GEO_1999_87_261_279

Ž .Geoderma 87 1999 261–279

Modelling mean nitrate leaching from spatiallyvariable 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 SoilScience, 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 effectivehydraulic parameters, which are estimated from point measurements. The use of effectivehydraulic parameters was evaluated on a coarse sandy soil and a sandy loam using theone-dimensional mechanistic model, DAISY. On each location, texture, soil water retention andhydraulic conductivity from 57 points were measured within an area of ca. 0.25 ha. The following

Ž .approaches for estimation of effective hydraulic conductivity were examined: 1 geometric mean;Ž . Ž . Ž .2 arithmetic mean; 3 estimated arithmetic mean from a lognormal distribution; and 4 meanestimated from a stochastic large-scale model for water flow, similar to the Richards equation inone dimension, but with large-scale effective parameters accounting for the local three-dimen-sional flow. The approach of interpreting the field as a number of non-interacting columns wasexamined by calculating the mean of the field as the mean of the 57 soil columns. The nitrateconcentrations simulated by DAISY were compared with nitrate concentrations measured byceramic suction cups at the 57 points at 25 cm and 80 cm depths during the winter period1989r1990. At both locations, the nitrate concentrations simulated by the geometric mean, thestochastic approach and the mean of the 57 simulations matched the observed nitrate concentra-

) Corresponding author. Tel.: q45-8999-1900; Fax: q45-8999-1719; E-mail:[email protected]

1 Tel.: q45-3528-3383; Fax: q45-3528-3384.

0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0016-7061 98 00057-3

( )J. Djurhuus et al.rGeoderma 87 1999 261–279262

tions while the other approaches gave unreliable results on the coarse sand. Hence, to simplify thecalculations 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 observa-tions; coarse sand; sandy loam

1. Introduction

Simulation models are useful tools for analyzing water and nitrogen dynamicsin agroecosystems. Several models based on the Richards equation for soil waterdynamics and the convection–dispersion equation for movement of inorganic

Ž .nitrogen have been developed e.g., Diekkruger et al., 1995 . The usual ap-¨proach is the one-dimensional model. When using simulation models forestimating the mean nitrate leaching on different soil types, the models have tobe applied at field scale, either by upscaling from point simulations to fieldscale, e.g., using geostatistical methods, or by interpreting the field as an

Žequivalent soil column using effective hydraulic parameters e.g., Jensen and.Refsgaard, 1991; Jensen and Mantoglou, 1992; Smith and Diekkruger, 1996 .¨

The use of effective parameters reduces the number of simulations significantlyand it would be convenient if this approach can be used. Due to the assumptionthat measurements of water retention are normally distributed and hydraulicconductivity lognormally distributed, the common approach for effective param-eters is arithmetic mean for water retention and geometric mean for hydraulic

Ž .conductivity e.g., Jensen and Refsgaard, 1991; Sonnenborg et al., 1994 .However, the geometric mean estimates the median, which is not an unbiasedestimate of the expectation for a lognormal distribution. Alternatively, anunbiased estimate for the hydraulic conductivity, called estimated arithmetic

Ž .mean, can be used Webster and Oliver, 1990 . Another modelling approach isto assume that the field is composed of a number of one-dimensional non-inter-acting columns, each represented by a set of hydraulic functions. The mean ofthe field is then calculated in terms of statistical moments of the simulated

Ž .variables e.g., Jensen and Refsgaard, 1991 . Using a stochastic approach, atheoretical analysis of large-scale unsaturated transient flow in three dimensions

Žhas been developed and applied over the last decade 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 Richardsequation, and based on this an effective large-scale model of the flow field isderived. The mean model representation is similar in form to the local flowequation, but parameterized using large-scale effective properties of the hy-draulic parameters, subsequently called stochastic means, that depend on thestatistical moments of the local hydraulic properties and on the mean flowconditions.

( )J. Djurhuus et al.rGeoderma 87 1999 261–279 263

As water always follows the flow path offering the least resistance, evaluatingthe arithmetic mean of the hydraulic conductivity as an effective parameter isalso relevant, as this approach ensures that observed high values are given moreweight compared with, e.g., a geometric mean.

