Modelling extreme flood heights in the lower Limpopo River basin of Mozambique using a time-heterogeneous generalised Pareto distribution

In this paper we fit a time-heterogeneous generalised Pareto distribution (GPD) to the flood heights in the lower Limpopo River basin of Mozambique (LLRB). The maximum likelihood method is used for parameter estimation of the nonstationary GPD. We take an in-depth review of the merits of peaks-over-threshold and block maxima. We also show the relationship between generalised extreme value (GEV) distribution and GPD in a mathematical proof and discuss the link between the mathematical proof and the findings. Nonstationary time-dependent GPD models with a trend in the scale parameter are considered in this study. The results show overwhelming evidence in support of the existence of a linear trend in the scale parameter of the GPD models at all the three sites in the LLRB. The time-heterogeneous GPD models developed in this study were found to be statistically worthwhile and provide an improvement in fit over the time-homogeneous GPD models based on the goodness-of-fit tests. This study shows the importance of extending the time-homogeneous GPD models to incorporate climate change factors such as trend in the LLRB. The models developed in this study are expected to be more reliable than their stationary counterparts for planning and decision making processes in Mozambique.

Keywords

extremes, peaks-over-threshold, Limpopo River, generalised Pareto distribution

2010 Mathematics Subject Classification

Primary 62-xx. Secondary 62-07.

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Published 27 September 2016