© E.O. Oyeyemi et al., Published by EDP Sciences 2025

1 Introduction

For decades, the occurrence of spread F and associated irregularities arising from the electrodynamics of the ionosphere has been linked with disruptions to the propagation of communication and navigation signals (Gentile et al., 2006). In comparison with high- and mid-latitude regions, the threat to L-band communication and navigation signal propagation is more severe at equatorial and low-latitude regions. This is due to the peculiar ionospheric electrodynamics of the equatorial and low-latitude regions. For example, at equatorial latitudes, zonal neutral winds can cause an enhancement in the eastward electric field during local evening hours. This enhancement is the well-known pre-reversal enhancement (PRE) of the electric field at equatorial latitudes. The PRE, acting in combination with the magnetic field at these latitudes, facilitates the upward vertical drift or post-sunset rise (PSSR) of plasma via the Hall Effect. With the disappearance of the E-layer after local sunset, favorable conditions are established for the generation of instabilities in the uplifted F-layer plasma (Rishbeth, 1971). The equatorial spread F (ESF) is a direct consequence of plasma instabilities that develop in the post-sunset equatorial ionosphere. In ionograms, the ESF is seen as a spread in the F-layer trace. Similarly, ESF is observed in HF Doppler spectrograms as a spread in the Doppler trace of the signal reflected from the F-layer. This spread occurs when a radio signal, incident on a turbulent region of the ionosphere, undergoes reflection from multiple sources.

Another peculiarity of the equatorial and low-latitude ionosphere is the upward vertical movement of plasma due to the E × B drift, which occurs as a result of the orthogonal alignment of the E and B fields at these latitudes. Under the influence of gravity and pressure gradient forces, the elevated plasma diffuses along geomagnetic field lines to higher latitudes, resulting in the build-up of plasma at latitudes ~15°–25° (depending on factors such as time of day and geomagnetic activity), north and south of the dip equator (Balan et al., 2018). The formation of peaks of ionospheric plasma on both sides of the dip equator relative to the depletion of plasma at the dip equator is known as the equatorial ionization anomaly (EIA). Ionospheric irregularities are also known to cause scintillation or rapid random fluctuations in the amplitude and phase of navigation signals from Global Navigation Satellite System (GNSS), thereby compromising the quality of these signals and the reliability of GNSS (Gentile et al., 2006; Akala et al., 2012). As a result, in systems where the use of these signals is critical for application purposes, these ionospheric-induced errors adversely impact the applications and their users. In incoherent scatter radar (ISR) measurements, ionospheric irregularities are seen as plumes extending upwards in the range-time plots of the ISR (Woodman & La Hoz, 1976). Another term that is used to describe the occurrence mechanism of these irregularities is the plasma bubble (Burke et al., 2004; Gentile et al., 2011), which manifests as regions of depletion in ionospheric electron density and Total Electron Content (TEC) (Seemala & Valladares, 2011).

Although the first report of equatorial spread F occurrence was several decades ago (Booker & Wells, 1938), a puzzle that has persisted is the variability in its day-to-day occurrence. The PSSR, arising from the evening PRE, has been the most widely accepted precursor for the occurrence of the equatorial spread F. However, several studies have pointed out the inability of the PSSR/PRE alone to predict equatorial spread F occurrence on a day-to-day basis (Sultan, 1996; Tsunoda, 2007; Kil et al., 2009). Indeed, there have been suggestions that the PRE may not be a necessary condition for the occurrence of post-sunset equatorial spread F (Tsunoda et al., 2018; Olugbon et al., 2022). When the PRE is weak or absent, other likely seeding mechanisms for ESF and plasma bubble occurrence have been reported. For instance, the association of large-scale wave structures with the development of equatorial spread F and equatorial plasma bubbles was detailed by Tsunoda (2005, 2006, 2008), Tsunoda & Ecklund (2007), and Tsunoda et al. (2010). Buhari et al. (2014) also studied the evolution of equatorial plasma bubbles (EPBs) in south-east Asia during a night of low solar activity. The EPBs, which were observed to develop during the passage of the solar terminator, were accompanied by quasi-periodic structures. Hence, atmospheric gravity waves, or their manifestation in the ionosphere – travelling ionospheric disturbances, were suggested a seeding mechanism for the observed bubbles.

The results from a multi-instrument study of the evolution of an equatorial plasma bubble event that occurred in the South American region were presented by Aa et al. (2020). The equatorial plasma bubble event was accompanied by wave perturbations visible in the bottomside F-layer height derived from ionosonde measurements. Detrended TEC also revealed the simultaneous occurrence of wave structures with a wavelength corresponding to the inter-bubble spacing. From the analysis of cloud temperature data, Aa et al. (2020) suggested that atmospheric gravity waves provided the seeding mechanism for the generation of the observed equatorial plasma bubbles. In another study, Aa et al. (2023) presented results from coordinated observations of equatorial plasma bubbles during geomagnetically quiet conditions over the American sector during 7–10 December 2019. They observed large day-to-day variabilities in post-sunset equatorial plasma bubble intensities within the same UT intervals on the four consecutive days. Distinct wave structures, consistent with strong medium-scale travelling ionospheric disturbances, were observed concurrently with large equatorial plasma bubbles on two nights. On two other nights when weak and suppressed travelling ionospheric disturbances were present, the equatorial plasma bubble intensities were correspondingly small. Their findings showed that the intensities of the plasma bubbles showed better agreement with the amplitudes of the travelling ionospheric disturbances, compared with the peak growth rate of the Rayleigh-Taylor instability.

In the study by Das et al. (2020), the results from a low-latitude study of the association of wave structures with the occurrences of equatorial plasma bubbles using an ionospheric radar interferometer and a digisonde were presented. They found a significant correlation between the horizontal wavelength of wave structures preceding equatorial plasma bubble formation and the inter-bubble spacing. Their results suggested the potential for the wave structures as a precursor for equatorial plasma bubble development. However, they noted a variability in the association of the wave structures with equatorial plasma bubble development when events were analyzed in greater detail. They attributed the observed variability to the assumption of zero neutral winds in their data analysis, and also an assumption of unrealistic orientations of the wave structures. In a subsequent study, Das et al. (2021) attributed day-to-day variabilities in equatorial plasma bubble occurrence to longitudinal variations in ionospheric parameters. Das et al. (2021) suggested that a dense longitudinal distribution of measuring instruments would be required to investigate the day-to-day variabilities in plasma bubble occurrence.

The results from previous studies clearly showed that there is no debate about the role of wave structures in the development of equatorial plasma bubbles and equatorial spread F. However, questions still remain about the sources of these wave structures and how they trigger the development of equatorial plasma bubbles and equatorial spread F. In this study, the interaction of waves in the generation of equatorial plasma bubbles and equatorial spread F is examined as well as their role in the day-to-day variability of these irregularities.

