VZJ sign up for etocs
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 26 April 2005
Published in Vadose Zone J 4:240-254 (2005)
DOI: 10.2136/vzj2004.0070
© 2005 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via ISI Web of Science (1)
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Herbst, M.
Right arrow Articles by Vereecken, H.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Herbst, M.
Right arrow Articles by Vereecken, H.
GeoRef
Right arrow GeoRef Citation
Agricola
Right arrow Articles by Herbst, M.
Right arrow Articles by Vereecken, H.
Related Collections
Right arrow Lysimeter/Rhizosphere Studies
Right arrow Pesticides
Right arrow Coupled Flow/Transport Models

ORIGINAL RESEARCH

Intercomparison of Flow and Transport Models Applied to Vertical Drainage in Cropped Lysimeters

M. Herbsta,*, W. Fialkiewiczb, T. Chenc, T. Pütza, D. Thiéryb, C. Mouvetb, G. Vachaudd and H. Vereeckena

a Agrosphere Institute ICG-IV, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany
b Bureau de Recherches Geologiques et Minieres, BRGM, Avenue Claude Guillemin F 45060 Orleans Cedex 02, France
c ISRN\DPRE\SERLAB\LMODE, CEN Cadarache 13115 St Paul-Lez-Durance, France
d Laboratoire d'etude des Transferts en Hydrologie et Environnement, LTHE (UMR CNRS 5546, UJF, INPG, IRD), BP53, 38041, Grenoble CX 09, France
* Corresponding author (m.herbst{at}fz-juelich.de)

Received 30 April 2004.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 METHODS AND DATA
 RESULTS
 DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Models predicting flow and transport in the vadose zone differ in their conceptual approach, their complexity, and their mathematical formulation. Four models (MARTHE, TRACE, ANSWERS, and MACRO), which differ significantly in their model concepts and complexity, were applied to a common data set to evaluate and compare the different model approaches. Five free-draining lysimeters, cropped with winter wheat, barley, and oat were used to monitor actual evapotranspiration, soil moisture, and drainage for 627 d. One of the five lysimeters was also treated with methabenzthiazuron (MBT), and soil residues as well as leaching were experimentally determined. In Europe, MBT has been commonly used as a herbicide for almost 30 years. Generally, the use of given model inputs is recommended, apart from plant parameters, which need calibration. The use of validation criteria revealed proper simulation of water flow for the four models. After calibration, the Richards' equation–based models MARTHE, TRACE, and MACRO performed better for water flow predictions than the capacity-based ANSWERS. A small amount of preferential flow, which is not included in the model structures of MARTHE, TRACE, and ANSWERS, did not influence the simulation of water flow significantly. But preferential flow was associated with the leaching of 0.0059% of the applied mass of MBT, causing relevant concentrations in the leachate. Leaching could be described well with MACRO after calibration. The difficulty of estimating parameters for modeling macropore transport is seen as an obstacle to common application.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
METHODS AND DATA
 RESULTS
 DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
DURING THE PAST several decades an increasing number of water bodies have been found contaminated with pesticides in various areas worldwide. Pesticide fate models are now increasingly used as tools for risk assessment and registration purposes. These models differ in their conceptual approach, in their degree of complexity for the description of subprocesses, and in their mathematical formulation. Therefore, four models were selected, which cover a broad range of model complexity and concepts, to apply to a common data set, consisting of leaching experiments conducted in cropped lysimeters. Application of the four models MACRO, TRACE, MARTHE, and ANSWERS thus allows a comparison and evaluation of different model concepts concerning water flow and pesticide transport in the unsaturated zone at the local scale.

MARTHE and TRACE are two computer codes originally developed for the description of three-dimensional groundwater transport at regional scales (Thiéry, 1995; Yeh et al., 1992). They have recently been extended to pesticide transport from the soil surface to groundwater (Mouvet et al., 2004). TRACE, which allows the computation of variably saturated water flow, is an extension of 3DFEMWATER (Yeh et al., 1992). MACRO is a one-dimensional model accounting for dual-porosity. This model was previously used in several model comparison studies on pesticide fate (Bergström and Jarvis, 1994; Diekkrüger et al., 1995b; Vink et al., 1997; Vanclooster et al., 2000). In these studies MACRO has proved broad applicability to several pesticide transport problems. During this study we used version 5.0, which incorporates modified soil physical parameterizations (Larsbo et al., 2005). ANSWERS is a capacity-based regional scale model for the vadose zone transport of solutes. This model was earlier evaluated against other agricultural nonpoint source water quality models (Kosky and Engel, 1997).

All the above four models are applicable to regional scale problems. They were all used within the framework of the EU Project PEGASE (Pesticides in European Groundwaters: detailed study of representative aquifers and simulation of possible evolution scenarios, Mouvet et al., 2004). The concepts of the four models evaluated here are rather contrasting (Table 1). MACRO is the only model accounting for preferential flow and transport. Except for ANSWERS, all models are based on the Richards' equation for calculating soil water flow. MACRO and ANSWERS solve the convection–dispersion equation (CDE) with a common numeric scheme, whereas TRACE is coupled with 3dLEWASTE, which uses a hybrid Lagrangian–Eulerian method to solve the CDE. For pesticide degradation, only TRACE coupled with 3dLEWASTE uses a simple first-order kinetics approach, whereas the other models allow the use of a soil temperature and moisture dependent biodegradation approach.


View this table:
[in this window]
[in a new window]
  		Table 1. Considered processes and related modeling approaches of the four codes used in this study.

