A Numerical Model for Integrated Form of Richards Equation

ABSTRACT Modelling volumetric water content and fluxes in unsaturated soils is fundamental to land surface‐groundwater coupling simulations. Richards equation (RE) provides relatively accurate predictions of soil moisture due to its fundamentally sound physical basis. However, numerical solutions of RE are often computationally demanding and can be challenging to obtain under highly variable hydro‐climate conditions due to its high nonlinearity, especially when used in large‐scale hydro‐climate applications. By adopting the integrated form of RE, this paper presents a Layer‐Averaged solution of RE (LARE) to simulate volumetric water content and fluxes in stratified soil profiles. To this end, a coupled system of ordinary differential equations was developed, which addresses complex hydroclimate boundary conditions at the soil surface and dynamic water table conditions at the soil bottom. The model was verified by comparison against analytical solutions, HYDRUS 1‐D, and finite difference schemes for homogeneous and heterogeneous soil profiles. Robustness of the model to reproduce and interpret real field was demonstrated under real time‐variable hydrometeorological conditions imposed at the soil surface. Uncertainty bounds for model simulated volumetric water content were constructed using the Bayesian Monte Carlo method, revealing that hydrometeorological inputs and model structural errors were major source of predictive uncertainty and the contribution of parametric uncertainty was marginal. The accuracy and numerical efficiency of LARE makes it a suitable, alternative numerical scheme for solving RE at finer spatial resolution and at sufficiently coarser resolutions. The model has the potential to be integrated into land surface models for large‐scale watershed soil moisture dynamics simulations.