The features of the low-latitude ionosphere are quite unique. During the daytime, a double-peaked ionization structure appears over the low-latitude region, a phenomenon often referred to as the equatorial ionization anomaly (EIA). The EIA is normally explained in terms of the plasma fountain theory . The daytime E-region eastward electric field in combination with the nearly horizontal magnetic field of Earth generate a large vertically directed E×B drift force at the dip equator that raises the plasma to higher altitudes. The raised plasma diffuses away from the geomagnetic equator under gravity and pressure gradient forces along the equipotential magnetic field lines to form ionization peaks at dip latitudes ∼±15∘ and a trough that extends over the dip equator . Prior to the electric field turning westwards at night, it is enhanced (pre-reversal enhancement – PRE), resulting in plasma uplift into regions of low recombination. Associated with the electron density at the EIA enhancement is a density gradient instability of the Rayleigh–Taylor (RT) type which creates a spectrum of plasma irregularities that fill the post-sunset low-latitude ionosphere . The EIA and the PRE vary with location, solar activity and season, even on daily basis. These variations make it difficult to predict the characteristics of the low-latitude ionosphere.

The state of the ionosphere is of great importance in space-based navigation systems such as the global navigation satellite systems (GNSS). The total electron content (TEC) is of particular interest to users of GNSS systems. For many practical purposes in the GPS, the desired ionospheric parameter is the TEC. This is because many of the effects on transionospheric satellite links (e.g., time delay, polarization, Faraday rotation and Doppler shift) are related to the TEC in one way or another . The low-latitude ionosphere exhibits the highest values of the TEC globally. Therefore, pronounced ionospheric effects are experienced by radio signals transiting the low-latitude ionosphere. Understanding the low-latitude ionospheric dynamics in a bid to forecast its day-to-day conditions is key for advancement of space technology and the improvement of GNSS accuracy.

Ionospheric variability over the low-latitude region of Africa, based on TEC analysis, has been reported before (e.g., ). From these studies, the diurnal, seasonal, disturbed and quiet-time TEC characteristics over the region have been revealed. However, these analyses made use of TEC data of either the same solar phase or the same solar cycle. Now with a relatively longer record of data in the achieves, it is imperative to extend these studies to the long-term TEC characteristics over the African low-latitude region for practical applications.

A common approach to TEC prediction is through modeling. Various TEC models (e.g., ) have been developed; however, many of these models are limited in geographical extent. A widely used model to describe the global TEC climatology is the International Reference Ionosphere (IRI) model . The IRI is an empirical model synthesized from global data sets comprised of ionosonde, radar and in situ measurements . Averaging and smoothing applied when deriving the model coefficients may limit its accuracy in capturing peculiar features such as the TEC variability in the EIA region. Under such circumstances, regional models are superior in characterizing the background TEC.

Long term trends in ionospheric parameters are indicative of the deviation in the ionospheric parameters from their background values. Ionospheric trends are important in understanding the changes in Earth's energy balance . Various studies (e.g., ) have reported on long-term trends in ionospheric parameters derived from ionosonde data. A conclusion from these studies is that trends in the F2-layer critical frequency (foF2) and F2-layer maximum electron density height (hmF2) are negative. Some studies on ionospheric trends have also revealed latitudinal dependence of these trends . , using a database of global ionospheric maps (GIMs), reported that global TEC trends are positive and are dependent on the geomagnetic latitude. Also cases of negligible or no trends in the TEC have been observed. For instance, results obtained by show a weak negative trend or no trend in ionospheric TEC. Despite the various studies on trends of different ionospheric parameters, those relating to TEC remain limited, hence the question on the nature of ionospheric TEC trends still needs to be answered. There is a need to investigate whether TEC has a negative , positive or no trend. The objective of this paper is therefore twofold: first to attempt to model the low-latitude TEC, and second to estimate trends in the variation of the ionospheric TEC over the African low-latitude region using actual TEC measurements by means of regional GPS receivers and data from the GIMs.