 
Large undisturbed lysimeters are a common experimental setup for investigations of pesticide transport (Bergström, 1990; Boesten, 1994; Keller and Weber, 1995; Vink et al., 1997; Schoen et al., 1999; Mikata et al., 2003); they are often used also for pesticide registration purposes. The representativeness of lysimeter observations for the field-scale behavior of transport processes is still being debated. Comparing to field measurements with suction plates, Jene et al. (1997) measured 40% more bromide leaching in lysimeters. Comparative modeling of pesticide transport has been the subject of several studies, mainly with a focus on registration purposes. Model comparisons of pesticide transport have been performed for lysimeters (Bergström and Jarvis, 1994; Vink et al., 1997; Francaviglia et al., 2000) as well as for field studies (Pennel et al., 1993; Diekkrüger et al., 1995b; Armstrong et al., 2000; Gottesbüren et al., 2000; Tiktak, 2000; Vanclooster and Boesten, 2000). The most recent and probably most extensive model comparison was summarized by Vanclooster et al. (2000). The major outcome of this comparative pesticide study involving simulation of both lysimeter and field data by Armstrong et al. (2000), Francaviglia et al. (2000), Gottesbüren et al. (2000), Tiktak (2000), and Vanclooster et al. (2000) is what Diekkrüger et al. (1995b) also stressed: the influence of the modelers' experience on model results is great, probably greater than the influence of the selected model concept. Bergström and Jarvis (1994) found very similar results for the five models included in their comparison. They also noted that, besides accounting for the relevant processes, proper identification of model input parameters is critical to accurately predicting pesticide transport.

Preferential flow and solute transport due to soil cracking (Vink et al., 1997; Ghidey et al., 1999) or earthworm activity (Shipitalo and Gibbs, 2000) has been reported by several authors. Kladivko et al. (1991) detected carbofuran, atrazine, cyanazine, and alachlor in subsurface drains within three weeks after application, whereby the detected pesticide amount was related to the degree of sorption. Kumar et al. (1998) was able to predict the observed atrazine leaching only after taking the preferential flow component of the Root Zone Water Quality Model into account, whereas Jaynes et al. (2001) were unable to predict the leaching of two herbicides by using a two-dimensional, convective–dispersive model without an explicit preferential flow component. Due to the interaction of chemical properties such as the sorption coefficient with macropore geometry, volume, and connectivity, predictions of the preferential transport of pesticides are rather difficult. Thus, a model calibration is usually required (Vink et al., 1997; Kumar et al., 1998; Francaviglia et al., 2000; Aden and Diekkrüger, 2000). Nevertheless, an increasing number of models used for registration purposes were equipped with a macropore module (e.g., Jarvis et al., 2003). This study has two main objectives: (i) to evaluate the models MACRO, TRACE, MARTHE, and ANSWERS for simulating water flow and MBT transport, and (ii) to compare the performance in terms of the different model concepts included in these codes.


   METHODS AND DATA
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND DATA
RESULTS
 DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Experimental Data
Five undisturbed soil monoliths (free-draining lysimeters) containing an Orthic Luvisol were used to monitor the soil water balance. The monoliths were 1.1 m deep and had a surface area of 1.0 m2. Three pedogenetic soil horizons were distinguished (Table 2). One of the lysimeters was treated with a dose of 2.8 kg ha–1 TRIBUNIL (Bayer, Germany) during the pre-emergence period of winter wheat on 25 Nov. 1988. This dose corresponds to an active ingredient application of 248.11 mg m–2 [phenyl-U-14C]methabenzthiazuron. The winter wheat (Triticum aestivum L.) was harvested and four parallel samples were taken in the lysimeter with a hand auger on 3 Aug. 1989 (252 d after application). Before MBT extraction, the four samples were mixed for every vertical 10 cm section. In the following vegetation period, winter barley (Hordeum vulgare L.) was cropped and harvested on 11 May 1990. The next vegetation was oat (Avena sativa L.), which was harvested on 13 Aug. 1990, at which time a second soil sampling was performed 627 d after application. Again, four samples were taken and mixed for the 10 cm sections. All lysimeters followed the aforementioned crop rotation. The crops were treated according to common farming practice.


View this table:
[in this window]
[in a new window]
  		Table 2. Physical and chemical properties of the Orthic Luvisol.

 
From 25 Nov. 1988 until 13 Aug. 1990 the meteorological variables precipitation, air humidity, air temperature, wind speed, and radiation were monitored on a daily basis (Fig. 1) . Soil moisture was measured approximately every 4 to 5 d with a neutron probe at depths of 25, 35, 55, 75, and 85 cm. Leachate was collected on a five-week basis. The amount of lysimeter drainage could be measured directly, while actual evapotranspiration Eta (mm) was calculated from the soil water balance,

[1]
where P is the measured precipitation (mm), D is the measured drainage (mm), and {Delta}{theta} is the change of soil moisture (mm) during the considered period of time. Changes in soil moisture were calculated from the neutron probe measurements at five depths.



View larger version (39K):
[in this window]
[in a new window]
  		Fig. 1. Measured atmospheric conditions and calculated reference evapotranspiration rates during the experimental period.

 
Methabenzthiazuron has been commonly used for almost 30 yr in Europe as an effective herbicide for grain and certain vegetable crops. Having laboratory determined half-lives of up to 75 d (Rouchaud et al., 1988), MBT is a rather persistent compound. Furthermore, having a sorption coefficient Kd of 6.0 cm3 g–1 (Diekkrüger et al., 1995a), MBT could be classified as a higher sorptive compound. Methabenzthiazuron was extracted from the soil with acetone–ethyl acetate–chloroform. Using thin-layer chromatography the detection limit of 14C-labeled MBT was 0.67 µg L–1.

TRACE and 3dLEWASTE
TRACE (Vereecken et al., 1994) simulates three-dimensional unsaturated–saturated water flow in porous media. For this study the model was run in a one-dimensional mode. A modified Picard-iteration scheme (Celia et al., 1990) was used in combination with a preconditioned conjugate gradient method to solve the following Richards' equation numerically,

[2]
where K is the hydraulic conductivity (L T–1), x is the vertical coordinate (L), h is the pressure head (L), Q is the source/sink term (T–1), {theta} is the soil water content (L3 L–3), t is time (T), Sh is the specific storage coefficient (L–1), and Fh is the specific water capacity (L–1). For the spatial discretization, hexahedral Galerkin-type finite elements were used.

To take plant-related processes into account the crop growth module SUCROS (Simplified and Universal Crop growth Simulation, Spitters et al., 1988) was implemented. In contrast to many other plant modules (e.g., MACRO [Larsbo et al., 2005], PEARL PEARL [Tiktak et al., 2000] and SIMULAT SIMULAT [Aden and Diekkrüger, 2000]) SUCROS estimates the assimilation rate from plant specific photosynthesis parameters and radiation. The calculated increase in biomass is used to predict leaf area growth and leaf area index (LAI), which is therefore not a model input. The required plant data values can be found in van Heemst (1988), among others. The crop coefficients (Kc values) for scaling of the reference evapotranspiration were assigned to different seasonal stages according to the approach of Doorenbos and Pruitt (1977). Based on LAI, the potential evapotranspiration was split into the fractions of potential evaporation and potential transpiration according to Beer's law (Ritchie, 1972). The actual transpiration was calculated from the potential transpiration as a function of the pressure head according to the approach of Feddes et al. (1978). For the soil evaporation, a flux boundary was applied to the uppermost element until a given minimum pressure head hmin was reached (e.g., –10–4 cm). At this point TRACE switches to a fixed head boundary condition set to hmin.

