1. Introduction
Equatorial plasma bubbles (EPBs) refer to plasma depletions frequently observed in the evening and are the major sources of electron density irregularities in equatorial and low-latitude regions [
1,
2]. The plasma density irregularities within the bubbles can scatter and diffract radio waves, leading to rapid fluctuations in the signal amplitude and phase in a received electromagnetic wave [
3]. The significant magnitude of total electron content (TEC) gradients associated with the side walls of bubbles or with plasma density irregularities could potentially cause very large Global Navigation Satellite System (GNSS) positioning errors [
4,
5].
Physically, the occurrence of an EPB largely depends on the mechanism for producing initial density perturbations and the conditions affecting the Rayleigh–Taylor (R-T) growth rate [
6]. Through the R-T instability mechanism acting on the steep density gradient of the F region bottom side, equatorial spread F (ESF) develops shortly after sunset and propagates both upward and toward off-equatorial latitudes [
7,
8,
9]. As the lower-density ionosphere moves upward into the higher-density topside ionosphere, a plasma bubble is created. Most ionospheric density irregularities are created by velocity shear mixing within the bubble gradients along with the formation of drift waves [
1,
3]. The irregularities start to decay first with the shortest scale length as the night progresses, and then they disappear when solar ionization refills the flux tube at sunrise [
3].
Nighttime equatorial irregularities have been observed in ionograms as ESF for a long time in history [
1,
9]. The EPB/ESF occurrence was found to be dependent on the solar cycle, season, local time (LT), and longitudinal sector based on many studies using observational techniques such as ionosondes [
8], very-high-frequency (VHF) radar systems [
10], and in situ satellites [
11]. Since EPBs cause depletions and irregularities in total electron content (TEC) time series when satellite-to-receiver ray paths pass through the region of plasma bubbles, studies of EPB occurrence based on TEC or rate of TEC change index (ROTI) have also been conducted in recent years [
12].
Previous studies have demonstrated that the easily accessible ROTI is an appropriate indicator to describe the strength of ionospheric irregularities [
13]. Monthly, seasonal, semiannual, and latitudinal variations in EPB occurrence based on the Global Positioning System (GPS) ROTI over five global regions between 2000 and 2006 were analyzed [
14]. The regional diurnal and seasonal variability in the GPS-TEC depletions over South America in 2008 were studied [
15]. The occurrence rate, time duration, and depth of TEC depletions and their dependence on the LT and season from 2002 to 2014 were analyzed at the global scale [
16]. The characteristics and causes of seasonal variations in EPB over Hong Kong from 2014 to 2017 were studied [
17].
Through previous studies, the characteristics of EPB occurrence were observed to be seasonally and longitudinally dependent [
14,
18]. Based on ROTI observations, Nishioka [
14] showed that the two maxima were seen in the annual occurrence variations in African, Asian, and Atlantic regions. Furthermore, the maxima of occurrence rates in the Asian region were in March/April and September/October. The analysis of EPB occurrences over Hong Kong found a maximum during equinoctial months and a minimum during December from 2001 to 2012, except during the solar minimum in 2007–2009 [
19]. Although a geometric relationship between the geomagnetic field line and the sunset terminator line was proposed to successfully explain the observed maxima in the occurrence rates during spring and autumn [
18], two asymmetries of EPB occurrences observed in previous studies reveal that other factors need to be studied [
14,
17,
19].
An EPB could affect different aspects of received GPS signals. In addition to temporal and spatial variations in EPB occurrences based on solitary observations, potential correlations among multiple observations, such as scintillation indices, ROTIs, and TEC depletions, have been studied. Occurrences of deep GPS-TEC depletions over China’s low-latitude region during the equinoctial seasons from 2011 to 2012 were found to coincide qualitatively with the scintillation index and ROTI [
20]. The correlation coefficients between the ROTIs and scintillation indices over Hong Kong from 2012 to 2013 were found to be 0.6 if the data from all GPS satellites were used together [
21]. The statistical relationship between the intensity scintillation index S4 and the ROTI was analyzed over the Indian equatorial region [
22].