The International GNSS Service (IGS) operates a number of GPS ground-based receivers over the African low-latitude region. In this study, data were obtained from one of the IGS receivers located at Malindi, Kenya, which archived data from 1995 to date (December 2017). Prior to 2008, the IGS receiver (station code MALI) was installed at 40.19439∘ E, 2.99591∘ S, and was then replaced with another (station code MAL2) installed at 40.19414∘ E, 2.99606∘ S. These receivers had nearly the same location and therefore sampled the same geographical region of the ionosphere. We obtained the receiver independent exchange (RINEX) files from ftp://cddis.gsfc.nasa.gov/ (last access: 15 June 2018) and then extracted the TEC along the line-of-site, slant TEC (sTEC) from the RINEX files using the GPS-TEC software of Boston College . This software uses the thin shell mapping function to map the sTEC to be vertical to obtain the vertical TEC (vTEC) at an assumed ionospheric height of 350 km. The vTEC for the different viewing geometries for satellites with elevation angles greater than 30∘ were averaged epoch by epoch to give a representation of the vTEC above the receiver. Due to data paucity from 1995 to 1998, only data from 1999 to 2017 were used in this study. Hourly averages of the daily TEC data were then calculated to minimize noise in the data. The hourly averages were organized into a data matrix Md×h (day × hour) which was used to model and estimate trends in the TEC over Malindi. To study the TEC over the African low-latitude region, the TEC from the GIMs, a reliable source of ionospheric data , was used. Though these maps have been available since 1998, for comparison purposes with the GPS data, we have used data from 1999–2017. It is worthy noting that the 2-hourly GIMs were linearly interpolated to hourly data using a similar approach as in .

The first step in the regional TEC modeling was to extract the TEC for the African low-latitude region from CODE's GIMs. The daily GIMs were organized into bins of 2.5∘ × 5∘ × 1 h (latitude × longitude × LT). The binned data were then decomposed into the spatial and temporal components according to the equation TEC(lat,lon,LT,m)=∑i=1rUi(lon,lat)×Pi(LT,m). In Eq. (), Ui(lon,lat) is the basis modes representing the spatial TEC variability, and Pi(LT,m) is the coefficients that describe the temporal TEC variations in terms of local time (LT) and month (m). The temporal component in Eq. () was further broken into the diurnal and long-term (seasonal, annual and solar cycle) variations by another decomposition which we refer to here as the second-layer decomposition expressed as Pi(LT,d)=∑i,j=1mUi,j(LT)×Ai,j(d). In Eq. (), Ui,j(LT) is the basis functions of the ith first-layer coefficients, and Ai,j(d) is the coefficients of Ui,j(LT). Figure a shows the first basis modes for each of the first four expansion coefficients in the first-layer decomposition. Equations ()–() were then used to model the coefficients Ai,j(d). Figure b shows the coefficients Ai,j(d) together with their model-predicted values. Using the modeled values of the coefficients, the regional TEC was then reconstructed in a reverse order. We first used Eq. () to obtain the coefficients for the first-layer decomposition and then applied Eq. () to determine the TEC in each grid cell. Figure  shows the modeled TEC, CODE's TEC and the IRI TEC for DOY 070 in 2015. It can be seen from Fig.  that the model has reproduced the main features of the EIA region quite well. Higher correlations are observed between the EOF-modeled TEC and CODE's TEC (Fig. a and b). This high correlation is an indication that the model-predicted results could offer a good alternative to estimating the background TEC, since CODE's TEC is derived from GNSS measurements.

