## 3 Simulations of Atmospheric-Based Disruption Including Turbulence and Clouds
### Atmospheric Turbulence Attenuation Based on RAOB Database  
A key challenge is the generation of accurate atmospheric turbulence data considering the required resources for a real measurement campaign. Therefore, a precise solution is used to obtain the vertical profile of refractive index structure parameter \(C_{\mathrm{n}}^{2}\) based on RAOB databases containing meteorological information for various geographical locations [7; 23]. The radio sounding data include atmospheric vertical profile up to 30 km of various atmospheric parameters such as height \(z\), pressure \(P\), geopotential height, absolute temperature \(T\), dew point temperature, relative humidity, mixing ratio, wind orientation and velocity, potential temperature \(\theta\), equivalent potential temperature, and virtual potential temperature. The proposed model is based on the Tatarski energy spectrum [24]. In  
Figure 3: Beam camera shots of the propagated laser beam at LP\({}_{01}\) mode in (**a**) vertical and (**b**) horizontal planes. particular, the \(C_{\rm n}^{2}\) model that applies the structure-function formulation of Tatarski is given in Equation (1) [25]. \[C_{\rm n}^{2}=a^{2}(K_{\rm H}/K_{\rm M})M^{2}L_{0}^{\frac{4}{3}} \tag{1}\]  
where \(a^{2}=2.8\) is an empirical constant, \(K_{\rm H}/K_{\rm M}=1.35\) is an exchange coefficient for heat and momentum, \(M\) provides information for the changes of the index of refraction in terms of height \(z\), and \(L_{0}\) is the turbulence outer scale parameter. \(M\) is calculated based on (2) given in [22], and \(L_{0}\) is expressed with an experimentally validated Equation (3) [7]. \[M=\frac{-79\times 10^{-6}P}{T^{2}}\frac{dT}{dz} \tag{2}\]  
\[L_{0}=\frac{5}{\left(1+\left(\frac{z-7500}{2500}\right)^{2}\right)} \tag{3}\]  
Consequently, \(C_{\rm n}^{2}\) is expressed with Equation (4), which allows the use of ROAB data for precise investigation of atmospheric-turbulence-induced fading. \[C_{\rm n}^{2}=3.78\bigg{(}\frac{-79\times 10^{-6}P}{T^{2}}\bigg{)}^{2}\bigg{(}5 /\left(1+\left(\frac{z-7500}{2500}\right)^{2}\right)\bigg{)}^{4/3}\bigg{(} \frac{dT}{dz}\bigg{)}^{2} \tag{4}\]  
The applied absolute temperature \(T\) in [K] is dependent on the atmospheric pressure \(P\) (hPa) that changes with altitude. Consequently, this causes inaccuracies in calculating \(C_{\rm n}^{2}\), and potential temperature parameter \(\theta\) is instead introduced [26]. The potential temperature is invariant in terms of atmospheric pressure changes that provide higher precision. Furthermore, \(\theta\) is calculated with Equation (5) [26] in terms of reference pressure that is equal to 1000 hPa. \[\theta=T\bigg{(}\frac{P_{0}}{P}\bigg{)}^{0.286} \tag{5}\]  
Having in mind Equations (4) and (5), the final equation for \(C_{\rm n}^{2}\) is provided in (6). \[C_{\rm n}^{2}=3.78\bigg{(}\frac{-79\times 10^{-6}P}{T\theta}\bigg{)}^{2} \bigg{(}5/\left(1+\left(\frac{z-7500}{2500}\right)^{2}\right)\bigg{)}^{4/3} \bigg{(}\frac{d\theta}{dz}\bigg{)}^{2} \tag{6}\]  
Having obtained the RAOB data set for Vienna, Austria, including height \(z\), pressure \(P\), potential temperature \(\theta\), and absolute temperature \(T\) for a period of 12 months between January and December, the slant profile of \(C_{\rm n}^{2}\) is modeled and shown in Figure 4. The irradiance fluctuation due to the atmospheric \(C_{\rm n}^{2}\) parameter is modeled with a number of statistical distributions. While new generalized statistical models such as Malaga distribution exist, straightforward modeling based on Log-Normal and Gamma-gamma distributions is applied. Rytov variances of Log-Normal intensity distribution for horizontal terrestrial (\(L\) is the link distance) and slant FSO downlinks are provided in (7) and (8) [27]. \[\sigma_{\rm r}^{2}=1.23C_{\rm n}^{2}k^{7/6}L^{11/6} \tag{7}\]  
\[\sigma_{\rm r}^{2}=2.25k^{\frac{7}{6}}\frac{1}{\cos^{11/6}(\gamma)}\int\limits _{h_{0}}^{H}C_{\rm n}^{2}(z)(H-z)^{5/6}dz \tag{8}\]  
In particular, \(\sigma_{\rm r}^{2}\) is used as a scintillation index in case of weak atmospheric turbulence.