A physically-based flood volume distribution model

An analytically derived distribution model for flood volume is presented. The model is based on water balance computations during a rainstorm at the soil surface. It is applicable for mountainous watersheds with alluvial channels. Three hydrologic processes are considered: precipitation, infiltration, and runoff generation. Rainfall intensity and duration are presented with exponential distributions. They are assumed to be statistically independent. A linear rainfall-runoff relationship is proposed for the mountainous areas. The mountain runoff is regarded as a uniformly distributed water depth on the alluvial channels. The rainfall excess in the alluvial channels is computed to be equal to this depth plus the rainfall depth minus the infiltration losses. Infiltration in the channels is presented with Philip's expression, coupled with an empirical model for the computation of a long-term average value for the soil moisture content. The distribution model is verified through applications for three gauged watersheds in Saudi Arabia: Wadi Liyyah (174 km²), Wadi Turrabah (3720 km²), and Wadi Khulays (5220 km²). The results are found to be in a good agreement with observations.On leave from the Irrigation and Hydraulics Department, Faculty of Engineering, Cairo University, Giza, Egypt.