Longitudinal Day-to-Day Variability of the Rate of Change of the TEC Index (ROTI) over the African Equatorial Ionization Anomaly Region

1. Introduction

The low-latitude ionosphere is a highly dynamic plasma environment characterized by the Equatorial Ionization Anomaly (EIA), which exhibits enhanced electron density north and south of the geomagnetic equator at approximately ±20° geomagnetic latitude. This region is strongly variable and frequently affected by ionospheric irregularities [1] that degrade space-based systems by producing phase and amplitude fluctuations and sometimes loss of lock in GNSS receiver tracking. ROTI, derived from GNSS total electron content [2] is one of the most widely used proxies for monitoring the occurrence and intensity of such irregularities. It also correlates well with radio scintillation [3] and therefore provides an efficient basis for regional and temporal studies of irregularity behavior.

Previous studies have used ROTI to investigate ionospheric irregularities in several regions, including Africa, South America, and Asia [4,5,6,7,8,9,10,11,12,13,14,15,16]. These works show that irregularities are most common around the geomagnetic equator, usually after sunset, and that their occurrence depends strongly on longitude and local time. However, relatively few studies have focused specifically on the longitudinal day-to-day variability of ROTI over the African EIA region. The present work addresses that gap by examining daily variability in ROTI during 2014 using six GNSS stations distributed across eastern and western sectors of equatorial Africa.

2. Materials and Methods

2.1. Data Set and Stations

Calibrated TEC data from six GNSS receiver stations in equatorial Africa were obtained from the Abdus Salam International Centre for Theoretical Physics archive. The selected stations represent two longitude sectors: East Africa (MBAR, MOIU, MAL2) and West Africa (YKRO, BJCO, NKLG). Their geographic, geomagnetic, and MODIP coordinates are provided in Table 1, and their distribution relative to the magnetic equator and EIA region is illustrated in Figure 1.

2.2. ROTI Computation

ROTI is derived from slant total electron content using 30-second GNSS observations and a 5-minute sliding window, with an elevation mask of at least 30° to reduce multipath effects [2]. The rate of TEC (ROT) is computed from consecutive slant TEC values. The measurement of ionospheric fluctuations by calculating the rate of TEC (ROT) is defined as follows:

$${\mathrm{ROT}}_{\mathrm{k}}={\displaystyle \frac{STE{C}_k^i-STE{C}_{k-1}^i}{t_k-t_{k-1}}}$$

(1)

Where i is the visible satellite, k is the epoch time in TECU units, t is the time and STEC is the slant total electron content.

ROTI is defined as the standard deviation of ROT over the selected time interval, as shown in Equation 2:

$$\mathrm{ROTI}=\sqrt{〈RO{T}^2〉-{〈ROT〉}^2}$$

(2)

Where the parentheses <> around ROT denote the mean value. ROT measurements indicate small-scale variations at the peak of the STEC index. This approach captures short-scale TEC fluctuations while minimizing phase bias effects.

2.3. Day-to-Day Variability Metrics

To quantify day-to-day variability, four complementary metrics are used. First, the difference between two consecutive daily ROTI values is calculated as ΔROTI, which isolates short-term changes from slow seasonal variability. The ∆ROTI evaluates the forward first-order difference of the ROTI from one day to the next day. The dynamic interpretation of the ∆ROTI formula is presented as follows in equation 3.

∆ROTI = ROTI(x+1) - ROTI(x)

(3)

Where x is the current Day of Year (DOY) and x+1 represents the next consecutive day in the yearly dataset.

Second, relative ROTI (RROTI) expresses the daily variation as a percentage of the annual mean, allowing inter-station comparison despite differences in absolute ROTI magnitude. The dynamic interpretation of the RROTI formula is indicated in Equation 4 below:

$$\mathrm{RROTI}(\%)={\displaystyle \frac{{\mathrm{ROTI}}_{\mathrm{daily}}-{\mathrm{ROTI}}_{\mathrm{mean}}}{{\mathrm{ROTI}}_{\mathrm{mean}}}}x100\%$$

(4)

Where ROTI_daily is the value of ROTI in each DOY in a yearly dataset and ROTImean presents the yearly mean values of ROTI.

Third, a 27 day moving average is used as a climatological background (ROTI_Clim), and daily deviations from that background are computed to isolate short-term departures. ROTI_Clim is defined as the 27 day window moving average corresponding to the solar rotation period as presented in Equation 5:

$$ROT{I}_{Clim}\left(x\right)=ROTI\left(x\right)-\overline{ROT{I}_{27}}\left(x\right)$$

(5)

Where ROTI_Clim is the daily deviation climatology, x is the DOY in the dataset, ROTI(x) is the ROTI value on day x and the $\overline{ROT{I}_{27}}\left(x\right)$ is the climatology calculated ROTI values over 27-day window on day x.

