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

A N Rohith,Margaret W Gitau,I Chaubey,K P Sudheer

doi:10.1007/s00477-020-01939-1

Abstract

The 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.

Highlights

Statistical analysis and characterization of extreme rainfall is a critical part of the design of various hydraulic structures related to urban stormwater management
It was observed that the extreme rainfall events of Indian cities could be classified into five groups based on the pattern of DRMC and the duration, which are: 1 h, 2 h, 3–6 h, 7–12 h, and 13 h and above
Extremes of 7–12 h had slightly less dominant peaks compared to 3–6 h events, as evidenced by relatively smoother DRMC in Fig. 3, and extremes of greater than 13 h had more of uniform intensity in nature

Summary

Introduction

Statistical analysis and characterization of extreme rainfall is a critical part of the design of various hydraulic structures related to urban stormwater management. Recent studies have endorsed the use of event-based multivariate analysis over a critical duration-based univariate design storm approach for this purpose (Park et al 2013; Balistrocchi and Bacchi 2017; Jun et al 2017, 2018). This is due to the flexibility that event-based analysis provides, allowing critical rainfall properties to be characterized more realistically than through critical duration-based analysis. With a univariate design storm approach, the frequency analysis is carried out only on the maximum rainfall depth that occurred over a predefined critical duration This critical duration is usually less than the actual rainfall event duration, only a part of the rainfall event is considered. With event-based analysis, the actual duration, depth, and peak intensity of rainfall events are studied together, which results in a more realistic analysis

Methods

Results

Discussion

Conclusion