Spatial gradient of total electron content ( TEC ) between two nearby stations as indicator of occurrence of ionospheric irregularity

The relation between the occurrence of ionospheric irregularity and spatial gradient of total electron content 1 (TEC) during the post-sunset hours over the equatorial region is studied. The ionospheric irregularities could pose se2 rious challenges to satellite-based navigation and positioning applications when trans-ionospheric signals pass through 3 them. Different instruments and techniques have been applied to study the behavior of these ionospheric irregularities. 4 In this study, the Global positioning system (GPS) based derived total electron content (TEC) was used to investigate 5 the spatial gradient of TEC between two nearby stations as indicator of occurrence of ionospheric irregularity over the 6 East African sector. The gradient of TEC between the two stations (ASAB: 4.34◦ N, 114.39◦ E and DEBK: 3.71◦ N, 7 109.34◦ E, geomagnetic) located within the equatorial region of Africa were considered in this study during the year 8 2014. The rate of change of TEC based derived index (ROTIave) is also used to observe the correlation between the 9 spatial gradient of TEC and the occurrence of ionospheric irregularities. The result obtained shows that most of the 10 maximum positive/depletions in the spatial gradient of TEC observed in March and September equinoxes are more pro11 nounced between 19:00 LT 24:00 LT as the large-scale ionospheric irregularities do. Moreover, the observed spatial 12 gradient of TEC shows two peaks (in March and September) and they exhibit equinoctial asymmetry where the March 13 equinox is greater than September equinox. The enhancement in the spatial gradient of TEC and ROTIave during the 14 evening time period also show similar trends but lag 1-2 hrs from the equatorial electric field (EEF). The spatial gra15 dient of TEC between the two nearby stations could be used as an indicator of the occurrence of ionospheric irregularities. 16 17


