1 INTRODUCTION

Ionospheric irregularities, as one of the earliest known effects of space weather, have a great impact on the Global Navigation Satellite System (GNSS) and satellite communication because they can result in rapid random fluctuations or degradation of the signal amplitude, phase and delay. Moreover, ionospheric scintillation can simultaneously accompany the occurrence of cycle slips or the complete loss on GNSS signals. Similarly affected by irregular ionospheric activities, GNSS has become a powerful tool for investigating the total electron content (TEC) and TEC fluctuations associated with irregular ionospheric activities along signal paths, which have become essential to the way we live and work (Aggarwal et al., 2012; Balan et al., 1993; Bilitza, 2000; Chen et al., 2008; Gorney, 1990; Kassa et al., 2015; Kassa et al., 2017; Zhao et al., 2005).

The amplitude/phase scintillation index S4 = and ROT I are typically used to quantitatively describe the intensity of ionospheric scintillation or TEC fluctuations. Measurements of both S4 and can be derived from GNSS scintillation monitoring receivers sampled at high frequencies, but the number and regional/global distribution of scintillation monitoring receivers are limited due to high costs. This sparsity of scintillation monitoring receivers restricts the extensive use of S4 and indices (Afraimovich et al., 2006; Bilitza, 2000; Gorney, 1990; Judge et al., 1998; Zhao et al., 2005).

The Total Electron Content fluctuation index ROTI, which is derived from ordinary non-scintillation GNSS receivers sampled at low frequencies, was first proposed in 1997. Since then, it has been widely used to detect irregular ionospheric activities, which are defined as the standard deviation of the rate of TEC (ROT) in a given 5 min interval. Previous studies have demonstrated close correlations between ROTI and scintillation indices. Over the past two decades, ROTI has been widely used to detect regional and global TEC fluctuations, especially with the growing number of GNSS tracking sites (Balan, 1993; Bilitza, 2000; Chen et al., 2008; Chen et al., 2015; Guo et al., 2007; Hedin, 1984; Lean et al., 2011; Li et al., 2013).

There exist thousands of dual-frequency geodetic GNSS receivers that have been deployed at globally and regionally distributed permanent stations. The networks of such receiver stations include the global GNSS network managed by the International GNSS receiver (IGS), the Continuously Operating Reference Stations (CORS) network managed by the U.S. National Geodetic Survey, the GPS Earth Observation Network (GEONET) developed by the Geographical Survey Institute of Japan, etc. The standard GNSS data collected from these networks have been used for many scientific and technological applications, including geodetic survey, precise GNSS orbit determination, global differential GPS System, global total electron content (TEC) mapping, ionospheric irregularity and scintillation measurements, etc (Afraimovich et al., 2006; Akala et al., 2013; Kelly 2009; Klobuchar et al., 1996; Li et al., 2013).

In this paper, we further introduce the rate of TEC index (ROTI) maps that measure regional ionospheric irregularity and scintillation activities using the standard dual-frequency GNSS phase data. The measurement technique was originally proposed in 1997. The coverage of GNSS-inferred ROTI maps has significantly improved since then as the GNSS networks continuously expand. The map has performed from a chain of 10 ground-based GPS receivers in East African region. Details about the receiver stations are illustrated by Table I and Fig. 1. Furthermore, a correlation analysis has presented in order to verify that ROTI is a good indicator of ionospheric scintillation occurrence traditionally measured by S4 and indices.

Fig. 1.
figure 1

Parts of Ethiopian GPS Network used for the current vTEC and ROTI mapping.

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2 MOTIVATION

Specialized receivers that can generate the ionospheric scintillation indices, namely the amplitude scintillation index (S4) and phase scintillation index are not available worldwide, which limits the application of these approaches. In order to overcome this problem, it is proposed to investigate the relationship of rate of change of total electron content index (ROTI) that can be obtained from standard generic receivers to represent scintillation indices.

Pi et al., 1997 proposed the ROT index ROTI as indicator of ionospheric irregularities. Being ionospheric scintillation of radio signals an important phenomenon under focus, the relationship between ROTI and scintillation indices has been widely studied. Basu et al., 1999 noted that ROTI/S4 varies in correspondence to the zonal velocity of ionospheric irregularities. Yang and Liu, 2016 considered each satellite-receiver propagation path, and found larger correlation between ROTI and S4 can be achieved under stronger scintillation circumstances. The study also found that more often poor correlations between them exist.

