|
F. Ferrer and C.O. Stockle, Biological Systems Engineering Department Washington State University, Pullman, USA |
SUMMARYCropSyst, a comprehensive crop growth/management model was modified for assessing crop response and water management in saline conditions. The osmotic effect of salinity was included in the existing water uptake term, and a function was developed to account for salinity effects on root permeability. Sensitivity analysis showed that the model was able to simulate the effects of cultivar salt tolerance, environmental conditions, and soil water availability on crop response to salinity. Comparison with field data showed that the model was able to predict the effect of salinity and the combined effect of water stress and salinity on crop yield. Observed deviations were mainly attributed to the estimation of the crop salt tolerance parameters from field data.
Irrigated agriculture in arid and semi-arid areas of the world may eventually lead to salt build up in the soil and deterioration of productivity. Salts come with the irrigation water, and are accumulated and concentrated in the soil as water evaporates and is taken up by the crop. Management practices have to be selected so that the levels of salinity in the soil are not harmful for the crop. This is generally done by applying enough water to satisfy the crop requirements and leach the salts out from the root zone (Rhoades, 1974). The implementation of this approach to control soil salinity is limited by drainage and shallow water table problems, new environmental regulations concerning the amount and composition of the drainage effluents, less quantity and quality of the water for agriculture, as well as economic aspects (Tanji, 1990). Therefore, it seems necessary to re-evaluate the scope of management practices and technologies available for salinity control. These include different irrigation systems and scheduling (interval and quantity), leaching fraction and frequency of leaching, blending of waters and re-use of saline drainage waters, and selection of tolerant crops and agronomic practices (Rhoades, 1990).
The selection of appropriate practices for salinity control requires the quantifying of the movement of salts and water in the soil, the response of the crop to soil water and salinity, and how the environment and management conditions affect these interactions. Mathematical models can help to integrate these interactions and be a useful tool to define the best management of a system for saline conditions. The models available can be broadly classified as transient and seasonal (Hoffman et al., 1990). Seasonal models consist basically of an equation that relates yield to the amount of seasonal applied water of a given salinity. This relationship results from the combination of the relation between yield and evapotranspiration, yield and average root zone salinity, and average root salinity and leaching fraction (Letey and Knapp, 1990). Seasonal models assume steady-state conditions for the soil, and do not include the effects of soil salinity variation in space and time on the crop response (Bresler, 1986). Shahevet et al. (1986) demonstrated the importance of the irrigation interval on the response of sweet corn to salinity, and Bresler and Hoffman (1984) concluded that steady-state models are not suitable for irrigation management in saline conditions.
Transient models compute water and solute flow in the soil, and include a water uptake term. Available transient models differ in their conceptual approach, degree of complexity, and in their application for research or management purposes (Wagenet and Hutson, 1989). Transient models for management and research applications in saline conditions require a mechanistic treatment of relevant processes in the soil-water-plant-atmosphere system (Majeed et al., 1994). Usually, water and solute flow in the soil and root water uptake are modelled in detail (Cardon and Letey, 1992b), but the crop growth is simple, and does not consider interactions with environmental variables and agronomic management. CropSyst (Stockle et al., 1994) is an existing multi-year, multicrop, daily time step model with a mechanistic approach to the modelling of the soil-water-plant-atmosphere system, including a variety of agronomic management options (irrigation, fertilization, tillage, residue management, cultivar selection, and rotation selection), and environmental impact analysis capabilities (erosion and chemical leaching). Incorporation of crop response to salinity into CropSyst would result in an excellent tool for comprehensive salinity management.
In order to use CropSyst for analyses under saline conditions, the Richard's equation for water transport and a convective equation for solute transport were incorporated. The water uptake term, and therefore crop growth response, was modified to account for the presence of salts in the soil. The presence of a shallow water table, the effect of different irrigation scheduling and water salinity levels, environmental conditions, and salt crop tolerances can be simulated and analysed.
This paper describes: a) modifications to CropSyst to account for salinity effects; b) a sensitivity analysis to evaluate simulated crop responses to soil salinity, environmental conditions, cultivar selection, and soil water availability; and c) comparisons of model outputs with experimental data.