Introduction
The ionosphere is a dispersive medium in which radio signals are refracted depending upon signal frequency and ionospheric density.After sunset, the ionospheric plasma interchange instabilities present in the equatorial/low-latitude ionosphere generate large-scale depletions in the ambient electron density which leads to the formation of plasma density irregularities that affect radio communication and navigation system (Basu and Basu, 1981).The generation of the plasma irregularities can be related to the lack of plasma production immediately after sunset and the fast recombination rate in the E-region ionosphere, which results in a steep gradient in electron density.In the evening hours, the large enhancement of F region vertical plasma drift attest to the presence of enhanced eastward electric field is also another parameter which controls the generation of plasma density irregularities (Fejer, 1991;Fejer et al., 2008).This prereversal enhancement in the vertical plasma drift moves the F region to higher altitudes (Abdu et al., 2009).When the altitude of F-region is high enough to overcome recombination effects, the Rayleigh-Taylor instability mechanisms initiates a growth in plasma fluctuations.Kelley (2009) reported that the existence of equatorial plasma bubbles (EPB) is attributed to the instability of the Rayleigh-Taylor (R-T) plasma which is triggered by the intensification of the eastward equatorial electric field just before its reversal.The R-T instability mechanism is considered the primary mechanism responsible for the generation of ionospheric plasma density irregularities or plasma bubbles in equatorial and low-latitude region (Rao et al., 2006;Fejer et al., 1999).A perturbation at the base of the F-region, such as that caused by a gravity wave, can also lead to the growth of the instability, resulting in the formation of plasma bubbles, that is, structures with depleted plasma density that produce ESF (Abdu, 2001;Abdu et al., 2009;Kelley, 1989).
Several studies have indicated that ionospheric irregularities show strong diurnal, seasonal, geographic and solar cycle variations (Chu et al., 2005;Kintner et al., 2007).Longitudinal and geomagnetic activity dependency of ionospheric irregularities over the different equatorial region has also been reported (Burke et al., 2004;Susnik and Forte, 2011;Paznukhov et al., 2012;Oladipo and Schuler, 2013a;Seba and Tsegaye, 2015).Oladipo and Schuler (2013a) studied large-scale ionospheric irregularities at Franceville, Gabon, an equatorial station in the African sector for a year (2001/2002) during the last high-solar activity.Their results showed the seasonal dependency of the occurrence of ionospheric irregularities.
Furthermore, the study of Seba and Tsegaye (2015) showed seasonal and annual scintillation characteristics over Bahir Dar, Ethiopia.Also, they indicate that the high-level intensity of scintillation occurred in March and April, and was low on Solstice days.Tsunoda (1985) proposed that the seasonal and longitudinal occurrences of the plasma bubble are most frequent when the solar terminator is most closely aligned with the geomagnetic meridian.
In the past years, several techniques both from the ground and space-based instruments have been used to study the occurrence of ionospheric irregularities.The widely used instrument was the GPS scintillation index, S4.In the recent years, GNSS (Global Navigation Satellite System) based technique has become an important tool for the study the behavior of ionospheric irregularities (Pi et al., 1997;Nishioka et al., 2008) because of its growing application in civilian and military applications.Using ground-based GPS measurements over African equatorial and low-latitude regions, the seasonal occurrence of the ionospheric irregularities has been studied by the several workers (Olwendo et al., 2013(Olwendo et al., , 2016;;Ngwira et al., 2013;Seba and Tsegaye, 2015;Oladipo and Schuler, 2013b;Oladipo et al., 2014;Mungufeni et al., 2016).
The ionospheric irregularities have adverse effects on trans-ionospheric signals.Therefore, forecasting the probability of occurrence of ionospheric irregularities has become the topic of major research and has drawn the attention of the scientific community.Due to these effects, modeling ionospheric irregularities has been carried out by several researchers (Aarons, 1985;Scherliess and Fejer, 1999;Abdu et al., 2003;Iyer et al., 2006;Mungufeni et al., 2015;Taabu et al., 2016).Aarons (1985) developed an analytical equation to yield scintillation excursions based on a series of observations at 254 MHz taken at Huancayo, Peru, as a function of different parameters.Abdu et al. (2003) developed a regional model for the quiet time spread-F distribution in the Brazilian longitude sector.Iyer et al. (2006) developed an empirical model of magnetic quiet time scintillation occurrence at Indian equatorial and low-latitudes.Mungufeni et al. (2015) developed an empirical model for the probability of occurrence of ionospheric irregularities during geomagnetic quiet conditions over the African equatorial region.Moreover, Taabu et al. (2016) predicts ionospheric scintillation over East African region using neural network during the ascending phase of sunspot cycle 24.
The evening prereversal enhancement (PRE) of the vertical plasma drift has important consequences for the Appleton density anomaly and the stability of the nighttime ionosphere.Studies show that the occurrence of ESF is dependent on an increase with maximum E × B drift velocity (Whalen, 2001).Using multi-instrument observation, Dabas et al. (2003) suggested that the equatorial electrojet (EEJ) is a useful parameter for predicting the EPBs development.The PRE in the eastward electric field component near sunset in the equatorial ionosphere is a phenomenon that has been well reported and studied (see., Kelley, 2009).Several theories have been proposed to explain the PRE (Rishbeth, 1971;Farley et al., 2008;Haerendel and Eccles, 1992).Low-latitude/equatorial F-region vertical plasma drifts have been measured extensively using coherent and incoherent scatter radar measurements at the Jicamarca Radio Observatory and they have also been inferred from daytime magnetometer (e.g., Anderson et al., 2004) and nighttime ionosonde observations (e.g., Abdu et al., 1981).It has been suggested that the longitudinal gradient of integrated Pederson conductivity in the E-region at sunset time can play a positive role in strengthening the evening pre-reversal enhancement magnitudes (Tsunoda, 1985;Batista et al., 1986).However, over African longitude sector, it may not be easy to have the longitudinal gradient of electron density as ionosondes are not available in nearby locations and see the correlation between electron density gradient and occurrence of irregularities.A closely found GPS receivers may be a good option to investigate the relation between longitudinal gradient of total electron content derived from GPS receivers and occurrence of ionospheric irregularities.
In the present study, we investigate the longitudinal gradient of total electron content derived from two close by GPS stations over Ethiopia (Debark) and Eritrea (Asab) as indicator of occurrence of ionospheric irregularities, and discuss the probability of occurrence of ionospheric irregularities.The relation between the daytime eastward equatorial electric field derived from the equatorial electric field (EEF) model and the daytime equatorial electrojet derived from magnetometer measurements will be discussed.

