Ionospheric single crest events at different altitudes and activity levels observed by Swarm constellation

The current work makes use of eight years of electron density data observed by the Swarm constellation to study the characteristics of the equatorial ionospheric single crest phenomenon recorded at the altitudes of these satellites. The features of single crests have been investigated at different altitudes and geomagnetic activity levels. Results showed that the occurrence rate of a single crest was not significantly different between the lower and higher satellite altitudes. The relationship between the occurrence of single crests and the Kp index has shown a dramatic enhancement at high level activities. In addition, the occurrence of single crest has dramatically enhanced with the strength of both the interplanetary electric field and the north-south interplanetary magnetic field. Also, irrespective of season, the South Atlantic Anomaly (SAA) region has always shown a large occurrence of single crest events compared to other longitudes. In addition, the occurrence of the events is always larger during equinoxes than during summer and winter solstices. The significant occurrence of single crest recorded during both equinoxes and the maximum phase of the solar cycle (F10.7 index) and those observed over the SSA region, suggests an alignment between the strength of electron density and the occurrence rate of single crests.


Introduction
The dayside equatorial ionospheric structure is primarily controlled by a common phenomenon known as the equatorial fountain effect. Its main driver is the large-scale eastward electric field which drift plasma in the upward direction according to (E × B) force direction Yeh et al. 2001;Kelley et al. 1979). This common phenomenon formed via this field structure is denoted by the Equatorial Ionospheric Anomaly (EIA). It is characterized by double crests of the electron density locate within ±15°a part from the geomagnetic equator and trough at the geomagnetic equator (Appleton 1946;Moffet and Hanson 1965;Zhao et al. 2009). Significant attempts have been made to investigate its behavior and features since it was reported by Appleton (1946). These efforts investigated its diurnal and seasonal variations and solar cycle variability using the Total Electron Content (TEC) measurements from ground and satellite data and modelled data (Yeh et al. 2001).
Its seasonal variability showed that the most developed EIA appears larger and earlier in winter than in summer through using radio transmitted signals (Huang and Cheng 1996). They also reported that crests locate in latitudinal region close to the magnetic equator in summer solstice than other seasons. Liu et al. (2001) set a model that explains the evolution and shifting of both hemispheric equatorial TECs toward and away from the equator. Milward model had schematically explained by Tsai et al. (2001) in terms of the effect of the joule heating which drives trans-equatorial neutral wind and the auroral-equator wind. Tsai et al. (2001) reported that the auroral heating forces the two EIA crests to move significantly equatorward in winter and slightly poleward in summer and autumn. Xiong et al. (2013) showed that, on a global scale, the summer EIA crest locates farther from the dip equator than other seasons. Yeh et al. (2001) reported that, after the formation of the crest around 09:00 local time, it moves toward the pole with a speed of 1°/hour for the next 2 hours and remains at this latitude until the early afternoon; subsequently it begins to weaken while receding back towards the geomagnetic equator at a speed of 0.5°/hour. Liu et al. (2007) reported that, However, the EIA crest's electron density growth rate is larger than that of the trough, but both grow linearly from solar minimum to solar maximum. Stolle et al. (2008) found that the typical response time of the EIA to variations in the zonal electric field is approximately 2 hours through studying the correlation between the eastward electric field and the EIA in the Peruvian sector.
The north-south asymmetry has paid the attention of several authors in the last decade. It has been reported that the northern hemispheric winter crest is generally more significant on a global scale than the southern hemispheric summer crest. Yonezawa (1959) reported that because the sun is closer to the earth in winter, the amount of EUV reaching the earth is 6% greater in December than in March. Therefore, the developed winter EIA crest is always more prominent than the summer EIA crest. Huang and Cheng (1996), Lin et al. (2007), Zhao et al. (2009) revealed that, the EIA crest is the largest within the March equinox and the lowest within the June solstice. The analysis of the north-south asymmetry by Huang et al. (2013) showed that the northern hemispheric crest is generally more significant than the southern hemisphere crest especially during December solstices. Several authors attributed this north-south EIA asymmetry to the action of the neutral wind (Walker et al. 1991;Lin et al. 2007;Rishbeth 1972;Xiong et al. 2013). This wind suppresses summer hemispheric crest formation and enhances the crest in the winter hemisphere crest formation before noontime. This process is being reversed in the afternoon region because of the summer hemispheric region's rapid cooling, which reverses the wind direction (Rishbeth 1972;Xiong et al. 2013). Results from CHAMP and SAMI2 model at the altitude of CHAMP satellite (400 km) showed that, the meridional wind plays a significant role in driving the EIA crest asymmetry (Xiong et al. 2013). At higher altitudes (e.g., GRACE satellite), Xiong et al. (2013) showed that the noon time EIA inter-hemispheric asymmetry no longer exists because there is no reversal from winter to summer hemisphere.
