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Dagan and Bresler (1983) and Bresler and Dagan (1983) developed models for water flow in the upper In this study we investigate effective soil hydraulic parameter aver- soil layer of spatially variable fields where spatial vari- aging schemes for steady-state flow with plant root water uptake in heterogeneoussoils."Effective"soilhydraulicparametersofahetero- ability of the saturated hydraulic conductivity is as- geneous soil formation are obtained by conceptualizing the soil as sumed to take place in the horizontal plane. They found an equivalent homogeneous medium. The "effective" homogeneous that effective properties may be meaningful only under medium is only required to discharge the same ensemble-mean flux very restricted and special conditions, such as steady across the soil surface. One-dimensional flow at the local scale has gravitational flow where the effective saturated hydrau- been used as an approximation for various simplified problems under lic conductivity varies between the geometric mean and investigation (e.g., a shallow subsurface dominated by vertical flows). the arithmetic mean. Kim and Stricker (1996) employed The domain is assumed to be composed of homogeneous one-dimen- Monte Carlo simulation to investigate the independent sional soil columns without mutual interactions. Using Gardner's un- and simultaneous effects of horizontal heterogeneity in saturated hydraulic conductivity model, we derive the effective value soilhydraulicpropertiesandrainfallintensityonvarious for the parameter . While root water uptake influences the overall water budget, its impact on the effective hydraulic parameter averag- statisticalpropertiesofthecomponentsoftheone-dimen- ing scheme was found to be secondary. Results show that the arithme- sional water budget for a large area up to 10 4 km 2 . The tic mean of Gardner's is usually too large to serve as an effective effective hydraulic parameters were calculated by min- parameter. Deviations of the effective parameter from the arithmetic imizing the squared differences of the capillary pressure mean become larger as the surface suction increases; that is, the profiles in the formation. Zhang et al. (1998) developed flow scenario switches from infiltration to evaporation. The results first-order stochastic models for stationary media using consistently show a smaller effective parameter for evaporation sce- both the Brooks-Corey and the Gardner-Russo hydrau- narios than for infiltration scenarios. The effective parameter eff lic property models. Kim et al. (1997) investigated the decreases with an increase in the mean value of . Spatial variability impact of heterogeneity of the soil hydraulic properties in also decreases the effective value of eff. Alternative root water

Soil Hydraulic Parameter Upscaling for Steady-State Flow with Root Water Uptake