Diffusion Wave Modeling of Catchment Dynamics

Abstract

A diffusion wave method for catchment dynamics is presented. The method has better convergence properties than kinematic wave models which use off‐centered derivatives in their numerical formulations. Unlike the off‐centered schemes, the diffusion wave scheme is formulated by matching physical and numerical diffusivity. This results in an effective control of numerical diffusion and leads to simulations which are essentially independent of grid size. The diffusion method is further extended to the realm of dynamic waves by including the Froude number dependence of the physical diffusivity. The resulting formulation is believed to represent as complete a description of the wave dynamics as is possible within the framework of diffusion wave theory. Numerical experiments show that the diffusion wave method has better convergence properties than existing kinematic wave models featuring uncontrolled numerical diffusion.