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).

Attach file: 

Qu_Duffy_2006WRR.pdf