scale (Seibert & McDon-

ment. It can integrate both point and non-point sources of

nell ; Wade et al. ). Another factor contributing to

nitrogen (Whitehead et al. a, b; Wade et al. ). The

the uncertainty of experimental data is that experiments

model incorporates hydrology and different nitrogen pro-

often provide a wide range of potential process rates based

cesses such as mineralization and denitriﬁcation to

on a limited number of measurements. These two problems

simulate the mass of nitrogen in each part of the system.

prevent the results of some ﬁeld experiments from being

A vital step in the process of modeling scenarios for

used as hard data during model calibration, but the soft

planning and management purposes is to prove a model is

data can be used to specify a realistic parameter range to

capable of simulating what is currently occurring in a catch-

reduce model parameter uncertainty and provide a more

ment through the calibration and validation process (Santhi

realistic simulation of what is occurring in the catchment

et al. ; Jarvie et al. ; Granlund et al. ). In model

(Seibert & McDonnell ).

calibration, the parameters are adjusted to more accurately

Some work has been done on the issue of parameter

simulate the observed results. The model parameters set

uncertainty in the INCA-N model (McIntyre et al. ;

during calibration are then applied to another period of

Wade et al. ; Rankinen et al. ). McIntyre et al.

time to assess the accuracy of the model in the validation

() used a Monte Carlo analysis to show that the most

phase (Refsgaard ).

sensitive model parameters had high uncertainty. They rec-

A problem with this procedure is the possibility of

ommended the use of observed soil and groundwater

obtaining a numerically correct result for the wrong

concentrations to constrain model parameters, but did not

reason (McIntyre et al. ; Kirchner ; Rankinen

have these data available for their simulations. The use of

et al. ). The overestimation of nitrogen inputs to a

experimental data to reduce parameter uncertainty in the

system can be numerically compensated for by increasing

INCA-N model was recommended based on work with a

nitrogen removal through plant harvest or denitriﬁcation,

virtual catchment by Raat et al. (). Rankinen et al.

for instance. In this case, the modeled nutrient concen-

() used the Generalized Likelihood Uncertainty Esti-

trations at the outlet of the catchment may provide a good

mation (GLUE) methodology to determine the usefulness

ﬁt with observed data, but the process rates within the

of soft data for automatic calibrations. Their work showed

model are not accurate. If the model does not accurately

that the ﬂow hydrograph and in-stream nutrient concen-

estimate what is occurring during normal conditions

trations were not enough to adequately constrain the

where there is observation data available for calibration, it

model parameters, but soft data could be used to reduce

is unlikely that the model will be reliable as the conditions

equiﬁnality or the occurrence of multiple parameter sets

move outside of those experienced currently (Kirchner

producing the same simulation results. Despite these rec-

).

ommendations, the method and impact of using results

In water quality and hydrology modeling, soft data are

from ﬁeld experiments in manual calibrations and vali-

knowledge about a catchment or process that is gained

dations has not been fully explored for the INCA-N model.

through experimentation, but cannot be compared directly

In previous studies, annual process rates from the literature

to model output due to high uncertainty (Seibert & McDon-

have been used to adjust the nitrogen process parameters

nell ; Winsemius et al. ). Soft data do not provide

(e.g. Wade et al. ; Bärlund et al. ), but the steps

an absolute number that can be used in calibration of the

to use this soft data in calibration are rarely shown.

model such as in-stream nutrient concentrations or a con-

The purpose of this paper is to show how soft data can be

tinuous ﬂow record, which are referred to as hard data.

used to constrain model parameters in the manual cali-

Hard data have an acceptable level of certainty and are

bration of the INCA-N model through a case study of the

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

45.1

2014

Yläneenjoki catchment in Finland. The INCA-N model was

on the modeled hydrograph if the tracer experiments/chan-

calibrated for the years 2003–2008 and validated for the

nel properties are not available (Whitehead et al. a).

years 1997–2002. This study will focus on the use of pub-

The land-based nitrogen processes of mineralization,

lished nitrogen process rates and an examination of the

nitriﬁcation, plant uptake, denitriﬁcation and immobiliz-

groundwater portion of the model to calibrate the in-stream

ation are simulated in the model. All of these process rates

nitrate (NO3-N) and ammonium (NH4-N) concentrations.

are temperature and moisture dependent. The process rates can be defined for up to six land use classes. Denitrification and nitrification are simulated in the in-stream

METHODS

portion of the model. The in-stream process rates are temperature dependent and can be altered between reaches.

Model description

INCA-N models transformation of nitrogen within the catchment, as well as leaching of inorganic nitrogen. It is

INCA-N is a process-based model that uses a mass-balance

assumed in the model that there is an inﬁnite source of

approach to track mineral nitrogen in a watershed (White-

organic nitrogen that can be mineralized. Fertilizer appli-

head et al. a; Wade et al. ). The model is semi-

cations (NO3-N and NH4-N), atmospheric deposition, point

distributed and incorporates point sources, non-point

sources of nitrogen and biological nitrogen ﬁxation are the

source, hydrology, land-based nitrogen processes and in-

other sources of nitrogen considered in the model. A mass-

stream nitrogen processes to simulate the daily ﬂow, NO3-

balance approach is taken to account for the transformations

N and NH4-N concentrations in catchment streams. In

and movement of nitrogen through the watershed. The

this study, model version 1.11.10 was used.

volume of water and mass of nitrogen is accounted for in

The land-based portion of the model includes two zones:

each land use within each subcatchment. As water leaves

the groundwater zone and the soil zone. The model uses

one zone of the model and enters another zone, a mass of

hydrologically effective rainfall (HER) as the input to the

nitrogen is transferred between the modeled zones.

soil water. HER is deﬁned as the portion of precipitation that reaches stream channels either through surface runoff

Study site

or by groundwater discharge (Rankinen et al. ). The HER can be supplied for the whole catchment or for individ-

The River Yläneenjoki is one of two major rivers that dis-

ual subcatchments within the model. The time it takes for

charge into Lake Pyhäjärvi (Figure 1). It is located in

rainfall to make it to the stream is driven by the base ﬂow

south-western Finland, which is a hotspot for agricultural

index (BFI), residence time constants and soil properties

nitrogen loading. Lake Pyhäjärvi eventually drains along

that lead to direct runoff. All of the HER that does not

the Eurajoki River to the Gulf of Bothnia to the west. The

runoff inﬁltrates and passes through the soil zone. The BFI

Yläneenjoki catchment has an area of 233 km2 with 31%

determines the portion of water that will pass through the

of the land in agricultural production. The agricultural pro-

groundwater zone after going through the soil zone. A

duction in the Yläneenjoki catchment is considered

higher BFI means a higher proportion of the water passes

intensive for Finland with the primary products being cer-

through the groundwater zone instead of going directly to

eals and animals (Lepistö et al. ). The soils in the

the stream after passing through the soil zone. The residence

river valley of the Yläneenjoki catchment are mainly clay

time constants are deﬁned separately for the groundwater

and silt. Approximately 11% of the precipitation falls as

and soil water zones. Stream ﬂow is modeled using a multiple reach approach

snow and the long-term (1961–1990) average annual precipitation

was

630 mm

the

Yläneenjoki

catchment

that relates discharge Q to a mean ﬂow velocity v based on

(Hyvärinen ). The average discharge from the River

the equation v ¼ aQb. Ideally, the a and b constant ﬂow par-

Yläneenjoki is 2.1 m3 s–1 (Mattila et al. ) with the highest

ameters can be estimated from tracer experiments and/or

ﬂows typically occurring during the spring snow melt and

based on channel properties, but can be calibrated based

fall.

J. Randall Etheridge et al.

Figure 1

Reducing uncertainty in model calibration and validation by using soft data

The Eurajoki River catchment; the Yläneenjoki catchment is outlined in black.

Figure 2

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45.1

2014

The Yläneenjoki catchment showing the INCA-N subcatchments and the agricultural lands in dark grey.

Data collection

that was required to run the model and included soft data, i.e. any available information that could be used to improve

The daily discharge of the River Yläneenjoki has been moni-

the calibration of simulated nitrogen processes (Table 1). An

tored since the 1970s at the Vanhakartano measuring site

example of soft data would be the nutrient process rates in

(Figure 2), while nutrient concentrations have been monitored

agricultural soils determined through experimentation

on a weekly to monthly basis. These data were available

(Table 2). Scientiﬁc literature contains useful information

through the Environmental Information System (HERTTA)

about ﬁeld experimentation, but collected data should also

maintained by the Finnish environmental administration.

include reports of local agricultural practices and infor-

The HERTTA data were supplemented by results from an auto-

mation on fertilization practices and crop yields, which

matic water quality station in the spring and the autumn of

are seldom available for Finnish catchments.

2007 (Lepistö et al. ; Koskiaho et al. ). NO3-N concentrations from the river were collected using sensor-based

Model calibration: steps A–F

technology on an hourly interval during 27 March–27 April 27 and 4 October–20 November 2007. The measurements

The INCA-N model has both a hydrologic and a nutrient

from the automatic water quality station provided a continu-

component. Manual calibration of the INCA-N model

ous record of observed data for two short periods of time,

begins with the hydrologic component because the move-

constituting only 4% of the calibration period. The daily aver-

ment of nitrogen is driven by water ﬂow (Wade et al. ).

age of these measurements was used in this work.

Although the calibration process is iterative, the process gen-

The model requires an input time series of HER, soil

erally follows a path similar to the path a drop of water would

moisture deﬁcit, air temperature and actual precipitation.

follow through the catchment, speciﬁcally by starting the cali-

These inputs were taken from the Watershed Forecast

bration process in the land portion of the model then working

System (WSFS) of the Finnish Environment Institute (Veh-

to the stream portion of the model. The process used to com-

viläinen & Huttunen ). For this study, the data

plete the hydrologic calibration in this study was based on

collection went beyond the minimum time series inputs

methods described in Rankinen et al. () and Granlund

J. Randall Etheridge et al.

Table 1

Reducing uncertainty in model calibration and validation by using soft data

Source, extent and type of data that can be used to more accurately model

Table 2

Hydrology Research

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Nutrient process rates used as soft data for model calibration

catchment N processes using the INCA-N model Rate (kg N ha–1 a–1)

Data type

Source

Preferred extent

Land use

Process

Fertilizer application rates and time of year

Producer interviews or published values

Each land use

Spring cereals

Nitrogen leaching

4–26

Salo & Turtola ()

Published values or direct measurement

Each land use

Agriculture production

Nitrogen leaching

2–99

Ranges of nitrogen process rates (e.g. denitriﬁcation, mineralization)

Vuorenmaa et al. (); Salo & Turtola (); Rankinen et al. ()

Crop nitrogen uptake

Published values or direct measurement

Each land use

Forest

Nitrogen leaching

0.6–2.5

Vuorenmaa et al. ()

40–112

Published values or direct measurement

Each land use

Spring cereals

Nitrogen uptake

Crop growth rates

Winter cereals

Nitrogen uptake

30–116

Soil water NO3-N concentration

Direct measurement or monitoring database

Each land use

Grass

Nitrogen uptake

149–296

Information Centre of the Ministry of Agriculture and Forestry ()

Agriculture production

Mineralization

40–55

Rankinen et al. ()

Groundwater NO3-N concentration

Direct measurement or monitoring database

Each land use or subcatchment

Agriculture production

Denitriﬁcation

3–17

Svensson et al. (); Barton et al. ()

Forest

Denitriﬁcation

Soil water NH4-N concentration

Direct measurement or monitoring database

Each land use

Barton et al. ()

Groundwater NH4-N concentration

Direct measurement or monitoring database

Each land use or subcatchment

Source

concentrations during the fall of 2007 (Figure 4). Many animal producers in Finland apply manure to their ﬁelds in the autumn to empty their manure storage before winter. To address this issue, a fall manure application was added at the beginning of this calibration process. The mod-

et al. (). After satisfactory hydrologic calibration, nitro-

eled fall manure application rates in the calibration varied

gen calibration is then conducted. As a rule, if the

between 24 and 50 kg N ha–1 depending upon the crop.

hydrologic parameters are adjusted, the nutrient calibration

The simulated annual application rates of fertilizers/

process should be restarted.

manure did not exceed the regulation levels of the Nitrates

In this work, calibration of the nitrogen portion of the

Directive (EEC ) or the Finnish Agri-Environmental Pro-

INCA-N model was completed for the years 2003–2008

gramme, which promotes sustainability in agricultural

with the use of soft data. A ﬂow chart of the nitrogen cali-

practices (Rankinen et al. ). The addition of a new

bration process using soft data is shown in Figure 3. This

source of nitrogen required the calibration of the nitrogen

chart follows the example by Santhi et al. () for the

portion of the model to start at step A in Figure 3.

Soil and Water Assessment Tool (SWAT). An initial cali-

The soft data were used in step B (Figure 3), where the

bration was completed for the Yläneenjoki catchment by

simulated nitrogen process rates were compared to literature

Lepistö et al. (). One problem noted by Lepistö et al.

values. In this step of the calibration procedure, the quality

() was that a fall application of manure was missed in

of the calibration was judged primarily by the simulated

their calibration. This was a likely cause of the simulated

process rates, but the ﬁt of the in-stream nitrogen concen-

peak NO3-N concentrations being lower than the observed

trations

the

observed

concentrations

were

still

Figure 3

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

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Calibration procedure for the nitrogen portion of the INCA-N model using soft data.

considered as they show potential sources of error in the

experimental data. Leaching was the only process that did

calibration. The processes include leaching, plant uptake,

not have an associated process rate that can be adjusted.

mineralization, nitrification, denitrification and fixation.

The amount of leaching was based on the amount of ﬂow

The mass of nitrogen consumed or released by the individ-

through the soil and groundwater zones along with the

ual processes were modeled for each land use. The model

mass of nitrogen stored in these zones. Elevated fertilizer

parameters were adjusted for each land use so that the simu-

inputs or mineralization rates are potential causes of leach-

lated loads were in the range of values available from

ing rates being above the expected range.

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

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application of fertilizer at the wrong time to applying too little fertilizer for a certain crop. If a new source or sink was added to the model after a potential source of error was found, the nutrient calibration process was restarted at the beginning in step A. A change in timing or rate of fertilizer application has the potential to alter the annual amount of uptake, denitriﬁcation, nitriﬁcation and leaching. Once the land-based portion of the calibration had all of the loads in reasonable ranges and the general dynamics of the simulated concentrations followed the observed nutrient concentrations, the calibration process continued to step E of Figure 3. Here the simulated nutrient concentrations were compared to the observed nutrient concentrations. Figure 4

INCA-N simulated NO3-N concentrations from Calibration 1 and Calibration 2 compared to grab samples and continuous automatic monitoring for the Yläneenjoki catchment in 2007.

Based on this evaluation, the in-stream processes of nitrification and denitrification were adjusted for each reach to improve the goodness of fit. The calibration was completed

Step C (Figure 3) in the calibration process is closely linked to step B where the process rates were adjusted. The

after the rates of the in-stream processes were adjusted so that the goodness of ﬁt results were reasonable.

values reported in the load tables take into account both

The model results were evaluated based on visual com-

the soil and groundwater zones. Initial concentrations of

parison to the observed data, the R 2 value and the Nash–

NO3-N and NH4-N in both the groundwater and soil water

Sutcliffe (NS) efﬁciency. An NS efﬁciency greater than

zones are input values of INCA-N. The use of water samples

zero indicates that the model output is better than using

collected in the catchment can provide a guide to the accep-

the mean of the observed data (Nash & Sutcliffe ).

table range of initial values, but may not provide the true concentration if the samples were collected at a time other

Model validation

than the beginning of the modeling period, or if there is heterogeneity of concentrations within each subcatchment.

A model validation period was used to evaluate the model

Denitriﬁcation and leaching are the only two nitrogen pro-

predictions. The INCA-N input parameters that were set

cesses modeled by INCA-N in the groundwater zones, so

during calibration were tested for a different set of dates

the initial nutrient concentrations and rate of denitriﬁcation

that had an adequate set of observed nutrient concentrations

in the groundwater zone were adjusted to alter these process

and ﬂow rates in the same catchment. Visual inspection,

loads. Details about how these were adjusted in steps B and C

the R 2 value and the NS efﬁciency were used to evaluate

are discussed in the results and discussion section.

the validation results as for the calibration procedure. The

After the process rates were constrained to the expected range and the nitrogen concentrations in the land portion of

INCA-N model was validated for the Yläneenjoki catchment for the period 1997–2002.

the model were deemed to be reasonable, the calibration proceeded to step D (Figure 3). In this step, the timing and relative magnitude of simulated peaks and drops in concen-

RESULTS AND DISCUSSION

trations were examined to see if they matched the observed increases and decreases in concentrations. If the timing and

Calibration phase 1: preliminary calibration

magnitude of changes in concentrations did not match well, knowledge of the nitrogen processes and the study catch-

The preliminary calibration (Cal 1) is shown in Figure 4

ment were used to look for a potential source of error.

and was developed by adding a fall manure application

The cause of errors in this case ranged from modeling the

to the calibration completed by Lepistö et al. ().

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

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Comparing the discrete water quality samples to Cal 1 in

calibration procedure, the process rates required further exam-

2007, there are observed NO3-N concentrations above

ination after each model run. It was clearly evident from the

3 mg L

–1

that were not adequately simulated. The discrete

process rates in Cal 2 that the simulated denitriﬁcation rates

samples provided information about the nutrient concen-

(26–35 kg N ha–1 a–1) were too high in spring and winter cer-

trations for only a brief period of time. The continuous

eals when compared to the values reported in Table 2.

NO3-N data in the fall show that the NO3-N concen–1

Groundwater denitriﬁcation is included in the process

for longer than 2 weeks.

rates calculated in INCA-N, so the groundwater NO3-N con-

Visual inspection showed that simulated results do not

centrations were inspected as a part of the next calibration

adequately capture the long period of elevated NO3-N

loop. This incorporates both step B and step C in the calibration

concentration, despite the addition of a fall manure appli-

process. Once NO3-N reaches the deeper groundwater, a lack

cation to the model.

of carbon often reduces the potential for denitriﬁcation to

tration was above 3 mg L

This initial model calibration (Cal 1) was checked against

occur. Some soils have an organic layer that provides the

published values of annual nitrogen process rates to make

carbon needed for denitriﬁcation (Ambus & Lowrance ;

sure they were within the range of published values (Step B).

Hill et al. ) and this has repeatedly been shown to be true

These published values were obtained from primary scientiﬁc

in riparian zone soils (Gurwick et al. ; Messer et al. ).

literature, producer surveys or reports of local agricultural

In the INCA-N model, the water and nitrogen from the ground-

production practices. Examples of the published data used

water zone is modeled as ﬂowing directly into the stream. This

in this calibration are listed in Table 2. The results for Cal 1

does not allow for the modeling of a separate riparian or

show that the nitrogen uptake rates for spring and winter cer-

carbon-rich area where groundwater denitriﬁcation is likely

eals (111–121 kg N ha–1 a–1) were modeled at the upper end

to occur, so this NO3-N removal is incorporated into the

of the reported range. It is unlikely that the crop yields were

groundwater zone in the model calibration.

at the upper end of the range continuously for 6 years. The

The groundwater NO3-N concentrations for all of the land

modeled mineralization rates for both spring and winter cer-

uses from Cal 2 are shown in Figure 5. The initial groundwater

eals (71–101 kg N ha–1 a–1) were also too high.

concentrations are set for each subcatchment instead of each land use. Figure 5 shows an increase of groundwater concen-

Calibration phase 2: including soft data

tration over the 6-year calibration period for the three land uses where large amounts of fertilizer were applied. The con-

Using the information provided by these soft data, a second

stant increase shows that the groundwater denitriﬁcation

calibration loop was performed (Cal 2). Figure 4 shows the result of lowering the total nitrogen uptake and mineralization rates for spring and winter cereals to levels that were within the range of published values to produce Cal 2. The predicted NO3-N concentrations during the fall of 2007 decreased slightly in Cal 2 due to the reduction in mineralization rate. The biggest change from Cal 1 to Cal 2 was with respect to the peak NO3-N concentration values predicted for the summer. One observed concentration in early June was 4.7 mg L–1. Cal 1 showed a peak NO3-N concentration during this time of 0.5 mg L–1, while Cal 2 had a peak NO3-N concentration of 2.6 mg L–1, showing an improvement of the calibration for peak summer NO3-N concentrations. Simulated increases in NO3-N concentration during the summer were due to the reduction in the plant nitrogen uptake rates guided by soft data. In this portion of the

Figure 5

INCA-N simulated groundwater NO3-N concentrations from Calibration 2 for the Yläneenjoki catchment from 2003 through 2008.

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

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rate was set too low. Due to the setup of the model, adjusting

initial NO3-N concentration in Cal 2 caused a large amount

the groundwater processes at the subcatchment level is a pro-

of nitrogen to be removed through denitriﬁcation. With the

cess of balancing what is likely to occur for each land use.

adjustments in initial NO3-N concentration and groundwater

As an example, consider the two different land uses of

denitriﬁcation rates, the groundwater NO3-N concentrations

spring cereals and forests. If the initial NO3-N concentration

in the forest area approach a value near zero throughout

for the subcatchment is set too high, this will cause the

the calibration period. The land uses that are heavily fertilized

forested area to have high NO3-N leaching and a high rate

show a trend of increased groundwater concentrations, but

of denitriﬁcation. If the NO3-N concentration is set too

the impact of denitriﬁcation can be seen in the seasonal

low, the NO3-N leaching from land planted in spring cereals

dips in concentration that were not present in Cal 2 (Figure 5).

will be too low and the denitriﬁcation rate in these soils will

It is clear that having to set the initial groundwater concen-

be lower than normal. There will also be a large increase in

trations for each subcatchment has a large impact on the

the spring cereal groundwater NO3-N concentrations

modeling results, especially in short-term modeling studies,

throughout the simulation period.

as the groundwater concentrations change considerably during a modeling period of only 6 years (in this case

Calibration phase 3: denitriﬁcation and groundwater

±200%). Accurately simulating the amount of NO3-N that

nitrate

ﬂows from the groundwater to the stream is critical for correctly modeling stream water NO3-N concentrations.

The issue of denitriﬁcation rates being too high and the

In addition to the changes made to the groundwater

steady increase of groundwater NO3-N concentrations in

zone, the denitriﬁcation rates of spring and winter cereals

Cal 2 were addressed in Cal 3. One of the changes made in

(12–15 kg N ha–1 a–1) were adjusted in the soil water zone

Cal 3 was adjusting the initial groundwater NO3-N concen-

in Cal 3 so that the process rates were within the range

tration and the groundwater denitriﬁcation rate to better

found in the literature. The change in model output from

balance the process loads expected in each land use. The

adjusting the land based denitriﬁcation rates is shown in

resulting groundwater NO3-N concentrations are shown in

Figure 7. The simulated peak NO3-N concentrations

Figure 6. The initial NO3-N concentration was adjusted

increased from Cal 2 to Cal 3 from June 2007 through the

from 3 to 1.75 mg L–1 to lower the simulated denitriﬁcation

end of the year. NO3-N returns to base level concentrations

rates to reasonable values in the forested area. The higher

(<0.5 mg L–1) quicker in Cal 3 because there was less

Figure 6

INCA-N simulated groundwater NO3-N concentrations from Calibration 3 for

Figure 7

INCA-N simulated NO3-N concentrations from Calibration 2 and Calibration 3

the Yläneenjoki catchment from 2003 through 2008. (Note: y-axis range of

compared to grab samples and continuous automatic monitoring for the

NO3-N has been retained from Figure 5.)

Yläneenjoki catchment in 2007.

J. Randall Etheridge et al.

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Hydrology Research

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2014

contribution from the groundwater sources as a result of the

The ﬁnal NO3-N calibration is shown in Figure 9 for

changes in this step of the calibration process. This is most

2007 and the ﬁnal process parameters are in Table 3. The

evident in January and February 2007 where the NO3-N con-

R 2 value for the entire calibration period for Cal 1 (0.35)

centration drops from over 2 mg L–1 to less than 0.6 mg L–1 in

increased to 0.45 for the ﬁnal calibration. The NS efﬁciency

22 days in Cal 3 instead of 35 days as it was in Cal 2.

increased from 0.33 to 0.42 from Cal 1 to the ﬁnal

Calibration phase 4: adjusting N process rates The calibration process proceeded and adjustments were made to nitrogen process rates for all the different land uses to put them in the expected ranges, which produced Cal 4. These adjustments were made by following the same process (steps A–C) used for spring and winter cereals to produce Cal 2 and Cal 3. By visually inspecting the output, it was determined that the simulated NO3-N concentration dynamics matched the changes in observed values reasonably well and step D was completed. Final calibration Figure 9

The calibration process continued to step E and the in-

INCA-N simulated NO3-N concentrations from Calibration 3 and the ﬁnal calibration compared to grab samples and continuous automatic monitoring for the Yläneenjoki catchment in 2007.

stream process rates were adjusted to produce the final calibration. The in-stream denitrification rate required little adjustment to provide the best fit, so the impact of adjusting in-stream process rates is better illustrated using NH4-N. Figure 8 shows the reduction of in-stream NH4-N concentrations from Cal 4 to the final calibration by increasing

Table 3

Nutrient process parameters in the ﬁnal INCA-N calibration

Nutrient process

Land use

Parameter value

Soil water denitriﬁcation (m day–1)

Forest Spring cereal Winter cereal Grass Fallow Beets

0.0001 0.00025 0.0001 0.0001 0.0001 0.0003

Mineralization (kg N ha–1 day–1)

Forest Spring cereal Winter cereal Grass Fallow Beets

0.3 0.4 0.38 0.41 0.3 0.5

Nitriﬁcation (m day–1)

Forest Spring cereal Winter cereal Grass Fallow Beets

0.001 0.85 0.75 0.95 0.6 0.8

Groundwater denitriﬁcation (m day–1)

All

0.002

In-stream denitriﬁcation (day–1)

All

0.21

All

0.19

the in-stream nitriﬁcation rate.

Figure 8

INCA-N simulated NH4-N concentrations from Calibration 4 and the ﬁnal calibration compared to grab samples for the Yläneenjoki catchment in 2007.

–1

In-stream nitriﬁcation (day )

J. Randall Etheridge et al.

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calibration. The major differences in the model output were the peak NO3-N concentration values and how quickly the simulated NO3-N concentrations decreased after a peak. The final calibration showed higher simulated NO3-N concentrations during November 2007, but the concentrations were still lower than the observed values. The model output during April 2007 did not improve from Cal 1 to the final calibration. The Cal 1 output shows the NO3-N concentrations between 0.1 and 0.2 mg L–1 above the observed data. The final calibration shows peak concentrations 0.4 mg L–1 above the observed peak concentrations, but during that period some concentrations are lower than the observed data. The final model simulation does show a higher peak NO3-N concentration in June, when the observed concentration was 4.7 mg L–1. The results of the final calibration for 2003–2008 are shown in Figure 10. The R 2 and NS efficiency comparing the observed and simulated discharge were 0.69 and 0.67, respectively, for the whole calibration period. As stated earlier, the flow parameters were not altered during the calibration process described in this work. The timing of the observed discharge peaks was simulated well, but many of the observed peaks were higher than simulated flows. The variations between the model and the observed values could be caused by the inputs from WSFS not accurately capturing the spatial variability of precipitation in the catchment, or because the spatial heterogeneity of the catchment soils was not simulated in this semi-distributed model. The results of the NO3-N calibration for the entire period are shown in Figure 10 (R 2 ¼ 0.45; NS ¼ 0.42). The model simulated the low observed NO3-N concentrations in summer well. In 2005, the modeled NO3-N concentration does not drop to the low summer levels as quickly as the observed concentrations. The modeled maximum NO3-N concentrations were also lower than the highest observed concentrations during many periods, primarily during the winter months. These missed peaks could have been caused by modeled denitrification rates that were too high

Figure 10

Observed and simulated discharge, NO3-N and NH4-N concentrations at the outlet of the Yläneenjoki catchment as produced by the ﬁnal calibration (2003–2008).

in the winter. The shape of the simulated NH4-N curve ﬁt the

could be caused by the simulated ﬂow being above the

observed ﬂow and diluting the NH4-N concentrations simu-

value for NH4-N was 0.28 and the NS efﬁciency was 0.25.

lated during this time period. During the summer periods,

observed data well, based on visual inspection. The R

The observed NH4-N concentrations above 0.1 mg L–1 are

the simulated NH4-N concentrations dropped below

simulated well except in late 2005 and early 2006. This

0.05 mg L–1 for long periods of time, while the observed

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Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

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2014

concentrations are often above 0.05 mg L–1. This is especially noticeable in 2003 and 2007. It is possible that a point source of NH4-N that existed in the catchment was not simulated in the model. The high concentrations from a point source would not be diluted during the summer low-flow periods. The impact of a small point source may be more difficult to see during periods of higher flow. Model validation The model was validated for the years 1997–2002 and the model output is shown in Figure 11. The flow validation provided good results with R 2 ¼ 0.80 and NS ¼ 0.79. Although the goodness-of-fit statistics show good results, a visual inspection of the results show that most of the observed flow peaks were underestimated in the model. The timing of these peaks is modeled well, so the underestimation may have been caused by the a and b flow constants (responsible for relating discharge to mean flow velocity) being incorrect. It is also possible that the daily time series model inputs from WSFS could cause these errors. WSFS is used for flood prediction in Finland, so it is constantly being re-calibrated to most accurately model the most recent data. The inputs for this work were retrieved from WSFS in 2010, so the daily time series inputs for the validation period may not have been as accurate as they were for the calibration period. The NO3-N concentration results during the validation period were not as good as the flow results. The NO3-N validation produced an R 2 of 0.34 and an NS efficiency below 0. These results and a visual inspection indicate that the timing of peak concentrations was simulated well, but that overall the NO3-N concentrations were too high. The higher NO3-N concentrations were most obvious during each spring. The overestimation occurred during the spring snow melt before any fertilizer was applied to the fields. Most of the nitrogen process loads were within the expected range of values, with the exception of the leaching loads. The

Figure 11

Observed and simulated discharge, NO3-N and NH4-N concentrations at the outlet of the Yläneenjoki catchment from the validation period (1997–2002).

amount of nitrogen lost to leaching was higher than expected. The rates of denitriﬁcation were lower than they were in the

model, the soil water NO3-N concentrations and the mini-

calibration period, but were still reasonable.

mum temperature at which nitrogen processes are allowed

These results suggest that during the calibration period

should be investigated further.

the simulated denitriﬁcation rates were high enough to pre-

The model performed well during the validation period

vent excess leaching from occurring. To further improve the

for simulating NH4-N concentrations with an R 2 of 0.40 and

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an NS efﬁciency of 0.25. The timing of peaks in observed

NO3-N concentrations. However, the nitrogen process

NH4-N concentrations was simulated well. The modeled

rates in Cal 1 were not within the range of published

NH4-N concentrations are above the observed concen-

values and were not as accurate in representing the pro-

trations from late 1997 to the summer of 1998. There are a

cesses actually occurring in the catchment as the ﬁnal

–1

calibration. Using soft data to constrain process rates does

that are not simulated well near the end of the validation

not always lead to better goodness-of-ﬁt results as it did in

few observed NH4-N concentrations above 0.25 mg L

period. The simulated summer NH4-N concentrations are

this case, but better goodness of ﬁt should be sacriﬁced for

a mix of overestimation and underestimation of observed

a model that produces a more accurate representation of

values. The model does a better job of modeling the

the system (Seibert & McDonnell ; Rankinen et al.

summer NH4-N concentrations during the validation

) and the potential that future simulations outside the

period than it does during the calibration period.

calibration period may be more accurate.

The two short periods of continuous water quality data

Sensitivity analysis provides a method of determining

provided a glimpse into the usefulness of continuous water

what soft data are most important for model calibration.

quality monitoring for calibration of nutrient models. Collec-

Rankinen et al. () showed that, for simulations in an

tion of continuous records provides more insight into

agriculturally dominated catchment in Finland, the INCA-

watershed hydrology and nutrient transformations than

N model was most sensitive to parameters that altered the

that provided by discrete sampling (Kirchner et al. ).

nutrient process rates in the primary agricultural land use

The continuous data in this study showed that a signiﬁcant

in the catchment. In the Yläneenjoki catchment, further

export of NO3-N was missed in the initial simulations.

research in quantifying the nitrogen process rates in spring

Long-term continuous water quality monitoring may

cereals would likely be the most useful experimentation

prove useful for reducing parameter uncertainty. In this

for further improving the model calibration. The sensitivity

study, however, continuous data were not available over a

of the parameters change between watersheds with some

long enough period of time to test its impact on constraining

of the variation being caused by differences in the land use

the model. Raat et al. () found that continuous data may

and the relative importance of groundwater and surface

not prove useful enough to warrant the effort and expense of

water (McIntyre et al. ; Rankinen et al. ; Futter

its collection, based on simulations in a virtual catchment.

et al. ). To better guide modeling and data collection

The effort required to collect continuous data is being

efforts, a sensitivity analysis should be conducted following

reduced through the introduction of new technology, so

initial calibration. The results of the sensitivity analysis

the collection of this high-frequency data should be encour-

could direct resources to areas that need more research or

aged in future modeling studies.

further constraints on the model parameters.

