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Occurrence characteristics of equatorial plasma bubbles over Kisumu, Kenya during Solar maximum of Solar Cycle 24

Equatorial Plasma Bubbles (EPBs) are irregular plasma density depletions in the ambient electron density in the equatorial F-region ionosphere generated after sunset. EPBs are known to bring disruptions to telecommunication and navigation systems. This paper investigates the occurrence of EPBs over Kisumu, Kenya (Geomagnetic coordinates: 9.64 S, 108.59 E; Geographic coordinates: 0.02 S, 34.6 E) for a few selected quiet and storm days between 1 January 2013 and 31 December 2014 which was a high Solar activity period for Solar Cycle 24. The study brings out EPB occurrence pattern over Kisumu, Kenya for the selected quiet and storm days of 2013 and 2014. The Receiver Independent Exchange (RINEX) data was retrieved from the Kisumu high data-rate NovAtel GSV4004B SCINDAGPS receiver. The data was unzipped and processed to obtain Vertical Total Electron Content (VTEC), amplitude scintillation (S4) and Universal Time (UT) which were then fed into MATLAB to generate VTEC and S4 plots against UT for each selected quiet and storm day within the years 2013 and 2014. The Total Electron Content (TEC) depletion depths and S4 index values between 16:00 and 20:00 UT for each selected quiet and storm day were extracted from the VTEC and S4 plots and used to plot TEC depletion depths and S4 plots. The Rate of Change of TEC (ROT) and Rate of Change of TEC Index (ROTI) between 16:00 and 20:00 UT were generated from VTEC and used to plot ROT and the corresponding ROTI plots against UT. TEC depletion depths and ROTI values for each selected quiet and storm day between 16:00 and 20:00 UT were extracted and used to plot TEC depletion depths and ROTI plots and S4 index and ROTI plots. In this study, the enhancement of S4 index corresponded well with TEC depletions, increased fluctuation of ROT and higher ROTI values between 16:00UT and 20:00UT for most days. This correspondence was used in inferring the occurrence of EPBs during the selected quiet and storm days of the years 2013 and 2014. The obtained results showed that the highest EPB occurrence was during March equinox with 33.33% occurrence in the year 2013 and 30.76% occurrence in the year 2014, followed by the September equinox which had 20.38% occurrence in 2013 and 17.26% occurrence in 2014. The seasonal variation of EPB occurrence was attributed to the variation in the daytime E x B drift velocities. Larger E x B drift velocities resulted in increased EPB occurrence in the equinoctial period (March, April, August and September) and November solstice period (November and December) while lower E x B drift velocities resulted in reduced EPB occurrence in the June solstice period (June and July). The percentage EPB occurrence in the year 2013 was 6.49% while in the year 2014 was 4.32%. The storm period had percentage EPB occurrence of 21.42% in the year 2013 and 21.88% in the year 2014 while the quiet period had percentage EPB occurrence of 18.75% in the year 2013 and 7.89% in the year 2014. These results clearly showed that the percentage EPB occurrence was higher during the storm period than in the quiet period. Hence the development of EPBs was enhanced by geomagnetic activity through several competing dynamics such as Prompt Penetration Electric Field (PPEF), Disturbance Dynamo Electric Field (DDEF) and reduction in electron density due to increased recombination rates.


