Medium-term ionospheric response to the solar and geomagnetic conditions at low-latitude stations of the East African sector

Abstract

In this study, we used GPS-TEC measurements from six stations in East Africa located in low/equatorial latitudes to investigate medium-term ionospheric response to solar and geomagnetic circumstances during 2014–2016. Daily mean solar proxies (F10.7 and SSN) and geomagnetic activity indices (Kp and Dst) were used to determine solar and geomagnetic activity effects on ionospheric vertical Total-Electron-Content (vTEC). We have applied statistical analysis and quadratic fits with solar indices to find the type of trends, forecast vTEC, and describe the daily fluctuations of vTEC. Asab and Debark had the highest vTEC values among the six stations during the months of equinoxes in which they are located at 13.06⁰ and 13⁰ geographic latitudes, respectively. The highest vTEC values were 86, 80, and 75 TECU in March, October, and April 2014, respectively; 72 TECU in March and April 2015, and 70 TECU in February 2015. Within 24 hours, the magnitudes of vTEC were greater in February, March, and April 2014, 2015, and 2016 than in the remaining months. The changes in vTEC have demonstrated good agreement with the trend of solar parameters, and F10.7 has a stronger correlation with vTEC than SSN by 20%. The effects of solar activity on GPS-vTEC were positive, whereas the vTEC was disturbed during the storm’s main and recovery phases, which led to positive and negative ionospheric effects, respectively. We found both linear and non-linear trends. Nevertheless, when we approximated (F10.7)² and (SSN)² coefficients, linear trends in vTEC were dominant. The anticipated and observed vTEC measurements are in moderately good agreement.

Keywords:

• solar and geomagnetic activity
• ionosphere
• TEC
• GPS
• East-Africa
• medium-term

1. Introduction

The Sun is a highly variable star with sporadic events consisting of outbursts and huge amounts of energy. Our planet obtains energy from the Sun through electromagnetic radiation, solar wind, and the IMF (Interplanetary Magnetic Field). The Earth’s atmosphere can be classified into several different layers based on the activity of the Sun, the gravity and magnetic field of the Earth, the temperature, and the degree of ionization. A neutral atmosphere can extend up to 60 km, and the ionosphere can extend from about 60 km to more than 1,000 km altitude (Appleton & Barnett, 1925; Breit & Tuve, 1925; Chapman, 1931; Heaviside, 1902; Kennelly, 1902; Ratcliffe, 1972; Taylor, 1903). There are numerous ways that active solar areas affect the magnetosphere and ionosphere of Earth. The various driving mechanisms collectively contribute to the variation of neutral and ionized densities (Kutiev et al., 2013). The ionospheric response is latitude-dependent and causes large horizontal gradients. These gradients are evaluated using Global Navigation Satellite Systems (GNSS) measurements of the total electron content (TEC). The ionosphere activity can be monitored by considering TEC observations derived from a network of GPS stations using dual-frequency measurements (Wanninger, 1993).

The influenced ionosphere layers can cause major changes, such as changing the density distribution in the ionosphere, increasing or decreasing the TEC values, and impairing the current balance in the ionosphere (Komjathy, 1997). It is necessary to define the solar and geomagnetic activity indices and determine the solar and geomagnetic effect levels to model the changes in the ionosphere. We have used the following space weather condition indices: 1) solar activity indices (solar proxies): solar radio flux index (F10.7) and sunspot number (SSN); 2) geomagnetic storm index (Dst) and geomagnetic activity indices (Kp). The frequency of solar parameters and charged particle events from the Sun increases during solar maximum and causes significant variations in Earth’s magnetosphere and ionosphere. We have chosen the years 2014 to 2016 for this study due to 1) 2014 and 2015 being the years of the highest phase of the solar activity cycle-24, and 2016 being the year of the start of the solar decline; and 2) several geomagnetic events occurring during the interval. A typical mid-term response of the neutral atmosphere and ionosphere to the changes in solar and geomagnetic activity is known as ”quasi-27-day periodicity,” and the primary cause of such changes is the repeatable influence of active regions on the Sun’s surface that rotate with a period of 27 days (connected with solar rotation; Kutiev et al., 2013).

In the past decades, many investigations have been conducted globally with limited observations around East African regions to explore the solar and geomagnetic activity effects of several ionospheric parameters, such as electron density $N_e$ and plasma temperatures at different altitudes, TEC, and peak electron density ($N_m{F}_2$) and peak height ($h_m{F}_2$) of the $F_2$ layer, in terms of observations and theoretical models as well (e.g., Blanch et al., 2013; Choi et al., 2011; Kassa et al., 2017; Kutiev et al., 2012, 2013; Liu & Chen, 2009; Ogwala et al., 2018). From 2000 to 2008, Kutiev et al. (2012) investigated the 27-day response of the mid- and low-latitude ionosphere to solar activity as measured by relative deviations of TEC over Japan and discovered a correlation between relative deviation, rTEC, and F10.7. Kutiev et al. (2013) studied the solar activity impact on the Earth’s upper atmosphere and ionosphere. They showed the correlation of ionospheric TEC with changes in solar activity using TEC obtained at three selected sites in Europe (cf. http://swaciweb.dlr.de) during $1995-2009$. Liu and Chen (2009) analyzed the data series of the global ionosphere map (GIM) TEC derived at Jet Propulsion Laboratory (JPL) from GPS observations to study the solar activity effects of TEC on a global scale over seven geographic latitudes along longitude ${120}^0$ E versus F10.7, F10.7P, and solar EUV during the day of the year (DOY), [250, 310], in the years from 1998 to April 2009. They reported that three kinds of patterns, such as linearity, saturation, and amplification, can be detected in TEC versus F10.7P and EUV. But, a saturation feature exists in TEC versus F10.7 in the daytime, which is more pronounced at low latitudes than at middle and high latitudes, and the amplification was not found.