Liu et al., 2019 further addressed the impacts of receivers and sampling rates on the behaviors of ROTI. Carrano et al., 2019 showed evidences that only under certain geometry ROTI and S4 are highly correlated. The same study clarifies the differences between ROTI and S4 considering that S4 is more influenced by the scintillation spectrum and Fresnel scale. From the above-mentioned reports, we came to infer that there is no conclusive and homogenous relationship between ROTI and S4 index. Thus, further investigation in their relation should be carried out in both temporal and spatial domains and even in different circumstances. In this paper, the relationship between ROTI with S4 in both the spatial and temporal domains is investigated.

3 DATA AND METHODS

According to Akala et al., 2013, Kumar et al., 2012, Okoh et al., 2014, Sharma et al., 2012 and Tariku, 2015, the rate of TEC index (ROTI, in TECU/min) was proposed for the first time in 1997 to describe the measurements of ionospheric irregularity and scintillation activity. The rate of TEC (ROT, in TECU/min) is measured by utilizing dual-frequency GPS observation phase data, and computing the relative TEC changes, epoch by epoch, along the signal paths from each individual to the receiver, as shown in Equation (1). The ROTI is defined as the standard deviation of ROT over 5 min time intervals, as shown in Equation (2).

$$\sqrt {{\text{ROT}} = \frac{{\Delta S{\text{TEC}}}}{{\Delta t}}} ,$$
(1)
$$\sqrt {{\text{ROTI}} = \sqrt {\left\langle {{\text{RO}}{{{\text{T}}}^{{\text{2}}}}} \right\rangle - {{{\left\langle {{\text{ROT}}} \right\rangle }}^{2}}} } .$$
(2)

In this paper, dual-frequency GPS data has been obtained from IGS in Ethiopian GPS network and about 10 continuously operating GNSS tracking stations have been selected to detect TEC fluctuations associated with ionospheric disturbances over East Africa (See Table 1 and Fig. 1). The recorded GPS-TEC data at these stations are obtained from (http://sopac.ucsd,edu). Dual-frequency GPS observations have sampled at 30 s intervals; the cut-o elevation angle has set at 30°; and the selected time period is from 2012 to 2013, although some data are missing. Figure 2 illustrates the coverage of ionospheric pierce point (IPP) by GPS from 10 Ethiopian ground-based stations on 27 September 2013 at 1700‒2400 UT. The IPP trace shows that the mapping is from real observations.

Table 1.   Geographic Coordinates of GPS receivers used for the study
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Fig. 2.
figure 2

Coverage of Ionospheric Pierce Point (IPP) by GPS satellite from Ethiopian stations on September 27, 2013 at 1700–2400 UT (nighttime depression).

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4 RESULTS AND DISCUSSIONS

We studied the correlations between ROTI and S4 using data from each individual satellite as well as the amalgamated data from all the satellites. Both pattern and person statistical correlations have employed to clearly show the relation between S4 and ROT indices. The analysis was done for the period of 2012 and 2013 in both quiet and disturbed conditions.

4.1 Quiet-time Correlation Analysis between S4 Index and ROTI

The hourly variations of Kp and Dst indices of the selected quiet days (01 January, 01 February, 01 March and 01 April 2012) are depicted by the top and bottom panels of Fig. 3 respectively. As one can see from this figure, relatively small positive Kp and small negative Dst values were recorded during these days. The blue bar stands for the Kp and Dst values for 01 January, red for 01 February, orange for 01 March and purple for 01 April 2012 respectively.

Fig. 3.
figure 3

Hourly variations of Kp and Dst quiet time indices.

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The quiet-time correlation between S4 index and ROTI in the year 2012 during the first day of January, February, March and April months of 2012 are displayed by Figs. 4 and 5.

Fig. 4.
figure 4

Hourly variations of S4 and ROTI indices during January 1, February 1, March 1 and April 1, 2012 over Bahir Dar, Ethiopia.

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Fig. 5.
figure 5

Scatter plot of S4 and ROTI indices during January 1, February 1, March 1 and April 1, 2012 over Bahir Dar, Ethiopia.

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From Figure 4 one can easily infer the pattern correlation between S4 and ROTI whereas from the scatter plot of Fig. 5 we could see the one to one statistical correlation obtained from each satellite coded by their respective PRN. The maximum correlation and their respective satellite elevation at which the maximum correlation was observed are displayed by Table 2.

Table 2.   Quiet time correlation between S4 and ROTI indices
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Figures 1–4 and Table 1 clearly demonstrate in most cases a positive correlation be-tween S4 index and ROTI. However, minimum correlation coefficient was also observed and this might be due to the fact that these satellites have very low elevation angle. Compared with other satellites, the relatively higher noise in their measurements may lead to weaker correlation between ROTI and scintillation indices (Zhe and Zhizhao, 2015).