DESCRIPTION OF THE MODEL
A detailed description of CropSyst is given by Stockle et al. (1994). Only the modifications required to account for salinity are described here. The model divides the soil profile into elements separated by nodes, at which soil water potential, water content, salt concentration, and root fraction are defined. The change in water content at each node is given by:
, (1)
where r w is the density of water (1000 kg m-3), q is the volumetric water content (m3 m-3), t is time (s), y is soil water potential (J kg-1), K is the hydraulic conductivity (kg s m-3), z is soil depth (m), and S is a sink term (kg m-3 s-1). Water content and the hydraulic conductivity are related to soil water potential at a node and the physical properties of the surrounding elements. Vapour flow is also included in the Richard's equation (Campbell, 1985). A system of equations is constructed by computing equation 1 at each node, and appropriate boundary conditions are defined to simulate irrigation and free drainage or a shallow water table. The system is solved numerically with a finite difference scheme, using the Kirchhoff transform and the Newton-Raphson method (Annandale, 1991). Soil is allowed to be non-homogeneous by using the approach of Ross and Bristow (1990).
Solute flow in the soil is calculated considering only convective transport. However, when solving the transport equations numerically, numerical dispersion is introduced (Campbell, 1985). The equation for the change of mass at a node is:
, (2)
where S is the solute concentration in the soil (kg m-3), t is time (s), fw is the water flux (kg m-2 s-1), c is the solute concentration in the soil solution (kg m-3), and r w, is the water density (kg m-3).
Water uptake term at a node is approximated as (Stockle et al., 1994):
, (3)
where WUi is the water uptake at node i (kg m-2 day-1), Kt corresponds to 86 400 (day-1), RCi is the node root conductance (kg s m-4), y si is the soil water potential at the node (J kg-1), and 
is the crop canopy average leaf water potential (J kg-1). The root conductance at a node is obtained from:
RCi =fi . RCmx .fCint, (4)
where fi is the fraction of total root length present at a node, RCmx is a crop parameter that represents the maximum total root conductance for a fully developed crop, well supplied with water (Stockle et al., 1994), and fCint is the fraction of incident radiation intercepted by the crop canopy (Stockle et al., 1994). The canopy average leaf water potential 
is calculated by matching the total crop water uptake with the transpiration from the canopy. Rearranging the terms, the following equation is obtained:
, (5)
where Tmx is the maximum transpiration to meet atmospheric evaporative demand (kg m-2 day-1), RCt is the total root conductance (sum of conductances from individual layers, kg s m-4), 
is an average soil water potential for the profile, weighted by root fraction at each node. If the 
calculated from equation 5 is smaller (more negative) than the critical leaf water potential for stomatal closure, water uptake and transpiration are reduced. If is smaller than the leaf water potential at wilting point, stomates close totally and water uptake is zero (Stockle et al., 1994).
Salinity effects on crop water uptake are accounted for in two ways. The first effect adds a soil water osmotic potential term to the matric potential. The second is a direct salt effect on root conductance. O'Leary (1970) suggested the reduction of root conductance as salinity increases. The root extraction term proposed by Van Genuchten (1987) incorporates the osmotic effect of salinity as well as some additional effect of salinity on water uptake. This additional effect implicitly accounts for a reduction of root permeability as salinity increases. Using a similar functional form to that of Van Genuchten (1987), root conductance at each node (equation 4) is modified to account for salinity effects as follows:
, (6)
where y soi is the soil osmotic potential (J kg-1) at the node, y so50 is the soil osmotic potential at which crop yield is reduced by 50%, and p is a empirical parameter that represents the rate of change of the salinity response (Royo et al., 1991). Both the osmotic potential and the osmotic potential at 50% reduction are expressed in a saturation extract base. The total root conductance used in equation 5 is recalculated using the new conductance values as affected by salinity.
MODEL EVALUATION METHODOLOGY
Sensitivity analysis
The sensitivity of simulated crop responses to salinity was analysed considering variations in atmospheric vapour pressure, soil water availability, and cultivar salt tolerance. The baseline conditions for these simulations were those reported for an experiment at Zaragoza, Spain, in 1989 (Royo and Aragues, 1993). To avoid the influence of other factors that may affect crop response, salinity and water content were set to a constant value for the whole profile and the season. Ten salinity levels were simulated, with electrical conductivities of the saturation extract ranging from 0 to 18 dS m-1. Relative values of transpiration (mm), above ground biomass (kg ha-1), and grain yield (kg ha-1) were plotted against soil salinity. The change in atmospheric vapour pressure was simulated by multiplying the daily vapour pressure calculated from observed data by a factor of 1.3 and 0.7, to obtain a drier and a more humid environment, respectively. Two plant available water (PAW) levels of 0.2, 0.3 and 0.4 were considered. For the analysis of the effect of cultivar salt tolerance, three distinctive tolerance levels for barley were assumed. These corresponded approximately to the varieties Albacete (y 50 = -297 J kg-1, p = 2.5), Soledad (y 50 = -280 J kg-1, p = 5.5) and Dacil (y 50 = -230 J kg-1, p = 4.5), (Royo and Aragues, 1993).
