Channel Routing by Finite Difference Method

A finite difference model that can be easily incorporated into a watershed model is presented for flood routing through natural stream channels. The advantages of the method lie not only in its simplicity but also in the ease with which channel data can be determined from topographic maps. The required input on discharge-flow area relationship can be computed by Manning's formula or obtained directly from the water surface profile computer programs. Both the linear and nonlinear methods of channel routing are described. It was found that linear routing is unconditionally stable and yields good results if the time increment is kept sufficiently small. The use of smaller time increments not only reduces the discrepancy between linear and nonlinear routings but also gives more consistent results when different input data are used to characterize the discharge-flow area relationship. The method was incorporated into MOPSET, a self-calibrating Kentucky Watershed Model, and found to be satisfactory.