Effective hydraulic parameters for steady state vertical flow in heterogeneous soils
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In hydroclimate and land-atmospheric interaction models, effective hydraulic properties are needed at large grid scales. In this study, the effective soil hydraulic parameters of the areally heterogeneous soil formation are derived by conceptualizing the heterogeneous soil formation as an equivalent homogeneous medium and assuming that the equivalent homogeneous soil will approximately discharge the same total amount of flux and produce same average pressure head profile in the formation. As compared to previous effective hydraulic property studies, a specific feature of this study is that the derived effective hydraulic parameters are mean-gradient-dependent (i.e., vary across depth). Although areal soil heterogeneity was formulated as parallel homogeneous stream tubes in this study, our results appear to be consistent with the previous findings of mean-gradient unsaturated hydraulic conductivity [Yeh et al., 1985a, 1985b]. Three widely used hydraulic conductivity models were employed in this study, i.e., the Gardner model, the Brooks and Corey model, and the van Genuchten model. We examined the impact of parameter correlation, boundary condition (surface pressure head), and elevation above the water table on the effective saturated hydraulic conductivity and shape parameter. The correlation between the saturated hydraulic conductivity Ks and the shape parameter increases the effective saturated hydraulic conductivity, while it does not affect the effective . The effective is usually smaller than the mean value of , while the effective Ks can be smaller or larger than the mean value depending on no correlation or full correlation between K s and fields, respectively. An important observation of this study is that Gardner and van Genuchten functions resulted in effective parameters, whereas it is difficult to define effective parameters for the Brooks Corey model since this model uses a piecewise-continuous profile for hydraulic conductivity.