Experimental data
The model was tested using data from two experiments. The first experiment was conducted at the experimental station of the SIA in Zaragoza, Spain (Royo and Aragues, 1993), using a triple sprinkler line source (TLS) to create a continuous gradient of salinity in the soil, with the same amount of water applied between the laterals (Aragues et al., 1992). Water was applied to satisfy crop ET requirements in the nine saline treatments established between the lines of sprinklers. Saline water started to be applied after plant establishment, and irrigation water amount and salinity were monitored during the growing season. The soil ranged from loam to silt loam (Mixed, mesic, Typic Torrifluvent). In this simulation study, data from 1986 and 1989, corresponding to winter barley (var. Albacete) were used. The second experiment consisted of two sets of data from 1975 obtained at the experiment station of the University of California, Davis, CA, and at the Agronomy Research Center of the Colorado State University, Fort Collins, CO (Stewart et al., 1977). This experiment used a single sprinkler line source to provide data of the response of sweet corn to different levels of water and salinity. At Fort Collins, a 90-day hybrid corn variety (Pioneer 3955) was used and three levels of soil salinity at pre-planting were established (0, 3 and 5 dS m-1 saturation extract). The crop was irrigated throughout the growing season with non-saline water. The experimental design provided eight levels of applied water for each salinity level. The soil was a Nunn clay loam (Aridic Argiustoll). At Davis, a similar design was used, except that there were only two soil salinity levels at pre-planting (0 and 5 dS m-1 saturation extract) and that saline (2 dS m-1) and no saline irrigation water were used throughout the growing season. The variety of corn utilized was Funks 4444, a medium maturity hybrid, and the soil was a Yolo silt loam.
Simulation conditions
For all the experimental sites, daily maximum and minimum temperatures and precipitation were available. Daily solar radiation at Zaragoza was generated using CLIMGEN (Ndlovu, 1994). The same was done for some missing days at Davis and Fort Collins. Dates, quantity and salinity of applied irrigations, initial soil water content and salinity, and planting and harvest dates were available. Soil and some crop input parameters were obtained from the literature describing the experiments. Other crop parameters were either calibrated against field data or taken from tables in the CropSyst manual (Stockle et al., 1993). Crop parameters are summarized in Table 1.
TABLE 1 - Crop input parameters
|
|
Zaragoza (Barley) |
Fort Collins (Corn) |
Davis (Corn) |
|
Biomass Transpiration Coeff. (Kg kPa m-3) |
5.2 (C) |
7.0 (C) |
8.6 (C) |
|
Light-Biomass conversion (g MJ-1) |
0.003(CropSyst) |
0.004 (CropSyst) |
0.004 (CropSyst) |
|
Harvest Index |
0.35 (F) |
0.43 (F) |
0.54 (F) |
|
Max. root depth (m) |
1.2 (F) |
2.2 (F) |
2.8 (F) |
|
Max. LAI (m m-1) |
4 (F) |
6 (CropSyst) |
6 (CropSyst) |
|
Max. water uptake (mm) |
10 (CropSyst) |
12 (CropSyst) |
12 (CropSyst) |
|
ET crop coeff |
1.2 (*) |
1.2 (*) |
1.25 (*) |
|
AT/PT at which growth ceases |
0.8 (C) |
0.90 (C) |
0.90 (C) |
|
Critical y leaf (J kg-1) |
-1500(CropSyst) |
-1200 (CropSyst) |
-1200 (CropSyst) |
|
Wilting Point y leaf (J Kg-1) |
-2200 (CropSyst) |
-1800 (CropSyst) |
-1800 (CropSyst) |
|
Leaf duration to sensitivity stress |
1.0 (CropSyst) |
0.5 (C) |
0.5 (C) |
|
y 50 (J Kg-1) |
-297 (F) |
-200 (F) |
-320 (F) |
|
p value |
2.5 (F) |
3 (F) |
3 (F) |
(F). Obtained from field data
(C). Calibrated against field data
(CropSyst). From the CropSyst manual. (Stockle et al, 1993)
(*). From Doorenbos and Pruitt (1977)
At Zaragoza, the non-saline treatment in 1986 was used to calibrate a few cultivar-dependent crop growth parameters, particularly the biomass-transpiration coefficient. The same parameters were calibrated for corn at Davis using data from a 1974 experiment with six water levels (non-saline). At Fort Collins, these parameters were calibrated using four 1975 non-saline plots. Data used for calibration were not used for model validation.