3dLEWASTE (Yeh et al., 1992) is a hybrid Lagrangian–Eulerian finite element model of reactive solute transport through unsaturated–saturated media. 3dLEWASTE numerically solves the Lagrangian form of the CDE, which can be written for the one-dimensional case as:

[3]
where C is the solute concentration (M L–3), dC/dt is the material derivative of C with respect to time t, D is the dispersion coefficient (L2 T–1) and x* is the location of the fictitious particle [L] representing the chemical travelling at a velocity of V (L T–1). The advection term was solved in a mobile (Lagrangian) coordinate system using single step reverse particle tracking, while the diffuse term was solved in a fixed (Eulerian) coordinate system. A backward differencing scheme in time was applied. A more detailed description of the hybrid Lagrangian–Eulerian approach can be found in Yeh et al. (1992). For microbial decay, a first-order degradation rate coefficient was applied to the sorbed and the liquid concentrations. A linear, Freundlich, or Langmuir isotherm can be used for sorption. For simplicity, the coupled TRACE–3dLEWASTE model is referred to as "TRACE" throughout the following text.

ANSWERS
The Areal Nonpoint Source Watershed Environmental Response Simulation, ANSWERS (Bouraoui et al., 1997), is originally a watershed-scale, diffuse-pollution model designed for long-term simulations. The core of the system is a one-dimensional vertical model based on a capacity approach for the soil water flux. A variable vertical discretization was used for the water flow part and the solute transport part. Infiltration into the uppermost layer was simulated with the Green and Ampt equation (Green and Ampt, 1911). Soil water redistribution from the upper layer of soil to the root zone (discretized into a maximum of nine layers) was determined with the help of a Brooks and Corey–type equation (Brooks and Corey, 1964) on the basis of vertical downward gravity flow, with a hydraulic conductivity related to the average water content of the upper layer. Similarly, percolation from the root zone to the underlying unsaturated zone (drainage) was determined using a hydraulic conductivity related to the average water content of the root zone. The main parameters describing the hydraulic properties of the soil were the saturated hydraulic conductivity Ks (cm h–1), the porosity {Phi} (cm3 cm–3), the residual water content {theta}r (cm3 cm–3), the pore size distribution index {lambda}b (-), the bubbling pressure {psi}b (cm), and the field capacity Fc (cm3 cm–3). They were obtained from soil texture and organic matter content using the pedotransfer functions of Rawls and Brakensiek (1989).

Soil evaporation and plant transpiration were modeled separately using Ritchie's equation (Ritchie, 1972), where soil evaporation is related to the soil moisture of the upper layer and the LAI (m2 m–2). Plant transpiration was extracted from the root zone assuming a uniform root profile. The parameters describing plant behavior in terms of water uptake and actual evapotranspiration were obtained from a database including 78 different types of crop (Knisel and Davis, 1999). Values of the LAI and root depth need to be given for phenological stages from sowing to harvest.

The transport of solutes was calculated with the CDE. For sorption, degradation, and plant root uptake of pesticides the approach of ANSWERS is similar to that of GLEAMS (Knisel and Davis, 1999). For the degradation of pesticides we alternatively used an equation of Graham-Bryce et al. (1982) accounting for soil temperature and soil moisture dependent decay:

[4]
where {lambda} is the degradation rate (d–1), T is the soil temperature (°K), M is the gravimetric soil moisture (%), and a (-), b (-), and g (°K) are parameters.

MACRO
MACRO 5.0 (Jarvis et al., 2003, Larsbo et al., 2005) is a one-dimensional dual-permeability model, operating at the scale of a soil profile. The model accounts for preferential flow and transport in soil macropores by dividing the soil pore system into two parts, one part with a high flow and low storage capacity (macropores) and the remainder with a low flow and a high storage capacity (micropores). The boundary between the pore regions is defined by the fixed pressure head Cten (L) having a corresponding water content {theta}b (L3 L–3) and corresponding hydraulic conductivity Kmi (L T–1). The one-dimensional form of the Richards' equation is used to model flow in the micropores. The equation is similar to Eq. [2], except for the specific storage coefficient Fh, which is equal to {partial}{theta}/{partial}h. The equation is solved in MACRO using finite differences based on the implicit iterative procedure proposed by Celia et al. (1990). Soil water retention and unsaturated hydraulic conductivity are calculated using a modified form of the Mualem–van Genuchten approach (van Genuchten, 1980; Vogel et al., 2001) accounting for the macropore–micropore dichotomy by using the boundary pressure head partitioning the total porosity into micropores and macropores (Wilson et al., 1992; Mohanty et al., 1997). Flow in the macropores is calculated using the kinematic wave equation (Germann, 1985), assuming gravity-dominated flow (i.e., neglecting capillarity). The hydraulic conductivity function in the macropores is given as a simple power law expression of the macropore degree of saturation.

MACRO uses the following one-dimensional CDE for solute transport in the micropores:

[5]
where the source–sink term Ui (M L–3 T–1) represents different processes like mass exchange between the flow domains, kinetic sorption, solute uptake by the crop, biodegradation, and lateral leaching losses to drains or groundwater. In Eq. [5], S is the sorbed concentration (M L–3), fmac is the mass fraction of solid material in contact with water in the macropores (-), fne is the fraction of the solid material providing nonequilibrium sorption (-), {rho}b is the soil bulk density (M L–3), {theta}m is the mobile water content (L3 L–3), q is the water flow (L T–1) and D is the dispersion coefficient (L2 T–1). Transport in the macropores is calculated neglecting dispersion–diffusion, but accounting for adsorption by using the parameter fmac that partitions the sorption constant between the two flow regions. Diffusive mass exchange between the two pore regions is calculated using approximate first-order equations based on an effective diffusion path length ascale (L). Solute transport is solved by means of a Crank–Nicolson finite difference scheme utilizing an iterative, fully upstream weighting procedure with an empirical correction for numerical dispersion.

