Variations of the peak positions in the longitudinal profile of noon-time equatorial electrojet

In this study, the seasonal variations of the EEJ longitudinal profiles were examined based on the full CHAMP satellite magnetic measurements from 2001 to 2010. A total of 7537 satellite noon-time passes across the magnetic dip-equator were analyzed. On the average, the EEJ exhibits the wave-four longitudinal pattern with four maxima located, respectively, around 170° W, 80° W, 10° W and 100° E longitudes. However, a detailed analysis of the monthly averages yielded the classification of the longitudinal profiles in two types. Profiles with three main maxima located, respectively, around 150° W, 0° and 120° E, were observed in December solstice (D) of the Lloyd seasons. In addition, a secondary maximum observed near 90° W in November, December and January, reinforces from March to October to establish the wave-four patterns of the EEJ longitudinal variation. These wave-four patterns were divided into two groups: a group of transition which includes equinox months March, April and October and May in the June solstice; and another group of well-established wave-four pattern which covers June, July, August of the June solstice and the month of September in September equinox. For the first time, the motions in the course of seasons of various maxima of the EEJ noon-time longitudinal profiles have been clearly highlighted.


Introduction
The equatorial electrojet (EEJ) is a daytime ionospheric current that flows eastward along the magnetic equator at about 105 km altitude (Chapman 1951). Most of the EEJ characteristics like day-to-day, seasonal, latitudinal, longitudinal variability and the counter-electrojet phenomenon have been described through its magnetic effect recorded on ground as well as onboard polar orbiting satellites (Cain and Sweeney 1973;Gouin 1967;Gurubaran 2002;Langel et al. 1993). During the International Equatorial Electrojet Year (IEEY), simultaneous measurements were carried out in the longitude sectors of Asia, Africa and South America (Amory-Mazaudier et al. 1993;Arora et al. 1993). Magnetic data recorded along station chains across the dip-equator resulted in important advances for understanding the EEJ characteristics. Based on this dataset, Doumouya et al. (2003) established the longitudinal profile of EEJ, which was found to be inversely correlated with the geomagnetic main field intensity. However, Doumouya and Cohen (2004) noticed a relative amplified EEJ intensity in the longitude sector around 100° E when they included the magnetic data from Baclieu (105.44° E, in Vietnam. This observation was confirmed by the CHAllenging Minisatellite Payload (CHAMP) satellite magnetic data (Doumouya and Cohen 2004). The geomagnetic field measurements operated onboard Satelite de Applicaciones Cientificas-C (SAC-C), Oersted and CHAMP satellites resulted in improved descriptions of the EEJ longitudinal variation (Alken and Maus 2007;Doumouya and Cohen 2004;Jadhav et al. 2002). Thus, the EEJ longitudinal profiles are now known to exhibit up to three or four maxima located approximately around − 90° E, 0°, Open Access *Correspondence: zietuo@hotmail.fr 1 Laboratoire de Physique de l' Atmosphère et de Mécanique des fluides, UFR-SSMT, Université Felix Houphouet Boigny, Abidjan, Côte d'Ivoire Full list of author information is available at the end of the article Tuo et al. Earth, Planets and Space (2020) 72:174 100° E and 180° E (Alken and Maus 2007;Doumbia et al. 2007;Doumbia and Grodji 2016;Doumouya and Cohen 2004;Jadhav et al. 2002). According to Alken and Maus (2007), Doumbia et al (2007) and Doumbia and Grodji (2016), these longitudinal structures of the EEJ can be subject of seasonal variations. Indeed, it was shown that the EEJ longitude profiles with three maxima are observed during the December solstice, while the profiles with four maxima are observed during equinoxes and the June solstice. However, the transitions between the EEJ longitudinal patterns of three maxima and those of four maxima and the background physical processes are not well understood.
In the present study, the seasonal variations of the EEJ longitudinal structures are examined. In that purpose the longitudinal variation of the EEJ is revisited from the full CHAMP satellite magnetic data recorded from 2001 to 2010. In particular, the progressive changes from three maxima to four maxima, and vice versa, of the EEJ longitude patterns in the course of the year is analyzed on the basis of the average monthly longitude profiles. The motions of the upper mentioned maxima according to the seasons are also examined.