Results from the literature on whether effective parameters can be used atfield scale are ambiguous. Based on numerical analyses of infiltration, Bresler

Ž . Ž .and Dagan 1983 and Smith and Diekkruger 1996 , among others, concluded¨that effective soil hydraulic parameters are not adequate for modelling water

Ž .flow in spatially variable fields, while Jensen and Refsgaard 1991 , Jensen andŽ . Ž .Mantoglou 1992 and Sonnenborg et al. 1994 , comparing field observations

of water content and suction vs. simulated data, found that effective soilhydraulic parameters provided a practical approach for estimating the field-aver-aged water balance. However, the evaluation of effective parameters for simula-tions 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 fourapproaches to effective means of hydraulic conductivity for simulations of

Ž . Ž .nitrate leaching at field scale, i.e., 1 the geometric mean, 2 the estimatedŽ . Ž .arithmetic mean, 3 the stochastic mean and 4 the arithmetic mean, as well as

Ž .5 the approach of a number of non-interacting columns, and to compare thesimulated nitrate concentrations with field observations.

2. Materials and methods

The different modelling approaches were compared with each other for twofields during the period 1 April 1989 to 31 March 1990. Additionally, thesimulations were compared with measured nitrate concentrations in soil waterduring the winter 1989r1990.

2.1. Experimental areas and design

ŽThe investigations were conducted on a coarse sandy soil Orthic Haplohu-. Ž X X .mod at Jyndevad, Denmark 54854 NL, 09807 EL, 16 m above sea level and

Ž . Ž Xon a sandy loam soil Typic Agrudalf at Rønhave, Denmark 54857 NL,X .09846 EL, 19 m above sea level , representing the most lightly textured and

Ž . Ž .more clayey Danish soil types. The clay -2 mm , silt 2–20 mm , fine sandŽ . Ž . Ž .20–200 mm and coarse sand 200–2000 mm content at Jyndevad 0–20 cm

Ž . Ž .was 4.2, 2.7, 19.3 and 71.2% wrw , respectively. At Rønhave 0–20 cm , theŽ .values were 15.2, 15.6, 48.8 and 17.9% wrw , respectively. Both locations are

experimental stations of the Danish Institute of Agricultural Sciences. The areasŽ .of investigation were ca. 0.25 ha at both locations Fig. 1 , and both fields were

flat with a gradient of -0.01 m my1 at Jyndevad and 0.01–0.02 m my1 atRønhave.


Fig. 1. Experimental layout at Rønhave. The experimental layout was similar at Jyndevad, exceptthat distance a was 12.5 m. The samples for soil texture, total-N and the hydraulic properties weretaken close to where the suction cups at 80 cm had been placed.

Prior to the investigations, the cropping history of the Jyndevad field was asfollows. Since 1981, it has been uniformly cultivated and, in 1986, it wascropped with potatoes fertilized with 150 kg N hay1 as calcium ammonium

Ž . y1nitrate CAN . In 1987, it contained varieties of maize receiving 181 kg N hay1 Ž y1.as CAN and 80 kg NH –N ha as cattle slurry 40,000 kg ha . In 1988 and4

1989, it was grown with spring barley receiving 110 and 111 kg N hay1 asCAN. The field was harrowed after harvest 1989 and kept bare during the periodof investigation by repeated harrowing.

The cropping history of the Rønhave field was as follows. From 1983to 1989, it was grown with spring barley, oats, winter wheat and maize ina crop rotation with winter wheat the last year. The crops received normalrates of CAN, and in 1986–1989 the amount of CAN was 142, 108, 110 and


150 kg N hay1. The field was ploughed at the beginning of November 1989 andkept bare during the following winter period.

2.2. Sampling programme

2.2.1. Soil water contentSoil 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 wereŽ .placed close to each of the six groups of suction cups Fig. 1 . At Jyndevad, the

equipment was calibrated for each soil layer, using gravimetric measurements ofwater content in soil samples. At Rønhave, standard calibration curves for drysoil bulk density were used. Soil water content was measured on the same datesas soil water was sampled by means of the ceramic suction cups, except in casesof technical or weather problems.

2.2.2. Nitrate in soil waterDuring 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

Ž .sampling procedure were as described by Djurhuus and Jacobsen 1995 . TheŽ .NO –N in soil water was determined according to Best 1976 using a Techni-3

con autoanalyzer.

2.2.3. Soil physical and chemical analysesAt each of the 57 points where the suction cups at 80-cm depth had been

Ž .placed, soil texture was measured on soil samples taken as follows Fig. 1 .Immediately after the last date of soil water sampling, soil samples were taken ata distance of about 10 cm from where the suction cups at 80 cm depth wereplaced. Two samples were taken for each of the depths 0–20, 20–40, 40–60 and60–80 cm. For each point and depth, the samples were bulked before further

Ž .analysis. The two upper depths 0–40 cm were analyzed for total-N, and alldepths were analyzed for texture.

