Modelling temperature extremes in the Limpopo Province of South Africa using extreme value theory

Abstract

Temperature extremes have a crucial impact on agricultural, economic, health and energy sectors due to the occurrence of climate extreme events such as heat waves and cold waves. Limpopo province is among the hottest provinces of South Africa and experiences little rainfall which affect the water availabil ity, food production and biodiversity. In the Limpopo province, temperature extremes are expected to become more frequent as a result of climate change. The aim of this study was to model temperature extremes in the Limpopo province of South Africa using extreme value theory (EVT). The stationarity of the data was tested using augmented Dickey-Fuller (ADF), Phillips-Peron (PP) and Kwiatkowski-Phillips-Schmit-Shin (KPSS). Four candidate parent distri butions: normal, log-normal, gamma and Weibull distributions, were fitted to the average monthly maximum and minimum daily temperatures. Prior to the selection of the parent distributions, the data set at each station was subjected to normality test using the Shapiro-Wilk (SW) and Jarque-Bera (JB) tests. The stationarity and normality tests revealed that the maximum and minimum temperature data series at all the stations are neither stationary nor normally distributed. Akaike information criterion (AIC) and Bayesian information cri terion (BIC) were used to select the best fitting distribution at a particular site. The findings revealed that both maximum and minimum temperatures series at all the stations belong to the Weibull domain of attraction. The findings from the Mann-Kendall (M-K) test and time series plots trend analyses showed that there is a monotonic downward and upward long-term trend in minimum and maximum temperature data, respectively. Two fundamental approaches of EVT, block maxima and peaks-over-threshold (POT), were used in this dissertation. The generalised extreme value (GEV), generalised Pareto (GP) and Poisson point process distributions were fitted to the data set for each station. In order to account for climate change impact, non-stationary models were considered with Seasonal Oscillation Index (SOI) as covariates of the parameters of the GEV distribution. The findings revealed that both the maximum and minimum temperature data can be modelled by the Weibull family of distribution. The EVT return level analysis findings of above 400C for maximum temperature suggests impending heat waves and droughts in the Limpopo province. The bivariate conditional extremes ap proach with a time-varying threshold was used. The findings revealed both significant positive and negative extremal dependence in some pairs of meteo rological stations. The findings of this study play an important role in revealing information useful to meteorologists, climatologists, agriculturalists and plan ners in the energy sector where temperature extremes play an important role. The scientific contribution of this study was to reduce the risk and impact of temperature extremes on agricultural, energy and health sectors in the Limpopo province. An understanding of temperature extremes will help gov ernment and other stakeholders to formulate mitigation strategies that will minimise the negative impact resulting from temperature extremes in the Limpopo province. Among the major contributions of the study was the use of a pe nalised cubic smoothing spline to perform a nonlinear detrending of the tem perature data, before fitting bivariate time-varying threshold excess models based on Laplace margins, to capture the climate change effects in the data. Future studies may consider exploring the use of extreme value copulas, as well as spatio-temporal dependence between temperature extremes using the conditional extremes model of Heffernan and Tawn (2004).