## 3 Statistical Analysis of the Collected Data for Different Seasons
### Pre-Summer and Summer Measurements
There were interesting results during the winter and spring seasons, which could be further verified in Figure 3, which shows the relation between PDR and the environment parameters for the winter and spring seasons from December until February. The environment parameters are not high enough to cause any effect to the FSO communication (refer Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \multicolumn{5}{c}{_Regression Statistics_} \\ \hline Multiple R & 0.793993074 & & & & \\ R Square & 0.630425002 & & & & \\ Adjusted R Square & 0.613999446 & & & & \\ Standard Error & 1.892772476 & & & & \\ Observations & 48 & & & & \\ \hline  & _Coefficients_ & _Standard Error_ & _t Stat_ & \begin{tabular}{c} _T Value with df = 46_ \\ and Alpha/2 = 0.025_ \\ \end{tabular} & _t-Test Value_ \\ \hline Intercept & 132.033 & 13.546 & 9.747 & & \\ Temperature & \(-\)1.052 & 0.303 & \(-\)3.471 & 2.021 & \begin{tabular}{c} Strong relation as \\ \(\dagger\) t stat (Temperature) \\ \end{tabular} & \
\begin{tabular}{c} Strong relation as \\ \(\dagger\) t stat (Temperature) \\ \end{tabular} \\ Humidity & \(-\)0.079 & 0.090 & \(-\)0.875 & 2.021 &
\begin{tabular}{c} No Strong Relation \\ \(\dagger\) t stat (Humidity) \(\dagger\) \(\dagger\) \(\dagger\) \(\dagger\) \(\dagger\) \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 2: Regression analysis output and t-test approach on the data for month of May. Closed Form Expression and Behavior of FSO Link Based on the Variation of the Strength of Atmospheric Turbulences  
It is quite clear that the FSO performs better in Qatar during the winter than the summer and it is verified using the statistics with the data recorded in Section 3. One more significant result seen in the previous section is the variation of PDR throughout the day in the different seasons. For a reliable communication, consistent communication link would be a requirement for application to avoid changing of communication links. This changing of communication links can lead to unnecessary delays. The PDR variation is very small or could be considered constant during a single day in winter, which is a great advantage in addition to high PDR; refer Figures 3 and 4. Whereas during summer there is a great variation in PDR and fall less than 80 % during the middle of the day, refer Figure 6.  
The reason for this variation could be attributed to an environmental phenomenon called as scintillation [1; 16; 17]. This phenomenon is the major reason for the degradation of the FSO communication link, which uses laser beams for transmitting information. The major environmental parameter that results in scintillation phenomenon is the higher levels of temperature and solar irradiance, which are more in summer than in winter. This clearly explains the reason for the greater degradation of FSO performance in summer than in winter. In this section, we will support the obtained results by mathematical models developed and verified by the authors in [18], which shows the effect of weather factors on FSO behavior. The models will help in relating the variation of the strength of atmospheric turbulence i.e., \({C_{n}}^{2}\) with the environmental parameters. In addition, the authors will also provide a closed form expression relating the PDR with respect to the environmental parameters with the uncertainties. The cumulative environmental parameter refractive index is depending on weather factor such as temperature, humidity, and solar irradiance, which is also considered as the strength of atmospheric turbulence. Experimentally, the refractive index can be measured directly using a scintillometer by measuring the variance of the fluctuations of received signal [19; 20]. There are various models that can be used to get the refractive index such as the ones in [20; 21]; three such models can be stated: [PERSON] developed the first model in 1994. Later, this model is improved by [PERSON], [PERSON], and [PERSON] to present a new model called \"the Rocky Terrain\" (BKB) model.