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Global temperatures have increased since the beginning of the last century hence the need for the use of mathematical models like extreme value distributions to understand the dynamics of extreme temperatures.
In a recent paper by Mothupi, Thupeng, Mashabe and Mokoto, extreme value models are used to model quarterly surface air temperatures for the Sir Seretse Khama (SSK) International Airport Weather Station. Using block maxima approach and the blocks as quarterly surface air temperatures, the generalised extreme value (GEV) distribution was used and appeared to be the appropriate model for the data. Empirical statistical test shows the quarterly surface air temperature data to be stationery and with no monotonic trend.
“Extreme value distribution is an appropriate method for modelling maximum or extreme weather conditions as they are inherent distributions to identify the return of the worst case scenario of extreme temperatures”
Mothupi, Thupeng, Mashabe and Mokoto also demonstrated how extreme value theory can be used in the estimation of extreme quantiles of surface air temperatures in a weather station in Gaborone. With the fitted GEV model the return levels for different return period are estimated and the result shows that the surface air temperature for SSK international Airport will increase for the next 120 years.
The theory of extreme value provides a rigorous framework for analysis of climate extremes and their return levels. In fact, given the potential disastrous social, economic and public health impacts of weather related events such as heat waves, droughts and floods and the rarity of the nature of events, applying the insights of extreme value theory to environmental risk analysis is a necessity. The two commonly used approaches for modelling extremes are the block maxima and peaks over threshold (POT) method which focuses on exceedances over a fixed high threshold. However, the focus of the paper was on the block maxima approach using GEV distribution as it appeared to be a suitable distribution compared to the the Weibull, Frechet and Gumbel distributions. Therefore, all predictions and estimations made are based on the GEV model which appears to be a plausible choice for this quarterly surface air temperature data for the SSK International Airport Weather Station.
Thuto Mothupi, Wilson Moseki Thupeng; Department of Statistics, University of Botswana, Gaborone, Botswana
Baitshephi Mashabe; Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
Botho Mokoto; Department of Risk Management, Insurance and Actuarial Science, Ba Isago University, Gaborone, Botswana
A paper about the study appeared recently in American Journal of Theoretical and Applied Statistics