Statistical Modelling of Botswana’s Monthly Maximum Wind Speed using a Four-Parameter Kappa Distribution

Abstract

Wind speed modelling has been key to many environmental and engineering applications, particularly in environmentally friendly wind power generation to meet energy demands. Efficient assessment of wind speed at different recurrence intervals requires the choice of a suitable statistical distribution and an unbiased method of parameter estimation. This study suggests the use of a four parameter Kappa distribution, with its parameters estimated using the method of L-moments, to model Botswana's monthly maximum wind speed data at six meteorological weather stations. These synoptic weather stations are Gaborone, Sir Seretse Khama Airport, Tsabong, Tshane, Gantsi and Maun which are broadly spread across the country's economic activity centres. . These results can reliably be used by environmentalists and technologists working in the energy sector in Botswana.

Modeling Wind Speed Using Parametric and Non-Parametric Distribution Functions

“…The Kappa distribution function parameters consist of the location parameter, the first and second shape parameters, and the scale parameter. The Kappa PDF, CDF, and QF are given below in (14) to (16), respectively [5,6,10,15].…”

“…L-moments are linear combinations of order statistics used to determine the location, scale, shape (skewness) and kurtosis of a distribution function [16]. L-moments of a distribution function are given by ( 17) below [15][16][17]. The first four L-moments relating to a distribution function's location, scale, shape and kurtosis are evaluated using (18) to ( 21) respectively [15][16][17].…”

“…L-moments of a distribution function are given by ( 17) below [15][16][17]. The first four L-moments relating to a distribution function's location, scale, shape and kurtosis are evaluated using (18) to ( 21) respectively [15][16][17].…”

Transfer Function-Noise Modeling of the Dynamic Relationship between Botswana's Monthly Maximum Temperature and Evaporation

“…Botswana's climate can be summarised as hot and semi arid to arid (Pike, 1971;Bhalotra, 1984;1987;Moses, 2007). The country's weather conditions are influenced by synoptic scale weather systems such as the Atlantic Ocean high pressure cell, Indian Ocean high pressure cell, cut-off lows, frontal systems, surface lows, high pressure cells, Inter Tropical Convergence Zone (ITCZ) and westerly and easterly troughs (Moses and Parida, 2016). The study area is represented by three meteorological stations located in three areas of national significance, which are Francistown, Maun and Gaborone.…”

Heavy Daily Rainfall Characteristics over the Eastern Botswana

“…Botswana, being part of southern Africa, at times also experiences heavy or extreme daily rainfall that can persist for a number of days. Rainfall in Botswana is mainly triggered by rain bearing weather systems such as surface lows, cut-off lows, frontal systems, Inter Tropical Convergence Zone (ITCZ), easterly and westerly troughs [9], which under favourable conditions can generate heavy daily rainfall and severe weather within a couple of hours. Heavy daily rainfall is defined in this study as rainfall at individual stations with an intensity that is greater than or equal to 50 mm in 24 hours [6,[10][11][12][13].…”