*4.2. Crest-to-Trough Differences (CTD)*

Despite the EIA intensity, it is easy to notice in Figures 3 and 4 that the local time of the first appearance of the crests also showed interhemispheric asymmetry. That is, a stronger crest corresponding to earlier emergence. Extensive studies have investigated the interhemispheric asymmetry of the EIA intensity; hence, in the following, we provide another perspective to investigate asymmetrical behavior concerning the time evolution of EIA. In particular, to assess the time evolution of EIA, we defined crest-to-trough difference (CTD):

$$\text{CTD} = \text{TEC}\_{\text{off-equator}} - \text{TEC}\_{\text{equator}} \tag{1}$$

That is, the difference between the TEC at off-equator (set as fixed dip latitude bin of 10◦–15◦ N/S) and the TEC at the equator (set as fixed dip latitude bin of 2.5◦ S–2.5◦ N), where the EIA crest and trough normally reside, respectively. Note that the 'crest' location we defined here is not the accurate position of the EIA crest; thus, the calculation of CTD does not require the presence of a clear EIA crest feature.

Another criterion used to quantify the developed EIA intensity is the crest-to-trough ratio, defined as the ratio of the mean of the northern and southern EIA crest peak value to the minimum TEC in the EIA trough:

$$\text{CTR} = \text{(TEC}\_{\text{ncrest}} + \text{TEC}\_{\text{screst}}) / \text{(2} \times \text{TEC}\_{\text{trough}}) \tag{2}$$

CTR is much more extensively used in other studies [2,3,27,32,33]. The CTR provides information on the overall intensity of the developed EIA normalized by the background TEC at the EIA trough. As we intend to monitor the full development of the EIA throughout the daytime, even when the EIA crests have not been developed, the defined CTD is a more suitable parameter to achieve the goal.

Figure 5 shows an example of the northern crest-to-trough difference (NCTD) and southern crest-to-trough difference (SCTD), extracted from GPS TEC and IRI TEC maps (Figure 5a,b). GPS TEC measurements (Figure 5a) show that at 0600–1000 LT the double crest had not been developed and CTD experienced a falling and then a rising (Figure 5c). The falling occurred right after the sunrise, due to that the ionization creates more plasma around the equator. The rising should be related to the ambipolar diffusion that transports equatorial plasma to higher latitudes. Thus, the transition of the falling and rising marks the time that the transportation term dominates, i.e., the net accumulation of plasma at the off-equator exceeds that at the equator. This transition is marked as the inflection points on the CTD curved in the morning hours and is defined as the onset of EIA.

**Figure 5.** Top panels: TEC at Indian sector as a function of local time and dip latitude, using data from (**a**) IGS GPS TEC and (**b**) IRI-2016. Bottom panels: Local time evolution of the extracted NCTD and SCTD from (**c**) IGS GPS TEC and (**d**) IRI-2016. Dash curves are the original calculation from TEC data; solid curve is the smoothed results. The triangles, circles, and diamonds mark the time of the onsets, first emergences, and the peaks of the EIA crests during the evolution.

In the GPS TEC map (Figure 5a), the EIA northern crest appears earlier than the southern crest, at a local time near 0900. The emergence of the EIA has been marked as circles on the CTD (Figure 5c) curves as the CTD equals 0, which also exhibit northern crest priority. However, the local time of the marked emergence lags behind the crest's appearance on the TEC map (Figure 5a). This is because the calculation of CTD set the crest at fixed latitudes of 10◦–15◦ N/S, while the real emergence of the EIA crest appeared at latitudes closer to the magnetic equator where the fountain effects launch. After the first emergence, CTD grows continuously, representing the development of EIA. The peaks of the CTD mark that the EIA is fully developed and the TEC at the EIA crest reaches its peak value. Thus, we mark the peak CTD in the afternoon as the peaks of EIA.

Figure 5b,d show the IRI-2016 predicted TEC map and the corresponding CTD profiles, respectively. Besides a clearly different morphology of EIA structure (Figure 5b) compared with the GPS TEC measurements (Figure 5a), the IRI-2016 derived CTD also exhibited abnormal local time evolution. In detail (Figure 5d), there is no post-sunrise falling that ends in negative vales for NCTD; SCTD showed persistent positive value during 0700–2300 LT. Thus, the onset, as well as the first emergence of the EIA crest, can neither be identified on the IRI-2016 CTD. Only the peaks of the EIA crest can be marked as the peaks of CTD profiles. Note that a similar situation is a common feature for IRI-2016, though the three time points can be occasionally identified.

In summary, the local time of the onset, first emergence, and peak of EIA crest can be identified from GPS TEC measurement, while IRI-2016 cannot regularly capture the real time evolution process of the EIA development.