Root water uptake in MACRO is calculated from the evaporative demand, the root distribution and soil moisture using a modified version of the approach developed by Feddes et al. (1978) accounting for water stress compensation (Jarvis, 1989). It is assumed that the crop can adjust to stress in one part of the root system by increasing uptake from other parts where the soil moisture conditions are more favorable. Root density is assumed to be distributed logarithmically with depth. Beer's law is used to partition the potential evapotranspiration into one fraction transpired by the canopy and the remaining fraction of evaporation from the soil. This is based on the green and total LAIs, given as a function of the day number in the year as user-specified input.

The heat conduction equation in MACRO is solved using a standard Crank–Nicholson finite difference scheme. The effect of soil moisture and temperature on the first-order kinetics degradation of pesticides is estimated with the approach of Boesten and van der Linden (1991):

[6]
where {lambda} is the degradation rate coefficient (d–1), {lambda}ref is the reference rate coefficient (d–1), {theta}ref is the reference water content (cm cm–3), T is the soil temperature (°C), Tref is the reference temperature (°C), and {alpha} (°C–1) and ß (-) are empirical parameters. The pesticide uptake by the roots is modeled as a function of root water uptake and pesticide concentration. An empirical concentration factor is used to define the fraction of pesticide concentration taken up by the roots.

MARTHE
MARTHE (Modelling Aquifers with an irregular Rectangular grid, Transport Hydrodynamics and Exchanges) was originally developed as a three-dimensional groundwater model designed to compute water flow and solute transport in saturated porous media (Thiéry, 1995). Additional routines allow the computation of unsaturated flow. MARTHE also solves the Richards' equation numerically using a fully implicit scheme with a three-dimensional finite difference discretization. For the vadose zone, the Richards' equation is solved using prescribed retention and relative hydraulic conductivity functions (van Genuchten, 1980; Gardner, 1958). Advective, diffusive, and dispersive transport is computed simultaneously with the hydraulic calculation. Mass transport is simulated using a total variation diminishing (TVD) scheme. Calculations for energy, temperature, mass, and water fluxes are performed in a fully coupled manner within the model.

The main features of the plant module (Thiéry and Golaz, 2002) are very similar to MACRO. The evolution of the LAI is a function of the main development stages (i.e., germination, maturity, and harvest). As for MACRO, an exponential function is used to divide potential evapotranspiration into transpiration and evaporation. Canopy interception is not considered. Linear growth from germination until maturity is assumed for the development of root depth. Between maturity and harvest the specified maximum root depth remains constant. The root density can be calculated using several functions. During this study an exponentially decreasing root density was assumed. For estimation of actual transpiration, reductions according to a water stress compensation concept (Jarvis, 1989) are taken into account.

The root uptake of solutes is simply calculated by means of a solution uptake factor (-) describing the fraction of mass lost to root uptake by plants. Solute degradation is described using a temperature and soil moisture dependent first-order decay term or assuming simple first-order decay (Thiéry et al., 2004). For soil temperature and moisture dependent first-order decay, a parameterized Graham-Bryce approach (Graham-Bryce, 1982) or the concept of Boesten and van der Linden (1991) can be used.

Model Input
The functional relation between pressure head, soil water content, and unsaturated hydraulic conductivity plays a key role in modeling water flow (Vereecken and Kaiser, 1999; Herbst and Diekkrüger, 2002). MARTHE and TRACE use the soil water retention function of van Genuchten (1980) with the parameter m = 1, which is equivalent to an equation proposed by Brutsaert (1966):

[7]
where {theta} denotes the water content (cm3 cm–3), h is the pressure head (cm), {theta}r is the residual water content (cm3 cm–3), {theta}s is the water content at saturation (cm3 cm–3), {alpha} is the inverse of the bubbling pressure (cm–1), and n is a dimensionless shape parameter (-).

By assuming m = 1 instead of m = 1 – 1/n, the closed-form analytical expression of the Mualem–van Genuchten approach (van Genuchten, 1980) for the K(h) function cannot be used. Therefore, the unsaturated hydraulic conductivity function of Gardner (1958) was adopted:

[8]
where K is the unsaturated hydraulic conductivity (cm d–1), Ks is the saturated hydraulic conductivity (cm d–1), and b (cm–1) and c (-) are empirical parameters. The soil hydraulic parameters listed in Table 3 were determined by Vereecken and Kaiser (1999) from the soil properties listed in Table 2 using the pedotransfer functions (PTF) of Vereecken et al. (1989)(and 1990) and fitted {theta}r and {alpha} values. The PTFs of Vereecken et al. (1989)(and 1990) are based on Eq. [7] and [8]. TRACE and MARTHE allow the use of these functions, while MACRO is based on the common Mualem–van Genuchten approach (with m = 1 – 1/n), but modified for the dual porosity approach (Wilson et al., 1992; Mohanty et al., 1997; Vogel et al., 2001). To obtain comparable soil hydraulic functions for the Richards' equation–based models, the retention and unsaturated hydraulic conductivity functions for MACRO (Mualem–van Genuchten, m = 1 – 1/n) were derived in a two-step procedure. First {theta}r, {theta}s, {alpha}, n, and Ks were fitted to the already available functions (with m = 1) using the least squares procedure of RETC (van Genuchten et al., 1991). In a second step, the parameters defining the macropore system were calibrated. For ANSWERS, soil hydraulic parameters like Ks and field capacity were calculated internally with the PTFs of Rawls and Brakensiek (1989) from the properties given in Table 2. The initial values for the soil moisture content or pressure head for the simulations were derived from neutron probe measurements.


View this table:
[in this window]
[in a new window]
  		Table 3. Retention and unsaturated hydraulic conductivity parameters for the soil horizons of the Orthic Luvisol.

