Abstract
Abstract. Accurately capturing the complex soil-water and groundwater interactions is vital for describing the coupling between subsurface–surface–atmospheric systems in regional-scale models. The nonlinearity of Richards' equation (RE) for water flow, however, introduces numerical complexity to large unsaturated–saturated modeling systems. An alternative is to use quasi-3-D methods with a feedback coupling scheme to practically join sub-models with different properties, such as governing equations, numerical scales, and dimensionalities. In this work, to reduce the nonlinearity in the coupling system, two different forms of RE are switched according to the soil-water content at each numerical node. A rigorous multi-scale water balance analysis is carried out at the phreatic interface to link the soil-water and groundwater models at separated spatial and temporal scales. For problems with dynamic groundwater flow, the nontrivial coupling errors introduced by the saturated lateral fluxes are minimized with a moving-boundary approach. It is shown that the developed iterative feedback coupling scheme results in significant error reduction and is numerically efficient for capturing drastic flow interactions at the water table, especially with dynamic local groundwater flow. The coupling scheme is developed into a new HYDRUS package for MODFLOW, which is applicable to regional-scale problems.
Highlights
Numerical modeling of the soil-water and groundwater interactions has to deal with flow components and governing equations at different scales
Compared with the HYDRUS-1D model, the switching-form method was numerically more robust, i.e., with larger minimal time-step sizes and a lower computational cost, where a minimal time-step size 10−3 days was stable for convergence
At the beginning of the sudden infiltration into a dry sandy soil, in Fig. 7a, the tmin for a switching method was 10−3 days, even at early infiltration times, while for the h-form methods, including HYDRUS-1D and the coupled h-form method, tmin was constrained to 10−8 days before reaching a painstaking convergence
Summary
Numerical modeling of the soil-water and groundwater interactions has to deal with flow components and governing equations at different scales. This adds significant complexity to model development and calibration. Unsaturated soilwater and saturated groundwater flows with similar properties are usually integrated into a whole modeling system. Parsimonious approaches, which appear in different governing equations and coupling schemes, are developed for modeling the soil-water and groundwater interactions at regional scales. Simplifying the soil-water flow details into upper flux boundaries has been widely used to simulate large-scale saturated flow dynamics, such as the MODFLOW package and its variants (Langevin et al, 2017; Leake and Claar, 1999; McDonald and Harbaugh, 1988; Niswonger et al, 2011; Panday et al, 2013; Zeng et al, 2017). In contrast, the unsaturated flow processes are usually approximated with reasonable simplifications and assumptions in RE (Bailey et al, 2013; Liu et al, 2016; Paulus et al, 2013; Šimunek et al, 2009; van Dam et al, 2008; Yakirevich et al, 1998; Zha et al, 2013b)
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