In the past, few studies (e.g., ) have derived long-term TEC trends, and these mainly used TEC data from GIMs. In this work, we have used the GPS-derived TEC and GIMs to study TEC trends over the low-latitude region of Africa. A key aspect in trend studies is the art of suppressing the solar and magnetic activity influences on these trends. We used the EOF-modeled TEC as background the TEC to remove the solar and magnetic effects in influencing the TEC trends. First, the monthly median TEC values were calculated from the daily TEC. The median TEC values were then modeled using similar equations as in Eqs. ()–(). In these equations, the daily inputs were replaced with their monthly averages. The modeled TEC values were then subtracted from the monthly medians to obtain the TEC residuals. The monthly TEC residuals from 10:00–14:00 LT were averaged for each year to give a representation of the noontime annual TEC residuals (ΔTEC). The trend was then determined using the equation ΔTEC=A+B⋅time(year), where A is the constant part, and B is the slope (trend) of the time-dependent TEC residuals. attributed the positive global TEC trends reported in to lower TEC values in CODE's GIMs, especially prior to 2003. To test this assertion, we have estimated the long-term trends in the TEC for the periods 1999–2017 and 2003–2017 using the GPS-derived TEC, CODE's TEC and the TEC from IGS GIMs. Figure  shows the TEC trends obtained from the GPS-derived TEC and the TEC from GIMs of CODE and IGS over Malindi. Trends of 0.139±0.063, -0.119±0.061 and -0.057±0.042 TECU yr-1 were obtained using the GPS TEC, CODE's GIMs and IGS GIMs over Malindi respectively. Though the trend values in Fig. a were slightly different, their 95 % confidence bounds reveal a slight positive TEC trend for the period 1999–2017. For the period 2003–2017, the trend estimates from the three data sets show that TEC trends over MAL2 are positive. To study the trends in the TEC over the African low-latitude region, we used the GIMs and estimated the trends in each of the 2.5∘ × 5∘ (latitude × longitude) grids. The trends are shown in Fig. a and c for the period 1999-2017 and in Fig. b and d for the period 2003–2017. The trends in Fig.  show a latitudinal dependence, with the trends in the vicinity of the crest of the EIA region being more positive than those near the magnetic equator, where the trend was negative over most of the African equatorial region. Analysis of the data from 1999–2017 revealed higher average values of TEC trends than that from 2003–2017 for both CODE's and IGS GIMs, though the general pattern of the trends remained unchanged. The trend pattern observed in this study confirms the latitudinal variation in TEC trends reported in . The difference in the trend magnitudes for the periods 1999–2017 and 2003–2017 could be as pointed out earlier due to a bias towards lower values of GIMs prior to 2002 . If so, the trends in the TEC over African low latitudes are therefore mainly negative, though cases of slight positive trends are also possible, especially at the crest of the EIA region. Geomagnetic or anthropogenic factors are often the plausible physical mechanisms for explaining trends in upper atmospheric parameters. The anthropogenic contributions to trends arise through the accumulation of greenhouse gases, which result in a decrease of atomic oxygen in the upper atmosphere. While the geomagnetic control of the trends is either due to the long-term changes in geomagnetic activity or to Earth's magnetic field secular variations , the latter view may explain the latitudinal dependence in the trends over the African low-latitude region. However, a detailed study is required to quantify the relative contribution of the different trend drivers over the African low latitudes.

We have used EOF expansion together with least-squares regression to model the TEC over the African low-latitude region. We first developed a single-station model over MAL2, a station at the southern crest of the EIA, and then constructed a regional model to predict the TEC over the African low latitudes. Despite the complicated nature of the low-latitude ionosphere, the model over MAL2 was able to satisfactorily reproduce the diurnal, seasonal and solar activity variations in the observed TEC. Comparison of the model results with IRI-2016-derived TEC showed that the EOF-based TEC model was more accurate in predicting the daytime TEC over Malindi than IRI-2016. In contrast, CODE's GIMs were better correlated with GPS TEC than the TEC from the EOF-based model, though CODE's GIMs mainly overestimated the GPS TEC over MAL2 during higher solar activity years. The large discrepancy of the IRI-2016-predicted daytime TEC from the observed TEC over MAL2 during periods of low solar activity and during the winter solstice could be due to the overrepresentation of the effects of the low-latitude E×B plasma drifts and thermospheric winds in the model. The regional model reproduced the known features of the low-latitude ionosphere quite well. Using the TEC from the EOF-based model as the background TEC to suppress solar and magnetic activity dependence of the TEC, we estimated trends in the TEC over the African low-latitude region. The regional trends showed a latitudinal dependence, with the trends in the vicinity of the magnetic equator being more negative than those at the crest of the EIA.