The structure of the INCA-N model makes it possible for

Restrictions on ﬁnancial and time resources often pre-

two wrongs to result in a numerically correct answer. For

vent modelers from conducting experiments to measure the

instance, if mineralization rates in the model were set too

various nitrogen process rates that are simulated in the

high, higher simulated denitriﬁcation rates could remove

INCA-N model. Process rates for biogeochemical processes,

excess nitrogen resulting in reasonable NO3-N concen-

such as mineralization, denitriﬁcation and leaching, are

trations during the calibration period. In this case study,

often available in a similar geographic region that can be

published literature values and other soft data were used

used as soft data. The results of ﬁeld experiments to measure

to restrict nitrogen process rates to a reasonable range of

biogeochemical process rates will generally have such high

values. Comparing the initial calibration to the ﬁnal cali-

variability due to the heterogeneity of soils that using limited

bration shows an improvement in the goodness-of-ﬁt

resources to measure these rates is not recommended if the

statistics, but does not show a visual improvement in the

sole purpose is for use in calibration of the INCA-N model.

results over the whole calibration period. A comparison of

With regards to biogeochemical processes, effort should

Cal 1 and the ﬁnal calibration results during April 2007

be expended in ﬁnding the previous studies with the most

does not show improvement in the simulation of in-stream

similar climate, hydrologic regime and soil type that use a

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Hydrology Research

45.1

2014

quality method of measuring the process rate. When

processes can be improved through the use of soft data to

resources for collection of soft data are limited, it is rec-

constrain the nitrogen process loads to reasonable values.

ommended that the modeler focus on gaining information

The modeler should also pay attention to model output

on the local agricultural practices and crop yields. Variances

other than the in-stream nitrogen concentrations to improve

in agricultural practices, such as using crop residues as

the accuracy of the model, as was illustrated through the

animal feed instead of leaving them on the ﬁeld surface,

examination of groundwater NO3-N concentrations. A

can have a large impact on nutrient loads in a catchment

thorough examination of all model outputs and the use of

and can vary widely within a region (Lagzdins et al. ).

soft data to constrain nitrogen process rates does not guaran-

Information on crop yields, the use of animal manure and

tee that the resulting calibration is a completely accurate

fertilization rates is unlikely to be available in the scientiﬁc

depiction of the modeled catchment. Further work should

literature, but may be available from government publi-

be done to increase the conﬁdence in model calibrations;

cations. This local information that cannot be obtained

modeling scenarios of climate, land use and management

from the scientiﬁc literature is where modelers should

changes should proceed with the knowledge of potential

focus their resources for collection of soft data.

sources of uncertainty within the INCA-N model.

The results of the model validation show that the use of published process rates to assist in calibrating the model does not guarantee that the calibration is a completely accu-

ACKNOWLEDGEMENTS

rate depiction of the processes occurring in the catchment. Despite the in-stream NO3-N concentrations being modeled

The authors would like to thank the two anonymous

reasonably well in the calibration period, the simulated con-

reviewers for their helpful comments. This material is

centrations were above the observed concentrations in the

based upon work supported by the National Science

validation period. The timing of major changes in the concen-

Foundation under Grant No. DGE-0750733 and by the

trations was simulated well, but the value of the simulated

EU REFRESH project (FP7-ENV-2009-1/244121).

concentration was always too high. This result points to at least one nitrogen process being modeled incorrectly. It is possible that more information could be gained through vali-

REFERENCES

dation of this calibration over a period of time that had different conditions in climate, land use or agricultural practices (Kirchner ). To further increase the accuracy of semi-distributed model in heterogeneous catchments, longterm calibrations are recommended (Wade et al. ). Long-term simulations will allow for the impact of changes in climate, agricultural practices and land use to be observed in the calibration phase of the model. These changes are not as drastic in short-term modeling periods and cannot be adjusted for in the calibration. The challenge to completing long-term simulations is the availability of long-term observed data to compare to the results of the model.

CONCLUSIONS The results of this case study show that the accuracy of the INCA-N representation of a catchment and its internal

Ambus, P. & Lowrance, R.  Comparison of denitrification in two riparian soils. Soil Science Society of America Journal 55 (4), 994–997. Bärlund, I., Rankinen, K., Järvinen, M., Huitu, E., Veijalainen, N. & Arvola, L.  Three approaches to estimate inorganic nitrogen loading under varying climatic conditions from a headwater catchment in Finland. Hydrology Research 40 (2–3), 167–176. Barton, L., McLay, C. D. A., Schipper, L. A. & Smith, C. T.  Annual denitrification rates in agricultural and forest soils: a review. Soil Research 37 (6), 1073–1094. Cherry, K. A., Shepherd, M., Withers, P. J. A. & Mooney, S. J.  Assessing the effectiveness of actions to mitigate nutrient loss from agriculture: A review of methods. Science of the Total Environment 406 (1–2), 1–23. EEC  Council Directive 91/676/EEC of 12 December 1991 concerning the protection of waters against pollution caused by nitrates from agricultural sources. Official Journal L 375 (31), 1–8. Futter, M., Helliwell, R., Hutchins, M., Aherne, J. & Whitehead, P.  Modelling the effects of changing climate and nitrogen

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

deposition on nitrate dynamics in a Scottish mountain catchment. Hydrology Research 40 (2–3), 153–166. Galloway, J. N., Townsend, A. R., Erisman, J. W., Bekunda, M., Cai, Z., Freney, J. R., Martinelli, L. A., Seitzinger, S. P. & Sutton, M. A.  Transformation of the nitrogen cycle: Recent trends, questions, and potential solutions. Science 320 (5878), 889–892. Granlund, K., Rankinen, K. & Lepistö, A.  Testing the INCA model in a small agricultural catchment in southern Finland. Hydrology and Earth System Sciences 8 (4), 717–728. Gurwick, N. P., Groffman, P. M., Yavitt, J. B., Gold, A. J., Blazejewski, G. & Stolt, M.  Microbially available carbon in buried riparian soils in a glaciated landscape. Soil Biology & Biochemistry 40 (1), 85–96. HELCOM  The Fifth Baltic Sea Pollution Load Compilation (PLC-5). In Baltic Sea Environment Proceedings No. 128. Helsinki Commission. Helsinki. Heng, H. H. & Nikolaidis, N. P.  Modeling of nonpoint source pollution of nitrogen at the watershed scale. Journal of American Water Resources Association 34 (2), 359–374. Hill, A. R., Vidon, P. G. & Langat, J.  Denitrification potential in relation to lithology in five headwater riparian zones. Journal of Environmental Quality 33 (3), 911–919. Howarth, R. W., Sharpley, A. & Walker, D.  Sources of nutrient pollution to coastal waters in the United States: Implications for achieving coastal water quality goals. Estuaries 25 (4B), 656–676. Hyvärinen, V. (ed.)  Hydrological Yearbook 1995. The Finnish Environment 280 ed. Finnish Environment Institute, Helsinki. Information Centre of the Ministry of Agriculture and Forestry  Yearbook of Farm Statistics 2006. Information Centre of the Ministry of Agriculture and Forestry, Helsinki. Jarvie, H. P., Wade, A. J., Butterfield, D., Whitehead, P. G., Tindall, C. I., Virtue, W. A., Dryburgh, W. & McGraw, A.  Modelling nitrogen dynamics and distributions in the River Tweed, Scotland: an application of the INCA model. Hydrology and Earth System Sciences 6 (3), 433–453. Kirchner, J. W.  Getting the right answers for the right reasons: Linking measurements, analyses, and models to advance the science of hydrology. Water Resources Research 42 (3), W03S04. Kirchner, J. W., Feng, X. H. & Neal, C.  Fractal stream chemistry and its implications for contaminant transport in catchments. Nature 403 (6769), 524–527. Koskiaho, J., Lepistö, A., Tattari, S. & Kirkkala, T.  Online measurements provide more accurate estimates of nutrient loading: a case of the Ylä neenjoki river basin, southwest Finland. Water Science and Technology 62 (1), 115–122. Lagzdins, A., Jansons, V., Sudars, R. & Abramenko, K.  Scale issues for assessment of nutrient leaching from agricultural land in Latvia. Hydrology Research 43 (4), 383–399. Lepistö, A., Granlund, K., Kortelainen, P. & Räike, A.  Nitrogen in river basins: Sources, retention in the surface

Hydrology Research

45.1

2014

waters and peatlands, and fluxes to estuaries in Finland. Science of the Total Environment 365 (1), 238–259. Lepistö, A., Huttula, T., Bärlund, I., Granlund, K., Härmä, P., Kallio, K., Kiirikki, M., Kirkkala, T., Koponen, S., Koskiaho, J., Kotamäki, N., Lindfors, A., Malve, O., Pyhälahti, T., Tattari, S. & Törmä, M.  New measurement technology, modelling and remote sensing in the Säkylän Pyhäjärvi area – Catchlake. Reports of Finnish Environment Institute 15, 13–43. Lunn, R., Adams, R., Mackay, R. & Dunn, S.  Development and application of a nitrogen modelling system for large catchments. Journal of Hydrology 174 (3), 285–304. Mattila, H., Kirkkala, T., Salomaa, E., Sarvala, J. & Haliseva-Soila, M. (eds)  Pyhäjärvi. Pyhäjärvi-instituutin julkaisuja 26 ed. Pyhäjärven suojelurahasto. McIntyre, N., Jackson, B., Wade, A. J., Butterfield, D. & Wheater, H. S.  Sensitivity analysis of a catchment-scale nitrogen model. Journal of Hydrology 315 (1–4), 71–92. Messer, T. L., Burchell II, M. R., Grabow, G. L. & Osmond, D. L.  Groundwater nitrate reductions within upstream and downstream sections of a riparian buffer. Ecological Engineering 47, 297–307. Nash, J. E. & Sutcliffe, J. V.  River flow forecasting through conceptual models part I – a discussion of principles. Journal of Hydrology 10 (3), 282–290. Raat, K. J., Vrugt, J. A., Bouten, W. & Tietema, A.  Towards reduced uncertainty in catchment nitrogen modelling: quantifying the effect of field observation uncertainty on model calibration. Hydrology and Earth System Sciences 8 (4), 751–763. Räike, A., Pietiläinen, O. P., Rekolainen, S., Kauppila, P., Pitkänen, H., Niemi, J., Raateland, A. & Vuorenmaa, J.  Trends of phosphorus, nitrogen and chlorophyll a concentrations in Finnish rivers and lakes in 1975–2000. Science of the Total Environment 310 (1–3), 47–59. Rankinen, K., Granlund, K., Futter, M. N., Butterfield, D., Wade, A. J., Skeffington, R., Arvola, L., Veijalainen, N., Huttunen, I. & Lepistö, A.  Controls on inorganic nitrogen leaching from Finnish catchments assessed using a sensitivity and uncertainty analysis of the INCA-N model. Boreal Environment Research 18. http://www.borenv.net/BER/ pdfs/preprints/Rankinen.pdf. Rankinen, K., Lepistö, A. & Granlund, K.  Hydrological application of the INCA model with varying spatial resolution and nitrogen dynamics in a northern river basin. Hydrology and Earth System Sciences 6 (3), 339–350. Rankinen, K., Karvonen, T. & Butterfield, D.  An application of the GLUE methodology for estimating the parameters of the INCA-N model. Science of the Total Environment 365 (1– 3), 123–139. Rankinen, K., Salo, T., Granlund, K. & Rita, H.  Simulated nitrogen leaching, nitrogen mass field balances and their correlation on four farms in south-western Finland during the period 2000–2005. Agricultural and Food Science 16, 387–408.

J. Randall Etheridge et al.

Reducing uncertainty in model calibration and validation by using soft data

Rankinen, K., Valpasvuo-Jaatinen, P., Karhunen, A., Kenttamies, K., Nenonen, S. & Bärlund, I.  Simulated nitrogen leaching patterns and adaptation to climate change in two Finnish river basins with contrasting land use and climatic conditions. Hydrology Research 40 (2–3), 177–186. Refsgaard, J. C.  Chapter 2: Terminology, modelling protocol and classification of hydrological model codes. In: Distributed Hydrological Modelling (M. B. Abbott & J. C. Refsgaard, eds). Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 17–39. Salo, T. & Turtola, E.  Nitrogen balance as an indicator of nitrogen leaching in Finland. Agriculture, Ecosystems & Environment 113 (1–4), 98–107. Santhi, C., Arnold, J. G., Williams, J. R., Dugas, W. A., Srinivasan, R. & Hauck, L. M.  Validation of the SWAT model on a large river basin with point and nonpoint sources. Journal of the American Water Resources Association 37 (5), 1169–1188. Seibert, J. & McDonnell, J. J.  On the dialog between experimentalist and modeler in catchment hydrology: Use of soft data for multicriteria model calibration. Water Resources Research 38 (11), 1241. Svensson, B. H., Klemedtsson, L., Simkins, S., Paustian, K. & Rosswall, T.  Soil denitrification in three cropping systems characterized by differences in nitrogen and carbon supply. Plant and Soil 138 (2), 257–271. Townsend, A. R., Howarth, R. W., Bazzaz, F. A., Booth, M. S., Cleveland, C. C., Collinge, S. K., Dobson, A. P., Epstein, P. R., Keeney, D. R., Mallin, M. A., Rogers, C. A., Wayne, P. & Wolfe, A. H.  Human health effects of a changing global nitrogen cycle. Frontiers in Ecology and the Environment 1 (5), 240–246. Vehviläinen, B. & Huttunen, M.  Hydrological forecasting and real time monitoring in Finland: the Watershed Simulation and Forecasting System (WSFS). Finnish Environment Institute. Available at: http://www.ymparisto.fi/download. asp?contentid=115457&lan=en. Vitousek, P. M., Aber, J. D., Howarth, R. W., Likens, G. E., Matson, P. A., Schindler, D. W., Schlesinger, W. H. & Tilman, D. G.  Human alteration of the global nitrogen cycle: Sources and consequences. Ecological Applications 7 (3), 737–750.

Hydrology Research

45.1

2014

Vuorenmaa, J., Rekolainen, S., Lepistö, A., Kenttämies, K. & Kauppila, P.  Losses of nitrogen and phosphorus from agricultural and forest areas in Finland during the 1980s and 1990s. Environmental Monitoring & Assessment 76 (2), 213–248. Wade, A. J., Butterfield, D. & Whitehead, P. G.  Towards an improved understanding of the nitrate dynamics in lowland, permeable river-systems: Applications of INCA-N. Journal of Hydrology 330 (1–2), 185–203. Wade, A. J., Durand, P., Beaujouan, V., Wessel, W. W., Raat, K. J., Whitehead, P. G., Butterfield, D., Rankinen, K. & Lepistö, A.  A nitrogen model for European catchments: INCA, new model structure and equations. Hydrology and Earth System Sciences 6 (3), 559–582. Wade, A. J., Jackson, B. M. & Butterfield, D.  Overparameterised, uncertain ‘mathematical marionettes’ – How can we best use catchment water quality models? An example of an 80-year catchment-scale nutrient balance. Science of the Total Environment 400 (1–3), 52–74. Ward, M. H., Mark, S. D., Cantor, K. P., Weisenburger, D. D., Correa-Villasenor, A. & Zahm, S. H.  Drinking water nitrate and the risk of non-Hodgkin’s lymphoma. Epidemiology 7 (5), 465–471. Whitehead, P. G., Wilson, E. J. & Butterfield, D. a A semi-distributed Integrated Nitrogen model for multiple source assessment in Catchments (INCA). Part I: model structure and process equations. Science of the Total Environment 210 (1–6), 547–558. Whitehead, P. G., Wilson, E. J., Butterfield, D. & Seed, K. b A semi-distributed integrated flow and nitrogen model for multiple source assessment in catchments (INCA). Part I: application to large river basins in south Wales and eastern England. Science of the Total Environment 210–211 (0), 559–583. Winsemius, H., Schaefli, B., Montanari, A. & Savenije, H.  On the calibration of hydrological models in ungauged basins: A framework for integrating hard and soft hydrological information. Water Resources Research 45 (12), W12422.

First received 13 February 2013; accepted in revised form 5 May 2013. Available online 25 June 2013

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Effect of temperature on streambed vertical hydraulic conductivity Weihong Dong, Gengxin Ou, Xunhong Chen and Zhaowei Wang

ABSTRACT In this study, in situ and on-site permeameter tests were conducted in Clear Creek, Nebraska, USA to evaluate the effect of water temperature on streambed vertical hydraulic conductivity Kv. Fifty-two sediment cores were tested. Five of them were transferred to the laboratory for a series of experiments to evaluate the effect of water temperature on Kv. Compared with in situ tests, 42 out of the 52 tests have higher Kv values for on-site tests. The distribution of water temperature at the approximately 50 cm depth of streambed along the sand bar was investigated in the ﬁeld. These temperatures had values in the range 14–19 C with an average of 16 C and had an increasing trend W

along the stream ﬂow. On average, Kv values of the streambed sediments in the laboratory tests increase by 1.8% per 1 C increase in water temperature. The coarser sandy sediments show a W

greater increase extent of the Kv value per 1 C increase in water temperature. However, there is no W

Weihong Dong Key Laboratory of Groundwater Resources and Environment, Ministry of Education, Jilin University, Changchun 130021, China Weihong Dong Gengxin Ou (corresponding author) Xunhong Chen Zhaowei Wang School of Natural Resources, University of Nebraska-Lincoln, Lincoln, NE 68583, USA E-mail: ougengxin@gmail.com

distinct increasing trend of Kv value for sediment containing silt and clay layers. Key words

| clear creek, streambed sediment, temperature, vertical hydraulic conductivity

INTRODUCTION Streambed vertical hydraulic conductivity Kv is a key par-

can be expressed with respect to the ﬂuid and medium

ameter in modeling surface water and groundwater

properties:

interactions and simulation of contaminant transport in the hyporheic zone. A higher streambed Kv produces a more intensive exchange of water both in quantity and quality. Chen & Shu () reported that a higher streambed Kv

K¼

kρg μ

(1)

induces a higher depletion of stream water due to ground-

where k is the intrinsic permeability; ρ is the density of

water pumping nearby streams. It is therefore of great

water; μ is the dynamic viscosity and g is the acceleration

signiﬁcance for hydrogeologists to estimate streambed Kv

due to gravity. The intrinsic permeability k is a property of

accurately and cost-effectively for water resources manage-

the porous medium independent of the ﬂuid. Hydraulic con-

ment. Measurement of Kv can be conducted either in the

ductivity for a given medium therefore depends mainly on

laboratory or in the ﬁeld by different methods (Bagarello et al. ; Butler et al. ; Dietze & Dietrich ). The standpipe method has proven to be an easily performed

the ﬂuid viscosity. The viscosity of water is a function of temperature such that (Fulcher ):

and economical method to measure Kv in situ, on-site or in the laboratory (Chen , , ; Cheng & Chen

μ ¼ A × 10B=(T C)

(2)

; Song et al. ; Chen et al. ; Genereux et al. ; Dong et al. ).

where T is temperature (K); A ¼ 2.414 × 10 2 mPa; B ¼

For saturated porous sediments, hydraulic conductivity

247.8 K; and C ¼ 140 K. The viscosity of water decreases

K is derived from Darcy’s law and Newton’s equation and

with temperature. Equations (1) and (2) indicate that the

doi: 10.2166/nh.2013.021

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Hydrology Research

45.1

2014

hydraulic conductivity is strongly dependent on water temp-

& Moore ). In the Sierra Nevada Mountains, for

erature and will increase exponentially with temperature

example, the annual stream temperature variations can

(Darzi et al. ). The temperature of water entering the

range from 0 to 25 C. In summer, diurnal stream tempera-

soil or variation in soil temperature therefore has a direct

ture ﬂuctuated by as much as 30–40% of the annual

impact on soil hydraulic conductivity via the effect of temp-

variations in two large streams, due to reduced stream

erature on water’s viscosity (Kresic ; Ma & Zheng ).

ﬂows and increased atmospheric heating (Constantz ).

Early soil column studies also reported that soil hydraulic

Conant () also observed a 9 C spatial change in temp-

conductivity increased with soil column temperature; this

eratures at both the Pine streambed surface and a depth of

change was partly or entirely attributed to a decrease in

20 cm. Considerable temperature changes of stream water

soil water viscosity (Haridasan & Jensen ). Many

and streambed are obvious both spatially and temporally,

researchers have found that soils showed an increase of

and they can affect the Kv values of streambed as mentioned

one to two orders of magnitude in hydraulic conductivity

above.

after freeze–thaw conditions (Othman et al. ; Konrad

Although the diurnal and seasonal temperature changes

& Samson ). The magnitude of hydraulic conductivity

in river system and the inﬂuence of temperature on hydrau-

is therefore strongly temperature dependent as a result of

lic conductivity are well known, the effect of temperature

the strong temperature sensitivity of the viscosity of water.

variations on determination of streambed hydraulic conduc-

The effect of temperature should be taken into account

tivity has not experienced as much interest. Very few

when measuring hydraulic conductivity.

existing studies examine the effect of temperature on

Spatial and temporal variability of temperature in a river

streambed vertical hydraulic conductivity, except for some

system is universal; it is inﬂuenced by numerous natural

studies of temperature effect on soil permeability. The objec-

variables such as solar radiation, air temperature, ground

tives of this study were: (1) to investigate the distribution of

temperature, precipitation, surface water inﬂows and

water temperature at about 50 cm depth of streambed along

groundwater exchanges (Sinokrat & Stefan ). The

Clear Creek sand bar in Nebraska, USA; and (2) to evaluate

exchange of water between the river and shallow aquifer

the magnitude of the temperature effect on Kv of Clear

plays a key role in inﬂuencing temperature not only in

Creek streambed.

rivers, but also in their underlying sediments (Baskaran et al. ). In a losing system, the sediment temperature is inﬂuenced by river temperature as the seepage ﬂux is

METHODS

downwards. In a gaining river, sediment temperature is inﬂuenced by groundwater temperature as the ﬂux is

The determination of streambed Kv involved three steps in

upwards (Silliman & Booth ; Bendjoudi et al. ).

this study: in situ permeameter test, on-site permeameter

The temperature of sediment at different depths of

test and in-laboratory permeameter test. Details of the test

streambed is varied because of the exchange of stream

procedures are described as follows.

water and groundwater in the hyporheic zone (Evans & Petts ; Alexander & Caissie ; Su et al. ;

In situ permeameter test

Hoehn & Cirpka ; Schmidt et al. ; Baskaran et al. ). Temperature has been used as a good tracer in

The in situ falling head permeameter test procedure for

the study of vertical hydraulic conductivity variation and

streambed has been well documented (Chen , ;

interactions between stream water and groundwater (Con-

Song et al. ; Genereux et al. ; Cheng et al. ).

stantz & Thomas ; Ronan et al. ; Hatch et al.

In this study, a transparent plastic tube of length 147 cm

; Westhoff et al. ).

and inner diameter 5.1 cm was vertically pushed to a

The characteristics of temperature variability of stream

depth of about 50 cm in the streambed. This depth was

water and streambed are well documented in many rivers

chosen at which to conduct a permeameter test for the fol-

(Constantz ; Conant ; Cadbury et al. ; Leach

lowing two reasons: (1) the active hyporheic zone depth

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Hydrology Research

45.1

2014

was commonly reported to be about 50 cm (Schindler &

Being held vertically by a tripod, the plastic sediment core

Krabbenhoft ; Weigelhofer & Waringer ); and (2)

liner acted as a container for permeameter tests. Stream

when the ratio of sediment length in the tube Lv to the

water was continuously added to the upper end until the

inner diameter of the tube D is close to 10, the estimation

bucket placed under the tube overﬂowed, which ensured

error of Kv can be minimized by arbitrarily choosing a

the fully saturated condition of sediment during the falling

value of m in Equation (3) (Chen ).

head test. The water level within the tube fell as the test

The vertical hydraulic conductivity Kv is calculated as

began. A series of drawdown of the water level was measured and recorded (Chen et al. ).

(Hvorslev ):

For on-site permeameter tests, Kv was calculated accordπD þ Lv Kv ¼ 11m ln (h1 =h2 ) (t2 t1 )

ing to Darcy’s law: (3) Kv ¼

where h1 and h2 are the hydraulic heads measured inside the pipe at elapsed times t1 and t2, respectively; and pffiffiffiffiffiffiffiffiffiffiffiffiffiffi m ¼ Kh =Kv (where Kh is the horizontal hydraulic conductivity of the channel sediment), which is often unknown at

(4)

Equation (4) does not require the m term used in Equation (3), reducing uncertainty. The measurement procedure of sediment temperature at

the time of computation. Lu et al. (b) suggested an average value of 2.37 for Kh =Kv at this study site. If Lv ¼ 10D, a

Lv ln (h1 =h2 ) (t2 t1 )

50 cm depth in streambed is described in Dong et al. ().

choice of m ¼ 1 or m ¼ 10 in Equation (3) gives a very small difference in the result of Kv (Chen ). In this study, m ¼ 2 was applied in the Kv computation for in situ permeameter tests.

In-laboratory permeameter test After the in situ and on-site tests, ﬁve of the streambed cores (IV-1-A, IV-1-B, IV-4, IV-5 and VI-3) were transferred to the

On-site permeameter test

laboratory for permeameter tests. These ﬁve sediment cores consist mainly of sand and gravel, but their structures

An on-site falling head permeameter test was conducted

and sediment compositions are different. The objective of

immediately in a water bucket on the stream bank after

the in-laboratory permeameter test was to examine the

the in situ test was ﬁnished. The test used the same sediment

dependence of Kv on water temperature changes.

core as that used for the in situ test.

A series of in-lab falling head permeameter tests were

After the in situ test at each location, the tube contain-

conducted on the ﬁve sediment cores. During these tests,

ing sediment core was pulled out of the streambed

water temperature in the bucket was adjusted to 10, 15, 23,

following the methods described below. Stream water was

30 and 40 C. Water used in the experiment came from the

poured into the tube to fully ﬁll the tube and a rubber cap

tap in the laboratory with a temperature of about 23 C.

was secured on the top of the tube to disconnect the sedi-

The desired water temperature was maintained by adding

ment and water inside the tube from the atmosphere. The

ice or hot water in the bucket. The water temperature was

tube with the sediment core was then slowly pulled out

measured by the Multi-Parameter Testr35 during the falling

upright from the streambed. This procedure was to prevent

head permeameter test. Air temperature in the laboratory

sediment dropping from the lower end of the tube. After

was accordingly set at 10, 15, 23 and 30 C by the air condi-

the tube and sediment were brought out of the stream

tioner during the tests; air temperature at 40 C was hard to

water, the bottom end of the tube was immediately covered

maintain by the air conditioner in the laboratory, so was

by several layers of ﬁne wire mesh. Water in the tube could

simply maintained at 30 C for the permeameter tests at

seep out but sediment particles could not pass through the

40 C water temperature. The impact of air temperature on

mesh. The length of the sediment core was measured.

the falling head permeameter test was limited because the

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

tests for core IV-1-A, IV-1-B, IV-4 and IV-5 lasted no more

Hydrology Research

45.1

2014

STUDY AREA AND TEST SITES

than 10 min and no more than 20 min for core VI-3. However, by controlling air temperature, the temperature

The study area is located in Clear Creek, Nebraska, USA

difference between air and water can be minimized which

(Figure 1; Dong et al. ). Clear Creek was chosen for this

helps to maintain water temperatures during the test.

study based on its two advantages. One is that Clear Creek is

Before each in-lab permeameter test, water with the

a gaining stream according to the in situ permeameter tests

same temperature as that in the bucket was poured into

conducted in 2010 (Lu et al. a). For a small creek with shal-

the top part of the tube until water in the bucket overﬂowed.

low water depth, the stream water temperature can be easily

After ﬁnishing in-lab falling head permeameter tests, Kv

warmed due to strong solar radiation in the summer. Accord-

values were calculated using Equation (4). Each permea-

ing to the historic records of the US Geological Survey

meter test for each sediment core was carried out three

(USGS), the stream water temperature can reach about 30 C

times at a speciﬁc temperature in order to reduce exper-

compared to about 15 C for groundwater. The water tempera-

imental bias. The average Kv value produced by the three

ture gradient in the vertical direction was obvious in Clear

falling head permeameter tests was regarded as the vertical

Creek sediment. The other advantage is that an electrical con-

hydraulic conductivity for each core at a speciﬁc water

ductivity log and a sequence of sediment cores were collected

temperature.

in the bank with Geoprobe, which suggested unstratiﬁed

Figure 1

Location of the study site (modiﬁed from Dong et al. (2012)).

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Hydrology Research

45.1

2014

streambed sediments. However, water temperature differences

streambed. Figure 2 shows the locations of permeameter

between stream water and groundwater were not measured in

tests conducted in the channel of Clear Creek. Twenty-one

2010 and on-site permeameter tests had not been conducted.

tests were conducted along the Clear Creek ﬂow direction

Fifty-two different locations were selected to conduct

and close to the left bank, with an interval of 1.6 m between

both in situ and on-site falling head permeameter tests to

two adjacent locations. The other 31 test locations were

determine the vertical hydraulic conductivity Kv of the

arranged in six transects (I–VI) along the creek, with ﬁve locations along each transect except for the test location IV-1-B which is close to IV-1-A (Figure 2).

RESULTS Spatial distribution of Kv The Kv results from both in situ and on-site permeameter tests at the 52 locations are shown in Figure 3. The Kolmogorov-Smirnov tests indicate that both on-site and in situ Kv values are from normally distributed populations. As shown in Figure 3, these Kv values have a signiﬁcant spatial variability. In situ Kv values vary from 0.4 to 48.0 m day–1 with an average of 15.9 m day–1 whereas on-site Kv values fall within the range 0.2–85.0 m day–1 with an average of 24.0 m day–1. About 81% (42 of the 52 test locations) of the Kv values obtained by the on-site tests (on-site Kv) are greater than in situ values for the same sediment core. Spatial variation of temperature Water temperature at the 50 cm depth (the same as sediFigure 2

Schematic of permeameter test locations.

Figure 3

Kv values from in situ permeameter tests and on-site permeameter tests at 52 locations.

ment

temperature

the

50 cm

depth)

and

water

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Hydrology Research

45.1

2014

temperature of a sample collected in a bucket are plotted in

(which shows a slightly decreasing trend). A thin layer of

Figure 4 for each test location. The water temperatures at the

clay with black organic matter was observed at the bottom

depth of 50 cm vary over the range 14–19 C with an average W

of 16 C. The water in the bucket, taken from the creek, has W

temperatures ranging from 19.5 to 30.9 C with an average W

of 23.9 C. The differences between on-site and in situ W

water temperatures ranged from 1 to 15.5 C with an average

end of sediment core VI-3, which was not present in the other four sediment cores. In addition, after the experiments on core VI-3 sediment stratiﬁcation was observed in the lower part of the sediment core, which can resist the movement of water in the sediments.

of 7.9 C. In addition, stream water temperature was also dependent upon time of day due to the inﬂuences of solar radiation and air temperature (Sinokrat & Stefan ).

DISCUSSION

Some of the on-site permeameter tests were performed in the morning while others were performed in the afternoon.

The data in Table 1 indicate that the Kv values of sediment

Water temperature at the 50 cm depth under streambed is

cores IV-1-A, IV-1-B, IV-4, IV-5 and VI-3 change by 3.1,

controlled by groundwater, and remains almost constant

1.8, 1.0, 1.5 and –1.5%, respectively, for an increase of

during the day relative to the stream water (Loheide &

1 C in water temperature. The average increase in Kv is

Gorelick ). Water temperatures of the samples collected

1.8% with 1 C increase in water temperature (if excluding

in the bucket ﬂuctuate over a greater range (Figure 4).

the sediment core VI-3 due to its inverse temperature

effect compared to other cores). In-laboratory water temperature effect on Kv

Although the ﬁve sediment cores consist mainly of sand and gravel, their structures and sediment compo-

Five sediment cores of different structure and sediment com-

sitions are different. Sediment cores IV-1-A, IV-1-B and

position were selected on which to conduct experiments

VI-3 have a similar structure with coarse particles in the

investigating the effect of temperature on Kv. The vertical

upper part and ﬁne particles in the lower part of the

hydraulic conductivity was well reproduced, as similar Kv

core. However, the particle size and the length of sedi-

values were produced in the three falling head permeameter

ment group are different between the three cores. VI-3

tests for each core at a speciﬁc water temperature. The aver-

contains a black clay and silt layer about 11.4 cm long

age Kv values are listed in Table 1.

in the lower part of the core whereas no clay layer was

It is evident from Figure 5 that the values of Kv have an

observed in IV-1-A and IV-1-B. The lengths of the top

increasing trend with an increase in water temperature in

part of the sediment with coarser particles in IV-1-A, IV-

each sediment core except for the VI-3 sediment core

1-B and VI-3 are 24.1, 30.5 and 25.4 cm with total

Figure 4

Water temperatures at the 50 cm depth of streambed (in situ) and in the bucket (on-site) for the 52 pairs of tests.

W. Dong et al.

Table 1

Temperature effect on streambed vertical hydraulic conductivity

Average Kv values (m day–1) measured in different water temperatures for ﬁve samples

45.1

2014

Krabbenhoft ). The generation of gases can interfere with water inﬁltration in the tube. Further, water temperature may have an effect on the clay structures and

Water temperature ( C) Sample

Hydrology Research

compactions in our experiment. High temperatures can cause swelling of the clay structure and therefore partly

IV-1-A

1.2

IV-1-B

1.4 15

2.1

2.2

2.7

17.5

18.8

20.5

IV-4

6.3

7.5

7.8

IV-5

1.4

1.5

1.8

2.1

VI-3

0.8

0.6

0.5

0.6

0.5

obstruct the soil pores (Hansen et al. ). Our conjecture is that these effects predominated the change of hydraulic conductivity compared to water viscosity. The Kv value of core VI-3 therefore shows a slight deviation from the expected trend of an increase with increasing water temperature. In this study, the sediment temperature at the 50 cm depth of the streambed represents water temperature during in situ tests, whereas water temperature in the bucket represents water temperature in the on-site test. As shown in Figure 4, on-site water temperature is higher than in situ water temperature for each paired test. Because the streambed upper sediments (about 50 cm in depth) consist mainly of sand and gravel, most (about 81%) of the Kv values increased with an increase in water temperature when the cores were transferred from in situ tests to onsite tests. However, the increase extents are very different. For example, although the water temperature difference is W

only 1 C between in situ and on-site tests for location 13, the on-site Kv increases by 77% compared with the in situ Figure 5

Kv. In contrast, although the water temperature difference Changes of Kv values with temperatures for ﬁve sediment cores.

is more than 5 C, on-site Kv values are very close to in situ Kv, for example, at locations III-3, V-2, and VI-4. The W

sediment lengths of 49.5, 47.0 and 48.9 cm, respectively.

average increase of on-site Kv is 12% for a 1 C increase in

The other two sediment cores, IV-4 and IV-5, have an

water temperature, compared with in situ Kv. The difference

inverse sediment distribution structure with ﬁner particles

in increase between on-site Kv and in situ Kv may be caused

in the upper part and coarser particles in the lower part.

by the difference of coarse particle content as suggested by

The lengths of upper coarse sediments of IV-4 and IV-5

the in-lab test results. Ten on-site Kv values are smaller

are 22.9 and 14 cm with total sediment lengths of 52.5

than in situ Kv. The reduction in the 10 on-site Kv values

and 51.9 cm, respectively.

with water temperature increase may be a result of the

The measured Kv values indicate that sediment cores consisting mainly of coarse particles have an obvious

high clay content in the cores as suggested from the in-lab test results of core VI-3.

increasing trend of Kv values with an increase in water

To examine the effect of the water temperature change

temperature; this is not observed for sediments containing

on the difference between in situ Kv and on-site Kv, the

a clay layer, however. Generally, a variation of water temp-

on-site Kv values were recalculated using Equations (1)

erature causes a viscosity change, therefore affecting Kv.

and (2) on the basis of in situ Kv values for the 52 test

Gases such as CO2 and CH4 were possibly generated by

locations. We assumed that the parameters k, ρ, μ and g in

organic matter in the lower part of the VI-3 core with a cor-

Equation (1) were constant for the same sediment core.

responding increase in water temperature (Schindler &

Thus, a relationship between on-site Kv (Kv O) and in situ

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Kv (Kv I) can be established:

Hydrology Research

45.1

2014

Nevertheless, other factors such as packing condition also contribute to the greater on-site Kv than in situ Kv.