Choi et al. (2011) studied the correlation between TEC responses and geomagnetic activity indices (Kp and Dst) at mid-latitudes using TEC data over South Korea in 2003. They reported that the variations in the GPS-TEC showed similar fluctuations to the changes in the geomagnetic indices. Ogwala et al. (2018) investigated the diurnal, seasonal, and solar cycle dependence of GPS-TEC using TEC data over Northern Nigeria from 2011 to 2014. They analyzed the annual variation of TEC and SSN by plotting the mean TEC and SSN against each month of that year. Their plots reveal the strong dependence of TEC on solar activity (SSN). Kassa et al. (2017) investigated the solar variations of vTEC as a function of solar activity parameters like EUV and F10.7 during $2010-2014$ over Bahir Dar, Ethiopia, by considering only quiet day observations.

Geomagnetic storms happen when the solar wind speed increases significantly and abruptly, as explained in Schunk and Sojka (1996). When the enhanced solar wind speed is accompanied by a significant southerly IMF component, storms can be especially potent. Large storms have the potential to drastically alter the ionosphere-thermosphere system’s density, composition, and circulation on a global scale, and these changes may last for several days after the geomagnetic activity has subsided. As a result of storm dynamics, an increase in electron density is referred to as a ”positive ionospheric storm,” and a drop in electron density is referred to as a ”negative ionospheric storm.” The following factors are involved in the mechanisms that account for the positive ionospheric storm: First, a rise in oxygen density; second, the meridional winds change, causing the ionosphere to ascend to higher altitudes where the recombination rates are lower; third, an eastward electric field that uplifts the ionosphere and directs it to areas with lower recombination rates; and fourth, plasma redistribution as a result of disturbed electric fields. A reduction in the $\mathit{O}/N_2$ density ratio as a result of atmospheric disturbances, on the other hand, is what triggers the negative storm phase, which is brought on by changes in neutral composition (De Abreu et al., 2014, 2010; Blanch et al., 2013; Fagundes et al., 2016; Goncharenko et al., 2007; Huang et al., 2005).

Significant achievements have been reported in the variability of the ionosphere with the solar cycle. These inquiries demonstrate prominent and complex solar cycle variations in the ionosphere. In general, several researchers were interested in investigating the impact of solar activity on the ionosphere (e.g., Buresova et al., 2014; Ikubanni et al., 2013; Iyer et al., 2006; Kutiev et al., 2013; Liu et al., 2006); and since solar activity is the main source of disturbances and fluctuations in the Earth’s environment, in particular the magnetosphere and the ionosphere layers, we have been motivated to investigate the solar activity impact on the Earth’s ionosphere. Because the previous researchers studied only short- and long-term trend variations, we focused on medium-term variations of solar activity in the ionospheric observable. So far, nobody has investigated the medium-term ionospheric response to the solar and geomagnetic conditions at low-latitude stations in East Africa. Although Kassa et al. (2017) investigated the long-term trend variations of vTEC as a function of solar activity parameters in East Africa, this study has the limitation of a limited coverage area. That is, their study area was limited to one station over Bahir Dar, Ethiopia.

There have not been a lot of studies on the medium-term ionospheric response to solar and geomagnetic conditions in the African region. The effects of medium-term solar and geomagnetic activity on the ionosphere and associated processes are still not fully understood. These factors led us to perform this study. Therefore, the primary goal of this paper is to investigate the medium-term ionospheric response to solar and geomagnetic conditions at low-latitude stations in the East African sector from 2014 to 2016. Our report, in particular, aimed to examine the variability of vTEC observations in relation to solar and geomagnetic activity in the region. Also, we obtained linear and non-linear coefficients of the vTEC variations to capture the trends of variations and predict the vTEC of 2015 and 2016. We have employed second-order polynomial fitting to indicate the variability. Straightforward analyses of the linear and non-linear trends of the variability were presented based on the coefficients of the fitted polynomial.

2. Study area

Figure 1 shows the locations of the GPS receivers’ stations that were used to collect data for this study.

Figure 1. Locations of the GPS receivers’ stations for this study.