In spring 1993 at Jyndevad and in the autumn 1993 at Rønhave, three3 Ž .undisturbed samples of 100 cm each 6.10 cm in diameter, 3.42 cm in height

were taken at a distance of maximum 40 cm from where the suction cups at 80cm depth had been placed at depths of 35–39 and 58–62 cm. Equilibrium waterretention between pFs1.0 and pFs2.2 was determined for each sample by

Ž .draining on sandbox and in pressure chambers according to Schjønning 1985Ž .and Klute 1986 . Unsaturated hydraulic conductivity was determined on one of

the three samples at each sampling point by estimating the van GenuchtenŽ .parameters Mualem, 1976; van Genuchten, 1980 on data from ‘one-step

Žoutflow’ experiments and the water retention characteristics Kool et al., 1985;


.Jacobsen, 1992 . The statistical analysis of the hydraulic data was facilitated byoptimizing the van Genuchten model parameters for each set of local retention

Ž .data, using the RETC optimization code van Genuchten et al., 1991 . Thematrix saturated hydraulic conductivity was obtained by the optimization to theone-step outflow data. Further, the saturated hydraulic conductivity was mea-sured on the same samples as unsaturated hydraulic conductivity by the constanthead method. Due to macropores, the one-step outflow method tends to underes-timate hydraulic conductivity near saturation in the clayey soil at Rønhave.Thus, for Rønhave a log–linear interpolation was introduced between hydraulicconductivity at pFs1.3 and measured saturated conductivity.

2.3. Model description

ŽThe simulations were performed by the model DAISY 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 nitrogenin the soil profile is modelled by numerical solutions of the Richards equationand the convection–dispersion equation. Parameters not addressed in this paper

Žhave been adopted from previous studies Hansen et al., 1991; Svendsen et al.,1995; and EU-project: Danubian Lowland-Ground Water Model, PHARE Pro-

.ject No. PHARErECrWATr1 . In order to take into account the influences ofthe 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 and50–80 cm. At both Jyndevad and Rønhave, the dispersion length was set to 0.08m.

Ž .Information on soil organic matter SOM is utilized in the initialization ofthe pools of the mineralization submodel. The sum of the SOM-pools is assessedon the basis of the SOM and soil organic-N measurements, assuming thatorganic-N corresponds to the measured total-N. For 40–80 cm, where total-N

Ž .was not measured, data from Lamm 1971 were used. The initialization of themineralization model also requires information of the ratio SOM1rSOM2, i.e.,

Ž .the ratio between the more recalcitrant organic matter SOM1 and the moreŽ .easily decomposable organic matter SOM2 . By use of the measured nitrate

concentrations at both depths, the ratio SOM1rSOM2 was used as a calibrationparameter in order to obtain a correct level of yearly mineralization in theconsidered soils. After a few simulations, the final ratio SOM1rSOM2 forJyndevad was set to 60r40 for 0–20 cm, 70r30 for 20–40 cm and 80r20 for40–80 cm. These ratios were also found to be appropriate for Rønhave. Notethat although the calibration of the ratio SOM1rSOM2 is significant for theannual level of mineralization, it has only a negligible influence on the temporalvariation, which is mainly influenced by the prevailing soil moisture and soiltemperature regime.


2.4. Simulation of nitrate leaching at field scale

2.4.1. Using effectiÕe hydraulic parametersSimulations were performed at each site introducing effective hydraulic

Ž . Ž .parameters assuming: 1 lateral stationarity; 2 that the mean flow of the fieldŽ .is expected to be one-dimensional; and 3 that the lateral correlation scale of the

Žsoil hydraulic properties is less than the scale of the area 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 dis-tributed. Effective hydraulic conductivity was estimated according to the se-

Ž . Ž . Ž .lected four approaches, i.e., 1 the geometric mean, 2 the arithmetic mean, 3Ž .the estimated arithmetic mean, and 4 the stochastic mean.