2 Instruments and data analysis

The HF Doppler system in Nigeria comprises a transmitter and a receiver, with the transmitter located in Abuja (ABU: geographic: 7.39° E, 8.99° N; dip latitude −1.37°) and the receiver stationed in Lagos (LAG: geographic: 3.27° E, 6.48° N; dip latitude −1.72°). The components of the receiver system a digital receiver (WR-G313i), an external reference oscillator, and an active loop antenna. The Doppler shift of the received radio signal is logged at 10 s intervals, and the Doppler trace can be viewed in near real time on a personal computer (Olugbon et al., 2021). The transmitter set-up consists of: HF transceiver ICOM IC-718, external reference oscillator, terminated folded dipole antenna, and a computer. A continuous wave signal at a frequency of 6.957 MHz is emitted with 30 W power.

The spectrogram trace and time series of HF Doppler shift on 7 March 2022 are shown in Figure 1. The steady trace from ~0900 to 1500 UT is indicative of reflection from the relatively undisturbed E-layer. The PSSR during local evening hours is registered in the HF Doppler data as a steady decrease in the Doppler shift, as highlighted by the grey dashed rectangle in the interval ~1730 to 1915 UT. For the purpose of data analysis, the PSSR is recorded as the lowest point in the dip, which corresponded to a value of −2.5 Hz on 7 March 2022. It is important to note that the absolute (positive) value was used for data analysis. Relevant background to the principle of Doppler sounding is available in Chum et al. (2010).

Figure 1 (a) Doppler spectrogram and (b) Time series, 7 March 2022. The signature of the PSSR and the subsequent drop in the reflecting layer height are highlighted by the grey dashed rectangle in the interval ~ 1730–1915 UT (LT = UT + 1). A PSSR of −2.5 Hz was recorded.

Ionospheric scintillation, measured by the S4 index, was obtained from a Septentrio PolaRx5S receiver co-located with the HF Doppler receiver. ISMR data files were processed to extract the S4 index at 1-minute cadence. GPS TEC was obtained from RINEX files logged in the same receiver. The RINEX files were processed with the analysis software developed by G. K. Seemala to obtain GPS TEC at 30 s cadence (Seemala, 2017). The signature of plasma bubbles is clearly visible in raw GPS TEC. However, to detect the presence of wave activity, the data were low-pass filtered with a 40-minute smoothing algorithm and then subtracted from the original time series (Olugbon et al., 2021). In order to minimize errors arising from the multipath effect, a satellite elevation mask of 25° was applied to the data. However, applying this threshold implied making a tradeoff between minimizing multipath errors and missing important signatures in the data. For instance, Figure S1 shows TEC measurements from LAG on 6 March 2022 with four different elevation masks applied. The bubble signature, highlighted by the red oval, is seen to be partly blanked out when the elevation mask is raised to 25°. Akala et al. (2016) stressed that the use of high elevation masks potentially screens important features from the data. The study’s data coverage was from March to September 2022. Geomagnetic activity and solar wind conditions were mostly quiet during the period of investigation.

Plasma bubble depth was computed by first visually selecting the time interval during which the bubble signature appeared in the time series of GPS TEC. The bubble depth was then automatically computed as the (positive) difference between the point in the time series where a sharp decrease in TEC is first encountered and the lowest point in the bubble signature. A sharp decrease in TEC was defined as |T_i − T_i-1| ≥ 0.5 TECU, where T_i is sTEC at time point i and T_i-1 is sTEC at the immediate preceding time point. The value 0.5 TECU was set because it automatically detected the commencement of the bubble signature in all the visually selected intervals in the dataset. However, the automated results were still manually checked because the lowest point in the bubble signature was not automatically determined in all cases, especially when a shallower dip occurred in close proximity to the lowest point. In the cases where more than one bubble signature was evident in the selected time interval, the larger/largest bubble was retained. Only S4 index values ≥ 0.12 were retained in the analysis. The threshold of 0.12 for the S4 index was chosen because the days that recorded lower S4 indices were unaccompanied by spreading in the Doppler trace. To determine the amplitudes of wave structures in TEC, the FFT of detrended sTEC during the interval of wave occurrence was obtained. The maximum spectral peak was taken as representative of the wave amplitude during the period of interest. Plasma bubble depth and wave amplitude were computed from the GPS link or PRN that detected the maximum S4 index during the period of interest. Although the occurrences of plasma bubbles in GPS TEC from the equatorial region were scanty, the amplitudes of spectral components in the filtered time-series, in some cases, exceeded 1 TECU. Previous studies have reported the typical amplitudes of medium-scale TIDs/large-scale TIDs as < 1 TECU (Oluwadare et al., 2022; Thaganyana et al., 2022). Hence, spectral components in the time series with amplitudes ≥ 1 TECU were considered to be plasma bubble signatures and were therefore not included in the FFT analysis. In addition, spectral components with amplitude ≤ 0.05 TECU were considered to be below the receiver noise floor and were not included in the analysis (Olugbon et al., 2022).

During March–September 2022, data were simultaneously available from the HF Doppler sounder and the Septentrio receiver for a total of 77 days. The distribution of data availability over this period is shown in Figure 2.

Figure 2 Number of days for which data was simultaneously available from the HF Doppler sounder and Septentrio receiver in 2022.

Data from the Septentrio receiver during this period can be found in Olugbon et al. (2023).

3 Results

The tracks of ionospheric pierce points (IPPs) of satellites in view of the receiver during post-sunset hours (1830–2300 UT; LT = UT + 1) on 7 March 2022 are shown in Figure 3. Typically, S4 index is observed to peak in amplitude at latitudes 7°–10° south of the dip equator, with a smaller amplitude peak appearing in the vicinity of the dip equator, as shown in Figure 2b and Figure S2. The term “typically” in this context means that this observation was true for more than half of the days in the dataset. The crests of the EIA are known to appear at latitudes ~ 15°–25° north and south of the dip equator. In this study, the IPPs of the satellites in view of the GNSS receiver in Lagos did not extend as far as ~ 15°–25° south of the dip equator. However, since a peak in amplitude of S4 index was observed on latitudes 7°–10° south of the dip equator, we refer to these latitudes as the southern crest of the EIA in the remainder of the text – for ease of reference. The representative value of the S4 index for each day was obtained by first plotting the IPP tracks from all PRNs in view during post-sunset hours. Next, the PRN that registered the maximum S4 index over the dip equator was identified. The maximum S4 index from that PRN was then recorded as the representative value at the dip equator for that day. The same procedure was repeated for the EIA crest.

Figure 3 IPP tracks of satellites in view during post-sunset hours (1830–2300 UT; LT = UT + 1) on a typical day are imposed on a map of Nigeria. The blue line across the map is the approximate position of the dip equator. The approximate ionospheric reflection point of the HF signal is indicated by the black star.