3. Data set and methods

3.1. Data sources

i) Solar and Geomagnetic Indices Data

The solar and geomagnetic activity indices, like $F_{10.7}$, SSN, Dst, and Kp, that are available from NASA’s Goddard Space Flight Center through the OMNIWeb Plus database (https://omniweb.gsfc.nasa.gov/), have been used to observe the solar and geomagnetic activity effects on the ionosphere.

ii) GPS/GNSS data

A global chain of GPS/GNSS (Global Navigation Satellite Systems) receivers’ data in Receiver-Independent Exchange (RINEX) format was obtained from the International GPS Geodynamics Service (IGS) network (http://www.unavco.org/data/gps-gnss/data-access and UNAVCO ftp://data-out.unavco.org/pub/rinex) that has been used to derive TEC values. RINEX files have been converted to TEC using the GPS-TEC analysis application program developed by Gopi Seemala in 2020. In vTEC conversion, the vertical TEC (vTEC) from all the visible satellites with an elevation mask of ${30}^0$ has been considered to minimize multi-path errors and also reduce errors related to the changes in the ionospheric pierce point (IPP) caused by the ionospheric gradient over the equatorial region. In this study, GPS/GNSS TEC data was used to characterize the solar and geomagnetic activity effects on the ionosphere.

3.2. Methods

To investigate the relationship between ionospheric parameters like GPS-TEC and solar and geomagnetic activity indices, such as F10.7, SSN, Dst, and Kp in the time series, we have designated statistical analysis and polynomial fitting. For both methods, we have used the MatLab Programming Language.

The correlation between the two variables is a measure of the linear dependence between them. The correlation coefficient between X and Y is defined by

(1) $\mathit{Cor}(\mathit{X},\mathit{Y})=\frac{\mathit{Cov}(\mathit{X},\mathit{Y})}{\sqrt{\mathit{Var}(\mathit{X})\ast \mathit{Var}(\mathit{Y})}}$(1)

Where the covariance is defined as $\mathit{Cov}(\mathit{X},\mathit{Y})=\mathit{E}[(\mathit{X}-\mathit{E}[\mathit{X}])\ast (\mathit{Y}-\mathit{E}[\mathit{Y}])]=\mathit{E}[\mathit{XY}]-\mathit{E}[\mathit{X}]\mathit{E}[\mathit{Y}].$ The covariance of two variables is a measure of how much they vary together.

Correlation measures the linear relationship between variables. If the correlation is positive, then Y increases as X increases. If X increases, Y will decrease if the correlation is negative. The correlation coefficient is a number between −1 and 1 that determines whether two paired sets of data are related. The closer to 1, the more confident we are of a positive linear correlation, and the closer to −1, the more confident we are of a negative linear correlation. When the correlation coefficient is close to zero, there is no evidence of any relationship.

4. Results and Discussion

We have used MatLab to develop our code, and using this code, the values of vTEC and solar and geomagnetic activity indices like $F_{10.7}$, SSN, Dst, and Kp data have been plotted (see, Figures 2 to 9). In this paper, we have presented the solar and geomagnetic activity effects on vTEC over East Africa from 2014 to 2016. For statistical analysis, we have used the hourly and daily averaged vTEC.

Figure 2. The hourly mean monthly variations of vTEC observed at the study area during 2014 - 2016.

Figure 3. The contour plots for monthly variations of GPS-vTEC measured in the study area, the white section of this plot depicts the lack of data at the rcnn and asab stations in 2015 and 2016, respectively.

Figure 4. The daily mean variations of vTEC at six stations versus F10.7 and SSN indices during 2014 to 2016; the broken line in this plot shows the unavailability of data.

Figure 5. The daily mean variations of vTEC at six stations versus the Dst and Kp indices during 2014 to 2016; the broken line in this plot shows the unavailability of data.

Figure 6. Daily averaged F10.7 index versus vTEC scatter plot from 2014 to 2016.

Figure 7. Dependence of daily mean vTEC on the SSN index during 2014 to 2016.

Figure 8. Comparison between modeled (predicted) (blue) and observed (yellow) vTEC in the period of 2014 to 2016.

Figure 9. Error bar of predicted vTEC versus observed vTEC from 2014 to 2016.

4.1. Solar activity (${\mathit{F}}_{\mathit{\hspace{0.17em}}}$_10.7 and SSN indices) effects on vTEC

i) Hourly Mean Monthly Variations of vTEC

Figure 2 shows hourly averaged, monthly variations of vTEC versus Universal Time (UT) in hours at an elevation mask angle of ${30}^0$ from 2014 to 2016 in the study area. The GPS-vTEC has a maximum value at noon and a low value during the night. Figures 2 and 3 depict that there are significant vTEC differences in magnitude over 12 months for each of the six stations in the study area, where the maximum vTEC value for all stations occurred near noon and the highest vTEC value was obtained at 12:00 UT.

From Figures 2 and 3 (see also, Tables 1, 2 , 3 and 4), one can see that February, March, and April recorded the maximum vTEC values, and the months of June, July, and December recorded the minimum vTEC values. Among the six stations, Asab and Debark recorded the highest vTEC values of 86, 80, and 75 TECU in March, October, and April 2014, respectively; 72 TECU in March and April 2015; 68 and 70 TECU in February 2015; and 57 TECU in March 2016 during the months of the equinoxes since they are located around ${15}^0$ geographic latitude and seasonal variations. Hence, we have indicated that during the equinox and solstice months in the years 2014, 2015, and 2016, the vTEC revealed increasing and decreasing trends like the increasing and decreasing of the solar parameters, respectively. Monthly variations of the vTEC in Figure 2 over 12 months for each of the six stations are also shown in the contour plot of Figure 3. The features mentioned above are very well illustrated in this figure. Our results confirm the reported work of Abdu and Brum (2009) and Maruyama (2010). Since the sun is the main source of ionization, the time-to-time variability in TEC is due to the changes in the activity of the sun itself and the related changes in the intensity of the incoming radiations and the zenith angle at which they are incident on the Earth’s atmosphere. Accordingly, hourly mean monthly values of vTEC (see, Figures 2 and 3) can be altered by the intensity of solar radiation and the emission of particles from the sun. This result supports the reported work of Aragaw et al. (2019) and Tyagi (1974).

