Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2. Numerical simulations

Two models for horizontally averaged unsaturated flow have been developed from two different approaches in the first (Chen et al., this issue) of these companion papers. In this paper the results from both the spatially horizontally averaged Richards equation (SHARE) model and the averaged Green‐Ampt model are compared with the results from a three‐dimensional finite difference model of unsaturated flow which is perceived as the reference solution. The results of the averaged Green‐Ampt model show very good agreement with the averaged results from the three‐dimensional model, while SHARE model results are applicable only when fluctuations in soil parameters are small with respect to their mean values. It is also shown that methods of simple parameter averaging (arithmetic or geometric averages) with the local Richards equation does not yield meaningful results in heterogeneous soils. This study suggests that spatially horizontally averaged simplified models (such as the averaged Green‐Ampt model) are attractive alternatives to perturbation models (such as the SHARE model) in heterogeneous fields. Due to their simplicity in formulation, accuracy in predicting average behaviors, and minimal requirement of computer effort, the spatially horizontally averaged simplified models can be easily implemented in large‐scale models, such as atmospheric mesoscale models.