JH_2004_299_136-158

Journal of Hydrology 299 (2004) 136–158 www.elsevier.com/locate/jhydrol

Modelling of macropore flow and transport processes at catchment scale Jesper Skovdal Christiansend, Mette Thorsena, Thomas Clausena, Søren Hansenb, Jens Christian Refsgaardc,* a DHI Water and Environment, Hørsholm, Denmark Royal Veterinary and Agricultural University, Copenhagen, Denmark c Geological Survey of Denmark and Greenland, Department of Hydrology, Oster Voldgade 10, DK-1350 Copenhagen, Denmark d Atkins Danmark, Copenhagen, Denmark b

Received 15 August 2002; revised 20 April 2004; accepted 26 April 2004

Abstract Macropores play a significant role as a preferential flow mechanism in connection with pesticide leaching to shallow groundwater in clayey and loamy soils. A macropore description based on some of the same principles as those of the MACRO code has been added to the coupled MIKE SHE/Daisy code, enabling a physically based simulation of macropore processes in a spatially distributed manner throughout an entire catchment. Simulation results from a small catchment in Denmark suggest that although the point scale macropore processes have no dominating effect on groundwater recharge or discharge at a catchment scale, they will have significant effects on pesticide leaching to groundwater at a catchment scale. The primary function of macropores in this area is that they rapidly transport a significant part of the infiltrating water and solutes from the plough pan at 20 cm depth some distance downwards before most of it flows back into the soil matrix. This has a very significant effect on the leaching of pesticides from the surface to the groundwater table, because some of the pesticides are transported rapidly downwards in the soil profile to zones with less sorption and degradation. It is concluded that the spatial variations of macropore flows caused by the variation in topography and depth to groundwater table within a catchment are so large that this has to be accounted for in up-scaling process descriptions and results from point scale to catchment scale. q 2004 Elsevier B.V. All rights reserved.

Keywords: Preferential flow; Leaching; Pesticide; Catchment; Modelling

1. Introduction The importance of macropores as a preferential flow mechanism for infiltrating water and transport of solutes has been generally recognised during * Corresponding author. Fax: þ 45-3814-2050.

E-mail address: jcr@geus.dk (J.C. Refsgaard).

0022-1694/$ - see front matter q 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2004.04.029

a couple of decades (Beven and Germann, 1982; Barbash and Resek, 1996). Macropores play significant roles in many contexts such as leading to more infiltration and thus reducing overland flow and is rapidly transferring pesticides and other pollutants through the soil toward the groundwater. Pesticides have been detected in shallow groundwater worldwide (US Environmental Protection Agency, 1990,

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1992; EEA, 2000; Stockmarr, 2000) and preferential flow is recognised as an important mechanism in this connection (Barbash and Resek, 1996; Thorsen et al., 1998).

Field scale studies of tracer movements to the groundwater system in clayey till areas (Sidle et al., 1998; Nilsson et al., 2001) show that rapid transport of solutes to shallow groundwater at 4 –7 m depth can be explained by preferential flow mechanisms. Similarly, field scale studies of preferential flow to the drains in glacial till agricultural soils (Villholth et al., 1998; Villholth and Jensen, 1998) have shown that macropore flow is essential in describing the observed flows and concentrations in tile drains. The results from these field studies emphasised the importance of taking the considerable spatial variability of hydraulic parameters into account.

At the point scale, where only vertical flows are considered, the classical modelling approach for preferential flow and transport phenomena is a twodomain or dual permeability description in one (vertical) dimension. An example of a model code of this type is the MACRO (Jarvis, 1994; Jarvis and Larsson, 1998; Larsson and Jarvis, 1999), where the vertical flow in the matrix is described by Richards’ equation and the preferential flow is assumed to take place in a separately defined pore domain. The interaction between the macropore and the matrix is described by an approximation to a diffusion equation.

This macropore modelling approach has shown to provide significantly improved description of the pesticide breakthrough curves as compared to models not considering preferential flows (Bergstro¨m and Jarvis, 1994; Thorsen et al., 1998; Larsson and Jarvis, 1999; Armstrong et al., 2000). This model type may be characterised as physically based, because it is based on the point scale partial differential flow and transport equations and contains process descriptions and parameters, which are recognisable in the field.

Thus, it is in principle rather easy to modify this model type to incorporate new knowledge on process descriptions as it becomes available (Jarvis, 1998).

Hydrological models at catchment scale may be classified according to the description of the physical processes as conceptual or physically based, and according to the spatial description of catchment processes as lumped or distributed (Refsgaard, 1996 and many others). In this respect, two typical model

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types are the lumped conceptual and the distributed physically based ones. Examples of the two model types are the Stanford Watershed Model (Crawford and Linsley, 1966) and the MIKE SHE (Abbott et al., 1986; Refsgaard and Storm, 1995), respectively.

In lumped conceptual catchment models preferential flow and transport are treated in a relatively simple manner by empirical approaches. Thus, catchment model codes that include pesticide transport components such as HSPF (Donigian et al., 1995), CREAMS (Knisel and Williams, 1995) and SWRRB (Arnold and Williams, 1995) do not consider preferential flow explicitly by a two-domain approach.

Instead, the equations describing e.g. infiltration have implicitly built in some kind of spatial variability or preferential flow dynamics. In the CREAMS and SWRRB, the core of the infiltration equation is the curve number approach, while the HSPF that is based on the classical Stanford Watershed Model considers a combination of catchment average infiltration capacity with its dependence on the average soil moisture content and the spatial variability of this average catchment infiltration capacity. However, the spatial variability is not considered explicitly and all state variables represent average catchment conditions, and hence, the knowledge existing at point scale on macropore processes and parameter values is incompatible with the catchment scale equations built into these model codes.

While it is thus fundamentally very difficult to include a physically based macropore description in lumped conceptual catchment models, it is in principle easier in the more sophisticated catchment models of the distributed, physically based type, where the process equations and parameters at the individual computational grids are point scale equations and as such compatible with e.g. macropore formulations such as the one in MACRO. However, none of the existing model codes of the distributed physically based type presently includes a physically based macropore description. In most of them, such as Thales (Grayson et al., 1995), preferential flow is not considered, while in others, such as MIKE SHE (DHI, 2000a), an empirical ‘bypass flow’ formulation is built in as an optional add-on description. This bypass flow is required to match observed hydrographs when a model like MIKE SHE is used for large scale modelling, in order to compensate for the lack of

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spatial variability of soil parameters, topography, climate input etc that is often a problem when the data basis is scarce and/or the model grid size is very large (Overgaard, 2000).

Many factors influence leaching of pesticides to the phreatic aquifer. The present paper focuses on the importance of macropore flow and transport and specifically on the interaction between the depth to ground water table and macropore flow processes at the catchment scale. As macropore flow is dependent on the soil moisture content at the beginning of the rainfall events, it is as such sensitive to the depth of the groundwater table that is varying considerably in time and space throughout a catchment. The assumption usually made in pesticide leaching models is to use either a lower boundary condition that is constant in time and space (e.g. constant gradient or constant dept to groundwater table) or, at best, a time variable groundwater table. No studies have so far been reported on the possible differences of the macropore processes between a point scale and a natural catchment with a temporally and spatially varying groundwater table.