Data
The present work is based on CHAMP satellite OVerhauser Magnetometer (OVM) data that were recorded from 2001 to 2010 (Rother and Michaelis 2019) (https ://isdc-old.gfz-potsd am.de/index .php). CHAMP was a near-polar orbiting satellite that was launched on July 15, 2000 onto a low altitude (about 460 km) circular orbit, with an inclination of 87.3° and orbital period of 93.55 min (Alken and Maus 2007;Lühr et al. 2004;Lühr and Maus 2006). The satellite was deorbited on September 19, 2010. One of the advantages of CHAMP orbit is that it provides a good latitudinal and local time coverage allowing accurate studies of the ionospheric current systems.
The geomagnetic force F was recorded with the OVM magnetometer at a sampling rate of 1 s, in the range from 18,000 to 65,000 nT, with 10 pT resolution and noise level of 50 pT. The absolute error is estimated at about 0.5 nT. The magnetic data recorded on board CHAMP satellites are composed of the sum of the geomagnetic main field, the crustal anomaly fields, the magnetic effects of ionospheric and magnetospheric currents and their induced effects in the ground. Thus, any study of one of these sources requires its contribution to be isolated from that of the other magnetic sources. The purpose of the present work is to study the EEJ by analyzing its magnetic effect, extracted from the total observed magnetic force F.

Data processing
The geomagnetic main field that represents about 99% of the total measured field, is estimated and removed by using the International Geomagnetic Reference Field (IGRF-12) model (Thébault et al. 2015). The remaining residual field, shown in Fig. 1, is designated as total residuals (�F ) . ( F ) is expected to include the crustal fields and the magnetic effects of ionospheric and magnetospheric currents. The EEJ magnetic effect is confined to a relative narrow latitude band and produces a V-shape depression at the magnetic dip-equator. This effect seems to overlap a long-wavelength background signal, from which it will be isolated. The approach consists of polynomial fitting of the background signal (Doumouya and Cohen 2004).
For this study, magnetically quiet time data are selected according to the values of the K p index that is set to be smaller than 3 + . Noon-time data for satellite passes between 11 and 13 LT are considered to estimate the EEJ strength ( F eej ). Table 1 depicts the numbers of satellite noon-time passes selected per month. Figure 2 shows the monthly distribution of satellite passes per year. A total number of 7537 noon-time satellite passes have been selected.

Extracting the EEJ magnetic effect by using a polynomial fitting
The magnetic effect of the EEJ was extracted from the total magnetic residuals by subtracting the background signal (Fig. 3). The background signal was fitted with a 12-degree polynomial. This degree was chosen by trialand-error testing from 6° to 30° (Doumbia and Grodji Fig. 1 The total residuals ( F) isolated from the CHAMP satellite observed total force ( F ) by subtracting the geomagnetic main field estimated with IGRF model 2016; Doumouya and Cohen 2004). The solid line represents the total residuals and the dashed line represents the polynomial fitting of the background signal. The right panel of Fig. 3 shows the latitudinal profiles of the EEJ magnetic effect extracted for a CHAMP satellite pass across the dip-equator at 1° E on 17 September 2001. The EEJ magnetic effect exhibits a sharp depression with a minimum at the dip-equator. This depression is flanked by two maxima that are located on the average at about ± 7 • on either side of the magnetic dip-equator. The difference in amplitudes for the same day may be due to the longitudinal dependence of the EEJ. For different days, this difference also includes the day-to-day variability of the EEJ. (Doumouya and Cohen 2004;Thomas et al. 2017).