Kv O ¼ Kv I × 10TI C

B O C

(5)

During the passage of the tube through the streambed, there exists friction between sediment and the wall of the tube.

where TI and TO are water temperatures in the in situ and

This can enhance compaction of the sediment in some

on-site tests, respectively. Table 2 lists Kv O for the ﬁrst 21

cases (Chen et al. ). In order to minimize the inﬂuence

test locations.

of compaction on Kv, the wall of the plastic tube was very

The results show that all of the Kv O values are greater

thin. Its thickness was smaller than 2 mm and the bottom

than Kv I values for the 52 tests after the in situ Kv was

end of the tube was beveled in the permeameter test in this

adjusted based on the on-site test water temperature. The

study. We did not focus on the inﬂuence of packing condition

Kv O values increase by 2–44% with an average of 22%

on streambed Kv in this study, but only water temperature.

for each test, compared to the Kv I values under the inﬂuence of water temperature only which increase by 2.5– W

2.8% with an average of 2.7% for a 1 C increase in water

CONCLUSIONS

temperature. The increase in temperature obviously contribMeasurement of Kv by falling head permeameter test can be

utes to the increase of Kv in streambed sediment.

conducted both in situ and on-site for streambed sediment. However, on-site Kv is usually greater than in situ Kv in Table 2

Measured in situ Kv (Kv I) and calculated on-site Kv (Kv O, calculated using Equation (5)) for the ﬁrst 21 test locations Kv I

Kv O

Clear Creek due to the higher on-site water temperature. In-laboratory tests indicated that the Kv value increased W

by 1.8% on average with a 1 C increase in water tempera-

Difference D ¼

(Kv I–Kv O)/

Location

day–1)

Kv I (%)

( C)

(TO–TI) (% C–1)

26.4

30.9

17.0

23.5

2.6

24.2

28.2

15.9

22.1

2.7

11.6

12.4

19.4

22.0

2.5

30.7

35.4

15.8

21.6

2.7

22.5

26.0

15.6

21.5

2.7

25.4

29.7

15.1

21.4

2.7

17.8

20.1

15.8

20.6

2.6

30.0

37.7

14.6

23.9

2.8

4.5

5.6

15.6

24.9

2.7

28.4

35.3

16.4

25.5

2.7

26.3

34.5

14.7

25.9

2.8

33.5

45.2

14.0

26.3

2.8

21.3

30.6

15.4

30.9

2.8

26.7

34.7

16.7

27.8

2.7

39.1

52.0

15.5

27.4

2.8

8.2

10.2

17.7

27.0

2.6

48.0

58.6

18.5

27.0

2.6

23.5

28.7

18.5

27.0

2.6

16.3

17.1

18.1

20.0

2.5

5.2

5.3

19.0

20.0

2.5

10.9

11.8

18.3

21.5

2.5

TO W

Difference D/ W

ture. Sediments consisting mainly of coarse particles have an obvious increasing trend in Kv with increasing water temperature (except for sediment containing a clay layer). The on-site Kv recalculations showed that the values W

increased by 2.7% on average for a 1 C increase in water temperature, compared with in situ Kv after adjusting for the on-site test temperature. This further demonstrated that the variation of water temperature in a river system has a direct impact on streambed hydraulic conductivity via the changes in water viscosity. This paper presents our preliminary ﬁndings of the temperature effect on determination of streambed hydraulic conductivity. Such effects should be considered in future modeling work for a higher-accuracy representation of the stream–aquifer interaction. However, more work is required in order to produce a more complete theory of the relationship between temperature and streambed Kv, which will be an extension of this study.

ACKNOWLEDGEMENTS The study was funded by the Upper Big Blue Natural Resources

District.

The

analysis

was

also

partially

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

supported by the program for Changjiang Scholars and Innovative Research Team of the Chinese Ministry of Education (IRT0811, Utilization of groundwater resource and protection of the water environment in arid and semiarid areas).

REFERENCES Alexander, M. D. & Caissie, D.  Variability and comparison of hyporheic water temperatures and seepage fluxes in a small Atlantic Salmon Stream. Ground Water 41, 72–82. Bagarello, V., Iovino, M. & Tusa, G.  Factors affecting measurement of the near-saturated soil hydraulic conductivity. Soil Science Society of America Journal 64, 1203–1210. Baskaran, S., Brodie, R. S., Ransley, T. & Baker, P.  Timeseries measurements of stream and sediment temperature for understanding river-groundwater interactions: Borders Rivers and Lower Richmond catchments, Australia. Australian Journal of Earth Sciences 56, 21–30. Bendjoudi, H., Cheviron, B., Guérin, R. & Tabbagh, A.  Determination of upward/downward groundwater fluxes using transient variations of soil profile temperature: test of the method with Voyons (Aube, France) experimental data. Hydrological Processes 19, 3735–3745. Butler Jr., J. J., Dietrich, P., Wittig, V. & Christy, T.  Characterizing hydraulic conductivity with the direct-push permeameter. Ground Water 45, 409–419. Cadbury, S. L., Hannah, D. M., Milner, A. M., Pearson, C. P. & Brown, L. E.  Stream temperature dynamics within a New Zealand glacierized river basin. River Research and Applications 24, 68–89. Chen, X. H.  Measurement of streambed hydraulic conductivity and its anisotropy. Environmental Geology 39, 1317–1324. Chen, X. H.  Streambed hydraulic conductivity for rivers in south-central Nebraska. Journal of the American Water Resources Association 40, 561–574. Chen, X. H.  Hydrologic connections of a stream-aquifervegetation zone in south-central Platte River valley, Nebraska. Journal of Hydrology 333, 554–568. Chen, X. H. & Shu, L. C.  Stream-aquifer interactions: evaluation of depletion volume and residual effects from groundwater pumping. Ground Water 40, 284–290. Chen, X. H., Burbach, M. & Cheng, C.  Electrical and hydraulic vertical variability in channel sediments and its effects on streamflow depletion due to groundwater extraction. Journal of Hydrology 352, 250–266. Chen, X. H., Song, J. X., Cheng, C., Wang, D. M. & Lackey, S. O.  A new method for mapping variability in vertical seepage flux in streambeds. Hydrogeology Journal 17, 519–525.

Hydrology Research

45.1

2014

Cheng, C. & Chen, X. H.  Evaluation of methods for determination of hydraulic properties in an aquifer-aquitard system hydrologically connected to a river. Hydrogeology Journal 15, 669–678. Cheng, C., Song, J. X., Chen, X. H. & Wang, D. M.  Statistical distribution of streambed vertical hydraulic conductivity along the Platte River, Nebraska. Water Resources Management 25, 265–285. Conant Jr., B.  Delineating and quantifying groundwater discharge zones using streambed temperatures. Ground Water 42, 243–257. Constantz, J.  Interaction between stream temperature, streamflow, and groundwater exchanges in alpine streams. Water Resources Research 34 (7), 1609–1615. Constantz, J. & Thomas, C. L.  The use of streambed temperature profiles to estimate the depth, duration, and rate of percolation beneath arroyos. Water Resources Research 32, 3597–3602. Darzi, A., Yari, A., Bagheri, H., Sabe, G. & Yari, R.  Study of variation of saturated hydraulic conductivity with time. Journal of Irrigation and Drainage Engineering 134, 79–484. Dietze, M. & Dietrich, P.  Evaluation of vertical variations in hydraulic conductivity in unconsolidated sediments. Ground Water 1–7, 450–456. Dong, W. H., Chen, X. H., Wang, Z. W., Ou, G. X. & Liu, C.  Comparison of vertical hydraulic conductivity in a streambed-point bar system of a gaining stream. Journal of Hydrology 450–451, 9–16. Evans, E. C. & Petts, G. E.  Hyporheic temperature patterns within riffles. Hydrological Sciences Journal 42, 199–213. Fulcher, G. S.  Analysis of recent measurements of the viscosity of glasses. Journal of the American Ceramic Society 8, 339–355. Genereux, D. P., Leahy, S., Mitasova, H., Kennedy, C. D. & Corbett, D. R.  Spatial and temporal variability of streambed hydraulic conductivity in West Bear Creek, North Carolina, USA. Journal of Hydrology 358 (3–4), 332–353. Hansen, E. L., Hemmen, H., Fonseca, D. M., Coutant, C., Knudsen, K. D., Plivelic, T. S., Bonn, D. & Fossum, J. O.  Swelling transition of a clay induced by heating. Nature, Scientific Reports 2, Article number 618. Haridasan, M. & Jensen, R. D.  Effect of temperature on pressure head-water content relationship and conductivity of two soils. Soil Science Society of America Journal 36, 703–708. Hatch, C. E., Fisher, A. T., Revenaugh, J. S., Constantz, J. & Ruehl, C.  Quantifying surface water–groundwater interactions using time series analysis of streambed thermal records: Method development. Water Resources Research 42, 1–14. Hoehn, E. & Cirpka, O. A.  Assessing hyporheic zone dynamics in two alluvial flood plains of the Southern Alps using water temperature and tracers. Hydrology and Earth System Sciences Discussions 3, 335–364. Hvorslev, M. J.  Time lag and soil permeability in ground-water observations. US Army Corps of Engineers, Waterways Experiment Station Bulletin 36, 1–50.

W. Dong et al.

Temperature effect on streambed vertical hydraulic conductivity

Konrad, J. M. & Samson, M.  Inﬂuence of freezing temperature on hydraulic conductivity of silty clay. Journal of Geotechnical and Geoenvironmental Engineering 126, 180–187. Kresic, N.  Hydrogeology and Groundwater Modeling, 2nd edn. CRC Press, Boca Raton. Leach, J. A. & Moore, R. D.  Stream temperature dynamics in two hydrogeomorphically distinct reaches. Hydrological Processes 25, 679–690. Loheide, S. P. & Gorelick, S.  Quantifying stream-aquifer interactions through the analysis of remotely sensed thermographic proﬁles and in situ temperature histories. Environmental Science Technology 40, 3336–3341. Lu, C., Chen, X., Cheng, C., Ou, G. & Shu, L. a Horizontal hydraulic conductivity of shallow streambed sediments and comparison with the grain-size analysis results. Hydrological Processes 26, 454–466. Lu, C., Chen, X., Ou, G., Cheng, C., Shu, L., Cheng, D. & AppiahAdjei, E. K. b Determination of the anisotropy of an upper streambed layer in east-central Nebraska, USA. Hydrogeology Journal 20, 93–101. Ma, R. & Zheng, C. M.  Effects of density and viscosity in modeling heat as a groundwater tracer. Ground Water 48, 380–389. Othman, M. A., Benson, C. H., Chamberlain, E. J. & Zimmie, T. F.  Laboratory testing to evaluate changes in hydraulic conductivity of compacted clays caused by freeze-thaw: State-of-the-art. In: Hydraulic Conductivity and Waste Contaminant Transport in Soils (D. E. Daniel & S. J. Trautwein, eds). ASTM STP 1142, ASTM, West Conshohocken, pp. 227–254. Ronan, A. D., Prudic, D. E., Thodal, C. E. & Constantz, J.  Field study and simulation of diurnal temperature effects on

Hydrology Research

45.1

2014

infiltration and variably saturated flow beneath an ephemeral stream. Water Resources Research 34, 2137–2153. Schindler, J. E. & Krabbenhoft, D. P.  The hyporheic zone as a source of dissolved organic carbon and carbon gases to a temperate forested stream. Biogeochemistry 43, 157–174. Schmidt, C., Bayer-Raich, M. & Schirmer, M.  Characterization of spatial heterogeneity of groundwaterstream water interactions using multiple depth streambed temperature measurements at the reach scale. Hydrology and Earth System Sciences Discussions 3, 1419–1446. Silliman, S. E. & Booth, D. F.  Analysis of time-series measurements of sediment temperature for identification of gaining vs. losing portions of Juday Creek, Indiana. Journal of Hydrology 146, 131–148. Sinokrat, B. A. & Stefan, H. G.  Stream temperature dynamics: Measurement and modeling. Water Resources Research 29, 2299–2312. Song, J., Chen, X., Cheng, C., Summerside, S. & Wen, F.  Effects of hyporheic processes on streambed vertical hydraulic conductivity in three rivers of Nebraska. Geophys. Res. Lett. 34, L07409. Su, G. W., Jasperse, J., Seymour, D. & Constantz, J.  Estimation of hydraulic conductivity in an alluvial system using temperatures. Ground Water 42, 890–90. Weigelhofer, G. & Waringer, J.  Vertical distribution of benthic macroinvertebrates in riffles versus deep runs with differing contents of fine sediments (Weidlingbach, Austria). International Review of Hydrobiology 88, 304–313. Westhoff, M. C., Bogaard, T. A. & Savenije, H. H. G.  Quantifying spatial and temporal discharge dynamics of an event in a first order stream, using distributed temperature sensing. Hydrology and Earth System Sciences Discussions 15, 1945–1957.

First received 26 January 2013; accepted in revised form 21 May 2013. Available online 25 June 2013

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Simulating the hydrologic response of a semiarid watershed to switchgrass cultivation Justin C. Goldstein, Aondover Tarhule and David Brauer

ABSTRACT The conversion of land from existing uses to biofuel cultivation is expected to increase given concerns about the sustainability of fossil fuel supplies. Nonetheless, research into the environmental impacts of biofuel crops, primarily the hydrological impacts of their cultivation, is in its infancy. To investigate such issues, the response of a 1,649 km2 semiarid basin to the incremental substitution of the widely discussed biofuel candidate switchgrass (Panicum virgatum L.) for native land uses was modeled using the Soil and Water Assessment Tool (SWAT). Median discharges decreased by 5.6–20.6% during the spring and by 6.4–31.2% during the summer, depending on the quantity of acreage converted. These were driven by an increased spring and summer evapotranspiration of 3.4–32.0% and 1.5–18.9%, respectively, depending on the quantity of switchgrass biomass produced. The substitution of switchgrass also resulted in larger quantities of water stress days than in baseline scenarios. The authors encourage the exploration of alternative biofuel crops in semiarid areas to mitigate such negative impacts. Key words

Justin C. Goldstein (corresponding author) Aondover Tarhule Department of Geography and Environmental Sustainability, University of Oklahoma, 100 E. Boyd Street, SEC Suite 510, Norman, OK 73019, USA E-mail: Justin.C.Goldstein-1@ou.edu David Brauer Ogallala Aquifer Program, Conservation and Production Research Laboratory, 2300 Experiment Station Drive, PO Drawer 10, USDA Agricultural Research Service, Bushland, TX 79012, USA

| biofuels, great plains, land use change, semiarid regions, Soil and Water Assessment Tool, switchgrass

INTRODUCTION Land conversion from existing uses to biofuel crops cultiva-

alternative forms of ethanol (called cellulosic ethanol) com-

tion is an important form of land use change in the 21st

petitive with corn-based ethanol by 2012. That call resulted

century. According to the Renewable Fuels Association

ultimately in the Energy Independence and Security Act

(), annual US corn ethanol production increased

(EISA) of 2007. The goals of the EISA are to increase

nearly nine-fold from 6 billion to 52 billion liters between

energy security in the USA and to increase the production

2000 and 2010, while the number of ethanol plants quad-

of clean fossil fuels, among others, including the mandated

rupled from 54 to 204. Driving this increase are a number

production of 61 billion liters of cellulosic-based gasoline

of factors including increased oil prices, US demand for

additives by 2022 (One-hundred Tenth Congress of the

greater energy independence, increased awareness and

United States of America ).

interest in renewable energy sources and the policies and

The Ecological Society of America deﬁnes biofuels as

mandates of the United States Government. In his 2006

‘liquid fuels derived from biological materials’ (e.g. Mitchell

State of the Union address, US President George W. Bush

et al. ; Robertson et al. ). Common sources of bio-

proposed the Advanced Energy Initiative, which called for

fuel crops include corn (Zea mays L.), switchgrass

energy from biofuels to replace greater than 75% of

(Panicum virgatum L.), soybeans (Glycine max L.), sweet-

imported oil from the Middle East by 2025 (Bush ). It

gum (Liquidamber styraciﬂua L.), rapeseed (Brassica

also called for increased Federal investment in the pro-

napus L. rape), sugarcane (Saccharum ofﬁcinarum L.),

duction of ethanol from sources other than corn, including

palm oil (Elaeis guineensis), and jatropha (Jatropha

wood chips and switchgrass, with the goal of making these

curcus).

doi: 10.2166/nh.2013.163

Resultant

fuels

include

ethanol

(the

most

100

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

Hydrology Research

45.1

2014

common), methanol, propanol, butanol, methane, and

difference was likely due to land use changes, including

biodiesel.

deforestation and urbanization.

Native to the tallgrass prairies and a wide range of

Ma et al. () investigated the impacts of climate and

mesic environments in the eastern two-thirds of the

land use change in the Kejie watershed in China during

United States, the warm season perennial switchgrass

1965–2005. They found that the hydrologic effects of climate

(Parrish & Fike ) has received much attention as a

change were offset by land use changes and that, while sea-

possible cellulosic biofuel source because of its perceived

sonal changes in streamﬂow were mostly a function of

advantages over other biofuel crops. In their review

precipitation, mean annual changes in streamﬂow were lar-

paper, Simpson et al. () concluded that, compared to

gely inﬂuenced by land use change. Overall, they found that

corn, switchgrass facilitates improved nutrient retention

surface hydrology was more impacted by land use change

and carbon sequestration in soils, it has the ability to

than climate.

grow on marginal soils and it needs replacement only

Franczyk & Chang () assessed the impacts of cli-

once every 20 years. Also, it has been projected that switch-

mate change and future urbanization on the hydrology of

grass-based ethanol reduces the emission of greenhouse

the Rock Creek Basin, Oregon, USA, through the 2040s.

gases by 94% relative to those emitted by traditional gaso-

They found that climate change and urbanization combine

line (Schmer et al. ).

to amplify the magnitudes of the volumes of mean annual

As with any other major land use modiﬁcation, biofuel production is expected to have major (but not yet fully

runoff and evapotranspiration (eT) relative to those in the absence of one of those factors.

understood) impacts on regional hydrology. Acknowledging

Du et al. () found that the impacts of urbanization on

this point, the National Research Council (, p. vii) refers

mean annual runoff are a function of the magnitude of pre-

to the hydrology of biofuel production as an ‘emerging ﬁeld’

cipitation; in their investigation of the Qinhuai River

of scientiﬁc inquiry. Similarly, Georgescu & Lobell (,

watershed in China, they found that annual runoff in dry

p. 33) noted ‘changes to local hydrology caused by large-

years increases more than in wet years given a 10-fold

scale perennial systems may be complex, and thus require

increase in the area of impervious surfaces. Additionally,

careful evaluation’.

Raymond et al. () and Schilling et al. () attributed

Two other factors related to climate change and sustain-

the increased in discharges in the Mississippi River Basin

ability also make such evaluation imperative. A number of

to agricultural production, and explicitly discounted the

authors (e.g. Sala et al. ; Vorosmarty et al. ; Foley

role of climate.

et al. ; Turner II et al. ; Wagener et al. ) have

With speciﬁc respect to regional hydrology, a number of

noted that land use change dwarfs or is at least of compar-

studies have reported signiﬁcant stream depletion due to

able magnitude to the much more widely publicized topic

groundwater mining associated with agricultural expansion

of climate change, both as a driver and as an impact of

(e.g. Reisner ; Glennon ; Kustu et al. ; McGuire

future global environmental change.

; Scanlon et al. ). These ﬁndings underscore a critical

With speciﬁc respect to water resources, Ren et al. ()

need to unbundle and quantify the relative contributions of

and Jiang et al. () found that both climate change and

speciﬁc land use changes, especially in semiarid areas such

anthropogenic activities including reservoir construction

as the US Great Plains where the issue of the sustainability

and irrigation are responsible for changes in streamﬂow in

of scarce water supplies is of paramount importance (see

China’s Laohahae Basin during the late 20th and early 21st

below). This study is a contribution toward that goal.

century, although the relative contribution of each varies by a decade.

With regard to the sustainability of biofuel hydrology, the myriad of factors comprising the hydrologic impacts of

In their study of the Shaumalun Basin in China, Yang

biofuel production may be grouped into three broad

et al. () found a decline in annual runoff post-1998 far

categories, namely: the water footprint (WF) deﬁned as ‘the

in excess of what could be attributed to changes in basin pre-

total annual volume of fresh water used to produce goods

cipitation. The authors concluded that the unexplained

and services for consumption’ (see e.g. Gerbens-Leenes

101

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

Hydrology Research

45.1

2014

et al. (), pp. 10219); water quality (e.g. Nyakatawa et al.

soybeans, wheat and cotton with switchgrass in the vicin-

; Simpson et al. ; Chamberlain et al. ; Sarkar

ities of the cities of Nashville and Memphis (Tennessee,

et al. ); and impacts on the local or regional water bal-

USA) using the Environmental Policy Integrated Climate

ance. This paper focuses on the third category. Speciﬁcally,

(EPIC) model. They found that replacing such crops with

we investigate the impact of switchgrass production on

switchgrass would result in lower runoff, erosion, eT and

local-scale changes in constituent components of the water

phosphorus loss. Speciﬁcally, replacing soybeans with

balance, including runoff and eT.

switchgrass reduced eT by 20–60% and phosphorus by

A number of studies have investigated the impact of the

80–95%. Additionally, replacing corn with switchgrass

planting of different biofuel crops on local water balances

reduced eT by up to 10–50% and phosphorus loss by

(e.g. Schilling et al. ; Thomas et al. ). These studies

80–95%. Finally, replacing wheat with switchgrass reduced

suggest that increased biofuel crop cultivation can signiﬁ-

eT by 15–40% and phosphorus loss by approximately 90%.

cantly alter local water balances through altering local eT

Vanlocke et al. () investigated the hypothetical impact

and discharge rates, although the results are mixed due to

on regional water balance of planting increasing proportions

variations in crop management (i.e. till, no till, etc.), climate

(i.e. 10% of area, 25, 50, 75, and 100%) of miscanthus in the

and topography. Generally, switchgrass and the biofuel-

Upper Midwest of the USA. By simulating the different

grass

miscanthus

(Miscanthus × giganteus)

been

land cover conﬁgurations using the Integrated Biosphere

shown to increase soil moisture retention and to reduce

have

Simulator – Agricultural Version, the authors found that the

the volumes of river discharge relative to other crops.

planting of miscanthus signiﬁcantly increased eT and

For example, Schilling et al. () simulated the impact

decreased discharge relative to its predecessor land cover

of various land use scenarios involving combinations of bio-

type. In yet another experimental study, McIsaac et al. ()

fuel crops in the Raccoon watershed in Iowa, USA, on the

found that late-season soil moisture under switchgrass plots

water balance using the Soil Water and Assessment Tool

exceeded that of miscanthus and maize-soybean because of

(SWAT). They devised nine scenarios, ranging from an

the higher transpiration levels of miscanthus and maize-

expansion of corn acreage to cover solely United States

soybean relative to switchgrass (due to higher leaf-area indices

Department of Agriculture (USDA) lands to those in

and biomass) throughout much of the growing season.

which switchgrass became the dominant biofuel crop and,

Estimated eT from miscanthus exceeded that of switchgrass

ﬁnally, those in which cool season biofuel crops (i.e.

by 140 mm and that of maize-soybean by 104 mm.

fescue) dominated. They found that the conversion of grass-

In addition to differences in management practices,

land to corn decreases mean annual eT by 1% and increases

impacts of biofuel cultivation have been shown to be region

mean annual runoff by nearly 8%, but the conversion of

speciﬁc as a result of differences in climatic conditions (e.g.

cropland to warm season biofuel crops (switchgrass)

Garoma et al. ). For example, soybeans and cotton require

increases mean annual eT by 2.6% and decreases mean

more water than corn when planted in the Paciﬁc and Moun-

annual runoff by 17%.

tain regions of the USA, but the opposite is true in the

On the other hand, Thomas et al. () suggested that

semiarid Great Plains (National Research Council ).

planting corn on an annual basis increases eT. In an investi-

These differences, and sometimes contradictory results,

gation using SWAT in a watershed in Eastern Kansas,

point to a need for more studies investigating the impacts of

United States, Nelson et al. () modeled the percent

biofuel production generally in different regions and biocli-

reduction in surface runoff when the planting of switchgrass

matic environments. This study contributes to that goal.

replaced the planting of traditional crop rotations, including corn-soybean, corn-soybean-wheat, grain sorghum-soybean, and grain sorghum-soybean-wheat. They found that the

STUDY AREA

planting of switchgrass reduced surface runoff by 55% over a 24-year period relative to baseline. Graham et al.

The study area is part of the Middle North Canadian River

() modeled the hydrologic impact of replacing plots of

(MNCR) watershed located in Western Oklahoma, USA. It

J. C. Goldstein et al.

102

Response of a semiarid watershed to switchgrass cultivation

Hydrology Research

45.1

2014

covers approximately 1,649 km2 within the US Geological

The MNCR overlies two geological provinces: the Wes-

Survey (USGS) Hydrologic Unit Code 11100301 (Figure 1).

tern Sand-Dune Belts and the Western Sandstone Hills

The headwaters of the basin are located at 36 260 12″ N,

(Goins & Anderson ). The sand dune belts, which

99 160 41″ W and the watershed outlet is situated at

were blown from Quaternary alluvium and terrace depos-

36 11 00″ N, 98 55 15″ W. Because of its predominantly

its, are found on the north side of the North Canadian

agricultural character, the MNCR could be considered

River and are oriented southeast. These deposits create

representative of other basins in the semiarid US Great

the Alluvium and Terrace aquifer of the Beaver/North

Plains. Largely rural, the largest settlements in the MNCR

Canadian River (BNCR A&T), which originates upstream

are Mooreland (population 1190), Seiling (population

of the MNCR and ends at Lake Eufaula, 290 km down-

860), and Vici (population 699). Elevation varies from

stream from the MNCR. This aquifer serves as an

762 m at the headwaters to 512 m at its outlet, a distance

important water source for irrigation and public water

of approximately 53 km. For the period 1980–2010, average

supplies in this region. The Quaternary deposits vary in

annual precipitation was 666 mm with precipitation peaking

thickness; the alluvium deposits average 10 m in thickness

during May and June (PRISM Climate Group ). Average

while the high terrace deposits average 21 m in thickness.

daily temperatures range from 1 C during January to 27 C

The terrace and alluvium deposits are the main water-bear-

during July and August. Like other portions of the Great

ing portions of the aquifer, and it is believed that these

Plains, the study area is drought prone and suffers from

deposits are hydraulically continuous and comprise a

water shortages associated with evaporative losses (Zume

single aquifer system. These deposits contain poorly

& Tarhule , ).

sorted sand and minor portions of gravel, silt and clay

Figure 1

Location of the Middle North Canadian River Basin (MNCR), located within the US state of Oklahoma.

103

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

Hydrology Research

45.1

2014

(Davis & Christenson ). It is believed that the base of

; Ng et al. ). The model, along with associated docu-

the aquifer coincides with the relatively impermeable Per-

mentation and related software, is available free of charge

mian Red Beds Formation (Zume & Tarhule ).

from the Texas A&M AgriLife Research Center (http://

The depth to bedrock at the BNCR A&T varies

swatmodel.tamu.edu). It has been applied to a variety of

spatially up to a maximum of 100 m, although it does out-

water resource issues in a large range of locations and

crop at a few locations outside of the MNCR. Hydraulic

spatial scales from 0.004 to 491,665 km2 (Gassman et al.

; Douglas-Mankin et al. ). SWAT divides a water-

(Davis & Christenson ; Adams et al. ), with speciﬁc

shed into smaller user-deﬁned sub-basins, and then into

yield around 0.28 (Zume & Tarhule ) and trans-

still smaller hydrologic research units (HRUs) which are

conductivity values vary over the range 18–24 m d

(Davis &

areas of homogeneous land use, soil and slope based on

Christenson ). Recharge is 1.39 × 10 4 m d 1 (Zume &

user-provided information. The model operates on a water-

Tarhule ), or approximately 7% of mean annual

balance principle on a daily time-step.

missivity values within the range 0–749 m d

precipitation.

A key convenience of SWAT is that it is linked to various

The vegetation of the watershed is dominated by non-

databases containing the data and information required for

irrigated native range grasses and winter wheat, which is

simulation, greatly simplifying model set-up and operation.

fertilized and irrigated. Grasses include buffalo grass, big

The crop database contains alterable biophysical infor-

and little bluestem, sideoats grama and blue grama. Winter

mation (e.g. extinction coefﬁcient, leaf area index) for 108

wheat is planted during the middle of September and is

crops, including many biofuels, such as Alamo Switchgrass,

harvested in the middle of June of the following summer.

corn, oil palm, sugarcane, grain sorghum and soybeans. The

Most of the irrigation originates from the BNCR A&T.

sources for the input data used in this investigation are listed

Heavy groundwater pumping for irrigation since 1970

in Table 1.

in portions of the North Canadian River watershed

The MNCR was delineated in SWAT using a 30 m digi-

upstream of the MNCR has contributed to decreases in

tal elevation model (DEM) and by the subsequent ‘burning

the medians of the peak annual streamﬂow values of

in’ of the National Hydrography Dataset Plus dataset. Thir-

about 40% in the MNCR (see Wahl & Tortorelli ).

teen sub-basins were delineated. To reduce the quantity of

The two largest uses of BNCR A&T water are irrigation

HRUs to a manageable number without sacriﬁcing model

and municipal use (Tortorelli ). More groundwater is

accuracy, a threshold of 3% land use, 10% soil and 0%

used from BNCR A&T for municipal use than in any

slope for each sub-basin was used. In other words, land

other aquifer in Oklahoma, and 50–89% of the total withdrawals in the study area counties are BNCR A&T water. The MNCR lacks large impoundments although several

Table 1

Data sources for items used in investigation

small reservoirs exist. Data for simulation

Source

Elevation: 30 m DEM

USGS

MODEL DESCRIPTION AND METHODS

Groundwater: values for effective hydraulic conductivity

Zume & Tarhule ()

The response of the MNCR to the substitution of native land

Land use: 56 m Crop Dataset Layer (CDL) 2006–2009

National Agriculture Statistics Service

Management: Planting, irrigation, and fertilization schedules

Agriculture extension agents

Soil: 1:15,000 scale Soil Survey Geographic (SSURGO) dataset

Natural Resources Conservation Service (NRCS)

Weather: Daily temperature and precipitation data

National Climatic Data Center

uses with switchgrass was investigated using SWAT, a physics-based semi-distributed hydrologic model (Arnold et al. ). Developed by the US Department of Agriculture in Temple, Texas, SWAT has been employed in over 600 published studies (Gassman et al. ; Douglas-Mankin et al. ), including many investigations of the impacts of crop substitution (e.g. Schilling et al. ; Baskaran et al.

J. C. Goldstein et al.

104

Response of a semiarid watershed to switchgrass cultivation

use types were retained if they covered greater than 3% of

Hydrology Research

45.1

2014

RESULTS

the sub-basin; otherwise they were incorporated into other HRUs. This led to the retention of 529 HRUs. The land

Calibration

use composition of the watershed post-threshold delineation is displayed in Table 2.

The result of the calibration on total monthly discharge (in

Driven primarily by the availability of streamﬂow

cubic meters per second or cms) at the watershed outlet is

data for calibration, SWAT was run for the period

depicted in Figure 2(a). The simulated model reproduces

1977–2009 with 1977–1979 as the initialization period,

the observed discharges reasonably well without evidence

1980–1994 as the calibration period and 1995–2009 as

of systematic under- or overestimation. The Nash–Sutcliffe

the simulation period. Following calibration, simulations

Efﬁciency (NSE, Nash & Sutcliffe ) estimate is 0.86,

of switchgrass replacement were conducted to quantify

well above the 0.75 threshold generally regarded as indica-

the response of the MNCR, speciﬁcally discharge (Q)

tive of a ‘very good’ simulation (Moriasi et al. ). The

and eT, to the cultivation of switchgrass during the

calculated percent bias (PBIAS; Gupta et al. ) estimate

spring and summer seasons which were the seasons

is 3.87% (values less than 10% are considered ‘very good’).

with the best calibration results. The replacement scen-

Finally, the calibration ﬁt was evaluated using the root

arios are the following:

mean square error (RMSE) observations standard deviation ratio (RSR), a measure of the ratio of the normalized sum of

1. nowwht: replacement of winter wheat with non-fertilized 2. nornge: replacement of range grasses with nonfertilized alamo switchgrass (74.5% of the MNCR).

0.5 are considered ‘very good’; Moriasi et al. ). The simulation therefore performed satisfactorily on all three

3. noag: replacement of agricultural land uses (range grass and winter wheat) with non-fertilized alamo switchgrass (86.8% of the MNCR).

commonly used evaluation criteria. Sensitivity analysis (van Griensven et al. ) was performed on 26 parameters, using observed data. The results

4. fert: similar to ‘noag’, except switchgrass is managed as follows: (a) fertilize April 15 (56 kg ha

squares to the standard deviation of the observed values (Singh et al. ). The RSR estimate is 0.38 (values below

Alamo switchgrass (12.3% of the MNCR).

showed that the curve number for soil moisture condition

N); (b) harvest

II (‘average’ moisture) was the most sensitive parameter, fol-

May 15 (90% efﬁciency), July 15, November 1; and (c)

lowed by maximum vegetation canopy storage and

fertilize (56 kg ha

N) May 17, July 17.