Correlation studies are appealing not only because the very large number of conventional geodetic receivers provides much more data coverage for research opportunities than the limited number of ionospheric scintillation monitoring receivers (ISMRs) [
23] but also because there exists a straightforward relationship between the ROTI, irregularity strength, and intensity scintillation index [
24]. For instance, the degree to which ionospheric irregularities produce scintillations is dependent on the frequency of the signal compared to the plasma frequency, propagation geometry, and strength of the irregularities [
3,
24].
In this paper, depletions and irregularities due to EPBs are identified by using the GPS-TEC time series extracted from nine GNSS stations over the Hong Kong region from 2013 to 2019. The temporal variations in the occurrence rate, depletion depth, duration, and ROTI are analyzed on daily, monthly, and semiannual time scales. The relation between TEC depletion and irregularities is studied by conducting correlation analyses between the ROTI and three characteristic parameters of EPBs: the occurrence rate, depth, and duration. The seasonal and yearly variations in the EPB occurrence rates, depths, and durations and their solar activity dependences are presented. The paper shows that the seasonal dependence and asymmetries are manifested not only in the monthly variations of occurrence rate and ROTI but also in the variations of depth and duration. In addition, EPB occurrence rate, depth, and duration are found to be impacted greatly by solar activity and the impact degree is more significant on an annual than on a monthly basis.
4. Discussion
4.1. Diurnal Variation in EPB Occurrence, Depth, and Duration
Based on the analysis from a single station (HKWS) during 2013–2019, the diurnal variations in the EPB occurrences, depths, and durations corresponded well with that of ROTI. They showed similar patterns in maximum and minimum in seasonal scale and solar cycle. On the diurnal scale, the EPB occurrence rate, depth, and duration were highly correlated with the ROTI, with correlation coefficients equal to 0.85, 0.85, and 0.72, respectively.
The magnitude of EPB depth determines the degree of decrease in plasma density of the bubbles. The EPB duration reflects the degree of spatial or temporal scale that a plasma bubble would impact. The ROTI is the metric used to measure the strength of ionospheric irregularity inside or around the region of plasma bubbles with a much larger gradient [
5,
12]. Ionospheric irregularities occurring inside or around plasma bubbles usually lead to large ROTIs [
13]. The relationship between the three EPB parameters and the ROTIs reflects the degree of correlation between electron density depletions and density irregularities. The significant correlation coefficients indicate that greater value in the ROTI is usually closely associated with larger occurrence rate, depth, and duration of EPBs.
4.2. Monthly and Seasonal Variation in EPBs
The paper analyzed monthly EPB variations from 2013 to 2019 for the nine Hong Kong stations. The monthly variations in EPBs occurrence rates, depths, and durations were generally consistent with those of the ROTI from 2013 to 2019, and they all showed strong seasonal variations, especially during moderate-to-high solar activity years 2013–2016. The maximum observations in EPB occurrence and ROTI during spring and autumn in this paper were consistent with those from previous reports [
14,
17,
19]. Additionally, the paper showed that the maximum observations in EPB depth and duration also occurred in the spring and autumn.
The correlation coefficients between these parameters and the ROTI were 0.83, 0.94, and 0.85, respectively. Although the correlation coefficient of the monthly variation in EPB occurrences was slightly smaller than that of the daily variation, the correlation coefficients of the monthly variations between the EPB depth and duration and the ROTI were greater than those of the daily variations. This finding indicates that daily variations are more scattered than monthly variations, which might be because subtle variations in various factors that contribute to the nocturnal variations in the EPBs and ROTI are smoothed out during monthly correlation analysis.