Fourth, a 30 day moving standard deviation (σ) is used to characterize the magnitude of the variability around the detrended series. Variability magnitude (σ) was computed over a 30-day moving daily deviation as illustrated in Equation 6 below:

$$\sigma \left(x\right)=\sqrt{{\displaystyle \frac{1}{N-1}}{\displaystyle \sum _{j=x-14}^{x+15}{\left(ROT{I}_{Clim}\left(j\right)-\overline{ROT{I}_{Clim}}\right)}^2}}$$

(6)

Where σ(x) is the variability magnitude of the standard deviation for a day x, N is the number of the data within the moving window, x is the DOY, N-1 is the Bessel’s correction used to provide an unbiased calculation of the sample standard deviation, ROTI_Clim (j) is the daily deviation detrended for each day j in that window, $\overline{ROT{I}_{Clim}}$ is the mean of the deviations within the 30-day window, the j = x-14 and x+15 is a 30-day window summation running from 14 days before to 15 days after a day x.

2.4. Correlation and Periodicity Analysis

Pearson correlation coefficients between station pairs are used to assess the spatial coherence of daily ROTI variability within and across longitude sectors. In addition, continuous wavelet transform analysis is applied to identify characteristic periodicities in the daily ROTI series over periods from 4 to 32 days.

3. Results

3.1. Diurnal Longitudinal Variations

ROTI remains close to background levels during daytime and increases after sunset at all stations (Figure 2). The strongest irregularity activity occurs between about 19:00 and 23:00 local time, then gradually weakens after midnight. This diurnal behavior is consistent with post-sunset enhancement of the vertical drift and the associated growth of plasma instabilities.

A clear longitudinal contrast is observed. In East Africa, peak ROTI values are generally around 2 TECU/min and remain concentrated before midnight. In West Africa, values are larger overall, with NKLG reaching about 3 TECU/min and preserving strong irregularity activity beyond midnight. This difference is consistent with the lower magnetic field strength in the western sector and with the position of NKLG near the southern EIA crest, where higher background electron density amplifies TEC fluctuations.

3.2. Day-to-Day Longitudinal Variability

Daily ROTI time series show abrupt changes between consecutive days, particularly during the equinoctial periods, rather than smooth seasonal transitions (Figure 3). This confirms the presence of strong day-to-day variability in both African sectors. The effect is more pronounced in West Africa, especially at NKLG, where the amplitude of the daily ROTI series is nearly double that observed at the other stations.

Pearson correlation analysis confirms that daily variability is more coherent within each longitude sector than across sectors (Figure 4). Correlation coefficients within East Africa range from 0.810 to 0.841, while those within West Africa range from 0.678 to 0.848. By contrast, cross-sector correlations are weaker, ranging from 0.476 to 0.689. These results show that the day-to-day variability of ROTI is strongly localized in longitude and likely controlled by regional electrodynamics and localized atmospheric forcing.

3.3. ΔROTI and RROTI Behavior

The ΔROTI series highlights rapid day-to-day transitions in irregularity activity (Figure 5). Positive values indicate abrupt increases from one day to the next, whereas negative values indicate sudden decreases after an active day. The largest oscillations occur during equinoxes, when the instability threshold appears to switch on and off rapidly over consecutive days. During solstices, ΔROTI is generally close to zero, indicating a more stable day-to-day ionospheric state.

RROTI removes the bias introduced by different absolute ROTI magnitudes and reveals relative changes between about -70% and +150% (Figure 6). Negative values are most common during solstices, while equinoctial months show the strongest positive excursions. East African stations reach relative peaks up to +150%, while West African stations typically range up to about +120%. These oscillations confirm that equinoctial irregularity growth is highly sensitive to daily variations in background electrodynamics and atmospheric forcing.

Figure 7 shows the detailed representation of the plasma irregularity day-to-day longitudinal variability of time series. In the left column (Figures 7a-7f), the blue dots present raw daily ROTI values, and the red curved line presents the 27-day running mean climatology, which highlights the slow-moving seasonal trends. While the right column (Figures 7g - 7l) shows the isolated daily deviation climatology (ROTI_Clim) indicated by the blue line, the red line plotted alongside the climatology running presents the variability magnitude (σ). The variability magnitude (σ) captures the true and high-frequency day-to-day variability from the 30-day window. Figure 7 (left panel) is very important for strengthening the scientific evidence for day-to-day variability of ROTI by separating the seasonal climatology from the short-term variability of plasma irregularity. During equinoxes, the 27-day running mean climatology filters out short-term variability by leaving a clear semiannual pattern maximum. The terminator alignment and seasonal variations in solar zenith angle are the drivers of this smooth baseline climatology [30]. The daily deviation (right panel) also shows the 30-day running mean climatology filters out short-term variability by leaving a clear semi-annual pattern of peaks.