The estimated arithmetic mean of hydraulic conductivity is based on theŽassumption that the distribution is lognormal, and was calculated by Webster

.and Oliver, 1990 :2x sexp jqs r2 1Ž .Ž .g

where x is the estimated arithmetic mean and j and s is arithmetic mean andg

standard deviation of log-transformed values, respectively.For the stochastic mean of hydraulic conductivity we used the stochastic

Ž .model of Mantoglou 1992 for vertical flow in a stratified soil and steady state¨Ž .conditions, assuming lateral stationarity and ergodicity Unlu et al., 1989 . In the¨

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 thecapillary tension head c . The two parameters are linearized around the mean

Ž .capillary tension head H in the following way

ln K c s ln K H ya H hŽ . Ž . Ž .u c su H yC H hŽ . Ž . Ž .

Ž . Ž .where h is the fluctuation of c around the mean H csHqh , a H is theŽ . Ž . Ž .slope of the ln K c curve at csH pore size distribution and C H is the

Ž . Ž .negative slope of the u c curve at csH specific moisture capacity .Ž . Ž . Ž .The local parameters ln K H , u H and a H are assumed to be random

spatial functions that can be decomposed into means and fluctuations as follows:Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .ln K H s Y H q y H ; a H s A H q a H ; and u H s Q H q

XŽ .u H . The large-scale components Y, A and Q are assumed to be deterministicand smooth functions in space. The small-scale components y, a and u

X areassumed to be three-dimensional, zero mean, second-order stationary randomfields.

Ž .The spatial variation of the specific moisture capacity C H was not assumedto affect the large-scale flow as significantly as the variability of the hydraulic

ˆŽ . Ž .conductivity, and the local C H was taken to be represented by its mean C .


Operationally, this means that the effective hydraulic properties for retentionwere the same as for the other approaches of effective parameters.

The large-scale flow equation is obtained by substituting the random pro-cesses into the local Richards equation. This produces a partial differentialequation with stochastic parameters and a stochastic dependent variable, csHqh. Taking the expected value of the partial differential equation and neglect-ing higher order terms yields the large-scale unsaturated flow equation, similarto the local Richards equation but parameterized with large-scale effective

ˆŽ .properties of specific soil moisture capacity C and vertical hydraulic conduc-ˆŽ .tivity K .

The effective parameters can be evaluated and analytic expressions derivedŽfor specific cases when assuming that the variation of the fluctuations h, y and

.a is small. The mean soil properties are assumed to be practically constant inspace, and the length scale of the flow domain must be large compared with thecorrelation length of the fluctuations. Further, the time and space derivatives of

Ž .the mean tension H are assumed to be small. For one-dimensional flow it isassumed that the spatial gradient of H in the horizontal direction is zero.

ˆŽ .In the case of a stratified soil and nearly steady state flow EHrEtf0 , K isŽ .given by Mantoglou, 1992 :

2s q2 r Jly yaKsK exp y 2Ž .m 2 1qALlŽ .

where K is the geometric mean of unsaturated hydraulic conductivity, s 2 ism y

the variance of ln K , r is the cross correlation between ln K and a , l is theyaŽ . Ž .vertical correlation length, LsJq EHrEz , JsE Hqz rEz and A as ex-

plained 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 functionallayer can be considered as stratified at both locations. Hence, we have applied

Ž .Eq. 2 to both functional layers in the model.Ž .It is seen from Eq. 2 that the hydraulic conductivity depends on the spatial

derivative of the mean tension. A large value of the vertical derivative will causethe effective hydraulic conductivity to become unrealistically large. In order to

Ž .avoid numerical instabilities in our simulations Sonnenborg et al., 1994 and toˆobtain an explicit expression for K , we assumed the spatial derivative of the

Ž .mean tension EHrEz to be equal to zero, in accordance with other applicationsŽ .of the theory McCord et al., 1991; Sonnenborg et al., 1994 . The assumption

ˆyields LsJs1, and consequently K can be calculated explicitly from astatistical analysis of the hydraulic properties of the field.

2.4.2. AÕerage of simulations of indiÕidual columnsThe simulations were run for each individual column represented by the

points at which the soil hydraulic properties were measured, which is near the


Ž .points at which the suction cups at 80 cm were placed see Section 2.2.3 .Afterwards the field scale average and standard deviation were calculated. Asthe simulations were run for 57 points in each field, the results using thisapproach are subsequently referred to as ‘the 57 simulations’. Thus, both thevariation in the retention data as well as the hydraulic conductivity are expressedin 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

Ž .conductivity were calculated at discrete values of the tension head c .In order to obtain the stochastic mean of hydraulic conductivity, the statistical

Ž .properties means, covariances, variances were evaluated at discrete values ofŽ .the large-scale mean tension head H and the stochastic mean was calculated at

Ž .the same discrete values of H using Eq. 2 .