Spatial gradient of T EC
where d represents the separation distance between the two stations.
∆H values (∆H refers to the deviation of the horizontal component of the earth's magnetic field H from its mean night time level) at Addis Ababa and Adigrat have also been used for this study in computing the equatorial electrojet (EEJ).
Table 1 gives the list of all the stations for which data has been used in this study.The other data source used in this study was the Real-time model of the Ionospheric Electric Fields (http://geomag.org/models/PPEFM/RealtimeEF.html).We have used this model to observe the relation between the equatorial electric field (EEF) and the spatial gradient of TEC between the two receivers.The Prompt Penetration Electric Field Model (PPEFM) (Manoj and Maus, 2012) is a transfer function model which to models the daily variations coming from the solar wind, To do this, ground based magnetometer stations one located at magnetic equator and another one at (6 • − 9 • ) off-equator (Rastogi and Klobuchar, 1990;Anderson et al., 2002;Yizengaw et al., 2014)  respectively.The difference of the horizontal component (H) of geomagnetic field of these station, ∆H gives the equatorial electrojet contribution which is a proxy to daytime electric field.The connection between the occurrence of ESF during evening sector preceded by the rapid rise in F-layer and the strength of EEJ before sunset has been presented (Kelley, 2009;Burke et al., 2004).Sreeja et al. (2009) reported observational evidence for the plausible linkage between the EEJ electric field variations with the postsunset F-region electrodynamics.Furthermore, Hajra et al. (2012) indicate that the afternoon/evening time variation of eastward electric field as revealed through EEJ seems to play dominant role in dictating postsunset resurgence of EIA and consequent generation of spread-F irregularities.Once the relation between equatorial electric field model and is ∆H determined, and the model is found to be reliable the equatorial electric field derived from the model will be used in this study to explain the gradient of TEC and occurrence of irregularities.
We also used rate of change of TEC derived index (ROT I ave ) to observe the presence of ionospheric irregularities.The time variation of TEC also known as rate of change of TEC (ROT) and its derived indices are a good proxy for the phase fluctuation, which is a measure of large-scale ionospheric irregularities (Aarons et al., 1997).These kinds of indices can be used to characterize all the known features of equatorial spread F (ESF) (Mendillo et al., 2000).The rate of change of TEC (ROT) is given by where i is the visible satellite and k is the time of epoch and ROT is in units of TECU/min.The ROTI was introduced by over a 5-min period.Usually, ROTI > 0.5 TECU/min indicates the presence of ionospheric irregularities at scale lengths of a few kilometers Ma and Maruyama (2006).
where ROT can be obtained from Eq. ( 2).Oladipo and Schuler (2013b)  Nigeria.In this study, the rate TEC fluctuation index (ROTI) (Pi et al., 1997;Oladipo and Schuler, 2013b;Oladipo et al., 2014) were used to observe the occurrence of irregularities the stations.
ROT I ave (0.5hr) = 1 where n is the satellite number, 0.5hr is half an hour (0, 0.5, 1,..  Mendillo et al., 2001;Valladares et al., 2001Valladares et al., , 2004)).Hence, in this study we have used the equatorial electric field derived from EEFM model to show its effect on the post-sunset enhancement of the spatial gradient of TEC and explain the possibility that it could be used as indicator of occurrence of ionospheric irregularities.over Asab.In the post-sunset hours, after 18:00 LT, the pattern of the two parameters shows a similar trend.The enhancement in the gradient of TEC and occurrence of irregularities in the post-sunset period could be explained by the presence of ionospheric electrodynamics.The post-sunset period electrodynamics is influenced by F-region dynamo which is governed by a longitudinal gradient of the electrical conductivity and thermospheric zonal wind (Crain et al., 1993).Anderson et al. (2004) showed that the scintillation activity is related to the maximum E × B drift velocity between 1830 and 1900 LT.
It has been reported that the eastward component of electric field manifested by the vertical plasma drifts over equator and intensified around/shortly after sunset before reversing to westward is one of the most important parameters responsible for driving many interesting ionospheric phenomena, like the Appleton density anomaly and the stability of the nighttime ionosphere (e.g., Horvath and Essex, 2003;Abadi et al., 2015).In the evening sectors, the vertical drift enhancement is of particular significance as it is the major drivers for the generation of ESF (Farley et al., 1970;Woodman, 1970;Basu et al., 1996;Fejer et al., 1999;Martinis et al., 2005).Tulasi Ram et al. (2006) reported that the rapid enhancement of postsunset of the zonal electric field leads to a large vertical plasma drift (E ×B), thereby lifting the F-layer to higher altitudes to the Ground-Based Augmentation System (GBAS) and they attribute the large ionosphere spatial gradient to the TEC enhancements and the ionosphere irregularities (Rungraengwajiake et al., 2015;Saito and Yoshihara, 2017).An ionosphere gradient of 518 mm/km was discovered, generated by a plasma bubble (Saito and Yoshihara, 2017).(2008).The magnitude of peak vertical drift is known to control the seasonal and day-to-day variations in the occurrence of equatorial spread F (Manju et al., 2009;Tulasi Ram et al., 2006).where the magnetic field lines aligned with a geographic meridian (Burke et al., 2004;Tsunoda, 2005Tsunoda, , 2010)).The seasonal variation of ionospheric irregularities exhibit an equinoctial asymmetry in its occurrence especially at the two peaks (i.e., in March and September), where March equinox is greater than that of September equinox.Based on a few station observations, earlier studies indicated that equinoctial asymmetry in the occurrence of L-band scintillations may be attributed to differences in the meridional winds during two equinoxes (e.g., Nishioka et al., 2008;Maruyama et al., 2006;Otsuka et al., 2006).Nishioka et al. (2008) have shown the occurrence characteristics of plasma bubbles using GPS TEC obtained all over the globe and found equinoctial asymmetry in the occurrence of plasma bubbles in the Asian region.They have suggested that equinoctial asymmetry could be due to asymmetric distribution of integrated conductivities during these equinoctial periods.Using three ionosondes observations Maruyama et al. (2006) reported that meridional wind is the key factor for the equinoctial asymmetry.Using multi-instrument observations, Sripathi et al.
(2011) examined the equinoctial asymmetry in scintillation occurrence in the Indian sector and proposed the asymmetry in the electron density distribution and meridional winds as possible causative mechanism.Manju (2013) also reported equinoctial asymmetry in ESF occurrence and discussed the possible role of asymmetric meridional winds.Dasgupta et al. (1983) studied the equinoctial asymmetry in equatorial and low latitude F region ionization distribution and attributed it to neutral composition changes.Manju and Haridas (2015) observed significant asymmetry in the threshold height between the vernal equinox and autumn equinox and underlines the distinct differences in the role of neutral dynamics in ESF triggering during the two equinoxes.The local time and seasonal trends of occurrence of ionospheric irregularities observed in this study are similar to those reported in the previous studies (Aarons, 1993;Basu et al.;Olwendo et al., 2013;Amabayo et al., 2014;Seba and Tsegaye, 2015).The occurrence of equatorial F-region irregularity has been studied, and the frequency of occurrence of equatorial spread F has been found to be higher during solar maximum (Abdu et al., 1998;Mendillo et al., 2000).Similarly, Susnik and Forte (2011) In terms of local time, monthly, and seasonal behavior the enhancement in the spatial gradient of TEC and occurrence of ionospheric irregularities show similar trends.And, it is evident from the above result that the spatial gradient of TEC between two nearby stations where the two receivers lie nearly along the same latitudes could be used as an indicator of the occurrence of large-scale ionospheric irregularities.In the current study, the minimum distance between the two stations and the threshold value of the gradient of TEC that could indicate the probability of occurrence of ionospheric irregularities has not been seen and needs further investigation.

