Modelling temperature in South Africa using extreme value theory
Nemukula, Murendeni M.
This dissertation focuses on demonstrating the use of extreme value theory in modelling temperature in South Africa. The purpose of modelling temperature is to investigate the frequency of occurrences of extremely low and extremely high temperatures and how they inﬂuence the demand of electricity over time. The data comprise a time series of average hourly temperatures that are collected by the South African Weather Service over the period 2000−2010 and supplied by Eskom. The generalized extreme value distribution (GEVD) for r largest order statistics is ﬁtted to the average maximum daily temperature (non-winter season) using the maximum likelihood estimation method and used to estimate extreme high temperatures which result in high demand of electricity due to use of cooling systems. The estimation of the shape parameter reveals evidence that the Weibull family of distributions is an appropriate ﬁt to the data. A frequency analysis of extreme temperatures is carried out and the results show that most of the extreme temperatures are experienced during the months January, February, November and December of each year. The generalized Pareto distribution (GPD) is ﬁrstly used for modelling the average minimum daily temperatures for the period January 2000 to August 2010. A penalized regression cubic smoothing spline is used as a time varying threshold. We then extract excessesabovethecubicregressionsmoothingsplineandﬁtanon-parametricmixturemodel to get a sufﬁciently high threshold. The data exhibit evidence of short-range dependence and high seasonality which lead to the declustering of the excesses above the threshold and ﬁt the GPD to cluster maxima. The estimate of the shape parameter shows that the Weibullfamilyofdistributionsisappropriateinmodellingtheuppertailofthedistribution. The stationary GPD and the piecewise linear regression models are used in modelling the inﬂuence of temperature above the reference point of 22◦C on the demand of electricity. The stationary and non-stationary point process models are ﬁtted and used in determining the frequency of occurrence of extremely high temperatures. The orthogonal and the reparameterizationapproachesofdeterminingthefrequencyandintensityofextremeshave i been used to establish that, extremely hot days occur in frequencies of 21 and 16 days per annum, respectively. For the fact that temperature is established as a major driver of electricity demand, this dissertation is relevant to the system operators, planners and decision makers in Eskom and most of the utility and engineering companies. Our results are furtherusefultoEskomsinceitisduringthenon-winterperiodthattheyplanformaintenance of their power plants. Modelling temperature is important for the South African economy since electricity sector is considered as one of the most weather sensitive sectors of the economy. Over and above, the modelling approaches that are presented in this dissertation are relevant for modelling heat waves which impose several impacts on energy, economy and health of our citizens.
Dissertation submitted for Masters of Science degree in Mathematical Statistics in the FacultyofScience, SchoolofStatisticsandActuarialScience, University of the Witwatersrand Johannesburg, January 2018
Nemukula, Murendeni Maurel, (2018) Modelling temperature in South Africa using extreme value theory, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/24840.