#### *4.3. Time Evolution of EIA: Seasonal and Longitudinal Effects*

In the last subsection, the time points of the onset, first emergence, and peak during the evolution of EIA can be marked on the CTD profiles. Figure 6 presents the variations of these time points as a function of months in 2013.

**Figure 6.** Local time of the onsets (solid lines), emergence (dash lines), peaks (dotted lines) of the EIA northern crest (green) and southern crest (red), at Peruvian (**a**–**c**) and Indian sector (**b**–**d**), extracted from GPS TEC (top panels) and IRI-2016 (bottom panels). The data gap in Figure 6c,d is due to that the time points sometimes cannot be identified in the IRI model.

Results from GPS TEC (Figure 6a,b) revealed that the patterned annual variations were generally shared by the three time points. The time lag between the first emergence of EIA crests with the onset is ~2 h, and it takes another ~4 h for the EIA crest to reach peak values. Specifically, semiannual and annual cycle patterns in the Peruvian and Indian sectors, respectively, can be captured. Take the onset of the northern EIA crest as an example, the

semi-annual cycle (Figure 6a) is characterized by an earlier onset time near two equinoxes and a later onset time near two solstices; the annual cycle (Figure 6b) is characterized by an earlier onset time in the winter and a later onset time in the summer. As for the southern crests, the time points generally exhibit reversed seasonal patterns compared with those of the northern crests, except that the emergence time at the Peruvian sector (Figure 6a) stays constantly near 1200 LT throughout the year 2013. Besides, the semiannual variation of the onset of the southern crest at the Peruvian sector is not as prominent as the northern crest, resulting in an earlier onset of southern crest than northern crest during winter seasons, which is similar to that at the Indian sector.

Figure 6c,d show the IRI-2016 predictions. As has been mentioned above, the onset and the emergence of EIA sometimes cannot be identified from IRI-2016 data. It can be witnessed that the onset and emergence data are sparse, due to the incapability for identifying those time points on CTD profiles. Nevertheless, the available time points generally predicted earlier onset and emergence, compared with those of the GPS observations. Interestingly, the annual cycle of EIA onset time is a prevailing phenomenon in both Peruvian and Indian sectors, while GPS revealed a semiannual cycle seen in the Peruvian sector. However, a similar semiannual cycle seen in GPS observation can be found on the peak time of the northern crest in the Peruvian sector (Figure 6c). Besides, the emerging time of the southern crest also exhibits semiannual variation (Figure 6c), but in the same phase of the time points of the northern crest seen in GPS observations (Figure 6a). It can be concluded that, although the semiannual cycle can be occasionally found on the emerging and peak time of EIA crest from IRI-2016, the onset time of EIA still shows the classic picture that the crest in the winter hemisphere develops earlier than that in the summer hemisphere. Note that the IRI-2016 derived peak time of EIA sometimes shows abnormal values (e.g., April at Peruvian sector, July and August at Indian sector, as shown in Figure 6c,d); this also indicated the inaccuracy of the IRI-2016 in retrieving EIA evolution.

The annual cycle shown in the Indian sector represents a classical picture of the neutral wind modulated ambipolar diffusion during the development of EIA. That is, the transequatorial wind blows from the summer hemisphere to the winter hemisphere, which pushes the plasma equatorward and poleward along the field line (referred to as pile-up effects) in the summer and winter hemispheres, respectively. These neutral wind effects contradict/favor the ambipolar diffusion in the summer/winter hemisphere; hence, the development of EIA crest in the summer/winter hemisphere is inhibited/promoted, resulting in that the time points of EIA's development show clear winter hemispheric priority.

Take the onset of the northern crest during the winter season as an example, the essential difference between the annual cycle (Indian sector, Figure 6b) and the semiannual cycle (Peruvian sector, Figure 6a) occurs during winter seasons. That is, the semiannual cycle consists of a delayed northern crest onset during northern winter (Figure 6a), which ought to occur earlier (Figure 6b) to exhibit the annual cycle. Thus, the fundamental question is what causes the retarded EIA northern crest development that is supposed to be advanced.

#### **5. Discussion**

The semi-annual cycle is a common feature on the overall intensity of plasma density at low and middle latitudes, which appears as density maximums at two equinoxes. The causes of the semi-annual cycle are discussed as follows. There is the ratio of atomic oxygen to molecular nitrogen O/N2, which also shows similar semiannual variation, especially at middle latitudes [34]. In detail, during high O/N2 ratio seasons (i.e., equinoxes), the chemical recombination rate is low, which causes a relatively high plasma density. He O/N2 ratio is higher in the winter hemisphere, leading to a higher ionization rate [35]. However, this effect is more suitable to explain the middle latitudes winter anomaly [36] rather than that at low latitudes, since the hemispheric difference in the O/N2 ratio is smaller in the low latitudes during the daytime. Thus, the O/N2 ratio is less likely to contribute to the interhemispheric asymmetry of EIA's evolution seen in this study.