The altitude above the sea surface where the electron density reaches a maximum is defined as the height maximum of the F2 layer (hmF2). So, the maximum height of the F2 (hmF2) layer is an index to the altitude where the electron density is maximum (Richard 2001). Wichaipanich et al. (2013) found that, the predicted International Reference Ionospheric (IRI) hmF2 data approximates the observed hmF2 data during the daytime. They also showed that it is underestimated at the magnetic equator and overestimated at the two-night crests. Authors have showed that the hourly median hmF2 did not exceed 400 km altitude and its hourly mean dayside hmF2 decreases to less than 250 km compared to the nightside which reaches 300 km (Mohammed 2015). At solar maximum, the electron density below the hmF2 was greater in September than in March, while above it, the density was more significant in March (Balan et al. 1997(Balan et al. , 2000Richard 2001). The summer hmF2 has reported to be located at lower altitudes than winter hmF2 (Richard 2001;Wichaipanich et al. 2013). Also, the hmF2 layer rises from 300 km altitude in the morning to 500 km during the noon time over the dip equator, and reaches its maximum altitudes at the pre-reversal dusk period (Lee and Reinisch 2006). The low latitude hmF2 (at about ±15°) during the morning hours appears at about 300 and 400 km in both winter and summer hemispheres, respectively (Xiong et al. 2013). The midlatitude hmF2 has not only showed solar activity dependence, but it also, increases from 230 km during the day to 310 km at night (Richard 2001). Also, magnetic activity has been reported to affect the hmF2. It lifts the plasma into higher altitudes due to an enhanced electric field. Liu et al. (2007) suggested that the cause of the depletion post-sunset equatorial trough at a high solar activity at CHAMP altitude may be located below the hmF2.
It's clearly shown that intensive studies discussed the morphological features of the EIA phenomenon such as the EIA double crest asymmetry, its hmF2 altitude and the shift motion of the crest . . . etc, but few studies concerned with the EIA single crest formation. Even these few studies which discussed the single crest phenomenon did not report the features of a single ionospheric crest at different altitudes using satellite data. The first statistical study of single crests was presented by Huang et al. (2014) using the total electron content at 120°E longitudes within a quiet geomagnetic activities. Their findings revealed that the single crest occurs primarily on days with low solar activity. Fathy and Ghamry (2017) studied the features of single crest using Swarm-A satellite data at different seasons and local times. They found that the single crest displaces its location away from the equator to the northern hemisphere in summer and in the winter to the southern hemisphere. In this paper, we study the morphological features of the single crest phenomenon from the in-situ electron density measurements of Swarm A, C and B constellation in order to find the altitudinal profile of the single crest. The current work is structured as follow: Sect. 1, explains the data sets and the algorithm we have used to select the single crest events. Section 2 presents the results of the local time statistical analysis, geographic and latitudinal distribution of events, seasonal variation, and finally the solar and magnetic activity dependence. In Sect. 3, we give the summary and conclusion.

