A multistate first-order Markov model for modeling time distribution of extreme rainfall events
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ORIGINAL PAPER
A multistate first-order Markov model for modeling time distribution of extreme rainfall events A. N. Rohith1,2 • Margaret W. Gitau2
•
I. Chaubey3 • K. P. Sudheer1,2,4
Received: 29 June 2020 / Revised: 12 October 2020 / Accepted: 12 November 2020 The Author(s) 2020
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. Keywords Extreme rainfall events Time-distribution of rainfall First-order Markov model Dimensionless mass curve Return periods
1 Introduction
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00477-020-01939-1) contains supplementary material, which is available to authorized users. & Margaret W. Gitau [email protected] 1
Department of Civil Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India
2
Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, Indiana, USA
3
College of Agriculture, Health and Natural Resources, University of Connecticut, Storrs, Connecticut, USA
4
Kerala State Council for Science, Technology, and Environment, Thiruvananthapuram, Kerala, India
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 m
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