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a Dep. of Plants, Soils, and Biometeorology, 4820 Old Main Hill, Utah State Univ., Logan, UT 84322-4820
b Dep. of Soil and Water Sci., Faculty of Agricultural, Food, and Environmental Sci., POB 12, Rehovot 76100, Israel
* Corresponding author (ldud{at}cc.usu.edu)
Received 19 December 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Abbreviations: PF, potential-flow function • PFTA, combination of potential-flow and transition-apportioning functions • TA, transpiration-apportioning function
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Hydrochemical models that simulate the interplay among the previously enumerated factors provide an attractive alternative to the laborious process of field-testing irrigation management schemes for optimizing water use for plant production and for protection of water and soil resources (Huston et al., 1990). Transpiration is often the dominant component of the water budget in arid and semiarid environments, and as such has a major effect on water flow and contaminant transport under both natural and agricultural settings. Estimates of water uptake are important to predictions of crop response, impacts of irrigated agriculture on ground and surface water quality, and to extension of models to nonagricultural settings. In a review of hydrochemical modeling of physical, chemical, and biological processes within the vadose zone, Huston et al. (1990) commented that plant response functions have received much less attention than other components of most hydrochemical models.
Mechanism-based, vadose-zone hydrochemical models developed for use in irrigated systems such as LEACHC (Huston and Wagenet, 1992), SOWACH (Dudley and Hanks, 1991), V-H (Cardon and Letey, 1992b), and UNSATCHEM (Simunek and Suarez, 1996) use a macroscopic approach to modeling water uptake by roots wherein a root-sink term is added to the Richard's Equation (Zhang and Elliot, 1996). According to Mmolawa and Or (2000), the macroscopic approach has the advantage of requiring simpler flow geometry and avoids problems in the microscopic formulation of scaling the simulated uptake by individual roots to root systems (see Aura, 1996 as an example of the microscopic approach). Of the models listed above, LEACHC and SOWACH use a formulation categorized as a PF theory by Zhang and Elliot (1996), and V-H and UNSATCHEM uses a TA formulation (Zhang and Elliot, 1996). Some relative merits of the two approaches, as specifically used in the hydrochemical models listed above, were discussed by Cardon and Letey (1992a). In LEACHC and SOWACH, the root-sink term is computed from the product of the soil hydraulic conductivity and the difference between the water potential in the root and the soil (Childs and Hanks, 1975). An underlying assumption of this formulation of the root-sink term is an equal and additive effect of matric and osmotic potentials on water availability as shown by the equation (Childs and Hanks, 1975)
 | [1] |
) is the bulk-soil hydraulic conductivity, 
x and z are the radial and vertical distance from the root to where water is extracted (usually taken as 1.0 cm), Hroot is the root water head bounded by minimum value, Hmin [e.g., -150 m, (Nimah and Hanks, 1973) or -90 m (Bresler, 1987)], Rr is a root resistance term, h(z,t) is the matric head, and 
(z,t) is the osmotic head. For apportioning transpiration in response to matric and osmotic potentials within the root zone, van Genuchten (1987) proposed an S-shaped function with an initial plateau and a decreasing section that approximates the Maas-Hoffman response curve (Maas and Hoffman, 1977). The root-sink term for water uptake as a function of the matric and osmotic potentials as used in the V-H model is written
 | [2] |
50 is the osmotic head that causes a 50% yield loss, h50 is the matric potential that causes a 50% yield loss, and p is a constant that is usually taken as 3. UNSATCHEM uses the van Genuchten equation but separates matric and osmotic response functions as discussed below. The two formulations of the root-sink term differ in the way water is extracted from a specific depth increment (node) and the way water is extracted from the entire soil profile. Cardon and Letey (1992a) were approximately correct in stating that Eq. [1] operates as a step function within each node. More precisely, the water extraction rate may change very quickly as the soil water potential approaches Hmin and the hydraulic conductivity decreases. Moreover, water uptake from a node may be prohibited by low values of the matric potential, low values of the osmotic potential, or a combination of the two. Thus, the model may predict a response to relatively low salinity levels as the soil matric potential nears Hmin. The empirical plant-based root-sink term, on the other hand, permits differentiation in the sensitivity to matric and osmotic stress through the constant a. Even though the relative effects of matric and osmotic stresses are added, the effects are independent and a crop response is not predicted until the osmotic head falls on the decreasing portion of the curve.
The extraction of water across the entire profile should also be considered when comparing the two root-sink terms. The process for obtaining the values for Hroot in the PF formulation causes water to be taken from nodes having water potential values greater than Hroot to meet potential transpiration. This simulates the plant's ability to differentially take water from the root zone according to the distribution of water, salinity, and roots. For the TA formulation, values of the soil matric or osmotic potential that fall on the decreasing portion of the response function curve at any node decrease the amount of water extracted irrespective of the availability of water at other nodes. With respect to water extraction across the root zone, the PF formulation better represents the behavior of the plant. Differential extraction of water within the root domain may prove to be important in the simulation of water-limited systems including nonagricultural environments.