Data set and selection criterion
The ionospheric electron density data were obtained from the Swarm mission. The Swarm constellation is three satellites (Swam A, B, and C) orbiting the Earth's ionosphere in a polar orbit. Swarm A and C are flying at 470 km altitudes with an inclination angle of 87.4°, while Swarm B is flying at higher altitudes (520 km) with an inclination angle of 86.8°. Both Swarm A and Swarm C are separated by about 150 km in longitude. The Swarm three satellites have identical datasets, and the data observed by these satellites are processed and archived by European Space Agency (ESA). Once the electron density data observed by the Langmuir probe is corrected, it has archived and released to the public as level 1b data. A detailed description of the content of the data file can be found on the ESA server (https://earth.esa.int/eogateway/missions/swarm/data [access date: December 11, 2022]). In the current work, we used electron density data observed from January 2014 to December 2021. So, the current work is different from previously published (Fathy and Ghamry 2017), as all local times during all seasons and longitudes have been covered by the Swarm mission. Because of the long period of observation (eight years), it is worth studying a single crest according to different activity levels (low and high) using OMNIWeb data (https://omniweb.gsfc.nasa.gov/form/dx1.html [access date: December 11, 2022]). We consider the Interplanetary Magnetic Field (IMF) and the Interplanetary Electric Field (IEF) data from the solar wind data and the solar flux index and the Kp magnetic index as main parameters to study the relationship between the features of single crests and the geomagnetic activities.

Single crest detection algorithm
The detection algorithm we have implemented to the electron density for detecting single crest events along the path of the satellite could be summarized in the following steps: 1. The electron density data within ±55°latitude has been selected for each equatorial crossing. 2. Subsequently, we fitted it to a cubic spline function with a piecewise constant equal to 4°latitudes. This piecewise constant corresponds to 68 (∼4 × 17 s) observational data points. 3. Then, peaks in the fitted data have been counted. Because of multiple peaks appear at low electron density, especially at midlatitudes, only peaks exceeding a threshold value (1.2 × 10 5 cm −3 ) have been chosen as candidate crests. If the number of candidate peaks within ±55°latitudes equals one, the event is selected as a single crest. This background limit (1.2 × 10 5 cm −3 ) has been set according to manipulation processes with data.
A typical example of single crest events according to our algorithm is shown in Fig. 1. The upper row of Fig. 1 shows a one-day time profile of the electron density data observed on October 1, 2014 by Swarm A satellite. The lower row shows an example of double and single crests in left and right panels respectively. The red curve represents the cubic spline fitting of the observed data binned to 4°latitudes. The big dot in magenta color corresponds to the location of the magnetic equator, while the circle in the cyan color corresponds to the single crest event identified by our algorithm.. The universal time instant, latitude, longitude and electron density for every peak are recorded. According to these criteria, a list of 18748 single crest events is tabulated for the three Swarm satellites. The ratio between these number of events to the total number of equatorial paths (272357), used in the current study, is approximately 7%.

Results
Our main goal is to study the morphology and the occurrence of EIA single crest phenomena recorded within the period (2014)(2015)(2016)(2017)(2018)(2019)(2020)(2021). In this section, we introduce observational data obtained from the three Swarm satellites. First, we present a statistical analysis of the data obtained from the three Swarm satellites to investigate the variations of a single crest with respect to latitude, longitude, season, and local time. Second, we study the influence of the geomagnetic activity on the occurrence of the single crest phenomena.

The EIA single crest local time dependence
The number of single crest events detected every two hours is presented in Fig. 2a. It shows that the maximum number of events are observed at two different periods; the first period from 08:00 to 12:00 LT, while the second period from 17:00 to 19:00 LT. The lowest number of single crests events is observed within the early morning local time (06:00 LT) and before midnight (22:00 LT). Figure 2b introduces the variation in the electron density concerning the local time of single crests during summer, winter, autumn, and spring seasons in red, blue, black, and green circled lines, respectively. The median value of the electron density marked in the magenta solid color shows a gradual increase after 8:00 LT until the sunset (18:00 LT) and then it begins to decrease till the predawn hours. It also has two maxima of the electron density; the first around the 12:00 LT and the other around the 16:00 LT, which are coincide with the maxima of the number of events presented in Fig. 2a. Figure 3 shows the latitudinal distribution of single crest events during different seasons. The dashed line at 0°magnetic latitude is the magnetic dip equator which is defined as the line at which the inclination angle is zero. The dip equator has been calculated for the International Geomagnetic Reference Field (IGRF). Fig. 3 shows that, the majority of single crest events observed within the day time (08:00 to 18:00 LT) and locate closer to the magnetic equator (±15°). On the other hand, events recorded from the pre-midnight to

Latitudinal and seasonal variations of EIA single crest
This section presents the distribution of the EIA single crest events recorded by the three Swarm satellites A, B, and C in regard to its location from the magnetic equator and their observational season at different local times. Figure 4 shows a statistical distribution of the single crests with respect to the magnetic latitudes. The upper row is a histogram of the number of the single crests versus magnetic latitudes. It clearly shows that, the number of crests observed by the three satellites in the northern hemisphere is larger than those observed in the southern hemisphere. The maximum number of single crests are located within a latitudinal region varies from 20°N to 8°S. The middle and bottom rows of Fig. 4 show the spatial location of single crests by illustrating the latitudinal magnetic distribution of crests with respect to the geographic longitude. The green, black, blue, and red colors correspond to the spring, autumn, winter, and summer seasons. Irrespective of the type of satellite, the remarkable features of the spatial variations are summarized in the following points: 1. Most single crest events are concentrated around ±30°m agnetic latitudes at all longitudinal sectors. During equinoxes, the number of single crest events locates in the northern hemisphere seem to be larger than those observed in the southern hemisphere.