Manning’s roughness coefﬁcient (Table 3). A list of the curve numbers for the various land use classes in the cali-

Switchgrass production was simulated using the default

bration simulation is provided by Table 4. However,

biophysical settings for Alamo switchgrass provided in the

further ﬁne tuning was deemed unnecessary given the low

SWAT crop database with 1,187 heat units for growth and

values of the sensitivity indices as well as the excellent cali-

with increased rooting depth from 2 to 3 m (Baskaran

bration agreement already achieved.

et al. ).

Accordingly, the model was used to simulate total monthly discharge for the simulation period of 1995–2009

Table 2

Land use composition (%) of the MNCR post-land use threshold delineation

Land use

% of watershed

Native range grasses

74.59

Winter wheat

12.30

Low-density development

5.90

Evergreen forest

4.03

Shrubland

3.18

(Figure 2(b)). The results are likewise satisfactory with NSE of 0.80, PBIAS at 0.53 and RSR of 0.45. Next, the model performance at seasonal timescale (i.e. winter: December, January, February; spring: March, April, May; summer: June, July, August, and fall: September, October, November) was evaluated for the calibration and simulation periods. The results are listed in Table 5. The statistics for winter during the calibration and

105

Figure 2

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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45.1

2014

Plot of simulated and observed monthly discharges at the watershed outlet during (a) the calibration period and (b) the simulation period.

simulation periods were problematic due to relatively low

four switchgrass substitution simulation scenarios for the

NSE values and unsatisfactorily high PBIAS values

spring and summer appear in Figure 5(a), (b). All four scen-

(>25%, which is the threshold for satisfactorily monthly

arios result in decreased discharges relative to baseline.

values according to Moriasi et al. ). Subsequent analy-

Such decreases are consistent with the ﬁndings of Nelson

sis was therefore conﬁned to the spring and summer

et al. () and Schilling et al. (), both of whom

seasons. Figures 3(a), (b) and 4(a), (b) depict plots of the

found decreased discharges when replacing pre-existing

simulated and observed spring and summer discharges

cropland with warm-season grasses. As may be expected,

during

the magnitude of the decreased discharges is a function of

the

calibration

and

simulation

periods,

respectively.

the area converted to switchgrass, a ﬁnding which also echoes that of Schilling et al. ().

Spring and summer discharge

On the one hand, the magnitude of the reduction in median spring discharge for all scenarios is directly pro-

The changes in hydrology discussed below are driven solely

portional to seasonal precipitation in Oklahoma Climate

by the impacts of land use change, as climatic parameters

Division 2, in which the majority of the MNCR is situated

were not adjusted during the simulations. The results of

(Figure 6(a)–(d)). All relationships are statistically signiﬁcant

J. C. Goldstein et al.

106

Table 3

Response of a semiarid watershed to switchgrass cultivation

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45.1

2014

Sensitivity index rankings for the MNCR (10 most sensitive shown, in order of decreasing sensitivity)

Sensitivity ranking

Parameter

Description

Initial value

Range tested (max, min)

CN2

Curve number for soil condition II

Default

10%, 10%b

0.199

Canmx

Maximum canopy storage (mm H2O)

0, 10

0.112

Ch_N2

Manning’s n value for the main channel

Varies within range tested

0.035, 0.11

0.0909

Alpha_bf

Baseﬂow recession factor (days)

0.75

0, 1

0.0816

Blai

Maximum potential leaf area index

Default

0, 1

0.0308

Sensitivity index

Surlag

Surface runoff lag coefﬁcient (days)

Default

1, 24

0.0261

Sol_Z

Depth from soil surface to bottom of soil layer (mm)

Default

4%, 4%b

0.0205

Esco

Soil evaporation compensation factor

0.7

0.65, 0.80

0.0166

Ch_K2a

Effective hydraulic conductivity in main channel alluvium (mm hr 1)

6.4–7

3, 20

0.0141

Sol_Awc

Available water capacity of the soil layer (mm)

Default

4%, 4%b

0.0113

Only applied to sub-basins with intermittent or ephemeral main channels. Values based on those reported by Zume & Tarhule (2008).

Initial value multiplied by values in range.

Table 4

CNs for crops in this investigation, by National Resources Conservation Service Hydrologic Soil Group (Soil Group A: lowest runoff potential; Soil Group D: highest runoff potential). Source: SWAT crop database

(p < 0.05). We hypothesize that higher rainfall results in greater switchgrass biomass accumulation, which then results in higher evaporative losses and therefore less

Soil Group

Crop

Winter wheat

the fact that winter wheat relies more heavily on fertilizer

water for discharge. Notice that the relationship is relatively weak for the ‘nowwht’ scenario. This may be explained by

Native range grasses

applications, and less on precipitation, for growth. On the

Shrubland

other hand, no statistically signiﬁcant correlations exist

Low-density development

between the magnitude of reduction in summer discharge

Alamo switchgrassa

Evergreen forest

and summer precipitation, implying that depletions in summer discharge are not a function of precipitation, explained below.

Not included in calibration simulation.

Table 5

Spring and summer eT Effectiveness of calibration during the calibration and simulation periods. Thresholds for satisfactory calibration on the monthly timescale for NSE, PBIAS and RSR are 0.50, þ/ 25% and 0.75, respectively (Moriasi et al. 2007).

Criterion

Winter

Spring

Summer

Fall

0.64

PBIAS (%)

29.34

RSR

0.60

by sizeable, statistically signiﬁcant (p < 0.05) increases in eT (Figure 7(a), (b)). Median increases during the spring

Calibration period NSE

The reductions in spring and summer discharge are driven

0.76

0.97

0.87

6.00

9.90

14.39

0.49

0.18

0.36

Simulation period NSE

0.61

0.93

0.88

0.69

PBIAS (%)

25.17

6.75

8.23

29.63

RSR

0.62

0.27

0.35

0.56

vary from 4.3 mm (‘nowwht’ scenario) to 46.0 mm (‘fert’ scenario)

and

from

2.2 mm

(‘nowwht’

scenario)

24.0 mm (‘fert’ scenario) during the summer. These increases appear not to be functions of land area converted, but of the quantity of switchgrass biomass produced (Figure 8). This is evident from the disparate eT values under the ‘noag’ and ‘fert’ scenarios, despite these scenarios converting an identical acreage of switchgrass.

107

Figure 3

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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2014

Calibration of seasonal discharges at the watershed outlet for (a) spring and (b) summer.

It is evident that summer eT is greatly limited by avail-

summer days are water stressed. The increase in water

able moisture, as the increases in spring eT exceed those

stress days also explains the lack of a statistically signiﬁcant

of the summer by a factor of 1.3–2.3 despite higher

relationship between precipitation and change in discharge

summer temperatures relative to spring (Figure 7(a), (b)).

(see above), as most of the MNCR’s summer moisture

Higher water stress during the summer is evident in the

supply is exhausted by the high evaporative demands.

higher ratio of summer eT to rainfall (0.632) relative to

Additionally, the statistical relationship between the

that during the spring (0.536). These results are consistent

change in eT (mm) and the change in discharge (cms)

with those reported by Lakshmi et al. () for an area situ-

during the simulation years is stronger during spring

ated just north of the MNCR. Additionally, the number of

months than in summer, which indicates a lack of requisite

summer water stress days increases under all scenarios rela-

moisture during the latter period (Table 7). Simply stated,

tive to baseline, resulting in an almost 300% increase under

the increase in summer eT associated with switchgrass pro-

the ‘fert’ scenario in which the most switchgrass biomass is

duction increases the quantity of summer water stress days

produced (Table 6). Under the ‘fert’ scenario, 48% of all

in the MNCR.

108

Figure 4

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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Comparison of observed and predicted discharges at the watershed outlet for (a) spring and (b) summer during the simulation period.

Table 7 indicates that moderately strong, statistically sig-

CONCLUSIONS

niﬁcant (p < 0.05) relationships exist between changes in eT and changes in discharge during all seasons and scenarios

The current interest in biofuel crops is likely to lead to major

except for ‘nowwht’. We therefore conclude that changes

land use changes in some watersheds with major impacts on

in discharge in the MNCR are driven by eT except in this

regional hydrology. However, due to the still-evolving nature

scenario, which may be driven by the application of spring

of so-called biofuel hydrology, the dynamics and magnitudes

fertilizer with the subsequent increase in the growth of

of the possible hydrologic responses in different bioclimatic

winter wheat. Ignoring the ‘nowwht’ scenario, it is also note-

zones, as well as management practices, are not yet fully

worthy that the coefﬁcient of determination for this

understood. Efforts toward achieving that understanding

relationship decreases with the volume of switchgrass pro-

have tended to adopt a modeling approach because of the

duction. This is further evidence of the occurrence of

complexity and futuristic nature of the processes involved.

water stress mentioned above, as only so much moisture is

Even though one of the largest experimental switchgrass

available to be lost by eT.

plots is located in Guymon, Oklahoma, USA, in the

109

Figure 5

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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Differences in (a) spring (solid) and summer (striped) discharge associated with switchgrass production and (b) the percent change in spring and summer discharge relative to baseline in all scenarios during the simulation period 1995â&#x20AC;&#x201C;2009. The value of the median change is located to the left of each box. The proportion of the watershed converted in each scenario is shown as a percentage in brackets underneath the x-axis label. The boxplots are read as follows. The dots comprise the observations. The top and bottom of each box comprise the 75th and 25th percentiles, respectively, of the observations. The lengths of the boxes comprise the interquartile range (IQR), or the difference between the 75th and 25th percentiles. The white lines inside the boxes represent the median observations. The upper inner fence (downward-facing square bracket) categorizes 1.5 IQR above the 75th percentile observation, and the lower inner fence (upward-facing square bracket) categorizes 1.5 IQR beneath the 25th percentile observation. The upper outer and inner fences, represented by horizontal lines above and below the brackets, where applicable, identify 3 IQR above the 75th percentile observation and 3 IQR below the 25th percentile observation, respectively.

shortgrass prairies, few studies have investigated the hydro-

A SWAT model of the 1,649 km2 MNCR watershed was

logic response to switchgrass cultivation in a semiarid

developed. Model calibration resulted in excellent agree-

environment. This study was carried out to help ďŹ ll that

ment between total simulated and observed discharges on

gap and to contribute to the emerging literature on the poss-

three widely used model performance evaluation metrics

ible environmental effects of biofuel production in various

(i.e. the NSE, PBIAS and RSR). At a seasonal scale, the

regions.

evaluation yielded satisfactory simulations for the spring

110

Figure 6

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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Relationship between change in spring discharge relative to baseline and precipitation, 1995–2009 in the (a) nowwht, (b) nornge, (c) noag and (d) fert scenarios.

and summer seasons only. These seasons were therefore

switchgrass produced the largest increase in eT. Since cli-

used to explore the hydrologic impacts of replacing various

mactic inputs are identical in all scenarios, we

current land use types with switchgrass under different man-

hypothesize that increased eT is most likely the result

agement practices. The major ﬁndings of the study are as

of the quantity of switchgrass biomass generated.

follows.

3. The summer impacts of managed switchgrass scenario are the most acute in the MNCR. This approach is

1. Replacing any land use type with switchgrass reduces

responsible for a 31% decrease in discharge and 19%

streamﬂow discharge. The decreases ranged from 6 to

increase in eT. Such impacts are signiﬁcant in semiarid

21% (spring) and from 6 to 31% (summer). Overall, the

areas where evaporative losses are already high and dis-

reduction was greatest for the scenario in which native

charges are relatively low (baseline discharges of 7.4

land uses were replaced by heavily managed switchgrass.

and 5.03 cms during the spring and summer, respectively,

The degree of the reduction is a function of the amount of

in the MNCR).

area replaced. 2. Switchgrass substitution also leads to increased eT rela-

These results suggest that the hydrologic impacts of

tive to base period for all scenarios investigated. The

switchgrass cultivation may be non-trivial. The possible

increases ranged from 3 to 32% (spring) and 2 to 19%

effects of such impacts on the sustainability of the water

(summer). The scenario involving heavily managed

supplies in a groundwater-dependent region already facing

111

Figure 7

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

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Differences in basin-wide (a) spring (solid) and summer (striped) eT associated with switchgrass production and (b) the percent change in spring and summer eT relative to baseline in all scenarios during the simulation period, 1995–2009. The boxplots are read as for Figure 5.

the effects of groundwater depletion deserve careful con-

as well as investigations into the possible confounding

sideration. We recognize that any decision about land use

effects of the impact of climate change.

modiﬁcation on the scale analyzed here will likely involve a cost-beneﬁt analysis that includes many more variables than just the regional hydrology. These results can be an

ACKNOWLEDGEMENTS

important component of such a decision matrix. The study highlights the need for further simulations that include a

David Brauer receives ﬁnancial support from the Ogallala

larger variety of biofuel crops, an analysis of all seasons,

Aquifer Program, a research and education consortium

J. C. Goldstein et al.

112

Response of a semiarid watershed to switchgrass cultivation

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45.1

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consisting of ARS-USDA, Kansas State University, Texas AgriLife/TAMU, Texas Tech University and West Texas A&M University. Additionally, the authors express their gratitude to Dr Raghavan Srinivasan (Texas A&M University) for his insights into the SWAT model. Finally, the authors thank the two anonymous reviewers for providing insightful comments which improved the quality of this manuscript.

REFERENCES |

Figure 8

Relationship between the change in seasonal eT in the four switchgrass scenarios relative to baseline, and the quantity of switchgrass biomass (in 100,000 metric tons) during the spring and summer.

Table 6

Average quantity of spring and summer water stress days, by scenario, 1995– 2009

Scenario

Spring

Summer

Baseline

5.74

11.02

Nowwht

5.57

13.23a

Nornge

7.32

16.05a

Noag

7.15a

18.26a

43.33a

Fert a

13.03

Quantities are statistically signiﬁcant (p < 0.05) relative to baseline.

Table 7

The strength of the relationship between changes in eT (mm) and discharge (cms) in each scenario by season, as measured by R 2 and p-values

Scenario

p-value

Spring Nowwht

0.11

0.232

Nornge

0.81

5.2 × 10 6

Noag

0.64

0.003

Fert

0.59

0.0008

Summer Nowwht

0.01

0.77

Nornge

0.50

3.36 × 10 3

Noag

0.47

0.0047

Fert

0.48

0.004

Adams, G. P., Runkle, D. L. & Rea, A.  Digital data sets that describe aquifer characteristics of the alluvial and terrace deposits along the Beaver-North Canadian River from the Panhandle to Canton Lake in Northwestern Oklahoma. Open-File Report 96–446. US Geological Survey, Oklahoma City, USA. Arnold, J. G., Srinivasan, R., Muttiah, R. S. & Williams, J. R.  Large area hydrologic modeling and assessment. Part 1: Model development. Journal of American Water Resources Association 34, 73–89. Baskaran, L., Jager, H. I., Schweizer, P. E. & Srinivasan, R.  Progress towards evaluating the sustainability of switchgrass as a bioenergy crop using the SWAT model. Transactions of the ASABE 53, 1547–1556. Bush, G. W.  Address before a Joint Session of the Congress on the State of the Union. Government Printing Office, Washington, DC, USA. Chamberlain, J. F., Miller, S. A. & Frederick, J. R.  Using DAYCENT to quantify on-farm GHG emissions and N dynamics of land use conversion to N-managed switchgrass in the Southern U.S. Agriculture, Ecosystems and Environment 141, 332–341. Davis, R. E. & Christenson, S. C.  Geohydrology and numerical simulation of the alluvium and terrace aquifer along the Beaver-North Canadian River from the Panhandle to Canton Lake, Northwestern Oklahoma. Open-file Report 81–483. US Geological Survey, Oklahoma City, USA. Douglas-Mankin, K. R., Srinivasan, R. & Arnold, J. G.  Soil and water assessment tool (SWAT) model: current developments and applications. Transactions of the ASABE 53, 1423–1431. Du, J., Qian, L., Rui, H., Zuo, T., Zheng, D., Xu, Y. & Xu, C. Y.  Assessing the effects of urbanization on annual runoff and flood events using an integrated hydrological modeling system for Qinhuai River basin, China. Journal of Hydrology 464, 127–139. Foley, J. A., DeFries, R., Asner, G. P., Barford, C., Bonan, G., Carpenter, S. R., Chapin, F. S., Coe, M. T., Daily, G. C., Gibbs, H. K., Helkowski, J. H., Holloway, T., Howard, E. A., Kucharik, C. J., Monfreda, C., Patz, J. A., Prentice, I. C.,

113

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

Ramankutty, N. & Snyder, P. K.  Global consequences of land use. Science 309, 570–574. Franczyk, J. & Chang, H.  The effects of climate change and urbanization on the runoff of the Rock Creek basin in the Portland metropolitan area, Oregon, USA. Hydrological Processes 23, 805–815. Garoma, T., Ben-Khaled, M. & Beyene, A.  Comparative resource analyses for ethanol produced from corn and sugarcane in different climatic zones. International Journal of Energy Research 36, 1065–1076. Gassman, P. W., Reyes, M. R., Green, C. H. & Arnold, J. G.  The soil and water assessment tool: historical development, applications, and future research directions. Transactions of the ASABE 50, 1211–1250. Georgescu, M. & Lobell, D. B.  Perennial questions of hydrology and climate. Science 330, 33. Gerbens-Leenes, W., Hoekstra, A. Y. & van der Meer, T. H.  The water footprint of Bioenergy. Proceedings of the National Academy of Sciences of the United States of America, 106, pp. 10219–10223. Glennon, R. J.  Unquenchable: America’s Water Crisis and What to Do About It. Island Press, Washington, DC. Goins, C. R. & Anderson, J. H.  Geomorphic provinces. In: Historical Atlas of Oklahoma, 4th edition (C. R. Goins & D. Goble, eds). University of Oklahoma Press, Norman, OK, USA. Graham, R. L., Downing, M. & Walsh, M. E.  A framework to assess regional environmental impacts of dedicated energy crop production. Environmental Management 20, 475–485. Gupta, H. V., Sorooshian, S. & Yapo, P. O.  Status of automatic calibration for hydrologic models: comparison with multilevel expert calibration. Journal of Hydrologic Engineering 4, 135–143. Jiang, S., Ren, L., Yong, B., Fu, C. & Yang, X.  Analyzing the effects of climate variability and human activities on runoff from the Laohahe basin in northern China. Hydrology Research 43, 3–13. Kustu, M. D., Fan, Y. & Robock, A.  Large-scale water cycle perturbation due to irrigation pumping in the US High Plains: a synthesis of observed streamflow changes. Journal of Hydrology 390, 222–244. Lakshmi, V., Hong, S., Small, E. E. & Chen, F.  The influence of the land surface on hydrometeorology and ecology: new advances from modeling and satellite remote sensing. Hydrology Research 42, 95–112. Ma, X., Xu, J. C., Luo, Y., Aggarwal, S. P. & Li, J. T.  Response of hydrological processes to land-cover and climate changes in Kejie watershed, south-west China. Hydrological Processes 23, 1179–1191. McGuire, V. L.  Water-level changes in the High Plains Aquifer, predevelopment to 2009, 2007–08, and 2008–09, and change in water in storage, predevelopment to 2009. US Geological Survey Scientific Investigations Report 2011– 5089. US Geological Survey, Reston, USA.

Hydrology Research

45.1

2014

McIsaac, G. F., David, M. B. & Mitchell, C. A.  Miscanthus and switchgrass production in central Illinois: impacts on hydrology and inorganic nitrogen leaching. Journal of Environmental Quality 39, 1790–1799. Mitchell, R., Wallace, L., Wilhelm, W., Varvel, G. & Wienold, B.  Grasslands, Rangelands, and Agricultural Systems. Biofuels and Sustainability Reports: Ecological Society of America, Washington, DC, USA. Moriasi, D. N., Arnold, J. G., Van Liew, M. W., Bingner, R. L., Harmel, R. D. & Veith, T. L.  Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of the ASABE 50, 885–900. Nash, J. E. & Sutcliffe, J. V.  River flow forecasting through conceptual models: Part 1 – a discussion of principles. Journal of Hydrology 10, 282–290. National Research Council  Water Implications of Biofuel Production in the United States. National Academy Press, Washington, DC, USA. Nelson, R. G., Ascough, J. C. & Langemeier, M. R.  Environmental and economic analysis of switchgrass production for water quality improvement in Northeast Kansas. Journal of Environmental Management 79, 336–347. Ng, T. L., Eheart, J. W., Cai, X. & Miguez, F.  Modeling miscanthus in the soil and water assessment tool. Environmental Science & Technology 44, 7138–7144. Nyakatawa, E. Z., Mays, D. A., Tolbert, V. R., Green, T. H. & Bingham, L.  Runoff, sediment, nitrogen, and phosphorus losses from agricultural land converted to sweetgum and switchgrass bioenergy feedstock production in north Alabama. Biomass & Bioenergy 30, 655–664. One-hundred Tenth Congress of the United States of America  Energy Independence and Security Act. Government Printing Office, Washington, DC, USA. Parrish, D. J. & Fike, J. H.  The biology and agronomy of switchgrass for biofuels. Critical Reviews in Plant Science 24, 423–459. PRISM Climate Group  Oregon State University. Data available at: http://prism.oregonstate.edu (accessed January 2013). Raymond, P. A., Oh, N.-H., Turner, R. E. & Broussard, W.  Anthropogenically enhanced fluxes of water and carbon from the Mississippi River. Nature 451, 449–452. Reisner, M.  Cadillac Desert: The American West and its Disappearing Water. Penguin Books, New York, USA. Ren, L., Liu, X., Yuan, F., Xu, J. & Liu, W.  Quantitative analysis of runoff reduction in the Laohahe basin. Hydrology Research 43, 38–47. Renewable Fuels Association  Available from: http://www. ethanolrfa.org/ (accessed January 2013). Robertson, G. P., Hamilton, S. K., Del Grosso, S. J. & Parton, W. J.  Growing Plants for Fuel: Predicting Effects on Water, Soil, and the Atmosphere. Biofuels and Sustainability Reports: Ecological Society of America, Washington, DC, USA. Sala, O. E., Chapin, F. S., Armesto, J. J., Berlow, E., Bloomfield, J., Dirzo, R., Huber-Sanwald, E., Huenneke, L. F., Jackson,

114

J. C. Goldstein et al.

Response of a semiarid watershed to switchgrass cultivation

R. B., Kinzig, A., Leemans, R., Lodge, D. M., Mooney, H. A., Oesterheld, M., Poff, N. L., Sykes, M. T., Walker, B. H., Walker, M. & Wall, D. H.  Global biodiversity scenarios for the year 2100. Science 287, 1770–1774. Sarkar, S., Miller, S. A., Frederick, J. R. & Chamberlain, J. F.  Modeling nitrogen loss from switchgrass agricultural systems. Biomass & Bioenergy 35, 4381–4389. Scanlon, B. R., Faunt, C. C., Longuevergne, L., Reedy, R. C., Alley, W. M., McGuire, V. L. & McMahon, P. B.  Groundwater depletion and sustainability of irrigation in the US High Plains and Central Valley. Proceedings of the National Academy of Sciences of the United States of America 109, 9320–9325. Schilling, K. E., Chan, K.-S., Liu, H. & Zhang, Y.-K.  Quantifying the effect of land use land cover change on increasing discharge in the Upper Mississippi River. Journal of Hydrology 387, 343–345. Schilling, K. E., Jha, M. K., Zhang, Y. K., Gassman, P. W. & Wolter, C. F.  Impact of land use and land cover change on the water balance of a large agricultural watershed: historical effects and future directions. Water Resources Research 44, W00A09. Schmer, M. R., Vogel, K. P., Mitchell, R. B. & Perrin, R. K.  Net energy of cellulosic ethanol from switchgrass. Proceedings of National Academy of Sciences of the United States of America 105, 464–469. Simpson, T. W., Sharpley, A. N., Howarth, R. W., Paerl, H. W. & Mankin, K. R.  The new gold rush: fueling ethanol production while protecting water quality. Journal of Environmental Quality 37, 318–324. Singh, J., Knapp, H. V. & Demissie, M.  Hydrologic Modeling of the Iroquois River Watershed Using HSPF and SWAT. CR 2004–08. Illinois State Water Survey, Champaign, IL, USA. Thomas, M. A., Engel, B. A. & Chaubey, I.  Water quality impacts of corn production to meet biofuel demands. Journal of Environmental Engineering (ASCE) 135, 1123–1135. Tortorelli, R. L.  Water Use in Oklahoma 1950–2005. Scientiﬁc Investigations Report 2009–5212. US Geological Survey, Reston, USA.

Hydrology Research

45.1

2014

Turner, B. L. II, Lambin, E. F. & Reenberg, A.  The emergence of land change science for global environmental change and sustainability. Proceedings of the National Academy of Sciences of the United States of America 104, 20666–20671. van Griensven, A., Meixner, T., Grunwald, S., Bishop, T., Diluzio, A. & Srinivasan, R.  A global sensitivity analysis tool for the parameters of multi-variable catchment models. Journal of Hydrology 324, 10–23. Vanlocke, A., Bernacchi, C. J. & Twine, T. E.  The impacts of Miscanthus × giganteus production on the midwest US hydrologic cycle. Global Change Biology Bioenergy 2, 180–191. Vorosmarty, C. J., Green, P., Salisbury, J. & Lammers, R. B.  Global water resources: vulnerability from climate change and population growth. Science 289, 284–288. Wagener, T., Sivapalan, M., Troch, P. A., McGlynn, B. L., Harman, C. J., Gupta, H. V., Kumar, P., Rao, P. S. C., Basu, N. B. & Wilson, J. S.  The future of hydrology: an evolving science for a changing world. Water Resources Research 46, W05301. Wahl, K. L. & Tortorelli, R. L.  Changes in ﬂow in the BeaverNorth Canadian River basin upstream from Canton Lake, Western Oklahoma. Water-Resources Investigations Report 96–4304. US Geological Survey, Oklahoma City, USA. Yang, X., Ren, L., Singh, V. P., Liu, X., Yuan, F., Jiang, S. & Yong, B.  Impacts of land use and land cover changes on evapotranspiration and runoff at Shalamulun River watershed, China. Hydrology Research 43, 23–37. Zume, J. T. & Tarhule, A.  Precipitation and streamﬂow variability in northwestern Oklahoma, 1894–2003. Physical Geography 27, 1–17. Zume, J. T. & Tarhule, A.  Simulating the impacts of groundwater pumping on stream–aquifer dynamics in semiarid Northwestern Oklahoma, USA. Hydrogeology Journal 16, 797–810. Zume, J. T. & Tarhule, A.  Modelling the response of an alluvial aquifer to anthropogenic and recharge stresses in the United States Southern Great Plains. Journal of Earth System Science 120, 557–572.

First received 27 September 2012; accepted in revised form 6 January 2013. Available online 31 January 2013

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Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada): an evaluation of regional climate model simulation with respect to two gridded datasets Loubna Benyahya, Philippe Gachon, André St-Hilaire and René Laprise

ABSTRACT This study proposes an assessment procedure to compare two gridded (Cubic Spline, CS, and ANUSPLIN) datasets and one regional climate model simulation series (CRCM 4.1.1) of seasonal maximum precipitation (SMP) over southern Quebec (Canada). This study consists of: (1) identifying the appropriate models that could provide the most accurate SMP estimates at a particular grid point; (2) delineating the climatic homogeneous regions; and (3) providing sub-regional intensity– duration–frequency (IDF) estimates. More speciﬁcally, ﬁve popular probability distributions (Generalized Extreme Value, Generalized Logistic, Weibull, Gamma, Log-Normal) are compared; cluster analysis was employed to delineate a set of homogeneous sub-regions and one empirical model (Montana) was used to represent IDF relationships. From the results, it was found that: (1) CS product is more compatible with mean and maximum observed SMP time series than that of ANUSPLIN and CRCM 4.1.1 datasets, especially in summer; (2) Generalized Extreme Value represents the primary distribution pattern for the study area; (3) southern Quebec can be delineated into two

Loubna Benyahya (corresponding author) Philippe Gachon René Laprise ESCER Centre, University of Quebec at Montreal (UQAM), Montréal (Quebec) Canada, H3C 3P8 E-mail: loubna_benyahya@hotmail.com Philippe Gachon Canadian Centre for Climate Modelling and Analysis, Climate Research Division, Environment Canada, Montréal (Quebec) Canada, H5A 1L9 André St-Hilaire Institut National de la Recherche Scientiﬁque, Eau-Terre-Environnement (INRS-ETE), Quebec (Quebec) Canada, G1K 9A9

distinct homogeneous sub-regions, especially in winter; and (4) Montana equation provides an accurate IDF model. This study can be viewed as an initial step towards the development of IDF curves under non-stationary conditions within the context of seasonal features in the regional precipitation regime. Key words

| duration and occurrence, frequency analysis, precipitation extremes, seasonal maximum series

INTRODUCTION Under the global warming scenario, climate models gener-

trend of observed extreme precipitation events during recent

ally project an increase in large-scale precipitation events

decades in the USA and Australia (Easterling et al. ;

(Houghton et al. ). Indeed, alterations in patterns of

Groisman et al. ; Kunkel ), in the UK in winter

global atmospheric circulation are projected to modify

(Osborn & Hulme ), and in South Africa (Fauchereau

mean annual precipitation and to increase inter- and intra-

et al. ). In Canada, extreme rainfall events show no sig-

annual variability of precipitation (Easterling et al. ;

niﬁcant and/or consistent trends (Zhang et al. ; Kunkel

Seneviratne et al. ; IPCC ). However, at the

; Vincent & Mekis ). However, Vincent & Mekis

regional and local scales, impacts of climate changes are

() noted that the inconsistency in these trends could

felt most strongly through changes in extreme events.

be due to the high variability of the extreme precipitation

Recent studies have shown that there has been an increasing

events or to the sparse station network, especially in

doi: 10.2166/nh.2013.066

116

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Hydrology Research

45.1

2014

northern Canada. The lack of consistent patterns in extreme

scale and acknowledged that they may be improved by

precipitation highlights the need to explore local character-

using point estimates. Other detailed descriptions of the

istics of precipitation extremes for regional studies.

future changes of extreme precipitations from regional cli-

In engineering projects, when it comes to making

mate model simulation in intensity and duration can be

operational water resources planning and designing infra-

found in Mladjic et al. (), as well as from statistical down-

structure, it is important for water managers to be informed

scaling results over southern Quebec in Jeong et al. ().

adequately concerning the frequency of extreme precipi-

In Canada, except for the Maritime and Western pro-

tations in a region. According to Brian et al. (,

vinces (where large-scale inﬂuences play an important role

unpublished paper), rainfall frequency analyses are used

in the annual maximum precipitation during the winter

extensively in the design of systems to handle storm runoff,

season), the extremes are prominent during the summer

including roads, culverts, and drainage systems. The objec-

period for most of the country. That is why a seasonally

tive of the frequency analysis is to relate the magnitude of

and regionally based analysis needs to be done to explore

an extreme event to its frequency of occurrence through the

local characteristics of precipitation extremes. As noted by

use of probability distributions (Bobée ). This method

Mladjic et al. (), it should be recognized that there is cur-

has been the subject of several studies dealing with ﬂoods

rently no comprehensive high-resolution observed dataset of

(e.g., Bobée & Ashkar ) and low streamﬂow (e.g., Kroll

precipitation that would allow a satisfactory analysis of pre-

& Vogel ; Ouarda et al. ; Benyahya et al. ). In

cipitation extremes. In view of these issues, the main goal of

order to better understand extreme events, the focus needs

the present study is to compare two gridded product data

to be not only on their intensity but also on their duration.

interpolated using Cubic Spline (CS) and ANUSPLIN

This is why the evaluation of extreme events, as embodied

(Australian

National

University

SPline

INterpolator;

in the intensity–duration–frequency (IDF) relationship, has

Hutchinson ; Hutchinson et al. ) methods and

been a major focus of both theoretical and applied hydrology

one series of CRCM 4.1.1 simulation throughout southern

(Langousis & Veneziano ). IDF curve development and

Quebec (Canada). For each product and for winter and

characterization of regional rainfall extremes are areas of

summer periods, the speciﬁc objectives are: (1) to determine

continuing research, as evidenced by many studies (Madsen

the ‘best’ probability distribution for multi-day seasonal

et al. ). Prodanovic & Simonovic () developed IDF

maximum precipitation (SMP) (i.e., 1, 2, and 3 consecutive

curves for the current and future climate for the city of

days); (2) to delineate the climatic homogeneous regions

London (Ontario, Canada) using a K-Nearest Neighbor

for SMP; and (3) to provide sub-regional IDF estimates, in

(K-NN)-based weather generator. Artiﬁcial Neural Networks

order to provide those sub-regions with relevant risk assess-

(ANN) have been successfully used for the rainfall IDF pro-

ment and adaptation strategies. To the best of our

cess (Garcia-Bartual & Schneider ; Senocak & Acar

knowledge, this study is the ﬁrst attempt to conduct an

). Kim et al. () improved the accuracy of IDF

evaluation (in terms of regional frequency analysis) of var-

curves by using long and short duration separation techniques.

ious regional climate products in southern Quebec. This

They derived the IDF curve by using cumulative distribution

investigation is expected to contribute to exploring the com-

function of the site of interest and a multi-objective genetic

plex feature of extreme precipitation in southern Quebec,

algorithm (MOGA). Ben-Zvi () estimated IDF relation-

which is beneﬁcial to engineers and water resource man-

ships using a partial duration series and pointed out

agers, and future climate change studies.

improvements in the prediction of maximum rain intensity

The remainder of the paper is structured as follows. The

values, compared to intensity values estimated from the

next section presents the study area and the data. This is fol-

annual series. Huard et al. () applied a Bayesian analysis

lowed by the methodology used for local frequency analysis,

to the estimation of IDF curves. Mailhot et al. () used out-

delineation of homogeneous sub-regions and IDF analysis of

puts from Canadian Regional Climate Models (CRCM A2) to

SMP and application of an empirical regional prediction

develop IDF over southern Quebec, for the grid scale of

model. The results and discussion follow and ﬁnally, con-

45 km. The results indicated the limitation of using grid

clusions are drawn.

