Application and Validation of an Upscaling Method for Unsaturated Water Flow Processes in Heterogeneous Soils

Upscaling of soil water flow processes and soil hydraulic properties is one of the most important issues in vadose zone research. The difficulties in such upscaling come from the heterogeneity and nonlinearity of the soil properties. Sharing some common element with the multiscale methods, an upscaling method was previously proposed for a class of nonlinear parabolic equations including the Richards equation, which is often used for modeling flow processes in soils. To verify its applicability in more realistic and varied flow scenarios, in this study we applied the method to one‐ and two‐dimensional simulations of unsaturated water flow through heterogeneous soil profiles under different boundary conditions including infiltration, evaporation, and drainage. The Gardner–Basha model and the Mualem–van Genuchten model were used as the constitutive relations to close the Richards equation. Results show that the upscaling method can effectively capture the large‐scale structure of fine‐scale behavior in these realistic and varied scenarios. Note that in this study we pre‐calculated the effective hydraulic functions by solving the local problems outside the coarse‐scale simulation to avoid the expensive computation of upscaling these functions, which need to be updated at each time step on each coarse block. In our examples, we observed that, compared with the upscaling method that calculates the effective hydraulic functions by solving the fine‐scale problems during the coarse‐scale simulation, the upscaling method with pre‐calculation saved more than 83 and 90% of the central processing unit time in the one‐ and two‐dimensional simulations, respectively, without compromising accuracy.