Correction of satellite altitude effects on the EEJ strength
The CHAMP satellite mission lasted about 10 years from 2000 to 2010. This duration is close to the length of one solar cycle. During this period, the satellite orbit continuously drifted from the initial altitude of 460 km to 250 km at the end of the mission (Fig. 4). The decreasing altitude of CHAMP gradually moved it closer to the EEJ. As a consequence, the observed EEJ effects may have gradually where F 400 is the EEJ strength at h 400 = 400 km, F sat is the EEJ strength at a given altitude h sat , h sat is the distance between the satellite and the EEJ altitude. h 400 is the distance between the normalized altitude and the EEJ altitude. (1)

Longitudinal variation of EEJ
The EEJ strength ( F eej ) is estimated from the latitudinal profiles by the difference between the minimum at the dip-equator and the average of the maxima on either side for each satellite pass across the magnetic equator. Figure 5 depicts Figure 6 shows the monthly averages of the EEJ longitudinal variations. The blue and green curves represent, respectively, the first quartile (25% of data) and third quartile (75% of data). The solid red line and the smoothed black line are the same as Fig. 5. The patterns of the EEJ longitudinal profiles evolve from month to month. These patterns can be divided into two main kinds. Profiles with three maxima are observed from November to February, while those with four maxima, referred to as "wave-four" pattern are observed from March to October. The patterns with three maxima are mainly observed during the December solstice, while the wave-four patterns include June solstice, March and September equinoxes. However, the patterns observed from March to May and in October seem to be transition phases between the three maxima and wave-four patterns. According to these remarks, the longitudinal profiles of the EEJ are classified into three categories in Fig. 7. In the top panel, the EEJ longitudinal profiles with three maxima are shown. These profiles exhibit three main maxima that are located, respectively, from left to right, near − 150° E, 0° E and 120° E, which are referred to as L1, L3 and L5. However, on the west side, one can observe a secondary maximum near − 90° E (L2) in November and December, which is slightly visible in January, but totally vanished in February. On the east side, another secondary maximum can be observed near 70° E (L4) in January and February. In the middle panel, in addition to the three main maxima observed above, the west side secondary maximum (L2) stabilizes and gets matured at about − 80° E, while the east side secondary maximum (L4) is slightly visible in March and April, but totally vanished in May and it does not appear in October. It is as if this secondary maximum (L4) and the east side main maximum (L5) combine to form a single maximum around 120° E. This process completes the wave-four pattern establishment as depicted in the bottom panel. In summary, we have two west side maxima around about − 150° E, − 80° E, one maximum around 0° E and another maximum around 100° E. Figure 8 shows the motions of the maxima in longitude in the course over a year. It is to be noticed that the locations L1, L3 and L5 of the three main maxima move, respectively, over 50°, 20° and 60° longitudes in the course of the year. They oscillate, respectively, around the meridians − 160° E, − 10° E and 120° E. L1 and L5 move in the same phase from the east sides to the west side of the − 160° E and 120° E meridians, respectively, while L3 moves from the west side to the east side of the − 10° E meridian, in opposite phase with respect to L1 and L5. However, during the transition phase, while L1 seems to stabilize at − 160° E, L5 moves across the 120° E meridian westward from March to May and eastward in October. L2 is almost stable at − 80° E meridian in the transition phase and moving very little to east during the rest of time. L4 appears on January at 70° E and move to 55° E on February before combining with L5 during March and April.

