Equatorial ionization anomaly response to lunar phase and stratospheric sudden warming

This study examines the ionosphere response to gravitational forces of the lunar phase and dynamical disturbances of the stratospheric sudden warmings (SSWs). The total electron content (TEC) of global ionosphere maps is employed to examine responses of the equatorial ionization anomaly (EIA) crests to lunar phases and twelve SSW events during 2000–2013. The most prominent feature in the ionosphere is the EIA, characterized by two enhanced TEC crests at low latitudes straddling the magnetic equator, which can be used to observe ionospheric plasma dynamics and structures. Results show that the EIA crest appearance time on new/full moons (first/third quarters) leads (lags) that of the overall 14-year average, which causes a pattern of TEC morning enhancements (suppressions) and afternoon suppressions (enhancements). A statistical analysis shows that SSWs can also significantly cause the early appearance of EIA crests, regardless of the lunar phase. Thus, both lunar phase and SSWs can significantly modulate the appearance time of EIA crest and ionospheric plasma dynamics and structures.

www.nature.com/scientificreports/ ference between observation and reference is further computed (i.e. ΔTEC). In Fig. 1, the northern and southern EIA crests appear at 11:00 SLT (with the strength of 27.7 TECu (1 TECu = 10 16 #/m 2 )) and 13:00 SLT (27.2 TECu) on the SSW day ( Fig. 1a), as well as 13:00 SLT (26.5 TECu) and 14:00 SLT (26.1 TECu) on the reference day ( Fig. 1b), respectively. Figure 1c shows that the TECs are enhanced in the morning and suppressed in the afternoon, which suggests that the EIA crests appear earlier on the SSW day. The TEC enhancement/suppression pattern is consistent with previous findings on SSW effects 14 . To observe global GIM TEC responses to SSWs, we compute the zonal mean of 24 longitudes around the globe with an interval of 15° (i.e. 1 h) and plot the averaged LTT on the SSW day, reference, and their difference. The northern and southern EIA crests appear at 12:15 SLT (22.7 TECu) and 13:39 SLT (22.8 TECu) on the SSW day ( Fig. 1d), as well as at 12:45 SLT (21.1 TECu) and 13:50 SLT (22.3 TECu) on the reference day (Fig. 1e), respectively. Figure 1a- www.nature.com/scientificreports/ www. timea nddate. com/) is used to find the lunar phase day of the 12 SSWs. Since lunar gravitational effects on new moon and full moon are almost the same, lunar phase day 0 stands for the new or full moon day, where the minus "−" and the plus "+" sign mean the event occurs before and after that day, respectively. To see if an SSW could cause the early appearance of EIA crests, we compare EIA crest appearance times along the 24 longitudes across the entire 14 years in both hemispheres. We first isolate the same lunar day as an SSW event for the other 13 years without (w/o) SSWs, which are considered as the associated references, and compute the mean of EIA crest appearance times of the 24 longitudes in both hemispheres for each event and its 13 references. Figure 5 shows the mean of the EIA crest appearance times of each event and that of the associated 13 references. We further examine the mean EIA crest appearance time of the 24 longitudes of each SSW event and compare to that of the 13 reference year one-by-one. If the mean time of SSW event year is earlier (later) than the reference year, it is denoted as E (L). Odds in the ratio of numbers of E to those of L are then calculated. If the odds are greater than 1, the SSW event can cause early EIA crest appearance, regardless the lunar phase of the event. Finally, we examine the odds of the 12 SSW events being greater than 1. In the Northern Hemisphere, the odds of Events H, I, and J are infinite (∞; 13/0), while those of Events B, C, E, F, G, K and L are generally much greater than 1. Therefore, the sign test of the 12 SSW odds being earlier to later is 5 (= 10/2). The events with the odds greater than 1 in the Southern Hemisphere generally are the same as those in the Northern Hemisphere, except Event D, which is also greater than 1. Thus, the sign test is 11 (= 11/1) in the Southern Hemisphere. If we remove Event C, due to that event being affected by a magnetic storm of Dst < − 58 nT, the sign test becomes 4.5 (= 9/2) in Northern and 10 (= 10/1) in the Southern Hemisphere. Since these sign test among the 12 SSW odds are much greater than the rejection value 22 , which is 2.5 under a significance level of 0.01, SSWs can prominently result in early appearances of EIA crests. We further find the average of time differences resulting from the SSWs  Table 1). Detailed information of the above results is summarized in Table 1, which lists the event date, the lunar phase day, the EIA crest appearance time with (w)-without (w/o) SSW day, and the ratio of the EIA crest on the SSW day being earlier to later (E/L) than that of the reference.