Table 1. Geographic and geomagnetic coordinates of the GPS receivers’ stations

Code	Station	Country	Geographic Coordinates		Geomagnetic Coordinates
			Lat (deg)	Lon (deg)	Lat (deg)	Lon (deg)
asab	Asab	Eritrea	13.06	42.65	4.91	114.34
debk	Debark	Ethiopia	13.00	37.65	4.32	109.48
bdmt	Bahir Dar	Ethiopia	11.60	37.36	2.65	108.97
adis	Addis Ababa	Ethiopia	9.04	38.77	0.16	110.48
nege	Negele	Ethiopia	5.34	39.59	−3.60	111.35
rcmn	Nairobi	Kenya	−1.22	36.90	10.76	108.51

Table 2. Using the hourly mean, the maximum and minimum vTEC values of the six stations in our study area

Stations and Years	Months	TEC value (TECU)	Time (UT)
Negele, 2014	March	78	11:30 to 12:30
	April	70	11:30 to 12:30
	October	72	11:30 to 12:30
	June	36.3	10:30
	July	36.5	10:30
Negele, 2015	March	69	11:30
	February	66	12:00
	April	66.4	11:00
	July	33.4	13:00
	August	33	10:00
Negele, 2016	March	45	12:00
	February	44	12:00
	July	22.5	10:00 to 12:00
	December	23.5	10:00 to 12:00
Addis Ababa, 2014	March	82	13:00
	April	71	13:30
	June	32	10:00
	July	31	10:00
Addis Ababa, 2015	March	68	11:00
	April	64	11:00
	February	63	12:00
	July	30	14:00
	August	29	10:00
Addis Ababa, 2016	March	46	12:00
	February	43	12:00
	July	22	10:00
	August	24	10:00

Table 3. Using the hourly mean, the maximum and minimum vTEC values of the six stations in our study area

Stations and Years	Months	TEC value (TECU)	Time (UT)
Bahir Dar, 2014	March	83.7	13:00 to 13:30
	April	73.5	13:00 to 13:30
	June	33.5	10:00
	July	34	10:00
Bahir Dar, 2015	March	71	11:00
	February	69	13:00
	April	68	12:00
	July	33	10:00
Bahir Dar, 2016	March	48	12:00 to 13:00
	February	45	12:00 to 13:00
	July	23	10:00 to 12:00
	December	26.5	10:00 to 12:00
Asab, 2014	March	86	12:00 to 13:00
	October	79.5	12:00 to 13:00
	April	75	12:00 to 13:00
	June	35	10:00
	July	33	10:00
Asab, 2015	April	72	12:00
	March	71.8	12:00
	February	68	13:00
	July	31	14:00
Asab, 2016	March	57	13:00 to 14:00
	April	54	13:00 to 14:00
	January	8	11:00 to 13:30
	June	24	11:00 to 13:30

Table 4. Using the hourly mean, the maximum and minimum vTEC values of the six stations in our study area

Stations and Years	Months	TEC value (TECU)	Time (UT)
Debark, 2014	March	86	13:00 to 14:00
	April	75	13:00 to 14:00
	June	36	10:00 to 11:00
	July	33	10:00 to 11:00
Debark, 2015	March	72	12:00
	April	71.6	12:00
	February	69.5	13:00
	July	31	10:00
Debark, 2016	March	48	11:00 to 13:00
	February	44	11:00 to 13:00
	July	20	10:00
rcmn(Nairobi), 2014	March	76.5	12:00 to 13:00
	April	68	12:00 to 13:00
	August	32	10:00 to 11:00
	June	39	10:00 to 11:00
rcmn(Nairobi), 2015	March	72.7	12:00
	April	68	11:00
	February	65	12:00
	July	26	14:00
rcmn(Nairobi), 2016	March	47.5	12:00
	February	44	12:00
	June and July	20	10:00

During the solar cycle, the sun emits a wide variety of solar radiation with high-energy particles. This radiation peaks during periods of high solar activity, which has its own effect on the TEC of the Earth’s ionosphere. Consequently, electron concentrations in the region of the ionosphere are expected to reflect these variations. To observe the solar activity effects on the GPS-TEC, we used the solar radio flux (F10.7) and SSN data (see, Figure 4) since F10.7 is a useful indicator of solar activity as a proxy for solar EUV and has a correlation with SSN. Jee et al. (2014) reported the direct control of solar activity on the ionization level, with higher values during the maximum solar activity period and low values during the minimum solar activity period. The figure for solar radio flux (see, Figure 4 top) can vary from as low as 50 to as high as 300 for 2014 and 2015. However, because 2016 marks the beginning of the solar decline, it ranges from 60 to 120. Low values show that the maximum usable frequency will be low. Reversely, high values generally indicate that there is sufficient ionization. Therefore, due to the close relationship between the solar radio flux and the solar EUV radiation, F10.7 is well matched to describe the level of total ionization of the ionosphere, based on what Jakowski et al. (1991) reported.

