Natural hazards (events that may cause actual disasters) are established in the literature as major causes of various massive and destructive problems worldwide. The occurrences of earthquakes, floods and heat waves affect millions of people through several impacts. These include cases of hospitalisation, loss of lives and economic challenges. The focus of this study was on the risk reduction of the disasters that occur because of extremely high temperatures and heat waves. Modelling average maximum daily temperature (AMDT) guards against the disaster risk and may also help countries towards preparing for extreme heat. This study discusses the use of the r largest order statistics approach of extreme value theory towards modelling AMDT over the period of 11 years, that is, 2000-2010. A generalised extreme value distribution for r largest order statistics is fitted to the annual maxima. This is performed in an effort to study the behaviour of the r largest order statistics. The method of maximum likelihood is used in estimating the target parameters and the frequency of occurrences of the hottest days is assessed. The study presents a case study of South Africa in which the data for the non-winter season (September-April of each year) are used. The meteorological data used are the AMDT that are collected by the South African Weather Service and provided by Eskom. The estimation of the shape parameter reveals evidence of a Weibull class as an appropriate distribution for modelling AMDT in South Africa. The extreme quantiles for specified return periods are estimated using the quantile function and the best model is chosen through the use of the deviance statistic with the support of the graphical diagnostic tools. The Entropy Difference Test (EDT) is used as a specification test for diagnosing the fit of the models to the data.

Weather and climate extremes such as heat waves, droughts and floods are projected to become more frequent and intense in several regions. There is compelling evidence indicating that changes in climate and its extremes over time influence the living conditions of society and the surrounding environment across the globe. This study applies max-stable models to capture the spatio–temporal extremes with dependence. The objective was to analyse the risk of drought caused by extremely high temperatures and deficient rainfall. Hopkin’s statistic was used to assess the clustering tendency before using the agglomerative method of hierarchical clustering to cluster the study area into $n=3$ temperature clusters and $n=3$ precipitation clusters. For the precipitation and temperature data, the values of Hopkin’s statistic were 0.7317 and 0.8446, respectively, which shows that both are significantly clusterable. Various max-stable process models were then fitted to each cluster of each variable, and the Schlather model with several covariance functions was found to be a good fit on both datasets compared to the Smith model with the Gaussian covariance function. The modelling approach presented in this paper could be useful to hydrologists, meteorologists and climatologists, including decision-makers in the agricultural sector, in enhancing their understanding of the behaviour of drought caused by extremely high temperatures and low rainfall. The modelling of these compound extremes could also assist in assessing the impact of climate change. It can be seen from this study that the size, including the topography of the location (cluster/region), provides important information about the strength of the extremal dependence.

The point process (PP) modelling approach is considered a more elegant alternative of extreme value analysis. This is because of its capability in modelling both the frequency and intensity rates of the occurrence of extremes. In this paper, we demonstrate the use of the PP modelling approach in which stationary and non-stationary models are used in modelling average maximum daily temperature (AMDT) in South Africa. The data constitutes average daily temperature observations that are collected by the South African Weather Services over the period 1 January 2000 to 30 August 2010. This study is interested on the occurrence of extreme high temperature and because of that the data for non-winter season (1 September to 30 April) of each year is used. A penalised regression cubic smoothing spline function is used for non-linear detrending of the data and determining a fixed threshold above which excesses are extracted and used. An extremal mixture model is then fitted to determine a threshold in which a boundary corrected kernel density is fitted to the bulk model and a generalised Pareto distribution (GPD) fitted to the tail of the distribution. The data exhibits properties of short-range dependence and strong seasonality, leading to declustering. An interval estimator method is used to decluster data for the purpose of fitting PP models to cluster maxima. The models that are used in this paper are nested and, as a result, likelihood ratio tests are conducted using the deviance statistic. The tests support the fit of the stationary PP model. We further fitted the stationary GPD and used the formal tests which are the Cramer-von Mises test and the Anderson-Darling test to diagnose fit. These tests and the diagnostic plots support fit of the stationary GPD to cluster maxima. Uncertainty of the estimates of GPD parameters is assessed in this paper using bootstrap re-sampling approach. The stationary PP model was used with the reparameterisation approach to determine frequency of the occurrence of extremely hot days, which are found to be 15 times per year. The modelling framework and results of this study are important to power utility companies in scheduling and dispatching electricity to customers during a hot spell.