A multistate first-order Markov model for modeling time distribution of extreme rainfall events

Abstract

AbstractThe time distribution of extreme rainfall events is a significant property that governs the design of urban stormwater management structures. Accuracy in characterizing this behavior can significantly influence the design of hydraulic structures. Current methods used for this purpose either tend to be generic and hence sacrifice on accuracy or need a lot of model parameters and input data. In this study, a computationally efficient multistate first-order Markov model is proposed for use in characterizing the inherently stochastic nature of the dimensionless time distribution of extreme rainfall. The model was applied to bivariate extremes at 10 stations in India and 205 stations in the United States (US). A comprehensive performance evaluation was carried out with one-hundred stochastically generated extremes for each historically observed extreme rainfall event. The comparisons included: 1-h (15-min); 2-h (30-min); and, 3-h (45-min) peak rainfall intensities for India and (US) stations, respectively; number of first, second, third, and fourth-quartile storms; the dependence of peak rainfall intensity on total depth and duration; and, return levels and return periods of peak discharge when these extremes were applied on a hypothetical urban catchment. Results show that the model efficiently characterizes the time distribution of extremes with: Nash–Sutcliffe-Efficiency > 0.85 for peak rainfall intensity and peak discharge; < 20% error in reproducing different quartile storms; and, < 0.15 error in correlation analysis at all study locations. Hence the model can be used to effectively reproduce the time distribution of extreme rainfall events, thus increasing the confidence of design of urban stormwater management structures.