In addition to the O/N2 ratio, the semi-annual cycle is also the property possessed by the daytime equatorial E×B drift that exhibits two equinoctial maximums and two solstitial minimums [37,38], via atmospheric tides modulated E-region dynamo [39]. Hence, the E×B drift is widely recognized as a major mechanism for the appearance of semiannual variation of the general EIA intensity [33]. However, there exist arguments regarding the E×B drift effects on the detailed EIA morphology. Wu et al. [40] attributed the semiannual variation of the northern EIA crest location to the E×B drift, while Liu et al. [14] doubt the mechanism as the daytime EEJ shows poor correlation with the EIA crest location.

The semiannual cycle of either the O/N2 ratio or the E×B drift is a global phenomenon, if the O/N2 ratio or the E×B drift is indeed involved in altering the efficiency of the EIA development, the earlier onset during equinoxes should also be witnessed in the southern hemisphere, and in other longitudes (i.e., Indian sector). However, this is not supported by the current observations. Hence, neither the O/N2 ratio nor the E×B drift is responsible for the abnormal semiannual variation of the onset, emergence, and peaks of the EIA at the Peruvian sector, at least in a sole way.

The meridional neutral wind is recognized as the major impact of the asymmetric development of EIA. Thus, we raise a question of whether the semiannual cycle seen in the Peruvian sector is due to the local abnormal neutral wind configurations. To answer the question, the neutral wind result from TIEGCM simulation during two solstices and two equinoxes is adopted, during the geomagnetic quiet periods. Note that when discussing the pushing effects from neutral wind to plasma, the zonal wind contribution under the presence of magnetic declination should be considered. Hence, the effective magnetic meridional neutral wind velocity (U) could be written as:

$$
\mathcal{U} = \mathcal{U}\_{\theta} \cos D + \mathcal{U}\_{\phi} \sin D \tag{3}
$$

where *U<sup>θ</sup>* (positive southward) and *U<sup>ϕ</sup>* (positive eastward) are the meridional and zonal wind velocities, and *D* (positive eastward) is the declination angle [11]. Figure 7 presented the effective magnetic meridional wind as a function of local time and dip latitudes, in the Peruvian sector and Indian sector during March Equinox, June Solstice, September Equinox, and December Solstice. The dashed lines mark the dip equator; the two shaded bars in each plot mark the 'fixed crest' defined in this study at dip latitude of 10◦~15◦ S/N.

To illustrate the wind's effects on the ambipolar diffusion during the initial stage of the EIA development, we focus on regions of the equatorward side of the two 'fixed crests' (regions between the dip equator and the crests, 0◦~10◦ S/N in dip latitude). All three time points shown in Figure 6 are generally within 0600~1500 LT, so we focus on this local time bin.

In the Peruvian sector, the southward winds prevail through geomagnetic low latitude regions (i.e., regions between two shaded bars), except for the region near the northern crest (still in the geographic southern hemisphere) during December Solstice. For the southern crest, the southward wind is strongest/weakest at June Solstice and December Solstice, respectively. Thus, the promotion of the ambipolar diffusion to the southern crest is most/least prominent at June/December Solstice, which should result in the earliest/latest onset of EIA southern crest, consistent with the results shown in Figure 6a (red solid line). For the northern crest, the strongest southward wind occurs during June Solstice, while the northward wind appears during December Solstice. Thus, the ambipolar diffusion is inhibited/promoted during June/December Solstice that would result in an earlier/latest onset of northern EIA crest, which is inconsistent with the observed semiannual cycle (Figure 6a).

**Figure 7.** Effective magnetic meridional winds (positive northward). Avergaed winds centered on the days of (**a**,**b**) March Equinox, (**c**,**d**) June Solstice, (**e**,**f**) September Equinoxes, and (**g**,**h**) December Solstice, at Peruvian (left column) and Indian sector (right column). The dash line marks the dip equator, the two shaded bars in each plot mark the 'fixed crest' defined in this study at dip latitude of 10◦~15◦ S/N.

In the Indian sector, the locations at both the northern and southern crests exhibit the strongest northward wind during December Solstice and the strongest southward wind during June Solstice. Hence, the ambipolar diffusion is severely retarded/promoted near southern/northern crest during December Solstice, and vice versa for June Solstice, resulting in an annual cycle on the onset of EIA, which is consistent with the observations (Figure 6b). We conclude that, under the assumption that the meridional wind only takes direct effects on the ambipolar diffusion, the wind configuration simulated by the TIEGCM would result in the typical annual cycle (winter crest priority) of the EIA evolution in both Peruvian and Indian sectors.