117

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

METHODS

Hydrology Research

45.1

2014

dimensions: latitude, longitude, and elevation. These are analogous to cubic splines in one dimension. For the validation of the above two methods, the CRCM simulations

Data and study area

driven by NCEP/NCAR (National Centers for EnvironThe study region encompasses the southern Quebec W

(Canada) area (south of 50 N) (Figure 1). In order to com-

mental Protection, National Centre for Atmospheric Research) version 4.1.1 data (e.g. Brochu & Laprise ;

pare with CRCM simulations, two gridded datasets

Music & Caya ) were selected. This selection was

obtained by interpolation technique are used. The ﬁrst pro-

based on the availability of continuous daily series for the

duct corresponds to CS data in which we have used a

period 1961–2001 at a spatial resolution of 45 km.

Cubic Spline method for interpolating daily precipitation

We ﬁrst reasoned that, as smoothing effect is inherent to

from Environment Canada meteorological stations (69) in

all interpolation methods, there is still no interpolation

southern Quebec onto a 45-km polar stereographic grid

method which will guarantee the best results for all datasets.

over the 1961–1999 period. The second product corre-

Second, smoothing always increases as the number of neigh-

sponds to ANUSPLIN data developed by Hutchinson

bors increases (Herzfeld et al. , Figure 3). However, to

et al. (), who have developed a Canada-wide spatial

assess the smoothing effect, the cross-validation technique

interpolation tool (≈10-km gridded climate dataset) for

(i.e., Jackknife resampling) can be used. It should be kept

daily precipitation from Environment Canada stations. The

in mind that even if interpolation methods tend to smooth

10-km gridded dataset of daily precipitation has been down-

data in space and time, they remain widely used. Indeed,

graded to 45-km grid spacing by Eum et al. () over the

as part of the European Union Framework 6 ENSEMBLES

same area. ANUSPLIN data were generated using thin-

project, Haylock et al. () used a two-stage process in

plate smoothing splines ﬁtted to observations in three

their methodology: station data are ﬁrst interpolated as

Figure 1

Location map of the study area and position of the meteorological stations (red circles) and the ANUSPLIN grid points (crosses) from the CRCM polar stereographic projection.

L. Benyahya et al.

118

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Hydrology Research

45.1

2014

point estimates to a ﬁne grid, after which the point estimates

Independence was tested using the autocorrelation coefﬁ-

are averaged to obtain area averages for the 25 and 50-km

cient of lag-1, homogeneity was veriﬁed using the Wilcoxon

grids used by various regional modeling centers to validate

test (Wilcoxon ), and stationarity was assessed using

regional-scale simulations over Europe (see the recent

the Kendall test (Kendall ). For all tests, a signiﬁcance

study of Kjellström et al. ()).

level of 1% was used to accept or reject the null hypotheses. If all hypotheses are veriﬁed, statistical distributions can be

Local frequency analysis of seasonal maximum

ﬁtted to the data. In engineering practice, the choice of a suit-

precipitation (SMP)

able probability model is still a problem since there is no general agreement as to which distribution(s) should be

SMP values for the winter (January, February, and March)

used for extreme events. Hence, ﬁve candidate distributions

and the summer (June, July, and August) were extracted

were considered at each grid point: Generalized Extreme

from the original time series of daily precipitation. In tra-

Value (GEV), Weibull (WEI3), Generalized Logistic

ditional design frequency analysis, the following steps are

(GLO), Gamma (GAM), and Log-Normal (LN2). Table 1 pre-

used:

sents the probability density function and the associated

•

parameters for each of these models. In general, more par-

• • • •

verify hypotheses of independence, stationarity, and homogeneity; select a group of ‘candidate distributions’; fit each statistical distribution to the observed maxima by estimating the distribution parameters; select the most adequate frequency distribution based on goodness-of-fit; estimate quantiles for specific return periods.

ameters lead to greater flexibility and hence, to a better fit to the data. However, in some cases, difficulties in the parameter estimation arise. Testing two- and three-parameter distributions allows for selecting the best trade-off between goodness-of-fit and parsimony. To estimate the parameters for each of the aforementioned distributions, different procedures exist, including the method of L-moments, the maximum likelihood method, and the method of prob-

The time series should be composed of independent (no

ability-weighted moments (e.g., Kite ; Hosking & Wallis

autocorrelation), homogeneous (i.e., all data come from a

). However, in the present study, the method of maxi-

single population), and stationary (absence of trend) data.

mum likelihood was used since it gives asymptotically

Table 1

Statistical distributions and their probability density functions

Distribution

Generalized Extreme Value (GEV)

Weibull (WEI3)

Probability density function

! 1 x ξ 1=k x ξ 1 1=k f(x) ¼ exp 1 þ k 1þk α α α ∞< x ξ þ α/k if k > 0 and ξ þ α/k < x ∞ if k < 0 α x γ α 1 x γ α f(x) ¼ exp β β β

Generalized Logistic (GLO)

x μ e σ 1 f(x) ¼ 0 x μ σ A σ @1 þ e

Gamma (GAM)

f(x) ¼

1 xa 1 e x=b ba Γ(a)

Log-Normal (LN2)

f(x) ¼

( ln x μ)2 1 pffiffiffiffiffiffi e 2σ2 xσ 2π

Parameters

α: scale parameter; k: shape parameter; ξ: location parameter

α: shape parameter; β: scale parameter; γ: location parameter

σ: scale parameter; μ: location parameter

a: shape parameter; b: scale parameter; Γ(.): gamma function σ: scale parameter; μ: location parameter

119

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Hydrology Research

45.1

2014

optimal estimators of the parameters (i.e., unbiased with

by splitting them into small and homogeneous clusters such

minimum variance; Ashkar et al. ) and it is one of the

that the data inside the same cluster are more similar to

most commonly used methods for estimating parameters of

each other than to the data inside the other clusters. The

a statistical distribution. Moreover, this method can produce

resulting clusters can be represented in the form of the joining

good estimators for three parameter distributions (Bobée

diagram, e.g., dendrogram with similar groups appearing on

).

the same ‘branches’. As there is no formal measure of an ‘opti-

Local estimates of SMP quantiles were obtained using

mal’ number of clusters, the choice of a suitable threshold is

the selected statistical distribution for each season. The

subjective. In the present study, as the study area is relatively

goodness-of-ﬁt between the frequency of occurrence of the

small, the threshold is chosen to deﬁne two sub-regions.

gridded/simulated data and the expected frequencies

Then, in order to combine the multiple partitions obtained

obtained from the hypothesized distribution was assessed

by each data product into a single consensus cluster, the

using statistical criteria. They include the Anderson–Darling

Cluster-based Similarity Partitioning Algorithm (CSPA;

(AD) (D’Agostino & Stephens ) and Kolmogorov–

Strehl & Ghosh ) was used. The CSPA is a novel, robust,

Smirnov (KS) statistics. The best-ﬁtted distribution is the

and efﬁcient combination method that uses the combined simi-

one associated with the smallest value of each criterion.

larity matrix to recluster the data using a similarity-based

Finally, the grid-point SMP quantiles corresponding to the

clustering algorithm (METIS; Karypis & Kumar ).

return periods T ¼ 5, 10, 20, 50, and 80 years were produced. All frequency analyses and statistical tests were performed using the Matlab (version 7.8.0 R2009a) software. It is

Intensity–duration–frequency analysis of SMP and

important to note that for the remainder of the document,

development of regional prediction models

the term ‘gridded’ is related to CS and ANUSPLIN datasets, the term ‘simulated’ is related to CRCM, and the slash ‘/’

The third part of the study was devoted to the SMP IDF

character means ‘or’ depending on the type of data used.

analysis, in which the objective is to estimate the maximum

Delineation of homogeneous sub-regions

ation d (in days) and return period T (in years). The IDF

intensity i of seasonal precipitation (in mm/d) for any durrelation is expressed mathematically as follows:

In the present study, the task is to delineate the study area into sufﬁciently small numbers of homogeneous sub-regions by

i ¼ f(T, d)

(1)

grouping grid points or area according to their similarities in precipitation regime. Several attempts have been made

In the ﬁrst step, samples of seasonal maximum 1, 2, and

by different authors to identify homogeneous regions based

3-day precipitation amounts were drawn from each grid-

on geographical, hydrological, climatic, and physiographic

point record using a moving window. In the second step,

variables. These techniques include the regression analysis,

the quantiles of a set of selected return periods (e.g., 5, 10,

L-moment method (Onibon et al. ), multivariate

20, 50, and 80 years) were estimated for each duration.

methods (Chokmani & Ouarda ), and non-parametric

This is done by using the ‘best’ probability distribution func-

approaches (Ouarda & Shu ). Chen & Hong ()

tions obtained from 1-SMP analysis. In the third step, the

used the principal component analysis, self-organizing

empirical formulas are used to construct the SMP IDF

maps, and the L-moment method, for improving estimation

curves. The least-square method is applied to determine

of desired rainfall quantiles of ungauged sites in Taiwan. As

the parameters of the empirical IDF equation that is used

there is no unique approach for identifying homogeneous

to represent intensity–duration relationships. As the selected

regions, in the present study, the hierarchical cluster analysis

durations are less or equal to 3 days, a simple empirical for-

was employed based on quantiles of daily SMP estimated

mula with fewer parameters is selected to avoid the problem

from the ‘best’ distribution. For each data product and over

of over-parameterization. In the present study, one IDF

the 83 grid points, the technique synthesized the SMP data

model was tested, as it is one of the most commonly used

120

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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2014

functions in water resources engineering (Montana type; i.e.,

statistics is greater than that of the gridded/simulated data

Mohymont & Demarée ).

products, which means that these products systematically underestimate the observed variance. This result can be

i(d, T ) ¼

a(T) dη(T )

(2)

where a and η are coefﬁcients to be estimated.

the consequence of the so-called ‘smoothing effect’ often associated with interpolation (or the search neighborhood). Moreover, with respect to the mean, it is clear that, for both seasons, CS shows values close to the observations, while ANUSPLIN and CRCM tend to show negative (underestimation) bias. For the minimum SMP, in winter, the two

RESULTS AND DISCUSSION

gridded products (CS and ANUSPLIN) overestimate the observed values, while the CRCM underestimates them. In

The SMP data over the 83 grid points obtained from each

summer months, the gridded/simulated SMP values repro-

dataset (CS, ANUSPLIN, and CRCM4.1.1) are ﬁrst com-

duced the observed data quite well; while there is a slight

pared with the observed meteorological stations (69) over

overestimation from the CS values. For the maximum

the whole study area and the entire time window (1961–

SMP, in winter, the values are also quite well reproduced

1999). The summary of various statistics (i.e., minimum,

by all gridded/simulated data, except for the ANUSPLIN

maximum, mean, skewness, and coefﬁcient of variation)

which underestimates the observed values. In summer, this

for 1-day SMP is presented in Figure 2. For both summer

location parameter is systematically underestimated by all

and winter seasons, the observed variability of all the

gridded/simulated values, especially with the CRCM

Figure 2

Box plots of statistics of seasonal 1-day maximum precipitation of observed meteorological stations, CS, ANUSPLIN, and CRCM 4.1.1 (1961–1999) for winter season (upper panels) and summer season (lower panels).

L. Benyahya et al.

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Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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datasets (i.e., by more than 20 mm/d in median values). It

(2.4%) grid points for durations of 2 days and 3 days, respect-

may be noted that the range of coefﬁcient of variation

ively (Table 2). In terms of serial autocorrelation, with the

values of all data products are generally less than 0.5 both

exception of some grid points for CRCM4.1.1 (between 1

in winter and summer seasons, which indicates that the

and 3), the results showed that all the autocorrelation coefﬁ-

data are relatively closely clustered. More differences

cients of lag-1 achieved values lower than 0.4 (in absolute

between CS and ANUSPLIN vs. CRCM values are present

value). This implies, in the present study, that the SMP

in the winter season for this parameter than for summer.

data are serially independent. In the present study, grid

Also, it is indicated that the distributions of precipitation

points for which the above-mentioned conditions are not

are more positively skewed in summer than in winter, and

fully satisﬁed were further removed from the analysis.

all gridded/simulated products reproduce relatively well

As stated earlier, in order to determine the ‘best’ ﬁt model(s) at each grid point that met the requirements for fre-

these features. The hypotheses of independence, homogeneity, and sta-

quency analysis, ﬁve probability distribution models were

tionarity were veriﬁed using respectively, autocorrelation

subjected to two (2) statistical criteria: the Anderson–

coefﬁcient of lag-1, Wilcoxon and Kendall tests, on each

Darling (AD) and Kolmogorov–Smirnov (KS) tests. The

grid point for winter and summer (Table 2). All time series

assessment of the probability distribution models was

of seasonal maximum precipitations were tested for statio-

based on the total test score obtained from all the criteria.

narity (Kendall test), independence (serial autocorrelation),

Criteria scores ranging from one to ﬁve (1–5) are awarded

and homogeneity (Wilcoxon test), as a prerequisite for fre-

to each distribution model based on the criteria that the dis-

quency analysis. Table 2 shows the percentage of grid

tribution with the highest total score is chosen as the ‘best’

points that successfully passed these tests at signiﬁcance

distribution model for the data in the study area. In general,

levels of 1%. The test results conﬁrmed that the majority

the ‘best’ distribution is awarded a score of ﬁve (5), the next

of the grid-point series are homogeneous and independent

best is awarded four (4), and so on, in descending order.

(Table 2). However, an exception has occurred in cases

Overall ranks of each distribution were obtained by sum-

where the stationarity and homogeneity conditions have

ming the individual ranks of each criterion. Table 3

not been satisﬁed. For example, during the winter,

summarizes the overall ranking results for winter and

CRCM4.1.1 product displayed signiﬁcant trend for only 6

summer seasons, with ranks given in parentheses. Examin-

and 8% of grid points for durations of 1 day and 2 days,

ation of the goodness-of-ﬁt test results reveals that in many

respectively (Table 2). Also, during the summer, a non-

cases there was negligible difference between the various

homogeneity in CS was detected for three (3.6%) and two

distributions for the whole study area. The overall ranks

Table 2

Results of the Mann–Kendall and Wilcoxon tests as well as autocorrelation coefﬁcients on SMP for various durations (1, 2, and 3 days) and for CS, ANUSPLIN, and CRCM4.1.1. Percentages of grid points that showed p-values values greater to the signiﬁcance level of 0.01

CS (winter)

ANUSPLIN (winter)

CRCM 4.1.1 (winter)

1 day

2 days

3 days

1 day

2 days

3 days

1 day

2 days

3 days

Independence

100%

97.34%

99.12%

100%

Stationarity

100%

94%

91.7%

100%

Homogeneity

98.8%

100%

CS (summer)

ANUSPLIN (summer)

CRCM 4.1.1 (summer)

1 day

2 days

3 days

1 day

2 days

3 days

1 day

2 days

3 days

Independence

100%

99.12%

Stationarity

100%

96.4%

100%

98.8%

100%

Homogeneity

100%

96.4%

97.6%

100%

98.8%

100%

L. Benyahya et al.

122

Table 3

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Hydrology Research

45.1

2014

Summarized results of the ﬁtted distributions (GEV, GLO, GAM, LN, and WEI3) on SMP for 1-day duration of CS, ANUSPLIN, and CRCM 4.1.1 and their corresponding test scores (in parentheses)*. The values are averaged from all grid-point information of the study area

Average values (winter) CS

Criterion

Distribution

GEV GLO GAM LN WEI3

0.39 (5) 0.57 (1) 0.43 (2) 0.41 (3) 0.40 (4)

0.29 (5) 0.43 (1) 0.34 (3) 0.36 (2) 0.33 (4)

0.26 (5) 0.76 (1) 0.50 (2) 0.34 (4) 0.40 (3)

0.27 (5) 0.78 (1) 0.53 (2) 0.37 (4) 0.41 (3)

0.34 (5) 1.03 (1) 0.87 (2) 0.64 (3) 0.63 (4)

0.29 (5) 0.78 (1) 0.61 (2) 0.44 (3) 0.42 (4)

GEV GLO GAM LN WEI3

0.10 (5) 0.10 (5) 0.10 (5) 0.10 (5) 0.10 (5)

0.10 (5) 0.10 (5) 0.11(4) 0.10 (5) 0.10 (5)

0.08 (5) 0.11 (2) 0.11 (2) 0.09 (4) 0.10 (3)

0.08 (5) 0.11 (2) 0.11 (2) 0.096 (4) 0.10 (3)

0.09 (5) 0.10 (4) 0.11 (3) 0.10 (4) 0.11 (3)

0.09 (5) 0.11 (3) 0.12 (2) 0.10 (4) 0.10 (4)

Total scores

GEV GLO GAM LN WEI3

10 6 7 8 9

ANUSPLIN

Average values (summer)

10 6 7 7 9

CRCM 4.1.1

10 3 4 8 6

ANUSPLIN

10 5 5 7 7

CRCM 4.1.1

10 4 4 7 8

KS: Kolmogorov–Smirnov test; AD: Anderson Darling statistic; RMSE: root mean square error. *Best distribution is awarded a score of ﬁve (5), the next best is awarded four (4), and so on, in descending order.

combined show that the GEV distribution was the most

possible to estimate the SMP for different return periods.

appropriate probability distribution model to describe the

Since the dataset covers 39 years, in practice, the highest

SMP series for all products for summer and winter seasons

return period to be considered for further analysis is typi-

in southern Quebec (Table 3). It was also found that LN and

cally less or equal to twice the length of record (T 2 ×

WEI3 gave quite good performances, depending on the pro-

39 ≅ 80 years). Quantiles associated with return periods of

duct and the season. For instance, the WEI3 distribution

2, 5, 10, 20, and 80 years (corresponding respectively to

was found to be the second ‘best’ ﬁtted distribution for CS

probabilities of non-exceedance of 0.80, 0.90, 0.95, 0.98,

and ANUSPLIN in winter and for CRCM 4.1.1 in

and 0.9875) were estimated. For each data series and each

summer. The GLO and the GAM distributions ranked con-

season, the degree of ﬁt of each distribution was visually

sistently poorly compared to the others. However, the fact

examined (Figures 3 and 4) with gridded/simulated vs.

that a distribution has a low ranking does not necessarily

values produced by the frequency analysis for the whole

mean that it performed poorly, since the differences in good-

study area (considered as one population). For low return

ness-of-ﬁt between different distributions was relatively

periods, no noticeable differences between the GEV, LN

small in some cases. Moreover, it can be expected that distri-

and between GEV and WEI3 distributions were suggested,

butions with three parameters (GEV and WEI3) could

whereas for high return periods (e.g., 50 and 80 years),

provide better ﬁt to the data. This appropriateness of the

more consistent probabilities were revealed from LN and

GEV distribution was also suggested in the literature by Over-

WEI3 distributions, respectively for CS and CRCM4.1.1

eem et al. (), Veneziano et al. (), and Kingumbi &

datasets, irrespective of the season (Figures 3 and 4). More-

Mailhot (). The popularity of the GEV stems, in part,

over, in winter, the overall quantiles for ANUSPLIN and

from the fact that it has been shown to be a combination of

CRCM4.1.1 were more often lower than those for the CS

the three families of extreme value distributions: Weibull,

product (Figure 3), conﬁrming the systematic underestima-

Fréchet, and Gumbel (e.g., Katz & Brown () for details).

tion with respect to observed values suggested in the box

With series of SMP modeled by the two ‘best’ distri-

plots (i.e., Figure 2). This is also the case in summer, but

butions (namely GEV and/or LN and WEI3), it becomes

more clearly for high return periods (e.g., 50 and 80 years,

123

Figure 3

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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Plots of SMP gridded/simulated probabilities of non-exceedence (PNE) vs. values produced by the frequency analysis for different return period for all grid points and for the winter period.

124

Figure 4

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Same as Figure 3 but for the summer season.

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L. Benyahya et al.

125

Figure 5

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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Climate classiﬁcation resulting from the hierarchical cluster algorithm and based on winter maximum quantiles (d ¼ 1 day) estimated by GEV for CS (a), ANUSPLIN (c), and CRCM 4.1.1 (e) data and geographical representation of their respective sub-regions (SR) (b), (d), and (f); (g) is the cluster ensembles (black unﬁlled circles represent the grid points that were removed from the analysis).

126

Figure 6

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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Climate classiďŹ cation resulting from the hierarchical cluster algorithm and based on summer maximum quantiles (d Âź 1 day) estimated by GEV for CS (a), ANUSPLIN (c), and CRCM 4.1.1 (e) data and geographical representation of their respective sub-regions (SR) (b), (d), and (f); (g) is the cluster ensembles.

L. Benyahya et al.

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Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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as also revealed in mean and maximum SMP values in

case, the statistical distributions tested on the SMP with var-

Figure 2).

ious durations were limited to the GEV. Over the whole area,

Before performing the IDF analysis, it was necessary to

the average values of the KS and AD tests’ performance cri-

delineate homogeneous regions in southern Quebec for

teria revealed that the GEV was accepted for all durations

each data product. Hierarchical clustering was performed

(with a signiﬁcance level of 1%) and was shown to provide

for the 5, 10, 20, 50 and 80th quantiles of SMP estimated by

the ‘best’ ﬁt for southern Quebec (see Tables 3 and 4). For

GEV for each data product and season. The dendrograms

instance, locally, for the winter period and for all durations,

are presented in the left panels of Figures 5 and 6, while the

GEV was selected for 53%, 55%, and more than 65% of the

geographical representation of each cluster is shown in the

analyzed grid points of ANUSPLIN, CS, and CRCM4.1.1,

right panels. Using the linkage distance of 15 speciﬁed in

respectively, followed by LN and WEI3 distributions that

Figure 5(a), two sub-regions (SR) have been identiﬁed (SR1

account for 35% and less than 45% of the grid points of

and SR2). The results of the reclustering classiﬁcation for

CRCM4.1.1 and of both CS and ANUSPLIN, respectively.

southern Quebec are shown at the bottom of Figures 5 and

Having deﬁned the homogeneous sub-regions, the next

6 for winter and summer, respectively. In winter, the two

step was to develop IDF estimates. Figure 7 represents the

sub-regions are deﬁned along the axis of the St-Lawrence

sub-regional IDF curves in which the quantiles were

River (southwest–northeast axis), reﬂecting some of the clima-

obtained by ﬁtting the GEV distribution to d-SMP

tological differences in the precipitation regime associated

(duration-SMP) data. According to this ﬁgure, for the

with the known synoptic patterns of storm tracks coming

entire data products and for the same return period, short

from the Great Lakes area toward the Gulf of St-Lawrence.

SMPs are more intense than long SMPs, especially in

However, in summer, these regional features disappear

summer and for higher return periods. It is also noted that

whereas the spatial variability of precipitation increases, i.e.,

the spreading of the IDF curves is relatively similar among

as those are more driven by regional and local forcing factors

the various datasets for high return period values, but is

as topography or surface conditions with a decrease in inﬂu-

much larger in the case of the SR2, especially in summer

ence of large-scale systems during such season.

and for CS values (Figure 7). For example, for 1-day SMP

For each of the analyzed grid points, the frequency analy-

based on CS data, the ratio between the intensity corre-

sis described earlier is carried out using the time series of

sponding to T ¼ 80 years and the intensity corresponding

SMP with durations of 1, 2, and 3 days. In the present

to T ¼ 5 years is equal to 1.89 for SR2 but to 1.69 for SR1

Table 4

Same as Table 3 but for 2 and 3 days’ duration

Average values (winter)

Average values (summer)

Duration

Criterion

Distribution

ANUSPLIN

CRCM 4.1.1

ANUSPLIN

CRCM 4.1.1

2 days

GEV WEI3/LN GEV WEI3/LN GEV WEI3/LN

0.32 (2) 0.37 (1) 0.09 (2) 0.10 (1) 4 2

0.26 (2) 0.28 (1) 0.09 (2) 0.10 (1) 4 2

0.26 (2) 0.29 (1) 0.08 (2) 0.09 (1) 4 2

0.36 (2) 0.50 (1) 0.09 (2) 0.11 (1) 4 2

0.27 (2) 0.49 (1) 0.09 (2) 0.11 (1) 4 2

0.27 (2) 0.36 (1) 0.09 (2) 0.10 (1) 4 2

GEV LN/WEI3 GEV LN/WEI3 GEV LN/WEI3

0.34 (2) 0.39 (1) 0.09 (2) 0.10 (1) 4 2

0.33 (2) 0.41 (1) 0.09 (2) 0.10 (1) 4 2

0.28 (2) 0.31 (1) 0.09 (2) 0.09 (2) 4 3

0.34 (2) 0.50 (1) 0.09 (2) 0.10 (1) 4 2

0.27 (2) 0.50 (1) 0.09 (2) 0.10 (1) 4 2

0.30 (2) 0.42 (1) 0.09 (2) 0.10 (1) 4 2

KS Total scores 3 days

AD KS Total scores

KS: Kolmogorov–Smirnov test; AD: Anderson Darling statistic; RMSE: root mean square error. *As we have two distributions the best distribution is awarded a score two (2) and the next best is awarded one (1).

128

Figure 7

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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Sub-regional IDF curves (gridded/simulated): intensity SMP vs. duration d (1, 2, and 3 days) for different return periods T (5, 10, 20, 50, and 80 years) from CS, ANUSPLIN, and CRCM 4.1.1 during the winter (four top panels) and summer (four bottom panels) seasons obtained from the GEV distribution, and for the two sub-regions (SR1 and SR2) deďŹ ned in Figure 5(g).

0.39 0.37

0.39 0.71

0.75 0.77 59.67 65.76

49.15 0.36

0.30 0.25 0.69 0.69

0.68 46.34

54.98 59.76 0.15 0.25

0.02 0.74

0.78 0.80 63.58 69.36

53.23 0.29

0.37 0.40 0.72 0.73

0.70 49.89

59.00 63.97 0.57 0.78

0.27 0.76

0.78 0.79 76.73 84.50

63.10

2014

0.08 0.22

0.08

56.81

66.43 71.51

50 80

0.76 0.76

0.32 0.36 0.72 0.73

0.20 0.15

45.03 53.80

0.72 0.74

0.01 0.12

36.99 43.37

0.68 0.69

0.17 0.23

39.01 46.00

0.69 0.72

0.05 0.03

34.35 40.25

0.66 0.67

0.33 0.36

35.57 42.11

0.65 0.68

0.09 0.87 51.02 0.21 0.66 23.14 0.74 0.72 42.13 0.23 0.59 33.36 0.91 0.73 49.30 0.96 0.68

0.23

RMSE

0.21 0.14 0.77 0.84 37.88 46.28 0.02 0.19 0.70 0.73 31.64 37.45 0.49 0.65 0.72 0.72 36.45 40.31 0.24 0.23 0.60 0.59 28.09 31.59 0.60 0.80 0.73 0.73 41.12 46.57

0.73 32.11 0.13 0.68 27.38 0.40 0.71 33.21 0.23 0.61 25.35 0.47

0.69

η a

26.67 0.21

RMSE

0.66 23.14

a RMSE

0.31 0.70

η a

29.54 0.23

RMSE

0.61

SR2

45.1

42.56 49.71

from two gridded product data (CS and ANUSPLIN

5 10

The present study compared extreme seasonal precipitation

Table 5

CONCLUSIONS

Summer period

that the slope parameter (η) is small (η 1) for all three data products and for all seasons (Table 5).

42.55

equation. Moreover, in terms of parameters, it was noted

and between 2.20 and 2.24 for those estimated by Montana

0.66 0.85

periods were between 2.21 and 2.26 for the gridded values

0.66 0.67

the 3-day extreme quantity corresponding to all return

34.86 39.94

data, the ratios between the 1-day extreme quantity and

20 50

less than 1 mm/d. Indeed, in the case of CS/SR2/winter

0.72

tana equation may ﬁt well in southern Quebec, with RMSE

36.80

summer (Table 5). Table 5 and Figure 8 show that the Mon-

0.53

20, 50, and 80 years) were calculated for winter and

0.66

square errors (RMSEs) for different return periods (5, 10,

30.97

The parameters of the IDF equations and the root mean

investigated for each data product in southern Quebec.

22.43

lations, one empirical IDF equation (Equation (2)) was

managers without necessarily carrying out complex calcu-

0.36

In order to provide the regional intensity–duration relationships information for engineers and water resources

RMSE

CRCM over most of Canada.

0.72

suggests an underestimation of extreme events by the

single- and multi-day events against the observed values

tation quantiles with 20-, 50-, and 100-yr return periods for

32.16

arrived at similar conclusions. Their validation of precipi-

RMSE

and CRCM4.1.1 products. Indeed, Mladjic et al. ()

0.41

Again, caution should be required when using ANUSPLIN

by the ANUSPLIN and the CRCM-simulated values.

0.65

normals/index_f.html). These features are not reproduced

http://climate.weatherofﬁce.gc.ca/climate_

26.92

see

Return period (years)

the domain (i.e., values corresponding to 1971–2000 climate normal;

period at the Val-d’Or station located in the northwest of

Winter period

comparison with only around 93 mm during the same

SR1

on average more than 119 mm during the August month, by

SR2

located in the southeastern corner of the study area, receives

SR1

northwestern area. For example, the Lennoxville station,

SR2

Appalachian Mountains that are more intense than in the

SR1

for convective summer precipitations in the vicinity of the

CRCM 4.1.1

CRCM4.1.1, respectively). SR2 is a region that is known

ANUSPLIN

(1.73 and 1.79 for ANUSPLIN and 1.75 and 1.85 for

Hydrology Research

0.75

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

the IDF equation for different return periods (5, 10, 20, 50, and 80 years) for the winter and the summer periods and for the two sub-regions (SR1 and SR2)

L. Benyahya et al.

Parameters of Montana empirical equation as IDF curves and the values of the root mean square error (RMSE. in mm/d) between the values obtained from the cumulative density function GEV and those estimated by

129

130

Figure 8

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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Subregional IDF curves (produced by the frequency analysis): intensity SMP vs. return period T and duration d for CS estimated using Montana equation for winter and summer seasons obtained from the GEV distribution.

131

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Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

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interpolated products) and one series of Regional Climate

the local variability of precipitation increases, as it is

Model simulation (CRCM4.1.1) using frequency analysis.

more driven by some regional-scale forcing factors, such

This analysis provides a better overall understanding of the

as topography or surface conditions.

extreme precipitation regime and will contribute to improve

4. One empirical function with two parameters (Montana

climatological and engineering studies. The major con-

equation) was tested to represent IDF relationships. The

clusions of this study are as follows:

IDF empirical model of Montana was appropriate to estimate SMP intensity values for short time duration in the

1. CS gridded data are more compatible with the mean and maximum observed SMP, as the ANUSPLIN and CRCM4.1.1

datasets

underestimate

these

observed

values, especially in summer. Indeed, over most of Canada, Mladjic et al. () have shown an underestimation of extreme events by the CRCM. Therefore, ANUSPLIN and CRCM4.1.1 products should be used

study area. This study is a ﬁrst step towards providing an accurate prediction of seasonal maximum precipitation in southern Quebec. In fact, it is anticipated that the research presented in this paper will be built upon to examine the further possibilities of:

with care for winter and summer SMPs. In particular,

1. quantifying the uncertainties by using multi-model

ANUSPLIN shows important biases for daily precipi-

ensemble systems for future changes in IDF curves (as

tation extreme. 2. Among the ﬁve distributions considered, the GEV, WEI3, and LN distributions provided the best performance for

suggested by Mailhot et al. ) for seasonal maximum rainfall depth; 2. comparing seasonal maximum to peak-over-threshold

daily SMP in southern Quebec, depending on the season

(POT) approach to combine magnitude and duration;

and the data product. However, the highest scores of

3. combining multiple RCMs simulations from NARCCAP

Anderson–Darling and Kolmogorov–Smirnov tests were

and CORDEX runs (i.e., http://www.narccap.ucar.edu/

found for the GEV (three-parameter distribution), as it

and

best ﬁtted the SMP data series for all data products, as

along with multisite statistical downscaling simulations

http://wcrp-cordex.ipsl.jussieu.fr/,

respectively)

well as for various durations and seasons (winter and

to evaluate the potential changes in seasonal precipi-

summer). For the winter period and for all durations,

tation extremes in the study region (as shown recently

GEV was the best choice for 53%, 55%, and more than

in Jeong et al. ).

65% of the analyzed grid points of ANUSPLIN, CS, and CRCM4.1.1, respectively, followed by WEI3 distribution that accounted for less than 45% of the grid points of CS

ACKNOWLEDGEMENTS

and ANUSPLIN LN, and by LN that accounted for 35% of the grid points of CRCM4.1.1. Generally, if one

The authors gratefully acknowledge ﬁnancial support from

wishes to use a two-parameter distribution to model the

the National Sciences and Engineering Research Council

current datasets, the best choice is LN.

of Canada (NSERC). We would like to also acknowledge

3. There is a regionally varying change in seasonal extreme

the Data Access Integration (DAI, see http://loki.qc.ec.gc.

precipitation event occurrence across southern Quebec,

ca/DAI/) Team for providing the data and technical

and two sub-regions have been identiﬁed. In winter,

support, in particular the help of Ms Milka Radojevic in

they are deﬁned along the axis of the St-Lawrence River

preparing the data. The DAI data download gateway is

(southwest–northeast axis), reﬂecting some of the clima-

made possible through collaboration among the FQRNT-

tological

regime

funded Global Environmental and Climate Change Centre

associated with the known synoptic patterns of storm

(GEC3), the Adaptation and Impacts Research Section

tracks coming from the Great Lakes area toward the

(AIRS)

Gulf of St-Lawrence. However in summer, because of

Research Initiative (DRI). The Ouranos Consortium also

site speciﬁcity, the regional features disappear whereas

provides IT support to the DAI team. The CRCM time

differences

the

precipitation

Environment

Canada,

and

the

Drought

132

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

series data have been generated and supplied by Ouranos’ Climate Simulations Team.

