Finite Element Watershed Modeling: One‐Dimensional Elements

Abstract

A procedure for calculating the spatial and temporal distribution of a direct runoff hydrograph from an ungauged watershed is presented. Nodal values of hydraulic roughness and slope are used to avoid kinematic shock. This formulation allows the simulation of overland flow over spatially variable surfaces typical of natural watersheds. The procedure is compared to an analytic solution for a simple case of a watershed composed of two planes. Broader application to watersheds with spatially variable parameters is possible because of the flexibility of the finite element. The Galerkin formulation of the finite element method is used to solve the kinematic wave equations. The method of characteristic and the finite element method were compared on a two‐plane system with an abrupt change in slope. The numerical and analytical considerations are presented to enable practicing engineers to adopt this method for the calculation of flow depth and discharge rate in a distributed manner throughout a watershed dominated by overland flow. A procedure using two‐dimensional elements is being developed by the writers.