Peak-over-threshold analysis of extreme Rainfall in the North Western Region of Rwanda

Abstract

Extreme rainfall events over northwestern (N-W) of Rwanda causes floods and landslides which have a major impact on society and lead to loss of property and life. The main objective of this study is to study extreme rainfall in Northwestern of Rwanda using peak over threshold method. This research modelled and predicted extreme rainfall events in NW using extreme value theory, where daily rainfall data from Rwanda Meteorological Agency for three stations Gisenyi, Ruhengeri and Rubengera from the years 1981 to 2018 representing the area of study were utilized. Peak over threshold method (POT) was used to fit the generalized Pareto distribution, both the mean residual life plot and the parameter stability plot were chosen as the choice of threshold used in this study. Rainfall above threshold were selected with different threshold values which represents the 99 percentiles for each station. After threshold selection, the parameters such as scale 𝜎 and shape 𝜉were estimated using maximum likelihood estimator and these parameters are obtained numerically. To verify POT, we have made some diagnostic test such as quantile-quantile plot (Q-Q plots) and profile likelihood for all stations, almost all point lies to the line that means that our model is adequate. For all stations confidence interval of 95% include the zero for the shape parameter that is, the data fits the exponential distribution except Gisenyi station which indicated negative for shape parameter as estimated. Furthermore, prediction for the return periods of 20, 50, 80, 100, 150 and 200 years for all stations were made using return level estimates and their corresponding confidence interval were presented. It was found that an increase in return periods lead to an increase in return levels and this indicates that the frequency of occurrence is increasing.