Conclusions
In this study, we present the possibility that the spatial gradient of TEC between two nearby stations (ASAB and DEBK) over East African sector could be used as indicator of the occurrence of large-scale ionospheric irregularities.The following features were observed from the study.Most of the daily maximum positive/negative value of the spatial gradient of TEC was observed in the pre-midnight and post-midnight period.In terms of seasons, months and local times, the maximum positive of the spatial gradient of TEC and ROT I ave show similar tends.Both of them show enhancement during the months of March and September equinoxes.Seasonal asymmetry was also observed in both parameters, where March equinox was greater than September equinox.Peak values in the spatial gradient of TEC and ROT I ave was observed about 1-2 hrs later from post-sunset enhancement of equatorial electric field (EEF).There is also a case where the depletions of the gradient of TEC shows similar trends as the positive maximum value of the TEC gradient.Based on the above results, the spatial gradient of TEC between the two nearby stations which lies along the same geographic and Ann. Geophys.Discuss., https://doi.org/10.5194/angeo-2018-131Manuscript under review for journal Ann.Geophys.Discussion started: 7 December 2018 c Author(s) 2018.CC BY 4.0 License.which are mapped from interplanetary electric field (IEF) data.Eight (8) years IEF data from the ACE satellite, radar data from JULIA, and magnetometer data from the CHAMP satellite was used to derive the transfer function.Using the real-time data from ACE satellite, the transfer function models the current variations in the equatorial ionospheric electric fields.The model takes time and location as input parameters and calculates the best estimates of the equatorial electric field.In the present study, we have used only the background quiet-time electric field.Recently, Nayak et al. (2017) used the real-time model of electric field to observe the influence of prompt penetration electric field (PPEF) on the occurrence of ionospheric irregularities during 17 March 2015 geomagnetic storm over Indian and Taiwan longitudes.This model has not been applied yet to explain the electrodynamic phenomena over African low-latitude region.To use this model in this region, we first observed the relation between the daytime of quiet time equatorial electric field (EEF) and equatorial electrojet (EEJ), which has a direct relation with E × B vertical drift.
Figure 1apresents typical example of the diurnal variation of equatorial electric field and equatorial electrojet on 26 March 2012 while Fig.1bshows the correlation between the equatorial electrojet derived from (∆H) and equatorial electric field (EEF) derived from equatorial electric field model in the daytime period (07:00 to 17:00 LT) for some of selected quiet days of month of the year 2012.The equatorial electric field is a key factor in determining the dynamics and structure of the low latitude ionosphere(Fejer, 2011).For the first time it was detected by the Jicamarca (11.95 • S, 76.87 • W) incoherent scatter radar (ISR) and the Jicamarca Unattended Long-Term studies of the Ionosphere and Atmosphere (JULIA) system during the period from 1998 to 2008.However, there were no direct continuous electric field observations from ground based and when available, mostly limited to the daytime.Over African region there is no ground based measurements of the zonal electric fields.Anderson et al. (2002) used the ∆H deduced from magnetometers and vertical plasma drifts

