# Analysis of Scintillation Effects on Free Space Optical Communication Links in South Africa
## 4 Aerosol Scattering Losses  
The aerosol scattering coefficient in dB/km, as defined by the [PERSON] and [PERSON] models, is given in [42] as:  
\[L_{Sca}=\frac{17}{V}\bigg{(}\frac{\lambda}{\lambda_{\circ}}\bigg{)}^{-q_{\circ}} \tag{25}\]  
where \(V\) is the meteorological visibility in km, \(\lambda_{\circ}=550\) nm is the maximum spectrum wavelength of the solar band, and \(q_{\circ}\) is the particle size distribution parameter. In the Kim model, \(q_{\circ}\) is expressed in terms of visibility as [48]:  
\[q_{\circ}(V)=\left\{ \begin{array}{ccc}1.6&for&V>50\text{ km}\\ 1.3&for&6<V<50\text{ km}\\ 0.16V+0.34&for&1<V<6\text{ km}\end{array} \right. \tag{26}\]  
while \(q_{\circ}\) is expressed in terms of wavelength in the Ijaz model as [49; 50]:  
\[q_{\circ}(\lambda)=0.1428\lambda-0.0947 \tag{27}\]  
For visibility measurements less than 1 km, the Ijaz model is used to calculate scattering losses, while the Kim model is used to calculate the specific attenuation associated with visibility values greater than or equal to 1 km. The two models are used in estimating scattering losses encountered by the transmission wavelength of 1550 nm. The visibility data used in computing the aerosol scattering losses over different distances in Figure 4a-d was obtained from the SAWS for the nine major South African cities of interest investigated in this work. The data was collected three times daily (8:00 a.m., 2:00 p.m., and 8:00 p.m.) over an \(8^{1}_{2}\) year period (January \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**City**} & \multirow{2}{*}{\
\begin{tabular}{c} **Ground Wind** \\ **Speed (m/s)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **RMS Wind** \\ **Speed (m/s)** \\ \end{tabular} } & \multicolumn{6}{c}{**Propagation Length of 1 km**} \\  & & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\ \hline Johannesburg & 11.4 & 29.83 & 2.9277 \(\times\)\(10^{-14}\) & 0.2362 & 9.2025 & 8.6921 & 0.2956 & 7.4062 & 7.0664 \\ Bloemfontein & 10.1 & 28.61 & 2.9299 \(\times\)\(10^{-14}\) & 0.2364 & 9.1962 & 8.6859 & 0.2959 & 7.4009 & 7.0615 \\ Mafikeng & 13.2 & 31.53 & 2.9304 \(\times\)\(10^{-14}\) & 0.2364 & 9.1946 & 8.6844 & 0.2959 & 7.3996 & 7.0603 \\ Polokwane & 9.3 & 27.87 & 2.9308 \(\times\)\(10^{-14}\) & 0.2365 & 9.1934 & 8.6832 & 0.2960 & 7.3986 & 7.0593 \\ Kimberley & 13.0 & 31.34 & 2.9311 \(\times\)\(10^{-14}\) & 0.2365 & 9.1927 & 8.6826 & 0.2960 & 7.3980 & 7.0588 \\ Mbombela & 8.5 & 27.13 & 2.9340 \(\times\)\(10^{-14}\) & 0.2367 & 9.1841 & 8.6743 & 0.2963 & 7.3909 & 7.0522 \\ Durban & 11 & 29.46 & 2.9439 \(\times\)\(10^{-14}\) & 0.2375 & 9.1557 & 8.6469 & 0.2973 & 7.3673 & 7.0304 \\ Port Elizabeth & 17.2 & 35.33 & 2.9446 \(\times\)\(10^{-14}\) & 0.2376 & 9.1539 & 8.6451 & 0.2973 & 7.3658 & 7.0290 \\ Cape Town & 14.7 & 32.95 & 2.9450 \(\times\)\(10^{-14}\) & 0.2376 & 9.1526 & 8.6439 & 0.2974 & 7.3647 & 7.0280 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Atmospheric turbulence parameters not exceeded 99.9% of the time during clear weather. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**City**} & \multirow{2}{*}{\ \begin{tabular}{c} **Ground Wind** \\ **Speed (m/s)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **RMS Wind** \\ **Speed (m/s)** \\ \end{tabular}  } & \multicolumn{6}{c}{**Propagation Length of 500 m**} \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & &2010 until June 2018). Over a link distance of 1 km, FSOC links transmitting at 1550 nm in Mbombela would encounter scattering losses of ~0.34, 23, 94, and 188 dB based on the periods not exceeded 50%, 99%, 99.9%, and 99.99% of the time, respectively. Figure 4: (**a**) Average Aerosol scattering losses versus link distances under clear atmospheric conditions at 1550 nm for various cities. (**b**) Aerosol scattering losses versus link distances under clear atmospheric conditions at 1550 nm for various cities not exceeded 99% of the time.