REFERENCES Ashkar, F., Bobée, B., Rassmussen, P. F. & Rosbjerg, D.  A perspective on annual maximum flood approach for flood frequency analysis. In: Stochastic and Statistical Methods in Hydrology and Environmental Engineering, Vol. 1 Extreme values: floods and droughts (K. W. Hipel, ed.). Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 3–14. Benyahya, L., Caissie, D., Ashkar, F., El-Jabi, N. & Satish, M.  A comparison of the annual minimum flow and the deficit below threshold approaches: Case study of the province of New-Brunswick (Canada). Can. J. Civil. Eng. 36, 1421–1434. Ben-Zvi, A.  Rainfall intensity–duration–frequency relationships derived from large partial duration series. J. Hydrol. Amst. 367, 104–114. Bobée, B.  Comment on: The Log-Pearson type 3 distribution: The T-year event and its asymptotic standard error by maximum likelihood theory. Water Resour. Res. 15, 189–190. Bobée, B.  Estimation des événements extrêmes de crue par l’analyse des extrêmes: Une revue critique. Houille Blanche. 7, 100–105. Bobée, B. & Ashkar, F.  The Gamma Family and Derived Distributions Applied in Hydrology. Water Resources Publications, Fort Collins, CO, pp. 203. Brian, H., Zelinka, C., Castello, C. & Curtis, D.  Spatial analysis of storms using GIS. Unpublished paper, OneRain Inc., 9267 Greenback Lane, Orangevale, p. 1. Brochu, R. & Laprise, R.  Surface water and energy budgets over the Mississippi and Columbia river basins as simulated by two generations of the Canadian regional climate model. Atmos-Ocean 45, 19–35. Chen, L. H. & Hong, Y. T.  Regional Taiwan rainfall frequency analysis using principal component analysis, self-organizing maps and L-moments. Hydrol. Res. 43 (3), 275–285. Chokmani, K. & Ouarda, T. B. M. J.  Physiographical space based kriging for regional flood frequency estimation at ungauged sites. Water Resour. Res. 40, W12514. D’Agostino, R. B. & Stephens, M. A.  Goodness-of-fit Techniques. Marcel Dekker, Inc., New York. Easterling, D. R., Meehl, G. A., Parmesan, C., Changnon, S. A., Karl, T. R. & Mearns, L. O.  Climate extremes: Observations, modeling, and impacts. Science 289, 2068–2074. Eum, H.-I., Gachon, P., Laprise, R. & Ouarda, T. B. M. J.  Evaluation of regional climate model simulations versus gridded observed and regional reanalysis products using a combined weighting scheme. Clim. Dynam. 38, 1433–1457. Fauchereau, N., Trzaska, S., Roualt, M. & Richard, Y.  Rainfall variability and changes in southern Africa during the

Hydrology Research

45.1

2014

20th century in the global warming context. Nat Hazard. 29, 139–154. Garcia-Bartual, M. & Schneider, H.  Estimating maximum short-duration rainfall intensities from extreme convictive storms. Phys. Chem. Earth (B) 26, 675–681. Groisman, P. Y., Knight, R. W. & Karl, T. R.  Heavy precipitation and high streamflow in the contiguous United States: Trends in the twentieth century. B. Am. Meteorol. Soc. 82, 219–246. Haylock, M. R., Hofstra, N., Klein Tank, A. M. G., Klok, E. J., Jones, P. D. & New, M.  A European daily highresolution gridded data set of surface temperature and precipitation for 1950–2006. J. Geophys. Res. 113, D20119. Herzfeld, U. C., Eriksson, M. G. & Holmund, P.  On the influence of kriging parameters on the cartographic output – a study in mapping subglacial topography. Math. Giol. 25, 881–900. Hosking, J. R. M. & Wallis, J. R.  Regional Frequency Analysis: An Approach Based on L-moments. Cambridge University Press, Cambridge, UK. Houghton, J. T., Ding, Y., Griggs, D. J., Noguer, M., van der Linden, P. J., Dai, X., Maskell, K. & Johnson, C. A.  Climate Change 2001: The Scientific Basis. Contributions of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge, UK. Huard, D., Mailhot, A. & Duchesne, S.  Bayesian estimation of intensity–duration–frequency curves and of the return period associated to a given rainfall event. Stoch. Environ. Res. Risk. Assess. 2, 337–347. Hutchinson, M. F.  Interpolating mean rainfall using thin plate smoothing splines. Int. J. Geogr. Inf. Syst. 9, 385–403. Hutchinson, M., McKenney, D. W., Lawrence, K. & Pedlar, J. H.  Development and testing of Canada-wide interpolated spatial models of daily minimum–maximum temperature and precipitation for 1961–2003. J. Appl. Meteorol. Climatol. 48, 725–741. IPCC  Climate change 2007: the physical science basis, summary for policymakers. International Panel on Climate Change Secretariat, Geneva. Jeong, D. I., St-Hilaire, A., Ouarda, T. B. M. J. & Gachon, P.  Projection of future daily precipitation series and extreme events by using a multi-site statistical downscaling model over the great Montréal area, Quebec, Canada. Hydrol. Res. 44 (1), 147–168. Karypis, G. & Kumar, V.  A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20, 359–392. Katz, R. W. & Brown, B. G.  Extreme events in a changing climate: variability is more important than averages. Climatic Change 21, 289–302. Kendall, M. G.  Rank Correlation Methods. Charles Griffin, London. Kim, T., Shin, J., Kim, K. & Heo, J.-H.  Improving Accuracy of IDF Curves Using Long- and Short- duration Separation and

133

L. Benyahya et al.

Frequency analysis of seasonal extreme precipitation in southern Quebec (Canada)

Multi-Objective Genetic Algorithm. 2008 EWRI Congress, 12–16 May, Honolulu, Hawaii. Kingumbi, A. & Mailhot, A.  Courbes Intensité-DuréeFréquence (IDF): comparaison des estimateurs des durées partielles et des maximums annuels. Hydrol. Sci. J. 55 (2), 162–176. Kite, G. W.  Frequency and Risk Analyses in Hydrology. Water Resources Publications, Fort Collins, CO. Kjellström, E., Boberg, F., Castro, M., Christensen, J. H., Nikulin, G. & Sanchez, E.  Daily and monthly temperature and precipitation statistics as performance indicators for regional climate models. Climate Res. 44 (2–3), 135–150. Kroll, C. N. & Vogel, R. M.  Probability distribution of low streamﬂow series in the United States. J. Hydrol. Eng. ASCE 7, 137–146. Kunkel, K. E.  North American trends in extreme precipitation. Nat Hazards 29, 291–305. Langousis, A. & Veneziano, D.  Intensity–duration–frequency curves from scaling representations of rainfall. Water Resour. Res. 43, W02422. Madsen, H., Mikkelsen, P. S., Rosbjerg, D. & Harremoës, P.  Regional estimation of rainfall intensity–duration–frequency curves using generalized least squares regression of partial duration series statistics. Water Resour. Res. 38, 1239. Mailhot, A., Duchesne, S., Caya, D. & Talbot, G.  Assessment of future change in intensity–duration–frequency (IDF) curves for southern Quebec using the Canadian regional climate model (CRCM). J. Hydrol. 347, 197–210. Mladjic, B., Sushama, L., Khaliq, M. N., Laprise, R., Caya, D. & Roy, R.  Canadian RCM projected changes to extreme precipitation characteristics over Canada. J. Climate 24, 2565–2584. Mohymont, B. & Demarée, G. R.  Courbes intensité-duréefréquence des précipitations de Yangambi, Congo, au moyen de différents modèles de types Montana. Hydrol. Sci. J. 51, 236–253. Music, B. & Caya, D.  Evaluation of the hydrological cycle over the Mississippi River basin as simulated by the Canadian Regional Climate Model (CRCM). J. Hydrometeorol. 8, 969–988. Onibon, H., Ouarda, T. B. M. J., Barbet, M., St-Hilaire, A., Bobée, B. & Bruneau, P.  Analyse fréquentielle régionale des

Hydrology Research

45.1

2014

précipitations journalières maximales annuelles au Quebec (Canada). Hydrol. Sci. J. 49, 717–735. Osborn, T. J. & Hulme, M.  Observed trends in the intensity of daily precipitation over the UK. In Proc. 12th Conf. Applied Climatology, Asheville, May 2000, Boston, MA, pp. 111–114. Ouarda, T. B. M. J. & Shu, C.  Regional low-flow frequency analysis using single and ensemble artificial neural networks. Water Resour. Res. 45, W11428. Ouarda, T. B. M. J., Charron, C. & St-Hilaire, A.  Statistical models and estimation of low flows. Can. Water Resour. J. 33, 195–206. Overeem, A., Buishand, A. & Holleman, I.  Rainfall depth– duration–frequency curves and their uncertainties. J. Hydrol. 348, 124–134. Prodanovic, P. & Simonovic, S. P.  Development of rainfall intensity duration frequency curves for the City of London under the changing climate. Water Resources Research Report no. 58, Facility for Intelligent Decision Support, Department of Civil and Environmental Engineering, London, Ontario, Canada. Available at: http://ir.lib.uwo.ca/ wrrr/20/ (accessed October 13, 2012). Seneviratne, S. I., Luthi, D., Litschi, M. & Schar, C.  Landatmosphere coupling and climate change in Europe. Nature 443, 205–209. Ş enocak, S. & Acar, R.  Modelling of short duration rainfall intensity equations at the Agean region of Turkey. Fresenius Environ. Bull. 16, 1220–1226. Strehl, A. & Ghosh, J.  Cluster ensembles – A knowledge reuse framework in combining multiple partitions. J. Mach. Lear. Res. 3, 583–617. Veneziano, D., Langousis, A. & Lepore, C.  New asymptotic and preasymptotic results on rainfall maxima from multifractal theory. Water Resour. Res. 45, W11421. Vincent, E. & Mekis, E.  Changes in daily and extreme temperature and precipitation indices for Canada over the twentieth century. Atmos-Ocean 44, 177–193. Wilcoxon, F.  Individual comparisons by ranking methods. Biometrics 1, 80–83. Zhang, X., Hogg, W. D. & Mekis, K.  Spatial and temporal characteristics of heavy precipitation events over Canada. J. Climate. 14, 1923–1936.

First received 13 April 2013; accepted in revised form 4 June 2013. Available online 5 July 2013

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An assessment of the skill of downscaled GCM outputs in simulating historical patterns of rainfall variability in South Africa D. A. Hughes, S. Mantel and T. Mohobane

ABSTRACT Uncertainties associated with General Circulation Models (GCMs) and the downscaling methods used for regional or local scale hydrological modelling can result in substantial differences in estimates of future water resources availability. This paper assesses the skill of nine statistically downscaled GCMs in reproducing historical climate for 15 catchments in ﬁve regions of South Africa. The identiﬁcation of skilled GCMs may reduce the uncertainty in future predictions and the focus is on

D. A. Hughes (corresponding author) S. Mantel T. Mohobane Institute for Water Research, Rhodes University, Grahamstown, South Africa E-mail: d.hughes@ru.ac.za

rainfall skill as the GCMs show very similar patterns of change in temperature. The skill tests were designed to assess whether the GCMs are able to realistically reproduce precipitation distribution statistics and patterns of seasonality, persistence and extremes. Some models are consistently less skilful for the regions assessed, while some are generally more skilful with some regionally speciﬁc exceptions. There are differences in the GCMs skill across the different regions and in the skill ranking between coastal areas and inland regions. However, only a limited reduction in uncertainty is achieved when using only the downscaled GCM outputs identiﬁed as being skilled in a hydrological model for one of the regions. Further modelling studies are required to determine the general applicability of this observation. Key words

| climate change, downscaling, hydrological modelling, skill

INTRODUCTION While it is frequently suggested that climate change will

model ensembles that average the outputs across a group

have large impacts on hydrology and the water resources

of models (Hagedorn et al. ). The assumption behind

of the world (Bates et al. ), there remains a substantial

the use of multi-model ensembles appears to be based on

degree of uncertainty associated with the General Circula-

the fact that there are inherent errors in all the models (lar-

tion Models (GCMs) themselves, as well as the methods

gely due to the need to simplify highly complex atmospheric

used to downscale (Hewitson & Crane ; Segui et al.

physics) and that using multi-model output ensembles pro-

) the outputs for use with hydrological models

vides better coverage of the possible climate outcomes.

(Prudhomme et al. ; Chen et al. ). Part of the

However, using an ensemble average is essentially equival-

uncertainty lies in the different structures and initial con-

ent to ignoring the uncertainties and is contrary to the

ditions assumed for the different GCMs and various inter-

trend in the hydrological sciences to try and account for

comparison studies have demonstrated that there can be

all uncertainties (Pappenberger & Beven ). It is there-

substantial differences in the outputs representing both the

fore considered necessary to use all members of the

present climate (Reichler & Kim ) as well as

ensemble to represent the uncertainties in future climate

the future (Hughes et al. ). Pirtle et al. () discuss

change projections (Hughes et al. ). Whether any

the issue of GCM independence and refer to the use of

speciﬁc ensemble of models is able to reﬂect the real

doi: 10.2166/nh.2013.027

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uncertainty and whether the models within the ensemble

but that also are consistent with the expectations of the

can be considered independent are further issues that need

GCM outputs.

to be considered (Masson & Knutti ).

From a hydrological and water resources assessment

GCM outputs are inadequate for use with hydrological

perspective, it is essential that the GCMs are able to realisti-

models applied at the catchment scale as the spatial resol-

cally reproduce patterns of precipitation seasonality,

ution is too coarse. It is therefore considered necessary to

persistence and extremes. If they are not able to adequately

use some form of downscaling (Hewitson & Crane ;

reproduce these characteristics under present day forcing

Bouwer et al. ; Fowler et al. ; Segui et al. ;

conditions, it is unlikely that we can have much conﬁdence

Frost et al. ). However, while downscaling can address

in their ability to predict changes in these characteristics

the spatial scale issues it is likely to introduce different

under different forcing conditions in the future. This is not

uncertainties into the predictions (Buytaert et al. ).

the same as saying that skilful simulations of the past will

There are two general categories of downscaling in general

lead to skilful predictions of the future. It is, however,

use: dynamical and statistical. Dynamical downscaling can

suggesting that a lack of skill in simulations of the past is

be achieved by using a Regional Climate Model (RCM)

very likely to translate into a lack of skill in future predic-

nested within the GCM simulations (Leung et al. ),

tions. Past skill therefore becomes a necessary, but

while statistical downscaling is an empirical approach that

insufﬁcient, basis for conﬁdence in future predictions

establishes relationships between the GCM outputs and

(Knutti ).

local scale variables (Hewitson & Crane ). In the

Various approaches to assessing skill have been

latter case, the additional uncertainties will be related to

reported in the literature (Wilby & Harris ; Schmidli

the uncertainties in the observations of the local scale vari-

et al. ; Chiew et al. ) and they have included assess-

ables, as well as the assumptions used in developing

ments of the ability of downscaled GCM data to reproduce

appropriate relationships.

frequency characteristics of precipitation, mean seasonal

Given the inherent uncertainty in the outputs from

patterns, as well as durations above or below certain

downscaled GCMs it seems justiﬁed to assess their perform-

thresholds. Downscaled GCM data for future hydrological

ance in simulating past or present day climates (Wilby )

scenarios typically require some form of bias correction if

in an attempt to identify which (if any) of a range of models

they are to be used in comparison with hydrological simu-

are more skilled than others in a speciﬁc region. If this is

lations of the past using historically observed data (Chen

possible it may be possible to limit the number of GCMs

et al. ). Part of the skill analysis could therefore focus

used in the estimation of future possible scenarios which

on the assumptions implicit in any bias correction method

may reduce the range of uncertainty. However, if skill tests

and whether or not these are equally valid across the

are to be undertaken it is essential that they examine aspects

range of downscaled data sets being used.

of the downscaled GCM outputs that are consistent with the

This study forms part of a larger project to investigate the

structure and limitations of the GCMs (Huard ). It is gen-

uncertainties in hydrological model outputs based on simu-

erally not correct to base the skill assessment on temporal

lations using historical data (largely parameter and observed

correlations between climate model outputs and observed

forcing data uncertainty) combined with the additional uncer-

precipitation and temperature, despite that fact that

tainties associated with both climate change and future water

there are examples of such approaches in the literature

resources development impacts. The original objective of the

(Anagnostopoulos et al. ). This type of approach is

study was to identify whether the results of skill tests applied

considered invalid because of the way in which GCMs are

to nine downscaled GCMs could be used to either reduce the

externally forced, the internal (largely chaotic) dynamics

number of applicable models or to rank their levels of uncer-

of the climate system and the fact that they are not expected

tainty. A favourable outcome from a hydrological modelling

to ‘predict climate in a deterministic sense’ (Huard ). It is

point of view would be that the uncertainty in the predictions

therefore necessary to select skill measures that are not only

of the future could be reduced by focusing on the more skilful

appropriate for the purposes of the hydrological simulations,

GCMs.

D. A. Hughes et al.

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THE GCMS AND DOWNSCALING METHOD

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2014

The speciﬁc downscaled data products used in this study are the so-called quinary catchment-based data set. The

The downscaled data used in this study are those produced by

1946 quaternary catchments are the divisions used within

the Climate Systems Analysis Group of the University of Cape

South Africa for water management purposes (Middleton

Town which are available for the nine GCMs listed in Table 1

& Bailey ), while there are typically three or more quin-

for the SRES (Special Report on Emission Scenarios) A2 emis-

ary

sion scenario (IPCC ). The data are based on statistical

catchments are typically between 100 and 1,000 km2 in

downscaling using the methods discussed in Hewitson &

the wetter parts of the country, but can be much larger in

Crane (, ). An earlier version of this data set was

very dry areas. The ﬁnal downscaled data products are

used by Lumsden et al. () to assess patterns of future

daily time series of rainfall depths, maximum and minimum

change in rainfall statistics across the whole of South Africa.

temperatures at the quinary catchment scale for a baseline

The authors accept that the single emission scenario and pro-

period (1961–2000), as well as near (2046–2065) and far

jection data used from nine GCMs are not representative of

future (2081–2100) scenarios. In this study, the quinary

the full uncertainty in future climates. However, these are

scale daily rainfall data have been aggregated to quaternary

data that are based on the same methods of downscaling

scale monthly rainfall data using an inverse distance weight-

catchments

within

each

quaternary.

Quaternary

and that have been made readily available to hydrologists in

ing procedure (Wilk et al. ) based on points

South Africa for translating climate change signals into

representing the location of the quinary catchments. This

impacts on water resources availability. The differences in

approach does not affect the statistical properties of the orig-

both projections of change (direction and extent) and skill

inal downscaled rainfall data as there are very few

should therefore be treated as a sample of possible variations

differences in these properties between closely adjacent

and uncertainties. It is not suggested that this is a representa-

quinary catchments.

tive sample, it is simply a sample created from consistent

The study has focused on ﬁve groups of quaternary

downscaling methods that has been made available for hydro-

catchments: the H10 group in the headwaters of the

logical analyses in South Africa. The authors acknowledge

Breede River in the Western Cape; the K90 group represent-

that the issues noted by Masson & Knutti () about simi-

ing the Kromme River basin on the Southern Cape coast;

larities in climate model genealogy can be important in

the R20 group in the Buffalo River on the Eastern Cape

assessing GCM differences. However, as hydrologists, we

coast; the C/D group representing the inland (Free State

are constrained by the data that are recommended and

Province) catchments of the Caledon and Modder rivers;

made available by climatologists (Hewitson & Crane )

and the X31 group in the headwaters of the Sabie River

and these issues are not addressed further in this paper.

located on the eastern escarpment in Mpumalanga Province

Table 1

Global climate models used in the study

GCM abbreviation

Source of GCM

CCCMA

Canadian Centre for Climate Modelling and Analysis

CNRM

France Centre National de Recherches Meteorologiques

CSIRO

Australian Commonwealth Scientiﬁc and Industrial Research Organisation (CSIRO) Atmospheric Research

GFDL

USA National Oceanic and Atmospheric Administration (NOAA) Geophysical Fluid Dynamics Lab

GISS

USA Goddard Institute for Space Studies

IPSL

France Institut Pierre Simon Laplace

MIUB

Germany Meteorological Institute of the University of Bonn

MPI

Max-Planck Institute for Meteorology

MRI

Japan Meteorological Research Institute

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(Figure 1). The sites were chosen partly to cover a variety of climate conditions and rainfall types, but were also selected because of their relevance to parallel studies within the Institute for Water Research of the effects of climate change on water resources. All of the GCMs for all regions show very similar patterns of change in temperature, but not for rainfall. Figure 2 summarises the variation in projected rainfall changes for the nine GCMs using the per cent difference in the mean annual rainfall between the baseline and near future periods for all of the quaternary catchments in each region (12 for X, 11 for H, 7 for K, 42 for C/D and 11 for R). It is clear that there are substantial variations in both the degree and direction of change across different models

Figure 2

Summary of per cent change from baseline (1960–2000) to near future (2046– 2065) for all nine downscaled GCM data. The bars represent the variability across all of the quaternary catchments within each region.

and different regions, as well as (in some cases) within regions. Previous studies (Lumsden et al. ) have suggested that the Western Cape region (H) shows the

time series and the WR2005 (Middleton & Bailey ) rain-

most consistent projections of reduced rainfall across most

fall data that are routinely used in water resources analyses

GCMs. While the data in Figure 2 indicate that more

in South Africa. The WR2005 rainfall data were compiled at

GCMs suggest lower rainfalls in the H region than other

the scale of the quaternary catchments from all available

regions, three of the GCMs predict increased rainfall,

observed rainfall station data (Middleton & Bailey ).

while one suggests small changes. Using these results as

While the WR2005 data are less than perfect, largely

inputs into hydrological models will clearly introduce a

because of relatively low densities of measurement stations

large amount of uncertainty in future estimates of water

in some areas, they are the best representation of historical

resources availability, particularly for those areas where

rainfall patterns that are available for all parts of the

there is substantial disagreement between GCMs on both

country. While it would have been useful to include uncer-

direction and degree of rainfall change (X, K and C/D).

tainty bounds around the historical WR2005 rainfall data,

Figure 3 illustrates that there are very big differences in

this has not been possible as the authors do not have

the seasonal distributions between the nine baseline rainfall

access to the original station data nor any detailed

Figure 3 Figure 1

Map of South Africa showing the six study areas.

Mean monthly rainfall depths (mm) for the historical data (WR2005) and the nine downscaled GCMs for the baseline period (1960–2000) for quaternary catchment R20B.

138

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documentation of the methods used. The other regions show similar degrees of bias between the downscaled baseline data and the WR2005 historical data and it is therefore clear that bias correction is necessary before the future projections can be used to assess the potential impacts on water resources. It is also clear that the bias corrections will have to be different for individual months.

RAINFALL BIAS CORRECTION Figure 4

Example of the rainfall bias correction for downscaled CCCMA data and quaternary catchment R20A.

The ultimate objective of the main study is to use the downscaled rainfall data as inputs to hydrological and water

Several other correction approaches (such as using the cumu-

resources yield models and speciﬁcally the monthly time-step

lative frequency distributions of rainfall) did not preserve the

Pitman model (Hughes et al. ). Figure 3 illustrates that,

seasonality and structure of the downscaled future rainfalls.

compared to the WR2005 data, the baseline rainfall time

The square root transformation was used to account for the

series exhibit bias in monthly means and, although not

generally positive skewness evident in monthly rainfall data.

shown on the diagram, the same is true for the monthly stan-

Initial applications of the bias correction method used a natu-

dard deviations. The method used to remove this bias from the

ral logarithmic transformation, but this was found to

future (near and far) rainfall estimates is to express the future

introduce additional bias in some site/GCM combinations

monthly rainfalls as standard deviates of the baseline monthly

(related to the existence of low or even negative skewness

distributions (using a square root transformation) and to scale

values for some months in some GCM data), while the

the standard deviates with the monthly distribution statistics of

square root transformation was found to be more generally

the historical rainfall data (Equation (1)). Similar approaches

applicable. An example of the results of applying this bias cor-

have been applied in other studies (Haerter et al. ).

RFCijk

2 ¼ RHμj þ RHσ j × RFijk RBμ jk =RBσ jk

rection is provided in Figure 4 for the downscaled CCCMA rainfall data for quaternary catchment R20A. The patterns (1)

of differences between the baseline and historical data (and therefore the degree of bias correction required) are highly

where: RFCijk ¼ Future rainfall after correction for month i

variable across the regions and GCMs.

and calendar month j in the time series of GCM k. RHμj ¼ Mean of the square root transformed historical (WR2005) rainfalls for calendar month j. RHσj ¼ Standard deviation of the square root transformed historical (WR2005) rainfalls for

CONVERTING TEMPERATURE DATA TO MODEL EVAPOTRANSPIRATION INPUTS

calendar month j. RFijk ¼ Square root transformed future rainfall for month i and calendar month j in the time series of

Evaporation inputs to the Pitman model typically consist of an

GCM k. RBμjk ¼ Mean of the square root transformed baseline

annual potential evaporation (PE) depth (mm) and a ﬁxed sea-

rainfalls for GCM k and calendar month j. RBσjk ¼ Standard

sonal distribution. While it is possible to use a time series of

deviation of the square root transformed baseline rainfalls

PE inputs (Hughes et al. ) there is often not enough his-

for GCM k and calendar month j.

torical information to quantify these variations accurately

The objective of the correction equation is to remove the

and Sawunyama () noted that their inclusion did not

bias in the monthly means and variations between the his-

make much difference to the overall model results. In this

torical and GCM baseline estimates, while preserving the

study, it was decided to use the maximum and minimum

differences between the GCM baseline and future scenarios.

temperature data for the baseline and future climate model

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scenarios to determine the temperature component of the

the WR2005 data, but with the overall depth bias removed

Hargreaves (Hargreaves & Samani ) equation (Equation

(Equation (4)):

(2)). The per cent increases in these values, from baseline to

Seas skill jk ¼ ABS RB jk × ðRB MAPk =RH MAPÞ RHj = RHj (4)

future, were then used to scale the seasonal distributions of PE when running the model for future scenarios. (2)

where: Seas_skilljk ¼ Season skill score for month j, GCM k.

where: HCk ¼ Temperature component of the Hargreaves

GCM k. RB_MAPk ¼ Baseline mean annual rainfall for

equation for GCM k, calculated for baseline and future con-

GCM k. RHj ¼ WR2005 mean monthly rainfall for month

ditions. TMaxk ¼ Daily maximum temperature for GCM k.

j. RH_MAP ¼ WR2005 mean annual rainfall.

HCk ¼ ðTMaxk þ TMink Þ=2 × √ðTMaxk TMink Þ

RBjk ¼ Baseline mean monthly rainfall for month j and

TMink ¼ Daily minimum temperature for GCM k.

The equivalent of Equation (4) has also been used to

The daily values are used to compute mean monthly

calculate a seasonality skill measure for the temperature

values (MHCjk, where j is the month) for all calendar

data. Equation (2) was applied to some historical tempera-

months and the seasonal scaling factor computed from the

ture data (Schulze & Maharaj ) as well as the baseline

ratio of the HCk values for the individual GCM future

temperature data for the nine downscaled GCMs. The

scenarios to their baseline scenarios.

mean monthly values for the historical and GCM data were then used in Equation (4), replacing mean monthly rainfall with the MHCjk values (see above) and the mean annual rainfall values with the temperature equivalents.

SELECTED MEASURES OF SKILL

The rainfall seasonality skill measure does not ade-

Part of the rainfall transformation process relies, to a certain extent, on the WR2005 and baseline data for the different GCMs both having similar skewness values for the distribution of rainfall depths within each calendar month and that the square root transformation is appropriate (Equation (1)). The ﬁrst skill measure was therefore based on the absolute value of the relative difference in skewness between the GCM baseline and WR2005 data (Equation (3)): γ skill jk ¼ ABS

RBγ jk RHγ j =RHγ j

quately account for the variation in rainfalls across different years for the same calendar month and therefore an additional skill measure has been added to account for this and based on the coefﬁcient of variation, or the ratio of standard deviation to the mean (Equation (5)): CV skill jk ¼ ABS RB CV jk RH CVj =RH CVj

(5)

where: CV_skillk ¼ Coefﬁcient of variation skill score for month j, GCM k. RB_CVjk ¼ Coefﬁcient of variation of the (3)

baseline monthly rainfalls for calendar month j and GCM k. RH_CVj ¼ Coefﬁcient of variation of the WR2005

where: γ_skilljk ¼ Skewness skill score for month j, GCM k.

monthly rainfalls for calendar month j.

RBγjk ¼ Skewness of baseline monthly rainfalls for calendar

The ﬁnal skill measure has been based on calculations of

month j and GCM k. RHγj ¼ Skewness of the WR2005

serial auto-correlation within the individual time series

monthly rainfalls for calendar month j.

using lags of 1, 2, 11, 12 and 13 months. These lags were

The seasonality of the rainfall regime is clearly of great

chosen on the basis of the serial correlation patterns

importance in hydrological modelling and during the initial

observed in the WR2005 data that demonstrated weak

phases of the study it had already been observed that some

intra-season persistence (for example, 0.25 and 0.10 for

of the downscaled rainfall data did not appear to reproduce

lags 1 and 2 for sub-basin R20A), as well as weak persistence

historical seasonality patterns very well. A skill measure was

across two adjacent seasons (0.19, 0.22, 0.16 for lags 11, 12

therefore adopted that would measure the relative differ-

and 13, respectively for sub-basin R20A). The baseline rain-

ences between the GCM seasonal rainfall distributions and

fall time series for all nine GCMs exhibited similar patterns,

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but with quite different correlation values. The serial corre-

for each annual skill measure and then to sum and multiply

lation skill measure was therefore simply the sum (for all

the individual skill ranks to obtain two overall skill scores.

ﬁve lags) of the absolute differences in serial correlation

These were then averaged to obtain a ﬁnal rank. The process

(Equation (6)):

is illustrated in Table 2 for quaternary catchment R20B and these rankings have been used to order the climate models

SC skillk ¼ ΣABSðSClk SCl Þ

(6)

in the presentations of the more detailed results (Figure 5).

where: SC_skillk ¼ Sum of the skill values for all ﬁve lags.

the total annual skill value, as well as the maximum skill

A second approach was used to take into account both SClk ¼ Serial correlation coefﬁcient for lag l and baseline

score (applicable to γ_skill, Seas_skill and CV_skill

rainfall for GCM k. SCl ¼ Serial correlation coefﬁcient for

measures only) for the 12 months. For each skill measure,

lag l, WR2005 monthly rainfalls.

threshold values were calculated such that approximately

During the initial phase of the skill assessment, the GCMs

half of the skill values for all GCM/site combinations fall

were compared using the annual skill values detailed above

on either side of the threshold. This analysis was done for

(STAT_skillk ¼ ΣSTAT_skilljk for all j months, with STAT

the total skill measures (all months for γ_skill, Seas_skill

used to represent the γ_skill, Seas_skill and CV_ skill measures).

and CV_ skill measures and all lag values for the SC_skill)

However, many of the annual values are inﬂuenced by extre-

and for the maximum monthly skill measure (γ_skill,

mely high (poor skill) values for the dry season months where

Seas_skill and CV_ skill). Those GCM/site combinations

small absolute differences in rainfall amounts between the

with values above the thresholds were identiﬁed as failing

WR2005 data and the GCMs result in high values of the

the speciﬁc skill test, while those below the thresholds

skill indices. All of the monthly skill values for the ﬁrst

passed the speciﬁc test. The use of the terms passing and

three measures were therefore weighted by the ratio of the

failing are therefore relative and have no absolute meaning.

mean monthly WR2005 rainfall to the mean annual WR2005 rainfall (Equation (7)) and then summed for revised annual values:

RESULTS

STAT new skill jk ¼ STAT skill jk × RHj =RH MAP

(7)

The ﬁrst observation was that there is much less difference in the temperature skill measures across the different cli-

The ﬁrst approach to assessing the variations in skill

mate models for several of the regions where observed

across the various regions and GCMs was to use a rank

historical temperature data were available. It was therefore

Table 2

Rankings of the GCMs for the different measures of rainfall skill

Measure of skill

Cumulative measures and ranking

GCM

Skew

Season

Total multiplied

CCCMA

Rank

Total summed

Rank

Mean rank

2.5

CNRM

1,008

7.5

CSIRO

720

5.5

GFDL

1.5

GISS

896

7.5

IPSL

567

MIUB

2,880

MPI

2.5

MRI

141

Figure 5

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Overall skill rank and higher (white cells) or lower (grey cells) skill for all climate model/catchment combinations for the four skill criteria.

concluded that the rainfall skills are likely to be far more

the total annual skill score test or the maximum monthly

important in distinguishing between the climate models

skill score test are also identiďŹ ed. Figure 6 presents the

than the temperature skill differences.

models ranked in the same way as Figure 5 but with the

Figure 5 presents the detailed results for the four rainfall

shading designed to illustrate how many of the skill scores

skill measures. In all of the diagrams the climate models are

were above either of the thresholds. Figure 7 presents histo-

listed in order using the ranking approach referred to above

grams of the frequencies of between 0 and 4 skill scores

(and illustrated in Table 2), while those that passed (white

falling into the low skill categories for all climate models

background) and those that failed (grey background) either

across all the catchments (15 in total). All of these diagrams

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Skill of downscaled GCMs

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Figure 6

Number of skill criteria falling into lower skill categories for all climate model/catchment combinations.

Figure 7

Frequency of between none and four tests falling into the lower skill categories for the different climate models across all catchments.

should be viewed in the context of the variations in future projections illustrated in Figure 2.

â&#x20AC;˘

With respect to variations in the highest ranked models (combining all four skill criteria) across the different regions, there are some consistent patterns, but there are also a number of inconsistencies even within individual regions:

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The most consistent result for the coastal areas is that MIUB, CNRM and CSIRO are generally ranked in the lowest half, while MPI, GFDL, MRI and GISS are the

â&#x20AC;˘

models with the most frequent high rankings. There are differences in ranking between the W. Cape and the other coastal areas (S. and E. Cape), which

143

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Skill of downscaled GCMs

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might be related to the differences in weather patterns

about the potential value and use of the skill measures is

that result in winter season rainfall in the W. Cape, but

whether rejecting the less skilful models would reduce the

spring and autumn rainfall seasons in the S. and E. Cape.

uncertainty in future predictions of rainfall. For region X,

For the inland catchments, CCCMA, CSIRO and MRI

the best models are CNRM, IPSL and GISS which have a

perform the worst, while CNRM, IPSL and GISS perform

narrower band of uncertainty than all nine models, but

the best.

still represent predictions ranging from >10% increases to

For all regions, CSIRO has one of the biggest variations in

over 5% decreases. For the W. Cape region (H), the majority

predicted rainfall change (Figure 2) and this is also the

of the models suggest decreases in rainfall and even reject-

model that performs the worst in terms of skill ranking.

ing

In contrast, GISS which ranks as one of the most skilful

uncertainty considerably. Rejecting the four least skilful

models has a relatively lower range of variability in pre-

models for the K region (MIUB, CSIRO, MRI and

dicted future change.