 
All models assumed that sorption of MBT could be described with a linear isotherm. The values of the distribution coefficient Kd (cm3 g–1) were calculated from a partitioning coefficient Koc of 527 cm3 g–1, taken from the Agritox database (http://www.inra.fr/agritox; verified 11 Jan. 2005), and the organic matter content assuming Kd = Kocfoc. The resulting Kd for the 0 to 0.4, 0.4 to 0.6, and 0.6 to 1.1 m soil horizons were 5.27, 2.11, and 1.58 cm3 g–1, respectively. Thus the retardation factor calculated for the top horizon at saturation was 21.2, indicating considerable sorption of MBT. MARTHE and ANSWERS implemented a temperature and soil moisture dependent degradation rate based on the equation of Graham-Bryce et al. (1982) given by Eq. [4]. From batch experiments, Wüstemeyer (2000) found the following parameters for MBT:

[9]
from which the half-life (DT50) can be calculated as follows:

[10]

3dLEWASTE does not account for temperature or soil moisture dependent degradation. For this model we assumed a first-order decay process with a DT50 of 200 d found by calibration. To use this DT50 in MACRO, its value has to be converted into a DT50 at reference conditions. By using {alpha} = 0.01 K–1, ß = 0.2 (Eq. [6]), the mean measured soil temperature at 10 cm depth and the mean measured soil moisture content at 25 cm depth , we calculated a DT50 for reference conditions (Tref = 20°C and {theta}ref = 0.39) of 162 d according to the approach of Boesten and van der Linden (1991). This DT50 was subsequently used in MACRO. Figure 2 shows a comparison of the Graham-Bryce approach with the Boesten and van der Linden approach. Results indicate that the Boesten and van der Linden approach with a reference DT50 of 162 d yields half-lives that are 2 to 4.5 larger than those obtained with the Graham-Bryce equations. If biodegradation is a major process controlling MBT fate in the lysimeters, then the remaining mass of MBT in the soil thence should be smaller for MARTHE and ANSWERS, which use the Graham-Bryce approach, than for MACRO and TRACE, which invoke a higher DT50 value. For the four models the degradation rate for sorbed and dissolved MBT was assumed to be the same. The dispersion length was assumed to be 1.7 cm for all four models.



View larger version (32K):
[in this window]
[in a new window]
  		Fig. 2. Isoline plot of soil temperature and moisture dependent DT50 for methabenzthiazuron (MBT) calculated according to Graham-Bryce (Wüstemeyer, 2000) and Boesten and van der Linden (1991), with reference DT50 = 162 d, {theta}ref = 0.39 cm3 cm–3, {alpha} = 0.01 K–1, ß = 0.2, and Tref = 20°C (Eq. [6]). Volumetric water contents were transformed to gravimetric values using a topsoil bulk density of 1.57 g cm–3.

 
MACRO, MARTHE, and ANSWERS calculate the soil temperature from the daily mean air temperature by solving the equation of heat diffusion and convection. For MARTHE, the mineral thermal conductivity was set to 1.5 W m–1 °C–1, the water thermal conductivity to 0.6 W m–1 °C–1, the mineral volumetric specific heat to 2 x 106 J m–3 °C–1 and the water specific heat to 4185 J kg–1 °C–1. MACRO uses the approach of Jansson (1991) to estimate thermal conductivity and volumetric heat capacity from the soil properties summarized in Table 2.

The potential reference evapotranspiration ETp (Fig. 1) was calculated according to the approach of Penman and Monteith (Monteith, 1975). Potential evapotranspiration and precipitation were used as the upper boundary condition, whereas a seepage face was applied to the lower boundary at the bottom of the lysimeter. A seepage face boundary is characterized by a no-flow boundary for unsaturated conditions:

[11]
If the seepage face becomes saturated, the boundary changes to a prescribed head boundary with h(z,t) = 0.

The spatial discretization for MACRO, MARTHE, and TRACE consisted of 110 elements of 1-cm thickness each. Due to the adopted infiltration approach according to Green and Ampt (1911), the spatial discretization for ANSWERS required a thickness of 40 cm for the uppermost element, while eight elements of 8.75 cm each were used in the subsurface.

Model Calibrations
The previous section describes the various input data for the models, except for the plant parameters. Since no measurements or estimates of plant parameters were available, some calibration of the values taken from the three plant databases was essential. Except for the known harvest and sowing dates, a stepwise calibration procedure was performed for the plant parameters. The calibration was performed using measured evapotranspiration and drainage rates, and soil moisture contents at 25 and 85 cm depths. The calibration was terminated individually by the various model users, if the agreement between model result and measurement of each stepwise variable was judged to be sufficient. Table 4 summarizes the calibrated and the original values of three selected parameters. Changes in the LAI due to calibration were negligible. More substantial changes were necessary to the root depth, which defines the zone of the soil where transpiration directly influences the soil moisture, and the crop conversion factor Kc, which determines the ETp rate. Among the three plant parameters listed in Table 4, the largest differences between calibrated and uncalibrated plant parameters values occurred for Kc. For TRACE and MACRO the Rd and Kc values were significantly modified during the calibration procedure to improve predictions of the water balance. The same was true for MARTHE, except that the changes in Kc were slightly smaller. Several other parameters used in MACRO and TRACE also required further calibration. For MACRO, the parameters defining the macropore system were calibrated against measured MBT concentrations in the drainage water. The key soil physical properties for calibration of macropore flow were found to be the saturated hydraulic conductivity of the soil matrix Kmi (cm d–1) and the boundary pressure head Cten (cm). The default value of 2 cm for ascale was unchanged during calibration, while the default value of –12 cm for Cten was changed to –27 cm for the uppermost soil horizon. For this horizon Kmi was set to the smallest value among the three horizons (Table 3). Apart from calibration of the macropore parameters against the water balance components, the fraction of sorption sites in the macropores was calibrated using measured MBT leaching rates. Parameter fmac was set to 0.005, which corresponds to a small macropore volume fraction ({theta}s–{theta}b, Table 3). The default value of fmac was 0.02. For TRACE the measurements of soil residues 252 and 627 d after application revealed that the laboratory determined DT50 value of 75 d for MBT (Rouchaud et al., 1988) was not appropriate. Thus a stepwise calibration was performed also for this parameter.


View this table:
[in this window]
[in a new window]
  		Table 4. Calibrated values of the leaf area index (LAI), root depth, and the crop conversion factor. The uncalibrated values are given in parentheses.

