Power Bayesian Markov Chain Monte Carlo (MCMC) for Modelling Extreme Temperatures in Sumatra Island Using Generalised Extreme Value (GEV) and Generalised Logistic (GLO) Distributions

Abstract

Climate projections suggest that the frequency and intensity of some environmental extremes will be affected in the future because of climate change. Climate change has brought about new, unprecedented weather patterns, including changes in extreme temperature. Ecosystems and various sectors of human activities are sensitive to high and low temperatures, especially when these occur over extended periods. Sumatra Island is part of the Indonesian state, where most provinces are trough by tropical climates and have annual maximum daily temperatures varying from 72°F –97°F. This study focuses on the reduction and management of the disaster risk that occurs as a result of extreme high temperatures that lead to global change and heat waves. The main goal of this study is to find the best-fitting distribution to extreme daily temperatures measured over the 12 stations on Sumatra Island in 1999–2019 by using the power of Bayesian Markov Chain Monte Carlo (MCMC) approach. The study also predicts the extreme temperatures for the next 10, 50 and 100 years through return periods. In this study, extreme temperature events are defined by methods based on the annual maximum of daily temperature. Generalised extreme value (GEV) and generalised logistic (GLO) distributions are fitted to data corresponding to the methods to describe the extremes of temperature and predict its future behaviour. Graphical inspection [distribution function (cdf)] and numerical criteria [root mean square error (RMSE)] are used to select the most suitable model. In most cases, graphical inspection gives similar results but the RMSE results differ. Finally, we find evidence that suggests most regions (S1, S3, S5, S6, S7, S8, S9, S10, S11 and S12) have a GEV distribution, which provides the most appropriate model for the annual maximums of daily temperatures, while the GLO distribution gives the reasonable model for the daily temperature data for the S2 and S4 locations. Furthermore, estimates of 10-, 50- and 100-year return levels for extreme temperatures are derived on the basis of the identified model.