Abstract
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.
Highlights
Most of the classical statistical techniques that are frequently used in the energy sector and meteorological analysis are classified into regression analysis, time series, state space and Kalman filtering (Hahn, Meyer-Nieberg & Pickl 2009)
This study focuses on the reduction and management of the disaster risk that occurs as a result of extreme high temperatures that lead to global change and heat waves
One of the steps towards the preparation is to manage the risk of the http://www.jamba.org.za occurrence of heat waves, which is performed in this study through modelling the frequency of the occurrence of extremely high temperatures
Summary
Most of the classical statistical techniques that are frequently used in the energy sector and meteorological analysis are classified into regression analysis, time series, state space and Kalman filtering (Hahn, Meyer-Nieberg & Pickl 2009). The limitation that is commonly encountered among such techniques is that they concentrate on the mean instead of the tails of the distributions This leads to unreliable estimates as most of the sample values fall outside the tails of the distribution, as well as the difficulty in estimating the model parameters that would lead to a good fit in the tails (Byström 2005; Gencay & Selcuk 2004; Sigauke et al 2012; Soares & Scotto 2004). The problems that arise as consequences of using statistical techniques that do not concentrate on the tails of the distributions are overcome by the use of extreme value theory (EVT) because of its ability to model the asymptotic behaviour of thin- or heavy-tailed distributions (Gencay & Selcuk 2004). Most of the scientific areas including actuary, energy forecasting and meteorology are associated with the thin- or heavy-tailed data and consider the use of EVT techniques (Gencay & Selcuk 2004). Zhang et al (2014) used the change point approach of EVT in modelling stationary annual flood peaks during 1951–2010 in the Pearl River basin, China
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