In nearly all cases from the dataset, wave structures were conspicuous in detrended sTEC at about the same time that the maximum S4 index was recorded. Wave amplitudes were determined by computing the FFT of Δ sTEC over the interval of wave activity. In some cases, multiple spectral peaks were present in the data. In other cases, a single distinct peak appeared in the FFT. Examples of these spectra are shown in Figures 4–6. The lower panels in Figures 4–6 show the time series of filtered sTEC on three separate days when equatorial spread F and scintillation were observed. The upper panels in these figures show the FFT applied over the highlighted time intervals in Δ sTEC. The time series of unfiltered sTEC as well as S4 index for the three events (21 April 2022; 22 June 2022; and 7 August 2022) are displayed in Figure S3. In Figures 4a and 4b, the spectral components of two different segments of the time series are shown. The two segments are indicated in Figure 4c with boxes shaded with matching colours to the respective line spectra. The data interval highlighted in red is the interval over which ESF and elevated S4 indices were observed over the dip equator. Beyond the red-highlighted interval, the IPP had moved away from the dip equator. The amplitude of the highest FFT peak and the mean of the highest three peaks are indicated in the FFT plots. The values of the mean indicated in Figures 4a and 4b (0.39 and 0.34) are nearly equal. However, the maximum values (0.74, 0.51) indicated in the same figure are quite different when compared with the mean values. Hence, Figure 4 shows that when there are uncertainties pertaining to the time interval over which to compute the FFT, the mean of the largest 3 spectral peaks gives a better representative value of the wave amplitude than the maximum spectral peak. The data for 22 June 2022 are shown in Figure 5. Although a maximum S4 index of 0.57 was registered at ~ 2035 UT at the EIA crest on this day (Fig. S3e), Figure 5b shows that large amplitude waves were detected for over an hour after the maximum S4 index was recorded. This kind of observation usually leads to a subjective determination of the interval over which to compute the FFT. However, Figure 5a shows that the difference between the maximum FFT peak and the mean of the largest three peaks is not particularly significant. In this case, the mean of the three largest spectral peaks also provides a good representative value of the wave amplitude. Finally, Figure 6 shows a large amplitude wave which was detected over the EIA crest on 7 August 2022. The time of occurrence of this wave coincided with the time that a maximum S4 index of 0.32 was recorded. The spectrum in Figure 6a shows that there is a significant difference between the maximum and mean spectral peaks. Since the computation of wave amplitudes was automated (after visually selecting the time interval during which wave structures were coincident with maximum S4 index), the largest peak in the FFT and the mean of the largest three spectral peaks were determined for each wave interval.

Figure 4 Spectral and time series analysis of sTEC on 21 April 2022. The spectra in the upper panels (a) and (b) are shown with matching colours to the highlighted intervals in the time series in the bottom panel (c). Even though the FFT is determined over two different time intervals, the mean of the largest 3 spectral peaks for both time intervals is nearly the same.

Figure 5 (a) Spectral analysis of sTEC on 22 June 2022. (b) Time series analysis of sTEC on 22 June 2022. The highlighted interval is the interval over which the FFT in (a) was computed. The mean of the largest three peaks in the FFT and the largest spectral peak are nearly equal.

Figure 6 (a) Spectral analysis of sTEC on 7 August 2022. (b) Time series analysis of sTEC on 7 August 2022. The highlighted interval is the interval over which the FFT in (a) was computed. There is a significant difference between the mean of the largest three peaks in the spectrum and the largest spectral peak.

3.1 Trends in the dataset

In Figures 7–9, two sets of scatter plots are shown – one for the dip equator (right panel), and the other for the EIA crest (left panel). Each of Figures 7–9 shows a different parameter plotted with respect to the S4 index. The Doppler PSSR in Figure 7 refers to the PSSR signature in the Doppler trace as described in the preceding section. The maximum FFT peak in Figure 8 refers to the largest spectral peak in the FFT, while the mean FFT peak in Figure 9 refers to the mean of the largest three spectral peaks. The linear correlation coefficient is indicated in each plot. The highest correlation index is recorded in the correlation between the S4 index and the maximum FFT peak from the EIA crest. It should be noted that the total number of points plotted in each of the panels in Figures 7–9 is not the same. For example, the data for all 77 days displayed in Figure 2 are plotted in Figure 7. However, the days with plasma bubbles and/or spectral peaks ≥ 1 TECU are excluded from the data plotted in Figures 8 and 9, as explained in Section 2. If all available data are included in the correlation analysis, regardless of whether or not plasma bubbles or FFT peaks ≥ 1 TECU were present in the data, then the corresponding scatter plots are as shown in Figure S4. In Figures 7–9 and Figure S4, the linear correlation of FFT peak vs. S4 index is higher than the correlation of PSSR vs. S4 index. The scatter plots of more parameters are shown in Figure S5. Figure S5a shows the level of linear relationship between the S4 index at the EIA crest and plasma bubble depth computed from PRNs with IPP tracks over the southern crest of the EIA. There were hardly any bubbles seen at the dip equator during the period of study; hence, the plasma bubble analysis in Figure S4a is for the EIA crest only. Accordingly, the total number of days included in the plasma bubble analysis was 41. A significant correlation level of 0.56 was recorded for plasma bubble depth versus S4 index at the EIA crest. The correlation between the maximum S4 index recorded at the dip equator and the maximum S4 index recorded at the EIA crest was 0.55, as seen in Figure S5b. The results from Figure S5b show that there is a significant correlation between scintillation amplitude at the dip equator and at the EIA crest. From Figures 8 and 9, it is evident that there is a significant level of correlation between scintillation and wave activity. However, day-to-day variabilities were still present in the data. In order to gain deeper insight into the probable causes of the variabilities, the events were examined on a case-by-case basis.

Figure 7 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Doppler PSSR. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Doppler PSSR. The linear correlation indices are shown in the plots.

Figure 8 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Maximum FFT peak at EIA crest. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Maximum FFT peak at dip equator. The linear correlation indices are shown in the plots.

Figure 9 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Mean FFT peak at EIA crest. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Mean FFT peak at dip equator. The linear correlation indices are shown in the plots.

3.2 Wave interactions

The results from the preceding sections provide a sufficient basis to investigate the mechanisms by which the observed waves trigger irregularities in the ionosphere. As seen in the lower panels in Figures 4–6 and Figure S3, scintillation is usually accompanied by large amplitude waves occurring simultaneously or nearly simultaneously with the elevated S4 index. One possible mechanism for the generation of large amplitude waves is the constructive interference of waves with similar properties. Plasma bubbles are observed in ISR plots as vertical plumes in the ionosphere. The bubble is postulated to develop as perturbations on the bottomside ionospheric layer and rise to the topside ionosphere. As the bubble rises, irregularities develop around the perimeter of the bubble as well as within the bubble structure (Kil, 2015). A hypothesis for the generation of rising plumes can be constructed by considering the interaction of two oppositely directed waves. As the crests of the waves interact in phase, a rising structure is created by the resultant wave crest – similar to the generation of a plume in the ionosphere.

The Doppler trace during post-sunset hours on 3 September 2022 is shown in Figure 10. Figures 10a and 10b show the Doppler trace on the same day, but Figure 10b provides an expanded view so that the details of interest are more visible. The arrowed features in Figure 10b look like rising plumes in the ionosphere, similar to Figures 1–3 in Kelley et al. (1981). Two more examples of signatures in the Doppler trace, resembling wave interactions, are shown in Figures 11a and 11b, respectively. The higher frequency wave components in Figure 11a appear to be modulated by a lower frequency wave component, suggesting the interference of two waves of different frequencies – likely harmonic frequencies. In Figure 11b, the arrowed loop appears to be the signature of wave structures from opposite directions interfering to generate a vortex in the ionospheric plasma. The subplots in Figures 10 and 11 are included in the Supplementary Online Material (Figures S6–S9) as separate plots in order to improve the resolution of the plots. Figure 12a shows the map of Nigeria with the IPP tracks of satellites visible during the post-sunset hours, 11 July 2022. The IPP track of the PRN (PRN 30) that registered the highest level of scintillation over the dip equator is arrowed. The time series of detrended sTEC from PRN 30 after sunset is shown in Figure 12b. Large amplitude waves are evident in the interval ~ 2000–2100 UT, the same interval during which a maximum S4 index of 0.33 was recorded. The FFT of filtered sTEC over ~ 2000–2100 UT is shown in Figure 12c. Indeed, harmonic frequencies are distinct in the line spectrum, which confirms the initial presumption of the presence of harmonic frequencies in Figure 11a. In addition, Figure 13 shows the wave outline of two simulated waves of the same amplitude but different frequencies interfering over the boxed interval. The two interfering waves, shown outside the boxed interval, have harmonic frequencies. The frequency of the signal to the right of the boxed region is 4× the frequency of the signal to the left of the boxed region. In order to aid visual comparison of Figures 11a and 13, both figures are placed in the same frame in Figure S10.

Figure 10 (a) Spectrogram of HF Doppler signal on 3 September 2022, ~1500–2400 UT. Periodic structures are present in the post-sunset spread in the reflection layer. (b) An expanded view of the left panel. Rising plumes at the crests of the wave structures are indicated by the black arrows.

Figure 11 Spectrogram of HF Doppler signal on (a) 11 July 2022, ~1500–2400 UT. Higher frequency wave structures appear to be embedded in a lower frequency wave in the post-sunset activity. (b) 16 September 2022, ~1400–2100 UT. A loop in the trace is highlighted by the black arrow. This can occur when shear flow is generated between waves propagating in opposite directions, thereby creating a vortex in the ionospheric plasma. Beyond the loop, periodic structures are visible in the post-sunset spread ~1900–2100 UT.

Figure 12 (a) Map of Nigeria showing IPP tracks of PRNs in view during post-sunset hours, 11 July 2022. The IPP track of PRN 30, which recorded the maximum S4 index over the dip equator, is shown by the black arrow. (b) Filtered sTEC from PRN 30 during post-sunset hours. (c) FFT of Δ sTEC from PRN 30 over the interval ~2000–2100 UT. (LT = UT + 1).

Figure 13 Simulation of two signals of same amplitude but different frequencies interfering over the boxed interval. The lower frequency signal is to the left of the boxed interval, while the higher frequency signal, with frequency 4× the lower frequency signal, is shown to the right of the boxed interval.

4 Discussion

The phenomenon of rising bubbles and ionospheric plumes has significantly advanced understanding of the development of ESF in ionospheric studies. Among other findings, the study by Tsunoda & White (1981) showed that the appearance of plumes in ionospheric backscatter data was preceded by wave structures in the bottomside ionosphere. Their results also showed that these wave structures grew in amplitude and that plumes developed at the crests of the waves. The growth in amplitude of waves reported by Tsunoda & White (1981) can be compared to the amplification of waves interacting in phase. The development of plumes at the crests of the waves can be explained by the Rayleigh-Taylor instability, which develops as plasma is pushed through the ionosphere by rising wave crests. Tsunoda et al. (1982) provided a detailed morphological description of plasma bubbles as vertically elongated depletions extending from the bottomside F-layer, in the form of tilted wedges. Similar structures are evident in the Doppler spectrograms shown in Figures 1, 10, and 11. Periodic spacing between bubble structures, similar to those in Figures 1, 10, and 11, has also been reported by Makela et al. (2010) and Buhari et al. (2014). Although plasma bubbles were hardly seen in GPS TEC at the dip equator during this study, data from the southern crest of the EIA showed reasonable correlation of plasma bubble depth with S4 index (Fig. S5a), consistent with results from previous studies (Ngwira et al., 2013).

Clear evidence of quasi-periodic bubble patches from satellite measurements was presented by Singh et al. (1997). The development of the bubbles was attributed to gravity waves, which were observed by the satellite during its previous pass over the same longitude sector. On the other hand, Otsuka et al. (2012) reported the disappearance of a plasma bubble in airglow measurements after the bubble encountered medium scale travelling ionospheric disturbances. Otsuka et al. (2012) suggested that the electric field associated with the medium-scale travelling ionospheric disturbances caused ambient plasma to fill up the bubble, leading to the disappearance of the bubble. These reports showed that while wave structures can contribute to the development of equatorial plasma bubbles, the interaction of wave structures in ionospheric plasma can also suppress equatorial plasma bubble development. Results from the modeling studies by Wu et al. (2015) showed that gravity waves interacting in phase generate larger initial perturbations for the generation of plasma bubbles, thereby facilitating faster development of plasma bubbles. However, out-of-phase interaction of gravity waves was shown to suppress plasma bubble onset.

Shear flow instability in the bottomside F-region equatorial ionosphere was first reported by Kudeki et al. (1981) and Tsunoda et al. (1981). About the time of local sunset, westward drifts in bottomside F-layer plasma are reversed to eastward drifts with increasing altitude. This shear is reported to be strongest just after local sunset, and it extends to nearly midnight. The loop highlighted in Figure 11b, which is seen to occur at the typical time of occurrence of the evening PSSR, appears to be a signature of the evening vortex described by Kudeki & Bhattacharyya (1999). Kudeki & Bhattacharyya (1999) noted that the plasma drift circulation pattern closed in the east with downward drifts. It is then reasonable to expect that the downward drifts will eventually merge with the westward drifts to the east of the vortex. This merging action of the downward and westward drifts is the likely generation mechanism of rising plumes at the crests of waves, interacting in phase, beyond the post-sunset vortex and into midnight. The results presented by Hysell et al. (2005) and Lee et al. (2015) further demonstrate that the regions of turbulence in F-region plasma are the regions in which the eastward and westward drifts are present simultaneously.

Perhaps the clearest evidence, in this study, suggesting the interaction of eastward and westward plasma drifts is from Figure 14. In Figure 14a, the spectrogram from the HF Doppler instrument on 17 June 2022 is shown. An interval of ionospheric disturbance, flanked by wave structures to the left and right, is highlighted by the dashed rectangle. The IPP tracks of GNSS satellites that crossed the vicinity of the ionospheric reflection point of the Doppler signal before, during, and after the highlighted irregularity in Figure 14a are displayed as the blue, red, and black tracks, respectively, in Figure 14b. The time series of filtered sTEC from each of these satellites is shown in matching colours in Figure 15. Similarly, the FFT of Δ sTEC from these satellites is shown in Figure 16. The time series and line spectra confirm that large amplitude waves occurred only during the interval of irregularity shown in Figure 14a. A plausible explanation for this observation is that in-phase interference of the eastward and westward plasma drifts occurred over the interval of ionospheric disturbance. This event occurred at the typical time of occurrence of local evening PRE and PSSR, where the plasma shear described by Kudeki et al. (1981) and Tsunoda et al. (1981) is reported to be strongest.

Figure 14 (a) HF Doppler spectrogram in the interval ~ 1600–2400 UT, 17 June 2022. The dashed rectangle shows an interval of ionospheric irregularities from ~ 1930 to 2230 UT. Wave structures are visible to the left and right of the highlighted interval. (b) Map of Nigeria showing IPP tracks of satellites crossing the vicinity of the reflection point of the HF signal, before (PRN1), during (PRN7), and after (PRN14) the irregularities highlighted in (a) occurred.

Figure 15 Time series of filtered sTEC from satellites crossing the vicinity of the ionospheric reflection point of the HF signal (a) before, (b) during, and (c) after the irregularities shown in Figure 14a occurred. The time series are colour-matched with the respective PRNs in Figure 14b.

Figure 16 Line spectra of the time series in Figures 15a–15c are shown in (a)–(c), respectively. The arrowed peaks all show the same frequency of 0.52 mHz.

It should be noted that nearly all the PRNs, in view of the GNSS receiver registered similar wave characteristics as PRN1, PRN7, and PRN14 before, during, and after the wave amplification, respectively. Only the PRNs crossing the region of the HF Doppler ionospheric reflection point are shown here for the purpose of clarity. An interesting observation from Figures 15 and 16 is that the wave amplitude in the middle panels (Figs. 15b, 16b) is not a simple algebraic sum of the wave amplitudes to the left and right of these panels. This suggests that some other form of resonance mechanism may be responsible for the observed wave amplification. A question that may arise when considering the interaction of waves, which generates periodic irregularity patches, is how the eastward and westward plasma drifts are of similar frequencies. Olugbon et al. (2022) reported the presence of harmonic wave structures near the solar terminator. These waves were associated with the spreading of the F-layer on two evenings when the evening PRE was absent. The simulation results by Olugbon et al. (2022) suggested that the equatorial ionosphere at the location of the study in Nigeria has a fundamental frequency of oscillation of 0.065 mHz. Hence, it is expected that the ionosphere will oscillate at natural frequencies when set into motion by wave structures. It is interesting to note that all the spectral peaks identified in the present study were harmonics of 0.065 mHz.

In order to gain insight into the direction of propagation of the oscillations in TEC during the event on 17 June 2022 (Figs. 14–16), the IPP tracks that detected the 0.52 mHz wave component were plotted. Apart from the GPS receiver at the University of Lagos, data was available from other GPS receivers distributed across Nigeria during this event. A map of Nigeria showing the GPS receiver locations from which data were available is shown in Figure 17. The IPP tracks and TEC during the time intervals shown in Figure 15a (1600–1800 UT), Figure 15b (2000–2100 UT), and Figure 15c (2200–2330 UT) were plotted. For convenience, these time intervals are referred to as “before”, “during”, and “after” the ESF event, respectively.

Figure 17 Map of Nigeria showing the locations of the GPS stations with available data on 17 June 2022. The black star is the approximate ionospheric reflection point of the HF Doppler signal.

The IPP tracks and filtered sTEC from the satellite links that detected the 0.52 mHz wave component before the ESF event on 17 June 2022 are shown in Figure 18. The time series of GPS TEC shown on the right panels is arranged in increasing order of longitude from top to bottom. The wave appears at the west (CBCR) first, and it is easy to see a gradual progression of the wave from west to east. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave. All the IPP tracks in Figure 18 are moving southwards. Figure 19 shows the IPP tracks during the ESF event on 17 June 2022. An eastward progression of the wave from ASDE to CBCR is visible from the time series. However, the wave propagation direction from LAGO to ASDE and from CBCR to YLAD is not immediately apparent from the figure. The IPP tracks in Figure 19 are moving northwards. The IPP tracks after the ESF event on 17 June 2022 are shown in Figures 20 and 21. The tracks are shown in two different figures in order to separate the northward and southward progressing IPP tracks. Figure 20 shows the data for the southward progressing tracks, while Figure 21 shows the corresponding data for the northward progressing tracks. The double arrows in the time series are placed to identify the wave cycle in each sub-plot. In Figure 20, a westward progression of the wave from ASDE to IBOY is evident. Although the satellite over CBCR did not come into view until ~2240 UT, the time series from CBCR and ASDE were nearly in phase from ~2240 to 2300 UT. However, beginning from ~2300 UT, a reversal in phase in the wave from CBCR, in comparison to the wave from ASDE, starts to occur. This phase reversal suggests that waves propagating in opposite directions are present in this region of the ionosphere. Next, the waves from the northward progressing IPP tracks during the time interval 2200–2330 UT are examined. In Figure 21, the wave progression from the LAGO to IBOY is eastward, while a progression in the opposite direction is evident between IBOY and YLAD. The blue markers in the figure are to visualize the phase progression of the wave crests, while the red markers are to assist in visualizing the wave troughs. The double arrows are placed to identify the wave cycle in each sub-plot. One interesting observation from the time series is that a crest appears in the time series from LAGO at the position of the red marker instead of a trough (when compared with the corresponding wave cycles from IBOY and YLAD). This is suggestive of a reversal in wave phase or wave direction.

Figure 18 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 1600–1800 UT, 17 June 2022. The IPP tracks are progressing southwards. (b), (c) and (d) are the filtered sTEC from CBCR (PRN 17), LAGO (PRN 1), and IBOY (PRN 1), respectively, during the interval 1600–1800 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave.

Figure 19 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2000–2100 UT, 17 June 2022. The IPP tracks are progressing northwards. (b), (c), (d), (e) and (f) are the filtered sTEC from LAGO (PRN 7), ASDE (PRN 7), PHRI (PRN 7), CBCR (PRN 7), and YLAD (PRN 30), respectively, during the interval 2000–2100 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave.

Figure 20 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks are progressing southwards. (b), (c) and (d) are the filtered sTEC from IBOY (PRN 20), ASDE (PRN 20), and CBCR (PRN 5), respectively, during the interval 2200–2330 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave, while the double arrows are placed to identify the wave cycle in each sub-plot.

Figure 21 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks are progressing northwards. (b), (c) and (d) are the filtered sTEC from LAGO (PRN 14), IBOY (PRN 14), and YLAD (PRN 14), respectively, during the interval 2200–2330 UT, 17 June 2022. The blue markers in the time series visualize the phase progression of the wave crests, while the red markers assist in visualizing the wave troughs. The double arrows are placed to identify the wave cycle in each sub-plot.

The combined IPP tracks from Figures 20 and 21 are displayed in Figure 22. From Figure 22, it can be seen that the IPP track from LAGO crossed the IPP track from ASDE at some point. This may explain the appearance of the reversal in phase that was observed in the time series of Δ sTEC from LAGO in Figure 21b. The IPP track from IBOY also crossed the IPP track from ASDE. Although a reversal in the wave phase (or wave propagation direction) is not visible in the time series of Δ sTEC from IBOY, there appears to be a cancellation of the wave at IBOY beyond 2300 UT in Figure 21c. This may have been due to the interaction of oppositely directed waves. The results shown in Figures 18–22 buttress three main points suggested from the preceding results: (1) Eastward progressing waves were present in the vicinity of the HF signal reflection point before the ESF event on 17 June 2022, while westward propagating waves were present in the same region after the ESF event. (2) Oppositely directed waves were present simultaneously in this region of the equatorial ionosphere. (3) Interaction of oppositely directed waves can occur in this region of the equatorial ionosphere.

Figure 22 Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks in Figures 12a and 13a are combined. The southward-directed tracks appear in blue colour while the northward-directed tracks appear in red.

Hysell & Kudeki (2004) presented a mathematical formulation for a collisional shear instability in magnetized plasma. A model run of the collisional shear instability model produced growing wave structures, which were proposed to trigger the interchange instability. Observations from ionospheric radar experiments by Hysell et al. (2006) showed large-scale waves that preceded ESF depletions and irregularities. Hysell et al. (2006) postulated that the collisional shear instability generated the large-scale waves and that the vertical plasma drift speed of these waves initiated the RTI necessary for ESF occurrence. Hysell et al. (2006) proposed that the plasma depletions and irregularities (triggered by the large-scale waves) rise to altitudes where they grow according to the RTI theory.

The conditions that favour the development of the collisional shear instability presented by Hysell & Kudeki (2004) are present in the evening equatorial ionosphere before, during, and after the PRE. The sequence of events leading to the generation of ESF, based on the collisional shear instability postulated by Hysell & Kudeki (2004) and Hysell et al. (2006), is summarized in Figure 23a. However, when the PRE is low or absent, the collisional shear instability is unlikely to develop. The hypothesis of interacting plasma drifts, based on the findings from this study, is summarized in Figure 23b. This hypothesis suggests a mechanism of ESF generation when there is little or no displacement in altitude between the pre-sunset and post-sunset of the ionospheric reflecting layer (i.e., when the PRE is low or absent). Under these conditions, wave structures in the eastward and westward plasma drifts interfere, and the interference leads to the generation of large-amplitude waves. The Movie M1 is a simulation of two oppositely directed waves undergoing interference. The rising crest of the interfering waves is hypothesized to act as the mechanism, similar to the PRE/PSSR, which facilitates the rise of bottomside plasma to the topside, thereby triggering an interchange of topside and bottomside plasma. This process leads to the eventual development of the RTI, which manifests as plasma bubbles and ESF.

Figure 23 A schematic depicting the sequence of events leading to the generation of ESF based on (a) the postulation by Hysell & Kudeki (2004), (b) the hypothesis presented in this paper.

Finally, we address the issue of day-to-day variabilities observed in the dataset. Detailed analysis of the dataset from the dip equator showed that if a plume or a bubble was present in the vicinity of the track on which elevated S4 indices were recorded, then the amplitudes of wave structures associated with the elevated S4 indices were disproportionately large. Inclusion of wave amplitude and S4 index from such events resulted in a lower correlation index in the dataset. An example from 22 June 2022 is shown in Figure 24. The data from two satellites, PRN 7 and PRN 20, are shown. Figure 24a shows the IPP tracks of each PRN. The track of PRN 7, which crossed the ionospheric reflection point of the HF signal, is shown by the red arrow, while the track of PRN 20 is shown by the blue arrow. A plume which appeared in the Doppler trace, about the typical time of occurrence of the evening PSSR, is shown by the black arrow in Figure 24b. The upper and lower panels in Figure 25 show the scintillation indices and filtered sTEC, respectively, from both satellites. The interval over which elevated S4 indices were recorded is highlighted by the dashed rectangle. Although nearly equal amplitudes of maximum S4 index were recorded on both tracks during the highlighted interval (Fig. 25a), the wave amplitudes over the same interval were significantly different (Fig. 25b). Wave amplitudes from PRN7, which crossed the ionospheric reflection point of the HF signal where the plume was detected, were much higher than wave amplitudes from PRN 20. The plume shown in Figure 24b likely triggered the elevated S4 indices on 22 June 2022. However, it appears that the trigger was localized even though the resulting scintillation was detected over a much wider area. A high spatial resolution of a suite of monitoring instruments is necessary to detect these kinds of localized occurrences, as recommended by earlier studies like Das et al. (2021). Table S1 shows how the correlation between the S4 index and wave amplitude (maximum and mean) from the dip equator changes depending on which PRN is selected. The event on 22 June 2022 is one of several similar events that introduced variabilities to the linear relationship between the S4 index and wave amplitudes. The results for 17 June 2022, the same day for which data is displayed in Figure 14, are also shown in Table S1. Two sets of readings are displayed for each day. The set of readings in bold font is that from the PRN whose IPP track likely encountered a plume. The measurements for both PRNs on any given day were taken during the same time interval and when both IPP tracks were in the vicinity of the dip equator. Table S1 is intended to convey two key points; (1) Wave amplitudes from the tracks that likely encountered a plume are sometimes twice as large as the wave amplitudes from the tracks that did not, even when the maximum S4 index on both tracks are nearly equal; and (2) If the S4 index and wave amplitude from the tracks that did not encounter a plume are used in the correlation analysis, in place of the corresponding values from the tracks that encountered a plume, a higher correlation index is obtained. For the statistical analysis shown in Figures 8 and 9, if the five sets of readings in bold font in Table S1 are substituted with the readings in plain font, then the correlation indices shown in Figure 8b and 9b become 0.50 and 0.55, respectively. These findings support the reasoning that very large amplitude waves could be the signatures of plumes that develop via the interaction of waves. Therefore, variabilities in the linear relationship between the S4 index and wave amplitude can arise when plumes are encountered along/near the track of IPPs of a satellite.

Figure 24 Experimental data during post-sunset hours, 22 June 2022. (a) IPP tracks of PRNs 7 and 20, which registered highest S4 index near the dip equator, are marked by the red and blue arrows, respectively. (b) The signature of a plume in the HF Doppler spectrogram is indicated by the black arrow. The time of occurrence of the plume coincides with the time when elevated S4 indices were detected by the satellites.

Figure 25 (a) S4 indices and (b) time series of Δ sTEC during post-sunset hours, 22 June 2022.

5 Conclusions

The results from a coordinated study of equatorial ionospheric scintillation undertaken with ground-based instruments in Lagos, Nigeria, have been presented. A peak in ionospheric scintillation was observed at the southern crest of the EIA, while a lower peak was observed in the vicinity of the dip equator. Plasma bubbles were ubiquitous in the EIA crest, but hardly any bubbles were seen in the data from the dip equator. However, wave structures were conspicuous in time series of filtered sTEC from both the dip equator and the EIA crest. A higher correlation index was obtained from a linear correlation analysis of the S4 index and wave amplitude, compared with a similar analysis of the S4 index and PSSR. A more detailed inspection of selected events showed the possibility that the crests of waves interfering in phase can facilitate the upward rise of plasma through ionospheric layers. This action can facilitate the growth of the Rayleigh-Taylor instability and subsequent development of ionospheric irregularities. Earlier studies have reported a shear flow between eastward and westward plasma drifts, which commences about the time of local sunset and continues to midnight. The results from this study present a possibility that the wave structures associated with the eastward and westward plasma drifts can interact to generate the F-layer irregularities. These results can assist in developing predictive capabilities for occurrences of equatorial ionospheric irregularities, particularly for the equatorial African sector. Such predictive capabilities can facilitate the development of robust trans-ionospheric radio systems for the African sector.

Acknowledgments

The authors gratefully acknowledge the Office of the Surveyor General of the Federation and MiraNet (https://miranet.nignet.net/) for the GPS-TEC data from Nigeria. The HF radio data used in this work were obtained from the HF Doppler instrument jointly deployed by the United Nations African Regional Centre for Space Science and Technology Education, Nigeria; the Institute for Radio Astronomy, National Academy of Science, Ukraine; in collaboration with the Telecommunication and Information & Communication Technology for Development (T/ICT4D) Lab of the Abdus Salam International Centre for Theoretical Physics (ICTP), Italy. The maintenance and operation of the transceivers are supported by the United Nations African Regional Centre for Space Science and Technology Education and the University of Lagos, Nigeria. The editor thanks three anonymous reviewers for their assistance in evaluating this paper.

Funding

The authors are grateful to the Nigerian Tertiary Education Trust Fund (TETFund), through the National Research Fund (NRF), and the University of Lagos for funding.

Data availability statement

HF Doppler spectrograms are available at the Department of Radiophysics of Geospace website (http://geospace.com.ua/databrowser/Default.aspx?Observatory=14&Instrument=19&DataType=2). The GNSS data from the University of Lagos, used for TEC and S4 index analysis in the study, are available at Mendeley Data via https://doi.org/10.17632/zjb4f5z5gw.1 with CC BY 4.0.

Supplementary material

Figure S1: TEC from PRN 26, 6 March 2022, with different elevation masks applied. The plasma bubble signature, highlighted by the red oval, is partly obscured when the elevation mask is raised to 25°. (LT=UT+1).

Figure S2: Histograms comparing S4 index from the dip equator and from the EIA crest for all the days included in this study. The scintillation index at the EIA crest is usually higher compared with that from the dip equator.

Figure S3: (a) – (c) are the unfiltered sTEC corresponding to the Δ sTEC events shown Figure 3 d-f, respectively, in the main article file. The lower panels (d – f) show S4 index during the corresponding event displayed in the upper panel. Large amplitude wave structures in Δ sTEC are coincident with elevated S4 index.

Figure S4: The left panels show scatter plots of S4 indices obtained from IPP tracks over the EIA crest vs. (a) Doppler PSSR (c) Maximum FFT peak at EIA crest (e) Mean FFT peak at EIA crest. The right panels are scatter plots of S4 indices obtained from IPP tracks over the dip equator vs. (b) Doppler PSSR (d) Maximum FFT peak at dip equator (f) Mean FFT peak at dip equator. The linear correlation indices are shown in the plots. All available data, regardless of the occurrence of plasma bubbles or spectral peaks ≥ 1 TECU, are included in the plots.

Figure S5: Scatter plots and linear correlation indices of (a) Plasma bubble depth vs. S4 indices from the EIA crest. (b) S4 indices from the dip equator vs. S4 indices from the EIA crest.

Figure S6: Same as Figure 10a in the main article file.

Figure S7: Same as Figure 10b in the main article file.

Figure S8: Same as Figure 11a in the main article file.

Figure S9: Same as Figure 11b in the main article file.

Figure S10: (a) Figure 11a from the main article file and (b) Figure 13 from the main article file (with the horizontal axis cropped). The arrowed positions, numbered 1 – 4, show periodic structures in the HF Doppler spectrogram that match the crests of the waveform in the bottom figure. Apart from the tilt of the numbered structures in the HF Doppler spectrogram, the periodic structures in the upper plot and the crests of the waveform in the lower plot show a one-to-one correspondence.

Table S1: Discrepancies in the linear correlation between S4 index and wave amplitude, based on PRN selection. The data for five different days with similar characteristics, from the dip equator, are displayed. Two sets of readings are displayed for each day. The set of readings in bold font are those from the PRN whose IPP track likely encountered a plume. If the 5 sets of entries in plain font are substituted in place of the readings in bold font for the statistical analysis in Figure 4 (main article text), then the correlation indices shown in Figure 4d and 4f become 0.5036 and 0.5527 respectively. Access here

Movie M1: Simulation of two oppositely directed waves, with identical properties, undergoing interference. Access here

References

All Figures

	Figure 1 (a) Doppler spectrogram and (b) Time series, 7 March 2022. The signature of the PSSR and the subsequent drop in the reflecting layer height are highlighted by the grey dashed rectangle in the interval ~ 1730–1915 UT (LT = UT + 1). A PSSR of −2.5 Hz was recorded.
In the text

	Figure 2 Number of days for which data was simultaneously available from the HF Doppler sounder and Septentrio receiver in 2022.
In the text

	Figure 3 IPP tracks of satellites in view during post-sunset hours (1830–2300 UT; LT = UT + 1) on a typical day are imposed on a map of Nigeria. The blue line across the map is the approximate position of the dip equator. The approximate ionospheric reflection point of the HF signal is indicated by the black star.
In the text