For more deep analysis, the density amplitude of the single crest events observed during summer, winter and equinoxes have been investigated as shown in Fig. 5. It presents the density of single crest events with respect to latitudes at different local times for Swarm A, B and C satellites. Black, blue, green, and red colors corresponding to events recorded during dusk, night, dawn and day times respectively. It is clearly noticed that, the electron density is always larger during equinoxes in comparison with other seasons. During summer months, not only the density is the minimum, but also, the majority of events are shifted into the northern hemisphere. The dusk and noon time events are always having a large density irrespective of seasons. On the other hand, the dawn and night time events are characterized by low density in comparison with other local time events, in addition both are spread over large latitudinal regions.
The Upper row of Fig. 6 shows the location of single crest events with respect to months observed by Swarm A, B and C satellites from left to right column respectively. The lower row of Fig. 5 illustrates the monthly median latitudinal location of single crests. The black, blue, green and red colors in Fig. 6 corresponding to dusk, night, dawn, and day time events respectively. The upper row shows that, irrespective of month, events observed during noon and dusk times are located closer to the magnetic equator, while dawn and night time events are spread over large latitudes. However, the noon and dusk time events seem to be centered around the equator, the monthly median location shows that; the summer single crest events are relatively located farther from the equator in the northern hemisphere. On the other hand, the majority of single crests during the winter are located northern the magnetic equator. In addition, the monthly median magnetic latitudinal location of night and dawn time events are located much farther from the equator than the day and dusk time events. A general view that could be summarized from Fig. 6 is that irrespective of local time, the summer single crest events are observed in the southern hemisphere, while the winter events are observed in the northern hemisphere. It means irrespective of the satellite type, many crest Fig. 6 The location of each single crest event versus months (upper row) and the monthly median magnetic location of single crests (lower row). Columns from left to right corresponding to Swarm A, B and C Swarm satellites respectively. The Black, blue, green, and red color corresponding to dusk, night, dawn and day time respectively events observed in the southern hemisphere during summer months seem to be shifted to the northern hemisphere during winter months Figure 7a-b show the monthly average electron density and the monthly number of single crest events, respectively. Events observed by Swarm A, B, and C are marked in Red, Blue and Cyan dotted lines, respectively. Figure 7a shows that the electron density for the three satellites is always larger during equinoxes than during solstices. Summer months exhibits the lowest electron density in comparison with other seasons. Figure 7b shows that the number of events observed by the three satellites is the largest during the spring and autumn months and the lowest during the summer and winter solstices. However, the electron density observed by the three satellites is larger during both equinoxes than in solstices. It is generally smaller at the altitude of Swarm B than Swarm A and C. Figure 8 represents the number of EIA single crest events observed within a binned 5°× 10°spatial region during the daytime hours [09:00-15:00 LT]. The map was created by calculating the number of EIA single crest events observed within each binned area (5°× 10°) latitude and longitude, as indicated by the color bar indices on the right side of Fig. 8. The EIA single crest events distribution during summer, winter, and equinoxes seasons corresponds to rows from top to bottom. Columns from left to right correspond to Events observed by Swarm A, B, and C satellites, respectively. The most remarkable feature noted from this figure is that the EIA single events are located within ±20°of the  The global distribution day time (09:00:15:00) of single crest events observed by Swarm A, B and C from left to right column during summer, winter and equinoxes from top to bottom rows respectively. The color bar index represents the number of events within binned spatial area of (5°× 10°) latitude longitudes Fig. 9 The global distribution dusk time (15:00:21:00) of single crest events observed by Swarm A, B and C from left to right column during summer, winter and equinoxes from top to bottom rows respectively. The color bar index represents the number of events within binned spatial area of (5°× 10°) latitude longitudes Figure 9 is similar to Fig. 8, but for dusk time events. No more information can be obtained from Fig. 8 than those presented in Fig. 8 except that, dusk time events are relatively located farther from the equator than