A semidiscrete finite volume formulation for multiprocess watershed simulation

Abstract

Hydrological processes within the terrestrial water cycle operate over a wide range of time and space scales, and with governing equations that may be a mixture of ordinary differential equations (ODEs) and partial differential equations (PDEs). In this paper we propose a unified strategy for the formulation and solution of fully coupled process equations at the watershed and river basin scale. The strategy shows how a system of mixed equations can be locally reduced to ordinary differential equations using the semidiscrete finite volume method (FVM). Domain decomposition partitions the watershed surface onto an unstructured grid, and vertical projection of each element forms a finite volume on which all physical process equations are formed. The projected volume or prism is partitioned into surface and subsurface layers, leading to a fully coupled, local ODE system, referred to as the model “kernel.” The global ODE system is assembled by combining the local ODE system over the domain, and is then solved by a state‐of‐the‐art ODE solver. The unstructured grid, based on Delaunay triangulation, is generated with constraints related to the river network, watershed boundary, elevation contours, vegetation, geology, etc. The underlying geometry and parameter fields are then projected onto the irregular network. The kernel‐based formulation simplifies the process of adding or eliminating states, constitutive laws, or closure relations. The strategy is demonstrated for the Shale Hills experimental watershed in central Pennsylvania, and several phenomena are observed: (1) The enslaving principle is shown to be a useful approximation for soil moisture–water table dynamics for shallow soils in upland watersheds; (2) the coupling shows how antecedent moisture (i.e., initial conditions) can amplify peak flows; (3) the coupled equations predict the onset or threshold for upland ephemeral channel flow; and (4) the model shows how microtopographic information controls surface saturation and connectivity of overland flow paths for the Shale Hills site. The open‐source code developed in this research is referred to as the Penn State Integrated Hydrologic Model (PIHM).