## 3 Statistical Analysis of the Collected Data for Different Seasons
### Pre-Summer and Summer Measurements
Based on these two models, the \"Alternate BKB\" model was developed in [13]. All these models are using the environmental parameters such as temperature \(T\) (Kelvin), Humidity \(H\) (%), wind speed \(v\) (m/s), solar flux SF (KW/m\({}^{2}\)) and temporal hour of the day \(T\)th for calculating the refractive index parameter. The temporal hour is calculated based on the time of sunrise and sunset and the duration of one \(T\)th is \(1/12\) of the sunrise time subtracted from sunset time. The current temporal hour is the sunrise time subtracted from the current hour then divided by the duration of one \(T\)th. For each temporal hour exists a relative weight W and is given by [22]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{4}{c}{_Regression Statistics_} \\ \hline Multiple R & 0.197379363 & & & & \\ R Square & 0.038958613 & & & & \\ Adjusted R Square & \(-\)0.002825795 & & & & \\ Standard Error & 1.911861256 & & & & \\ Observations & 48 & & & & \\ \hline  & _Coefficients_ & _Standard Error_ & _t Stat_ & _T Value with df = 46_ & _t-Test Result_ \\ \hline Intercept & 109.206 & 12.489 & 8.744 & & \\ Temperature (Degree Celsius) & \(-\)0.357 & 0.338 & \(-\)1.055 & 2.021 & No Strong Relation \\ Humidity (\%) & \(-\)0.100 & 0.082 & \(-\)1.220 & 2.021 & \(\dagger\) t stat (Humidity) \(\dagger<\) T value \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Regression analysis output and t-test approach on the data for month of December. The previous models are given by [22]. In this work, the adapted Alternate BKB model can be represented as follows  
\[C_{n}^{2}=3.8\times 10^{-14}W+f(T)+f(v)+f(H)-5.3\times 10^{-13} \tag{2}\]  
where  
\[f(t)=2\times 10^{-15}T \tag{3}\]  
\[f(H)=-2.8\times 10^{-15}H+2.9\times 10^{-17}H^{2}-1.1\times 10^{-19}H \tag{4}\]  
\[f(v)=-2.5\times 10^{-15}+1.2\times 10^{-15}v^{2}-8.5\times 10^{-17}v^{3} \tag{5}\]  
\(W\) is the weight function based on the temporal hour and given by [22]. Based on the Alternate BKB model and on the data taken from the sensors installed at QU we can validate the cumulative effect of the environmental parameters on the FSO communication link in Figure 7.  
In Figure 7, the variation of the refractive index for the duration of the day and the effect on the PDR for certain days of the month of December, January, February and March are presented. As shown, \({C_{n}}^{2}\) reaches its minimum at night, which is due to the absence of solar irradiance and low temperature at that time. Then starts increasing with the increase of temperature reaching a maximum in the middle of the day. The PDR during the above months are almost constant without much variation as they are not high enough to affect its performance, which could be seen in Figure 7 and verified in the previous statistics shown in Table 4 and Figures 3 and 4. From the plots, the selected day of March has the highest refractive index followed by the selected day of February. This is because these 2 months have the highest temperatures compared to the other months. However, the refractive index of the selected day of December is more than January, which is due to the higher temperature recorded for the day of December. Even during winter season, it is noticed that the strength of turbulence reaches a high level in the order of \(10^{-13}\) m\({}^{-2/3}\). This is due to the high temperature, which does not fall below the \(14\)\({}^{\circ}\)C. However, the temperature was not high enough to affect the constant performance of the FSO unlike summer where the temperature is high. According to [22; 23], the BKB model is valid only for a specific range of weather parameters. In fact, the temperature has to be between \(9\)\({}^{\circ}\)C and \(35\)\({}^{\circ}\)C, the relative humidity in the range of \(14\%\) and \(92\%\) and the wind speed between 0 and 10 m/s.