the noon time events. Also, single crest events at the altitude of Swarm-B are less than those at the altitude of Swarm-A and C. Irre-spective of season, the probability of single crests seem to be equal, which means there is no preferable seasonal appearance of the single crests during the dusk time hours. Figure 10 illustrates the number of EIA single crest events observed within a binned 5°× 10°spatial region during the night time hours [21:00-03:00 LT]. Rows from top Fig. 10 The global distribution night time (21:00:03:00) single crest events observed by Swarm A, B and C satellites from left to right columns during summer, winter and equinoxes from the top to bottom row respectively. The color bar index represents the number of events within binned spatial area of (5°× 10°) latitude longitudes to bottom correspond to summer, winter, and equinoxes seasons. Columns from left to right correspond to Swarm A, B, and C, respectively. It is clearly shown that, most summer single crest events are located in the northern hemisphere, while most of the observed winter EIA single crest events are located in the southern hemisphere. Also, most summer events are observed in the western longitude (0°→ 90°W), while the winter events are observed in the eastern longitudes (50°→ 150°E). Also, almost EIA single crest events observed during equinoxes are located in the northern hemisphere. Both summer and winter events seem to be occurred at a specific location, while equinoxes events are broadly scattered around the equator. Figure 11 is the same as Fig. 10, but for dawn time [03:00-09:00 LT] events. It shows that most summer single crest events are observed in the northern hemisphere, while the winter events are located in the southern hemisphere. These summer and winter dawn time features of the EIA single crest is similar to that presented earlier for the nighttime events. The dawn time events are broadly distributed around the magnetic equator during the summer and equinoxes season, while during winter, it seems to be fixed within narrow latitudes closer to the magnetic equator. Figure 12 illustrates the local time distribution of the observed single crests with respect to longitudes. Events ob-served at the altitudes of Swarm A, B, and C are presented in left, middle, and right columns, respectively. Rows from top to bottom correspond to the seasonal distribution of observed events during summer, winter, and equinoxes, respectively. Results show that equinoxes exhibit a large number of single crest events while winter is the lowest among all seasons. Regardless, the single crests appear at almost local times; the morning local time is the preferable time for the appearance of single crests. The region of the South Atlantic Anomaly (SAA) shows the highest occurrence rate of single crest events in comparison with the other longitudinal regions. It could be clearly noticed that during the equinoxes in the lower row of Fig. 12 that the majority of observed events appear in the morning times, while those observed during the summer and winter seasons are spread over large local times. The summer events have no preferable local time appearance because it shows patches of large numbers over a wider local time. Also, the post-midnight events observed during Equinoxes are less than those equivalent events observed during other seasons.

Solar and geomagnetic activity variations with EIA single crest
Several studies concerned with the EIA single crest phenomena excluded the effect of geomagnetic activities due Fig. 11 The global distribution dawn time (03:00:09:00) single crest events observed by Swarm A, B and C satellites from left to right columns during summer, winter and equinoxes from the top to bottom row respectively. The color bar index represents the number of events within binned spatial area of (5°× 10°) latitude longitudes to the short period of study which is not suitable for seasonal dependance (Huang et al. 2014;Fathy and Ghamry 2017). The current work considers single crests observed within eight years (2014-2021) electron density data. This long period of observation is adequate enough to study the geomagnetic activity dependence. Therefore, we will introduce the characteristics of single crests with respect to different solar parameters. Figure 13 presents the variations in the Kp geomagnetic activity level/index and the interplanetary magnetic field component (IMF Bz) with the number of EIA single crests. The y-axis represents the normalized number of single crests. The normalization of the number of EIA single crest events has performed by dividing the number of events observed at a certain level by the number of days during which these events are observed. This normalization has been introduced to avoid temporal variations in the number of events. Figure 13a shows that, the probability of EIA single crest events is small and comparable during low activity levels (Kp < 4). During high activity levels (Kp > 4), the probability of single crest occurrence increases dramatically irrespective of the type of satellite.