Discussion and conclusion
In this study, the seasonal variations of the EEJ longitudinal profiles were examined based on CHAMP satellite magnetic measurements from 2001 to 2010. 7537 satellite noon-time passes across the magnetic dipequator were analyzed. The EEJ strength was estimated from the latitudinal profiles of its magnetic signatures, with dense coverage of all longitude sectors. Based on these results, the EEJ longitudinal variation was revisited. On the average, the EEJ exhibits the wave-four longitudinal pattern with four maxima located, respectively, around − 170° E, − 80° E, − 10° E and 100° E longitudes. This confirms the results obtained in previous studies (Alken and Maus 2007;Doumbia et al. 2007;Doumbia and Grodji 2016;Doumouya and Cohen 2004;Jadhav et al. 2002;Lühr et al. 2004). However, a detailed analysis of the monthly averages yielded the classification of the longitudinal profiles in two types. Profiles with three main maxima located, respectively, around − 150° E, 0° E and 120° E, were observed in November, December, January and February. In addition, a secondary maximum observed near − 90° E started in November, December and slightly in January, to finally establish the wave-four patterns from March to October. It is to be noticed that the period of wave-four patterns includes the months of equinoxes (E) and June solstice (J) of Lloyd seasons. According to our observations, this period was divided into a period of transition (March, April, May and October) and a period of well-established wave-four structure (June, July, August and September). The period of transition includes two phases. The first phase consists of transition from three to four maxima in March, April and May, and the second phase consists of a short transition from four to three maxima during October. In summary, the patterns the EEJ longitudinal variation have been divided into three groups of 4 months each: (i) the group of three maxima, (ii) the group of transition and (iii) the The locations of the three main maxima of the EEJ longitudinal profiles identified from West to East, respectively, as L1, L3 and L5, have been found to clearly oscillate around average positions in longitude. Thus, L1 and L5 move from the east sides to the west side of, respectively, − 160° E and 120° E meridians, while L3 moves from the west side to the east side of − 10° E meridian. During the transition phase, L1 stabilizes at − 160° E and L5 moves westward across 120° E meridian from March to May and eastward in October. In the transition phase, L2 almost stabilizes at − 80° E meridian, moving very little to east during the rest of time. Another secondary maximum (L4) was also observed near 70° E, but only in January and February.
The results above clearly demonstrate the dependence of the EEJ longitudinal structures on season and confirm the finding of previous studies by Alken and Maus (2007), Doumbia et al (2007) and Doumbia and Grodji (2016). Indeed, those studies have shown that the EEJ longitudinal profiles with three maxima were observed during the December solstice, while the profiles with four maxima were observed during equinoxes and the June solstice of Lloyd seasons. However, results are slightly different for the transition phases and well-established wave-four structures, which are instead inter-seasonal. In addition, it is the first time that the motions of various maxima of the EEJ longitudinal structures have been clearly highlighted. The original features of the present work can be summarized as: 1. The full CHAMP satellite 10-year magnetic data base was used, which statistically better supports the kind of detailed analysis conducted in this manuscript. 2. Previous works (Alken and Maus 2007;Doumbia et al. 2007;Doumbia and Grodji 2016;Doumouya and Cohen 2004;Jadhav et al. 2002;Lühr et al. 2004) have only made broad remarks on the EEJ longitudinal variations and attributed different morphologies to December solstice (three maxima) and four maxima for the other seasons. In the present study, these features of the EEJ longitude profiles are captured more finely on a monthly basis. 3. The present study yielded for the first time a special classification of the EEJ longitude profiles in three main categories as shown in this manuscript. In addition, we have shown how transitions are made from one structure to the other. 4. Our classification shows that most of the features of the EEJ longitude profiles are inter-seasonal, instead of coinciding with a single particular season. 5. The motions in longitudes of different maxima of the EEJ longitude profiles in course of the year were examined the first time. 6. These new features open the way to better perspectives in the analysis of the physical processes that govern the EEJ longitudinal variation, especially the roles of thermospheric winds and their seasonal behaviors in this longitudinal variation Immel et al. 2006;Lühr et al. 2008).
The structures and seasonal dependence of the EEJ longitudinal variation have been considered to be linked with the wave structures of the thermospheric winds (Doumbia et al. 2007;Doumbia and Grodji 2016;Immel et al. 2006;Kil et al. 2007;Lühr et al. 2008;Lühr and Maus 2006). In the ionosphere, winds and electric fields are known to be modulated by the tidal excitations that propagate upward from lower atmospheric layers. Doumbia et al. (2007) simulated such tidal excitations for migrating tides diurnal and semi-diurnal components based on the National Center for Atmospheric Research Thermosphere-Ionosphere Electrodynamics General Circulation Model (NCAR TIEGCM). Furthermore, the wave structures of the thermospheric winds described in many studies (Häusler et al. 2007;Häusler and Lühr 2009;Immel et al. 2006), have been found to exhibit similar longitudinal variations. In a companion paper, the influence of thermospheric winds will be examined with combined migrating and non-migrating tidal excitations, for a better understanding of the background physical processes involved in the transition between the various EEJ longitudinal patterns.