This quiet time correlation has revealed that between the mapped as well as the time series ROTI values can be used as a proxy for the presence of ionospheric irregularity. Thus, in the absence of SCINDA receivers, one can use ROTI as a proxy for the occurrence of ionospheric scintillation.

4.2 Disturbed-time Correlation Analysis between S4 Index and ROTI

The hourly variations of Kp and Dst values for the selected disturbed days in the year 2012 and 2013 are demonstrated by the top and bottom panel of Fig. 6 respectively. Dst was depressed to its minimum value (see the bottom panel of Fig. 6 and the second column of Table III) –80 nT on 05 April 2012; –82 nT on 12 and 17 June 2012; –120 nT on 01 June 2013; –83 nT on 06 and 14 July 2013.

Fig. 6.
figure 6

Hourly variations of Kp and Dst disturbed time indices.

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The disturbed-time correlation analysis of S4 and ROT indices is done based on the strength of Dst and Kp indices observed during the year 2012 and 2013.

The corresponding storm-time patterns of ROTI in the above-mentioned days are demonstrated by Figs. 7, and 8 respectively. In all cases, the patterns illustrated by S4 index due to geomagnetic storm are nicely captured by ROTI images. The suppression (negative effect) as well as enhancement (positive effect) of ionospheric scintillation are clearly illustrated by the time series as well as ROTI images. The summarized effect of the above-mentioned storm cases and maximum correlation coefficients are depicted by Table 3.

Fig. 7.
figure 7

Hourly variations of S4 and ROTI indices during June 12, 2012, Jun 17, 2012, April 5, 2012, June 1, 2013, July 6, 2013 and July 14, 2013 over Bahir Dar, Ethiopia.

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Fig. 8.
figure 8

Scatter plot of S4 and ROTI indices during June 12, 2012, Jun 17, 2012, April 5, 2012, June 1, 2013, July 6, 2013 and July 14, 2013 over Bahir Dar, Ethiopia.

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Table 3.   Effect of storm on nighttime scintillation inferred from S4 and ROTI indices
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Such variations on storm-time effect on ionospheric scintillation might be seen the categories reported by (Aarons et al., 1980). According to this report, the effect of storm on scintillation depends on the time of occurrence of storm i.e. the time at which the Dst gets its minimum value. Both S4 and ROTI indices have clearly responded to the geomagnetic storm effect and they are somehow in line with a report by (Aarons et al., 1980).

Besides, we have computed the ROTI values for the 2012 and 2013 and observed a little bit different correlation between S4 and ROTI. Such yearly variations on the correlation between S4 and ROTI might be due to year to year variations in solar and geomagnetic activities (Todd et al., 2010; Yu et al., 2009).

4.3 Temporal and Spatial Variations of Ionospheric Observables Inferred from Maps

The maps of ionospheric vTEC and rate of TEC index are displayed by Fig. 9. The top and bottom panels of Fig. 9 illustrate the hourly variations of the mapped vTEC and ROTI (1800‒2000 UT) on 27 September 2013 respectively. The pronounced ROTI is observed during depleted vTEC that could be considered as a proxy for nighttime ionospheric scintillation.

Fig. 9.
figure 9

Map of ionospheric TEC (top) and ROTI (bottom) at 18‒20 UT on September 27, 2013 (DOY = 270) over Ethiopia.

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According to the above figure, significant fluctuations and maximized values of ROTI were observed after sunset (1800‒2000UT). Maximum value of S4 during sunset time indicates that there are ionospheric irregularities during sunset time. This implies that ionospheric scintillation occurred during nighttime or post set time between 1800 to 2000 UT. The reason for this, during sunset period, the eastward electric field is enhanced (prereversal enhancement (PRE) electric field), which is coupled with the earths geomagnetic field to produce an upward vertical force derived from E B. The upward vertical force results in steep gradient of ion and electron densities between upper and lower layer, thereby producing plasma bubble irregularities arising from Rayleigh-Taylor instability process (Todd et al., 2010), which is the cause for ionospheric scintillation in equatorial region.

5 CONCLUDING REMARKS

In this paper, we have analyzed the capability of ROTI time series data as well as ROTI maps (images) in using as a proxy for the expected pattern of nighttime ionospheric irregularities. Both the spatial and temporal maps/patterns of ionospheric scintillation are analyzed. From the analysis, we came to conclude the following points.

1. The temporal and spatial values of ROTI could explain the expected ionospheric irregularity patterns and magnitude during both quiet and storm-times events.

2. In the absence of SCINDA receivers, we could use ROTI time-series values as well as maps to characterize at least the regional variations of ionospheric irregularities.