ii) Daily Variations of vTEC, and $F_{10.7}$ and SSN Indices

In this subsection, we analyzed the daily variations of vTEC. Figure 4 shows the daily variations of vTEC at six stations from 2014 to 2016. Most of the time, the diurnal variations of vTEC at all stations exhibit nearly the same patterns, but the vTEC values slightly vary in each month at the stations since the vTEC variation is not only time-dependent but also depends on latitude. In general, the vTEC patterns are consistent from 2014 to 2016, so that the vTEC increased from January to April, then decreased from May to August, and finally increased after August. In 2014, F10.7 has the values of 253.3, 210.3, and 229 sfu at DOY = 4 to 7; between 205 and 208 sfu at DOY = 187 to 190; between 200 and 216 sfu at DOY = 293 to 299; and between 200 and 208 sfu at DOY = 352 to 355. As a result, the vTEC for all stations reaches its peak at these F10.7 peaks. At minimum values of F10.7 less than 100 sfu at DOY = 173 to 175 and from 197 to 203, the five stations have their down-peaks, but Adis station has its up-peaks. These results are associated with solar activity since F10.7 recorded maximum and minimum values so that the vTCE values were maximum for each peak of F10.7, and there may be another factor that affects the vTEC at Adis station. In similar fashion to F10.7, the SSN has the values of 207, 220, and 196 at DOY = 57 to 59; the SSN is equal to 174, 197, and 182 at DOY = 162 to 164; the SSN is between 172 and 197 at DOY = 185 to 189; and the SSN is between 178 and 193 at DOY = 270 to 273; thus, as the SSN peaks, the vTEC of all stations has its own peaks. For minimum values of SSN less than 50 (between 0 and 39) at DOY = 196 to 203 and between 30 and 42 at DOY = 283 to 286, the six stations have their down-peaks. These results imply that the F10.7 and SSN are indicators of solar activity. But, when we observed the peaks of F10.7 and SSN, the SSN peaks deviated from vTEC peaks, unlike F10.7.

In 2015, F10.7 has no recorded data value at DOY = 13 and has 255 sfu at DOY = 173. In this case, almost all stations’ vTEC peaks occurred immediately before DOY = 13. But, in the second case, the vTEC of all stations reached their peaks immediately after the F10.7 peak (255 sfu). On the other days of 2015, the diurnal variations of F10.7 exhibited nearly the same patterns as vTEC. The SSN has the values of 153 at DOY = 30, SSN = 150 to 172 at DOY = 128 to 134, and SSN = 152 to 169 at DOY = 268 to 271. The vTEC values reached their peaks immediately after the SSN peak at DOY = 30, and the vTEC values reached their peaks with the SSN peak at DOY = 128 to 134. For the third peak of SSN at DOY = 268 to 271, the vTEC value does not show clear peaks, even though it fluctuates. In general, when we saw the fluctuations of SSN throughout the year, it showed nearly the same patterns as vTEC. In 2016, F10.7 has 119.8 sfu at DOY = 35, 111 to 117 sfu at DOY = 101 to 108, and 105 to 111.5 sfu at DOY = 197 to 203; for this and other peaks of F10.7, the vTEC values show the increment. The SSN has the values 111, 108, 97, and 90 at DOY = 64, 35, 9, and 119, respectively. For these peaks of SSN, the vTEC values increased. For this year, SSN has a minimum value of 0 for more than 20 days; hence, the vTEC values on these days are less than 20 TECU. The peaks of SSN in 2016 were very small compared with the peaks of SSN in 2014 and 2015. This result is due to 2016 being the year of the start of the solar decline. This day-to-day variability of TEC was contributed by solar activity and indicated by various parameters like F10.7 and SSN, which is consistent with the previous results obtained earlier by Rama Rao et al. (2006), Liu and Chen (2009), and Jakowski et al. (1991). From Figures 2 to 4, one can see that during periods of low or high solar indices, the provided GPS-vTEC has dropped or built up slowly. This outcome is in agreement with a study by Guo et al., 2015; Kassa et al., 2017; Liu & Chen, 2009. The hourly, daily, and monthly vTEC values over East Africa have shown very nearly similar patterns with variations in solar indices in all of the years we observed.

4.2. Geomagnetic activity (Kp and Dst indices) effects on vTEC

Since in this subsection we have used only the daily variations of vTEC versus Dst and Kp indices in the time period of 2014 to 2016, we have analyzed the general geomagnetic activity effect as follows: Figure 5 shows the daily variations of vTEC at six stations and Dst and Kp from 2014 to 2016. In 2014, when Kp $\ge$ 4, the Dst = −66, −62, 60, and −65nT at DOY = 50, 51, 59, 102, 159, and 255. For each storm time, the vTEC values increased compared with the initial and final phases of the storm and decreased after the storm times. From May to August 2014, Dst values were greater than −25 nT (between −24 and 18 nT), and vTEC values for all stations dropped to the minimum ($\le$ 22 TECU). In 2015, when Kp $\ge$ 5, the Dst = −117, −127, and −100 nT at DOY = 76 and 77, 174, and 355. The vTEC values increased during the storm compared with the initial and final phases of the storm and decreased after the storm. In 2016, when Kp $\ge$ 4, low storms were observed compared with 2014 and 2015 storm times. That is, Dst = −54, −60, and −65 nT at DOY = 20 and 21, 67, and 129. During these storm times, the vTEC values increased except for the first storm time at DOY = 20, and the vTEC values decreased after the storm time.

