Determining overland flow hydrographs from sections of nonuniform width

Abstract

Dimensionless hydrographs and equations for the time of equilibrium were developed for sections of nonuniform width. In order to determine the dimensionless hydrographs the equations of momentum and continuity were solved implicitly. This method was chosen because it is unconditionally stable independent of the time and distance increment. Using Manning's Equation for the frictional slope, a time increment of one-twelfth of the time of equilibrium, and boundary conditions of upstream depth and velocity equal to zero the dimensionless hydrograph for uniform sections matched that of the kinematic wave to nearly 60 percent of the equilibrium discharge. It also corresponded well with Morgali's results and Izzard's measured hydrograph.

When the model was applied to sections of nonuniform width it was found only the end ratio, defined as the downstream width over the upstream width, affected the shape of the dimensionless hydrograph and the time of equilibrium. Equations were developed to find the time of equilibrium for ranges of end ratios. Corrections to find the hydrographs for sections of nonuniform width were determined to be applied to the kinematic wave discharge equation. For storms of duration less than the time of equilibrium the recession limb coincides with the recession limb from total equilibrium some time T after the rain ends. The time T was found to be independent of the end ratio and only affected by the discharge when the storm ended.