CCCMA) would similarly reduce the uncertainty, but

just

the

CSIRO predictions

would

reduce

the

would remain between approximately þ20% and 8%. Perhaps the most immediately apparent result from

The impacts on uncertainty of rejecting some climate

Figures 5 and 6 is that there is a greater number of inland

models is much lower for the E. Cape coastal region (R)

areas falling into the lower skill groups than for the coastal

because the highest (MRI) and lowest (MPI) predictions

catchments, further emphasising differences in the skill

are both generated by models identiﬁed as skilful. The

results between the coastal and inland catchments. The impli-

same conclusion can be reached about the C/D region

cations, bearing in mind the limited sample size, are that

where IPSL and MPI are considered skilful, resulting in

either the climate models or the downscaling methods per-

an uncertainty range of between þ35% and 11%.

form less well for inland areas than for coastal areas of South Africa. This may be related to the differences in rainfall

producing

weather

patterns

that

occur

(Preston-Whyte & Tyson ) across the inland and coastal

IMPLICATIONS FOR SIMULATING FUTURE WATER RESOURCE AVAILABILITY

regions of the country, but such speculation would have to be further investigated by climatologists who have a better

One of the major issues associated with the use of down-

understanding of the differences in the climate models and

scaled GCM data within hydrological models is the

downscaling methods than the authors. These observations

uncertainty in the future predictions related to the range of

and conclusions about regional and GCM differences have

results given by, supposedly, equally credible GCMs. The

to be viewed in the context of the limited sample of GCM

Pitman monthly rainfall–runoff model (Hughes et al. )

data used in the study and it is not possible to reach any con-

clusions about whether they are statistically meaningful.

(Kapangaziwiri et al. ) to the historical data (1920–

being

applied

within

uncertainty

framework

Figure 7 clearly illustrates that, based on the number of

2005) as well as to the near future (2046–2065) period for

tests in the higher skill groups across all catchments, GISS,

all nine GCMs. The methods used for generating the rainfall

CNRM and MPI represent the top three most skilful models,

(Equation (1)) and PE (based on Equation (2)) inputs to the

while GFDL, MIUB, CCCMA and CSIRO fall into the least

model have been referred to above and the model has been

skilful grouping. Figure 2 represents the uncertainties in

initially applied to three headwater quaternary catchments

future projections across the climate models (variations in

of the Buffalo River (R20A to R20C).

the vertical position of the bars) and within the regions for

The model assumes uncertainty distributions (assumed

the same climate model (length of the bars). Two of the

to be normally distributed in this study) for the main

models identiﬁed as being generally less skilful (CSIRO

runoff generation and water balance parameters and gener-

and CCCMA) show some of the largest degrees of uncer-

ates ensemble outputs (typically 1,000–10,000) using

tainty across and within regions, while GISS and CNRM

independent Monte Carlo sampling from the parameter fre-

(identiﬁed as skilful) show fewer variations. One question

quency distributions. The ﬁrst step is to assign mean and

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standard deviations to define the uncertainty distributions of the most important model parameters and assess whether the ensemble results for the historical period (1920–2005) are appropriate given previous simulated flow patterns in the catchment (e.g., WR2005; Middleton & Bailey ). Five out of the total 18 model parameters were treated as uncertain and these are the parameters that largely determine the runoff responses at both high and low flows (Kapangaziwiri et al. ). The information available from stream flow gauges is also used to guide the process of establishing appropriate parameter distributions but it is recognised that the gauged records are impacted by a

Figure 9

Flow duration curve envelopes (the upper and lower bounds of 90% of the simulation ensembles) for the near future for all GCMs and the three most skilful, as well as the simulations using historical data.

number of ill-deﬁned upstream developments and abstractions and are therefore inherently uncertain. The same

data; the range of ensemble results for all GCMs; and the

parameter distributions are then used with the rainfall

ensemble range for the three most skilful models. The results

time series and PE seasonal distributions appropriate to

of the near future period simulations suggest that the uncer-

the near future scenarios of all nine GCMs.

tainty in future water resources availability is substantially

Figure 8 shows the seasonal distribution of near future

increased across the full range of monthly ﬂow volumes. If

climate change effects on mean monthly simulated runoff

only the apparently more skilful GCMs are used the uncer-

for all of the nine GCMs listed in order of skill. The data

tainty is marginally reduced only for high ﬂows (equalled

plotted are the percentage deviations of the GCM monthly

or exceeded less than 10% of the time) and the trend is for

means from the historical equivalents and the median simu-

generally larger high ﬂows. This is a modiﬁcation of the con-

lation ensembles are used in all cases. The overall

clusion reached above (based on only the rainfall data) that

impression is that the wet season runoff is increased and

suggested there would be little change in uncertainty by

the dry season runoff is decreased. There is, however, a sub-

selecting skilful models for this region.

stantial amount of variation in the changes across the nine GCMs and it is very difﬁcult to identify any pattern in the differences between the more skilful GCMs in this region

CONCLUSIONS

(MPI, GFDL and MRI) and those with less skill. Figure 9 shows the envelopes of ﬂow duration curves for

In common with many other studies, this contribution has

the simulations: the ensembles of simulations using historical

demonstrated that there is a great deal of variation in the projections of future climates based on downscaled outputs from nine supposedly equally credible climate models. These variations are more evident in the projections of future rainfall patterns than they are in temperature projections. Given the uncertainties associated with using all nine model outputs, this study has investigated the differences in the ability of the models to simulate the characteristics of historical rainfall patterns using four measures of skill. The relatively simple skill measures have been developed to reﬂect the assumptions used in the bias correction method, to be appropriate for the purposes of hydrological simulations and to acknowledge the

Figure 8

Seasonal distribution of climate change monthly means for the Buffalo River expressed as a per cent change from historical means (GCMs ordered by skill).

constraints of downscaled GCM outputs. They are therefore designed to assess the skill of the different models in

145

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45.1

2014

reproducing the main seasonal distribution (Seas_skill), stat-

be physically inconsistent. However, the authors consider

istical

that this is unlikely for two reasons. First, there was far

(γ_skill

and

CV_skill)

and

serial

correlation

(SC_skill) characteristics of monthly rainfall time series. Several methods of assessing the relative differences in

greater consistency among the downscaled GCM data sets in the historical temperature estimates than the rainfall.

GCM skill have been applied for a total of 15 catchments

Second, the PE inputs to the model are ﬁxed seasonal distri-

drawn from ﬁve regions of South Africa. The general con-

butions and therefore any differences in the predicted time

clusion is that some models are consistently less skilful for

series of temperature are buffered by the use of simple seaso-

the regions assessed (CSIRO and CCCMA), while some are

nal distributions.

generally more skilful (GISS, CNRM and MPI) with some

It must be acknowledged that the climate change projec-

regionally speciﬁc exceptions. There is a substantial variation

tions used in this study are not representative of all the

in skill across the different regions for most models and the

possible uncertainties that exist and have been constrained

results suggest that there are differences in skill, as well as

by the data that have been made readily available to the

differences in the GCMs skill ranking between coastal areas

hydrological modelling community by the climate modelling

and inland regions. It was speculated that this result may be

community in South Africa. The study cannot therefore be

a reﬂection of the well-documented differences in rainfall pro-

considered as a comprehensive assessment of climate

ducing weather patterns between inland and coastal regions

change uncertainty that includes inter alia different time hor-

of South Africa. However, further investigations with special-

izons, different emission scenarios or different earth system

ist inputs from climatologists familiar with the structure of the

feedback mechanisms. However, despite these limitations,

GCMs and the downscaling methods would be needed to

the study has highlighted the potential impact of climate

conﬁrm or reject this possibility.

model uncertainties on future water resources assessment

Figure 2 illustrates the large variation in the near future

uncertainties, and that was the main purpose of the study.

(2046–2065) projections of rainfall change across the ﬁve

The results suggest that although there are substantial differ-

regions and nine GCMs. Using the skill rankings to limit

ences in the skill of different downscaled climate model

the GCMs used in each region suggests that the variation

data products, choosing those outputs that can be identiﬁed

and therefore the future uncertainty could be reduced in

as skilful will not necessarily reduce uncertainty in all regions

the X (Eastern Escarpment), H (W. Cape) and K (S. Cape)

of the country. Liepert & Previdi () indicate that some of

regions but not in the R (E. Cape) and C/D (Caledon and

the largest discrepancies in global mean atmospheric water

Modder catchments) regions. To date, the bias corrected

balance are found among the models identiﬁed as skilful in

near future rainfall data and temperature-based estimates of

this study (such as CNRM and IPSL). Conversely, the least

future evaporation have been used in a hydrological model

skilful model for South Africa (CSIRO) has a low discrepancy

application (including model parameter uncertainty) within

at the global scale. It is therefore important to recognise that

the Buffalo River (R) region. As expected, the results suggest

the skill assessment results are speciﬁc to the geographic

that uncertainties in the availability of water resources based

scale and the regions used in this study.

on historical data are substantially increased when considering future water availability. The uncertainties in future high ﬂows are slightly reduced if only the skilful GCMs are

ACKNOWLEDGEMENTS

included, but the range of uncertainty in the moderate to lower ﬂows is not affected by excluding the less skilful

The work undertaken for this study was partially supported

models. These modelling studies will be expanded to the

through two Water Research Commission of South Africa

other regions of the country in the near future.

projects: K5/2018 that is focused on climate change and

During the review process of this paper, it was pointed

adaptation strategies for local water boards and K5/2056

out that using uncorrected temperature data to calculate

that is dealing with several issues of uncertainty in

PE, together with bias corrected precipitation data, poten-

hydrological and water resources assessment modelling.

tially means that the inputs to the hydrological model may

The third author is a post-graduate student supported by

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the Carnegie Foundation of New York through the SSAWRN (Sub-Saharan Africa Water Resources Network) component of the RISE (Regional Initiative in Science Education) programme. All of the downscaled GCM data were obtained from the Climate Systems Analysis Group (CSAG) of the University of Cape Town and the authors are particularly grateful to Lisa Coup and Mark Tadross for their assistance in accessing all the data.

REFERENCES Anagnostopoulos, G. G., Koutsoyiannis, D., Christpﬁdes, A., Efstratiadis, A. & Mamassis, N.  A comparison of local and aggregated climate model outputs with observed data. Hydrol. Sci. J. 56 (7), 1094–1110. Bates, B. C., Kundzewicz, Z. W., Wu, S. & Palutikof, J.  Climate Change and Water. Technical Paper of the Intergovernmental Panel on Climate Change, IPCC Secretariat, Geneva. Bouwer, L. M., Aerts, J. C. J. H., Van de Coterlet, G. M., Van de Giesen, N., Gieske, A. & Mannaerts, C.  Evaluating downscaling methods for preparing global circulation model (GCM) data for hydrological impact modelling. In: Climate Change and Contrasting River Basins (J. C. J. H. Aerts & P. Droogers, eds). CAB International, Wallingford, UK. Buytaert, W., Vuille, M., Dewulf, A., Urrutia, R., Karmalker, A. & Célleri, R.  Uncertainties in climate change projections and regional downscaling in the the tropical Andes: implications for water resources management. Hydrol. Earth Syst. Sci. 14, 1247–1258. Chen, J., Brissette, F. P. & Leconte, R.  Uncertainty of downscaling methods in quantifying the impact of climate change on hydrology. J. Hydrol. 401, 190–202. Chiew, F. H. S., Teng, J., Vaze, J., Post, D. A., Perraud, J. M., Kirono, D. G. C. & Viney, N. R.  Estimating climate change impact on runoff across southeast Australia: method, results, and implications of the modeling method. Water Resour. Res. 45, W10414, doi:10.1029/2008WR007338. Fowler, H. J., Blenkinsop, S. & Tebaldi, C.  Linking climate change modeling to impacts studies: recent advances in downscaling techniques for hydrological modeling. Int. J. Climatol. 27, 1547–1578. Frost, J. A., Charles, S. P., Timbal, B., Chiew, F. H. S., Mehrotra, R., Nguyen, K. C., Chandler, R. E., McGregor, J. L., Fu, G., Kirono, D. G. C., Fernandez, E. & Kent, D. M.  A comparison of multi-site daily rainfall downscaling techniques under Australian conditions. J. Hydrol. 408, 1–18. Haerter, J. O., Hagemann, S., Moseley, C. & Piani, C.  Climate model bias correction and the role of timescales. Hydrol. Earth Syst. Sci. 15, 1065–1079.

Hydrology Research

45.1

2014

Hagedorn, R., Doblas-Reyes, F. J. & Palmer, T. N.  The rationale behind the success of multi-model ensembles in seasonal forecasting. Part I. Basic concept. Tellus 57A, 219–233. Hargreaves, G. H. & Samani, Z. A.  Reference crop evapotranspiration from temperature. Appl. Eng. Agric. 1 (2), 96–99. Hewitson, B. & Crane, R.  Climate downscaling: techniques and application. Clim. Res. 7, 85–95. Hewitson, B. & Crane, R.  Consensus between GCM climate change projections with empirical downscaling: precipitation downscaling over South Africa. Int. J. Climatol. 26 (10), 1315–1337. Huard, D.  Discussion of ‘A comparison of local and aggregated climate model outputs with observed data’. A black eye for the Hydrological Sciences Journal. Hydrol. Sci. J. 56 (7), 1330–1333. Hughes, D. A., Andersson, L., Wilk, J. & Savenije, H. H. G.  Regional calibration of the Pitman model for the Okavango River. J. Hydrol. 331, 30–42. Hughes, D. A., Kingston, D. G. & Todd, M. C.  Uncertainty in water resources availability in the Okavango River Basin as a result of climate change. Hydrol. Earth Syst. Sci. 15, 931–941. IPCC  Emissions Scenarios. A Special Report of Working Group III of the Intergovernmental Panel on Climate Change. Cambridge University Press, New York. Kapangaziwiri, E., Hughes, D. A. & Wagener, T.  Incorporating uncertainty in hydrological predictions for gauged and ungauged basins in southern Africa. Hydrol. Sci. J. 57 (5), 1000–1019. Knutti, R.  Why are climate models reproducing the observed global surface warming so well? Geophys. Res. Lett. 35. L18704, doi:10.1029/2008GL034932. Leung, L. R., Quin, Y., Bian, X. M., Washington, W. M., Han, J. & Roads, J. O.  Mid-century ensembles regional climate change scenarios for the western United States. Clim. Change 62 (1), 75–113. Liepert, B. G. & Previdi, M.  Inter-model variability and biases of the global water cycle in CMIP3 coupled climate models. Environ. Res. Lett. 7, 014006, doi:10.1088/1748-9326/7/1/ 014006. Lumsden, T. G., Schulze, R. E. & Hewitson, B. C.  Evaluation of potential changes in hydrologically relevant statistics of rainfall in Southern Africa under conditions of climate change. Water SA 35 (5), 649–656. Masson, D. & Knutti, R.  Climate model genealogy. Geophys. Res. Lett. 38, L08703, doi:10.1029/2011GL046864. Middleton, B. J. & Bailey, A. K.  Water Resources of South Africa, 2005 Study (WR2005). WRC Report No. TT381/08, Water Research Commission, Pretoria, South Africa. Pappenberger, F. & Beven, K.  Ignorance is bliss: or seven reasons not to use uncertainty analysis. Water Resour. Res. 42, W05302. Pirtle, Z., Meyer, R. & Hamilton, A.  What does it mean when climate models agree? A case for assessing independence

147

D. A. Hughes et al.

Skill of downscaled GCMs

among general circulation models. Environ. Sci. Pol. 13, 351–361. Preston-Whyte, R. A. & Tyson, P. D.  The Atmosphere and Weather of Southern Africa. Oxford University Press, Cape Town, South Africa. Prudhomme, C., Jakob, D. & Svensson, C.  Uncertainty and climate change impact on the ﬂood regime of small UK catchments. J. Hydrol. 277, 1–23. Reichler, T. & Kim, J.  How well do coupled models simulate today’s climate? Bull. Amer. Met. Soc. 89 (3), 303–311. Sawunyama, T.  Evaluating Uncertainties in Water Resources Estimation in Southern Africa: A Case Study of South Africa. Unpublished PhD Thesis, Rhodes University, Grahamstown, South Africa. Schmidli, J., Goodess, C. M., Frei, C., Haylock, M. R., Hundecha, Y., Ribalaygua, J. & Schmith, T.  Statistical and dynamical downscaling of precipitation: an evaluation and comparison of scenarios for the European Alps. J. Geophys. Res. 112, D04105.

Hydrology Research

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Schulze, R. E. & Maharaj, M.  Development of a Database of Gridded Daily Temperatures for Southern Africa. WRC Report No. 1156/2/04. Water Research Commission, Pretoria, South Africa. Segui, P., Ribes, A., Martin, E., Habets, F. & Boé, J.  Comparison of three downscaling methods in simulating the impact of climate change on the hydrology of Mediterranean basins. J. Hydrol. 2383, 111–124. Wilby, R. L.  Evaluating climate model outputs for hydrological applications. Hydrol. Sci. J. 55 (7), 1090–1093. Wilby, R. L. & Harris, I.  A framework for assessing uncertainties in climate change impacts: low-ﬂow scenarios for the River Thames, UK. Water Resour. Res. 42, W02419, doi:10.1029/2005WR004065. Wilk, J., Kniveton, D., Andersson, L., Layberry, R., Todd, M. C., Hughes, D., Ringrose, S. & Vanderpost, C.  Estimating rainfall and water balance over the Okavango River basin for hydrological applications. J. Hydrol. 331, 18–29.

First received 27 January 2012; accepted in revised form 21 February 2013. Available online 28 March 2013

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Using radar altimetry to update a large-scale hydrological model of the Brahmaputra river basin Flemming Finsen, Christian Milzow, Richard Smith, Philippa Berry and Peter Bauer-Gottwein

ABSTRACT Measurements of river and lake water levels from space-borne radar altimeters (past missions include ERS, Envisat, Jason, Topex) are useful for calibration and validation of large-scale hydrological models in poorly gauged river basins. Altimetry data availability over the downstream reaches of the Brahmaputra is excellent (17 high-quality virtual stations from ERS-2, 6 from Topex and 10 from Envisat are available for the Brahmaputra). In this study, altimetry data are used to update a large-scale Budyko-type hydrological model of the Brahmaputra river basin in real time. Altimetry measurements are converted to discharge using rating curves of simulated discharge versus observed altimetry. This approach makes it possible to use altimetry data from river cross sections where both in-situ rating curves and accurate river cross section geometry are not available. Model updating based on radar altimetry improved model performance considerably. The Nash–Sutcliffe model efﬁciency

Flemming Finsen Christian Milzow Peter Bauer-Gottwein (corresponding author) Department of Environmental Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark E-mail: pbau@env.dtu.dk Richard Smith Philippa Berry Earth and Planetary Remote Sensing Laboratory, De Montfort University, The Gateway, Leicester, LE1 9BH, UK

increased from 0.77 to 0.83. Real-time river basin modelling using radar altimetry has the potential to improve the predictive capability of large-scale hydrological models elsewhere on the planet. Key words

| Brahmaputra, large-scale hydrological model, radar altimetry, real-time updating

INTRODUCTION Large-scale hydrological models have been developed for the

At the river basin scale, the dominant motivation for

majority of the planet’s major river basins. The reported mod-

hydrological modelling studies is decision support to water

elling studies have been motivated by two main purposes:

resources managers. In the context of the integrated water

(1) to understand large-scale hydrological dynamics and (2)

resources management paradigm, it has been widely recog-

to support water resources management. Continental to

nized that water resources management must operate at the

global-scale modelling work for purpose 1 has been driven

scale of the river basin, even if the basin extends over various

by the need to represent accurately the land phase of the hydro-

administrative units or nations. In highly developed and well-

logical cycle in global climate models. Most recent climate

monitored water resources systems, management models

models include sophisticated land surface schemes (e.g.

typically do not include a rainfall–runoff modelling com-

GLDAS (Rodell et al. ) and CLM (Oleson et al. )),

ponent. Instead, the models are forced with observed

and some of them were coupled to river routing components

inﬂows or with stochastic inﬂow time series, which are gener-

to simulate river discharge at the global scale (e.g. Nohara

ated based on observed runoff statistics. Good examples of

et al. ; Qian et al. ). Continental to global-scale mod-

such models are the regional information system on water

elling work for purpose 2 has been motivated by the need to

and land resources for the Aral Sea basin (Dukhovny et al.

produce global water availability and water stress information

) and the CALVIN model used to support water

to promote political and public awareness of global water

resources management in California (Draper et al. ).

problems (e.g. WaterGAP; Alcamo et al. ).

Many of the world’s major river basins are, however, poorly

doi: 10.2166/nh.2013.191

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monitored. Decision support systems in such basins should

radar altimeters (ERS, Envisat, Jason, Topex) have been devel-

include a rainfall–runoff modelling component. With the

oped. Such products are available from three websites: ESA

advent of global-scale precipitation products based on

River and Lake (Berry et al. ), CNES Hydroweb (Cretaux

remote sensing and reanalysis technology (see Stisen &

et al. ) and CropExplorer USA Global Reservoir and Lake

Sandholt () for a recent review) rainfall–runoff modelling

Elevation Database (Coe & Birkett ). Radar altimeter

in poorly monitored basins has become feasible. Rainfall–

measurements can be processed in near real time and can

runoff models typically use lumped conceptual represen-

complement in-situ river level data in poorly gauged basins.

tations of the hydrological cycle. Some approaches are

Depending on the size of the river and the orbit conﬁguration,

purely heuristic (e.g. the Budyko framework; Zhang et al.

the accuracy of water levels measured with radar altimeters

), while others use a more physically based represen-

ranges from better than 10 cm to more than one metre. Assim-

tation (e.g. NAM; Refsgaard & Knudsen ). Due to the

ilation of such data types into river models is similar to the

large inherent uncertainties in the precipitation forcing, par-

assimilation of in-situ water levels. Signiﬁcant differences

ticularly in mountainous regions, and the signiﬁcant

exist in terms of the spatio-temporal resolution of the data.

structural errors in the rainfall–runoff models, river discharge

While in-situ data are typically available from a limited

predictions from such models are typically not good enough

number of observation points at high temporal resolution,

for water resources management purposes. While the

radar altimetry data are available from many virtual stations

models pick up seasonal variations and overall hydrological

at low temporal resolution (e.g. 35 days for Envisat). The

dynamics, they fail to reproduce accurately extreme events

term ‘virtual station’ refers to an intersection point between

such as ﬂoods and droughts, which are most relevant in the

the ground track of a satellite carrying the nadir-looking alti-

context of water resources management.

meter and a surface water body. However, the low temporal

These shortcomings provide the motivation to investigate

resolution is partly balanced by constant temporal offsets

and explore the potential of innovative data sources based on

between the different virtual stations, which are due to the sat-

remote sensing to inform regional-scale hydrological models in

ellite orbit conﬁguration. Several studies have evaluated the

a real-time data assimilation framework. Assimilation of

performance of radar altimetry for speciﬁc river systems (e.g.

remote sensing data has become standard practice in the

Birkett et al. ; Maheu et al. ; Birkinshaw et al. ).

atmospheric and ocean modelling communities. For instance,

While most of these studies focused on large rivers (e.g.

in the MyOcean component of the European Commission’s

Amazon, Mekong River), Milzow et al. () obtained good

Global Monitoring for Environment and Security programme

results for rivers as narrow as 150 m in the Okavango river

(GMES), real-time ocean monitoring and forecasting are pro-

basin. The study by Pereira-Cardenal et al. () is an example

vided to a user community, based on in-situ data, remote

of successful assimilation of radar altimetry measurements

sensing data and ocean models. Real-time data assimilation

over reservoirs into a basin-scale hydrological model. The pre-

techniques are also well established in the river modelling

sent study is one of the ﬁrst to combine nadir radar altimetry

community (e.g. Madsen & Skotner ; Vrugt et al. ).

data and a hydrological model into an operational forecasting

However, in most applications, in-situ water levels or dis-

scheme for large river basins. The study uses a simple heuristic

charges from automatic gauging stations are assimilated.

assimilation procedure that does not provide or evaluate fore-

Published studies assimilating remotely sensed water levels

cast uncertainty. However, the results show that a forecast

fall into two categories: Assimilation studies using water

using both the model and the altimetry data outperforms

level maps derived from synthetic aperture radar (SAR)

forecasts produced by the model or the altimeter alone.

images (e.g. Hostache et al. ; Mason et al. ; Schumann et al. ) and assimilation studies using synthetic swath alti-

The Brahmaputra river basin

metry observations (e.g. Andreadis et al. ; Durand et al. ; Biancamaria et al. ), motivated mainly by the upcom-

The Brahmaputra River originates north of the main chain

ing Surface Water and Ocean Topography (SWOT) mission.

of the Himalayan mountain range and ﬂows east through

Recently, inland water level products based on space-borne

Tibet for approximately 1,500 km. The Tibetan portion of

150

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Hydrology Research

45.1

2014

the river is known as Yarlung Tsangpo. At the Chinese/

() used the Hydrologic Modelling System (HEC-HMS

Indian border, in the Indian federal state of Arunachal Pra-

3.0.1) to simulate water ﬂow in the Brahmaputra basin

desh, the river changes its course to westbound and crosses

together with satellite-based rainfall products and the

the border between India and Bangladesh before merging

Shuttle Radar Topography Mission Digital Elevation

with the Ganges into the Meghna and ﬂowing into the

Model (SRTM DEM). Akhtar et al. () have carried out

Bay of Bengal (Figure 1). In Bangladesh, the river is

a comparative analysis of multiple artiﬁcial neural network

known as the Jamuna River.

(ANN) models with different hydrological pre-processing

A number of previous modelling efforts have been

for the Ganges river basin. The ANN showed its ability to

reported for the Brahmaputra and Ganges river systems.

forecast discharges 3 days ahead with an acceptable accu-

Nishat & Rahman () set up a water resources manage-

racy. Within this forecast horizon, the inﬂuence of the pre-

ment

Ganges,

processed rainfall is marginal, because of dominant

Brahmaputra and Meghna (GBM) river basins. They demon-

inﬂuence of strongly auto-correlated discharge inputs. For

strate that it is possible to calibrate MIKE BASIN to a

forecast horizons of 7 to 10 days, the inﬂuence of the pre-

model

MIKE

BASIN,

over

the

satisfactory level and predict ﬂow in the Ganges and Brah-

processed rainfall is noticeable, although the overall model

maputra rivers at the entry points of Bangladesh at

performance deteriorates. Mondal & Wasimi () use per-

relevant scales for water resources management. Rao et al.

iodic autoregressive (PAR) models to capture the seasonal

Figure 1

Base map of the Brahmaputra river basin. Subcatchment outlets of the hydrological model are shown as crosses. Envisat altimetry targets are shown as ﬁlled circles. Numeric labels on the left side of the river refer to catchment outlets, numeric labels on the right side of the river refer to Envisat altimetry targets. Topex and ERS-2 targets are not labelled. The background shading indicates SRTM elevation in mamsl.

151

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Hydrology Research

45.1

2014

variability of the Ganges River ﬂow. The model performs

reasons of computational efﬁciency. In total, 19 sub-basins

reasonably well, preserving both its short- and long-term

were deﬁned. The outlet points of the sub-basins correspond

important historical statistics. For the Bangladeshi part of

to the available Envisat radar altimetry targets and to avail-

the Brahmaputra River, a detailed river model exists,

able in-situ monitoring stations. The Brahmaputra basin was

which is implemented in the DHI software Mike-11 (Jakob-

divided into an upstream part (sub-basins 1–6) and a down-

sen et al. ). However, this model is classiﬁed for

stream part (sub-basins 7–19). This division was motivated

national security reasons and is not accessible to the

by calibration data availability and geography: The upstream

research community.

part is located north of the main chain of the Himalayan

The main motivation for hydrological modelling in the

range, while the downstream part is located south of the

region is to improve the prediction of ﬂood waves in the

main chain and is dominated by a monsoon climate. Signiﬁ-

rivers, which are a signiﬁcant threat to life, property and

cant orographic effects are expected for the precipitation in

infrastructure in the affected regions.

the downstream portion. Snow melt modelling

MATERIALS AND METHODS Snow accumulation and melt processes were implemented Hydrological modelling approach

using a simple temperature index method (Hock ). Precipitation falls as snow if the air temperature is below the W

The hydrological model consists of a snow storage compart-

threshold of 0 C. Each sub-catchment is divided into 10

ment, a rainfall–runoff compartment and a river ﬂow

elevation zones and the air temperature is computed for

compartment. Figure 2 presents an overall modelling ﬂow

each elevation zone using a temperature lapse rate of 5

chart. A lumped-parameter semi-distributed approach is

degrees per kilometre. The precipitation is corrected for

used because of limited availability of in-situ data and for

elevation using a constant precipitation lapse rate of

Figure 2

Flow chart of the Brahmaputra river basin model.

152

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

100 mm/yr per kilometre elevation change. Precipitation

Hydrology Research

45.1

2014

Water use

correction terms are constant in time and are added to all daily precipitation records showing signiﬁcant amounts of

Water use for irrigation, domestic and industrial purposes is

precipitation. The precipitation correction procedure is

not simulated in the model. This can be justiﬁed because the

equivalent to the correction procedure used in the well-

main purpose of this study is improved prediction of peak

recognized SWAT (Soil and Water Assessment Tool) hydro-

ﬂows using radar altimetry. Peak ﬂows at the Bahadurabad

logical simulation package (Arnold et al. ). Snowmelt

station are on the order of 50,000 m3 s–1, about 10 times

occurs whenever the air temperature in the respective

higher than average low ﬂows. While water use likely has

elevation zone is above 0 C. Snow melt is computed using

a significant impact on low flows, peak flows are not

a constant degree-day factor of 1.5 mm per degree per day.

expected to be signiﬁcantly affected. During the peak ﬂow

period, model errors due to uncertainties in the precipitation Rainfall–runoff modelling

product (see the discussion of the precipitation input below) and structural errors due to the parameterization of the rain-

The sum of direct precipitation and snowmelt enters the

fall–runoff processes are most likely much larger than

rainfall–runoff model. For each sub-basin, the model uses

abstractions for water use.

a heuristic, lumped-parameter approach based on the Budyko framework (Zhang et al. ). The model operates with two storage compartments: a root zone storage and a groundwater storage. Budyko’s limits concept (Budyko ) is applied (1) to partition precipitation into catchment retention and direct runoff, (2) to compute groundwater recharge from catchment retention and soil storage carried over from the last time step and (3) to partition soil water availability into actual evapotranspiration and soil storage carried over to the next time step. The rainfall–runoff model requires four input parameters per sub-catchment. All four parameters of the rainfall–runoff model were calibrated. For details on the rainfall–runoff model, please consult the Zhang et al. () reference.

Model input and calibration/validation datasets Digital Elevation Model and catchment delineation A DEM was obtained from the NASA SRTM. The SRTM DEM has a spatial resolution of 3 arcseconds and was downloaded as a 5 × 5 degree mosaic (http://srtm.csi.cgiar.org/). The data were resampled to a resolution of 30 arcseconds in order to keep the processing time for the DEM hydroprocessing routine at a reasonable level. Subsequently, the drainage network and the sub-basins were derived from the DEM using a MATLAB DEM hydro-processing routine (TopoToolbox; Schwanghart & Kuhn ).