Our result indicates the overall signatures of the geomagnetic activity effect on the Earth’s ionosphere since we have used the daily variations of vTEC versus Dst and Kp indices in 2014 through 2016 (medium-term response). We have done this section study to know the general effects of geomagnetic activity due to our title, ”medium-term response,” with time scales from several days to a month being a typical medium-term response. Therefore, based on this result, we can suggest that the positive ionospheric storm peak perturbations were caused by eastward prompt penetration electric field (PPEF) and equatorial plasma drift uplifts, whereas the negative storm phase was brought on by changes in neutral composition that result in a drop in the $\mathit{O}/N_2$ density ratio as a result of atmospheric disturbances. These findings are due to the fact that they originate from the equatorial plasma drift uplifts and PPEFs that have an impact at low latitudes. The positive ionospheric storm disturbance must occur simultaneously from low latitudes to the equatorial area because electric field penetration occurs on a global scale. According to several studies (Fagundes et al., 2016; Fejer et al., 2008; Huang, 2012; Huang & Yumoto, 2006; Wei et al., 2015), the impact of PPEFs in the equatorial/low-latitude ionosphere may be related to electric fields of solar or magnetospheric origin or to dynamical processes in the magnetosphere, such as sub-storms. Both scenarios have the potential to produce an eastward electric field, which will lift the F layer to higher altitudes where there is significantly less recombination, increasing the F layer electron density (TEC). Most of the time, our results show a positive relationship between storm times and vTEC values due to geomagnetic storms. The ionospheric TEC values increased and decreased due to geomagnetic activity, which means it is apparent that geomagnetic storms provide positive and negative variations in vTEC.

If the storm effects on GPS-vTEC are positive, vTEC values may be greater than 60 TECU, which implies TEC enhancement; if the storm effects are negative, vTEC values may be less than 45 TECU, which implies TEC reduction. As we have seen from Figures 4 and 5, the solar indices have shown good agreement with the daily vTEC values across all of our observations. However, the geomagnetic storm times indicated by the indices Dst and Kp were mostly in agreement and rarely in opposition with the daily vTEC values. This result illustrated that the vTEC values might be reduced or increased by geomagnetic activity during storm times. Maximum TEC values were frequently recorded on days with maximum F10.7 and SSN, whereas minimum TEC values were recorded on days with minimal F10.7 and SSN. Based on these findings, F10.7 is more closely related to vTEC than SSN because solar radio flux is a useful indicator of solar activity as a proxy for solar extreme ultraviolet radiation for ionospheric ionization level.

4.3. Polynomial fitting and the correlation of observed vTEC with solar parameters

Figure 6 depicts the solar variations of the observed vTEC data and the corresponding quadratic-model vTEC, which is generated using F10.7 as input for daily values in the period of $2014-2016$. This figure shows the quadratic-model’s capability in presenting the linear and non-linear variations of vTEC as a function of F10.7, and Figure 7 shows the solar variations of observed vTEC and the corresponding quadratic-model vTEC, which is generated using SSN as input for daily values from 2014 to 2016. This figure shows the quadratic model’s ability to present linear and non-linear variations of vTEC as a function of SSN. These results hold up the reported works on long-term trends by Liu and Chen (2009), Aggarwal et al. (2012), and Kumar and Singh (2009). In the daily analysis, the correlation coefficients between vTEC and the solar indices (F10.7 and SSN) were 0.78 for F10.7 and 0.56 for SSN in 2014, 0.68 for F10.7 and 0.53 for SSN in 2015, and 0.63 for F10.7 and 0.49 for SSN in 2016. This implies that about 50% to 80% of the variations in GPS-vTEC could be explained by using the solar parameters (F10.7 and SSN) in our study area and time duration. As a result, these daily variations of vTEC showed positive associations with the solar indices (F10.7 and SSN) at our stations for the period of 2014 to 2016 (see, Figures 6 and 7). Therefore, when we look at the relationships of vTEC with F10.7 and SSN, we can see that the solar radio index (F10.7) outperforms the sunspot number (SSN) by 20% over 3 years. The observation of this research was consistent with the reports by Liu and Chen (2009) and Gao (2008), who showed a very close correlation between maximum vTEC and SSN in March and September but a poor correlation in July and August of the high solar activity period of 2003 at Hong Kong (found in the low latitude region).