As applied in the models SOWACH, LEACHC, and V-H, both the PF and TA formulations assume that the effects of salt and water stress are additive. In a study of water and salt stress, Shani and Dudley (2001) found the effect of salinity on yield appeared to decrease when water availability was limited. When irrigation was nearly equal to or greater than potential evaporation, crop yield was a function of the salinity level, but at ratios of irrigation to pan evaporation < 0.7, salinity had a negligible effect on yield. This led Shani and Dudley (2001) to hypothesize that the effects of water and salt are not equal or additive. Since both formulations assume additive matric and osmotic effects on plant transpiration and yield, neither formulation properly represents plant response to combined matric and osmotic stress across a broad range of values. Further, Shani and Dudley (2001) suggested that at low irrigation levels, transpiration and hence yield might have been moisture-flux limited. In this respect, the Darcy-based formulation represents the plant–soil relationship better than the crop-based formulation.
UNSATCHEM computes stress factors for the matric (fh) and osmotic (fm) heads separately from equations of the van Genutchen form, written (Simunek and Suarez, 1996)
 | [3] |
The stress factors are combined in a multiplicative approach to apportion potential water uptake:
 | [4] |
A multiplicative approach to combining stress factors was first proposed by Baule in 1918 (Paris, 1992) and has been reported to accurately represent yield response to combined plant stress factors (Wallace, 1990).
Our objective was to reformulate the root-sink term so it better represents the soil–plant system, accounting for differential water uptake by roots and differential response to water and salt stress. So that the results of this study could be readily incorporated in an existing hydrochemical model, elements of the root-sink terms already used in the models were selected as the foundation for the reformulation. The criteria used to evaluate model predictions were in agreement between measured and predicted yields and salinity profiles, and the ability of the model to predict a differential response to the matric and osmotic potentials. Predictions of SOWATSAL (Hanks and Cui, 1990) with three different formulations of the root-sink term are compared with data from field studies of crop yields under conditions of salt and moisture stress. The effects of the three root-sink formulations on predictions of salt and water distribution in the profile are also presented.
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THEORY |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Removing the osmotic potential from Eq. [1] permits reintroduction of the osmotic effect in a multiplicative model. Relative to an additive model, the multiplicative approach should better reproduce the "putative increase in salt tolerance under conditions of limited irrigation" reported by Shani and Dudley (2001) in a field study of the response of alfalfa (Medicago sativa subsp. sativa), melon (Cucumis melo subsp. melo cv. Galia), and corn (Zea mays L.) to irrigation and salinity. For example, if limited irrigation results in an fh value of 0.9 and the salt level results in an f value of 0.9 then transpiration would be 81% of potential or a decrease of about 10% per factor. These relative differences might be observable in field data. If, under the same salinity, the irrigation is severely limited such that fh is 0.5, then transpiration would be 45% of potential and the effect of salinity might not be observable given the variability commonly encountered in field data. If plant response to irrigation and salinity was additive, a 10% decrement in transpiration resulting from osmotic stress might be observable across a large range of irrigation levels. Thus, the transpiration partitioning approach of Simunek and Suarez (1996) was used as a basis for computing osmotic effects on water uptake.
So that the effects of different formulations of the root-sink terms on model predictions could be fairly compared, three options for the root-sink term were coded into the model SOWATSAL (Hanks and Cui, 1990). The three options for the root-sink term will be referenced as follows: Eq. [1] = PF, Eq. [2] = TA, and PFTA as described below. SOWATSAL is based on one-dimensional, second-order, Crank-Nicholson numeric approximations to the Richard's equation (with a root extraction term) and the equation of continuity for transport of a conservative solute. Details regarding the mathematical development of the model are given by Hanks et al. (1969), Nimah and Hanks (1973), Childs and Hanks (1975), and Hanks and Cui (1990) and a field test of the model was reported by Dudley et al. (1981).
For the PFTA formulation, the values of Hroot at each time step and for each node and f at each time step were computed through a simple, iterative algorithm. In the algorithm, transpiration was first reduced if necessary for osmotic stress, and then a PF equation computed uptake of water from the root zone. At the first iteration, a stress factor for the effect of salinity, f, was computed by weighting the relative effect of salinity on uptake from each node by the fraction of roots within the node:
 | [5] |
 | [6] |
 | [7a] |
 | [7b] |
The value of Hroot that makes S(z,t) = Tmax is obtained by rearranging Eq. [7a] such that
 | [7c] |
If a value of Hroot that is <Hmin is computed from Eq. [7c], then Hroot is set to Hmin and water can only be extracted from nodes with matric potentials > Hmin. After the first iteration, the salinity response function was recomputed by weighting to the relative uptake from each node
 | [8] |
Relative yield (Yr) at the end of the simulation was assumed to be equal to relative accumulated transpiration (Tr) (Letey and Dinar 1986; Shani and Dudley, 2001):
 | [9] |
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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v = 0.18).