River network modelling Precipitation Only the main Brahmaputra River channel was simulated in the model, because no calibration or validation datasets

The Tropical Rainfall Measuring Mission (TRMM) Multi-

were available from the tributaries and the radar altimetry

satellite Precipitation Analysis (TMPA) was used as precipi-

targets of interest are all located on the main channel. The

tation forcing dataset. This dataset combines the TRMM

discharge was routed from one catchment outlet node to

precipitation radar, the TRMM microwave imager, the

the next using Muskingum–Cunge river routing (e.g. Chow

TRMM visible infrared scanner and infrared sensors from var-

et al. ). Routing time constants of individual river seg-

ious other missions (Huffman et al. ). Gridded

ments are based on segment lengths and on average river

precipitation between 50 degrees south and 50 degrees

ﬂow velocity. Average river ﬂow velocities in the upstream

north is provided. The TMPA offers two products: the 3B42

and downstream portions of the basin are calibrated. The

product and the 3B42RT real-time product, both of which

Muskingum weighting factor was also calibrated for both

have a spatial resolution of 0.25 degrees and a temporal resol-

the upstream and the downstream portions of the basin.

ution of 3 hours. The product estimates total precipitation,

153

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

i.e. the sum of rain and snow. Because the hydrological model

Hydrology Research

45.1

2014

Temperature

was designed for real-time applications, the 3B42RT product was chosen as the primary precipitation forcing. However,

Real-time temperature data are obtained from the European

3B42RT was only available from October 2008 onwards. In

Centre for Medium-Range Weather Forecast (ECMWF)

order to extend the model calibration period, the 3B42 pro-

Operational Surface Analysis Data Set. The dataset includes

duct was used to force the model in the period from January

6 hourly data for 2 m temperature with a 0.5 degree spatial

2000 to September 2008. Spatio-temporal rainfall patterns

resolution (approximately 54 km at the equator) until 2006

of the two products are similar because they are based on

and a 0.25 degree (27.7 km) resolution from 2006 onwards.

the same set of remote sensing observations. Any bias

The data were provided via ftp in real time by the Danish

between the two precipitation products had to be removed

Metrological Institute. Maximum and minimum daily temp-

because simulated water balances would otherwise be differ-

eratures

ent for the calibration and forecasting periods. To compute

Hargreaves’ equation (Hargreaves & Samani ). Daily

the bias, total precipitation amounts between October 2008

minimum and maximum temperatures were assumed to be

and June 2011 were compared between the 3B42 and

equal to the maximum and minimum temperatures in the

3B42RT products for the Brahmaputra river basin. On aver-

6-hourly temperature record for each day.

are

used

calculate

reference

ET using

age 3B42RT precipitation was 25% higher than 3B42 precipitation. Consequently pre-October 2008 3B42 data

In-situ river gauge data

were scaled by a factor of 1.25 and were used to force the hydrological model in the period January 2000 to September

In-situ river discharge data are extremely hard to obtain

2008. After October 2008, the 3B42RT product was used as

for the Brahmaputra. Only a small amount of data is in

the precipitation input in the hydrological model.

the public domain, because ﬂooding data are classiﬁed

Using this precipitation dataset, average runoff coefﬁ-

information in Bangladesh. The Global Runoff Data

cients at Nuxia and Bahadurabad were calculated. The total

Center (GRDC ) global database only includes very

long-term average precipitation upstream of Nuxia is

few historical datasets and no recent data. In-situ data

4,483 m3 s–1, while the long-term average observed discharge

are available for three stations: Nugesha, Nuxia and

at Nuxia is 2,000 m3 s–1 (Montgomery et al. ). The result-

Bahadurabad (see Figure 1). Historical daily discharge

ing runoff coefﬁcient is 0.45. Total long-term average

data (1956–2000) for the Bahadurabad station were

precipitation

downloaded

between

Nuxia

and

Bahadurabad

from

http://cfab.eas.gatech.edu/Raingage/

16,616 m3 s–1. The long-term average ﬂow at Bahadurabad

Q_Bahadurabad.txt. For the recent ﬂooding seasons,

is 20,408 m3 s–1, which results in a runoff coefﬁcient of the

daily observed discharge data are published on http://

downstream portion equal to 1.11. This clearly is an unrea-

cfab.eas.gatech.edu/shortterm/ensemble.html. During the

sonable runoff coefﬁcient and the precipitation in the

baseﬂow period (December to April) variability in the

downstream portion of the basin was multiplied by a factor

observed historical discharge from 1956 to 2000 is

of 1.7 to achieve similar runoff coefﬁcients as in the upstream

small. Thus, for recent years, baseﬂow was estimated as

part of the river basin. The bias of the precipitation product in

the historical average ﬂow in the Brahmaputra River for

the downstream portions of the basin might be due to strong

the corresponding day of the year in order to provide a

topographic gradients and orographic lifting of air masses

baseﬂow time series for calibration. Data for two stations

during the monsoon, which may not be captured sufﬁciently

in Tibet (Nuxia and Nugesha) are available for the high

accurately by the TMPA products in the Brahmaputra river

ﬂow periods of 2005, 2006 and 2007. The data have

basin. This ad-hoc bias correction procedure is debatable

been downloaded from http://southasianﬂoods.icimod.

and may be changed if more hydroclimatological data

org/saf/reports/. In-situ water levels for the station

become available. It is considered acceptable here because

Bahadurabad for the time period 1995 to 2003 were pro-

this paper focuses on operational discharge forecasting and

vided by the Institute of Water Modelling in Dhaka,

not on understanding regional hydrological processes.

Bangladesh.

154

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Radar altimetry data

Hydrology Research

45.1

2014

is the delay for maximum correlation. The free parameter a was chosen as a ¼ –0.005 in this study. The derived conﬁ-

Radar altimetry time series were extracted from ERS-2, Topex

dence intervals do not represent a given probability, but are

and Envisat data over the Brahmaputra based on an updated

useful to compare the reliability of the ﬁtted values of tdelay

map of potential open water surfaces derived from automatic

at the different sites. The delay times could only be deter-

river network delineation from the SRTM elevation map. Retrie-

mined for the Topex and ERS-2 targets because the

val was carried out using the waveform analysis and retracking

temporal overlap between the available in-situ water level

algorithms developed in the ESA-funded River and Lake project.

records and the Envisat altimetry time series was too short.

These enable identiﬁcation of radar echoes from open water surfaces, and successfully convert these to yield inland water heights. Retrieval algorithms are described in Berry et al.  and global radar altimetry data availability is documented on the River and Lake webpage at earth.esa.int/riverandlake. In order to check quality and consistency of the radar altimetry dataset, the kinematic wave travel times (delay times) between the various upstream altimetry targets and the in-situ gauging station Bahadurabad on the Brahmaputra were determined using the following procedure: the correlation between the water levels from the virtual station and the in-situ station is:

Data assimilation A simple heuristic assimilation strategy was developed. In the assimilation procedure, river discharge in the river segment corresponding to the assimilated altimetry target is updated. The internal states of the rainfall–runoff model (root zone storage, groundwater storage) are not updated. The assimilation procedure has three steps: 1. The calibrated model is executed and historical altimetry levels are plotted against simulated discharge on match-

1 Xn yA (ti þ tdelay ) yA ½yS (ti ) yS i¼1 n CC ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn 1 Xn ½yA (ti ) yA 2 ½y (t ) yS 2 i¼1 i¼1 S i n n

ing days for all altimetry targets. Subsequently, a power (1)

law of the form Q ¼ aðh bÞc

Here, CC ( ) is the correlation coefﬁcient between the two time series, which is a function of the applied delay

(3)

is ﬁtted to the plot, using a least-squares adjustment. In this formula, Q is the river discharge in m3 s–1, h is the

time tdelay. The symbol yA denotes the water level measured

altimetry water level in mamsl and a, b, c are ﬁtting par-

by the altimeter (m), yS in m is the water level measured at

ameters. This rating curve is applied in the assimilation to

the in-situ station. Overbars denote temporal averaging and

convert altimetry water levels into altimetry-derived dis-

n is the number of available altimetry measurements. The

charge. The underlying assumption is that the simulated

delay time is found by maximizing CC. A Nelder–Mead sim-

river discharge is uncertain, but unbiased. The mean

plex search algorithm is used to perform the maximization

model error for the calibration period was þ4% at Nuxia, –33% at Nugesha and –10.5% at Bahadurabad.

(function fminsearch in MATLAB, Lagarias et al. ). Conﬁdence intervals on the determined tdelay are

Model bias is thus small, particularly for the downstream region, where all the radar altimetry targets are located.

derived as follows: tdelay,l ¼ tdelay CC tdelay ¼ CCmax þ a and tdelay < tdelay,max tdelay,u ¼ tdelay CC tdelay ¼ CCmax þ a and tdelay > tdelay,max (2)

2. The model is run in near real-time mode at daily time steps. Whenever an altimetry reading is available for any of the assimilated radar altimetry targets, the corresponding rating curve is used to convert the reading into a discharge estimate. The discharge in the corresponding river segment

Here, tdelay,l is the lower bound of the conﬁdence inter-

of the model is updated using the following equation:

val, tdelay,u is the upper bound of the conﬁdence interval, CCmax is the maximum achieved correlation and tdelay, max

Qass ¼ Qsim þ GðQalt Qsim Þ

(4)

155

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Hydrology Research

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2014

In this formula, Qass is the analysed discharge, Qsim is the

between the altimetry water level time series and the in-situ

simulated discharge prior to assimilation, Qalt is the dis-

water level time series is very high. Figure 4 shows the delay

charge estimate based on altimetry and G is a gain factor

times between the various altimetry targets and the Baha-

ranging from 0 to 1.

durabad in-situ station as a function of river chainage. As

3. The innovation GðQalt Qsim Þ is added to the simulated

expected, delay times increase with increasing distance

discharge at the river node representing the altimetry

from the in-situ station. Kinematic wave celerities can be

target. All updating terms are propagated to the next

extracted from the graph for three distinct sections of the

time step but are discounted in each time step using a

Brahmaputra River. Given that the friction slope can be

constant discount factor δ, which was set to 0.975 per

expressed using Manning’s equation and assuming a uni-

time step, using daily time steps. This value of the dis-

form, wide rectangular ﬂow cross section, the average

count factor was found by trial-and-error adjustment,

water ﬂow velocity (vw) can be estimated from the kinematic

maximizing the Nash–Sutcliffe model efﬁciency.

wave celerity (ck) using the formula (e.g. Chow et al. ):

vw ¼

RESULTS

3 dQ 3 ¼ ck 5 dA 5

(5)

where Q is the river discharge and A is the ﬂow cross-

Radar altimetry ﬁndings

sectional area.

Table 1 summarizes the characteristics of the virtual stations

Model calibration and validation results

on the Brahmaputra River. 17 ERS-2 virtual stations, 6 Topex virtual stations and 10 Envisat virtual stations are

The total model simulation period extends from 2000 to 2010.

available. The ﬁrst column gives the altimetry target ID.

However, in-situ data are only available for the period 2005 to

The second column gives the relative overpass time, relative

2010. The period with available in-situ data was split into a

to the ﬁrst ERS target (B-ERS-1). The third column gives the

calibration period (2005–2007) and a validation period

chainage of the altimetry target relative to the in-situ gauging

(2008–2010). The model was calibrated against the observed

station Bahadurabad. Negative numbers indicate a location

discharge at the Bahadurabad, Nuxia and Nugesha stations

upstream from the gauging station. The next two columns

for the 3-year calibration period. In total, 12 parameters were

contain the geographic coordinates of the targets. The next

automatically calibrated (6 for the upstream and 6 for the

column gives the approximate elevation of the target as

downstream portions of the basin) using a trust region reﬂec-

read from the SRTM. The next three columns contain the

tive algorithm (Coleman & Li ), which outperforms the

ﬁtted delay time and its lower and upper conﬁdence interval

Levenberg–Marquardt algorithm if the initial parameter esti-

bounds. The ﬁnal column contains the maximum achieved

mates are far from the optimum. The calibration objective

correlation between the altimetry target and the discharge

function was the root mean square error (RMSE) of simulated

station. This correlation is achieved for a delay time as

versus observed discharge. The upstream portion of the basin

given in the table. Targets shaded in grey are considered out-

was calibrated using the stations Nuxia and Nugesha, which

liers and were disregarded in the further analysis. They

were equally weighted in the calibration. The downstream por-

generally show a low degree of correlation with the in-situ

tion of the basin was calibrated using the Bahadurabad station.

gauging station and some of them are located on tributaries to the main river.

Table 2 provides an overview of the calibration parameters and the calibrated parameter values. Calibration parameters

To illustrate the quality of the radar altimetry targets

included four parameters of the Budyko rainfall–runoff

over the Brahmaputra, an example for target B-ERS-10 is

model (α1, α2, d and Smax), as well as two Muskingum routing

shown in Figure 3. Although the target is located about

parameters (vmax and X ). Generally, post-calibration par-

320 km upstream from the Bahadurabad station, correlation

ameter conﬁdence intervals are reasonably conﬁned, except

F. Finsen et al.

156

Table 1

Using radar altimetry to update a large-scale hydrological model

Hydrology Research

45.1

2014

Overview of available virtual stations from ERS-2, Envisat and Topex over the Brahmaputra River

Latitude

Longitude

SRTM

Delay time

Delay time upper CI

Chainage (km)

(deg)

(mamsl)

(days)

lower CI (days)

(days)

304

23.049

90.436

62.84

44.50

66.04

0.5033

Relative reading Target ID

time (days)

ERS-2 B-ERS2-1

B-ERS2-2

B-ERS2-3

–16

220

23.669

90.360

9.28

5.78

11.48

0.8752

Tributary

23.954

90.928

5.16

2.48

7.26

0.8577

B-ERS2-4 B-ERS2-5

–7

131

24.084

89.747

3.02

0.22

5.50

0.9234

–71

25.758

89.755

–0.81

–2.11

1.18

0.7809

B-ERS2-6

–82 (tributary)

25.787

89.457

16.92

–10.73

18.45

0.7944

B-ERS2-7

–7

–145

26.144

90.269

–8.48

–22.98

–1.34

0.7917

B-ERS2-8

–229

26.183

90.996

–1.48

–3.22

–0.02

0.9219

B-ERS2-9

–239

26.190

91.081

–2.10

–4.12

0.09

0.9307

B-ERS2-10

–13

–322

26.215

91.793

–0.72

–3.90

1.64

0.9651

B-ERS2-11

–406

26.541

92.427

–17.95

–20.01

–4.90

0.8036

B-ERS2-12

–1

–501

26.717

93.291

–1.86

–4.65

–0.23

0.9637

B-ERS2-13

–559

26.798

93.797

–4.17

–5.45

–2.44

0.9390

B-ERS2-14

–17

–591

26.866

94.047

–4.84

–15.45

–3.79

0.9317

B-ERS2-15

–17

–599

26.973

94.075

–4.42

–7.30

–2.58

0.9264

B-ERS2-16

–7

–640

27.036

94.456

–6.84

–21.48

–3.81

0.8737

B-ERS2-17

–727

27.588

94.954

103

–9.08

–13.78

–5.38

0.9045

B-Topex-1

24.686

89.687

–0.84

–2.67

2.04

0.9608

B-Topex-2

24.779

89.730

0.15

–1.99

3.51

0.9015

B-Topex-3

–157

26.160

90.375

–2.75

–4.46

0.17

0.8281

B-Topex-4

–161

26.193

90.391

–2.36

–4.91

–0.09

0.9205

B-Topex-5

–237

26.211

91.042

–2.47

–4.94

–0.23

0.9670

B-Topex-6

–537

26.772

93.609

–1.21

–3.98

1.01

0.7216

B-Envisat-1

344

22.804

90.494

B-Envisat-2

211

23.699

90.273

B-Envisat-3

–16

Tributary

23.954

90.927

B-Envisat-4

–71

25.756

89.753

B-Envisat-5

–16

–157

26.181

90.363

B-Envisat-6

–239

26.189

91.079

B-Envisat-7

–406

26.541

92.427

B-Envisat-8

–559

26.798

93.798

B-Envisat-9

–7

–640

27.036

94.454

B-Envisat-10

–735

27.620

95.021

111

Topex

Envisat

for the maximum soil water storage Smax and the Muskingum

is generally satisfactory as evidenced by the performance stat-

parameter X. Figure 5 shows a comparison of simulated and

istics listed in Table 3. Root mean square errors are 42% of

observed discharge at the three stations. Model performance

average discharge at Nuxia and 43% of average discharge at

157

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

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45.1

2014

Figure 3

Correlation between ERS-2 target 10 (B-ERS-10) and in-situ water levels at the Bahadurabad station, located 322 km downstream of the target. A time shift was applied to maximize the correlation between the two time series (see Table 1).

Figure 4

Delay times between the in-situ station at Bahadurabad and all altimetry targets on the Brahmaputra River.

F. Finsen et al.

158

Table 2

Using radar altimetry to update a large-scale hydrological model

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45.1

2014

Overview of calibration parameters and calibration results

Upstream sub-basins 1–6

Description and unit

α1

Budyko parameter, governs partition between catchment retention and runoff, dimensionless Budyko parameter, governs partition between groundwater recharge and ET, dimensionless Baseflow recession coefficient, per day Maximum soil water storage, mm Channel flow velocity, m per second Muskingum weighting factor, dimensionless

α2 d Smax vw X

Downstream sub-basins 7–19

Calibrated value

Parameter

α1 α2 d Smax vw X

Lower bound of 95% conﬁdence interval

Upper bound of 95% conﬁdence interval

0.337

0.267

0.407

0.454

0.417

0.491

0.0255 136.7 1.16 0.0011

0.0223 24.4 1.11 –0.24

0.0286 249.0 1.21 0.24

0.343

0.223

0.463

0.489

0.360

0.612

0.0138 145.8 0.86 0.0010

0.0117 44.5 0.789 –0.42

0.0158 247.1 0.907 0.42

Bahadurabad. Nash–Sutcliffe model efﬁciency ranges from

altimetry-derived discharge was subsequently assimilated

0.61 at Nugesha to 0.78 at Bahadurabad.

into the model. Model performance with and without

Data assimilation results

ments are most notable in the beginning of the base ﬂow

radar altimetry assimilation is shown in Figure 7. Improverecession period, when the calibrated model over-estimates For the validation period (2008–2010), model performance

the discharge. This bias is effectively corrected by the data

using various gain factors G (Equation (4)) was compared

assimilation scheme.

to the performance of the calibrated model. The results are documented in Table 3. Without using the available altimetry data for model updating, the calibrated model achieves

DISCUSSION

an NSE of 0.77 over the validation period. The model Nash–Sutcliffe efﬁciency can be increased to 0.83, if altime-

A number of high-quality virtual stations are available on the

try data are assimilated. The gain factor that yielded the

Brahmaputra. From the ERS-2, Topex and Envisat missions,

highest model efﬁciency was G ¼ 0.6. Available Envisat

time series for 33 virtual stations were obtained over a river

radar altimetry data from the time period prior to 2008

segment of about 1,000 km. This relatively dense spatial

were used to establish pseudo-rating curves of simulated dis-

sampling will become even denser once data from altimetry

charge versus altimetry levels (Figure 6). Note that the radar

missions, which are currently in planning or early operation

altimetry data from the validation period were not used in

stage (Cryosat-2, Sentinel-3, SWOT), become routinely avail-

the determination of the rating curves. This was done in

able. While the temporal resolution of the available

order to simulate operation of the model for real-time fore-

altimetry data is relatively coarse (e.g. 35 days repeat orbit

casting. Generally, the rating curves are consistent and the

for Envisat), reading times at individual targets are shifted

ﬁtted parameters of the power law (Equation (3)) are reason-

by constant time intervals (Table 1). This implies that

able. Pseudo rating curves show considerable scatter. For

during the simulation period readings from at least one of

the validation period, the model was run in assimilation

the targets are available at intervals of a few days (minimum

mode. The pseudo-rating curves were used to convert

interval: 3 days, mean interval: 4.9 days, maximum interval:

incoming altimetry measurements into discharge and the

13 days), which greatly augments the utility of radar

159

Figure 5

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Post-calibration model performance for the calibration period at the stations Bahadurabad, Nuxia and Nugesha.

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45.1

2014

F. Finsen et al.

160

Table 3

Using radar altimetry to update a large-scale hydrological model

Overview of model performance in the calibration period and in the validation period for various gain settings. Root mean square error (RMSE) and Nash– Sutcliffe model efﬁciency (NSE) are shown. Long-term average discharge is 3

20,408 m s

–1

at Bahadurabad and 2,000 m s

–1

at Nuxia

RMSE, m s

–1

45.1

2014

The information contained in the altimetry readings can be exploited to its full potential when combined with a river basin model. The model can be used to interpolate in time and smoothen out extreme values and outliers in the altime-

RMSE, percent of 3

Hydrology Research

average ﬂow

NSE, –

try dataset. The river basin model developed in this paper is

0.784

relatively simple and uses a minimum amount of in-situ data.

Bahadurabad Calibration period

8,800

Nugesha Calibration period

557

Nuxia Calibration period

843

0.698

Bahadurabad Validation period G¼0

10,200

0.772

Bahadurabad Validation period G ¼ 0.1

9,630

0.795

Bahadurabad Validation period G ¼ 0.2

9,270

Bahadurabad Validation period G ¼ 0.3

9,020

Bahadurabad Validation period G ¼ 0.4

8,860

0.827

Bahadurabad Validation period G ¼ 0.5

8,750

0.831

Bahadurabad Validation period G ¼ 0.6

8,710

0.833

Bahadurabad Validation period G ¼ 0.7

8,730

0.832

Bahadurabad Validation period G ¼ 0.8

8,850

0.827

Bahadurabad Validation period G ¼ 0.9

9,090

0.818

Bahadurabad Validation period G ¼ 1.0

9,510

It could be improved in several ways (enhanced spatial res0.611

olution,

enhanced

calibration

and

validation,

better

representation of water users). Due to the coarse resolution of the model and the lack of detail in the representation of both hydrological processes and abstractions for water use, model performance is variable, when evaluated for small sub-units of the basin. However, model performance expressed in terms of RMSE and NSE is satisfactory at all three stations where in-situ data were available and is com45

0.810

petitive compared to previous modelling efforts reported for the region (Nishat & Rahman ; Rao et al. ). The principal limitation for improving model performance is the

0.820

quality of the precipitation forcing product. However, even at this stage the model can be successfully combined with the radar altimetry datasets to provide real-time modelling and forecasting capabilities to water resources managers. The results show that the best performance is achieved when model simulation results and radar altimetry data are weighted 40 to 60. This implies that both the model simulation and the altimetry data contain valuable information, which is combined in an optimal way in the data assimilation scheme. Data assimilation techniques are efﬁcient tools in this context to synthesize model predictions and observations and produce the best possible estimate of model states at each point in time along with forecasts based on both model predictions and the latest available observations. The data assimilation technique used in this study is extremely simple. As a future research direction, the application of statistical data assimilation tools, such as the Ensemble

0.800

Kalman Filter (EnKF), can be investigated. Possibly, model performance could be enhanced if the states of the rainfall– runoff model (i.e. root zone storage and groundwater storage) were updated in the data assimilation scheme and not only the discharges in the river network.

altimetry for ﬂood forecasting and early warning. The near

The presented modelling and data assimilation approach

real-time altimetric monitoring capability for the Brahmapu-

is useful as a ﬁrst screening approach for large-scale river

tra was signiﬁcantly affected by the failure of Envisat in 2012

basins. The required amount of in-situ information is mini-

because this mission provided most of the operational data.

mal. The model can be expanded to cover all major river

161

Figure 6

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Hydrology Research

45.1

2014

Pseudo rating curves (altimetry versus simulated discharge). Only data from the calibration period are used. The ﬁtted equations for each rating curve are shown in the plots.

basins of the world. The assimilation approach used in this

alternative approach would be to generate rating curves

study is purely heuristic. The advantages are as follows:

based on in-situ river geometry and sparse historical dis-

•

charge observations only. Such approaches have been Any number of altimetry targets can be efﬁciently assimiexcessively. Expensive ensemble calculations as required

•

for the EnKF are avoided. The pseudo-rating curves used to convert altimetry read-

•

avenue for further research (Bjerklie et al. ). The assimilation scheme produces discharge estimates based on both model simulation and altimetry data but does not quantify their uncertainty.

ings into simulated discharge can be continuously updated, as more altimetry data become available. The disadvantages are as follows:

•

presented in the literature and could be a promising

lated into the model without increasing run-times

In the approach presented here, the discharge correction term (innovation) is added to only one river node, corresponding to the location of the radar altimetry target.

If the calibrated model produces biased discharge esti-

However, due to the fact that river discharge is correlated

mates that show correlated error structures, the pseudo-

in space, river discharge at neighbouring river nodes could

rating curve approach will fail. Such errors will not be

be updated as well. More sophisticated data assimilation

mitigated by the assimilation of altimetry data. An

algorithms, such as the EnKF, make use of the correlation

162

Figure 7

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

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45.1

2014

Model performance at Bahadurabad with and without data assimilation for the validation period.

between a measurement and any model state. Such an

This work has demonstrated the availability and quality

approach could potentially enhance model performance sig-

of radar altimetry water level time series over the Brahmapu-

niﬁcantly, particularly if internal states of the rainfall–runoff

tra River. A river basin modelling and data assimilation

model are included in the updating scheme. An assimilation

approach has been developed that enables the direct use

scheme based on the Kalman Filter would also provide esti-

of radar altimetry data for real-time modelling and hydrolo-

mates of forecast uncertainty along with the actual forecast.

gical forecasting. Model efﬁciency increased considerably

Such information would be extremely valuable for practical

due to the assimilation of multiple radar altimetry targets.

ﬂood hazard management. However, one of the main challenges for a potential application of the Kalman Filter is the estimation of the error of the various forcing variables derived from remote sensing as well as the estimation of forcing error correlations.

ACKNOWLEDGEMENTS We acknowledge the Institute of Water Modelling, Dhaka, Bangladesh,

for

in-situ

water

level

data

for

the

Bahadurabad gauging station. The authors thank the

CONCLUSIONS

European Space Agency for supply of altimeter data.

Overall, this study has demonstrated that the combination of a river basin mass balance model and radar altimetry data

REFERENCES

leads to increased model efficiencies for predicting flood events in the Brahmaputra basin, which is an encouraging finding in view of the increase of both availability and quality of radar altimetry time series over inland waters expected over the coming years.

Akhtar, M. K., Corzo, G. A., van Andel, S. J. & Jonoski, A.  River flow forecasting with artificial neural networks using satellite observed precipitation pre-processed with flow length and travel time information: case study of the Ganges river basin. Hydrol. Earth Syst. Sci. 13 (9), 1607–1618.

163

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Alcamo, J., Doll, P., Henrichs, T., Kaspar, F., Lehner, B., Rosch, T. & Siebert, S.  Development and testing of the WaterGAP 2 global model of water use and availability. Hydrol. Sci. J. 48 (3), 317–337. Andreadis, K. M., Clark, E. A., Lettenmaier, D. P. & Alsdorf, D. E.  Prospects for river discharge and depth estimation through assimilation of swath-altimetry into a raster-based hydrodynamics model. Geophys. Res. Lett. 34 (10), L10403. Arnold, J. G., Srinivasan, R., Muttiah, R. S. & Williams, J. R.  Large area hydrologic modeling and assessment – Part 1: Model development. J. Am. Water Resour. Assoc. 34 (1), 73–89. Berry, P. A. M., Garlick, J. D., Freeman, J. A. & Mathers, E. L.  Global inland water monitoring from multi-mission altimetry. Geophys. Res. Lett. 32 (16), L16401. Biancamaria, S., Durand, M., Andreadis, K. M., Bates, P. D., Boone, A., Mognard, N. M., Rodriguez, E., Alsdorf, D. E., Lettenmaier, D. P. & Clark, E. A.  Assimilation of virtual wide swath altimetry to improve Arctic river modeling. Rem. Sens. Environ. 115 (2), 373–381. Birkett, C. M., Mertes, L. A. K., Dunne, T., Costa, M. H. & Jasinski, M. J.  Surface water dynamics in the Amazon Basin: Application of satellite radar altimetry. J. Geophys. Res. Atmos. 107 (D20), 8059. Birkinshaw, S. J., O’Donnell, G. M., Moore, P., Kilsby, C. G., Fowler, H. J. & Berry, P. A. M.  Using satellite altimetry data to augment ﬂow estimation techniques on the Mekong River. Hydrolog. Process. 24 (26), 3811–3825. Bjerklie, D. M., Dingman, S. L., Vorosmarty, C. J., Bolster, C. H. & Congalton, R. G.  Evaluating the potential for measuring river discharge from space. J. Hydrol. 278 (1–4), 17–38. Budyko, M. I.  The Heat Balance of the Earth’s Surface. US Department of Commerce, Washington, DC. Chow, V. T., Maidment, D. R. & Mays, L. W.  Applied Hydrology. McGraw-Hill, Singapore. Coe, M. T. & Birkett, C. M.  Calculation of river discharge and prediction of lake height from satellite radar altimetry: Example for the Lake Chad basin. Water Resour. Res. 40 (10), W10205. Coleman, T. F. & Li, Y. Y.  An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6 (2), 418–445. Cretaux, J. F., Jelinski, W., Calmant, S., Kouraev, A., Vuglinski, V., Berge-Nguyen, M., Gennero, M. C., Nino, F., Del Rio, R. A., Cazenave, A. & Maisongrande, P.  SOLS: A lake database to monitor in the Near Real Time water level and storage variations from remote sensing data. Adv. Space Res. 47 (9), 1497–1507. Draper, A. J., Jenkins, M. W., Kirby, K. W., Lund, J. R. & Howitt, R. E.  Economic-engineering optimization for California water management. J. Water Resour. Plann. Manag. – ASCE 129 (3), 155–164. Dukhovny, V. A., Tuchin, A. I. & Sokolov, V. I.  Decision support system for water-user associations in the Aral Sea

Hydrology Research

45.1

2014

basin. Land and Water Management: Decision Tools and Practices 1 and 2, 268–274. China Agricultural Univ., Beijing. Durand, M., Andreadis, K. M., Alsdorf, D. E., Lettenmaier, D. P., Moller, D. & Wilson, M.  Estimation of bathymetric depth and slope from data assimilation of swath altimetry into a hydrodynamic model. Geophys. Res. Lett. 35 (20), L20401. Global Runoff Data Center (GRDC)  Major River Basins of the World. Koblenz, Germany. Hargreaves, G. H. & Samani, Z. A.  Estimating potential evapo-transpiration. J. Irrigat. Drain. Div. – ASCE 108 (3), 225–230. Hock, R.  Temperature index melt modelling in mountain areas. J. Hydrol. 282 (1–4), 104–115. Hostache, R., Matgen, P., Schumann, G., Puech, C., Hoffmann, L. & Pfister, L.  Water level estimation and reduction of hydraulic model calibration uncertainties using satellite SAR images of floods. IEEE Trans. Geosci. Rem. Sens. 47 (2), 431–441. Huffman, G. J., Adler, R. F., Bolvin, D. T., Gu, G., Nelkin, E. J., Bowman, K. P., Hong, Y., Stocker, E. F. & Wolff, D. B.  The TRMM multisatellite precipitation analysis (TMPA): Quasi-global, multiyear, combined-sensor precipitation estimates at fine scales. J. Hydrometeorol. 8 (1), 38–55. Jakobsen, F., Hoque, A., Paudyal, G. N. & Bhuiyan, M. S.  Evaluation of the short-term processes forcing the Monsoon river floods in Bangladesh. Water Int. 30 (3), 389–399. Lagarias, J. C., Reeds, J. A., Wright, M. H. & Wright, P. E.  Convergence properties of the Nelder-Mead simplex method in low dimensions. Siam J. Optimiz. 9 (1), 112–147. Madsen, H. & Skotner, C.  Adaptive state updating in realtime river flow forecasting – a combined filtering and error forecasting procedure. J. Hydrol. 308 (1–4), 302–312. Maheu, C., Cazenave, A. & Mechoso, C. R.  Water level fluctuations in the Plata basin (South America) from Topex/Poseidon Satellite Altimetry. Geophys. Res. Lett. 30 (3), 1143. Mason, D. C., Bates, P. D. & Amico, J. T. D.  Calibration of uncertain flood inundation models using remotely sensed water levels. J. Hydrol. 368 (1–4), 224–236. Milzow, C., Krogh, P. E. & Bauer-Gottwein, P.  Combining satellite radar altimetry, SAR surface soil moisture and GRACE total storage changes for hydrological model calibration in a large poorly gauged catchment. Hydrol. Earth Syst. Sci. 15 (6), 1729–1743. Mondal, M. S. & Wasimi, S. A.  Generating and forecasting monthly flows of the Ganges river with PAR model. J. Hydrol. 323 (1–4), 41–56. Montgomery, D. R., Hallet, B., Liu, Y. P., Finnegan, N., Anders, A., Gillespie, A. & Greenberg, H. M.  Evidence for Holocene megafloods down the Tsangpo River Gorge, southeastern Tibet. Quaternary Res. 62 (2), 201–207. Nishat, B. & Rahman, S. M.  Water resources modeling of the Ganges-Brahmaputra-Meghna River Basins using Satellite Remote Sensing Data. J. Am. Water Resour. Assoc. 45 (6), 1313–1327.

164

F. Finsen et al.

Using radar altimetry to update a large-scale hydrological model

Nohara, D., Kitoh, A., Hosaka, M. & Oki, T.  Impact of climate change on river discharge projected by multimodel ensemble. J. Hydrometeorol. 7 (5), 1076–1089. Oleson, K. W., Niu, G. Y., Yang, Z. L., Lawrence, D. M., Thornton, P. E., Lawrence, P. J., Stoeckli, R., Dickinson, R. E., Bonan, G. B., Levis, S., Dai, A. & Qian, T.  Improvements to the Community Land Model and their impact on the hydrological cycle. J. Geophys. Res. – Biogeosci. 113 (G1), G01021. Pereira-Cardenal, S. J., Riegels, N. D., Berry, P. A. M., Smith, R. G., Yakovlev, A., Siegfried, T. U. & Bauer-Gottwein, P.  Realtime remote sensing driven river basin modeling using radar altimetry. Hydrol. Earth Syst. Sci. 15 (1), 241–254. Qian, T. T., Dai, A., Trenberth, K. E. & Oleson, K. W.  Simulation of global land surface conditions from 1948 to 2004. Part I: Forcing data and evaluations. J. Hydrometeorol. 7 (5), 953–975. Rao, K., Bhanumurthy, V. & Roy, P. S.  Application of satellite-based rainfall products and SRTM DEM in hydrological modelling of Brahmaputra basin. J. Indian Soc. Rem. Sen. 37 (4), 587–600. Refsgaard, J. C. & Knudsen, J.  Operational validation and intercomparison of different types of hydrological models. Water Resour. Res. 32 (7), 2189–2202.

Hydrology Research

45.1

2014

Rodell, M., Houser, P. R., Jambor, U., Gottschalck, J., Mitchell, K., Meng, C. J., Arsenault, K., Cosgrove, B., Radakovich, J., Bosilovich, M., Entin, J. K., Walker, J. P., Lohmann, D. & Toll, D.  The global land data assimilation system. Bull. Am. Meteorol. Soc. 85 (3), 381–394. Schumann, G. J. P., Neal, J. C., Mason, D. C. & Bates, P. D.  The accuracy of sequential aerial photography and SAR data for observing urban ﬂood dynamics, a case study of the UK summer 2007 ﬂoods. Rem. Sens. Environ. 115 (10), 2536–2546. Schwanghart, W. & Kuhn, N. J.  TopoToolbox: A set of Matlab functions for topographic analysis. Environ. Model. Software 25 (6), 770–781. Stisen, S. & Sandholt, I.  Evaluation of remote-sensing-based rainfall products through predictive capability in hydrological runoff modelling. Hydrolog. Process. 24 (7), 879–891. Vrugt, J. A., Diks, C. G. H., Gupta, H. V., Bouten, W. & Verstraten, J. M.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation. Water Resour. Res. 41 (1), W01017. Zhang, L., Potter, N., Hickel, K., Zhang, Y. & Shao, Q.  Water balance modeling over variable time scales based on the Budyko framework – Model development and testing. J. Hydrol. 360 (1–4), 117–131.

First received 13 December 2011; accepted in revised form 16 March 2013. Available online 3 July 2013