On Climate Change and Its Impact on Extreme Rainfall in Bangladesh

In recent years extreme value distributions have attracted a fair amount of attention in literature for risk assessment based on climate data. This thesis focuses on modeling a series of rainfall data over 58 years in the period 1954-2012 recorded at five different stations in Bangladesh. Inference on the extreme rainfall is essential for making the necessary steps to reduce damage caused by natural calamities as well as to save life and property. One might ask if extreme rainfalls are occurring more frequently now or whether there is dependence in extreme rainfalls between two regions. To answer these questions, considering a bivariate framework, we model rainfall data from two stations simultaneously and investigate the dependence structure in extreme rainfall between the locations. As a starting point the generalized extreme value distributions are used for fitting annual maximum rainfall according to the Block Maxima approach. Also generalized Pareto distributions are fitted to daily rainfall data considering Peaks over Thresholds (PoT) method. We assess the uncertainty in the estimates of the parameters by constructing 95% confidence interval using both delta and profile likelihood methods. Return levels for different return periods are also estimated for both models. Monte Carlo simulation approach is suitable to predict future return level when the number of exceedances is uncertain. Thereafter, return levels with bootstrap confidence interval are estimated from simulated data. Finally, we model the tail dependence of extreme rainfall between two locations using bivariate extreme value distribution (BEVD) and bivariate generalized Pareto distribution (BGPD) with unit Fréchet margins. In recent years this extreme value distributions have attracted a fair amount of attention in literature for risk assessment based on climate data. Both parametric and non-parametric dependence functions are used in BEVD models. In addition, BGPD models are fitted considering 95% thresholds based on daily rainfall data but only parametric dependence structure are considered in this case. Finally we quantify risks by calculating joint probability of extreme rainfalls using BEVD models.