Mathematical Model for Sediment Wash-Off from Urban Impervious Surfaces

Mathematical models are significant tools for urban runoff management. A rational account of sediment-limited and energy-limited situations in developing a mathematical model may facilitate the improved simulation of total suspended solid (TSS) wash-off in urban impervious surfaces. In this study, a differential equation called the P/r model is proposed to improve the simulation of the sediment discharge process. In this equation, rainfall intensity and the ratio of sediment mass per unit catchment area to rainfall intensity are considered the main variables. The rationality behind the P/r model is analyzed. TSS wash-off from six rainfall events is investigated using the P/r model. Uncertainty analyses are performed to determine the best-fit parameters for the model, with the maximum Nash-Sutcliffe efficiency (NSE) criterion being 0.53 and the minimum normalized objective function being 0.40. The observation percentage within prediction bands is 75%, and the average relative interval length is 1.07 when the NSE is 0.50. Results show that the proposed mathematical model can fit well with the TSS data observed in the case study.