From the general expression of a quadratic model given by $\mathit{y}=\mathit{a}{x}^2+\mathit{bx}+\mathit{c}$, one can infer the degree of linear and non-linear variations of observation y as a function of parameter x. In our case, the sign of coefficient a indicates the possible non-linear solar variations (trend) of vTEC due to the variations in its corresponding F10.7 and SSN values. Figures 6 and 7 demonstrate the linear and non-linear variations of vTEC concerning solar indices (F10.7 and SSN). Hence, these Figs. indicate the existence of linearity (a = 0), amplification (a $>$ 0), and saturation (a $<$ 0) features of vTEC variations as a function of F10.7 and SSN for each station. From these Figs. and Table 5, we can infer that both linear and non-linear trends were observed during our observations. All the coefficients of $(F_{10.7}{)}^2$ are negative (saturation) for the stations of Asab, Debark, and Negele in the period of $2014-2016$, and the amplification has not yet been found using this parameter. However, the coefficients of $(\mathit{SSN}{)}^2$ are negative (saturation) for the same stations in 2014 and 2016, and the amplification was found using SSN in 2015. This result implies that the non-linear trend of solar variations of vTEC in the study area was almost saturated. Therefore, we have obtained the three kinds of patterns such as linearity, saturation, and amplification that can be detected in vTEC versus SSN. But only the saturation and linearity features exist in vTEC versus F10.7, and the amplification was not found. When we approximated the coefficients of $(\mathit{F}10.7{)}^2$ and $(\mathit{SSN}{)}^2$ for all stations, we had nearly zero values (see, Table 5 of columns 2 and 5). This approximation leads to the conclusion that the linear trend was significantly observed over East Africa from 2014 to 2016. This outcome agrees with the reported works on long-term trends by Liu and Chen (2009), Aggarwal et al. (2012), Kumar and Singh (2009), Kassa et al. (2017), Kutiev et al. (2012), Kutiev et al. (2013), and Choi et al. (2011).

Table 5. The linear and non-linear extent of solar variations in vTEC from 2014 to 2016

Station and Year	(SSN)^2	SSN	Trend	(F10.7)^2	F10.7	Trend
Asab, 2014	−0.001	0.3	Mixed	−0.0033	1.17	Mixed
Debark, 2014	−0.001	0.28	Mixed	−0.003	1.123	Mixed
Negele, 2014	−0.001	0.2	Mixed	−0.003	0.88	Mixed
Asab, 2015	0.0001	0.05	amplification	−0.0022	0.76	Mixed
Debark, 2015	0.0001	0.05	amplification	−0.002	0.73	Mixed
Negele, 2015	0.0002	0.02	amplification	−0.002	0.56	Mixed
Asab, 2016	−0.0004	0.09	Mixed	−0.005	0.964	Mixed
Debark, 2016	−0.001	0.14	Mixed	−0.005	1.144	Mixed
Negele, 2016	−0.001	0.13	Mixed	−0.006	1.23	Mixed

In general, Figures 6 and 7 and Table 5 represent the trends of linearity, saturation, and amplification that can be found in our study area to indicate the dependency of the daily vTEC variations on solar activity, which is indicated by F10.7 and SSN indices. Particularly, saturation and amplification effects on vTEC at low latitudes over East Africa may be due to different complicated processes such as meridional winds, $\mathbf{E}$ x $\mathbf{B}$ drift, equatorial electrojet (EEJ), and photoionization. These consequences are consistent with the previous works on long-term trends by Liu and Chen (2009), Aggarwal et al. (2012), Kumar and Singh (2009), Kassa et al. (2017), and Laštovička (2021). The medium-term variations of vTEC over East Africa in the period of $2014-2016$ were significantly correlated linearly with the variations of solar indices (as seen in Figures 6 and 7 and Table 5). Therefore, based on the medium-term dataset, one can deduce that the solar variations of vTEC were dominated by their linear trend pattern.

4.4. Prediction of vTEC using quadratic model and the deviation between the observed and modeled vTEC

We have predicted vTEC measurements using the quadratic model for the years $2014-2016$. The prediction of vTEC was made as a function of F10.7 and SSN. The predicted values are depicted by the blue colors in Figure 8, and the yellow stands for the corresponding observed daily vTEC values. By referring to this figure, one can infer relatively good agreements between the predicted and observed values of vTEC in terms of both their magnitude and pattern variations. Thus, our results revealed that the quadratic modeling of the vTEC is capable of demonstrating its linear and non-linear solar variations.

