Derivation of Travel Time Based on Diffusive Wave Approximation for the Time-Area Hydrograph Simulation

Abstract

Derivation of travel time based on Saint-Venant equations may substantially improve rainfall-runoff routing, particularly in the Clark approach and GIS-based hydrological routing models. Kinematic wave (KW) and diffusive wave (DW) approximations are often applied in lieu of the dynamic wave (DYW) solution to study overland flow regime. In this study, for the first time, travel-time relationships are presented based on DWapproximation. In terms of equilibrium time, the DWapproximation improved results from 5% up to 15% over the KW approximation. After obtaining the semianalytical solution of the DW travel time, discharge hydrographs over a rectangular plane through the well-known time-area method were derived. Considering the DYW solution as the benchmark, it was found that the time-area approach by adopting the proposed DW wave travel time formulation, provided satisfactory results for 2:5 0:1. Using the travel time based on KW approach, the time-area method was found fairly accurate for K0F 2 > 25 and F0 > 0:1. K0 and F0 are the well-known kinematic wave number and Froude number, respectively. Therefore, it is perceived that as K0F 2 decreases, the difference between KW and DW approximations becomes greater. DOI: 10.1061/(ASCE)HE.1943-5584.0000399. © 2012 American Society of Civil Engineers. CE Database subject headings: Hydrographs; Simulation; Travel time; Equilibrium; Kinematic wave theory. Author keywords: Diffusion wave; Travel time; Equilibrium time; Time-area method; Hydrograph; Kinematic wave; Isochrones.