Technical Note: Probability Distribution of Extreme Rainfall Series for Conservation Planning in a Sub-Humid Climate

Abstract

The magnitude of a design storm, which is defined as the rainfall depth expected at a specified location for a given storm duration and probability of occurrence, is usually estimated by analyzing the extreme value rainfall data. A reliable estimate of the design storm, typically expressed in terms of return period, is essential for the design of conservation structures and efficiently managing the water resources. This problem is generally addressed by employing appropriate probability distributions describing the events in a given location. In this study, the annual extreme daily rainfall data of four stations was collected and analyzed in a sub-humid climate. Six two-parameter probability distributions, namely extreme value I, extreme value II, log-normal, gamma, logistic, log-logistic, and four three-parameter probability distributions, namely log-normal, extreme value II, gamma and log-logistic were compared for selecting appropriate distribution(s) to adequately describe the annual maximum one-day rainfall data. Maximum likelihood estimation technique was employed for obtaining parameter estimates of these distributions. The study on suitability of additional parameter in a three-parameter distribution over the two-parameter distribution of the same family revealed that no three-parameter distribution described the present data adequately. Two-parameter extreme value I along with log-normal and log-logistic distributions was found to be the best-fit for annual extreme daily rainfall data of Sahastradhara, Mussoorie, and Fakot stations in Uttarakhand state of India. Analysis of similar data of another station namely, Selakui revealed that two-parameter probability distributions, such as log-normal, extreme value I, gamma and log-logistic were found to describe the data almost equally well. On the basis of smallest variance of estimated extreme rainfall values in different return period and sample size combinations, extreme value I probability distribution was found to be most appropriate, and provided most stable estimate for describing annual extreme daily rainfall data. Annual extreme daily rainfall was estimated for 5-, 10-, 15-, 20-, 25-, and 30-year return periods using the best-fit two-parameter probability distributions for different stations. The region was found to be homogeneous. The best-fit distribution used to compute annual extreme daily rainfall values is an essential pre-requisite for designing soil and water conservation structures economically and efficiently.