Bayesian modeling of flood frequency analysis in bangladesh using Hamiltonian Monte Carlo techniques

Abstract

In recent years, several Bayesian Markov chain Monte Carlo (MCMC) methods have been proposed in extreme value analysis (EVA) for assessing the flood risk in a certain location. In this study, the Hamiltonian Monte Carlo (HMC) method was employed to obtain the approximations to the posterior marginal distribution of the Generalized Extreme Value (GEV) model by using annual maximum discharges in two major river basins in Bangladesh. As a comparison, the well-known Metropolis-Hasting (MH) algorithm was also applied, but did not converge well and yielded skewness values opposite those of HMC and the statistical characteristic of the data sets. The discharge records of the Ganges and Brahmaputra rivers in Bangladesh for the past 42 years were analyzed. To estimate flood risk, a return level with 95% confidence intervals (CI) has also been calculated. Results show that the shape parameter of each station was greater than zero, which describes the heavy-tailed Fréchet cases of the GEV distributions. One station, Bahadurabad in the Brahmaputra river basin, estimated 141,387 m3·s-1 with a 95% CI range of [112,636, 170,138] for the 100-year return level, and the 1000-year return level was 195,018 m3·s-1 with a 95% CI of [122,493, 267,544]. The other station, Hardinge Bridge at the Ganges basin, estimated 124,134 m3·s-1 with a 95% CI of [108,726, 139,543] for the 100-year return level, and the 1000-year return level was 170,537 m3·s-1 with a 95% CI of [133,784, 207,289]. As Bangladesh is a flood-prone country, the approach of Bayesian with HMC in EVA can help policy-makers to plan initiatives that could result in preventing damage to both lives and assets.