1. Introduction
Ionospheric scintillation is one of the main error sources that can reduce the quality of positioning outputs or even lead to loss of lock on satellites, and hence can cause significant errors in Global Navigation Satellite System (GNSS) receiver operation [
1]. A series of methods have been implemented to mitigate scintillation effects on positioning. For instance, in Aquino et al. [
2], the tracking error variances of GNSS receiver phase locked loop (PLL) and delay locked loop (DLL) is used to modify the least squares stochastic model and the positioning accuracy was shown to be improved by 17–21%. Furthermore, Bougard et al. [
3] attempted to exclude scintillation affected satellites from the positioning calculation with the technique of receiver autonomous integrity monitoring (RAIM) specific for precise point positioning (PPP), which considerably improved the PPP accuracy. Loss of signal lock and cycle slips are the primary problems under scintillation, which are relatively severe when using a single satellite constellation. Therefore, it was proposed that the data of GPS and GLONASS could be integrated to obtain more reliable positioning solutions under moderate to strong scintillation [
4], which improves the accuracy of the positioning output by 60% compared to using GPS alone. By using these approaches, the effects of scintillation can be mitigated to a certain extent. However, specialized receivers that can generate the scintillation indices, namely the amplitude scintillation index (S4) and phase scintillation index (σ
φ) [
5] are not available worldwide, which limits the application of these approaches. Though the S4 index can be computed with low-cost receivers or common geodetic GNSS receivers [
6,
7], the σ
φ index cannot be generated in the same way. In order to overcome this problem, it is proposed to investigate the relationship of two parameters, namely multipath (MP) and rate of change of total electron content index (ROTI), that can be obtained from standard generic receivers to represent scintillation indices (S4 and σ
φ).
Studies on the relationship between scintillation and MP or ROTI were initiated respectively by Romano et al. [
8] and Basu et al. [
9]. According to Romano [
8], a certain relationship can be observed between MP and scintillation parameters. Specifically, MP has a negative influence on the presentation of ionospheric scintillation [
8]. Hancock et al. [
10] also demonstrated an agreement between MP and scintillation parameters. It has been demonstrated previously that ROTI can be used to indicate the occurrence of scintillation [
9]. It has been further demonstrated that the correlation between ROTI and scintillation parameters is strong with a correlation coefficient exceeding 0.6 on average, even higher than 0.8 sometimes [
11]. In this paper, the relationship between MP and ROTI with S4 and σ
φ in both the spatial and temporal domains is investigated. Additionally, propagation patterns of all four parameters are studied to investigate the spatial similarity over time.
The purpose of this study is to investigate the relationship of S4 and σφ with MP and ROTI. Several objectives are set as follows:
- (1)
Compare the time series plots of the four parameters to observe the temporal relationship to confirm if during periods of scintillation all parameters are similarly affected.
- (2)
Thereafter, two types of 2D maps are constructed, mean value maps and occurrence percentage maps, where the former is to evaluate whether abnormally high value areas are in similar spatial regions and the latter is to investigate the referred areas with clearer outputs. As scintillation mainly occurs at night and in the early morning local time, the maps are first generated with a period of 6 h.
- (3)
Furthermore, the maps with 5 min periods are generated to observe the relationship during times when the largest variations of the parameters are observed.
- (4)
Finally, the structural similarity (SSIMs) and Pearson correlation coefficient (CC) between maps are calculated to evaluate the similarity between the parameters. Variograms and cross-variograms are also used to evaluate the spatial correlation in the maps.
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 σ
φ. First, as shown in
Figure 3,
Figure 4,
Figure 11 and
Figure 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.
Figure 5 and
Figure 13 illustrate the spatial relationship for 6-h mean value maps, where high value regions occur at same location on maps. ROTI and σ
φ have different high value areas as compared with MP and S4 in
Figure 5. This is because the relationship between ROTI and σ
φ 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 σ
φ, 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 σ
φ. As shown in
Figure 15, MP and ROTI agree with σ
φ over different areas. Next, occurrence percentage maps for 5 min as shown in
Figure 8 and
Figure 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&σ
φ.
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 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 σ
φ correlates more with ROTI than MP. For the Antarctica data, both MP and ROTI sometimes have high similarities with σ
φ. The variograms and cross-variograms (
Figure 6 and
Figure 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°, 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°. There is less clear evidence for the dataset from 2016-05-09 (common range of approximately 3.5°) 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 Romano 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. Romano et al. [
8] also shows that a high percentage of the higher S4 values and CCD are below 30°. In this study, all data has a 30° satellite mask applied which should significantly reduce any MP effect in the vicinity of the station. Therefore, the high values of S4, σ
φ and MP in this study all occur for satellites at high elevations (>30°), giving support to the theory that the higher values of MP are being influenced by the scintillation events evidenced from the high scintillation indices values during the corresponding time window.
