Citation:

He, J., Mohamed M. Hantush, L. Kalin, M. Rezaeianzadeh, AND S. Isik. A two-layer numerical model of soil moisture dynamics: Model development (journal article). JOURNAL OF HYDROLOGY. Elsevier Science Ltd, New York, NY, 602:126797, (2021). https://doi.org/10.1016/j.jhydrol.2021.126797

Impact/Purpose:

Soil moisture plays an essential role in regulating hydrological and biogeochemical processes. Accurately modeling moisture content in variably saturated soil media is fundamental to land-surface coupling simulations in large-scale watershed models and land surface models (LSMs). Current large-scale watershed models and LSMs apply either reservoir cascade scheme or Richards equation (RE) to estimate vertical water movement and soil moisture content at a reasonable computational cost. RE provides relatively accurate predictions of soil moisture over other approaches due to its clear physical basis. However, solving RE numerically has always been challenging because of its high nonlinearity and computational burden, especially when RE is employed in large-scale watershed and hydro-climate applications. Recently, the authors developed a two-layer approximation of RE for the situations with shallow water table. The two-layer model has shown promising results in estimating average soil moisture contents in relatively thin soil root zone and the vadose zone below. To address situations that soil profile cannot be distinguished into two soil layers (e.g. stratified soil with varying soil textures or applications that require higher vertical resolution) and that higher vertical resolution of q distribution is required, the two-layer model was extended to multiple layers in this study, and a numerical scheme was developed to solve coupled ordinary differential equations (ODEs) describing layer-averaged soil moisture dynamics for predefined soil layers. The multiple layer-averaged RE (LARE) solution solves the coupled ODEs using Heun’s method with time adaptive algorithm and like the two-layer model it also accounts for prescribed flux and pressure head boundary conditions at the soil surface, including precipitation, ponding, soil evaporation, and plant transpiration, subject to deep and shallow dynamic water table. LARE was evaluated by five testing scenarios against analytical solutions, HYDRUS 1-D solver, and field soil moisture observations. The model provided accurate estimations of moisture contents for multiple soil layers, and it was computationally efficient in accounting for complex, dynamic prescribed boundary conditions without any convergence issues. LARE is numerically stable and computational efficient, it is suitable for modeling water movement, and soil moisture for multiple layered soils at both field and watershed scale.

Description:

Simulating water moisture flow in variably saturated soils with a relatively shallow water table is challenging due to the high nonlinear behavior of Richards' equation (RE). A two-layer approximation of RE was derived in this paper, which describes vertically-averaged soil moisture content and flow dynamics in the root zone and the unsaturated soil below. To this end, the partial differential equation (PDE) describing RE was converted into two-coupled ordinary differential equations (ODEs) describing dynamic vertically-averaged soil moisture variations in the two soil zones subject to a deep or shallow water table in addition to variable soil moisture flux and pressure conditions at the surface. The coupled ODEs were solved numerically using the iterative Huen's method for a variety of flux and pressure-controlled top and bottom boundary conditions (BCs). The numerical model was evaluated for three typical soil textures with free-drainage and mixed flux-pressure head at the bottom boundary under various atmospheric conditions. The results of soil water contents and fluxes were validated using HYDRUS-1D as a benchmark. Simulated values showed that the new model is numerically stable and generally accurate in simulating vertically-averaged soil moisture in the two layers under various flux and prescribed pressure BCs. 

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