At Zaragoza, the salt tolerance values for barley were obtained by Royo and Aragues (1993) using data from four growing seasons. The y o50 value that they report is about half of the one mentioned in the literature (-297 J Kg-1 and -600 J Kg-1 respectively). In this case, this difference may be attributed to the effect of leaf injury by the salts. At Fort Collins and Davis, the salt tolerance parameters for corn are calculated from three and two data points respectively. The y o50 value computed for Fort Collins is identical to the value in the literature (-200 J Kg-1). At Davis, the effect of the cultivar may explain a higher computed value for y o50 (-320 J Kg-1).
Following Willmott (1982), three indicators of agreement between simulated and observed values were calculated: Root Mean Square Error (RMSE), Relative Root Mean Square Error (RelRMSE), and the Index of Agreement (d).
RESULTS AND DISCUSSION
Sensitivity analysis
Many authors report the decrease of crop salt tolerance as the atmosphere becomes drier and soil water availability decreases (Francois and Maas, 1993. Hoffman et al., 1990). Salt tolerance data for many crops is available in literature (Francois and Maas, 1993). However, the applicability of this data to field conditions may be restricted (Bresler and Hoffman, 1984). A sensitivity analysis was performed to evaluate the model's ability to account for fluctuations of these factors (Figure 1). Relative yield of three barley cultivars follow their order of crop salt tolerance. As the value of the parameter p increased, the slope of the relative yield response function increased, and as y 50 increased, the threshold beyond which the relative yield started to decreased was higher. When the environment becomes drier, the model simulated less tolerance to soil salinity, consistent with field observations (Francois and Maas, 1993). Any factor affecting atmospheric evaporative demand (e.g., temperature) will produce a similar response. Finally, the model predicted larger crop salt sensitivity as soil water decreased.
Figure 1. Simulated relative yield in response to soil salinity levels and selected other factors (see text). ECe is the salinity of the saturation extract (dS/m). Water content and salinity are mantained constant in the profile and throughout the season. a) Cultivar salt tolerance; b) Atmospheric vapor pressure; c) Soil water availability.
Figure 2. Observed and predicted relative yields. At Zaragoza, salinity of the irrigation water increases from treatment 1 to 9. At Davis and Fort Collins, the amount of water applied increased from level 1 to 8. S0 and S5 refer to non-saline and saline plots at pre-planting, and WQ0 and WQ2 refer to non-saline and saline applied water, respectively.
TABLE 2 - Statistical of observed and predicted grain yield for salinity affected experimental plots at three locations
|
|
Oave |
Pave |
N |
RMSE |
RelRMSE |
d |
|
Davis |
9434 |
9210 |
16 |
867 |
9 |
0.95 |
|
Fort Collins |
4787 |
5488 |
24 |
1018 |
21 |
0.69 |
|
Zaragoza |
3631 |
3482 |
18 |
848 |
23 |
0.62 |
* Oave and Pave are the mean observed and predicted values respectively, N is the number of data points, RMSE is Root Mean Square Error, RelRMSE is the Relative Root Mean Square Error, and d is the index of agreement.
Comparison with experimental data
The prediction of absolute yields is important for the economic evaluation of management practices. Statistical comparison between observed and predicted absolute yields for the three locations is shown in Table 2.
In comparing individual data points at Davis, the index of agreement and relative RMSE were high and low, respectively, indicating excellent model performance. Figure 2b shows that the model predicted well the combined effect of salinity and water stress.