Introduction
The Sun produces highly energetic particles such as X-rays and Ultraviolet (UV) radiations (Milos, 2014) which are harmful to the living things and the environment. Increased solar activity leads to large release of Coronal Mass Ejections (CME) and solar flares which causes a change in TEC when they reach the Earth. TEC is the total number of electrons in a column of 1m 2 cross-section between a GPS satellite and a GPS receiver  Magdaleno et al., 2017). Changes in TEC causes heightened levels of hazards in the Earth-space environment, storms and disruptions, generation of strong electric currents in the atmosphere and changes in the reflective properties of the ionosphere. During the day, the F-layer splits into two layers: F1 layer which is about 170km and F2 layer which is about 250km altitude. Conversely, at night the F1 layer diminishes and leaves the F2 layer which persists through the night. Thus, the sporadic E-layer and D-layer disappears a few hours before midnight (Milos, 2014) due to recombination between positive ions and electrons and migration of charged particles to higher altitudes. At the same time, the F-layer's lower regions rapidly recombine than its upper regions leading to a situation known as the Rayleigh-Taylor Instability (RTI) (Kelley, 2009). RTI is an unstable condition where a heavy fluid is held on top of a lighter fluid (Adewale et al, 2012) leading to bubbles of low density plasma being formed and pushed upwards towards the upper denser part of the F-region and growing to form bubbles which are 'frozen' into the moving ionosphere. These 'frozen' structures in the moving ionosphere are known as the plasma bubbles (Olwendo et al., 2012;Paznukhov et al., 2012). Ionospheric irregularities and scintillations pose serious threats to technological systems that increasingly rely on trans-ionospheric radio propagation (Adewale et al., 2012) through signal degradation. In low latitude regions, these irregularities which are basically plasma bubbles are characterized by TEC depletions. During the day, dynamo electric fields which are generated by thermospheric winds in the equatorial E-region are propagated to the F-region altitudes along magnetic field lines. These dynamo electric fields are usually eastward during the day and brings an increase in the upward E x B plasma drift (Omondi et al., 2014;Caruana et al., 2018) that diffuses down the magnetic field lines and moves away from the equator due to action of gravity and pressure gradient force. This upward E x B plasma drift results in formation of ionization peaks in the sub-tropics on both sides of the equator called the Equatorial Ionization Anomaly (EIA) (Olwendo et al., 2012;Ndeda & Odera, 2014). The EIA is an important feature in the study of ionospheric scintillations and is responsible for the formation of plasma density irregularities that give rise to stronger scintillations than at the magnetic equator (Das Gupta et al., 2004;Ndeda & Odera, 2014). Various studies have been done on the chemical and physical processes taking place in the ionosphere leading to the occurrences of EPBs using the GPS due its accurate consistent performance worldwide and in these studies, TEC has been the key parameter (Adewale et al., 2012;Fayose et al., 2012;Wang et al., 2018) that has been very useful in the mitigation of ionospheric effects on radio systems (Makela et al., 2004;Paznukhov et carried out a study on equatorial plasma bubbles and L-band scintillations in Africa during solar minimum and their results showed increase in EPB rate during June solstice moving west to East. They observed that seasonal occurrence of EPBs tended to shift towards boreal summer with fewer occurrences in equinox seasons. Magdaleno et al., (2017) also used GPS data to study climatology characterization of EPBs between 1998-2008 using 67 international GNSS stations around geomagnetic Equator and the obtained results on spatial analysis of EPBs showed that the largest rate of EPBs occurred at the Equator and South American sector but decreased as the distance of magnetic equator increased. Barros et al., (2018) carried out a study on the characteristics of EPBs using ground based network of more than 220 GNSS ground based receivers by mapping TEC (TEC maps) over South-America between November 2012 and January 2016 for both quiet and disturbed days. Their results showed that EPBs occurred majorly between September to March. Bolaji et al., (2019) also investigated the dynamics of ionospheric irregularities at different sectors in the month of March 2015 which consisted of both quiet and disturbed ionospheric conditions. The obtained results showed that the presence of severe irregularities were prominent in African and American sectors but rarer in Asian sectors. The strength was however found to decrease eastward and was attributed to the eastward decrease in the equatorial electrojet. In the equatorial region, the characteristics of plasma bubbles usually depend on the detection technique. In Ionosonde, plasma bubbles would manifest as Spread-F; in Airglow, they would manifest as plumes, while in GPS, they would manifest as TEC depletions. Although studies on the characterization and occurrence of plasma bubbles have been carried out in various parts of the equatorial region, more work needs to be done on the occurrence of EPBs over Africa even with the few available SCINDA-GPS receivers. The quiet time and storm time effects in the equatorial Africa needs more investigation due to the highly dynamic nature of the equatorial ionosphere (Omondi et al., 2019). In this paper we infer the occurrence of EPBs over Kisumu, Kenya using SCINDA-GPS TEC data for a few selected quiet and storm days between 1 st January 2013 and 31 st December 2014. The occurrence of EPBs was inferred using TEC depletion depths, S4 index, ROT fluctuation and ROTI. The results presented in this paper on the occurrence of EPBs are needed so as to relate the extent of ionospheric irregularities to the possible disruptions of High Frequency communication signals as implied by S4. This has important implications for navigation and communication sectors.

Materials and methods
The Zipped RINEX data archived in the SCINDA-GPS receiver between 1 st January 2013 and 31 st December 2014 was retrieved and unzipped using the WinRAR program. The unzipped scintillation (.scn) files and position of the receiver (.psn) files were created in one folder and dragged into an open Gopi Software (Developed by Boston college and Dr. Gopi Seemala) which processed the raw GPS data to obtain a text (.Cmn) output file which was a more simplified ten column daily file of ionospheric observables separated by a tab: Jdatet, Time, PRN, Az, Ele, Lat, Lon, Stec, Vtec, and S4. To reduce multipath effects resulting from obstruction from trees, tall buildings and other antennas, only data having elevation angles of 40 o and above was considered for use in this study. The filtered average daily data of VTEC, S4 and UT for all PRNs was obtained using SQL Server2017 program. The SQL Server2017 program produced the average daily VTEC and S4 values by averaging the VTEC and S4 values for all identical pseudo-random numbers (PRNs) within a 24-hour period. The selected quiet and storm days of 2013 and 2014 period of study were obtained from the disturbance storm time (Dst) index using data obtained from the link: www.wdc.kug.kyoto-ua.ac.jp/dstdir. The quiet days considered in this study were days having Dst values ˃-25nT while storm days considered in this study were days having Dst values ≤ -50nT. The level of geomagnetic activity for the selected quiet and storm days was selected using the Planetary K (Kp) index obtained from the link: www.kugi.kyoto-ua.ac.jp/Kp, where the selected quiet days had Kp values ranging between 0 and 2 while the selected storm days had Kp values ranging between 3 and 9. The VTEC and S4 plots for each selected quiet and storm days of 2013 and 2014 were plotted against UT using MATLAB. TEC depletion depths and the corresponding S4 index for each selected quiet and storm day between 16:00 and 20:00UT were extracted and TEC depletion depths and S4 plots were plotted as indicated in Figures 1(a), 1(b), 1(c) and 1(d). TEC depletion depth was obtained by finding the difference between the TEC value at the time of TEC depletion and the TEC value at the time of a TEC enhancement. The correspondence between TEC depletion depths and S4 for the selected quiet and storm days of the years 2013 and 2014 were noted and discussed. ROT was calculated directly from the filtered average daily VTEC data within intervals of 120 seconds using equation (1) where, TEC = Total Electron content t and t-1 = time difference between the epochs in minutes ∆t = time range in minutes ROTI was computed from ROT at intervals of 4 minutes using equation 2. ROTI is the key component used to investigate ionospheric fluctuations (Bhattacharyya et al., 2000) and it provides spatial variation of electron density (Pi et al., 1997;Jacobsen, 2014).
ROT for each selected quiet and storm day and the corresponding ROTI were plotted against UT using MATLAB. The ROTI values for each selected quiet and storm day between 16:00 and 20:00 UT were extracted alongside their corresponding TEC depletion depths values. The extracted values were used to plot the TEC depletion depths and ROTI plots for the selected quiet and storm days of the years 2013 and 2014 as indicated in Fig. 2(a), 2(b), 2(c) and 2(d). The correspondence between TEC depletion depths and ROTI for the selected quiet and storm days of the years 2013 and 2014 were noted and discussed. The S4 values and their corresponding ROTI values for each selected quiet and storm days of 2013 and 2014 between 16:00 and 20:00 UT were also extracted and the obtained values used to plot the S4 and ROTI plots for the selected quiet and storm days of 2013 and 2014 as indicated Fig. 3(a), 3(b), 3(c) and 3(d). Their correspondence were also noted and discussed. In this study, the presence of EPBs were inferred by checking for TEC depletions and their correspondence with enhanced S4, fluctuation of ROT and ROTI values after sunset. Since not all TEC depletions leads to formation of EPBs, the threshold for TEC depletions were set at TEC depletion depths ≥7 TECU. The TEC depletion depths were to correspond with enhanced S4 index and increased fluctuations of ROT and high ROTI values ≥ 1.5 TECU/min after local sunset for each selected quiet and storm day. The TEC depletion depths and S4 index plots; TEC depletion depths and ROTI plots and S4 index and ROTI plots in Fig. 1 , 3(c) and 3(d) were analyzed with an aim of obtaining the days which met the set threshold for EPB occurrence. September 2013 were attributed to increased solar activity since the days were within the equinoctial period. Increased solar activity leads to photoionization of neutral molecules through Solar Extreme Ultra-Violet (SEUV) radiation in the ionosphere. The smallest TEC depletion depths were on 26 th June 2013, 4 th July 2013 and 24 th July 2013 and were attributed to low solar activity since the days were within the June solstice period. The TEC depletion depths were seen to correspond with enhanced S4 values of more than 0.2 after local sunset for most selected quiet days of 2013 as indicated by Fig. 1(a). In Fig. 1 Fig. 1(c). In Fig. 1(d) Fig. 1(d). Generally, the TEC depletion depths corresponded well with enhanced S4 values after local sunset for most selected quiet and storm days of the years 2013 and 2014 as indicated in Fig. 1(a), 1(b), 1(c) and 1(d). Higher amplitude scintillation values were seen for the selected days of March and April for both years. This is because, the eastward electric field during March and April was greater than for the other months. These variations of the eastward electric field was attributed to the zonal electric field in the equatorial ionosphere. It was also noted that the selected quiet days of the years 2013 and 2014 had larger TEC depletion depths than the selected storm days of the years 2013 and 2014. This might be due to the variation in the ionospheric behaviour during quiet period and storm period. During storm period, the ionospheric behaviour is controlled by several competing dynamics including the effect of PPEF, DDEF and a reduction in the electron density due to increased recombination rates.   In Fig. 2(c), TEC depletion depth of about 16 TECU was noted with a corresponding ROTI of 2.1 TECU/min on 11 th November 2013. 24 th April 2013 had a TEC depletion depth of 15 TECU with a corresponding ROTI of 1.8 TECU/min. 5 th August 2013 had a TEC depletion depth of 13 TECU with a corresponding enhanced S4 index of 3.5 TECU/min while 1 st June 2013, 6 th July 2013 and 10 th July 2013 had TEC depletion depths of 4 TECU, 5 TECU and 3 TECU respectively with a corresponding ROTI of 0 TECU/min. In Fig. 2(d), TEC depletion of depletion depth of 18 TECU was noted with a corresponding ROTI of 3.4 TECU/min on 1 st March 2014. 4 th May 2014 had a TEC depletion depth of 18 TECU with a corresponding ROTI of 2 TECU/min. 12 th April 2014 had a TEC depletion depth of 15 TECU with a corresponding enhanced ROTI of 2.2 TECU/min while 7 th June 2014 had TEC depletion depth of 3 TECU with a corresponding ROTI of 0 TECU/min. Increased TEC depletions lead to increased fluctuation of ROT and hence higher ROTI values after sunset. In this study, TEC depletion depths had a positive correspondence with ROTI where larger TEC depletion depths were seen to correspond with higher ROTI values after local sunset for most selected quiet and storm days of 2013 and 2014. This is in consistency with studies done by DasGupta et al., (2007) which showed that large TEC depletion depths resulted in larger ROTI values after sunset in both geomagnetically quiet and disturbed conditions. The variation of TEC depletion depths and ROTI for the few selected quiet and storm days resulted from variation in development of the EIA and geomagnetic activity level. As much as the TEC depletion depths corresponded well with increase in ROTI after local sunset for most days as shown in Fig. 2(a) Fig. 2(d). The lack of positive correspondence of TEC depletion depths and ROTI values after sunset for these days was attributed to the presence of short-lived peaks on ROT which were smoothened (detrenched) before calculating and plotting ROTI. A study by Jacobsen, (2014) revealed that when comparing different statistical studies using ROTI, smoothening of the short-lived peaks on ROT is important in obtaining exact ROTI values.  A close comparison of ROTI and S4 in Fig. 3(a), 3(b), 3(c) and 3(d), indicates that a rise in ROTI values which to some extend correlate with phase scintillation corresponded well with enhanced S4 index after local sunset for most of the selected quiet and storm days of the years 2013 and 2014. However, a few of the selected quiet and storm days of 2013 and 2014 did not show a direct correspondence between ROTI and the enhanced S4 values. This is because as much as amplitude scintillation index is able to show how disturbed the ionosphere is, in most cases the data used to compute ROTI does not cover the scale sizes required to make a complete comparison with S4 index (Beach & Kintner, 1999). Jacobsen, (2014) observed that ROTI index is seen not to contain information about the irregularity size but it only provides information on the existence of the irregularities within the range limited by the sample rate and the measurement interval. This might be the reason why there was no direct correspondence between S4 and ROTI for some of the selected quiet and storm days of 2013 and 2014 in this study.

Inferring occurrence of EPBs using TEC depletion, enhanced S4 index, ROT fluctuation and ROTI
It should be noted from Fig. 1(a), 1(b), 1(c), 1(d), 2(a), 2(b), 2(c), 2(d), 3(a), 3(b), 3(c) and 3(d) that TEC depletion depths corresponded well with enhanced S4 index between 16:00 and 20:00UT for most selected quiet and storm days of 2013 and 2014. These TEC depletion depths also corresponded well with higher ROTI values between 16:00 and 20:00 UT for most selected quiet and storm days of 2013 and 2014. The higher ROTI values between 16:00 UT and 20:00 UT resulted from electron density depletions in the ionosphere which a rise after sunset when the eastward electric field is enhanced, hence increasing the upward plasma drift to higher altitudes. Fejer et al., (1999) observed that the evening vertical drift and pre-reversal enhancement (PRE) plays an important role in the occurrence of post-sunset plasma irregularities since the onset or inhibition of these post-sunset plasma instabilities is majorly controlled by the variability of the PRE. In this study, the occurrence of EPBs were inferred for any selected quiet or storm day in which the enhancement of S4 corresponded well with TEC depletions of depletion depth ≥ 7 TECU, increased ROT fluctuations and higher ROTI values ≥ 1.

Yearly EPB occurrence for the years 2013 and 2014
The EPB occurrence for the selected quiet and storm days of the years 2013 and 2014 were analyzed to obtain the percentage occurrence in both quiet and storm period for each year as shown in Fig. 4. These percentage occurrences for the years 2013 and 2014 were defined as a ratio of the number of days when EPBs were inferred and the total number of selected quiet and storm days under study.  . It was noted that the percentage of EPB occurrence was higher in the storm period than in the quiet period. These results conform with those from previous studies reported by Abdu et al, (2003); Kil and Paxton, (2006); Li et al., (2006) and Basu et al., (2007) where the occurrence of EPBs were found to be enhanced by geomagnetic activity. Nakata et al., (2018) observed that most EPBs occurred during high geomagnetic activity period since the PPEF which is enhanced during storms favors the occurrence of EPBs during such periods. When geomagnetic storms occur, the ionospheric electric fields at the polar (high latitude) region penetrate towards the low latitude (Nakata et al., 2018). This penetrating electric field called PPEF (Basu et al., 2007;Kikuchi et al., 2008) (Kelley et al., 1979;Kikuchi et al., 2008) which increases the opposite polarity of the electric field hence inhibiting the occurrence of EPBs. This electric field is called DDEF (Blanc & Richmond, 1980;Bhattacharrya et al., 2019). Besides the effects of PPEF and DDEF, the occurrence of EPBs is also affected by storm winds which extend from high latitude regions to low latitude regions. Storm winds lift the ionized regions and modify the atmospheric composition of the equatorial ionosphere, hence affecting the EIA, PRE, VTEC and ROTI. The percentage occurrence of EPBs during storm days is therefore determined by the competing effects of PPEF, DDEF and the storm winds since the DDEF effect is usually delayed and lasts longer than PPEF (Richmond et al., 2003). During the quiet days, the interplanetary magnetic field (IMF) is northward and therefore the enhancement of the eastward electric field brings occurrence of EPBs (Cherniak et al., 2019). It should also be noted that the occurrence of EPBs over Kisumu, Kenya during this period might have been strongly influenced by neutral winds dynamo which is driven by the Eregion neutral winds which are usually generated by convection and flow from West to East in the evening in Kenya (Mukabana & Pielke, 1996) and leads to production of electric field enhancement (Omondi et al., 2014). Neutral winds are driven by pressure gradient of the neutral atmosphere as a result of solar heating (Otsuka, et al., 2006).

Seasonal occurrences of EPBs for the years 2013 and 2014
The  It was noted that the percentage of EPB occurrence was higher during the equinoctial period (March, April, August and September) than the solstice period (June, July, November and December) in the years 2013 and 2014. This is because during equinoctial period, the solar terminator is aligned with the local geomagnetic field lines and hence there is increased photoionization resulting from high SEUV radiation during the period, leading to formation of irregularities. Studies by Sahai et al., (2000) and Huang et al., (2002) have shown that the percentage of EPB occurrence increases during periods of high solar activity. The results obtained in this study conform with those obtained by Paznukhov et al., (2012) and Magdaleno et al., (2017) where highest occurrence of EPBs were observed during equinoctial months. The seasonal variation of EPB occurrence where equinoctial period had higher percentage EPB occurrence while solstice period had lower percentage EPB occurrence was attributed to the effect of the PRE of the eastward electric field which induces increase in vertical E x B drift (Abdu et al., 1981;Batista et al., 1996;Murkherjee et al., 2010). The equinoctial period (March, April, August and September) and the November solstice period (November and December) have larger daytime E x B drift velocities than the June solstice period (June and July). June solstice had the lowest percentage EPB occurrence and this was due to the lower E x B vertical drift during the June solstice resulting from reduced eastward electric field. These results conform with those obtained by Cherniak et al., (2019) where the lowest percentage of EPB occurrence was in June solstice. Fejer et al., (2008) showed that the vertical drift associated with PPEF is upward during daytime and downwards during nighttime in all seasons and they reach peak seasons during the June solstice. Consequently, the DDEF has a downward drift during daytime and an upward drift during nighttime and has been shown to increase with solar flux and are therefore largest during equinox and smallest in June solstice.

Conclusions
We have investigated the occurrence of EPBs over Kisumu, Kenya for a few selected quiet and storm days of 2013 and 2014 using TEC data obtained from SCINDA-GPS. The obtained results showed that TEC depletions and enhanced S4 index corresponded well with increased ROT fluctuations and higher ROTI values between 16:00UT and 20:00UT for most selected quiet and storm days and was used as a proxy for inferring EPB occurrence. The storm period exhibited a higher percentage of EPB occurrences than the quiet period for the 2013 and 2014 study period. The higher EPB occurrence during storm period was attributed to PPEF which favors development of EPBs during storm period by enhancing the eastward electric field which enhances the vertical E x B drift.
On the seasonal variation of EPBs, the results showed that the equinoctial period (March, April, August and September) had a higher percentage of EPB occurrence than the solstice period (June, July, November and December) for the years 2013 and 2014, which is in agreement with most ground-based observations. Furthermore, the asymmetry of EPB occurrence between equinoxes and between solstices was also observed where the March equinox had a higher percentage EPB occurrence than the September equinox for both years while November solstice had a higher percentage EPB occurrence than the June solstice for the year 2013. However, the year 2014 showed a similar solstice symmetry by having the same percentage EPB occurrence for June solstice and November solstice. Generally, the year to year percentage EPB occurrence showed a higher EPB occurrence in the year 2013 than in the year 2014. In conclusion, this study confirms the occurrence of EPBs over Kisumu, Kenya during both geomagnetically quiet and geomagnetically disturbed days for the years 2013 and 2014.