Development of a generalized Hayami solution for modelling of a diffusive flood wave in arid and non-arid regions

Abstract

Hayami analytical solution for the modelling of a diffusive flood wave is developed and generalized by introducing an additional term, the ‘decay coefficient’ which can influence the shape and the peak of the flood hydrograph while passing in an ephemeral stream and making it robust to handle any shape of the inflow storm hydrograph, respectively. Furthermore, a spreadsheet model of Hayami solution is proposed that takes the inflow flood hydrograph, comprising of unit floods (pulses). It is tested on two Hayami examples, showing identical results. Sensitivity analysis is performed for the selection of a number of pulses that can sway the accuracy of the simulated results. Taking 10 pulses as a reference case, the RMSE converges from 0.7 at one pulse to 0.03 at eight pulses. The significance of this model is proven by its application on the real field data of Yiba catchment, located in Saudi Arabia, where the diffusion coefficient larger than 400 m2/s shows the divergence of the RMSE and the values between 50 and 400 m2/s are the fair estimates in ephemeral streams. Besides, it can also be used as a benchmark tool for testing other numerical schemes.