Upscaling Hydraulic Parameters of Green-Ampt Model for Heterogeneous Layered Soils.

Green-Ampt infiltration model has been widely used but how to upscale the model for large-scale applications remains a challenge. In this study, we examine the effective upscaling soil parameters for Green-Ampt model in heterogeneous layered soils. The main idea of effective parameters is to capture infiltration behavior in heterogeneous soils by one set of soil parameters which are derived from the parameters of individual layers, such that the heterogeneous system is replaced by an equivalent homogeneous medium. Several p-order power mean schemes were examined for upscaling the soil parameters of the layered soils formed by repeated binary units. We found that reasonable p values can be obtained at the three scenarios that harmonic means for saturated hydraulic conductivity (K) for coarse-layer-on-top and fine-layer-on-top formations, and p-order power means for both K and wetting front suction head (H) for coarse-layer-on-top formations. The structure of the binary units influences the results significantly and leads to a reverse trend with the layers number for the total infiltration time, optimal p value and upscaled H. The scenarios of harmonic means for K result in better results of mean square error (MSE), mean relative error (MRE) and Nash-Sutcliffe efficiency (NSE) of infiltration rates than that of p-order power means for K. The coefficient of correlation (COC) of infiltration rates for coarse-layer-on-top formations is higher than that of fine-layer-on-top formations. The increasing layers number leads to the higher MSE, better MRE and NSE for each scenario. The MRE and NSE may have the threshold for each scenario when layers number increases. In general the upscaling soil parameters in the equivalent homogenous medium can describe the infiltration rate or cumulative infiltration of the heterogeneous layered soils well.