# Analysis of Scintillation Effects on Free Space Optical Communication Links in South Africa
## 2 Wind Speed Distribution  
Figure 1 shows the map of South Africa depicting the average wind speed (m/s) at 100 m above ground level for selected cities investigated in this work. The average wind speed data used in plotting Figure 1 spans January 2008 until December 2017 and was sourced from [34]. The data in Figure 1 is very similar to the average measurement values presented in Table I of [10; 32]. Wind speed data from January 2010 until June 2018 was also acquired from the South Africa Weather Service (SAWS) for major locations in each of the nine provinces of South Africa. The data was collected hourly for the \(8\frac{1}{2}\) year period. The locations of interest investigated in this work are: Bloemfontein, Cape Town, Durban, Johannesburg, Kimberley, Mafikeng, Mbombela, Polokwane, and Port Elizabeth. The data provided by the SAWS, which was collected from various weather stations placed a few meters above the ground, was statistically processed and used for all our computations in this work. Figure 2a-c, alongside all other analysis done in this work, are based on the measurement data obtained from the SAWS. Figure 2a shows the CDF of wind speed for various cities in South Africa, while Figure 2b presents the PDF of wind speed for the same locations. In Figure 2a, the coastal cities of Port Elizabeth and Cape Town have the highest probabilities of occurrence of high wind velocities compared to other cities in South Africa. The cities of Bloemfontein, Mbombela, and Polokwane have the highest likelihood of occurrence of low wind speeds. In Figure 2b, the probability of occurrence of wind speeds of 1 m/s in the cities of Mbombela and Polokwane is ~0.3, while the cities of Cape Town and Port Elizabeth have the lowest likelihood of occurrence (less than 0.15) of low wind velocities when compared with other cities in South Africa. Figure 2c shows the wind speed exceedance against the percentage of time for the various locations of interest. Figure 2c validates the results in Figure 2a,b. Figure 1: Map of South Africa showing the mean wind speed 100 m above ground level for selected cities investigated in this work. Figure 2: (a) Ground wind speed CDF during clear weather for various cities in South Africa. (b) Ground wind speed PDF during clear weather for different cities in South Africa. (c) Ground wind speed exceedance against percentage of time for various cities of South Africa during clear weather periods. Wind velocities greater than 4 m/s occur \(\sim\)60% of the time in the cities of Port Elizabeth and Cape Town, while in Polokwane, Mbombela, and Bloemfontein, wind speeds higher than 4 m/s occur less than 25% of the time. The \(C_{n}^{2}\) in m\({}^{-2/3}\) based on the Hufnagel-Andrews-Phillips (HAP) model is presented in [35; 36; 37] as:  
\[C_{n}^{2}(a)=M\left[\frac{297}{5\times 10^{4}}\left(\frac{W_{rms}}{27}\right)^{2 }\left(\frac{a+a_{s}}{10^{5}}\right)^{10}\exp\left(-\frac{\left(a+a_{s}\right) }{10^{5}}\right)+\left(2.7\times 10^{-16}\right)\exp\left(-\frac{\left(a+a_{s} \right)}{1.5\times 10^{5}}\right)+\left(1.7\times 10^{-14}\right)\left(\frac{a_{o} }{a}\right)^{-\frac{4}{3}}\right],\ a>a_{o} \tag{1}\]  
where \(M\) is the scaling factor, \(a_{s}\) is the reference height of the ground above sea level in metres, \(a_{o}\) is the height of the first FSOC transceiver above the ground in metres, \(a\) is the altitude from the reference height \(a_{o}\) to the height of the other (second) FSOC transceiver above the ground in metres, and \(W_{rms}\) is the root-mean-square (RMS) wind speed in m/s. The RMS wind speed in Equation (1) is calculated using the Bufton wind model, which is given in [35; 36; 38; 39] as:  
\[W_{rms}=\sqrt{\frac{1}{15000}\int\limits_{5000}^{20000}\left[b_{s}a+W_{g}+30\exp \left(-\left(\frac{a-9400}{4800}\right)^{2}\right)\right]^{2}da} \tag{2}\]  
where \(b_{s}\) is the beam slew rate associated with a satellite moving with respect to an observer on the ground in rad/s and \(W_{g}\) is the ground wind speed in m/s.