Also, Fig. 13b shows that, the probability of occurrence increases with increasing the IMF strength, which is strongly correlated to the level of the geomagnetic activity. The variation of the normalized number of EIA single crest events (probability of occurrence) with respect to the solar flux index (F10.7) which is measured in solar flux unit (sfu) and the Interplanetary Electric Field (IEF) are shown in Figs. 14a-b. The probability of occurrence increases gradually with the increasing the solar flux index until 160 (sfu) it dramatically enhanced. However, the normalized number of events enhances with increasing the strength of IEF, the negative IEF variation exhibits a dramatic enhancement in comparison with the positive IEF as shown in Fig. 14b.

Discussion
The data presented in the current work covers the period from 2014 up to 2021. These eight years of electron density data recorded by Swarm A, B and C is adequate to study the geomagnetic activity dependence of the formed equatorial ionospheric single crests at the different altitudes of Swarm satellites. Results from Figs. 1 to 7 showed that, irrespective of season the EIA single crest events are centered around the magnetic equator. In addition, the maximum number is observed during equinoxes while the minimum number is observed during winter and summer solstices. Also, the electron density is larger during equinoxes and smallest during summer months. The majority of events is observed during day and dusk times, while the minorities of events are observed during dawn and night time hours. The average loca- Fig. 12 The local time distribution of the number of single crest events with respect to longitudes. Rows from top to bottom corresponding to Summer, Winter and Equinoxes seasons respectively. Columns from left to right corresponding to Swarm A, B and C satellites respectively. The color bar index represents the number of events within binned spatial area of (5°× 10°) latitude longitudes Besides, Figs. 1 to 7 show that the characteristics of single crest events observed by the three satellites are similar. The only difference is that the occurrence rate of the EIA single crest events at the altitude of Swarm B is lower than those observed at the altitudes of Swarm A and C. This low occurrence of EIA at the altitude of Swarm B could be attributed in terms of the low density at this altitude. As has been stated in the introduction, the hmF2 median value does not exceed 400 km (Mohammed 2015), therefore, the electron density at the altitude of Swarm A and C is expected to be stronger than those at the altitude of Swarm B (520 km). So, these results suggest that the probability of EIA single crest occurrence is proportional to the density of the electron. Figure 6 shows that crests at night (21-03 LT) and dusk (15-21 LT) locate at distances up to about ±20 deg from the equator, while at dawn (03-09 LT) they are closer to the equator, and at day time (09-15 LT) pretty much at the equator. Therefore, we can suggest that the rapid cooling of the summer hemisphere especially during the dusk time inhibits the summer crest, therefore the probability of observing a single crest in the southern hemisphere is large during summer months. This scenario is reversed during the winter months as the crest of the northern hemisphere still developed, subsequently the probability of observing a single crest in the northern hemisphere is larger than those observed in the southern hemisphere. The trans-equatorial neutral wind which blows from the northern to southern hemisphere during summer months may be the cause of the noon time single crest. This wind causes a reduction in the local conductivity on the upwind side (summer hemisphere) where the layer is raised and cause an increase in the local conductivity on the downwind side (winter hemisphere) where the layer is lowered (Hussien et al. 2021). Therefore, the majority of single crests are observed in the southern hemisphere during summer months. Figure 12 shows that the majority of events are observed within the prenoon (08:00-12:00 LT). It has been interpreted by Fathy and Ghamry (2017), who stated that, the EIA is not fully developed because the EIA still in its initial growth phase and the EIA double crest is not yet developed. Therefore, it is observed as single crest at the altitude of Swarm satellite. Figure 12 gave some interpretations about the pre-noon events, but did not discuss single crest events occurred within the noon local where the EIA is fully developed. The deep investigations and the interpretation of single crests during noon times could be investigated in further studies. Results from Fig. 12 showed that, the SAA region has a large probability of single crest occurrence in comparison with other longitudinal regions irrespective of the season. Also, the largest occurrence rate has observed during the equinoxes. The large occurrence during equinoxes is suggested to be to be correlated with the enhanced ionospheric electron density as demonstrated by Figs. 7 and 8. These Figures showed that, the electron density is larger during equinoxes than during summer and winter months. This suggestion is in agreement with Olwendo et al. (2015), Huang et al. (2014), Chen et al. (2011), Galava et al. (2010) who reported EIA asymmetry and also Fathy and Ghamry (2017) who showed that the growth rate of single crest increases during equinoxes. In addition, several researchers stated that, the region of the SAA is exposed to strong contribution of electron from the magnetosphere, therefore the density of electron within this region is always larger in comparison with other longitudes (Nasuddin et al. 2021;Gledhill 1976;Abdu et al. 2005). All these observations confirm our suggestion of EIA single crest occurrence rate is proportional to the ionospheric density of electrons.