The present study was carried out within the framework of a research project aiming at modelling of pesticide leaching, transport and degradation at

catchment scale with particular emphasis on groundwater aspects. Some aspects of the pesticide modelling are reported elsewhere (Brun et al., 2000; Thorsen et al., 2000). The present paper, focusing on macropore flow, transport and leaching to shallow groundwater at catchment scale, has the following objectives: (1) to describe incorporation of a physically based macropore formulation into a physically based spatially distributed catchment model; (2) to investigate how the spatial and temporal variations of depth to the ground water table influence macropore flows and transport at the catchment scale; and (3) to test the extent to which the traditional approach of using pesticide leaching models at the point scale gives different results than using a spatially distributed model with similar macropore descriptions at catchment scale.

2. Catchment modelling framework 2.1. The integrated model concept The integrated modelling concept (Fig. 1), aiming at simulation of pesticide transport and fate at catchment scale, is based on a coupling between a spatially distributed hydrological model code

Fig. 1. A scetch of the integrated modelling system for simulation of pesticide transport and fate at catchment scale.

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operating at catchment scale (MIKE SHE) and a point scale agro-ecosystem model code (Daisy).

MIKE SHE (Abbott et al., 1986; Refsgaard and Storm, 1995) is a modelling system describing the flow of water and solutes in a catchment in a distributed physically based way. This implies numerical solutions of the coupled partial differential equations for overland (2D) and channel flow (1D), unsaturated flow (1D) and saturated flow (3D) together with a description of evapotranspiration and snowmelt processes. In addition an optional macropore flow module, described below, has been added. The solute transport processes are described by the classical advection dispersion equation.

Daisy (Hansen et al., 1991; Abrahamsen and Hansen, 2000) is a 1D modelling system describing crop production as well as water and nutrient dynamics in the root zone according to various management strategies, including crop rotations, fertilisation, irrigation, soil tillage and crop residue management. The model simulates processes such as: plant growth and crop production; heat flux and soil temperature; soil water uptake by plants and evapotranspiration; carbon and nitrogen mineralisation; nitrification and denitrification (nitrogen transformation); and nitrogen uptake by plants.

2.2. The MIKE—SHE DAISY coupling A full coupling has been developed between MIKE SHE and Daisy at the code level. The pesticide application, evapotranspiration, crop growth, and temperature calculations take place in Daisy while the flow and solute transport is described by MIKE SHE. All these sub modules are being executed simultaneously. The division of calculational tasks and the data flow between the MIKE SHE Water Movement, MIKE SHE Advection-Dispersion and Daisy modules are shown in Fig. 2.

The sorption and degradation processes of pesticides are simulated by use of the MIKE SHE that includes simplified descriptions of geochemical and microbiological processes (DHI, 2000b). The sorption may be described by linear or non-linear equilibrium or by kinetic sorption. Pesticide degradation is described by a first order process.

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Fig. 2. Sequence of calculation and data exchange between MIKE SHE AD, MIKE SHE WM and Daisy.

3. The macropore flow model component 3.1. Physical processes Macropores are defined as a secondary, additional continuous pore domain in the unsaturated zone, besides the matrix pore domain representing the microporous bulk soil. Macropore flow is initiated when the capillary head in the micropore domain is higher than a threshold matrix pressure head ðct Þ; corresponding to the minimum pore size that is considered as belonging to the macropore domain. Water flow in the macropores is assumed to be laminar and not influenced by capillarity, corresponding to gravitational flow. The vertical volumetric flux (positive upwards) qmp is then given by: qmp ¼ 2Kmp ðump Þ

ð1Þ

where Kmp ðump Þ is the hydraulic conductivity of the macropores depending on the volumetric soil moisture content of the macropores, ump : The continuity equation is expressed as:

›ump ›qmp ¼2 2 Smp ›t ›z

ð2Þ

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where Smp is a sink term for water exchange with the surrounding matrix. Combining Eqs. (1) and (2) yields the governing equation for the macropores:

›ump ›ðKmp ðump ÞÞ ¼ 2 Smp ›t ›z

ð3Þ

The term Smp becomes a source/sink term in Richards’ equation used in the matrix domain. This term is given by Smp ¼ bmp Kðumatrix Þðcmp 2 cmatrix Þ

ð4Þ

where cmp and cmatrix are the capillary heads in the macropores and in the matrix, respectively, and Kðumatrix Þ is the hydraulic conductivity in the matrix depending on the volumetric soil moisture content of the matrix, umatrix : The exchange flow from matrix to macropore is only considered when the capillary head in the matrix exceeds the threshold pressure ðcmatrix $ ct Þ:bmp is a first-order linear water transfer coefficient, which is expected to increase with decreasing distance between macropores and with increasing hydraulic matrix-macropore contact. It can be expressed as:

bmp ¼

Cf d2

ð5Þ

where d (m) is an effective diffusion path length. Cf (– ) is a contact factor to take care of coatings at the interior walls of the macropores. Such a coating could be present due to e.g. root remnants, worm slime or mineral precipitation and can decrease the contact between matrix and macropore significantly. The contact factor ranges from 0.0 (no contact) to 1.0 (full contact).

In the macropores, a simple power law function is assumed to represent the conductivity relation: !np ump Kmp ðump Þ ¼ Ks;mp ð6Þ us;mp where Ks;mp is the saturated hydraulic conductivity of the macropores, us;mp is the macroporosity, and n* is an empirical exponent accounting for size distribution, tortuosity, and continuity of the macropores. n* may vary from two to six, according to Jarvis (1994). The lower values represent soils of coarse structure with macropore networks of narrow pore size distribution and little tortuosity, whereas the higher values apply to soils with a wider macropore

size distribution and larger tortuosity. If macropores are included in the simulation the hydraulic conductivity used to represent the soil matrix should exclude the effect of macropores.

The actual size, form and number of macropores are not explicitly considered in the modelling.

Instead the macropore characteristics appear indirectly from ct ; n* and bmp that in the present formulation are dependent on soil type. The capillary head in the macropores cmp is supposed to vary linearly with the macropore moisture content ump between zero (at ump ¼ us;mp Þ and ct (at ump ¼ 0Þ: Neither root water uptake nor soil evaporation are considered to take place from the macropore domain.

The infiltration process description includes water entering the macropores as well as the soil matrix at the soil surface. In this case water is only ponded on the ground surface when the infiltration capacities of both pore regions are exceeded. Water flow into the macropores commences as the matrix infiltration capacity is surpassed.

The bottom boundary condition for flow in the macropores is a vertical flux at a unit hydraulic gradient. This flux is input to the saturated zone. A coupling of the saturated zone and the unsaturated zone is necessary when the groundwater level fluctuates. During groundwater rise, the water present in the macropores in the bottom unsaturated zone layer is released instantaneously to the groundwater and during groundwater decline, the macropores are exposed as empty.

Internally in the macropores, solute transport is assumed to be dominated by advection, neglecting the influence of dispersion and diffusion.

The source/sink term ðRc Þ describing solute exchange between matrix and macropores is given by a combination of a diffusion component and a mass flow component: ! ump ðcmp 2 cmatrix Þ þ Smp c0 Rc ¼ bc umatrix ð7Þ emp where bc is a mass transfer coefficient, cmp and cmatrix are the solute concentrations in the macropores and matrix, respectively, and c0 indicates the concentration in either matrix or macropores depending on the direction of the exchange flow ðSmp Þ:

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The mass transfer coefficient, bc ; can be derived as:

bc ¼ C k

3D0 f p d2

ð8Þ

where Ck ( –) is the contact factor to take care of an eventual coating at the interior walls of the macropores. The contact factor ranges from 0.0 (no contact) to 1.0 (full contact). D0 (m2s21) is the diffusion coefficient in free water of the solute species. f * (– ) is an impedance factor that represents and decreases with the tortuosity of the macropores. f * ranges from 0.0 (zero diffusivity) to 1.0 (full diffusivity). Thereby, bc depends on both solute species and soil type.

Even though the applied macropore description can be regarded as mechanistic with parameters having physical meaning, some of the parameters required to characterise the macropore system are either difficult or impossible to measure. This is particularly the case for the parameters regulating exchange between matrix and macropores.

Field observations of soil structure and the occurrence of biotic macropores can give indications of the mass exchange parameters (Jarvis et al., 1997; Jarvis, 1998), though recent experiences reveal that parameters obtained from such macroscopic observations often need adjustments towards longer diffusion lengths when applied to field measurements (Saxena et al., 1994; Larsson and Jarvis, 1999). The main reason for this is expected to be organic and clay coatings on the aggregate surfaces which reduce mass exchange rates between the two domains (Thoma et al., 1992; Vinther et al., 1999) 3.2. Numerical formulation The numerical formulation has to take into account the fact that flows in the macropore and in the matrix domains occur with significantly different velocities Priority in development of the numerical scheme has been put on preserving the water balance and ensuring numerical stability at time steps that are not much lower than the time steps used in solving the matrix flow equation (Richards) alone. The solution method is mass conserving. The time step length is controlled by specifying certain limits for flow and exchange flow (depths) per time step, partly for ensuring correct dynamics of the macropore flow description and

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partly to avoid instability of the Richards solution due to high source/sink terms. The time step is controlled by performing an extra (a priori) macropore computation at the start of each matrix flow time step—with the matrix conditions from the previous time step. In case the resulting maximum (a priori) macropore flows, infiltrations, and exchange flows exceed the specified limits, a reduced time step is estimated, assuming linear relationship between time step length and flow volumes (unchanged flow rates). The procedure is repeated until the estimated maximum flows are within limits.

After the time step check a normal time step simulation is performed, solving the Richards’ equation for the matrix flow—with reduced source/sink terms from macropore-matrix exchange flows of the previous time step. After this the corresponding macropore time step is performed.

The calculation procedure consists of a double sweep algorithm with the following characteristics: 3.2.1. Downwards sweep (sweep 1): † First, a downwards sweep is performed, i.e. downwards flow from each cell to the cell below (or ground water table) in the macropore and in the matrix domains, and exchange flows, are calculated. Mass conservation is ensured by reducing the outflow from a cell if it exceeds the storage volume of that particular cell. The flow is not influenced by the water content of the receiving cell below, but the flow is set to 0 if the cell below has no macropores. † In the downwards sweep the downwards flow from a cell is calculated as the average of two estimates, and exchange flow as average of four estimates: – First, flow and exchange flow estimates are calculated as function of the macropore water content at the start of the time step. The estimates are reduced, if they exceed the start volume plus the inflow from the cell above.

– Second estimate is flow and exchange flow as function of the resulting macropore water content from first estimate, including the inflow from the cell above (or the macropore infiltration if upper cell). Again a reduction is made if the resulting volume would become negative.

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–

†

The final flow and exchange flow are calculated as the average of the two estimates. The flow is used as inflow to the cell below (or macropore recharge to ground water if lower cell).

As mentioned above, each of the two macropore-matrix exchange flow estimates are calculated as two sub-estimates: The first estimate is calculated as function of the matrix water content at the start of the time step, and the second as function of the matrix water content as result of estimate one. The same macropore water content (pressure) is used for both exchange estimates. Each sub-estimate is limited by two conditions: Flow from macropore to matrix is reduced if the resulting matrix water content would exceed saturation. Flow from matrix to macropore is reduced if the resulting matrix pressure would be below the macropore pressure. The macropore pressure used for exchange calculation is calculated as the macropore saturation (i.e. actual water content divided by porosity) multiplied by the cell height, and then reduced by the entry pressure. If the macropores of the cell are fully saturated, the macropore pressure of the cell above is added (hydrostatic conditions).

to generate numerical instability. In case of an increase of the ground water table, the water content in macropores now located below the groundwater table will be added to the groundwater recharge.

Due to the complex flow description it was not possible to verify the code through tests against analytical solutions. Instead, several tests with different boundary conditions have indicated that the code is able to simulate the different aspects of the macropore flow events dynamically in accordance with the above theoretical basis. In addition, rigorous water balance tests have demonstrated that the continuity equation is simulated very well.

3.3. Test of numerical formulation The numerical algorithm for the macropore component was previously tested by Thorsen et al.

(1998). The only modification that has been made to the process descriptions since then is that the macroporosity that was described as a function of depth in the version used by Thorsen et al. (1998) now is described as a function of soil type.

4. Model construction at catchment scale 3.2.2. Upwards sweep (sweep 2): † In the second, upwards, sweep the macropore flows and the matrix-macropore exchange flows are reduced for situations where the macropores would otherwise become over-saturated. The resulting macropore water contents from sweep no. 1 are checked, and when they exceed the macropore porosity the flow from the cell above and the exchange inflow from the matrix are reduced accordingly. If the cell receives exchange inflow from the matrix, the exchange flow and the flow from the cell above are reduced by the same proportion, otherwise only the flow from the cell above is reduced. Mass conservation is ensured by adding the flow reduction volume to the volume of the cell above (converted to water content). † The calculational time step is automatically adjusted in situations with high macropore and exchange flows so that these flows do not exceed certain limits, which from experience is known

4.1. Study area To evaluate the importance of macropore flow at the catchment scale a 1.5 km2 area near the village Frankerup in the western part of Zealand, Denmark was selected (Fig. 3). Because such a small area, in a groundwater context, is very much influenced by its transient boundary conditions a three-step procedure was used. Firstly, a large area consisting of the ˚ catchment was modelled with a 62.3 km2 Bjerge A 250 m computational grid. Secondly, using a telescoping approach a more detailed model was constructed for the 13.7 km2 Øllemose Rende subcatchment with a 125 m computational grid. Finally, in many of the analyses, results from the 1.5 km2 Frankerup area were extracted from the Øllemose Rende model.

The boundaries of the larger Bjerge catchment and the smaller Øllemose catchment as well as

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the Frankerup area are shown in Fig. 3. The data required for the construction of the models have been obtained from existing data sources as outlined below.

4.2. Topography and river network The topography and the location of the Bjerge and Øllemose streams were digitised from geodetic maps provided by Kort og Matrikelstyrelsen The river geometry was digitised from municipal stream regulations. Ten sub-branches with numerous detailed cross-sections and level points were used in the construction of the model. A constant Manning number of 20 m1/3s21 and a leakage coefficient between the streams and the adjacent aquifer of 1028 s21 have been applied to the entire stream system.

In addition to the river network, sub-surface tile drains exist over the main part of the area. The exact location of these drains is not known. The effect of the drains is simulated by assuming drains located 1 m below the ground surface and all over the area. Runoff through the drains in a particular grid is simulated as being linearly proportional to the height of the simulated ground water table above the drain in the grid. The proportionality factor is a reciprocal time constant, which on the basis of experience from modelling of similar regimes was chosen equivalent to 30 days.

Discharge data from the two river gauging stations, 5614 and 5610 (Fig. 3), were available for the period from May 1978 to December 1996.

4.3. Hydrogeology ˚ catchment is a moraine landscape The Bjerge A characterised by a relatively flat surface and river valleys (Klint and Gravesen, 1999) The upper layer consists of a clayey and sandy till with a large number of fractures and biopores. Below this layer that acts as an aquitard, various layers and lenses of alluvial and glacial clay and sand are located. The local geology has been interpreted on the basis of borehole information from 509 boreholes obtained from the database of the Geological Survey of Denmark and Greenland. Six geological layers functioning as alternating aquifers and aquitards have been identified

143

and incorporated in the model. In Fig. 4 a west –east cross-section of the 3D interpretation of the geology is shown including some of the borehole information.

The adopted six-layer model is not able to describe all details of the geology. However, in general, there seems to be a good accordance between the borehole information and the geological interpretation.

The hydraulic parameters have been assumed spatially constant within each of the six geological layers. The only exception to this is the lower limestone aquifer that has a distributed hydraulic conductivity according to the different types of limestone in the area (the Danien limestone to the south has lower conductivity than the Selandien limestone to the north). The parameter values have been assessed through calibration (see below). The ˚ catchment model are boundaries for the Bjerge A assumed to be no-flow except for the region very close to the river outlet, where fixed heads have been assumed for the two lower aquifer layers.

Thirty one groundwater abstraction wells are present in the area for drinking water supplies Many of them are small, with abstractions less than 50,000 m3/year. The main part of the abstraction originates from two urban waterworks with pumping in the order of 1 million m3/year. Time series of groundwater abstractions with monthly data from the two urban and annual data from the small rural water works have been collected from the different sources (Geological Survey of Denmark and Greenland, the county of Vestsjælland and the respective water works). For the model calibration and validation, time series of piezometric heads have been obtained for 19 observation wells, some of which are equipped with multilevel screens from different geological layers. These data were collected from the same sources as the abstraction data.

4.4. Soil characteristics for matrix and macropore Four soil types were found to represent the Bjerge ˚ catchment, comprising three mineral soils and one A organic soil Soil 1 (Loamy sand) covers 16% of the model area, Soil 2 (Sandy loam) covers 74%, Soil 3 (Loam) covers 5%, and Soil 4 (Organic) covers 5% of the area.

The hydraulic parameters used for characterisation of the dominating soil type (Soil 2) originate from

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˚ and Øllemose Rende catchment areas as defined by their topographical divides, the Frankerup area and the location of the Fig. 3. The Bjerge A key hydrological stations and well sites.

˚ intact soil samples collected just north of the Bjerge A catchment and measured at the Danish Institute of Agricultural Sciences, Research Station Flakkebjerg.

Parameters for Soil 1 and Soil 3 were obtained from similar Danish soil types reported in Jacobsen (1989)

and parameters for the organic soil were obtained from a European database (Wo¨sten et al., 1998).

Matrix characteristics in terms of retention curves were fitted to a modified Campbell function (Campbell, 1974; Smith, 1992). The hydraulic

Fig. 4. Cross-section of the 3-dimentional interpreted geology of the area including some boreholes. The location of the cross-section is shown as A –A in Fig. 3.

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Table 1 Hydraulic parameters for the four soil types Soil characteristics

Bulk characteristics

Macropore characteristics

Soil name

us;bulk (–)

us;mp (–)

Depth below ground surface (m)

Ks;bulk (m/s)

ct (m)

Ks;mp (m/s)

Matrix characteristics

bmp (m22)

us;matrix (–)

Ks;matrix (m/s)

Campbel– Burdine parameters b

Soil 1 loamy sand

0.41

1.7 £ 1025

0

–

–

–

0.41

1.7 £ 1025

7.9

0.046

0.41 0.41 0.41 0.33 0.33

1.7 £ 1025 5.5 £ 1026 5.5 £ 1025 7.1 £ 1026 7.1 £ 1026

0.02 0.02 0.02 0.01 0

1.0 £ 1025 2.8 £ 1026 2.8 £ 1025 3.2 £ 1026 –

20.15 20.15 20.15 20.15 –

300 300 300 300 –

0.39 0.39 0.39 0.32 0.33

6.7 £ 10206 2.7 £ 1026 2.7 £ 1025 3.8 £ 1026 7.1 £ 1026

7.9 5.5 5.5 8.3 8.3

0.046 0.027 0.027 0.044 0.044

0.47

6.0 £ 1026

0

–

–

–

0.47

6.0 £ 1026

8.7

0.026

0.15–0.2 0.2–0.3 0.3–0.7 0.7–1.4 1.4–1.8

0.47 0.36 0.38 0.35 0.32

6.0 £ 1026 1.0 £ 1027 1.0 £ 1026 5.0 £ 1027 1.0 £ 1027

0.02 0.02 0.02 0.01 0

3.5 £ 1026 7.2 £ 1028 7.4 £ 1027 2.6 £ 1027 –

20.15 20.15 20.15 20.15 –

300 300 300 300 –

0.45 0.34 0.36 0.34 0.32

2.5 £ 1026 2.8 £ 1028 2.6 £ 1027 2.4 £ 1027 1.0 £ 1027

8.7 9.5 11.0 11.3 12.6

0.026 0.064 0.079 0.094 0.149

0–0.15 0.15–0.2 0.2–0.3 0.3–0.7 0.7–1.4 1.4–1.8

0.36 0.36 0.40 0.40 0.40 0.40

6.2 £ 1026 6.2 £ 1026 1.9 £ 1026 1.9 £ 1025 1.5 £ 1026 1.5 £ 1026

0 0.02 0.02 0.02 0.01 0

– 4.9 £ 1026 1.3 £ 1026 1.3 £ 1025 7.9 £ 1027 –

– 20.15 20.15 20.15 20.15 –

– 300 300 300 300 –

0.36 0.34 0.38 0.38 0.39 0.40

6.2 £ 1026 1.3 £ 1026 5.8 £ 1027 5.8 £ 1026 6.8 £ 1027 1.5 £ 1026

12.0 12.0 10.0 10.0 13.6 13.6

0.050 0.050 0.070 0.070 0.140 0.140

0.77

9.3 £ 1027

0

–

–

–

0.77

9.3 £ 1027

5.7

0.300

0–0.15 0.15–0.2 0.2–0.3 0.3–0.7 0.7–1.4 1.4–1.8

Soil 2 Sandy Loam

Soil 3 Loam

Organic soil

Hb (m)

0–0.15

0–1.8

conductivity function was calculated according to Burdine (1952). Table 1 shows the parameter values.

Simulations were made both with and without macropore flow included to test the importance of this process. As no data were available describing the macropore systems in the soils, parameters for the macropore model were estimated from experiences obtained in other studies. The macropore system was assumed to consist of biopores (worm and root channels) beginning just below the plough layer and ending at 1.5 m depth. The macroporosity was assumed to decrease with depth with a porosity of 2 volumetric percent in the upper layers. The water transfer coefficient ðbmp Þ governing water exchange flow between matrix and macropores was selected in order to represent a soil with approximately 11 cm between macropores (half aggregate length ¼ 5.5 cm). The threshold value for initiation of macropore

flow ðct Þ was selected to 2 15 cm. These parameter values are within the ranges recommended for the corresponding MACRO parameters ASCALE (half aggregate length) and CTEN ðct Þ in other studies (Dubus and Brown, 2002; Beulke et al., 2002; Boesten et al., 2000) as well as with parameterisation experience in similar Danish soils (Styczen, 2002).

The saturated hydraulic conductivities were only measured for the bulk soil samples. In order to seperate the conductivities in matrix and macropore values and ensure that the total saturated hydraulic conductivity was similar in simulations with and without macropores the saturated conductivities shown in Table 1 were calculated as follows:

! 2 þ3 us;bulk 2 us;mp 1=b Ks;matrix ¼ Ks;bulk ð9Þ us;bulk

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Ks;mp ¼ Ks;bulk 2 Ks;matrix

ð10Þ

where Ks;matrix saturated hydraulic conductivity for the matrix Ks;mp saturated hydraulic conductivity for the macropores Ks;bulk bulk saturated hydraulic conductivity, measured us;bulk soil porosity us;mp macroporosity This approach can be questioned. A more commonly accepted approach for catchment and regional scale applications, where the availability of measured hydraulic conductivity inevitably is limited, is to use pedotransfer functions such as Jarvis et al. (2002) where matrix conductivity is estimated from soil texture. A comparison of results from our approach (Eq. (9)) and the two pedotransfer functions recommended by Jarvis et al. (2002) is given in Table 2 for the dominant soil type in our catchment. The two pedotransfer functions, which are not recommended for arable topsoils, estimate the hydraulic conductivity at a pressure head of—10 cm, K10 : Table 2 reveals that the pedotransfer functions and our approach give conductivities of the same order of magnitude. The main difference is that the conductivities estimated by the pedotransfer functions show a smaller variation through the profile than the values from our approach, where the value in the plough layer (20 – 30 cm) is significantly smaller than the values for the other horizons. As the lower value for the plough layer is believed to be a consequence of soil structure (compaction) it is not reflected in the soil texture and can hence not be explained by the pedotransfer functions. Field studies Table 2 Comparison of matrix conductivity estimated from pedotransfer functions (Jarvis et al., 2002) and from Eq. (9) for Soil 2 Depth horizon (m)

K10 (mm/h) (Jarvis et al., 2002; Eq. (4))

K10 (mm/h) (Jarvis et al., 2002; Eq. (6))

Ks;matrix (mm/h) (This study, Table 1)

0.2–0.3 0.3–0.7 0.7–1.4 1.4–1.8

0.30 0.23 0.29 0.37

0.73 0.49 0.70 1.02

0.10 0.94 0.86 0.36

from a Danish site with similar soil and climate conditions and with similar tillage practise showed that the macropore flow is generated at the interface to the plough layer (Petersen et al., 1997). We find it essential to describe the macropore flow generation mechanism as correctly as possible in the model, and we therefore think that our approach (Eq. (9)) is justifiable in the present case. On the other hand it must be emphasised that Eq. (9), due to its empirical basis, should not be used in other cases without adequate support from field data 4.5. Land use Information on land use was retrieved from the Corine database 95% of the area is covered by farmland, 3% by permanent grass, while forest and urban (paved) areas each cover 1%. The dominating agricultural crop was winter wheat that in average covers 32% of the area (Landbrugsstatistik, 1995). ˚ catchment, the For the modelling of the Bjerge A entire agricultural area was assumed to be covered by a standard winter cereal. For the more detailed modelling of the Øllemose Rende catchment, the crop rotations actually used in the Frankerup areas have explicitly been simulated. The data on the crop rotations were obtained from the farmers and the agricultural extension service.

4.6. Climate data Time series of daily measurements of global radiation, mean air temperature, precipitation, and potential evapotranspiration were provided by the Danish Institute of Agricultural Sciences, Research Station Flakkebjerg The daily values were distributed uniformly within the day. The precipitation data were corrected for wind effect and wetting according to guidelines from the Danish Meteorological Institute (Allerup et al., 1998). The potential evapotranspiration was calculated from a modified Penman formula (Mikkelsen and Olesen, 1991).

5. Calibration and validation of catchment model The model calibration was carried out for the period 1990– 1996. A manual trial-and-error method

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147

Table 3 Hydraulic parameter values for the six geological layers assessed through calibration Geological layer

Material

Horisontal hydraulic conductivity (m/s)

Vertical hydraulic conductivity (m/s)

Specific storage coefficient (1/m)

Specific yield (–)

1 2 3 4 5 6

Till Sand Till Sand Till Limestone

1 £ 1027 5 £ 1025 1 £ 1026 1 £ 1024 2 £ 1027 2 £ 1025 2 2 £ 1024

1 £ 1028 5 £ 1026 2 £ 1028 1 £ 1025 2 £ 1028 2 £ 1026 2 2 £ 1025

0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

0.005 0.005 0.02 0.02 0.02 0.02

was used and the goodness of the simulations was assessed from visual inspections of the simulated versus observed discharge hydrographs at the two gauging stations and of groundwater level heads at the observation wells. The parameters assessed through calibration were the hydraulic conductivities and storage coefficients of the six geological layers (Table 3).

Examples of calibration results are shown for a two year period with respect to catchment discharge at ˚ and three selected observations wells with Bjerge A filters in the three aquifers (Fig. 5). From the figure it appears that the average level both with regard to runoff and groundwater heads are reasonably well simulated, while the model only partially describes the dynamics of the annual fluctuations of the groundwater system.

Subsequently, a split-sample validation test was carried out on the basis of data from the period 1986– 89, where only discharge data (no groundwater head data) were available. Two key numerical performance statistics are shown in Table 4 both for the calibration and the validation periods. It is seen that the average discharge is simulated quite well during the calibration period and even slightly better during the validation period. The hydrograph dynamics, as reflected by the Nash-Sutcliffe criteria for model efficiency (Nash and Shutcliff, 1970) on the other hand shows less accurate simulation during the validation period as compared to the calibration.

In order to obtain an indication of the capability of the model to simulate the stream-aquifer interaction, a few field measurements of discharge were made in the Øllemose Rende system during the low flow season of 1998. The field data showed low flows in the order of 2 –4 l/s in the Frankerup area, where the northern

Groundwater abstraction

Yes Yes

tributary joins Øllemose Rende (Fig. 3). The model was not run for the same period, but the low flows simulated throughout the simulation period at this location were in the order of 1 l/s. Hence this independent test suggests that the low flow simulations, and thus the baseflow contributions originating from the deeper aquifers, are simulated at the right order of magnitude.

On the basis of the validation tests, the model can be claimed valid for simulation of discharge with the given accuracy level. Although groundwater head observations were not available for the validation period it is likely that the accuracies are similar, or slightly poorer, than those obtained during the calibration period. Due to lack of data it has not been possible to validate the model with respect to the internal flow variables such as simulations of macropore flows or the individual flow components that constitute the water balance. Hence, except from noting that nothing in the limited validation tests actually conducted suggests completely wrong interpretations of these internal variables, it must be emphasised that it is not possible to prove any model validity for them.

6. Simulation results from catchment scale 6.1. Water balance and groundwater depths and recharges The flow regime simulated by the model is ˚ catchment in Fig. 6 as illustrated for the Bjerge A average figures for the period May 1987 to May 1995.

The period was selected so that the storage changes in the unsaturated zones as well as in the two aquifers

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J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158 Table 4 Model performance statistics for simulation of catchment discharge during the calibration and validation periods

Calibration period (1990–96) Validation period (1986–89)

Average discharge % deviation

Model efficiency on 15-days basis Nash– Sutcliffe criteria ðR2Þ

25

0.80

1

0.71

recharges the upper sandy aquifer. The upper aquifer is seen to interact considerably with the lower two aquifers, which in Fig. 6 are aggregated into one unit.

The total abstraction directly from the area is 16 mm/ year, while the groundwater flow across the catchment boundaries totals 25 mm/year. The significant boundary flows take place over the fixed head boundary near the river outlet and is directed towards the groundwater abstraction wells located just outside the boundary (Fig. 3). Such large boundary flow may be critical for simulating reliable flow conditions

Fig. 5. Discharge hydrograph from station 56.10 and selected hydraulic heads for the three aquifer layers from two years of the calibration period. The location of the observation wells and the discharge station are shown in Fig. 3.

were negligible. The net percolation out of the root zone ( ¼ upper till unit in Fig. 4) is seen to be 244 mm/year of which 196 mm/year runs through the drains to the river system, while 48 mm/year

˚ catchment as Fig. 6. The total water balance for the Bjerge A simulated during the period May 1987 to May 1995. All figures are averages over the eight years period (mm/year). The two upper layers shown on the figure correspond to the upper till unit and the upper sandy aquifer of Fig. 4, while the lower layer shows the aggregated water balance for the lower sandy aquifer and the limestone.

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158

for areas close to the boundary. However, as the focus of the present study is primarily the small Frankerup area and secondarily the Øllemose Rende catchment, both located at significant distances from the boundary, the importance of the uncertainties generated by the critical boundary conditions are not believed to be very significant. This is particularly the case, because the macropore flow does not depend on groundwater flows, but only on the groundwater heads.

149

Macropore flow is, according to the above process description, mainly governed by soil moisture conditions in the root zone, which in case of shallow groundwater table with upwards capillary flux is influenced by the depth to the groundwater table.

(Fig. 7) shows average figures for the period 1990 – 1996 for the depth to the ground water table in the Frankerup area together with the split of groundwater recharge into flows directly through macropores and flows reaching the groundwater table through the soil matrix. According to the model, the average depth to groundwater table varies between 1 m and 3 m over the area. This is mainly governed by the variation in topography and the location of the river. The minimum depth of 1 m is due to the existence of artificial tile drains at that depth. The total recharge varies between 200 mm/year and 300 mm/ year. This spatial variation is caused partly by differences in actual evapotranspiration between the different crops and partly by differences in the depth to the groundwater table causing differences in the rate of upwards capillary flux from the shallow groundwater table to the root zone. The recharge that enters the groundwater storage directly through the macropores are seen to be small, but with a relatively large variation, between 0.1 mm/year and 1.3 mm/year.

6.2. Macropore flows at plot scales within catchment

Fig. 7. The spatial variability of groundwater recharge and the depth to the upper groundwater table for the Frankerup area as simulated during the period 1990–96.

To illustrate the flow processes and the macropore dynamics, results for a two years period from two selected calculational grid points (soil columns) are shown in Fig. 8. The precipitation and recharge values are aggregated to monthly values in the figure while the water content in the macropores are shown as average weekly values. The two grid points are located within the Frankerup area on a hill and in the valley close to the river, respectively. As can be seen from the figure, the conditions at the two grid points differ significantly with respect to depth to groundwater table and as a result of this also with respect to groundwater recharge and soil moisture conditions. At the hill site, the groundwater table varies between 1 m and 4.5 m depth. At the valley site, the groundwater table is at the depth of the tile drains (1 m) most of the years with a decrease of only 0.5 2 1 m during the dry periods.

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Fig. 8. Simulation results for two soil columns at the Frankerup area during 1993–94. The two columns are located on a hill site (results to the left) and in the valley close to the stream (results to the right), respectively.

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158

Thus, the shallow groundwater table at the valley site is seen to cause significantly higher rate of upwards capillary flow during the summer season as compared to the site on the hill.

The macropores are seen to contain water frequently during the two years period. All the macropore events are generated by high water content at 20 –30 cm depth. Both locations have soil type 2 (Table 1), which is characterised by a decrease of saturated hydraulic conductivity by two orders of magnitude due to a plough pan at this depth. It is furthermore noticed that for both sites, all the macropore flux generated at this depth returns to the soil matrix before it reaches the groundwater table.

In Fig. 9, the distribution over the Frankerup area of macropore flows at different depths are shown as average values for the period 1990–96. In accordance with the results shown in Fig. 8, Fig. 9 substantiates that macropore flow is predominantly generated in the upper part of the profile and that almost all the macropore flow is diverted back to the soil matrix through diffusion before the water reaches the ground water table. While the macropore flow that directly recharges the groundwater is less than 0.5% of the total groundwater recharge (Fig. 7), the amount of macropore flow at 30 cm depth is more than two orders of magnitude larger. Thus, of the macropore flow of about 170 mm/year at 30 cm depth, there is a net ‘loss’ of about 80% before the water reaches 50 cm depth and of about 98% before 100 cm depth. This clearly shows that macropore flow has a very significant effect in terms of rapidly transporting some water downwards in the soil profile. According to the parameterisation

Fig. 9. The distribution of macropore flow at different depths over the Frankerup area as simulated during the period 1990– 96.

151

chosen here the transport distance in the macropores is typically between 20 and 80 cm.

6.3. Effects of macropore flows on catchment response An assessment of the effect of macropore flow on the catchment response in terms of river discharge and groundwater heads have been made by comparing results from two model simulations with and without macropores, respectively The results (not shown here) showed that the effect of macropores on both discharge and groundwater heads were negligible with differences generally much less than one percent of the natural variation.

6.4. Effects of macropore transport on catchment scale In order to assess the importance of the macropore flow processes on the transport of solutes at catchment scale, model simulations were conducted as follows for the Frankerup area In order to focus on macropore effects and eliminate the effects of rotating crops and associated varying pesticide applications, the entire area was assumed to be covered by the same crop, namely winter wheat. A tracer was applied uniformly over the area at a time in the autumn when pesticide is typically applied and with application rates corresponding to a typical autumn applied herbicide. The tracer was applied once and the effects over the subsequent years were simulated by the model. In order to investigate the effects of different climate conditions around the time of tracer application simulations were conducted for tracer applications in three different years, 1990, 1991 and 1992. The simulation period was in all cases 1990 – 1996.

The tracer simulations were carried out for two alternative tracers, namely a conservative non-reactive tracer, and a reactive tracer (hypothetical pesticide) with sorption and degradation parameters as given in Table 5. The simulations were carried out for two alternative conditions with respect to macropores, namely one simulation with macropores and another simulation without macropores (i.e. only matrix flow).

Summary results from the simulations with respect to fate of the tracers by the end of the simulation period are shown in Table 6 in terms of accumulated

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Table 5 Parameter values for description of degradation and sorption for the simulation with hypothetical pesticide Parameter

Value

Degradation rate, T 12 0–1 m depth Below 1 m depth

29 days (at 10 8C) No degradation (cm3/g)

Sorption distribution coefficient, Kd (linear equilibrium) (cm) Unsaturated zone, 0–20 1.174 Unsaturated zone, 20– 70 0.294 Unsaturated zone, 70– 150 Unsaturated zone, below 150 0.059 Saturated zone 0.029

mass fluxes and total mass balances. The tracer is applied as a pesticide, i.e. it is assumed to be sprayed on the leaves of the crop. The fate of the tracer in the canopy in terms of storage, degradation and throughfall to the soil surface is calculated by the model and results in different throughfall rates for the three years.

Therefore, in spite of the same application rate of 500 g/ha over the entire catchment (97 grids £ 125 m £ 125 m) ¼ . 75.8 kg for all three years, the fluxes into the soil varied and were approximately 75.8, 61.9 and 64.8 kg for the three respective years.

For the conservative tracer, the differences between the macropore and the no-macropore simulations are small. The amounts of tracer that reached the groundwater by the end of the simulation period are approximately 67, 65 and 63% of the total tracer inputs for the three respective application years. The remaining amount of tracer is still retained in the unsaturated zone at the end of the period.

The pesticide is seen to behave significantly different in several respects. First of all, almost all the applied amount is sorbed and degraded in the unsaturated zone with the result that the fractions of tracer reaching the groundwater are in the order of 1026 –1023. Secondly, the differences between the macropore and the no-macropore simulations are significant. Thirdly, the differences among the years are very significant. For one of the application years (1990) the effects of the macropores are approximately a doubling of the leaching to the groundwater, while the leaching for the two other years are increased by factors 4 and 8, respectively. This difference can be explained with differences in

climatic conditions and hence in macropore activities in the weeks following the tracer application for the three respective years.

In Table 6, a mass balance measure is calculated as an indicator of the numerical accuracy of the calculations. The mass balance error is simply calculated as the input at the soil surface minus the outgoing flux to streams minus the degradation and sorption in the unsaturated and saturated zones minus the storages in the unsaturated and saturated zones.

For the conservative tracer, the mass balance errors are between 0.6 and 1.1 g, which is negligible compared to the flux values. For the pesticide, the mass balance errors are between 0.0 and 0.5 g, which is negligible relative to the input at the soil surface, but in some cases of the same order of magnitude as the calculated flux to the saturated zone. This implies that absolute figures of the calculated mass in the saturated zone must be taken with reservation due to uncertainty in the basic numerical calculations. In this context it may be noted, however, that the uncertainty resulting from uncertainty of the assessed sorption and degradation parameters is significantly larger than the errors in the numerical calculations.

The variations within the Frankerup area of the pesticide flux at 100 cm depth are illustrated in Fig. 10 for the three application years and for the situations with and without macropores. It should be noticed that the y-axis is logarithmic. The significant differences among the three years clearly appear from this figure, with 1992 being the year generating the largest amount of leaching to the saturated zone and 1991 being the year with the lowest leaching and without effects of macropores. The variation across the catchment is significant. Thus, for the 1992 application, the variation over the catchment for the macropore simulation is between 2 and 61 mg/ha.

And even for the 90% of the area generating leaching closest to the average conditions, the range is from 8 to 60 mg/ha, i.e. a factor of 7.5. It is noted that the variation over the catchment is the same for simulations with and without macropores.

7. Discussion and conclusions A spatially distributed model code capable of describing macropore flow and transport processes at

Table 6 Mass balance elements for numerical simulations with three different years of tracer application, two macropore conditions and two different tracers. The fluxes are accumulated over the entire catchment (151.5625 ha) and the seven years simulation period (1990 –96) and the mass storages are status by the end of 1996 Conservative tracer

Reactive tracer (hypothetical pesticide)

No macropores

Mass storage by end of period (g) Storage in unsaturated zone Storage in saturated zone

Macropores

1990

1991

1992

1990

1991

1992

1990

1991

1992

1990

1991

1992

75781 0

61876 0

64804 0

75781 116

61931 110

64458 108

75781 0.00

61878 0.00

64808 0.00

75781 0.00

61932 0.00

64462 0.03

53892

42069

42452

55256

43335

43661

0.47

0.23

4.15

1.02

0.91

33.88

0

0

0

116

110

108

0.00

0.00

0.00

0.00

0.00

0.04

47497

36080

35510

48386

36848

36089

0.41

0.19

3.27

0.87

0.76

27.26

319 0

265 0

280 0

179 0

149 0

157 0

0.00 10394

0.00 8071

0.03 9369

0.00 10543

0.00 8323

0.05 9397

0

0

0

0

0

0

65388

53808

55439

65239

53610

55073

0

0

0

0

0

0

0.01

0.00

0.06

0.02

0.02

0.56

0

0

0

0

0

0

0.79

0.32

5.21

1.67

1.50

50.53

21570

19542

22072

20230

18336

20532

0.09

0.05

1.42

0.19

0.19

9.00

6396

5990

6943

6987

6599

7681

0.06

0.03

0.82

0.12

0.14

6.10

20.76 20.00001

20.59 20.00001

20.85 20.00001

21.11 20.00001

20.69 20.00001

20.84 20.00001

0.12 0.00000

20.34 20.00001

20.22 0.00000

20.54 20.00001

0.27 0.00000

20.03 0.00000

0.00

0.00

0.00

0.00

0.00

0.00

0.26

21.50

20.05

20.53

0.30

0.00 153

Mass balance errors in calculations Mass balance error (g) Error relative to input to soil surface Error relative to net flux to saturated zone

No macropores

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158

Mass fluxes accumulated over period (g) Input to soil surface Flux from soil matrix to macropores Flux from soil matrix to saturated zone Flux from macropores to saturated zone Flux from saturated zones to stream Uptake by vegetation Degradation in unsaturated zone Sorption in unsaturated zone Degradation in saturated zone Sorption in saturated zone

Macropores

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Fig. 10. The spatial variability of the accumulated flux of pesticide at 100 cm depth as simulated for the Frankerup area during the period 1990 – 1996 with three alternative years of pesticide application and with, respectively without, macropores included in the model simulations.

a catchment scale has been developed within the framework of the coupled MIKE SHE/Daisy code.

The adopted macropore formulation has many conceptual similarities to the principles behind the well tested MACRO code, but it differs in some important aspects. Most importantly, the water exchange between the two pore regions (Eq. (4)) is driven by the product of the matrix conductivity and the pressure head difference between the pore regions, while the approach in MACRO is based on an approximation to the water diffusion equation. In the existing dual-permeability model codes a variety of approaches exist for describing the water exchange between the two domains, and an accurate description is recognised as a great challenge (Simunek et al., 2003). As we have had no detailed field data to check our formulation we cannot document that our approach is better than other existing ones. Furthermore, the numerical formulation in our code is different from that in the MACRO by being based on an explicit algorithm. Our algorithm is quite fast and mass conserving, but we have not made direct comparison tests with MACRO or other codes.

The MIKE SHE/Daisy model was then set up for a small catchment. The model was subject to calibration and validation tests against discharge and groundwater levels corresponding to standard procedures in catchment modelling. As no field data exists for internal variables such as macropore flow, the model’s capability to correctly simulate macropore processes

at the catchment scale could not be documented.

The simulation results designed to investigate the importance of macropore processes at catchment scale can therefore not be claimed as valid, but should rather be seen as outputs from a numerical experiment. Hence, in order to confirm the findings from the present study it will be required to have support from dedicated field data.

There are several important sources of uncertainty related to using a model with macropore formulations at a catchment scale as in the present study. The most important source is related to assessment of macropore parameters, in particular the exchange coefficient, b; or the related diffusion length governing the exchange of water and solutes between macropores and matrix. In addition, soil characteristics are known to exhibit large spatial variations at catchment scale, but soil data in terms of soil texture, soil structure and hydraulic parameters will only be available for representative soils. Simple extrapolation of such data to similar soils in the area may not be valid with regard to representation of macropores, because other factors such as the management history of a particular soil (cropping and tillage practice) has major impact on frequency and extent of macropores (Edwards et al., 1990; Caron et al., 1996). Another critical assumption is the estimation of matrix hydraulic conductivity. As field data are seldom (or never) available at catchment scale pedotransfer functions such as the ones recommended by Jarvis et al. (2002) are often used. In order to preserve the vertical variation in conductivity with a low value in the plough pan we have instead used an empirical approach based on an estimation of matrix hydraulic conductivity from measured bulk hydraulic conductivity. Based on past Danish field studies (Petersen et al., 1997) we have argued that this is likely to provide a more realistic description of the macropore generation process in our particular case.

However, because this approach is empirical without a sound theoretical basis, one should generally be cautious about its use and it should not be applied in other areas without support from field data.

We have used daily rainfall data and distributed the rainfall evenly over the day. This approach is definitely not applicable in many hydrological regimes where overland flow is common and macropore flow is generated due to saturation of the top soil.

However, in our case the principal macropore

J.S. Christiansen et al. / Journal of Hydrology 299 (2004) 136–158

generation mechanism is related to saturation above the low permeable plough pan at 20– 30 cm depth.

Due to the soil moisture storage in the upper 20 cm, it is rather the volume than the intensity of rainfall that is important. A sensitivity analysis, where we distributed the daily rainfall over two hours instead of 24 hours, showed that the effect of the rainfall intensity was small for the total amount of macropore flow and had no impacts for the spatial variation of macropore flow over the catchment. This is supported by the field tracer experiments reported by Gjettermann et al. (1997) who found that application of 25 mm Brilliant Blue dye tracer with intensities varying from 3.1 to 25 mm/h resulted in macropore flow generated above the plough pan in all cases.

The simulation results show that the macropore processes, as they are formulated in the model for the particular catchment, has the primary function of rapidly transporting a significant part of the water (and solute) from the plough pan at 20 cm depth to a depth of 40– 100 cm, where most of it flows back into the soil matrix. Only a minor part of the macropore flow reaches the groundwater table directly through the macropores. It must be emphasised that we have no specific field data to support these findings. Therefore, we do not claim that the depths and amounts of flow in the macropores are correct, but rather that the process equations of the MACRO and similar codes using typical parameter values generate such results for our conditions. Other field studies (Villholth et al., 1998; Nilsson et al., 2001) in similar soils and climate suggest that the biopores in the upper soil layers are connected with geologically generated fractures in the deeper layers so that the combined macroporefracture system is able to transport tracers significantly deeper than found in the present study.

This indicates that either the macropore parameter values used in the present case or the process equations may not be fully adequate for catchment scale application.

The present study suggests that the macropore processes appear to have only negligible effects on the discharge and groundwater levels. This is interesting when comparing with other catchment modelling studies using similar distributed physically based models (Refsgaard and Hansen, 1982; Overgaard, 2000). They report that, in order to simulate the discharge hydrographs properly and in particular

155

the early peaks in the autumn after the dry summer period, a significant part of the infiltration through the root zone has to be routed through a fast track bypassing the lower part of the root zone. These hydrograph peaks are simulated quite well in our case (Fig. 5). The reason for the necessity of introducing the so-called bypass flow in catchment modelling is the need to account for the spatial variability of soil hydraulic properties, root zone depth, vegetation types, climate input, etc. within large computational grids (Refsgaard and Hansen, 1982; Overgaard, 2000). This is apparently not required in our case study, where the grid size is relatively small. In any case, our results indicate that the small scale macropore flow processes, included in our case, can not provide the same effects on simulated hydrographs as the bypass flows that can be considered a large scale phenomena.

In spite of the fact that macropore flow thus is not a dominating process for simulation of discharge at catchment scale, the simulation results suggest that it has a very significant effect on the leaching of pesticides from the surface to the groundwater table, because some of the pesticides are transported rapidly downwards in the soil profile to zones with less sorption and degradation. This is in agreement with the conclusions of Simunek et al. (2003).

An important finding from the study is the apparent erratic nature of the macropore processes. The generation of macropore flows depends in a very complex manner on both the soil characteristics and the hydrological regime. Investigation of the simulation results suggests that it is not possible beforehand to identify which rainfall events generate the highest macropore flows and as such posses the largest potential for pesticide leaching. The large variations of macropore transport among the three years of simulated tracer application show that three different years of tracer applications are not sufficient to estimate neither the average importance of the macropore transport nor the average pesticide leaching to groundwater.

Furthermore, the simulation results show a considerable spatial variation of macropore flows and transport throughout a catchment. Thus, the variation of pesticide leaching to the groundwater varies in the simulations with a factor of 30 over the catchment and a factor of 7.5 within the 90% of the catchment, where

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the leaching is closest to the median value. This spatial variation is not caused or increased by the macropore processes. It is simulated alone as a consequence of variations in topography, depth to groundwater table and distance to streams. In the actual field situation the variation in pesticide leaching will be significantly larger, because spatial variations in soil physical and chemical properties and vegetation parameters will also play a significant role.

The key finding of the present study that macropore flow is highly depending on depth to groundwater table is supported by Haria et al. (2003), who from two field experiments on sites with deep and shallow water tables, respectively, found that preferential flow only occurred at the site with shallow water table. Haria et al. (2003) explained this finding by the importance of the capillary fringe in sustaining a higher moisture content in the unsaturated zone at the shallow groundwater site.

The absolute figures on amount of leaching and quantities of flow in macropores should be taken with reservation. In order to assess this, the analysis should be supplemented by thorough sensitivity analyses and preferably also by additional field data to confine the uncertainty range. However, this need for further studies, does not disqualify the more general conclusions that we are making here on the spatial variation within a catchment.

An interesting question is how large an error one would experience by conducting pesticide leaching simulations on a soil column basis instead of carrying out catchment simulations. The present study with its lack of field data and with only one field site cannot provide the general answer to this question. However, the simulation results indicate that the variation of pesticide leaching within a catchment is very significant and should be taken into account. Thus, the present study suggests that results from column simulations often may not provide pesticide leaching results that are representative at a catchment scale.

The methodology applied in the present study is basically an up-scaling methodology, where the equations and parameter values, previously used only at point and field scales, through a spatially distributed approach have been applied for catchment modelling. In this way it is possible to combine the knowledge and experience existing at point/field scale with the other factors, such as topography

and groundwater depth, that is known to be of importance at catchment scale. Two general conclusions emerge from the simulation results: (1) The point scale macropore processes are not important for groundwater recharge and discharge at catchment scale, but are nevertheless dominating processes for pesticide leaching also at the catchment scale. (2) The presently adopted up-scaling methodology is significantly better than just assuming that the point scale column simulations are representative for an entire catchment with respect to simulation of leaching of pesticides at catchment scale. This methodology can be implemented by using a comprehensive 3D catchment model as we have done, but it may be sufficient to carry out several single column simulations, if the range of columns adequately represents the spatial and temporal variations of depth to groundwater throughout the catchment.

Acknowledgements This work was partly funded through the project ‘Large scale modelling of pesticide transport’ under the Danish Environmental Research Programme.

Karen Villholth is thanked for giving valuable comments to the manuscript.

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