Relationship between EPB occurrence and R-T growth rate
In the previous section, we found that there appears to be a fairly good relationship between the EPB occurrence and the R-T growth rate. To show the relationship more quantitatively, histograms of the number of days of EPB occurrence and non-occurrence sorted by the R-T growth rate are plotted in Fig. 3. The R-T growth rates are split into bins with a width of 10− 4 s− 1. Red bars indicate the number of days of EPB occurrence, and blue bars indicate the number of days of non-occurrence. Figure 4 shows histograms revealing the relationship between the rate of days of EPB occurrence and the R-T growth rate. The result clearly shows that EPB tends to occur more frequently as the R-T growth rate increases, although the correlation is weaker in 2013 than in 2011 and 2012.
Processes controlling variations in R-T growth rate
Figure 2 indicates that the R-T growth rate varies significantly in various time scales. To study which processes control the variations in the total R-T growth rate, we examined each term in Eq. (1). Figure 5 shows the variations in the terms of the R-T growth rate at 100°E for the years (a) 2011, (b) 2012, and (c) 2013. The red line is the upward E × B drift term \( \left[{\Sigma}_P^F/\left({\Sigma}_P^E+{\Sigma}_P^F\right)\right]{V}_p{K}^F \); the blue line is the vertical neutral wind term \( -\left[{\Sigma}_P^F/\left({\Sigma}_P^E+{\Sigma}_P^F\right)\right]{U}_L^P{K}^F \); the green line is the gravity term \( -\left[{\Sigma}_P^F/\left({\Sigma}_P^E+{\Sigma}_P^F\right)\right]\left({g}_e/{\nu}_{eff}^F\right){K}^F \). The chemical recombination term R
T
is much smaller than other terms where the maximum R-T growth rate occurs, and therefore is not plotted in Fig. 5.
Figure 5 indicates that the E × B term (red line) primarily contributes to the R-T growth rate most of the time, as was pointed in previous studies (Carter et al. 2014a, b; Wu 2015, 2017). Since our present analysis includes low and fixed polar energy inputs, the electric field variations arise from neutral wind variations driven by atmospheric waves propagating from the lower atmosphere. Variations in the electric field are also caused by variations in electric conductivities and angles between magnetic field lines and the terminator line. The gravity term occasionally becomes large and makes a significant contribution.
The term of the vertical-meridional component of the neutral wind perpendicular to the magnetic field \( {U}_L^P \) (blue line) tends to become larger after the March equinox and during June solstice periods. Variations in thermospheric winds are closely associated with atmospheric waves propagating from the troposphere (Miyoshi et al. 2017), which have significant seasonal dependence. In general, the larger meridional component of the thermospheric wind contributes to the larger value of the term. However, the variation in the \( {U}_L^P \) term is extremely complicated because it is a flux tube integrated quantity of the vertical-meridional component of neutral winds perpendicular to the magnetic field. Furthermore, thermospheric winds usually vary significantly near the terminator. Since the behavior of the neutral wind term becomes occasionally important around the June solstice, reproducing thermospheric winds accurately is the key to the analysis using the R-T growth rate. The results show that all terms except the chemical recombination term are highly variable and have significant contributions to the R-T growth rate especially in the June solstice.
Figure 6 indicates the local time when the maximum R-T growth rate occurred at the EAR site. The maximum R-T growth rate occurs around 18–19 LT most of the days. In the June solstice, the maximum R-T growth rate tends to appear in later hours than in other seasons, as pointed out in previous studies (e.g., Otsuka et al. 2009; Ajith et al. 2016). This is because the prereversal enhancement (PRE) is weaker during the period. Figure 7 shows the eastward electric field variations at the EAR site during 21–30 March 2011 and 21–30 June 2011. The PRE is clearly seen in March around 12 UT (i.e., 18–19 LT at the EAR site), while it is much smaller in June.
Effects of geomagnetic activity on R-T growth rate
Carter et al. (2014a, b) showed that geomagnetic activity influences EPBs, and that EPB development tends to be suppressed as a result of geomagnetic activity. Since the present GAIA model does not include the effect of varying polar energy inputs, we examined the relationship between geomagnetic activity and EPB occurrence by comparing ΣKp and the plasma bubble occurrence at the EAR site for the years 2011–2013. Figure 8 shows histograms of the numbers of EPB occurrence days (red bars) and non-occurrence days (blue bars) sorted by ΣKp (daily total of Kp) in the years 2011–2013. Figure 9 shows histograms of ΣKp for the ratios of EPB occurrence days in the years 2011–2013. Values of ΣKp are split into bins with a width of 5.
The result indicates that the EPB occurrence ratio tends to decrease as ΣKp increases, which is consistent with the result obtained by Carter et al. (2014b). However, the dependence of the occurrence ratio on ΣKp is not very clear for ΣKp larger than about 25, suggesting that strong geomagnetic activity occasionally induces EPB development (Basu et al. 2007; Tulasi Ram et al. 2008; Huang 2011). Since the present version of GAIA does not include varying polar inputs, the effects of geomagnetic activity are not included in our present study.