Statistical indices in Table 2 indicated that performance was less satisfactory at Fort Collins. Unfortunately, grain yields obtained from line source experiments are not very reliable due to the typically small size of samples and the absence of true replications, limiting a thorough evaluation of the model predictive capabilities. This factor may also affect the comparisons at Davis and Zaragoza. At Fort Collins the model overpredicted the relative yield for the saline treatments (Figure 2c). This poor performance resulted mainly from a reduction of the harvest index for the most saline field plots (S5-WQ2), (Stewart et al., 1977). The harvest index was unaffected by the large variation in water stress at each salinity level, but fluctuated with salinity levels, a fact that the model was unable to account for. A better understanding and characterization of this type of response is required before modelling improvements can be attempted.
Overall, the evaluation indices indicated a poor performance of the model at Zaragoza (Table 2). Deviations were mainly related to the calibration of the crop parameter relating transpiration and biomass production, which was done using the non-saline treatment in 1986. However, using this calibrated parameter, the model was unable to predict the high yields of 1989, a year very similar in climate to 1986. Royo and Aragues (1993) reported that observed yields in 1989 were much higher than expected, attributing this to possible overestimation resulting from the small size of the plots. Figure 2a shows that the model responded well to soil salinity in 1989, but was somewhat insensitive in 1986. The lack of simulated response in 1986 was associated with lower levels of salinity in the soil and a late establishment of salinity gradients (Royo and Aragues, 1993). This, coupled with an earlier sowing date in 1986, determined that in the simulation the crop had already accumulated 60-70% of the final biomass before the salinity levels began to be detrimental for growth. In this experiment, irrigations with saline water were applied using an overhead sprinkler system, and the larger response to soil salinity observed in the field in 1986 could be explained to a large extent by salt toxicity and tissue injury resulting from the accumulation of salts on the leaves (up to 20% yield reduction according to Aragues, personal communication). In 1989, the leaching fractions applied were increased (Royo and Aragues, 1991) so that the salinity distribution in the profile was more homogeneous and the salinity profiles were established earlier in the season. This probably increased the crop response to soil salinity and tended to mask the effect of other experimental factors such as direct salt toxicity on leaves.
CONCLUSIONS
The modifications introduced to CropSyst to account for salinity seems to perform reasonably well when compared to different sets of data. The model is able to account for the effects of atmospheric vapour pressure, water availability and cultivar on crop salt tolerance. It also simulates well the additive effect of water stress and salinity. Some problems exist in obtaining adequate crop salt tolerance parameters, because experimental results fluctuate with environmental conditions and cultivar choices. In its present form, the model could be used for long-term risk analysis of management strategies involving saline water and soils. Applications as a support tool for real-time on-farm tactical decisions are likely to be premature.
ACKNOWLEDGEMENTS
Data from Zaragoza, Spain, was provided by Dr. Antonio Martínez-Cob, Dr. Ramón Aragues and Dr. Antonio Royo from the Dept. of Soils and Irrigation, Agronomic Research Center, Diputación General de Aragón. The authors are also thankful to the following Catalan entities that sponsored the project: CIRIT, Caixa de Manresa and Caixa de Sabadell.
REFERENCES
Annandale, J.G. 1991. Two-dimensional simulation of nitrate leaching in potatoes. PhD Thesis. Washington State University, Pullman, Washington, USA.
Aragues, R., Royo, A. and Faci, J. 1992. Evaluation of a triple line source sprinkler system for salinity crop production studies. Soil Sci. Soc. Am. J. 56: 377-383.
Bresler, E. 1986. Application of a conceptual model to irrigation water requirement and salt tolerance of crops. Soil Sci. Soc. Am. J. 51: 788-793.
Bresler, E. and Hoffman, G.J. 1984. Irrigation management for soil salinity control: theories and tests. Soil Sci. Soc. Am. J. 50: 1552-1559.
Campbell, G.S. 1985. Soil Physics with Basic. Transport models for soil-plant systems. Elsevier.
Cardon, G.E. and Letey, J. 1992a. Plant water uptake terms evaluated for soil water and solute movement models. Soil Sci. Soc. Am. J. 32: 1876-1880.
Cardon, G.E. and Letey, J. 1992b. Soil-based irrigation and salinity management model: I. Plant water uptake calculations. Soil Sci. Soc. Am. J. 56: 1881-1887.
Doorenbos, J. and Pruitt, W.O. 1977. Crop water requirements. FAO Irrigation and Drainage Paper 24. FAO, Rome.