Figure 1 .
Figure 1.(a) Diurnal variation of Equatorial Electric field Model (EEF) and ∆H and (b) Day-time correlation between the equatorial electrojet (EEJ) and quiet-time equatorial electric field model (EEF) for quiet days of month of year 2012.

Figure 2 .Figure 3 .
Figure 2.An example of comparison of equatorial electric field model (EEFM) and the spatial gradient of TEC on a) 30 March 2014, b) 10 April 2014, c) 20 September 2014 and b) 10 October 2014.

Figure
Figure 4a and b, respectively, show the annual plots of phase fluctuation at Asab and Debark indicated by ROT I ave index during the year 2014.The ROT I ave values are indicated in color scale.The occurrence of ionospheric irregularities at the two stations, as indicated by ROT I ave value, is a post-sunset phenomenon.The implication of this is that the large-scale ionospheric irregularities, which are responsible for the scintillation of transionospheric signals at GNSS frequencies, are more pronounced during post-sunset hours.The observed phase fluctuation shows monthly variations and there is also a seasonal trend in the occurrence of ionospheric irregularity (see., Fig. 5).Maximum irregularities were observed in March equinox months and minimum in June/July.During this period, the occurrence of phase fluctuation showing irregularities is observed mainly between 19:00 LT and 24:00 LT.As stated by Oladipo and Schuler (2013b), the value of ROT I ave > 0.4 shows a presence of ionospheric irregularity.

