Abstract

Hydrological processes within the terrestrial water cycle operate over a wide range of space and time scales, and with governing equations that may be a mixture of ordinary differential equations (ODE) and partial differential equations (PDE). 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 (ODE) using the semi-discrete 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 using GIS tools, 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 PA, and several phenomena are observed: 1) the enslaving principal 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 micro-topographic information controls surface saturation and connectivity of overland flow paths

Citation

Qu, Y., Duffy, C. J. (2007): A semi-discrete finite volume formulation for multiprocess watershed simulation. Water Resour. Res., 43, W08419,. DOI: 10.1029/2006WR005752