## 4 Model Analysis and Results  
By substituting the experimental values of transmitted and received optical powerin Equation (4), the experimental attenuation coefficient was evaluated. According to existing models for turbulence and attenuation in FSO systems, the main meteorological factors that affect the propagation of the laser beam were the relative humidity, temperature, and wind speed [4, 13, 14, 18, 19]. Thus, the experimental model for the estimation of the attenuation factor would depend on these three parameters and was extracted using multiple linear regression method with the attenuation coefficient being the dependent variable and combinations of up to 3 rd order values of temperature, wind speed, and relative humidity being the explanatory variables \(x_{i}\)[33]:  
\[a_{tot}=b_{0}+\sum_{i=1}^{N}b_{i}x_{i} \tag{5}\]  
Data collected in the first three months of the year 2020 were used for the regression process for time-periods that fulfilled the requirements of Table 2.  
In order to simplify the regression model, factors with a negligible contribution were eliminated. Thus, the estimation model for the attenuation coefficient as a function of atmospheric temperature, relative humidity, and wind speed is given through the following mathematical expression:  
\[ \begin{array}{ll}a_{tot}=&b_{0}+b_{1}RH^{4}+b_{2}RH^{4}T^{3}+b_{3}T^{4}+b_{4 }RH^{2}TWS+b_{5}RH^{2}+b_{6}WS^{2}+b_{7}T^{2}\\ &+b_{8}RH^{3}+b_{9}T^{3}+b_{10}RH\times T^{2}WS+b_{11}RH^{2}T+b_{12}RH^{2}T^{ 2}+b_{13}RH^{3}T^{2}\end{array}  \tag{6}\]  
where \(T\) stands for the temperature in Celsius degrees, \(RH\) corresponds to the relative humidity, and \(WS\) represents the wind speed in m/s. The values of the coefficients of Equation (6) are presented in Table 3. \begin{table}
\begin{tabular}{l c} \hline \hline \multicolumn{1}{c}{**Parameter**} & **Range** \\ \hline Time & 00:00–05:00 and 20:00–23:59 \\ \hline Temperature & 10–25 \({}^{\circ}\)C \\ \hline Relative Humidity & 40–90\% \\ \hline Wind Speed & 0–20 m/s \\ \hline Rain Rate & 0 mm/h \\ \hline \end{tabular}
\end{table} 
Table 2: Weather conditions during measurements. Taking into account the parameter values of Table 3, the validity and the error parameters of the experimental model are presented in Table 4.  
From Table 4, it can be seen that the coefficient of multiple correlation that is the most important parameter for the fitting accuracy of the model is close enough to one, so the accuracy of the model is high enough. Furthermore, the residual mean variance is very low, three orders of magnitude lower that the experimental measurements, a sign of high precision model. Next, the outcomes for the attenuation factor obtained from the experiment and those that were obtained from the empirical model of Equation (6), were compared. In Figure 2, the experimental measurements of the attenuation coefficient according to Equation (4) and the predicted values of the regression model of Equation (6) were presented for 12,300 samples. It could be observed that the model that was extracted had a precise fit to the behavior of the experimental results and could predict the attenuation coefficient according to weather and atmospheric data. In Figure 3, the experimental versus the corresponding regression model results are presented. According to the linear fitting, the slope of the curve was 0.7612 and was near to 1, as it should theoretically be, while the constant term was very low, i.e., 0.09. It could also be seen, that as the attenuation coefficient increased, the accuracy of the model decreased. This was expected because an increment of attenuation coefficient meant worse weather conditions that could not be easily modelled. In Figure 4, the measurements of temperature, wind speed, and relative humidity are presented for every sample that was used for the extraction of the model. It could be observed that the model has a high accuracy in case of low wind speed and relative humidity.