Note that the classical scenarios of the transequatorial wind effect on EIA have been challenged in both simulation [12,13] and observations [14]. Abdu [12] showed that the northward thermospheric wind would drive both the southern and northern EIA crest to move southward (upwind direction) in simulations, while the height of the F region is lifted/lowered near the northern/southern crest. Liu et al. [14] found an abnormal annual variation of EIA in the American sector; that is, the northern EIA crest resides at the highest/lowest latitude during local summer/winter when the southward/northward winds prevail, consistent with upwind seasonal movement of EIA crest proposed by Abdu [12], but contradicting the classical scenarios of the transequatorial wind effect.

So far, the physical mechanism of the tilt (in upwind direction) development of EIA has not been addressed either in the aforementioned simulation studies [12] or observational study [13]. Nevertheless, the mechanical effects of neutral wind would push the plasma not only equatorward/poleward but also upward/downward. The uplifting of the ionosphere leaves a depleted bottom side which encourages more ionizations; hence, the TEC should increase, and vice versa. In other words, though the equatorward wind retards the ambipolar diffusion, the accumulation of TEC near the EIA crest can still be accelerated by the uplifting of the ionosphere. In the same manner, the poleward wind that lowers the ionosphere would retard the speed of the growth of TEC near the EIA crest. Near the northern EIA crest at the Peruvian sector, the northward winds only occur at December Solstice (Figure 7h) when the F region resides at lower altitudes [41]. Thus, during the development of EIA, the TEC growth of the northern crest might be retarded, resulting in a delayed onset.

We emphasized that the above-proposed opposite neutral wind effects on the EIA evolution would depend on the longitude (magnetic declination) seasons, and possibly the solar activities. Hence, it is necessary to extend this study to a longer interval and more longitudes to further validate the proposed scenario.

#### **6. Conclusions and Future Work Remarks**

The study adopted the IGS TEC map and IRI-2016 to investigate the seasonal, interhemispheric variations on the time evolution (onset, first emergence, and peak) of EIA at Peruvian and Indian sectors. Major findings are listed below:


An interesting question remains: Why the F region height effect seems invalid in the Indian sector where the development of EIA showed typical winter crest priority. A possible explanation is that this competition varies at different longitudes/seasons/solar activity levels. In the future, by including the ionosonde data, we intend to extend this study to more longitude sectors and longer time intervals to further address the competition between the modulation of ambipolar diffusion and F region height variations.

**Author Contributions:** Conceptualization, X.W., C.X. and J.Z.; methodology, X.W. and J.Z.; software, X.W.; validation, X.W., H.W., C.X. and J.Z.; formal analysis, X.W.; investigation, X.W.; resources, J.C. and J.Z.; data curation, X.W.; writing—original draft preparation, X.W.; writing—review and editing, X.W., J.Z., C.X., H.W., Y.L., Q.L. and J.K.; visualization, X.W.; supervision, J.Z. and J.C.; project administration, X.W., J.Z., J.C. and J.K.; funding acquisition, X.W., J.Z., J.C. and J.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Strategic Priority Research Program of the Chinese Academy of Sciences, grant number: XDB41000000; the National Natural Science Foundation of China, grant number: 41804150, 42104169, 42104147, 41804153, 41431073, 41521063, and 41674153; Guangdong Basic and Applied Basic Research Foundation, grant number: 2021A1515011216, 2020A1515110242; China Postdoctoral Science Foundation grant number: 2020M6830265, the Fundamental Research Funds for the Central Universities, Sun Yat-sen University, grant number: 2021qntd29; the Natural Science Fundation of Jiangsu Province, grant number: BK20180445; the Joint Open Fund of Mengcheng National Geophysical Observatory, grant number: MENGO-202018; the Opening Funding of the Chinese Academy of Sciences dedicated for the Chinese Meridian Project; the Open Research Project of Large Research Infrastructures of CAS—"Study on the interaction between low/mid-latitude atmosphere and ionosphere based on the Chinese Meridian Project".

**Data Availability Statement:** The International Global Navigation Satellite Systems Service (IGS) provide the GPS TEC map; data are available on the Coordinated Data Analysis Web (CDAWeb): Ftp://Cdaweb.Gsfc.Nasa.Gov/Pub/Data/Gps/Tec15min\_Is/. The Kp index can be accessed on http://wdc.kugi.kyoto-u.ac.jp/kp/index.html#LIST.

**Acknowledgments:** Geomagnetic field measurements were collected at Fuquene, Huancayo, Tirunelveli, and Alibag. The author thanks T. A. Siddiqui for providing the geomagnetic field data from Huancayo and Fuquene; Virendra Yadav for providing the geomagnetic field data from Tirunelveli and Alibag. We thank the Colombian Instituto Geográfico Agustin Codazzi, the Instituto Geofisico del Peru, and the Indian Institute of Geomagnetism for supporting geomagnetic observatory operations. We also thank the World Data Center for Geomagnetism at Kyoto for providing the Kp index product.

**Conflicts of Interest:** The authors declare no conflict of interest.

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