Effective scaling factor for transient infiltration in heterogeneous soils
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Effective hydraulic properties at large grid resolution are viable alternatives to heterogeneous soil medium in large-scale hydrologic and global circulation models. In this study, we investigate the effective hydraulic parameters for transient infiltration under ponding conditions in terms of the optimal averaging schemes for the input hydraulic and environmental parameter fields. The main idea of effective parameters is whether the interested process behavior in heterogeneous soils can be captured by a process that assumes only one set of soil parameters, such that the heterogeneous system is replaced by an equivalent homogeneous system. The 'effective' hydraulic parameters of the heterogeneous soil formation are derived by conceptualizing that the 'effective' homogeneous soil will approximately discharge the ensemble-mean surface flux and cumulative infiltration. The derived optimal effective powers for the random (input) parameters define an optimal averaging scheme for the random input fields, which can be used in large-scale hydrologic and global circulation models. Specifically, we discuss the effects of microtopography (as reflected in surface ponding depth), and hydraulic parameter correlation on the ensemble-mean behavior as well as on the optimal effective powers. For a large range of hydraulic properties from silty clay to sand with large uncertainties in the Miller-Miller scaling factor, the saturated water content, and the surface ponding depth, relatively small range of optimal effective power values has been found. Among the three, variability of the Miller-Miller scaling factor has the most significant effect on the ensemble flux behavior. The correlation among the Miller-Miller scaling factor, the saturated water content and the surface ponding depth increases the effects of soil heterogeneity. However, the ensemble-mean flux behavior can be more precisely mimicked through the idea of optimal effective powers when the random fields are better correlated. 2005 Elsevier Ltd All rights reserved.