Using twenty-three GPS receivers around the magnetic dip equator, Nishioka et at. [
14] showed that occurrence rates based on ROTI observations achieved maxima in March/April and September/October in the Asian region. Using GPS-TEC data from 2001 to 2012 over Hong Kong, Kumar et al. [
19] reported two clear seasonal maxima in the EPB occurrences corresponding to the spring and autumn months. Tang et al. [
17] reported that the seasonal occurrence rate was significantly larger in the two equinoctial seasons than in the solstitial seasons in 2014 and 2015. In the low solar activity year of 2017, the difference in the occurrence rate between summer and the two equinoctial seasons was not obvious. The correlation coefficients between the ROTIs and scintillation indices over Hong Kong from 2012 to 2013 were found to be 0.6 if the data from all GPS satellites were used together [
21].
The seasonal variation in plasma bubbles is controlled by the geometry between the geomagnetic field line and the sunset terminator line [
18]. In the equinoctial seasons, the E region conductivity is reduced most rapidly due to the closest alignment of the solar terminator with the magnetic meridian, and the rapid reduction is responsible for the enhancement of the vertical plasma drift, which creates a favorable condition for the formation of plasma bubbles.
The paper presented that the seasonal asymmetries were not only manifested in the monthly variation of occurrence rate but also in the variation of ROTI, depth, and duration of EPB during 2014–2019, especially during the moderate-to-high solar activity years of 2013–2016. The patterns of the two seasonal asymmetries were generally consistent with those from previous studies [
17]. However, during 2013, the maximum ROTI, depth, and duration were larger in December than in June, and the maximum duration in September was larger than that in March.
The seasonal asymmetries have been studied by previous researchers. Tang et al. [
17] reported that the seasonal occurrence rate was greater in spring than in autumn, especially during 2014–2015. Furthermore, Tang et al. [
17] observed that seasonal occurrences were more frequent in summer than in winter during 2014 and 2015. Kumar et al. [
19] found that the EPB occurrence rate had a higher value in September than in March during the high solar activity year of 2001.
The slight discrepancy between the result in the paper and previous studies indicated complicated mechanisms were involved in interpreting the seasonal asymmetries. The equinoctial asymmetry was assumed to be related to neutral wind in the F region [
14] or asymmetry in the electron density distribution [
17,
18]. The solstitial asymmetry was interpreted by monthly variations in flux-tube-integrated conductivities in the F regions [
14] or the seeding mechanism of thunderstorm-driven atmospheric gravity waves [
17]. Previous studies [
14] also suggested that the discrepancy in the observations of the occurrence rates could be due to the difference in measurement techniques and/or observational periods and/or the location.
Further analysis (not shown here) based on 90 percent instead of the maximum monthly ROTI, occurrence rate, depth, and duration indicates that the values are consistently larger in June than in December during 2013–2016, and they are larger in spring than in autumn. Therefore, the discrepancy in the asymmetries could be attributed to the difference in observation techniques.
4.3. Effect of Solar Activity
Annual variations in the EPB occurrence rates, depths, and durations were derived for the 7 years from 2013 to 2019 in this study. The solar cycle dependence was clearly observed from 2013 to 2019. They were highest in the high solar activity year of 2014, and then they decreased gradually from 2014 to the low solar activity year of 2019. The correlation coefficients between the semiannual EPB occurrence rate, depth, and duration and the F10.7 index were found to be 0.96, 0.94, and 0.95. This finding indicates that the EPB occurrence rate, depth, and duration are strongly dependent on solar activity on an annual basis.
Furthermore, the seasonal impacts of solar activity on EPB occurrence, depth, and duration indicated that the impacts of solar activity were most pronounced in the equinoctial months than during winter. Moreover, the differences on impact degree of solar activity were compared respectively between annual and monthly bases for EPB occurrences (annual R = 0.96 vs. monthly R = 0.59), depths (annual R = 0.94 vs. monthly R = 0.68), and durations basis (annual R = 0.95 vs. monthly R = 0.63). The results show that EPBs are influenced more obviously on an annual basis than on a monthly basis.
