# Analysis of the Relationship between Scintillation Parameters, Multipath and ROTI
## 4 Discussion  
Data obtained from three stations respectively located at equatorial and high-latitude areas are utilized in order to investigate the relationship between MP, ROTI, S4 and \(\sigma_{\varphi}\). First, as shown in Figures 3, 4, 11 and 12, the relationship in the temporal domain can be observed from all twelve time series plots, where all the parameters show the largest variations during the same time period. Figures 5 and 13 illustrate the spatial relationship for 6-h mean value maps, where high value regions occur at same location on maps. ROTI and \(\sigma_{\varphi}\) have different high value areas as compared with MP and S4 in Figure 5. This is because the relationship between ROTI and \(\sigma_{\varphi}\) and between MP and S4 may differ between satellites, due to different effects of ionospheric scintillation. In addition, as shown in Figure 13, high value areas of both MP and ROTI correspond to those of \(\sigma_{\varphi}\), but relate to different parts of the maps. Hence, it may be possible to identify areas affected by scintillation by combining MP and ROTI maps. It also suggests that MP and ROTI relate to different types of scintillation. This hypothesis can be further evaluated with the occurrence percentage maps. As shown in Figure 7, MP and ROTI separately show similar high value areas as S4 and \(\sigma_{\varphi}\). As shown in Figure 15, MP and ROTI agree with \(\sigma_{\varphi}\) over different areas. Next, occurrence percentage maps for 5 min as shown in Figures 8 and 16 suggest similar high value areas for all parameters. Finally, the propagation maps as shown in Figure 9, Figure 10, Figure 17, and Figure 18, where all the parameters move in the similar direction over time, further indicate the spatial similarity between MP&ROTI and S4&\(\sigma_{\varphi}\). The Pearson CC and SSIM were both used to quantify the relationship between pairs of maps. CC evaluates the linear correlation whereas SSIM provides a more complete evaluation of map similarity [30]. As discussed in Section 2.7\(s(m,\ n)\) can be inflated at low values of CC leading to an overoptimistic assessment of the map similarity. For the Brazil data, most of the SSIMs and CCs between S4 and MP exceed those between S4 and ROTI while \(\sigma_{\varphi}\) correlates more with ROTI than MP. For the Antarctica data, both MP and ROTI sometimes have high similarities with \(\sigma_{\varphi}\). The variograms and cross-variograms (Figures 6 and 14) were used to illustrate the spatial correlation in the parameters as well the cross-correlation between parameters. The variograms show clear spatial structure, with a range of 5 to 6\({}^{\circ}\), for the Brazil data. Likewise, the cross-variograms show a common spatial structure. Whereas CC quantifies the bi-variate correlation the cross-variograms quantifies whether the spatial structure is common between the different parameters. This gives evidence of strong spatial correlation between the four parameters and backs-up the results observed for the SSIM and CC. For the Antarctica case study there is clear evidence of spatial correlation for the dataset from 2016-10-13, with a common range of approximately 3.5\({}^{\circ}\). There is less clear evidence for the dataset from 2016-05-09 (common range of approximately 3.5\({}^{\circ}\)) and no evidence of spatial correlation for the dataset from 2016-04-02  
The purpose of this paper is to explore the relationship between MP, ROTI and scintillation parameters. We aim to better understand the relationships first, leaving open the possibility to use these relationships to provide supplementary information that may assist in overcoming the limitations of using specialized ionospheric scintillation monitoring receivers. The relationship between MP and scintillation has been investigated by [PERSON] et al. [8] and shows that the presence of obstacles in the vicinity of receivers can lead to the increase of S4 that shows some agreement with areas of MP measured using code-carrier divergence (CCD) standard deviation. [PERSON] et al.