## 3 Simulations of Atmospheric-Based Disruption Including Turbulence and Clouds
### Cloud-Induced Optical Attenuation  
Atmospheric cloud attenuation of an FSO optical signal is due to Mie scattering caused by suspended water particles and is well described by means of Mie theory and microphysics of cloud phenomena [11; 30]. The particle size distribution (PSD) is defined in regard to the three-parameters modified gamma distribution model given in Equation (16) [31; 32].  
\[n(r)=ar^{\alpha}\exp(-b) \tag{16}\]  
The positive constants \(a\), \(\alpha\), and \(b\) for the primary six types of clouds are listed in Table 1, and the resulting PSD graphs are given in Figure 8a [31].  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cloud Type** & **a** & \(\alpha\) & **b** \\ \hline Cumulus & 2.6 & 3 & 0.5 \\ Stratus 2 & 27 & 2 & 0.6 \\ Stratocumulus & 52.7 & 2 & 0.75 \\ Altostratus & 6.26 & 5 & 1.11 \\ Nimbostratus & 7.67 & 2 & 0.42 \\ Cirrus & \(2.21\times 10^{-12}\) & 6 & 0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Modified gamma PSD parameters for the primary six types of clouds.  
Figure 7: Normalized histogram of the simulated \(S_{\rm atm}\) using the Vienna RAOB dataset.  
Furthermore, Mie scattering efficiency factor \(Q_{sca}\) calculated using Mie theory for the full-size spectrum of cloud water droplets is provided in Figure 8b. Finally, having implemented both PSD and efficiency factor \(Q_{sca}\), the equation for the Mie scattering coefficient used to calculate cloud attenuation is given in Equation (17) [8].  
\[\beta_{sca}(n_{m},\ r,\lambda_{0})=\int_{r_{min}}^{r_{max}}Q_{sca}(n_{m},\ r, \lambda_{0})n(r)\pi r^{2}dr \tag{17}\]  
The average optical attenuation is determined for a single scattering case when the multipath propagation effect is neglected, and mainly ballistic photons reach the optical detector. Having used exponential Beer-Lambert law, the simulated minimum and maximum optical losses \(A_{c}\) due to main six types of clouds including Stratus, Stratocumulus, Altostarus, Nimbostratus, Cirrus, and Cumulus are 283.87-2.83 \(\times\) 10\({}^{3}\) (dB), 48.55-194.21 (dB), 32.2-128.82 (dB), 85.2-852.08 (dB), 692.7-1039 (dB), and 3.99-11.98 (dB), respectively. Cirrus and Stratus clouds are the only cloud types that can be overcome. Moreover, due to the high altitude of Cirrus, they are mainly composed of ice particles that random orientation additionally influences the polarization properties of the propagated FSO beam [33]. In order to statistically model the simulated cloud attenuation \(A_{c}\), an empirical approach is applied based on Log-Normal distribution (i.e., Equation (18)) that offers the most accurate fitting in terms of the measured and simulated optical attenuation data. Typical Log-Normal distribution for a region where Cirrus and Stratus clouds are predominately observed is characterized by \(\mu\) = 1.44 dB and \(\sigma^{2}\) = 2.31 [34].  
\[f_{A_{c}}(A_{c})=\frac{1}{\sqrt{2\pi\sigma A_{c}}}exp\left[-\frac{(lnA_{c}-\mu) ^{2}}{2\sigma^{2}}\right] \tag{18}\]  
Referring to the fact that only Cirrus and Stratus can be managed by ground-space FSO systems, the other types of clouds cause interruption of optical LoS communication links. Consequently, for the considered location of Vienna, Austria, for which the cloud cover is significant, a unique diversity technique combining 12 European OGS sites should be used in order to reach an availability of 99.9%. If such a network is built together with Germany, the outage probability is significantly higher even if the OGS number is increased to 12. Moreover, an international network considering 9 OGSs possesses outage probability reaching 10\({}^{-7}\) that can be considered as availability of 100% [13].