Computing Groundwater Recharge and Saturated Storage Dynamics: A Richards Equation-Based Recipe

In this study, expressions for saturated zone storage change fluxes are derived directly from the governing equation for flow in variably saturated porous media by treating the saturated zone as a subdomain with a moving boundary and using a combination of Gauss' divergence theorem and the Leibnitz rule (Reynolds transport theorem). This formulation is general and can be implemented in any Richards equation-based numerical solver, making it broadly applicable across hydrologic modeling platforms. The derived expressions allow for unambiguous tracking of the various contributing factors to saturated storage dynamics and accommodates both water table-centric definitions of groundwater recharge and broader conceptualizations that can include other sources, sinks, and boundaries. The derived equations are then implemented in a three-dimensional numerical model for integrated surface–subsurface flow, and their behavior is analyzed in three test cases representing a wide diversity of flow conditions and scenarios. By developing these storage and flux expressions directly from the continuous form of the governing flow equation, unlike previous approaches based on the numerical discretization or a post-processing analysis from a model simulation, important physical principles such as mass conservation are ensured, and the methodology is independent of parameterizations that are not present in the fundamental equation, such as occurs for instance when the capillary fringe rather than the water table is used as the upper boundary of the saturated zone. This opens new possibilities for accurately quantifying groundwater recharge and aquifer dynamics in diverse hydrological settings and at broader scales.