Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields: 1. Development of models

Abstract

Unsaturated flows within subsurface regions control many large‐scale hydrological and environmental processes. This study addresses the issue of spatial averaging of unsaturated flow equations at field scales. Two models for horizontally averaged unsaturated flow have been developed from two different approaches in this study. The spatially horizontally averaged Richards equation (SHARE) model is represented by a system of two coupled partial differential equations for the mean water saturation in each horizontal soil layer and the cross‐covariance of the saturated hydraulic conductivity and the water saturation in each horizontal soil layer in a heterogeneous field. As an alternative to the spatial averaging/perturbation approach which was used for SHARE, a spatially horizontally averaged form of Green‐Ampt model is obtained by field scale spatial horizontal averaging of the local soil water dynamics which are represented approximately by rectangular profiles. This strategy leads to analytical solutions for average water content and the results can be upscaled to large spatial areas. The computational effort required to evaluate such analytic expressions is trivial in comparison with that of the numerical solution of Richards equation. The averaged Green‐Ampt model, though approximate, yields good results when large variations exist in the soil properties in the horizontal directions.