 
Validation Criteria
A commonly used criterion for model validation is the root mean square error (RMSE). The RMSE has the unit of the considered variable. The squared residuals are also used for a second criterion used in this study, the coefficient of model efficiency (CME, Nash and Sutcliffe, 1970), which determines the proportion of the deviation from the observed mean that can be explained with the model:

[12]
where xo is the observed value at time t, xs is the simulation result at time t, and is the arithmetic mean of the observed values. The CME is a dimensionless criterion. Values between –{infty} and 1 can be calculated for this index, the latter indicating that observation and model are completely in agreement. We additionally used the Index of Agreement (IA, Willmott, 1981), which is also dimensionless and ranges between 0 and 1:

[13]

Because CME and IA are dimensionless, they can be used to compare the model quality of different variables, while the RMSE gives a measure of the model error in the units of the variable being considered. RMSE, CME, and IA are common validation criteria, previously used by Vanclooster et al. (2000), Jarvis et al. (2003), and Herbst and Diekkrüger (2002), among others.


   RESULTS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND DATA
 RESULTS
DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
Water Flow
The total water balance (Table 5) was adequately reproduced by TRACE. ANSWERS slightly overestimated the total amount of actual evapotranspiration ETa, whereas the other models slightly underestimated the total ETa. The amount of drainage was reproduced well with the four models. Relative to the amount of precipitation (1067 mm), the errors for single water balance components are acceptable, ranging between 1.6 and 63.7 mm. The relative error in the change in soil water storage was quite high for ANSWERS, MARTHE, and MACRO; 78% too high for ANSWERS, 49% too low for MARTHE, and 41% too low for MACRO. If an accurate description of the main processes is important, apart from the overall water balance, then a good match is needed of the temporal evolution of the water balance components. Figure 3 shows a comparison between observed and modeled cumulative actual evapotranspiration. In general, the four models provide a good match with the measurements, which exhibit only small standard deviations, except for two drying periods with high evapotranspiration demands. During the first spring period (between Days 180 and 250) all of the models slightly underestimated the amount of actual evapotranspiration. This is reversed for the second period (spring 1990, between Days 520 and 600), when MARTHE and MACRO showed a too early and too low increase in the actual evapotranspiration rate. ANSWERS simulated this increase too early and at a too high overall rate. The coefficient of model efficiency (CME) for the measured and simulated actual evapotranspiration rates reveals that ANSWERS, MACRO, and MARTHE are very similar in terms of their ability to reproduce evapotranspiration, while TRACE shows the highest CME and IA (Table 6), which is mostly due to a better fit of the measurements during spring 1990.


View this table:
[in this window]
[in a new window]
  		Table 5. Measured and modeled water balance for the model period. The amount of precipitation was 1067 mm. The error (mm) between model result and related measurement is given in parentheses. The change in soil moisture {Delta}{theta} pertains to the entire profile to a depth of 1.1 m.

 


View larger version (13K):
[in this window]
[in a new window]
  		Fig. 3. Cumulative measured and predicted actual evapotranspiration rates. Bars indicate standard deviations of the measurements.

 

View this table:
[in this window]
[in a new window]
  		Table 6. Root mean square error (RMSE), coefficient of model efficiency (CME), and index of agreement (IA) for the measured drainage, actual evapotranspiration ETa, soil moisture at 25 and 85 cm depths, and soil temperature at 10 cm depth.

 
A comparison of calculated and observed volumetric soil moisture at two depths is shown in Fig. 4 . The first significant deviations, both between the models and between the observed and modeled values at a depth of 25 cm occur during the drying period of spring 1989 (between Days 180 and 250). During this period TRACE reproduces the drying quite accurately, whereas ANSWERS, MACRO, and MARTHE exhibit a slightly delayed drying process. During the following wetting period in the autumn and winter of 1989 (between Days 350 and 450), ANSWERS slightly overestimates the re-wetting while TRACE and MARTHE slightly underestimate the re-wetting. At the end of this re-wetting period, MACRO is in good agreement with the measurements. Large deviations between measurements and model results in the upper layer can be observed during the second drying period of spring 1990 (between Days 520 and 600), especially for ANSWERS and to a lesser extent for MARTHE. In this case ANSWERS predicts the drying too early while MARTHE underestimates drying. MACRO underestimates the drying slightly more than MARTHE. TRACE provided the best fit to the data, with CME = 0.93 (Table 6).



View larger version (42K):
[in this window]
[in a new window]
  		Fig. 4. Measured and predicted soil moisture contents at two depths. Bars indicate standard deviations of the measurements.

 
The results of TRACE and MARTHE at 85 cm depth show much too high soil water contents during the spring and summer of 1989 (between Days 180 and 350), although the measurements show a high standard deviation during the summer of 1989 when the soil was very dry. In the following vegetation period (spring and early summer 1990, between Days 520 and 627) the results of both models match the measurements quite closely. ANSWERS reproduced the decrease in soil moisture during spring and summer 1989 (between Days 180 and 350) at 85 cm depth much better than TRACE and MARTHE, which could have been a result of assuming a uniform root profile for ANSWERS. Large deviations for ANSWERS occur for the second vegetation period when ANSWERS clearly underestimates the soil moisture content. The water content of the lower layer was best predicted with MACRO, yielding an IA of 0.96. Basically, the models produced a slightly different temporal behavior for the soil moisture at 85 cm depth.

Figure 5 shows a comparison of modeled and measured cumulative drainage. During winter 1988–1989 (between Days 50 and 200) MACRO and TRACE underestimated this amount, while the amount estimated with ANSWERS was very close to the end-of-season measurement. Compared to the measurements, the results of ANSWERS showed a delay during the second period of drainage (winter 1989–1990, between Days 400 and 450), although the amount of drainage was reproduced well. TRACE overestimates the amount of drainage. MARTHE, with the highest CME and IA of all models, showed the best agreement with the drainage measurements. Concerning drainage, MACRO produced a CME of 0.81, while the total amount of drainage water was underestimated.



View larger version (13K):
[in this window]
[in a new window]
  		Fig. 5. Cumulative measured and predicted drainage rates. Bars indicate standard deviations of the measurements.