With the exception of the crop response parameters h50, 50, and Hmin, the same set of model parameters, boundary, and initial conditions were used in all simulations. In addition to the initial soil water content and salinity profile, and water retention characteristic curve, a number of parameters relating to water flow and crop development are required. For all simulations, the root zone was divided into 12 nodes of 0.05 m. A daily average of the pan-estimated potential evaporation adjusted by a crop coefficient (taken from an extension service recommendation for the region) was used as potential transpiration in specifying surface boundary condition unless irrigation was simulated, in which case the irrigation rate was the surface boundary condition. The boundary condition at the bottom of the root zone for moisture flow was a constant gradient, and for solute transport the bottom boundary condition was constant concentration. The parameters related to crop cover and root development were crop cover at maturity = 100%, days to full crop cover = 41 DAP, time to mature root development = 41 DAP. Details regarding the model input parameters may be obtained from the users' manual (Hanks and Cui, 1990). The duration of all simulations was 1152 h.
The three models required estimates of some combination of the crop response function parameters: Hmin, 50, and h50. Childs and Hanks (1975) suggest a value of -150 m for Hmin, which was taken as an initial estimate. However, comparison of predicted and measured yield indicated that -150 m provided a poor estimate of the available water and that most of the available water was held at much higher values of the matric potential. An optimal value of Hmin was obtained by trial-and-error to fit yield data. The value for 50 was estimated by solving the Maas-Hoffman equation with slope = 0.5 and threshold EC = 2.5 dS m-1 (Maas, 1990) for Yr = 0.5 (resulting EC = 12.5 dS m-1) and multiplying by -3.6 (Richards, 1954) to obtain -45 m. As an initial estimate, h50 was assumed to be equal to 50 (van Genuchten, 1987). Because crops are more sensitive to the matric potential than the osmotic potential (Meiri, 1984), the value of h50 was also fine tuned by trail-and-error fitting to the data.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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50 = -45 m. Agreement between predicted and measured relative yield at the higher irrigation levels may be due, at least in part, to the calibration of 50 to salt tolerance data. In contrast, the value of h50 is estimated without benefit of similar matric potential response data. Increasing h50 to -15 m slightly improved the agreement between measured and predicted relative yield at the lowest irrigation level, but caused the model to underpredict relative yield at the other irrigation levels (Fig. 2b). Underprediction of Yr at irrigation levels > 0.2 may result from the inability of the TA formulation of the root-sink term to compensate for nodes with limited water by extracting water from nodes where it is available. If S < Smax at any node, then T < Tp for the time step.
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50 (from which h50 was initially obtained) was obtained from the melon response to salt stress.
Because PF produced the best agreement to the control when the Hmin value was -15 m and TA when 50 was -45 m, these values were used in executing PFTA. These values produced agreement between predicted and measured relative yields across all irrigation levels (Fig. 3). Linear regression of predicted vs. measured relative yield was used to compare the three models in Fig. 4. Of the three models, PFTA produced the greatest regression coefficient (0.9909) and r2 value (0.9471), indicating that it best reproduced the measured yield data. The TA model had a greater regression coefficient (0.9283) than the PF model (0.8741) that consistently underpredicted the data (Fig. 4).
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Predicted Water Contents and Salt Profiles
While it might be argued that the difference in predictions of relative yield among the models is not large, the three formulations predicted differences in the evolution of the water content profile and marked differences in predicted salt profiles. The two treatments shown in Fig. 5 through 9, E0/I = 1.0 + EC = 6.0 dS m-1 and E/I0 = 0.4 + EC = 6.0 dS m-1 illustrate differences in the response to salinity and to deficit irrigation, respectively. Figure 5a shows greater values of the water content throughout the profile than Fig. 5b and 5c that are similar. The similarity in water content profile through time shown in Fig. 5b and 5c was expected at high irrigation levels because the dominant stress is salinity and TA and PFTA use a similar function to compute salinity response. The difference between the water content profile through time simulated by PF and the other two formulations was due to the use of the water potential in computing the threshold for water uptake. The soil water potential was often <Hmin, preventing any water extraction from nodes and resulting in higher water contents throughout the profile.
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The greatest differences among the simulations were observed in the salt profiles. Thus, predicted salt profiles at the end of the simulation were compared with values measured after harvest. Because TA and PFTA provided better predictions of yield than PF, only the results of TA and PFTA simulations are shown in Fig. 9. Both TA and PFTA produced acceptable predictions of salt profiles when I/E0 was 1.0 (Fig 9a). Below 0.2 m when I/E0 = 0.4 (Fig. 9b), TA failed to reproduce the salinity profile indicating that PFTA better represents plant response to combined water and salt stress and the plant's ability to adjust uptake according to the distribution of available water, salt, and root density.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Hydrochemical models have been suggested to be efficient tools for evaluating irrigation management schemes that maintain crop yields and minimize deleterious effects of irrigated agriculture on water resources and soil resources. In arid systems, computation of transpiration is critical to prediction of the water budget that, in turn, strongly affects salt transport. The PFTA formulation gave significantly different predictions of salt dynamics in the profile and the final salt profile was in better agreement with the measured values than the TA formulation. Reformulation of the root-sink term along the lines of PFTA appears warranted.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONTHEORYMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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