Investigating the tail behaviour and associated risk with daily discharges in South Indian Rivers

Abstract

The adequate choice of a distribution that can fit a dataset, especially to its right tail (large extreme events), is a major problem in flood frequency analysis. Decision support systems (DSS) have been used in the past to define the appropriate class of distribution based on the tail behaviour of the data before its model selection. This paper investigates the tail behaviour of probability distribution of the daily streamflow data in south Indian rivers and also assesses the information related to tail risk, as it has many practical and societal consequences. In this paper, we apply and compare two DSS, (i) given by Martel et al. (J Hydrol Eng 18(1):1–9, 2013) and (ii) concentration profile–concentration adjusted expected shortfall (CP–CAES) based DSS, along with some newly developed graphical diagnostic tools, such as CP, CAES, discriminant moment ratio plot, maximum-to-sum plot, and Zenga plot to characterize the tails of probability distributions into an appropriate class. Further, the tail risk is analyzed using a novel risk management approach known as a concentration map (CM), which makes use of the concentration profiles of daily streamflow datasets. Results indicate that the proposed DSS is a potential tool for tail characterization. The study suggests the use of heavy-tailed distributions to model daily streamflow data over south Indian catchments. Neglecting heavy-tailed distributions, when found appropriate, can lead to an underestimation of the likelihood of floods and has catastrophic consequences for risk. CM is found suitable for assessing the tail risk associated with the daily streamflow dataset, which inherently represents the frequency and magnitude of extreme floods.