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

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 DW approximation. In terms of equilibrium time, the DW approximation 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 $2.5<K_0{F}_0^2<25$ and $F_0>0.1$ . Using the travel time based on KW approach, the time-area method was found fairly accurate for $K_0{F}_0^2>25$ and $F_0>0.1$ . $K_0$ and $F_0$ are the well-known kinematic wave number and Froude number, respectively. Therefore, it is perceived that as $K_0{F}_0^2$ decreases, the difference between KW and DW approximations becomes greater.