Ž .Fig. 2. Jyndevad. Effective hydraulic properties of retention a and b and hydraulic conductivitiesŽ .c and d . The stochastic mean with ls10 cm was nearly identical to the stochastic mean withls5 cm.


Ž .The vertical correlation length of the soil l was not known and had to beassessed. In order to evaluate the effect of different correlation lengths, twoestimates for each soil type were taken into consideration. The soil at Jyndevadwas more stratified than that at Rønhave and therefore we used l-values of 5cm and 10 cm at Jyndevad and 10 cm and 20 cm at Rønhave, similar in

Ž .magnitude to the applications by McCord et al. 1991 and Jensen and Man-Ž .toglou 1992 .

Fig. 2a–b and Fig. 3 a–b display the effective retention characteristics forJyndevad and Rønhave, respectively. The variance of the water content is largefor 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 conductivitiesfor Jyndevad and Rønhave, respectively. The arithmetic, estimated arithmetic,geometric and stochastic hydraulic conductivities are shown in the same figure

Ž .even if the variable on the first axis tension head is the deterministic c for thethree former and the stochastic H for the latter effective conductivity. The break

Ž .Fig. 3. Rønhave. Effective hydraulic properties of retention a and b and hydraulic conductivitiesŽ .c and d . The stochastic mean with ls10 cm was nearly identical to the stochastic mean withls20 cm.


Table 1Water balancea, yield and nitrogen balanceb at Jyndevad 1 April 1989–31 March 1990

Method

57 simulations Geometric Stochastic Arithmeticmean mean meanŽ .Mean S.D. range

ls5 cm ls10 cm

Ž . Ž .E mm 502 39 358–561 503 486 483 389aŽ . Ž .Percolation mm 519 35 474–645 517 540 540 589

y1Ž . Ž .Yield Mg ha 5.0 0.4 3.3–5.3 5.1 5.0 4.9 3.4Ž .N-uptake 168.9 10.5 116.5–181.3 172.2 172.2 171.5 109.8

y1Ž .kg N haŽ .Net mineralization 123.8 7.0 104.5–137.1 120.4 120.3 120.4 110.3

y1Ž .kg N haŽ .Denitrification 0.1 0.5 0.0–3.9 0.0 0.0 0.0 0.0

y1Ž .kg N haŽ .Leaching 79.0 14.4 61.0–143.5 70.1 71.7 71.9 123.3

y1Ž .kg N ha

a Precipitation and irrigation: 1007 mm; Ep: 600 mm.b Mineral fertilizer: 111 kg N hay1; deposition: 15.6 kg N hay1

of the curves at Hs0.20 in Fig. 3c–d is due to the log–linear interpolation inŽ .hydraulic conductivity between pFs1.3 and saturation see Section 2.2.3 . The

stochastic estimate tends to be extremely low at large tension heads, while the

Table 2Water balancea, yield and nitrogen balanceb at Rønhave 1 April 1989–31 March 1990

Method

57 simulations Geometric Estimated Stochastic Arithmeticmean arithmetic mean meanŽ .Mean S.D. range

meanls10 ls20cm cm

Ž . Ž .E mm 481 24 415–527 486 506 464 465 497aŽ . Ž .Percolation mm 293 29 243–406 284 265 305 300 274

y1Ž . Ž .Yield Mg ha 6.5 0.7 5.1–9.3 6.5 7.0 6.0 6.0 6.7Ž .N-uptake 189.8 7.8 169.7–208.7 190.1 193.1 187.4 188.0 193.1

y1Ž .kg N haŽ .Net mineralization 99.1 5.3 80.5–122.0 98.7 94.7 102.3 102.2 98.2

y1Ž .kg N haŽ .Denitrification 19.3 17.9 0.6–60.0 13.9 11.8 15.6 15.4 10.6

y1Ž .kg N haŽ .Leaching 35.1 15.0 8.5–61.7 38.1 34.8 42.5 41.8 39.5

y1Ž .kg N ha

a Precipitation: 770 mm; Ep: 622 mm.b Mineral fertilizer: 150 kg N hay1; deposition: 14.1 kg N hay1.


estimated arithmetic mean tends to increase unrealistically, most pronounced atJyndevad. Hence, we decided not to perform any model simulation employingestimated arithmetic conductivity at Jyndevad. The low stochastic mean isprobably due to the large variance of the hydraulic data. At large tension headsŽ .);10 m the stochastic theory is violated since the assumption of smallvariances in the lateral dimension is no longer valid.

