Abstract
In this paper, extremes of quarterly maximum surface air temperature are modelled by employing the block maxima approach to extreme value analysis. The aim of the paper is to predict the future behaviour of the quarterly maximum surface air temperatures by estimating their high quantiles using the generalized extreme value distribution, an extreme value distribution usually used to model block maxima. The data are derived from monthly maximum surface air temperatures recorded at the SSSK International Airport Weather Station from January 1985 to December 2015. The Jarque-Bera normality test is performed on the data, and shows that the quarterly maximum temperatures do not follow a normal distribution. The Seasonal Mann-Kendall test detects no monotonic trends for the quarterly maximum temperatures. The Kwiatkowski- Phillips-Schmidt-Shin test indicates that the data are stationary. Parameter values of the generalized extreme value distribution are estimated using the method of maximum likelihood, and both the Kolmogorov-Smirnov and Anderson-Darling goodness of fit tests show that the distribution gives a reasonable fit to the quarterly maximum surface air temperatures. Estimates of the T-year return levels for the return periods 5, 10, 25, 50, 100, 110 and 120 years reveal that the surface air temperature for the SSK International Airport will be increasing over the next 120 years.
Highlights
There is growing concern around the world about increased emissions by the industrialised nations of greenhouse gases (GHG), which will cause increase in the global temperature and changes of other climatic variables such as rainfall and evaporation [38], [35] and [36]
Let X = (x1, x2, x3, x4 ) represent the entire dataset collected over years consisting of data subsets x1, x2, x3, x4 where xi =,i = 1, 2, 3, 4, denotes the set of data for the ith quarter for n years, The null hypothesis H0 for the two-sided Seasonal Mann-Kendall (SMK) test is that there is no monotonic trend in the series and the alternative hypothesis HA is that for one or more seasons there is an upward or downward trend over time
The generalized extreme value distribution is used to model quarterly maximum temperatures using data obtained from the Sir Seretse Khama international Airport weather station in Gaborone for the period January 1985 to December 2015
Summary
There is growing concern around the world about increased emissions by the industrialised nations of greenhouse gases (GHG), which will cause increase in the global temperature and changes of other climatic variables such as rainfall and evaporation [38], [35] and [36]. The current investigation attempts to provide a better understanding of trends in temperature extremes as a possible source of vulnerability to residents of the City of Gaborone by studying the patterns in the quarterly maximum surface air temperatures and estimating their return levels for different return periods. Despite the potentially disastrous effects of high temperatures on public health and the socio-economic wellbeing of the people, not much research work has been done in terms of applying extreme value methods to study the behaviour of extreme temperature data for Botswana. The main purpose of developing a stationary GEV model for the SSK Airport quarterly maximum is to compare the estimated return levels (expected quantiles) from the GEV distribution with the currently used design value based on the some guideline, for example, the optimal temperature for human health.
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