Modelling of rainfall data using extreme value theory and a temporal stochastic model

Abstract

Climate change is contributing to unforeseen risks for the environment and society. Hence, scientists continuously seek and explore the relationship between past and future climates by virtue of observations and theoretical models. The outcome will help policy makers prepare for and therefore contain the impacts of extreme weather events when they happen. This work models daily precipitation data for the Maltese Islands and provides a statistically based description of probable future weather conditions. Different statistical methods pertaining to Extreme Value Theory, specifically the Block Maxima Model and the Points Over Threshold approach, are used to fit the Generalized Extreme Value distribution and the Generalized Pareto distribution to the yearly maxima and to the observations over a specified threshold, respectively. Future extreme events are predicted by the use of return level plots. Moreover, the method of de-clustering as proposed by Walshaw (1994) is adopted to cater for dependence. Finally, a temporal stochastic model for rainfall - the Neyman-Scott Rectangular Pulses model as proposed by Cowpertwait (1991) - is used to better comprehend the dynamic randomness of precipitation. Both the Generalized Extreme Value distribution and the Generalized Pareto distribution fit the data adequately. However, the Generalized Pareto seems to give better return levels since more data points are considered in the Points Over Threshold approach. The inadequacy of fit of the stochastic model shows that the Neyman-Scott Rectangular Pulses model is not ideal to model rainfall in the Maltese Islands.