Figure
Figure4cindicates the annual plots of the spatial gradient of TEC between the two nearby GPS stations, Debark(DEBK)    and Asab (ASAB) during the year 2014.As already stated in section (2), the two stations are located nearly on the same geographic and geomagnetic latitudes with a longitudinal separation of about 5 • or corresponding spatial separation of about 535.7 km.In the computation of the spatial gradient of TEC (Using Eq. 1), negative and positive values of the gradient of TEC were observed.From the figure, the maximum positive/negative value of the gradient of TEC was observed mostly during the post-sunset (18:00 -24:00 LT) and postmidnight (24:00 -06:00 LT) period.Equation (1) was applied to all days of the year 2014 in computing the spatial gradient of TEC.Out of total of observed daily maximum value of gradient of TEC, about 194 days (in percent about 53 %) of them fall in this time period intervals.There was also a case where the maximum positive and depletions in the value of gradient of TEC were observed in the early morning period.The positive enhancement in the gradient of TEC observed during post-sunset and postmidnight showing monthly and seasonal variations are the other features noticed from Fig.4c.The values of the spatial gradient of TEC observed on equinoctial months was greater than Solstice months.Equinoctial asymmetry in the occurrence of TEC gradient was also observed, where March equinox is greater than September equinox.Similarly, the depletions of the spatial gradient of TEC are mostly observed during post-sunset and post-midnight periods as the maximum positive TEC gradient.The depletions

Figure 4 .
Figure 4. a) Diurnal variation of the spatial gradient of TEC over ASAB and DEBK , b) Daily maximum value of the spatial gradient of TEC variation, c) Diurnal variation of ROT Iave over ASAB station and d) Daily maximum value variation of ROT Iaave over ASAB station in the year 2014

Figure
Figure4dand e present the daily maximum phase fluctuation index, ROT I ave , over Asab and Debark stations, respectively and Fig.4fshows the daily maximum of the gradient of TEC during the year 2014.It is clearly observed from the figures that the enhancement in ROT I ave and gradient of TEC shows monthly and seasonal variations, and the equinoctial asymmetry was also observed.To identify whether the spatial gradient of the total electron content (TEC) between the two nearby stations indicate the occurrence probability of ionospheric irregularity, the rate of change of TEC derived index (ROT I ave ) described in section (2) expressed by Equation (4) and the spatial gradient of TEC between the two receivers were compared.The daily maximum value of the spatial gradient of TEC between the two stations shows similar trends with the daily maximum value of ROT I ave observed over ASAB and DEBK stations.The trend they show has similarity with the time of occurrence of maximum enhancement, monthly and seasonal variations.Moreover, the seasonal variation observed in both variables exhibits equinoctial asymmetry, where the March equinox was greater than September equinoxes.The mechanism of generation of the enhancement in vertical drift just after sunset was detailed byFarley et al.

Figure 5
Figure 5 presents the percentage occurrence of ionospheric irregularities over ASAB in the year 2014.The percentage occurrence of irregularities was calculated by counting the number of days in a month with ROT I ave ≥ 0.4 TECU/min and dividing by the number of days in a month for which data are available, and multiplied by 100 %.The two peaks of irregularity seasons occur around the middle of the equinoxes (i.e., in March and September) were observed at this station.Previous studies indicated that the seasonal and day-to-day variations in the occurrences of EPB depend on the geographical longitude and latitude.The maximum occurrence of EPB was observed during the equinoxes at longitudes

;Figure 5 .
Figure 5. Percentage of occurrence of ionospheric irregularities over ASAB station during the year 2014 based on ROT Iave index.

Table 1 .
Location information and the type of data used in this study.
Oladipo et al. (2014))ndillo et al. (2000)to obtain a new index called ROT I ave index given in Eq. (4).ROT I ave index is the average of ROTI over 30 min interval for a satellite and then average over all satellites in view.The index gives average level of irregularities over half an hour.Recently,Oladipo et al. (2014)used ROT I ave to demonstrate and capture the level of ionospheric irregularity over