## 3 Simulations of Atmospheric-Based Disruption Including Turbulence and Clouds
### Atmospheric Turbulence Attenuation Based on RAOB Database
For the purpose of the current FSO downlink model, only Equation (8) is important where \(\gamma\) is the elevation angle, \(h_{0}\) is the height of the ground station, and \(H\) is the maximum height of the troposphere corresponding to approximately 12 km. Nonetheless, Log-Normal intensity is valid for weak turbulence conditions, while stronger FSO intensity fluctuations are probabilistically modeled with Gamma-Gamma distribution covering all regimes (i.e., weak, moderate, and strong). Furthermore, when it is considered that receiver apertures are parameterized with a finite length and power averaging needs to be considered, the power scintillation index \(\sigma_{\rm p}^{2}\) is introduced. Its final equation is given in (9), where parameter \(d\) is calculated based in (10) [27]. \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]0  
\[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]1  
Moreover, the typical elevation angle \(\gamma\) of an FSO feeder link is between \(20^{\circ}\) (in LEO case from \(5^{\circ}\)), and \(90^{\circ}\), as well as a typical accumulated OGS aperture diameter \(D\), is in the range of 1-8 m. Consequently, scintillations described with power scintillation index \(\sigma_{\rm p}^{2}\) are simulated for \(\gamma=20^{\circ}\) and \(D=1\) m (e.g., ESA's OGS at La Teide). When Gamma-Gamma and Log-Normal modeling are applied, the turbulence attenuation \(A_{\rm tur}\) for maximum availability of \(10^{-7}\) is calculated using Equation (11) [8]. \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]2  
The aperture averaging mitigation technique (1 m \(\leq D\leq\) 8 m) significantly decreases the strength of atmospheric turbulence, which leads to a reduction of the induced scintillations (\(\sigma_{\rm p}^{2}<<1\)). Consequently, the atmospheric-turbulence-induced fading is again well described with Log-Normal distribution, and the used power scintillation index \(\sigma_{\rm p}^{2}\) in Equation (11) corresponds to Rytov parameter value range. The normalized histogram of \(A_{\rm tur}\) is shown in Figure 5, characterized with a mean value of 3.43 dB and a standard deviation of 0.57 dB. \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]3 Atmospheric turbulence simulations providing average \(C_{\rm n}^{2}\) atmospheric profile based on 12 months of RAOB data for Vienna, Austria. In order to measure the strength of the turbulence apart from optical attenuation, the coherence length parameter (Fried parameter) is also introduced. Similar to the definition of Rytov variance parametrizing received intensity distribution of an FSO slant link that operates in clear-air atmospheric turbulence, the coherence length is defined based on the refractive index structure parameter, link distance \(L\), and wavelength. Keeping in mind that the downlink has a plane wave-front, the equation for the coherence length is given in (12) [28]. \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]4  
Moreover, the coherence length of a vertical slant link is also dependent on elevation angle \(\gamma\), namely \(r_{0}\propto\left(\sec(90^{\circ}-\gamma)^{-3/5}\right)\). Consequently, the coherence length of a slant space-to-ground FSO link is equal to [29]:  
\[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]5  
The normalized histogram of the simulated coherence length for the simulated \(C_{\mathrm{n}}^{2}\) parameter in Figure 4 is given in \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]6  
A lower coherence length \(r_{0}\), directly proportional to the telescope diameter \(D\), significantly decreases telescope resolving power \(R\) when the clear-air turbulence effect is present  
\[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]7 Normalized histogram of the simulated turbulence attenuation \(A_{\mathrm{tur}}\) using the Vienna RAOB dataset.