Ž . Ž .Fig. 4. Jyndevad. Simulated and measured concentrations of NO –N mgrl y-axis at the 573

points.


3. Results

3.1. Simulated Õs. measured soil water content

At both locations, the simulated soil water content resulting from the differentapproaches generally matched the measured values at all depths except for the

Ž . Ž .Fig. 5. Jyndevad. Simulated concentrations of NO –N mgrl y-axis at the 57 points and using3

geometric mean, stochastic mean and arithmetic mean of hydraulic conductivity.


Ž .arithmetic mean at Jyndevad data not shown . The accumulated water balancesfor 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 observedŽ .variation Figs. 4 and 6 . At Jyndevad, the measured values at 25 cm were

slightly higher than simulated concentrations at the beginning of autumn whileat 80 cm the measured values were generally a little lower than the simulations,

Ž .except at the end of October Fig. 4 . At Rønhave, the simulated concentrationsŽ .at 25 cm were slightly higher during most of the winter period Fig. 6 . Further,

the size of the variation in the simulations and the observations was about theŽ .same at both locations Figs. 4 and 6 , except from November until January at

Jyndevad when the measured values showed significantly larger variation at 80cm compared with the simulations.

Ž . Ž .Fig. 6. Rønhave. Simulated and measured concentrations of NO –N mgrl y-axis at the 573

points.


3.3. Nitrate concentration and N-balance as affected by the methods of simula-tion

At Jyndevad, the temporal variation of the nitrate concentrations was gener-ally the same except for the simulation using the arithmetic mean, which

Ž .differed considerably from the other simulations Fig. 5 . In spring and at thebeginning of autumn, the simulated concentrations using the stochastic meanwere lower than those obtained using the geometric mean, most markedly so at25 cm. The simulations using a stochastic mean conductivity with ls5 and 10cm, respectively, were nearly identical except in spring, when the concentrations

Ž .with ls10 cm were slightly higher at the 25 cm depth Fig. 5 . Compared withnitrate concentrations from the 57 simulations, the simulations using the geomet-ric and stochastic means were slightly lower except in late autumn and winter

Ž . Ž .Fig. 7. Rønhave. Simulated concentrations of NO –N mgrl y-axis at the 57 points and using3

geometric mean, estimated arithmetic mean, stochastic mean and arithmetic mean of hydraulicconductivity.


Ž .Fig. 5 . These differences were also expressed in the accumulated nitrateŽ .leaching Table 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

Ž .compared with the 57 simulations Table 1 .At Rønhave, the temporal variation of the different approaches was the same

Ž .Fig. 7 . However, the simulated concentrations using the geometric, stochasticand arithmetic means were slightly higher during the main part of the periodcompared with the nitrate concentrations of the 57 simulations. Accordingly, theleaching was about the same for the four effective parameter approaches, andslightly larger than that resulting from the 57 simulations. The lower leaching of

Žthe 57 simulations was caused mainly by a higher level of denitrification Table.2 .

4. Discussion

The measurements of nitrate concentrations by the ceramic suction cups atJyndevad have been found to represent volume-averaged concentrationsŽ .Djurhuus and Jacobsen, 1995 equivalent to the simulated concentrations. Thus,as the field at Jyndevad was harrowed in autumn 1989 and because the effect ofsoil tillage on mineralization is not included in DAISY, the higher values ofmeasured concentrations compared with the simulations at 25 and 80 cm in

Ž .autumn 1989 at Jyndevad Fig. 4 were probably due to enhanced mineralizationŽ .through soil tillage Hansen and Djurhuus, 1997 . At Rønhave, where the effect

Žof soil tillage is expected to be more pronounced than at Jyndevad 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 slightlyŽlower than the actual volume-averaged concentrations Djurhuus and Jacobsen,

.1995 , the lower simulated concentrations at 25 cm compared with the observa-Ž .tions Fig. 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

Žmid-December to the beginning of January compared with the observations 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 totalprecipitation of 71 mm in this period, causing the suction cups at 25 cm to bebypassed, and the decrease in the simulations to be more pronounced than itactually was in the field. Macropore flow was probably also the reason why thesimulated water content at 80 cm at Rønhave reached field capacity mid-Decem-

Ž .ber, about 1 month before the measured values 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


on the N-processes and N-uptake could account for the main part of theŽ .variation Figs. 4 and 6 . The larger observed variation at Jyndevad from

November to January at 80 cm could be explained by finger-flow in the sandysoil expressed in the observations but not taken into account by the modelŽ .convection–dispersion equation .