Discussion
Goncharenko et al. 14 14 agree well with that in GIM TEC (Fig. 1). Figure 1 further demonstrates that the 24 longitudes can be employed to examine ionospheric SSW signatures across the globe. The sinusoidal variation in Fig. 2 reveals that the EIA crests on new/full moon (first/third quarter) lead (lag) those of the overall 14-year average, which consequently results in morning enhancements and afternoon suppressions. Note that the sequential patterns of ΔTEC enhancements and suppressions during 19-31 January 2009 and 21-30 January 2008 shown in the previous study 14 agree well with the patterns of about the new moon and full moon in Fig. 2; of Event I (Fig. 3i) and Event H (Fig. 3h); and of Fig. 4i,h without SSWs. Note that the pattern of Event F occurring on lunar phase day 7 shown in Fig. 3f also agrees well with that of the first and third quarter shown in Fig. 2. These agreements confirm that the semimonthly lunar periodicity plays an important role. The statistical analyses of odds and sign tests in Fig. 5 and Table 1 show that SSWs can significantly cause early appearances of EIA crests. The agreement between the previous 14 and current studies 7,11,[14][15][16][17][18] indicates that owing to SSWs, the interactions between planetary waves and tides could alter the tides from the middle to the upper atmosphere, and thus significantly modify the ionospheric EIA. Figure 2 shows that the lunar phase results in the EIA crest appearance time during new/full moons leading that of first/third quarters by about 1 h, while Fig. 5 and Table 1 show that the SSWs cause the EIA crests advancing by about 0.47 h. The patterns in Fig. 3 are very similar to those in Fig. 4 accordingly. These results strongly suggest that the lunar phase can significantly modulate the EIA crests and dominate the pattern of TEC enhancements/suppressions, while SSWs can prominently advance EIA crest appearance time regardless lunar phase. In conclusion, the lunar phase from The EIA crest appearance times on day with and without SSW events. The EIA crest appearance times of the 24 longitudes on the SSW event day (red segment) and associated references lunar day without (w/o) SSW in the other 13 years (black segments) in the both hemispheres. Each segment consists of 24 data points in the 24 longitudes of the globe. Two end ticks of the segment stand for one standard deviation, while the center tick denotes the mean. E and L indicate the mean of the EIA crest appearance time of the event being earlier and later than the associated reference mean, respectively. If it's a tie, a sign of " = " is denoted. When tie, it will not be included the ratio calculation.

Methods
Data used in this study are the total electron content (TEC), date of the lunar phase, and date of stratospheric sudden warming (SSW). The TEC is defined as the total number of electrons integrated between ground-based receiver and GNSS (global navigation satellite system) satellites, along a tube of one meter squared cross section.
Here . TEC ref is calculated by a moving median at each SLT 7 days before and after a certain SSW observation day, the difference between observation and reference is further computed (i.e. ΔTEC). The reason why TEC ref is calculated by a moving median at each SLT 7 days before and after a certain observation day is because of close to the semimonthly lunar period of 14.76 days, which allows us to extract the lunar phase signature. By using the same approach, Liu et al. 20 study the lunar phase signatures on ionospheric solar eclipse signatures on 21 August 2017. They show that the lunar tide signature can be enhanced when the reference is constructed by using ± 7 days (semimonthly lunar period) or longer windows. Once again, the above processes have been conducted under the same solar local time but over a full semimonthly period, thus, which shall lead effects/signatures of the solar signature being removed and those of the lunar phase signature being enhanced. TEC response to lunar phase. By averaging TEC and ΔTEC on each lunar phase during the entire 14 years, we can examine the coherent of TEC to the lunar phase in detail. In addition to the TEC, the appearance time of the equatorial ionization anomaly (EIA) crest is utilized for statistical analysis. EIA crests are extracted from each LTT by determining the maximum TEC during 08:00 SLT-20:00 SLT. To discriminate the SSW effects from influences of the lunar phase, the EIA crest time on the same lunar phase day with and without SSW are compared one-by-one (Fig. 5).
TEC response to SSW. Similar to Fig. 1f Separation of SSW and lunar phase effects on the EIA. Figure 5 illustrates the EIA crest appearance times on the same lunar phase day with and without SSW for each of the 12 events. Owing to the same lunar phase day, the pure SSW effects can be obtained by subtracting the mean EIA appearance time with SSW event by that without (the reference) ( Odds. Odds provide a measure of the likelihood of a particular outcome. They are calculated as the ratio of the number of events that produce the outcome to the number that don't. For each SSW event, we first identify the averaged EIA crest time over the 24 longitudes in both hemispheres on the SSW day and that on the same lunar phase day in the rest other 13 years (Table S1). We then calculate odds as the ratio of the EIA crest time of the SSW day earlier (E) to later (L) than that of the rest 13 years. The ratio of E/L (odds) greater (less) than 1 is defined as "plus" ("minus"), which indicates that EIA crest time is early (later) activated by the SSW event (Table 1). We further find the sign test (or odds) for the entire 12 SSW events. If number of the pluses is greater than that of minuses, it can be claimed that SSWs can significantly advance the EIA crest time.

Data availability
The total electron content (TEC) of global ionosphere maps (GIMs) is provided by the Center for Orbit Determination in Europe (CODE) (ftp:// ftp. aiub. unibe. ch/). The lunar phase is obtained from Lunar Calendar (https:// www. timea nddate. com/). The daily solar flux and ap index are published by Space Physics Data Facility of NASA (National Aeronautics and Space Administration, https:// omniw eb. gsfc. nasa. gov/ html/ ow_ data. html).