Figure 9 portrays the error bar between the observed and modeled daily vTEC values as a function of F10.7 and SSN, respectively, in the period of $2014-2016$. Days with insignificant vTEC deviations less than 0.5 TECU have been observed; for example, modeling with respect to F10.7 at DOY = 4, 8, 9, 10, 20, 108, 113, 114, 147, 173, 198, 203, 204, 212, 304, 325, 327, 339, and 344; and modeling with respect to SSN at DOY = 147, 161, 242, 246, 248, 252, 254, 260, 267, 269, 271, 272, 275, 276, 284, and 297; and the days with the highest deviations, such as 15.7, 15.76, 15, and 15.7 TECU, were at DOY = 61, 78, 172, and 281 for F10.7 and 19.75, 17.4, 15, 18.2, 15.2, and 15.4 TECU at DOY = 61, 62, 65, 66, 77, and 79 for SSN in 2015. Insignificant vTEC deviations less than 0.5 TECU were observed during 2016; for example, modeling with respect to F10.7 at DOY = 41, 42, 52, 56, 64, 68, 77, 79, 116, 126, 258, 261, 262, 264, 271, 275, 276, 279, 284, 287, 288, and 298; and modeling with respect to SSN at DOY = 78 only; and maximum deviations of 11.6, 10.3, and 11.5 TECU were recorded at DOY = 198, 200, and 201 for the vTEC versus F10.7 case, and 10, 10, 11.5, 11, 12, 11, 14, and 13.4 TECU were recorded at DOY = 5, 146, 161, 173, 178, 314, 337, and 358 for the vTEC versus SSN case. The maximum deviations were observed during 2015 for both F10.7 and SSN as compared with the deviations in 2016. This result implied that there might be other parameters other than solar proxies that can affect the variations of vTEC during the 2015 solar maxima. These other parameters may be related to a geomagnetic storm. Overall, from Figures 8 and 9, we can see that the modeled result is worthy of using F10.7 and SSN. But, the modeled result is better using F10.7 than SSN.

5. Summary and Conclusion

5.1. Summary

To analyze the effects of solar and geomagnetic activity on ionospheric vTEC across the East African region, we used the data from the solar maxima years in solar cycle 24 during 2014 to 2016. According to the results of this study, GPS-vTEC can change depending on changes in solar and geomagnetic activity. The values of vTEC at hourly, daily, and monthly scales periodically increase and decrease due to solar rotation. Based on the daily relationship, our outcome reveals that the changes in vTEC respond more to F10.7 than SSN by 20%. This finding infers that solar radio flux (F10.7) is a stand-in for solar extreme ultraviolet radiation at the ionospheric ionization level and an indicator of solar activity. Within 24 hours, the magnitudes of vTEC were greater in February, March, and April 2014, 2015, and 2016 than in the remaining months due to seasonal fluctuations. We draw attention to the fact that from 2014 to 2016, vTEC showed gradually growing and falling trends as solar parameters increased and decreased, respectively, during the equinoxe and solstice months.

From the vTEC versus UT curve, the authors realize that TEC does not suddenly disappear but gradually increases and decreases before about 10:00 and after 16:00 UT, respectively. In this study, we obtained both linear and non-linear (saturation and amplification) trends. However, when we approximated the coefficients of $(\mathit{F}10.7{)}^2$ and $(\mathit{SSN}{)}^2$ for all stations, the solar variations of vTEC were dominated by their linear trends. In the predictions of vTEC, maximum deviations were observed during 2015 for both F10.7 and SSN as compared with deviations in 2016. This result implies that there might be other parameters other than solar proxies that can affect the variations of vTEC during 2015. These other parameters may be related to a geomagnetic storm. Generally, from Figures 8 and 9, we can see that the modeled result is worthy of using F10.7 and SSN. But, the modeled result is better using F10.7.

5.2. Conclusion

We have drawn the following conclusions based on our analysis:

(1) The trend in vTEC changes showed good agreement with the variations in solar parameters, and F10.7 has a stronger correlation with vTEC than the SSN by 20% over 3 years;

(2) Asab and Debark had the highest vTEC values among the six stations during the months of the equinoxes (they are located at ${13.06}^0$ and ${13}^0$ latitudes, respectively). The highest vTEC values in March, October, and April 2014 were 86, 80, and 75 TECU, respectively; 72 TECU in March and April 2015, 70 TECU in February 2015, and 57 TECU in March 2016;

(3) Due to solar and geomagnetic activity, the East African ionospheric sector produced an excessive amount of free electrons during the day and equinoxes;

(4) We found both linear and non-linear trends, but when we used approximation, the medium-term variations of vTEC over East Africa were significantly associated linearly with the variations of solar indices during $2014-2016$;

(5) The predicted and observed vTEC measurements being in good agreement in the region;

(6) The effects of solar activity on GPS-vTEC were positive, but the vTEC was disturbed during the storm’s main and recovery phases, resulting in positive and negative ionospheric effects, respectively;

(7) Positive ionospheric storms are caused by an eastward prompt penetration electric field (PPEF), which lifts the F region to higher altitudes with lower recombination rates and equatorial plasma drift uplifts, whereas negative ionospheric storms are caused by changes in the $N_2/\mathit{O}$ ratio; and

(8) For all of the observational characteristics, we saw that the ionospheric vTEC variations were caused by changes in solar and geomagnetic activity, such as the continued response of the ionosphere over East Africa from 2014 to 2016.

Data Availability

We obtained the data for our investigation from the UNAVCO archive (http://www.unavco.org/ or ftp://data-out.unavco.org/pub/rinex) and https://omniweb.gsfc.nasa.gov/.

Acknowledgements

We would like to thank: 1) all of the data providers: a) the NASA OMNIWeb Plus database (https://omniweb.gsfc.nasa.gov/), for F10.7, SSN, Kp, and Dst indices; and b) websites: ftp://data-out.unavco.org/pub/rinex for TEC data; 2) Dejene Ambisa, my friend, for his constructive support; and 3) the authors of cited articles, journals, and books are also acknowledged.

Above all, God of our Ancestors, thank you for making us do everything successfully!

Disclosure Statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

The authors have no funding to report.