Ž .The unrealistic results at Jyndevad using the arithmetic mean Fig. 5, Table 1are due to the fact that high values of hydraulic conductivity are given moreweight compared with the geometric mean. At Rønhave, the distribution of thehydraulic conductivity was less skewed so the arithmetic mean and the estimated

Ž Ž .. Žarithmetic mean Eq. 1 gave results similar to the other methods Fig. 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 isadequate as an effective parameter for hydraulic conductivity.

The fact that geometric and stochastic means of hydraulic conductivity gaveŽnearly similar and realistic results at both locations Figs. 5 and 7, Tables 1 and

.2 must be due to the fact that percolation was mainly vertical and that theprerequisites for using the geometric and stochastic means are valid or of lesssignificance. As both fields are rather flat and as no trend could be detected in a

Ž .geostatistical analysis of texture data not shown , lateral stationarity must haveŽ .been valid for both fields. As discussed by Kim and Stricker 1996 , the lateral

correlation length for the hydraulic properties of fields of our size or larger, canbe assumed to be relatively small compared with the entire flow domain, and sois the vertical correlation length compared with the lateral correlation length.Although it is not possible to estimate the vertical correlation length from ourdata, the chosen values, 5–10 cm at Jyndevad and 10–20 cm at Rønhave, must

Ž .thus be regarded as realistic Figs. 5 and 7 . The vertical correlation length mustŽalso be small compared with the vertical scale of each soil layer Jensen and

.Mantoglou, 1992; Mantoglou, 1992 . This has only been partly the case in ourstudy. Further, although the assumption that EHrEzf0 is clearly violatedduring the summer periods, the simplification of this gradient in the stochastic

Ž .approach see Section 2.4.1 does not seem to be significant. Hence, both thegeometric and the stochastic means can be used as effective parameters for areassimilar to our fields and the choice may therefore depend on the purpose of theanalysis and the data available. By use of the stochastic approach it is possibleto calculate an estimate of the variation for the local mean capillary head and the

Ž .soil moisture content Jensen and Mantoglou, 1992; Mantoglou, 1992 . Hence,the stochastic approach may be preferred if the variance as well as the mean ofsoil water is wanted. However, for reliable estimation of the variances andcovariances in the stochastic approach, a relatively large data set should beavailable.

Generally, the use of geometric and stochastic means gave similar results asŽ .the average of the 57 simulations Figs. 5 and 7, Tables 1 and 2 , and thus both

the concept of an ensemble of non-interacting columns and the concept of an


equivalent soil column seem reasonable, in agreement with Jensen and Refs-Ž .gaard 1991 , who evaluated the two approaches for water content and soil water

suction. The use of effective hydraulic parameters is to be preferred to reducethe number of simulations.

In our study we used a larger dataset representing the field conditionsŽcompared with previous applications Jensen and Mantoglou, 1992; Sonnenborg

.et al., 1994 and thus we have a good database for evaluating the stochasticŽ . Ž .approach. Both Jensen and Mantoglou 1992 and Sonnenborg et al. 1994

compared observed water content and suction with simulations using theŽ .stochastic and the geometric means. Jensen and Mantoglou 1992 included the

variation of EHrEz in their investigation, which was carried out for a field of0.5 ha also situated at Jyndevad, close to our field, while Sonnenborg et al.Ž . 21994 made their simulations for a catchment of 1 km , discretized intoelements of 25 m by 25 m for the catchment model MIKE SHE, and assumingEHrEzf0. Both studies concluded that the stochastic approach gave betterresults than the geometric mean. However, the differences between the twoeffective parameter approaches in both investigations were relatively small andthe results were ambiguous.

5. Conclusion

The simulations of the soil water dynamic, nitrate concentration and nitrateleaching by the stochastic approach and the geometric mean were similar to theapproach of assuming that the field is composed of a number of one-dimensionalnon-interacting columns, and generally all three approaches matched the ob-served nitrate concentrations. Hence, to simplify the calculations, the geometricmean can be used for simulations of mean nitrate leaching at field scale.

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