 
Methabenzthiazuron Degradation
The MARTHE, MACRO, and ANSWERS model assume that degradation is soil moisture and temperature dependent. A comparison of predicted soil residues with these models must first consider the simulated values of soil temperature, which are shown in Fig. 6 for the 10 cm depth. This depth was chosen since its soil temperature exhibited a large amplitude, which is a direct result of being close to the soil surface where the soil heat flux is mainly driven by atmospheric conditions. Furthermore, most of the degradation takes place in the uppermost soil layer with high organic matter content. The modeled soil temperatures of MARTHE, MACRO, and ANSWERS were very close to each other and to the measurements. The temporal variability in soil temperature was well reproduced with the models, as evidenced by the small RMSE and high CME and IA values (Table 6). For MARTHE, MACRO, and ANSWERS, degradation was calculated with the modeled soil temperature and soil moisture. Figure 7a reveals that 252 d after application the remaining total MBT mass was restricted to the upper 10 cm. This situation is generally reproduced with TRACE, MACRO, and MARTHE, although the three models show a small amount of MBT in the soil layer between 10 and 20 cm depth. The amount of MBT in the upper 10 cm estimated with MARTHE was very close to the measurement, with an error of –17%, while TRACE clearly overestimated the remaining mass of MBT in the upper 10 cm by 45%. MACRO also clearly overestimated the MBT residues at the first sampling date. With ANSWERS, no MBT was found in the upper compartment (0–40 cm depth). Nearly all of the mass of MBT was found at depths between 40 and 70 cm. Relative to the applied mass, the total mass left in the profile according to ANSWERS was 13.6% too high. After 627 d, the measurements show that the total mass left in the profile was only slightly lower than after 252 d, equally divided between the two uppermost layers (0–10 and 10–20 cm). Results obtained with MACRO and TRACE were the closest to the measurements (Fig. 7b). MACRO and TRACE underestimated the amount of MBT, but they reproduced the correct depth. MARTHE also reproduced the correct depth, but the degradation of MBT was clearly overestimated. With ANSWERS the degradation was also overestimated, whereas additionally the mass again was estimated to be deeper in the profile than measured. What cannot be seen from the graphs in Fig. 7 is that MACRO, TRACE, and MARTHE estimated the presence of very small amounts (close to zero) of residues at deeper depths, which is mainly a result of numerical dispersion. For example MARTHE estimates 0.001 and 0.067% of the applied mass at 20 to 30 cm depth 252 and 627 d after application, respectively, while ANSWERS estimated 0.23 and 0.30% of the applied mass at 70 to 80 cm depth 252 and 627 d after application, respectively. TRACE calculated 0.29% of the applied mass at a depth of 20 to 30 cm 627 d after application, while MACRO estimated very small amounts of residues up to depths of 110 cm, which is a result of the macropore transport process considered in this model.



View larger version (25K):
[in this window]
[in a new window]
  		Fig. 6. Measured and predicted soil temperatures at 10 cm depth.

 


View larger version (17K):
[in this window]
[in a new window]
  		Fig. 7. Measured and predicted methabenzthiazuron (MBT) residues (applied MBT = 100%) (a) 252 d and (b) 627 d after application.

 
As could be expected from differences between the modules for soil moisture and temperature dependent biodegradation (Fig. 2), the estimated mass of MBT residues was higher at both sampling dates for MACRO and TRACE than for MARTHE and ANSWERS. For the first sampling date, 252 d after application, RMSE values calculated for the 11 depths (see Fig. 7) were 30.8, 3.9, 9.7, and 11.7% of the applied mass for ANWERS, MARTHE, TRACE, and MACRO, respectively. For the second sampling, 627 d after application, the RMSEs for the 11 depths were 13.7, 10.1, 5.1, and 6.4% of the applied mass, respectively. Models using the higher DT50 value (TRACE and MACRO) reproduced the measurements of the second sampling date better than those of the first sampling date.

Methabenzthiazuron Leaching
The measured concentrations of MBT in the drainage water showed a small peak roughly 100 d after application (Fig. 8) . The total mass of MBT lost by leaching during the experimental period was 14.6 µg m–2, equivalent to 0.0059% of the applied mass. Only the calibrated MACRO correctly estimated MBT in drainage water, with a total amount of MBT leaching of 7.8 µg m–2. Figure 8 shows that the peak of MBT leaching predicted with MACRO was too sharp and delayed, and that the total amount of MBT leaching was underestimated.



View larger version (20K):
[in this window]
[in a new window]
  		Fig. 8. Precipitation and measured and predicted accumulated mass of methabenzthiazuron (MBT) in the drainage water. MBT application was at t = 0.

 

   DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND DATA
 RESULTS
 DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
As mentioned by Jarvis (1995), calibration of parameters related to the crop water uptake may be essential for accurate reproduction of the soil water dynamics. Except for ANSWERS, all models were calibrated for Kc of each of the crops. Care must be taken not to underestimate actual evapotranspiration rates by using too small Kc values. However, compared to the field situation, lysimeters often show slightly higher evapotranspiration rates. Bergström and Jarvis (1994) and Boesten (1994) attributed this to an "oasis effect," in that the lysimeters are partially surrounded by nonevaporating surfaces, which presumably causes air flowing over the lysimeter to be very dry, thereby increasing evapotranspiration from the lysimeters. The values of CME and IA indicate that all the model results for evapotranspiration and soil moisture at 25 and 85 cm depth are acceptable. Vanclooster and Boesten (2000) detected a broader range of CME values for soil moisture prediction after calibration, between –4.77 and 0.94. Our CMEs for soil moisture ranged between 0.65 and 0.93. However, in our study fewer models were investigated, while one must consider also that model performance is always a result of the capabilities of the model and the subjective choice of parameters by the model user (Diekkrüger et al., 1995b; Vanclooster et al., 2000). Water contents at depths of 25 and 85 cm, as influenced by root water uptake and drainage, were simulated reasonably well with all four models (Table 6), whereas the temporal course of drainage was reproduced with variable quality. Having a CME of 0.1, ANSWERS was deemed unacceptable, and TRACE only marginally acceptable (CME = 0.58). The IA values for drainage estimated with ANSWERS and TRACE (0.67 and 0.89, respectively) were in an acceptable range, while the total drainage values estimated with ANSWERS and TRACE were not significantly different from the measurements. For ANSWERS, the discrepancy between measured and predicted drainage rates may be attributed to the capacity-based approach for modeling soil moisture; ANSWERS had the lowest CME and IA for the reproduction of moisture contents at 85 cm depth. The accurate prediction of the overall drainage amount with ANSWERS appears to be due to compensating errors, rather than to physical realism in the process simulations.

