# Analysis of the Relationship between Scintillation Parameters, Multipath and ROTI
## 2 Materials and Methods
### Methodology  
Figure 1 shows the flowchart of the methodology. As shown in Figure 1, 30\({}^{\circ}\) cutoff is applied to all the data. The time series plots of all four parameters are generated before normalization to observe the general relationship and the scintillation intensity. Then all the data is normalized using the normalization method namely P-Norm [20] as described in Section 2.9 so that the different parameters vary in the same range. Next, two types of maps are generated, the mean value map and the occurrence percentage map, where each map is generated using data from a single station with a spatial resolution of 1\({}^{\circ}\). Mean value maps are generated first to investigate the spatial relationship, where the mean values are calculated for each grid cell. To achieve this the parameter values with the IPP coordinates located in the same grid are averaged and visualized on a map. After that, in order to more clearly visualize high values, occurrence percentage maps are generated. These show the percentage of values  
greater than a threshold for each \(1^{\circ}\) grid cell. The method for calculating the threshold is given in Equation (17). Compared with the mean value map, this map shows only the extreme values. To generate these extreme values a threshold is applied, which is determined using the standard deviation and mean of values for each parameter. For the Antarctic data, as the station is located in the high latitudes, phase scintillation is considerably more likely than amplitude scintillation [12; 21]. Therefore, S4 is not considered for the Antarctic data, where MP, ROTI and \(\sigma_{\varphi}\) fluctuate with different magnitudes from each other during the period with low scintillation and with similar magnitudes to each other during scintillation period. In order to mitigate biases, the different parameters values should be filtered first, where the values lower than a threshold as defined in Equation (17) are not used for occurrence percentage calculation. Figure 1: Flow chart for data processing and visualization. This is realized by applying two thresholds, determined using Equations (16) and (17) below:  
\[FT=STD+AVG \tag{16}\]  
\[ST=x\cdot STD^{*}+AVG^{*} \tag{17}\]  
where \(FT\) and \(ST\) respectively represent the first threshold and the second threshold; \(STD\) and \(AVG\) are the standard deviation and mean of all values for each parameter; \(STD^{*}\) and \(AVG^{*}\) are the standard deviation and mean of values higher or lower than \(FT\), dependent on the characteristics of the data, which is explained in more detail in Figure 1; x is a real number, which can be adjusted in order to distinctly show maps within different durations. For the Antarctic data, the size of the four parameters during the non-scintillation period are of different magnitude. Take the dataset in Antarctica on 2 April 2017 as an example, the mean of MP, ROTI, S4 and \(\sigma_{\varphi}\) during non-scintillation period (values lower than \(FT\)) respectively are 0.00026, 0.0032, 0.00051, 0.00066, where ROTI is not of the same magnitude as the other three parameters. Therefore, values higher than the \(FT\) is used for the \(ST\) calculation. For the Brazilian data, the situation is different, the sizes of all four parameters during non-scintillation period vary with similar magnitude to each other. Take the dataset in Brazil on 13 September 2017 as an example, the mean of MP, ROTI, S4 and \(\sigma_{\varphi}\) during non-scintillation period (values lower than \(FT\)) respectively are 0.00033, 0.00045, 0.00030 and 0.00057, which are similar to each other. Hence, the values lower than the \(FT\) are used for calculating \(ST\) for the Brazilian data. After following this process, the percentage of number of values larger than the thresholds can be drawn on each grid of maps. In this paper, thresholds are chosen to be relatively large (x is comparatively large) in order to show distinct extreme value areas on percentage occurrence maps.