The relationship between MP values from the TEQC software and σ
φ was observed by Hancock et al. [
10] through occurrence number plots and time series plots from data collected in Hong Kong, which provided initial evidence that the study of the relationship between MP and scintillation parameters may be interesting and of possible use in the mitigation of errors during scintillation events. Following on Romano et al. [
8] and Hancock et al. [
10] this study provides a much deeper statistical analysis of the relationships between MP, S4 and σ
φ. Furthermore, the ionospheric index ROTI is added in this study to give additional evidence that scintillation is real rather than a product of the physical environment around the receiver as claimed by Romano et al. [
8].
The relationship between ROTI and scintillation has been investigated [
9,
11,
31,
32,
33]. The scatter plot and the time series plot are common methods used in recent studies to demonstrate the linear relationship between ROTI, S4 and σ
φ [
9,
11,
31,
32]. Additionally, the relationship between ROTI and scintillation has been shown to be affected by changes in elevation angle [
11]. Correlation coefficients have shown distinctly higher values when the satellite elevation angle exceeds 60° when compared to satellites with elevation angles lower than 60°. However, this investigation focuses on elevations higher than 30°, focusing on satellites with higher elevation angles thus taking advantage of the stronger relationship between scintillation and ROTI shown by Yang and Liu [
11]. Analysis of the relationship between MP and the scintillation parameters with respect to the effects of elevation angle are not part of this study.
Acharya and Majumdar [
33], used statistical analysis to conclude that the probability density distribution of S4 can be obtained using ROTI, thereafter, the occurrence probability of scintillation can be estimated. Therefore, Acharya and Majumdar [
33] gives the conclusion about strong evidence of a relationship between ROTI and S4, which in general agrees with the analysis from this study. In addition, Carrano et al. [
31] also demonstrated the theoretical relationship between ROTI and S4 and has demonstrated that this relationship is highly dependent on the sampling rate. They also provide reasons why this relationship varies between different dates and in different regions. These factors have not been investigated in this study and further work is required in this area. Therefore, the investigation on the relationship based on first principles and on the formulae between MP and scintillation is required in future work.
Investigations [
9,
31,
32,
33] focus on S4, where σ
φ was not investigated. Therefore, the investigation on σ
φ is less thorough than that on S4 based on the past research [
9,
31,
32,
33]. Though σ
φ was investigated by Yang and Liu [
11], a comparison of how both scintillation indices are related to ROTI was not undertaken. According to the graphs given by Yang and Liu [
11], S4 is more correlated with ROTI than σ
φ, which is caused by the relative inactivity of σ
φ (σ
φ shows a maximum value less than 0.4). In contrast, both S4 and σ
φ are analyzed and compared in this paper with reference to their relationships with ROTI. Furthermore, analysis from the stations in this study show evidence that ROTI is more similar to σ
φ than to S4 both visually and statistically, giving new valuable insights into the relationships between ROTI, S4 and σ
φ.
Previous research has focused principally on the linear relationship between ROTI and the scintillation parameters, this study adds to this body of research by investigating the spatial relationship. This leads to the possibility of using these data sets to generate scintillation risk maps, that may be similar in principle to tracking jitter maps generated Sreeja et al. [
34], and also similar to
Figure 4,
Figure 5,
Figure 6 and
Figure 7 given by Koulour et al. in [
35], which visualize the effect of scintillation and can be used to identify and possibly mitigate risk caused by scintillation events.
Figure 2 from Sreeja et al. in [
34] shows the S4 maps as a function of time and IPP latitude where strong scintillation activity was observed between 18° S and 26° S from 8pm to 0am local time on March 9–11, 2011. By comparison,
Figure 3c,
Figure 5c and
Figure 7c in our paper show all the parameters are intense between 18° S and 26° S from 0 am to 4 am UTC (8 pm to 0 am in local time) on March 12 2011, which is similar to the output obtained by Sreeja et al. [
34].
Additionally, ROTI is the major proxy to the scintillation parameters proposed in previous research, which has shown weaknesses in the ability of ROTI to replace S4 and σ
φ. In this research the relationship between ROTI and the scintillation parameters S4 and σ
φ has been further investigated and in addition this study shows that it may be possible to add MP as additional parameter, in support of other parameters such as ROTI, computed from a standard GNSS receiver (i.e., non-scintillation monitoring receiver) that may be indicative of scintillation. However, the increase of MP does not generally indicate the occurrence of scintillation events as the scintillation measurements can be contaminated by real multipath effects [
8].