Flood Frequency Analysis Using Bayesian Paradigm

Abstract

At-site flood frequency analysis (FFA) of extreme hydrological events under Bayesian paradigm has been carried out and compared with frequentist paradigm of maximum likelihood estimation (MLE). The main objective of this chapter is to identify the best approach between Bayesian and frequentist one for at-site FFA. As a case study, the data of only two stations were used, Kotri and Rasul, and Bayesian and MLE approaches were implemented. Most commonly used tests were applied for checking initial assumptions. Goodness of fit (GOF) tests were used to identify the best model, which indicated that the generalized extreme value (GEV) distribution appeared to be best fitted for both stations. Under Bayesian paradigm, quantile estimates are constructed using Markov Chain Monte Carlo (MCMC) simulation method for their respective returned periods and non-exceedance probabilities. For MCMC simulations, as compared to other sampler, the M-H sampling technique was used to generate a large number of parameters. The analysis indicated that the standard errors of the parameters' estimates and ultimately the quantiles' estimates using Bayesian methods remained less as compared to maximum likelihood estimation (MLE), which shows the superiority of Bayesian methods over conventional ones in this study. Further, the safety amendments under two techniques were also calculated, which also show the robustness of Bayesian method over MLE. The outcomes of these analyses can be used in the selection of better design criteria for water resources management, particularly in flood mitigation.