Analytical Derivation of Overland Travel Time Based on Diffusive Wave Solution: Fid-Bau Portal

Analytical Derivation of Overland Travel Time Based on Diffusive Wave Solution

Niri, Mahmoud Zakeri / Saghafian, Bahram / Golian, Saeed

Derivation of spatial distribution of travel time is required in some conceptual rainfall-runoff transformation models. Application of a kinematic wave (KW) solution to delineate isochrones of travel time may be straightforward, particularly in an overland flow regime. In this article, a new analytical approach based on the diffusive wave (DW) solution is developed for calculation of travel time. The discharge hydrograph over a rectangular plane will be calculated based on the developed analytical DW method through the application of the time-area method. Differences between calculated maximum travel time (i.e., equilibrium time), isochrone locations, and outflow discharge between the KW and DW solutions are compared with those of the numerical dynamic wave (DYW) solution. It is shown that analytical DW results are closer to those of the DYW in comparison with those of the KW. The effect of the $K_{0} F_{0}^{2}$ number on the solution accuracy is investigated, where $K_{0}$ is the kinematic wave number and $F_{0}$ is the Froude number. It is perceived that as $K_{0} F_{0}^{2}$ decreases, the differences between KW and analytical DW solutions grow. For instance, at equilibrium time, the new DW solution improved the results by 5 to 12% over the KW solution. In addition, the DW isochrones lie upstream of the corresponding KW isochrones. Finally, the $1.5 < K_{0} F_{0}^{2} < 20$ interval is proposed for using an analytical DW solution in lieu of the KW and DYW solution.