In the East African sector stations of MBAR, MOIU and MAL2 during active periods, the daily deviation and its running variability magnitude (Figures 7g-7i) are highly limited and stay below 0.05 TECU/min. While in West African sector stations, particularly at NKLG (Figure 7l), the daily deviation shows substantially more variability. Its running variability magnitude frequently exceeds 0.05 TECU/min and can reach 0.1 TECU/min. This shows that there are clear longitudinal day-to-day variations across the East and West African sector, as in Figure 7.

3.4. Seasonal Variability

Seasonal mean ROTI and the standard deviation of day-to-day variability both peak during the September equinox, followed by the March equinox, with minima during the June and December solstices (Figure 8). This pattern is consistent with the known seasonal maximization of equatorial plasma irregularities during equinoxes.

A marked longitudinal difference is also present in the seasonal statistics. With the exception of YKRO during the June solstice, the western sector generally exhibits larger seasonal variability than the eastern sector (Figure 8). NKLG consistently shows the highest seasonal means and variability levels. These differences can be explained by longitudinal changes in geomagnetic declination, local magnetic meridian geometry, and alignment with the solar terminator, all of which affect pre-reversal enhancement and instability growth conditions.

3.5. Periodicity of Day-to-Day Variations

Wavelet analysis (Figure 9) identifies recurrent periodicities in the daily ROTI time series, mainly in the 4-8 day, 10-16 day, and 27 day bands. These periodic components are strongest during the equinoctial months, when background ionospheric conditions are favorable for instability growth.

The shorter periodicities are consistent with planetary-wave and tide-related forcing originating in the lower atmosphere and propagating upward into the ionospheric dynamo region. The 27 day component is associated with solar rotation. Together, these periodicities indicate that day-to-day ROTI variability results from the combined influence of lower-atmospheric wave coupling, seasonal instability conditions, and recurrent solar forcing.

4. Discussion

The results demonstrate that day-to-day ROTI variability over equatorial Africa cannot be explained by a spatially uniform forcing mechanism. If slow solar forcing were dominant, similar day-to-day changes would be expected at all longitudes. Instead, the stronger variability in West Africa, the reduced cross-sector correlations, and the larger amplitude at NKLG support a model in which localized electrodynamics, geomagnetic field geometry, and atmospheric wave seeding control daily irregularity development.

The higher variability in the western sector is consistent with weaker geomagnetic field strength and stronger effective vertical plasma drift, while the exceptional activity at NKLG reflects its position near the EIA crest, where enhanced background density increases the response of ROTI to fluctuations. The combined evidence from ΔROTI, RROTI, climatological deviation, and wavelet analysis further suggests that short-period atmospheric forcing is more important than slow global solar forcing in shaping daily irregularity changes.

These findings are important for understanding the forecasting limits of equatorial irregularities over Africa. A climatological expectation alone is insufficient to capture the strong day-to-day changes observed here, especially during equinoxes. Regional monitoring and models that incorporate atmospheric wave coupling and longitudinal electrodynamic differences are therefore essential for improved prediction of GNSS signal degradation in the African EIA region.

5. Conclusions

This study investigated the longitudinal day-to-day variability of ionospheric irregularities over the African EIA region during 2014 using ROTI derived from six GNSS stations. The analysis shows clear east-west differences in both absolute ROTI and short-term variability. West Africa exhibits stronger and more persistent irregularity activity than East Africa, with NKLG showing the largest amplitudes and variability.

Within-sector station pairs show stronger daily correlation than cross-sector pairs, confirming that ROTI variability is strongly localized in longitude. ΔROTI, RROTI, daily deviation, and wavelet analyses all indicate that the dominant drivers of day-to-day irregularity variability are short-period atmospheric and electrodynamic processes rather than slow solar background forcing. Seasonal maxima occur during equinoxes, and the main periodic bands are found at 4-8 days, 10-16 days, and 27 days.

Overall, the results highlight the importance of longitudinal structure and short-term atmospheric forcing in shaping ionospheric irregularities over equatorial Africa. These findings are relevant for regional space-weather characterization and for improving GNSS reliability assessments in low-latitude African sectors.