Effect of solar EUV/X-ray radiation on the R-T growth rate
Figure 10 shows the day-to-day variations in the R-T growth rate and F10.7 for the years 2011–2013. In 2011 (Fig. 4a), the R-T growth rate and F10.7 show similar seasonal variations in which they are maximum in the two equinoxes. This agreement appears to be coincidental because solar activity usually does not have seasonal variations as seen in 2012 and 2013. The agreement between the R-T growth rate and F10.7 is unclear on a short time scale (< 10 days). This is similar to the result given by Wu (2017) who used TIEGCM to obtain the R-T growth rate. Wu (2017) mentioned that the weak correlation between the R-T growth rate and F10.7 is due to the fact that the field-line integrated electron content gradient cancels out the positive correlation between the vertical ion drift and the F10.7 index. On the other hand, previous statistical analyses indicated that there are significant correlations between plasma bubble occurrences and F10.7 (Watanabe and Oya 1986; Huang et al. 2002; Nishioka et al. 2008), although the correlation depends on various parameters such as longitude, local time, and year. In our analysis, there appear to be some periods in which there are relatively good correlations between the R-T growth rate and F10.7, especially in the latter half of 2012. In 2012, variations of the 27-day period are seen in GRT and F10.7 between DOY 180 and DOY 310 (Fig. 10b). It seems that a very large F10.7 tends to increase the R-T growth rate.
On disagreement between R-T growth rate and EPB occurrence
Although the R-T growth rate agrees with the EPB occurrence for some periods, significant discrepancies are present. There seem to be three factors that lead to the discrepancies: (1) measurement problems, (2) errors in GAIA model, and (3) applicability of the R-T growth rate for the EPB occurrence index.
In this study, we have used the FAI observed by the EAR and the GPS scintillation observed by a GPS receiver at the EAR site to detect the plasma bubble occurrence. As shown in Fig. 2, the FAI occurrence is not always consistent with the GPS scintillation occurrence. This discrepancy could be attributed mainly to the following two reasons. (1) Since EAR is located at the magnetic latitude of 10.4°S, plasma bubbles that do not reach the latitude of the EAR are not observed. FAIs are mostly observed with the EAR at altitudes higher than 250 km. The apex altitude of the field-of-view of the EAR at a 250-km altitude is 420 km (Dao et al. 2016). Consequently, no plasma bubbles that are confined at an apex altitude lower than 420 km are detected with the EAR. On the other hand, the GPS scintillation measurement covers an area within a zenith angle of less than 60°, i.e., an area within a radius of approximately 470 km, and thus the plasma bubbles that do not reach the field-of-view of the EAR can be observed with the GPS measurements. (2) The ionospheric pierce points of the ray path of GPS radio waves move either from SSW to NNE or from NNW to SSE at approximately 100 m/s. Plasma bubbles immediately after sunset move eastward at 100–150 m/s on average (e.g., Otsuka et al. 2006). Since the movements of both the ionospheric pierce points and plasma bubbles have an eastward component, it is possible that the pierce points cannot come across the plasma bubbles although multiple satellites are available simultaneously, implying that GPS measurements at a single site may miss the plasma bubble occurrence. Consequently, in this study, we have used both FAIs and GPS scintillations and defined the day of plasma bubble occurrence as the day when either the FAIs or GPS scintillations are detected.
As mentioned earlier, the present analysis does not include the effect of magnetic disturbances, which are thought to control the occurrence of EPBs. Carter et al. (2014a, b) showed that geomagnetic activity is one of the key parameters for the occurrence of EPBs. Thus, it is necessary to include this effect to further improve the reproducibility of EPB occurrence. In addition, the present GAIA model employs a tilted dipole magnetic field model, which seems to give some errors in the R-T growth rate. There is likely to be some uncertainties in reproducing thermospheric neutral winds, which are parameters essential to ionospheric dynamo processes.
Although the linear growth rate of the Rayleigh-Taylor instability appears to be a good index of the plasma bubble occurrence, a high R-T growth rate does not necessarily mean a fully developed EPB structure. Even if the R-T growth rate becomes high instantaneously, EPBs do not grow unless a high R-T growth rate continues for 1 or 2 h. It is also likely that an EPB is produced somewhere else and drifts into the observation site. As studied by Ajith et al. (2015), there are two types of EPBs: evolving-type EPBs and drifting-in EPBs, suggesting that EPBs can be observed even if the R-T growth rate is low.
Prediction of EPB occurrence
Our study as well as other previous studies (e.g., Carter et al. 2014a, b; Wu 2015, 2017) suggest that the R-T growth rate calculated with numerical models could be a good index for the prediction of EPBs. However, we have compared past EPB occurrence data and R-T growth rates calculated with GAIA and past meteorological reanalysis data. For the practical forecast of EPBs, it is necessary to predict ionosphere-thermosphere variations one or more days ahead. One possible way to make a prediction is to introduce meteorological forecast data instead of the meteorological reanalysis data in the lower atmosphere. The other way is to run GAIA by itself without the meteorological reanalysis data. Since GAIA can reproduce meteorological processes in the troposphere to some degree, it is expected that the model can be used to predict the atmosphere-ionosphere system without forecast data. Further investigation is necessary for the development of a forecast technique.