Numerical solution of the Richards equation based catchment runoff model with dd-adaptivity algorithm and Boussinesq equation estimator

Abstract

This paper presents a pseudo-deterministic catchment runoff model based on the Richards equation model - the governing equation for subsurface flow. The subsurface flow in a catchment is described here by two-dimensional variably saturated flow (unsaturated and saturated). The governing equation is the Richards equation with a slight modification of the time derivative term, as considered e.g. by Neuman. The nonlinear nature of this problem appears in the unsaturated zone only, so it was possible to make use of adaptive domain decomposition algorithm. However delineating of the saturated zone boundary is a nonlinear computationally expensive issue. The simple one-dimensional Boussinesq equation was used here as a rough estimator of the saturated zone boundary. With this estimate the adaptive domain decomposition could always start with an optimal subdomain split, and thus it is now possible to avoid solving huge systems of linear equations in the initial iteration level. With this measure it is possible to construct an efficient two-dimensional pseudodeterministic catchment runoff model. Finally, the model is tested against real data originating from the Modrava 2 experimental catchment, Czech Republic.