Tang et al. [
17] showed that EPB occurrence from 2014 to 2017 was highest in 2014. Kumar et al. [
19] indicated that the EPB occurrence rate varied with solar activity from 2001 to 2012 and reached a maximum during the high solar activity year of 2002. They reported that the correlation coefficient between the annual total number of EPB occurrences and the annual mean F10.7 index was 0.92. Moreover, they observed that the effects of solar activity on EPB occurrences were more pronounced on an annual basis than on a monthly basis. They found that the annual correlation coefficient of 0.92 between the annual number of EPB occurrences and the annual mean F10.7 index was significantly larger than the monthly correlation coefficient of 0.63 between the monthly occurrences and the monthly mean F10.7 index. For the seasonal impacts of solar activity on the number of EPB occurrences, their seasonal analysis showed that EPB occurrences were influenced more during spring and autumn (R = 0.80) than during summer (R = 0.62) and winter (R = 0.68).
The paper shows that the results of solar impact on EPB occurrences are consistent with previous studies. Additionally, the analysis presents that EPB depths and durations are also impacted greatly by solar activity, and the impact degree is more significant on an annual than on a monthly basis. The solar cycle dependence of ionospheric irregularities on the F10.7 index is explained in terms of the enhancement of the pre-reversal electric field amplitude with an increase in the solar UV radiation intensity [
33]. The TEC depletion depth and duration characterize different aspects of EPBs, and they are controlled by the same electron dynamical process as the EPBs, and thus are indirectly related to solar activity in a similar manner.
5. Conclusions
The paper analyzed the features of plasma bubbles based on ionospheric STEC data extracted from GNSS observations over Hong Kong from 2013 to 2019 covering the solar maximum and the solar minimum in SC 24. By using MRMIT filtering, the detrended STEC time series containing plasma bubbles and related parameters were computed.
The diurnal analysis from a single station (HKWS) showed that the EPB occurrence rate, depth, and duration were highly correlated with the ROTI. The large correlation coefficient between the diurnal variation in the ROTI and that of the occurrence rate (R = 0.85), depth (R = 0.85), and duration (R = 0.72) indicated that TEC depletions and ionospheric irregularities are usually closely associated.
The monthly EPB occurrence rate, depth, duration, and ROTI over the region were derived from 2013 to 2019. They all showed strong seasonal variations, with maxima during equinoctial seasons, especially during the moderate-to-high solar activity years of 2013–2016. The correlation coefficients between these three parameters and the ROTI were 0.83, 0.94, and 0.85, respectively, on a monthly time scale. Although the correlation coefficient of the monthly variation in EPB occurrences was slightly smaller than that of the daily variation, the correlation coefficients between the monthly variations in EPB depths and durations and the ROTI were greater than those of the daily variations. Furthermore, two seasonal asymmetries could be clearly seen for these parameters during the moderate-to-high solar activity period from 2013 to 2016, although they had slightly different patterns, attributed to the difference in observation techniques.
The annual variations in EPB occurrence rate, depth, and duration were presented, which varied with solar activity exhibited by the F10.7 index. In the ascending phase of SC 24 from 2013 to 2014, a small increase was seen, and then they decreased gradually from 2014 to the low solar activity year of 2019. The correlation analysis of the EPB occurrence rate, depth, and duration were found to be more strongly correlated with the F10.7 index on an annual basis than on a monthly basis. The correlation analysis of the monthly variations for three seasonal categories showed that the impacts of solar activity on EPB occurrence, depth, and duration were seasonally dependent, which was obviously more significant in the equinoctial seasons and summer than in winter.
It should be noted that the stations are located near the region at the northern crest of the EIA, therefore the observed features in EPB and ROTI are mostly related to patterns over the specific region. Because of high variability in EPB morphology at the EIA, it is probable that distinct features of EPB may be observed in other different regions.