Relative to the mean, the RMSEs for the predicted MBT residues were much larger than those for any of the water balance components. MARTHE, ANSWERS, and MACRO accounted for soil temperature and moisture dependent degradation. These variables (soil temperature and soil moisture) were well described with the models in the uppermost part of the profile, whereas the degradation of MBT is not that well described. This suggests that modeling of soil moisture and temperature is easier than accurate quantification of the relationship between degradation and soil moisture or temperature. The four models in this respect can be divided into two groups. One group (TRACE and MACRO) used a relatively long half-life and predicted the concentrations after 627 d better than after 252 d. The other group (MARTHE and ANSWERS), using a much shorter half-life, correctly predicted the total amount of MBT residues in the profile at the first sampling date (252 d after application) but underestimated the residues 627 d after application. The first-order degradation approach used for all models was likely not suitable for MBT (Diekkrüger et al., 1995a; Beulke and Brown, 2001), while possibly a bi-exponential kinetics (Gustafson and Holden, 1990) might be more appropriate. This hypothesis cannot be tested using our data since it would require a much longer period for monitoring and more sampling dates. Neither the soil moisture and temperature dependent degradation approaches nor simple first-order decay were able to reproduce the field measured MBT soil residues properly using laboratory-determined degradation parameters; this is in accordance with findings by Bergström and Jarvis (1994) and Aden and Diekkrüger (2000).

Despite the high sorption affinity of MBT, 2.13 µg was collected in the drainage water 55 d after application. Since the amount of precipitation until that point in time was only 117 mm, whereas the total pore volume equaled about 426 mm, this is a clear indication of preferential transport. After calibration of the macropore soil hydraulic properties and the fraction of sorption sites in the macropores, the observed leaching of MBT could be described well by MACRO, although the total leached mass was underestimated. Because the overall losses were very low, this underprediction seems not very pertinent in terms of overall mass balance of MBT. For registration purposes in Europe, the relevant allowable limit is 0.1 µg L–1 (European Commission, 1998). The measured average MBT concentration in the lysimeter outflow (0.092 µg L–1) was very close to this drinking water limit. From this point of view, the small amount of MBT leaching is still relevant. The smallest amount of pesticide loss measured by Kladivko et al. (1991) was 0.01% of the applied mass for alachlor. The proportion of applied MBT mass detected in our drainage water was even smaller. Furthermore, the Kd of MBT was about five times higher than for alachlor. These findings corroborate the relationship between sorption affinity and macropore-induced mass losses stated by Kladivko et al. (1991).

After calibration, the plant modules of all models allowed a reasonably good reproduction of the actual evapotranspiration rate. The most complex plant module, implemented in TRACE, produced slightly better results than those in the other models. Compared to capacity-type models, Vanclooster and Boesten (2000) obtained better results after calibration with the Richards'–type approaches. In contrast, Keating et al. (2003) found a similar performance of the capacity and Richards'–type approaches. In our study, the Richards' equation–based models, MARTHE, TRACE, and MACRO, performed better than the capacity-based ANSWERS in terms of the water flow prediction. This notwithstanding the fact that the lower boundary condition of the lysimeter is well suited for the capacity-based approach. Application of the capacity approach to other lower boundary conditions, such as a given groundwater level close to the surface, should cause even more problems (Keating et al., 2003). The lack of preferential flow in ANSWERS, TRACE, and MARTHE was found to have little influence on the flow predictions. Still, these models were unable to describe the small amounts of pesticide leaching associated with preferential flow. This inability must however be balanced with the more difficult parameter identification process required for preferential transport. While MACRO after calibration was able to describe the preferential transport of MBT, such model calibration (Bergström and Jarvis, 1994; Jarvis 1995; Jarvis et al., 2003) currently constrains its effective extrapolation to policy-oriented application (Tiktak et al., 2000). The CDE approach worked reasonably well for MARTHE, TRACE, and MACRO, in that at least the depth of MBT soil residues was adequately predicted. In contrast to this, the center of mass predicted with ANSWERS was always far too deep in the soil profile, mostly caused by the use of a relatively thick uppermost element required for the implementation of Green and Ampt infiltration over coarse grid sizes in combination with having a relatively small dispersion coefficient.


   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND DATA
 RESULTS
 DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
The temporal dynamics of soil water flow observed in the cropped lysimeters were closely matched by the four models following calibration of plant parameters related to crop water uptake. Discrepancies between predicted and measured drainage rates for the capacity-based model are attributed to the approximate model approach with this method. Insufficient data were available to evaluate the different concepts used to predict MBT degradation. Nevertheless, the laboratory-measured degradation parameters were insufficient to properly describe the measured lysimeter-scale pesticide persistence. In spite of a high sorption coefficient, small traces of MBT were detected in the drainage water due to preferential transport. In total, 0.0059% of the applied mass was leached, causing average concentrations just below the EU drinking water limit of 0.1µg L–1. The lack of preferential water flow features in TRACE, MARTHE, and ANSWERS does not significantly influence the prediction performance concerning water flow. It was possible to describe the preferential transport of MBT with MACRO, but only after calibration, which puts constraints on the use of a pesticide transport model with preferential flow for purely predictive applications. We conclude that after calibration, the Richards' equation–based models should perform better than capacity-based approaches in terms of predicting soil moisture contents, drainage amounts, and actual evapotranspiration rates. However, this finding must be balanced because of the limited number of models investigated in this study and the fact that the calibrations were performed by different users. Since accurate modeling of pesticide fate and transport does require a realistic preferential flow component, such features should be added to the MARTHE, TRACE, and ANSWERS models. A major obstacle to modeling preferential transport is the difficulty of parameter identification. Methods should be improved to measure relevant macropore parameters (e.g., Shipitalo and Gibbs, 2000) or estimate them from other known soil properties (e.g., Mayr and Jarvis, 1999).


   ACKNOWLEDGMENTS
 
The authors acknowledge financial support by the EU within the framework of PEGASE, contract EVK1-CT1999-00028. The funding by STUDIUM for the post-doctoral grant of W. Fialkiewicz is gratefully acknowledged.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 METHODS AND DATA
 RESULTS
 DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES