# Analysis of the Relationship between Scintillation Parameters, Multipath and ROTI
## 3 Results  
### Brazil Data  
Figure 3a-c shows the time series of the four parameters, namely S4 (top row), \(\sigma_{\varphi}\) (second row from top), MP (third row from top) and ROTI (bottom row) respectively on 8 September 2017 and 13 September 2017 at SAOOP station and 12 March 2011 at PRU2 station. Figure 3 shows that all four parameters fluctuate during the first four hours on all the three days, which indicates a relationship between the parameters in the time domain. It can be seen from all the panels that there are fewer peaks on the MP plots which means that fewer satellites are affected by MP than scintillation. Figure 4a-c shows the time series plots of four parameters for a single satellite respectively on 8 September 2017 and 13 September 2017 at SAOOP station and 12 March 2011 at PRU2 station. As shown in Figure 4, the temporal relationship becomes clearer with the time series plots for a single satellite, where all four parameters have a similar peak period on each day. Figure 3: Time series plots of four parameters: (**a**) during 00:00:00-06:00:00 UTC on 8 September, 2017 at SAOOP station; and (**b**) during 00:00:00-06:00:00 UTC on 13 September 2017 at SAOOP station; (**c**) during 00:00:00-06:00:00 UTC on 12 March 2011 at PRU2 station. The panels a-c of Figure 5 show the spatial mean value 2D maps as a function of IPP latitude and longitude calculated in each 1\({}^{\circ}\) grid cell, for the four parameters respectively on 8 September and 13 September 2017 at SAOOP station and 12 March 2011 at PRU2 station. It can be observed from Figure 5a,b that the affected areas (shown in yellow) of all the parameters focus on the northwest corner on the maps, which indicates that there is a relationship between the parameters in the spatial domain. As shown in Figure 5c, high value areas of S4 and MP are both located on the left part of maps while ROTI agrees with \(\sigma_{\varphi}\) on the east part of maps, though ROTI also shows similarities in the northwest corner with S4. The same relationship pattern can also be observed from Figure 5a,b that MP mainly correlates with S4 while ROTI respectively correlates with part of S4 and \(\sigma_{\varphi}\). Tables 1-3 show the SSIM and CC calculated between the 4 parameters shown in Figure 5a-c respectively. From Tables 1-3, it is clear that MP is more correlated with S4 while ROTI is more highly correlated with \(\sigma_{\varphi}\), although the CC in Table 3 shows a different pattern of ROTI. Most of the SSIM and CC values exceed 0.6 and some exceed 0.8. This indicates a high correlation between the parameters and a high level of structural similarity. The variograms and cross variograms for Figure 5a,b,c are shown in Figure 6a,b,c respectively. The variogram and cross-variograms show clear evidence of spatial structure, with a range of approximately 5\({}^{\circ}\) to 6\({}^{\circ}\). This shows that the four variables (parameters) co-vary, suggesting that they have similar spatial structures. Figure 4: Time series plots of four parameters: (**a**) during 00:00:00-06:00:00 UTC on 8 September 2017 for PRN10 at SAO0P station; (**b**) during 00:00:00-06:00:00 UTC on 13 September 2017 for PRN10 at SAO0P station; (**c**) during 00:00:00-06:00:00 UTC on 12 March 2011 for PRN25 at PRU2 station. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**MP**} & \multicolumn{2}{c}{**ROTI**} \\ \hline Criteria & SSIM & CC (\(p\)-value) & SSIM & CC (\(p\)-value) \\ S4 & 0.83 & 0.77 (\(<\)0.01) & 0.70 & 0.66 (\(<\)0.01) \\ \(\sigma_{\varphi}\) & 0.69 & 0.56 (\(<\)0.01) & 0.71 & 0.98(\(<\)0.01) \\ \hline \end{tabular}
\end{table} 
Table 6: SSIM and CC between the maps shown in Figure 7c. \begin{table}
\begin{tabular}{c c c c c} \hline  & \multicolumn{2}{c}{**MP**} & \multicolumn{2}{c}{**ROTI**} \\ \hline Criteria & SSIM & CC (\(p\)-value) & SSIM & CC (\(p\)-value) \\ S4 & 0.71 & 0.52 (\(<\)0.01) & 0.75 & 0.02 (0.87) \\ \(\sigma_{\varphi}\) & 0.58 & \(-\)0.03 (0.80) & 0.79 & 0.83 (\(<\)0.01) \\ \hline \end{tabular}
\end{table}