Abstract
Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. They have also significant social, economical and environmental consequences because they considerably damage urban as well as rural areas. Early detection of extreme maximum rainfall helps to implement strategies and measures, before they occur. Extreme value theory has been used widely in modelling extreme rainfall and in various disciplines, such as financial markets, insurance industry, failure cases. Climatic extremes have been analysed by using either generalized extreme value (GEV) or generalized Pareto (GP) distributions which provides evidence of the importance of modelling extreme rainfall from different regions of the world. In this paper, we focus on Peak Over Thresholds approach where the Poisson-generalized Pareto distribution is considered as the proper distribution for the study of the exceedances. This research considers also use of the generalized Pareto (GP) distribution with a Poisson model for arrivals to describe peaks over a threshold. The research used statistical techniques to fit models that used to predict extreme rainfall in Tanzania. The results indicate that the proposed Poisson-GP distribution provide a better fit to maximum monthly rainfall data. Further, the Poisson-GP models are able to estimate various return levels. Research found also a slowly increase in return levels for maximum monthly rainfall for higher return periods and further the intervals are increasingly wider as the return period is increasing.
Highlights
Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life
Exceedances over threshold can be modelled by Generalized Pareto (GP) distribution, and dependence of exceedances can be modelled by de-clustering method
Distribution: A Case Study Tanzania of Peaks Over Threshold (POT) is that it produces dependent data, so we need to consider the dependence of data prior to its use
Summary
Extreme rainfall events have caused significant damage to agriculture, ecology and infrastructure, disruption of human activities, injury and loss of life. Since such extremes significantly affect societies [1], it becomes necessary to understand and analyse changes in them. According to the study [8], some towns in Tanzania, for example Dar es Salaam and Mwanza, experience floods almost every rainy season and causes significant damage. The study [18] using GEV and GP distributions to define the extreme, generalized pareto distribution was found to be the best to model extreme rainfall in Tanzania. In this research a threshold model (known as POT model) is used to model frequency of extreme rainfall occurrences and to quantify future return level of extreme rainfall in Tanzania
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