Francois, L.E. and Maas, E.V. 1993. Crop response and management on salt-affected soils. In: Handbook of Plant and Crop Stress. M. Pessarakle (ed.).
Hoffman, G.J., Rhoades, J.D., Letey, J. and Fang Sheng. 1990. Salinity management. In: Management of Farm Irrigation Systems. ASAE Monograph. G.J. Hoffman, T.A. Howell, and K.H. Solomon (eds.). pp. 667-715.
Letey, J. and Knapp, K. 1990. Crop-water production functions under saline conditions. In: Agricultural Salinity Assessment and Management. ASCE Manuals and Reports on Engineering Practice No. 17. K.K. Tanji (ed.). pp. 305-326.
Majeed, A., Stockle, C.O. and King, G. 1994. Computer model for managing saline water for irrigation and crop growth: preliminary testing with lysimeter data. Agricultural Water Management 26: 239-251.
Ndlovu, L.S. 1994. Weather Data Generation and its use in estimating Evapotranspiration. PhD Thesis, Washington State University, Pullman, WA, USA.
O'Leary, J.W. 1970. The influence of groundwater salinity on plant growth. In: R. B. Mattox (Editor), Proc. Symp. Ground Water Salinity. 46th Annual Meeting of the Southwestern and Rocky Mountain Div. of AAAS, Las Vegas, NV.
Rhoades, J.D. 1974. Drainage for salinity control. In: Drainage for Agriculture. J. Van Schilfgarde (ed.). ASA Monograph No. 17. pp: 433-467.
Rhoades, J.D. 1990. Overview: Diagnosis of salinity problems and selection of control practices. In: Agricultural Salinity Assessment and Management. ASCE Manuals and Reports on Engineering Practice No. 17. K.K. Tanji (ed.). pp. 1-17.
Ross, P.J. and Bristow, K.L. 1990. Simulating water movement in layered and gradational soils using the Kirchhoff transform. Soil Sci. Soc. Am. J. 54: 1519-1524.
Royo, A., Aragues, R. and Quilez, D. 1991. Descripción y evaluación de cuatro modelos de respuesta de cultivares de cebada a la salinidad. Inv. Agr., Prod. Prot. Veg. 6: 319-330.
Royo, A. and Aragues, R. 1993. Validation of salinity crop production functions obtained with the triple line source sprinkler system. Agron. J. 85: 795-800.
Shahevet, J., Vinten, A. and Meiri, A. 1986. Irrigation interval as a factor in sweet corn response to salinity. Agron. J. 78: 539-545.
Stewart, J.I., Danielson, R.E., Hanks, R.J., Jackson, E.B., Hagan, R.M., Pruitt, W.O., Franklin, W.T. and Riley, J.P. 1977. Optimizing crop production through control of water and salinity levels in the soil. Utah Water Lab. PRW-161-1.
Stockle, C.O., Nelson, R. and Campbell, G.S. 1993. CropSyst, cropping systems simulation model. User's Manual. Dept. of Biological Systems Engineering, Washington State University, Pullman, Washington, USA.
Stockle, C.O., Martin, S.A. and Campbell, G.S. 1994. CropSyst, a Cropping Systems Simulation Model: Water/Nitrogen Budgets and Crop Yield. Agricultural Systems 46: 335-359.
Tanji, K.K. 1990. Nature and extent of agricultural salinity. In: Agricultural Salinity Assessment and Management. K.K. Tanji (ed.). ASCE Manuals and Reports on Engineering Practice No. 17. pp: 1-17.
Van Genuchten, M.T. 1987. A numerical model for water and solute movement in and below the root zone. Research Rep. 121. USDA-ARS, U.S. Salinity Laboratory, Riverside, California, USA.
Van Genuchten, M.T. and Hoffman, G.J. 1984. Analysis of crop salt tolerance data. In: Soil Salinity under Irrigation. Processes and Management. Ecological Studies No. 51, pp: 130-142. Edited by I. Shainberg and J. Shalhevet, Springer-Verlag.
Wagenet, R.J. and Hutson, J.L. 1989. Leaching estimation and chemistry model: a process based model for water and solute movement, transformation, plant uptake and chemical reactions in the unsaturated zone continuum. Water Resources Inst., Center for Environ. Research., Cornell Univ., New York. 140 p.
