Geoderma 87 Ž1999. 261–279
Modelling mean nitrate leaching from spatially variable fields using effective hydraulic parameters Jørgen Djurhuus
a,)
, Søren Hansen b,1, Kirsten Schelde a , Ole Hørbye Jacobsen a
a
Danish Institute of Agricultural Sciences (DIAS), Department of Crop Physiology and Soil Science, Research Centre Foulum, P.O. Box 50, DK-8830 Tjele, Denmark b The Royal Veterinary and Agricultural UniÕersity, Department of Agricultural Sciences, Laboratory for Agrohydrology and Bioclimatology, ThorÕaldsensÕej 40, DK-1871 Frederiksberg C, Denmark Received 7 November 1997; accepted 29 May 1998
Abstract When using simulation models for estimating the mean nitrate leaching on different soil types, the common approach is to interpret the field as a single equivalent soil column using effective hydraulic parameters, which are estimated from point measurements. The use of effective hydraulic parameters was evaluated on a coarse sandy soil and a sandy loam using the one-dimensional mechanistic model, DAISY. On each location, texture, soil water retention and hydraulic conductivity from 57 points were measured within an area of ca. 0.25 ha. The following approaches for estimation of effective hydraulic conductivity were examined: Ž1. geometric mean; Ž2. arithmetic mean; Ž3. estimated arithmetic mean from a lognormal distribution; and Ž4. mean estimated from a stochastic large-scale model for water flow, similar to the Richards equation in one dimension, but with large-scale effective parameters accounting for the local three-dimensional flow. The approach of interpreting the field as a number of non-interacting columns was examined by calculating the mean of the field as the mean of the 57 soil columns. The nitrate concentrations simulated by DAISY were compared with nitrate concentrations measured by ceramic suction cups at the 57 points at 25 cm and 80 cm depths during the winter period 1989r1990. At both locations, the nitrate concentrations simulated by the geometric mean, the stochastic approach and the mean of the 57 simulations matched the observed nitrate concentra-
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Corresponding author. Tel.: q45-8999-1900; Fax: q45-8999-1719; E-mail: jorgen.djurhuus@agrsci.dk 1 Tel.: q45-3528-3383; Fax: q45-3528-3384. 0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 6 - 7 0 6 1 Ž 9 8 . 0 0 0 5 7 - 3
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tions while the other approaches gave unreliable results on the coarse sand. Hence, to simplify the calculations the geometric mean can be used. q 1999 Elsevier Science B.V. All rights reserved. Keywords: effective hydraulic parameters; simulation of nitrate leaching; upscaling; field observations; coarse sand; sandy loam
1. Introduction Simulation models are useful tools for analyzing water and nitrogen dynamics in agroecosystems. Several models based on the Richards equation for soil water dynamics and the convection–dispersion equation for movement of inorganic nitrogen have been developed Že.g., Diekkruger et al., 1995. . The usual ap¨ proach is the one-dimensional model. When using simulation models for estimating the mean nitrate leaching on different soil types, the models have to be applied at field scale, either by upscaling from point simulations to field scale, e.g., using geostatistical methods, or by interpreting the field as an equivalent soil column using effective hydraulic parameters Ž e.g., Jensen and Refsgaard, 1991; Jensen and Mantoglou, 1992; Smith and Diekkruger, 1996. . ¨ The use of effective parameters reduces the number of simulations significantly and it would be convenient if this approach can be used. Due to the assumption that measurements of water retention are normally distributed and hydraulic conductivity lognormally distributed, the common approach for effective parameters is arithmetic mean for water retention and geometric mean for hydraulic conductivity Že.g., Jensen and Refsgaard, 1991; Sonnenborg et al., 1994. . However, the geometric mean estimates the median, which is not an unbiased estimate of the expectation for a lognormal distribution. Alternatively, an unbiased estimate for the hydraulic conductivity, called estimated arithmetic mean, can be used Ž Webster and Oliver, 1990.. Another modelling approach is to assume that the field is composed of a number of one-dimensional non-interacting columns, each represented by a set of hydraulic functions. The mean of the field is then calculated in terms of statistical moments of the simulated variables Že.g., Jensen and Refsgaard, 1991. . Using a stochastic approach, a theoretical analysis of large-scale unsaturated transient flow in three dimensions has been developed and applied over the last decade Ž Mantoglou and Gelhar, 1987a,b,c; McCord et al., 1991; Jensen and Mantoglou, 1992; Mantoglou, 1992.. The local flow behaviour is described by a three-dimensional Richards equation, and based on this an effective large-scale model of the flow field is derived. The mean model representation is similar in form to the local flow equation, but parameterized using large-scale effective properties of the hydraulic parameters, subsequently called stochastic means, that depend on the statistical moments of the local hydraulic properties and on the mean flow conditions.
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As water always follows the flow path offering the least resistance, evaluating the arithmetic mean of the hydraulic conductivity as an effective parameter is also relevant, as this approach ensures that observed high values are given more weight compared with, e.g., a geometric mean. Results from the literature on whether effective parameters can be used at field scale are ambiguous. Based on numerical analyses of infiltration, Bresler and Dagan Ž 1983. and Smith and Diekkruger ¨ Ž1996., among others, concluded that effective soil hydraulic parameters are not adequate for modelling water flow in spatially variable fields, while Jensen and Refsgaard Ž 1991. , Jensen and Mantoglou Ž1992. and Sonnenborg et al. Ž1994., comparing field observations of water content and suction vs. simulated data, found that effective soil hydraulic parameters provided a practical approach for estimating the field-averaged water balance. However, the evaluation of effective parameters for simulations of nitrate leaching based on field data has not been carried out. The purpose of this study was, from a practical point of view, to evaluate four approaches to effective means of hydraulic conductivity for simulations of nitrate leaching at field scale, i.e., Ž1. the geometric mean, Ž2. the estimated arithmetic mean, Ž3. the stochastic mean and Ž4. the arithmetic mean, as well as Ž5. the approach of a number of non-interacting columns, and to compare the simulated nitrate concentrations with field observations.
2. Materials and methods The different modelling approaches were compared with each other for two fields during the period 1 April 1989 to 31 March 1990. Additionally, the simulations were compared with measured nitrate concentrations in soil water during the winter 1989r1990. 2.1. Experimental areas and design The investigations were conducted on a coarse sandy soil Ž Orthic Haplohumod. at Jyndevad, Denmark Ž54854X NL, 09807X EL, 16 m above sea level. and on a sandy loam soil ŽTypic Agrudalf. at Rønhave, Denmark Ž 54857X NL, 09846X EL, 19 m above sea level. , representing the most lightly textured and more clayey Danish soil types. The clay Ž- 2 mm., silt Ž2–20 mm., fine sand Ž20–200 mm. and coarse sand Ž200–2000 mm. content at Jyndevad Ž0–20 cm. was 4.2, 2.7, 19.3 and 71.2% Žwrw., respectively. At Rønhave Ž 0–20 cm. , the values were 15.2, 15.6, 48.8 and 17.9% Ž wrw., respectively. Both locations are experimental stations of the Danish Institute of Agricultural Sciences. The areas of investigation were ca. 0.25 ha at both locations ŽFig. 1., and both fields were flat with a gradient of - 0.01 m my1 at Jyndevad and 0.01–0.02 m my1 at Rønhave.
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Fig. 1. Experimental layout at Rønhave. The experimental layout was similar at Jyndevad, except that distance a was 12.5 m. The samples for soil texture, total-N and the hydraulic properties were taken close to where the suction cups at 80 cm had been placed.
Prior to the investigations, the cropping history of the Jyndevad field was as follows. Since 1981, it has been uniformly cultivated and, in 1986, it was cropped with potatoes fertilized with 150 kg N hay1 as calcium ammonium nitrate ŽCAN.. In 1987, it contained varieties of maize receiving 181 kg N hay1 as CAN and 80 kg NH 4 –N hay1 as cattle slurry Ž 40,000 kg hay1 . . In 1988 and 1989, it was grown with spring barley receiving 110 and 111 kg N hay1 as CAN. The field was harrowed after harvest 1989 and kept bare during the period of investigation by repeated harrowing. The cropping history of the Rønhave field was as follows. From 1983 to 1989, it was grown with spring barley, oats, winter wheat and maize in a crop rotation with winter wheat the last year. The crops received normal rates of CAN, and in 1986–1989 the amount of CAN was 142, 108, 110 and
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150 kg N hay1. The field was ploughed at the beginning of November 1989 and kept bare during the following winter period. 2.2. Sampling programme 2.2.1. Soil water content Soil water content was measured by use of neutron scattering at eight depths: 10, 20 . . . 80 cm. At each field six access tubes for the neutron probe were placed close to each of the six groups of suction cups ŽFig. 1.. At Jyndevad, the equipment was calibrated for each soil layer, using gravimetric measurements of water content in soil samples. At Rønhave, standard calibration curves for dry soil bulk density were used. Soil water content was measured on the same dates as soil water was sampled by means of the ceramic suction cups, except in cases of technical or weather problems. 2.2.2. Nitrate in soil water During the winter period 1989r1990, soil water was sampled by ceramic suction cups at 25 and 80 cm depths according to the experimental layout in Fig. 1. There were 57 suction cups at each depth. The equipment, installation and sampling procedure were as described by Djurhuus and Jacobsen Ž 1995. . The NO 3 –N in soil water was determined according to Best Ž 1976. using a Technicon autoanalyzer. 2.2.3. Soil physical and chemical analyses At each of the 57 points where the suction cups at 80-cm depth had been placed, soil texture was measured on soil samples taken as follows ŽFig. 1.. Immediately after the last date of soil water sampling, soil samples were taken at a distance of about 10 cm from where the suction cups at 80 cm depth were placed. Two samples were taken for each of the depths 0–20, 20–40, 40–60 and 60–80 cm. For each point and depth, the samples were bulked before further analysis. The two upper depths Ž0–40 cm. were analyzed for total-N, and all depths were analyzed for texture. In spring 1993 at Jyndevad and in the autumn 1993 at Rønhave, three undisturbed samples of 100 cm3 each Ž6.10 cm in diameter, 3.42 cm in height. were taken at a distance of maximum 40 cm from where the suction cups at 80 cm depth had been placed at depths of 35–39 and 58–62 cm. Equilibrium water retention between pF s 1.0 and pF s 2.2 was determined for each sample by draining on sandbox and in pressure chambers according to Schjønning Ž1985. and Klute Ž 1986. . Unsaturated hydraulic conductivity was determined on one of the three samples at each sampling point by estimating the van Genuchten parameters ŽMualem, 1976; van Genuchten, 1980. on data from ‘one-step outflow’ experiments and the water retention characteristics Ž Kool et al., 1985;
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Jacobsen, 1992. . The statistical analysis of the hydraulic data was facilitated by optimizing the van Genuchten model parameters for each set of local retention data, using the RETC optimization code Ž van Genuchten et al., 1991. . The matrix saturated hydraulic conductivity was obtained by the optimization to the one-step outflow data. Further, the saturated hydraulic conductivity was measured on the same samples as unsaturated hydraulic conductivity by the constant head method. Due to macropores, the one-step outflow method tends to underestimate hydraulic conductivity near saturation in the clayey soil at Rønhave. Thus, for Rønhave a log–linear interpolation was introduced between hydraulic conductivity at pF s 1.3 and measured saturated conductivity. 2.3. Model description The simulations were performed by the model DAISY Ž Hansen et al., 1990, 1991.. Briefly, the model is a one-dimensional mechanistic, deterministic model for the plant soil system. The vertical movement of water and inorganic nitrogen in the soil profile is modelled by numerical solutions of the Richards equation and the convection–dispersion equation. Parameters not addressed in this paper have been adopted from previous studies Ž Hansen et al., 1991; Svendsen et al., 1995; and EU-project: Danubian Lowland-Ground Water Model, PHARE Project No. PHARErECrWATr1.. In order to take into account the influences of the previous crop rotation, the simulations started in spring 1986. To provide functional modelling layers for the hydraulic characteristics, Jyndevad soil was divided into 0–55 and 55–80 cm and Rønhave into 0–50 and 50–80 cm. At both Jyndevad and Rønhave, the dispersion length was set to 0.08 m. Information on soil organic matter Ž SOM. is utilized in the initialization of the pools of the mineralization submodel. The sum of the SOM-pools is assessed on the basis of the SOM and soil organic-N measurements, assuming that organic-N corresponds to the measured total-N. For 40–80 cm, where total-N was not measured, data from Lamm Ž 1971. were used. The initialization of the mineralization model also requires information of the ratio SOM1rSOM2, i.e., the ratio between the more recalcitrant organic matter ŽSOM1. and the more easily decomposable organic matter Ž SOM2. . By use of the measured nitrate concentrations at both depths, the ratio SOM1rSOM2 was used as a calibration parameter in order to obtain a correct level of yearly mineralization in the considered soils. After a few simulations, the final ratio SOM1rSOM2 for Jyndevad was set to 60r40 for 0–20 cm, 70r30 for 20–40 cm and 80r20 for 40–80 cm. These ratios were also found to be appropriate for Rønhave. Note that although the calibration of the ratio SOM1rSOM2 is significant for the annual level of mineralization, it has only a negligible influence on the temporal variation, which is mainly influenced by the prevailing soil moisture and soil temperature regime.
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2.4. Simulation of nitrate leaching at field scale 2.4.1. Using effectiÕe hydraulic parameters Simulations were performed at each site introducing effective hydraulic parameters assuming: Ž1. lateral stationarity; Ž2. that the mean flow of the field is expected to be one-dimensional; and Ž3. that the lateral correlation scale of the soil hydraulic properties is less than the scale of the area Ž Kim and Stricker, 1996; Smith and Diekkruger, 1996. . Effective soil water retention was estimated ¨ as arithmetic mean due to the assumption that this variable is normally distributed. Effective hydraulic conductivity was estimated according to the selected four approaches, i.e., Ž 1. the geometric mean, Ž 2. the arithmetic mean, Ž 3. the estimated arithmetic mean, and Ž4. the stochastic mean. The estimated arithmetic mean of hydraulic conductivity is based on the assumption that the distribution is lognormal, and was calculated by Ž Webster and Oliver, 1990. : x g s exp Ž j q s 2r2 .
Ž1.
where x g is the estimated arithmetic mean and j and s is arithmetic mean and standard deviation of log-transformed values, respectively. For the stochastic mean of hydraulic conductivity we used the stochastic model of Mantoglou Ž1992. for vertical flow in a stratified soil and steady state ¨ ¨ et al., 1989.. In the conditions, assuming lateral stationarity and ergodicity Ž Unlu following, we briefly present the model. The stochastic model requires a simple representation of the local hydraulic conductivity K and the local soil moisture content u as a function of the capillary tension head c . The two parameters are linearized around the mean capillary tension head Ž H . in the following way ln K Ž c . s ln K Ž H . y a Ž H . h
u Žc . su Ž H . yCŽ H . h where h is the fluctuation of c around the mean H Ž c s H q h., a Ž H . is the slope of the ln K Ž c . curve at c s H Ž pore size distribution. and C Ž H . is the negative slope of the u Ž c . curve at c s H Žspecific moisture capacity. . The local parameters ln K Ž H ., u Ž H . and a Ž H . are assumed to be random spatial functions that can be decomposed into means and fluctuations as follows: ln K Ž H . s Y Ž H . q y Ž H .; a Ž H . s AŽ H . q aŽ H .; and u Ž H . s Q Ž H . q u X Ž H .. The large-scale components Y, A and Q are assumed to be deterministic and smooth functions in space. The small-scale components y, a and u X are assumed to be three-dimensional, zero mean, second-order stationary random fields. The spatial variation of the specific moisture capacity C Ž H . was not assumed to affect the large-scale flow as significantly as the variability of the hydraulic conductivity, and the local C Ž H . was taken to be represented by its mean Ž Cˆ . .
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Operationally, this means that the effective hydraulic properties for retention were the same as for the other approaches of effective parameters. The large-scale flow equation is obtained by substituting the random processes into the local Richards equation. This produces a partial differential equation with stochastic parameters and a stochastic dependent variable, c s H q h. Taking the expected value of the partial differential equation and neglecting higher order terms yields the large-scale unsaturated flow equation, similar to the local Richards equation but parameterized with large-scale effective properties of specific soil moisture capacity Ž Cˆ . and vertical hydraulic conductivity Ž Kˆ .. The effective parameters can be evaluated and analytic expressions derived for specific cases when assuming that the variation of the fluctuations Ž h, y and a. is small. The mean soil properties are assumed to be practically constant in space, and the length scale of the flow domain must be large compared with the correlation length of the fluctuations. Further, the time and space derivatives of the mean tension Ž H . are assumed to be small. For one-dimensional flow it is assumed that the spatial gradient of H in the horizontal direction is zero. In the case of a stratified soil and nearly steady state flow Ž EHrEt f 0., Kˆ is given by ŽMantoglou, 1992.: Kˆ s K m exp y
sy2 q 2 r y a Jl 2 Ž 1 q AL l .
Ž2.
where K m is the geometric mean of unsaturated hydraulic conductivity, sy2 is the variance of ln K, r y a is the cross correlation between ln K and a , l is the vertical correlation length, L s J q Ž EHrEz ., J s EŽ H q z .rE z and A as explained previously. At both locations, the upper functional layer consists partly of a plough layer and partly of a stratified layer below the plough layer, while the lower functional layer can be considered as stratified at both locations. Hence, we have applied Eq. Ž2. to both functional layers in the model. It is seen from Eq. Ž 2. that the hydraulic conductivity depends on the spatial derivative of the mean tension. A large value of the vertical derivative will cause the effective hydraulic conductivity to become unrealistically large. In order to avoid numerical instabilities in our simulations ŽSonnenborg et al., 1994. and to ˆ we assumed the spatial derivative of the obtain an explicit expression for K, mean tension Ž EHrEz . to be equal to zero, in accordance with other applications of the theory ŽMcCord et al., 1991; Sonnenborg et al., 1994.. The assumption yields L s J s 1, and consequently Kˆ can be calculated explicitly from a statistical analysis of the hydraulic properties of the field. 2.4.2. AÕerage of simulations of indiÕidual columns The simulations were run for each individual column represented by the points at which the soil hydraulic properties were measured, which is near the
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points at which the suction cups at 80 cm were placed Ž see Section 2.2.3. . Afterwards the field scale average and standard deviation were calculated. As the simulations were run for 57 points in each field, the results using this approach are subsequently referred to as ‘the 57 simulations’. Thus, both the variation in the retention data as well as the hydraulic conductivity are expressed in this approach. 2.5. Data analysis of hydraulic properties The arithmetic mean of the water content and the specific moisture capacity, and the arithmetic, estimated arithmetic and geometric means of the hydraulic conductivity were calculated at discrete values of the tension head Ž c .. In order to obtain the stochastic mean of hydraulic conductivity, the statistical properties Žmeans, covariances, variances. were evaluated at discrete values of the large-scale mean tension head Ž H . and the stochastic mean was calculated at the same discrete values of H using Eq. Ž2..
Fig. 2. Jyndevad. Effective hydraulic properties of retention Ža and b. and hydraulic conductivities Žc and d.. The stochastic mean with l s10 cm was nearly identical to the stochastic mean with l s 5 cm.
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The vertical correlation length of the soil Ž l. was not known and had to be assessed. In order to evaluate the effect of different correlation lengths, two estimates for each soil type were taken into consideration. The soil at Jyndevad was more stratified than that at Rønhave and therefore we used l-values of 5 cm and 10 cm at Jyndevad and 10 cm and 20 cm at Rønhave, similar in magnitude to the applications by McCord et al. Ž 1991. and Jensen and Mantoglou Ž1992.. Fig. 2a–b and Fig. 3 a–b display the effective retention characteristics for Jyndevad and Rønhave, respectively. The variance of the water content is large for water contents close to saturation and is larger at Jyndevad than at Rønhave. Fig. 2c–d and Fig. 3c–d give the calculated effective hydraulic conductivities for Jyndevad and Rønhave, respectively. The arithmetic, estimated arithmetic, geometric and stochastic hydraulic conductivities are shown in the same figure even if the variable on the first axis Ž tension head. is the deterministic c for the three former and the stochastic H for the latter effective conductivity. The break
Fig. 3. Rønhave. Effective hydraulic properties of retention Ža and b. and hydraulic conductivities Žc and d.. The stochastic mean with l s10 cm was nearly identical to the stochastic mean with l s 20 cm.
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Table 1 Water balancea , yield and nitrogen balanceb at Jyndevad 1 April 1989–31 March 1990 Method 57 simulations
Geometric Stochastic mean mean
Arithmetic mean
Mean
S.D. Žrange.
502 519 5.0 168.9
39 Ž358–561. 503 35 Ž474–645. 517 0.4 Ž3.3–5.3. 5.1 10.5 Ž116.5–181.3. 172.2
486 540 5.0 172.2
483 540 4.9 171.5
389 589 3.4 109.8
123.8
7.0 Ž104.5–137.1.
120.4
120.3
120.4
110.3
0.0
0.0
0.0
0.0
70.1
71.7
71.9
123.3
l s 5 cm l s10 cm Ea Žmm. Percolation Žmm. Yield ŽMg hay1 . N-uptake Žkg N hay1 . Net mineralization Žkg N hay1 . Denitrification Žkg N hay1 . Leaching Žkg N hay1 . a b
0.1
0.5 Ž0.0–3.9.
79.0
14.4 Ž61.0–143.5.
Precipitation and irrigation: 1007 mm; Ep: 600 mm. Mineral fertilizer: 111 kg N hay1 ; deposition: 15.6 kg N hay1
of the curves at H s 0.20 in Fig. 3c–d is due to the log–linear interpolation in hydraulic conductivity between pF s 1.3 and saturation Žsee Section 2.2.3. . The stochastic estimate tends to be extremely low at large tension heads, while the Table 2 Water balancea , yield and nitrogen balanceb at Rønhave 1 April 1989–31 March 1990 Method 57 simulations Mean S.D. Žrange.
Ea Žmm. 481 Percolation Žmm. 293 Yield ŽMg hay1 . 6.5 N-uptake 189.8 Žkg N hay1 . Net mineralization 99.1 Žkg N hay1 . Denitrification 19.3 Žkg N hay1 . Leaching 35.1 Žkg N hay1 . a b
Geometric Estimated Stochastic Arithmetic mean arithmetic mean mean mean l s10 l s 20
24 Ž415–527. 486 29 Ž243–406. 284 0.7 Ž5.1–9.3. 6.5 7.8 Ž169.7–208.7. 190.1
cm
cm
506 265 7.0 193.1
464 305 6.0 187.4
465 300 6.0 188.0
497 274 6.7 193.1
5.3 Ž80.5–122.0.
98.7
94.7
102.3
102.2
98.2
17.9 Ž0.6–60.0.
13.9
11.8
15.6
15.4
10.6
15.0 Ž8.5–61.7.
38.1
34.8
42.5
41.8
39.5
Precipitation: 770 mm; Ep: 622 mm. Mineral fertilizer: 150 kg N hay1 ; deposition: 14.1 kg N hay1.
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estimated arithmetic mean tends to increase unrealistically, most pronounced at Jyndevad. Hence, we decided not to perform any model simulation employing estimated arithmetic conductivity at Jyndevad. The low stochastic mean is probably due to the large variance of the hydraulic data. At large tension heads Ž); 10 m. the stochastic theory is violated since the assumption of small variances in the lateral dimension is no longer valid.
Fig. 4. Jyndevad. Simulated and measured concentrations of NO 3 –N Žmgrl. Ž y-axis. at the 57 points.
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3. Results 3.1. Simulated Õs. measured soil water content At both locations, the simulated soil water content resulting from the different approaches generally matched the measured values at all depths except for the
Fig. 5. Jyndevad. Simulated concentrations of NO 3 –N Žmgrl. Ž y-axis. at the 57 points and using geometric mean, stochastic mean and arithmetic mean of hydraulic conductivity.
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arithmetic mean at Jyndevad Ždata not shown. . The accumulated water balances for 1989r1990 are given in Tables 1 and 2. 3.2. Simulated Õs. measured nitrate concentration In general, the temporal variation of the simulations agreed with the observed variation ŽFigs. 4 and 6. . At Jyndevad, the measured values at 25 cm were slightly higher than simulated concentrations at the beginning of autumn while at 80 cm the measured values were generally a little lower than the simulations, except at the end of October Ž Fig. 4. . At Rønhave, the simulated concentrations at 25 cm were slightly higher during most of the winter period ŽFig. 6.. Further, the size of the variation in the simulations and the observations was about the same at both locations ŽFigs. 4 and 6. , except from November until January at Jyndevad when the measured values showed significantly larger variation at 80 cm compared with the simulations.
Fig. 6. Rønhave. Simulated and measured concentrations of NO 3 –N Žmgrl. Ž y-axis. at the 57 points.
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3.3. Nitrate concentration and N-balance as affected by the methods of simulation At Jyndevad, the temporal variation of the nitrate concentrations was generally the same except for the simulation using the arithmetic mean, which differed considerably from the other simulations Ž Fig. 5. . In spring and at the beginning of autumn, the simulated concentrations using the stochastic mean were lower than those obtained using the geometric mean, most markedly so at 25 cm. The simulations using a stochastic mean conductivity with l s 5 and 10 cm, respectively, were nearly identical except in spring, when the concentrations with l s 10 cm were slightly higher at the 25 cm depth ŽFig. 5.. Compared with nitrate concentrations from the 57 simulations, the simulations using the geometric and stochastic means were slightly lower except in late autumn and winter
Fig. 7. Rønhave. Simulated concentrations of NO 3 –N Žmgrl. Ž y-axis. at the 57 points and using geometric mean, estimated arithmetic mean, stochastic mean and arithmetic mean of hydraulic conductivity.
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ŽFig. 5. . These differences were also expressed in the accumulated nitrate leaching ŽTable 1.. Thus, the geometric and the stochastic means gave nearly the same results, which was slightly lower than the results of the 57 simulations. This difference was caused by a larger N-uptake and lower mineralization compared with the 57 simulations ŽTable 1.. At Rønhave, the temporal variation of the different approaches was the same ŽFig. 7.. However, the simulated concentrations using the geometric, stochastic and arithmetic means were slightly higher during the main part of the period compared with the nitrate concentrations of the 57 simulations. Accordingly, the leaching was about the same for the four effective parameter approaches, and slightly larger than that resulting from the 57 simulations. The lower leaching of the 57 simulations was caused mainly by a higher level of denitrification Ž Table 2..
4. Discussion The measurements of nitrate concentrations by the ceramic suction cups at Jyndevad have been found to represent volume-averaged concentrations ŽDjurhuus and Jacobsen, 1995. equivalent to the simulated concentrations. Thus, as the field at Jyndevad was harrowed in autumn 1989 and because the effect of soil tillage on mineralization is not included in DAISY, the higher values of measured concentrations compared with the simulations at 25 and 80 cm in autumn 1989 at Jyndevad Ž Fig. 4. were probably due to enhanced mineralization through soil tillage ŽHansen and Djurhuus, 1997. . At Rønhave, where the effect of soil tillage is expected to be more pronounced than at Jyndevad Ž Hansen and Djurhuus, 1997., and where the measurements of nitrate concentrations by the ceramic suction cups in periods of mineralization have been found to be slightly lower than the actual volume-averaged concentrations Ž Djurhuus and Jacobsen, 1995., the lower simulated concentrations at 25 cm compared with the observations ŽFig. 6. after ploughing at the beginning of November underlined the model error of not including the effect of soil tillage. At Rønhave, the larger decrease in simulated nitrate concentration at 25 cm in mid-December to the beginning of January compared with the observations Ž Fig. 6. may be due to the fact that macropore flow, which is not yet included in DAISY, probably took place between 15 to 21 of December due to a total precipitation of 71 mm in this period, causing the suction cups at 25 cm to be bypassed, and the decrease in the simulations to be more pronounced than it actually was in the field. Macropore flow was probably also the reason why the simulated water content at 80 cm at Rønhave reached field capacity mid-December, about 1 month before the measured values Ž data not shown. . In general, the variation of the variables included in the modelling, i.e., texture, retention and hydraulic conductivity and the effect of these parameters
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on the N-processes and N-uptake could account for the main part of the variation ŽFigs. 4 and 6. . The larger observed variation at Jyndevad from November to January at 80 cm could be explained by finger-flow in the sandy soil expressed in the observations but not taken into account by the model Žconvection–dispersion equation. . The unrealistic results at Jyndevad using the arithmetic mean Ž Fig. 5, Table 1. are due to the fact that high values of hydraulic conductivity are given more weight compared with the geometric mean. At Rønhave, the distribution of the hydraulic conductivity was less skewed so the arithmetic mean and the estimated arithmetic mean ŽEq. Ž1.. gave results similar to the other methods ŽFig. 3c–d and Fig. 7, Table 2.. However, as the type of distribution can only be estimated for large samples, neither the arithmetic nor the estimated arithmetic mean is adequate as an effective parameter for hydraulic conductivity. The fact that geometric and stochastic means of hydraulic conductivity gave nearly similar and realistic results at both locations Ž Figs. 5 and 7, Tables 1 and 2. must be due to the fact that percolation was mainly vertical and that the prerequisites for using the geometric and stochastic means are valid or of less significance. As both fields are rather flat and as no trend could be detected in a geostatistical analysis of texture Ž data not shown. , lateral stationarity must have been valid for both fields. As discussed by Kim and Stricker Ž1996., the lateral correlation length for the hydraulic properties of fields of our size or larger, can be assumed to be relatively small compared with the entire flow domain, and so is the vertical correlation length compared with the lateral correlation length. Although it is not possible to estimate the vertical correlation length from our data, the chosen values, 5–10 cm at Jyndevad and 10–20 cm at Rønhave, must thus be regarded as realistic ŽFigs. 5 and 7. . The vertical correlation length must also be small compared with the vertical scale of each soil layer Ž Jensen and Mantoglou, 1992; Mantoglou, 1992. . This has only been partly the case in our study. Further, although the assumption that EHrEz f 0 is clearly violated during the summer periods, the simplification of this gradient in the stochastic approach Žsee Section 2.4.1. does not seem to be significant. Hence, both the geometric and the stochastic means can be used as effective parameters for areas similar to our fields and the choice may therefore depend on the purpose of the analysis and the data available. By use of the stochastic approach it is possible to calculate an estimate of the variation for the local mean capillary head and the soil moisture content ŽJensen and Mantoglou, 1992; Mantoglou, 1992. . Hence, the stochastic approach may be preferred if the variance as well as the mean of soil water is wanted. However, for reliable estimation of the variances and covariances in the stochastic approach, a relatively large data set should be available. Generally, the use of geometric and stochastic means gave similar results as the average of the 57 simulations ŽFigs. 5 and 7, Tables 1 and 2., and thus both the concept of an ensemble of non-interacting columns and the concept of an
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equivalent soil column seem reasonable, in agreement with Jensen and Refsgaard Ž1991., who evaluated the two approaches for water content and soil water suction. The use of effective hydraulic parameters is to be preferred to reduce the number of simulations. In our study we used a larger dataset representing the field conditions compared with previous applications Ž Jensen and Mantoglou, 1992; Sonnenborg et al., 1994. and thus we have a good database for evaluating the stochastic approach. Both Jensen and Mantoglou Ž 1992. and Sonnenborg et al. Ž 1994. compared observed water content and suction with simulations using the stochastic and the geometric means. Jensen and Mantoglou Ž 1992. included the variation of EHrEz in their investigation, which was carried out for a field of 0.5 ha also situated at Jyndevad, close to our field, while Sonnenborg et al. Ž1994. made their simulations for a catchment of 1 km2 , discretized into elements of 25 m by 25 m for the catchment model MIKE SHE, and assuming EHrEz f 0. Both studies concluded that the stochastic approach gave better results than the geometric mean. However, the differences between the two effective parameter approaches in both investigations were relatively small and the results were ambiguous. 5. Conclusion The simulations of the soil water dynamic, nitrate concentration and nitrate leaching by the stochastic approach and the geometric mean were similar to the approach of assuming that the field is composed of a number of one-dimensional non-interacting columns, and generally all three approaches matched the observed nitrate concentrations. Hence, to simplify the calculations, the geometric mean can be used for simulations of mean nitrate leaching at field scale. References Best, E.K., 1976. An automated method for determining nitrate–nitrogen in soil extracts. Qld. J. Agric. Anim. Sci. 33, 161–166. Bresler, E., Dagan, G., 1983. Unsaturated flow in spatially variable fields: II. Application of water flow models to various fields. Water Resour. Res. 19, 421–428. Diekkruger, B., Sondgerath, D., Kersebaum, K.C., McVoy, C.W., 1995. Validity of agroecosys¨ ¨ tem models: a comparison of results of different models applied to the same data set. Ecol. Model. 81, 3–29. Djurhuus, J., Jacobsen, O.H., 1995. Comparison of ceramic suction cups and KCl extraction for the determination of nitrate in soil. Eur. J. Soil Sci. 46, 387–395. Hansen, E.M., Djurhuus, J., 1997. Nitrate leaching as influenced by soil tillage and catch crop. Soil Tillage Res. 41, 203–219. Hansen, S., Jensen, H.E., Nielsen, N.E., Svendsen, H., 1990. DAISY—soil plant atmosphere system model. NPO-Research Report No. A10. The National Agency for Environmental Protection, Copenhagen, 270 pp.
J. Djurhuus et al.r Geoderma 87 (1999) 261–279
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Hansen, S., Jensen, H.E., Nielsen, N.E., Svendsen, H., 1991. Simulation of nitrogen dynamics and biomass production in winter wheat using the Danish simulation model DAISY. Fertil. Res. 27, 245–259. Jacobsen, O.H., 1992. Unsaturated hydraulic conductivity determined by parameter estimation from one-step outflow experiments. Tidsskr. Planteavl, Ber. S2183. Jensen, K.H., Mantoglou, A., 1992. Application of stochastic unsaturated flow theory, numerical simulations, and comparisons to field observations. Water Resour. Res. 28, 269–284. Jensen, K.H., Refsgaard, J.C., 1991. Spatial variability of physical parameters and processes in two field soils: II. Water flow at field scale. Nord. Hydrol. 22, 303–326. Kim, C.P., Stricker, J.N.M., 1996. Influence of spatially variable soil hydraulic properties and rainfall intensity on the water budget. Water Resour. Res. 32, 1699–1712. Klute, A., 1986. Water retention: laboratory methods. In: Klute, A. ŽEd.., Methods of Soil Analysis: I. Physical and Mineralogical Methods, 2nd edn. Madison, WI, USA, pp. 635–662. Kool, J.B., Parker, J.C., van Genuchten, M.Th., 1985. Determining soil hydraulic properties from one-step outflow experiment by parameter estimation: I. Theory and numerical studies. Soil Sci. Soc. Am. J. 49, 1348–1353. Lamm, C.G., 1971. Det danske jordarkiv ŽThe Danish soil library.. Tidsskr. Planteavl 75, 703–720, In Danish. Mantoglou, A., 1992. A theoretical approach for modelling unsaturated flow in spatially variable soils: effective flow models in finite domains and non-stationarity. Water Resour. Res. 28, 251–267. Mantoglou, A., Gelhar, L.W., 1987a. Stochastic modelling of large-scale transient unsaturated flow systems. Water Resour. Res. 23, 37–46. Mantoglou, A., Gelhar, L.W., 1987b. Capillary tension head variance, mean soil moisture content, and effective specific soil moisture capacity of transient unsaturated flow in stratified soils. Water Resour. Res. 23, 47–56. Mantoglou, A., Gelhar, L.W., 1987c. Effective hydraulic conductivities of transient unsaturated flow in stratified soils. Water Resour. Res. 23, 57–67. McCord, J.T., Stephens, D.B., Wilson, J.L., 1991. Hysteresis and state-dependent anisotropy in modelling unsaturated hillslope hydrologic processes. Water Resour. Res. 27, 1501–1518. Mualem, Y., 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12, 513–522. Schjønning, P., 1985. Udstyr til afdræning af jordprøver for jordfysiske analyser ŽEquipment for drainage of soil samples.. Tidsskr. Planteavl, Ber. S1762 Žin Danish, with English abstract.. Smith, R.E., Diekkruger, B., 1996. Effective soil water characteristics and ensemble soil water ¨ profiles in heterogeneous soils. J. Geophys. Res. 32, 1993–2002. Sonnenborg, T.O., Butts, M.B. Jensen, K.H., 1994. Application of stochastic unsaturated flow theory. In: Kern-Hansen, C., Rosbjerg, D., Thomsen, R. ŽEds.., NHP-Report No. 34. Nordic Hydrological Conference, 2–4 August 1994. Torshavn, Faroe Islands, pp. 219–228. Svendsen, H., Hansen, S., Jensen, H.E., 1995. Simulation of crop production, water and nitrogen balances in two German agroecosystems using the DAISY model. Ecol. Model. 81, 197–212. ¨ ¨ K., Kavvas, M.L., Nielsen, D.R., 1989. Stochastic analysis of field measured unsaturated Unlu, hydraulic conductivity. Water Resour. Res. 25, 2511–2519. van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, 892–898. van Genuchten, M., Leij, Th. F.J., Yates, S.R., 1991. The RETC code for quantifying the hydraulic functions of unsaturated soils. EPAr600r2-91r065, 93 pp. Webster, R., Oliver, M.A., 1990. Statistical Methods in Soil and Land Resource Survey. Oxford Univ. Press, New York, 316 pp.