Stationary and Non-stationary Extreme Value Approaches for Modelling Extreme Temperature: the Case of Riyadh City, Saudi Arabia

Abstract

Climate change is one of the most fiercely debated scientific issues in recent decades, and the changes in climate extremes are estimated to have greater negative impacts on human society and the natural environment than the changes in mean climate. Extreme value theory is a well-known tool that attempts to best estimate the probability of adversarial risk events. In this paper, the focus is on the statistical behaviour of extreme maximum values of temperature. Under the framework of this theory, the methods of block maxima and threshold exceedances are employed. Due to the non-stationary characteristic of the series of temperature values, the generalized extreme value distribution and the generalized Pareto distribution were extended to the non-stationary processes by including covariates in the parameters of the models. For the purpose of obtaining an approximately independent threshold excesses, a declustering method was performed and then the de-clustered peaks were fitted to the generalized Pareto distribution. The stationary Gumbel distribution was found a reasonable model for the annual block maxima; however, a non-stationary generalized extreme value distribution with quadratic trend in the location was recommended for the half-yearly period. The findings also show that there is an improvement in modelling daily maxima temperature when it is applied to the declustered series and the given model outperforms the non-stationary generalized Pareto distribution models. Furthermore, the retained generalized Pareto distribution model proved better than the generalized extreme value distribution. Estimates of the return levels obtained from both extreme value models show that new records on maximum temperature event could appear within the next 20, 50 and 100 years.