The occurrence rate of single crest events showed a gradual increase up to F10.7 equals 160 sfu, that followed by a dramatic enhancement within the range from 160 sfu to 200 sfu. Studies concerned with the solar flux index have shown a high correlation of the F10.7 and the ionospheric density, because the ionospheric flux F10.7 index is an indicator to the intensity of solar radiation impinges the Earth's surface, subsequently, ionizes neutral particles and increases the number density of ionospheric plasma (Olwendo et al. 2015;Huang et al. 2014;Chen et al. 2011;Galava et al. 2010). Figure 15 shows that, the monthly median value of the ionospheric electron density (observed by Swarm-A satellites) marked in red circles is proportional to the strength of the solar flux index F10.7 marked in blue dots. Both decrease together from 2014 until 2019 which is the descending phase of the 24 solar cycle and the minimum of 25 solar cycle.
Therefore, this result confirms our suggestion of the probability of single crest increases with increasing the electron density. This single crest formation could be attributed to instability of the double crest formation of the Fig. 15 the Electron density and the Solar flux index with respect to years of observation in red circles and blue dots respectively EIA anomaly; therefore, a single crest has observed at the altitude of Swarm satellite.
Finally, Fig. 14b showed that, the occurrence of single crests increases with increasing the strength of the IEF. Balan et al. (2018), Amaechi et al. (2020), Resende et al. (2020) showed that the Prompt Penetration Electric Field (PPEF) enhances/inhibiting the EIA formation according the direction of the field and the local time of the observational point. Therefore, it increases the asymmetry of the EIA double crest formation. Subsequently, the probability of observing a single crest increases with increasing the IEF strength as shown in Fig. 14b.

Conclusion
In this article we have presented the EIA single crest events observed by Swarm satellites A, B and C and its relationship with respect to the geomagnetic activities. We have included eight years of Swarm electron density data since the launch date of the mission by November 2013 until 2021. The current study complements previous studies which reported EIA single crest events observed only by Swarm A satellite using 3 years electron density data.
The results indicate that the occurrence of single crests slightly decreased at higher altitudes (Swarm B), which could be interpreted in terms of the low electron density in comparison with the altitude of Swarm A and C. We also found that the results of the occurrence of the EIA single crest are clearly enhanced with increasing the level of geomagnetic activity. Moreover, the number of single crests have increased with increasing the rate of the solar flux impinges the Earth's ionosphere. In addition, single crests had a large occurrence during equinoxes than during summer and winter solstices. Finally, the region of the SAA has shown a dramatic enhancement in the number of EIA single crest events in comparison with other longitudinal regions, irrespective of the season. All these results emphasize that the occurrence of EIA single crests increases with increasing both the level of geomagnetic activities and the amplitude of the electron density.
Acknowledgements The author acknowledges the European space Agency for providing the Swarm electron density data used for the current study (https://swarm-diss.eo.esa.int/). The OMNIWeb data were provided from the Space Physics Data Facility https://spdf.gsfc.nasa. gov.

Competing interests The authors declare no competing interests.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.