	Figure 4 Spectral and time series analysis of sTEC on 21 April 2022. The spectra in the upper panels (a) and (b) are shown with matching colours to the highlighted intervals in the time series in the bottom panel (c). Even though the FFT is determined over two different time intervals, the mean of the largest 3 spectral peaks for both time intervals is nearly the same.
In the text

	Figure 5 (a) Spectral analysis of sTEC on 22 June 2022. (b) Time series analysis of sTEC on 22 June 2022. The highlighted interval is the interval over which the FFT in (a) was computed. The mean of the largest three peaks in the FFT and the largest spectral peak are nearly equal.
In the text

	Figure 6 (a) Spectral analysis of sTEC on 7 August 2022. (b) Time series analysis of sTEC on 7 August 2022. The highlighted interval is the interval over which the FFT in (a) was computed. There is a significant difference between the mean of the largest three peaks in the spectrum and the largest spectral peak.
In the text

	Figure 7 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Doppler PSSR. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Doppler PSSR. The linear correlation indices are shown in the plots.
In the text

	Figure 8 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Maximum FFT peak at EIA crest. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Maximum FFT peak at dip equator. The linear correlation indices are shown in the plots.
In the text

	Figure 9 (a) Scatter plot of S4 indices obtained from IPP tracks over the EIA crest vs. Mean FFT peak at EIA crest. (b) Scatter plot of S4 indices obtained from IPP tracks over the dip equator vs. Mean FFT peak at dip equator. The linear correlation indices are shown in the plots.
In the text

	Figure 10 (a) Spectrogram of HF Doppler signal on 3 September 2022, ~1500–2400 UT. Periodic structures are present in the post-sunset spread in the reflection layer. (b) An expanded view of the left panel. Rising plumes at the crests of the wave structures are indicated by the black arrows.
In the text

Figure 11 Spectrogram of HF Doppler signal on (a) 11 July 2022, ~1500–2400 UT. Higher frequency wave structures appear to be embedded in a lower frequency wave in the post-sunset activity. (b) 16 September 2022, ~1400–2100 UT. A loop in the trace is highlighted by the black arrow. This can occur when shear flow is generated between waves propagating in opposite directions, thereby creating a vortex in the ionospheric plasma. Beyond the loop, periodic structures are visible in the post-sunset spread ~1900–2100 UT.

In the text

	Figure 12 (a) Map of Nigeria showing IPP tracks of PRNs in view during post-sunset hours, 11 July 2022. The IPP track of PRN 30, which recorded the maximum S4 index over the dip equator, is shown by the black arrow. (b) Filtered sTEC from PRN 30 during post-sunset hours. (c) FFT of Δ sTEC from PRN 30 over the interval ~2000–2100 UT. (LT = UT + 1).
In the text

	Figure 13 Simulation of two signals of same amplitude but different frequencies interfering over the boxed interval. The lower frequency signal is to the left of the boxed interval, while the higher frequency signal, with frequency 4× the lower frequency signal, is shown to the right of the boxed interval.
In the text

Figure 14 (a) HF Doppler spectrogram in the interval ~ 1600–2400 UT, 17 June 2022. The dashed rectangle shows an interval of ionospheric irregularities from ~ 1930 to 2230 UT. Wave structures are visible to the left and right of the highlighted interval. (b) Map of Nigeria showing IPP tracks of satellites crossing the vicinity of the reflection point of the HF signal, before (PRN1), during (PRN7), and after (PRN14) the irregularities highlighted in (a) occurred.

In the text

	Figure 15 Time series of filtered sTEC from satellites crossing the vicinity of the ionospheric reflection point of the HF signal (a) before, (b) during, and (c) after the irregularities shown in Figure 14a occurred. The time series are colour-matched with the respective PRNs in Figure 14b.
In the text

	Figure 16 Line spectra of the time series in Figures 15a–15c are shown in (a)–(c), respectively. The arrowed peaks all show the same frequency of 0.52 mHz.
In the text

	Figure 17 Map of Nigeria showing the locations of the GPS stations with available data on 17 June 2022. The black star is the approximate ionospheric reflection point of the HF Doppler signal.
In the text

Figure 18 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 1600–1800 UT, 17 June 2022. The IPP tracks are progressing southwards. (b), (c) and (d) are the filtered sTEC from CBCR (PRN 17), LAGO (PRN 1), and IBOY (PRN 1), respectively, during the interval 1600–1800 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave.

In the text

Figure 19 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2000–2100 UT, 17 June 2022. The IPP tracks are progressing northwards. (b), (c), (d), (e) and (f) are the filtered sTEC from LAGO (PRN 7), ASDE (PRN 7), PHRI (PRN 7), CBCR (PRN 7), and YLAD (PRN 30), respectively, during the interval 2000–2100 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave.

In the text

Figure 20 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks are progressing southwards. (b), (c) and (d) are the filtered sTEC from IBOY (PRN 20), ASDE (PRN 20), and CBCR (PRN 5), respectively, during the interval 2200–2330 UT, 17 June 2022. The red markers in the time series are inserted to assist in visualizing the phase progression of the wave, while the double arrows are placed to identify the wave cycle in each sub-plot.

In the text

Figure 21 (a) Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks are progressing northwards. (b), (c) and (d) are the filtered sTEC from LAGO (PRN 14), IBOY (PRN 14), and YLAD (PRN 14), respectively, during the interval 2200–2330 UT, 17 June 2022. The blue markers in the time series visualize the phase progression of the wave crests, while the red markers assist in visualizing the wave troughs. The double arrows are placed to identify the wave cycle in each sub-plot.

In the text

	Figure 22 Map of Nigeria showing the IPP tracks of PRNs that detected the 0.52 mHz wave 2200–2330 UT, 17 June 2022. The IPP tracks in Figures 12a and 13a are combined. The southward-directed tracks appear in blue colour while the northward-directed tracks appear in red.
In the text

	Figure 23 A schematic depicting the sequence of events leading to the generation of ESF based on (a) the postulation by Hysell & Kudeki (2004), (b) the hypothesis presented in this paper.
In the text

Figure 24 Experimental data during post-sunset hours, 22 June 2022. (a) IPP tracks of PRNs 7 and 20, which registered highest S4 index near the dip equator, are marked by the red and blue arrows, respectively. (b) The signature of a plume in the HF Doppler spectrogram is indicated by the black arrow. The time of occurrence of the plume coincides with the time when elevated S4 indices were detected by the satellites.

In the text

	Figure 25 (a) S4 indices and (b) time series of Δ sTEC during post-sunset hours, 22 June 2022.
In the text

	Figure S1: TEC from PRN 26, 6 March 2022, with different elevation masks applied. The plasma bubble signature, highlighted by the red oval, is partly obscured when the elevation mask is raised to 25°. (LT=UT+1).
In the text

	Figure S2: Histograms comparing S4 index from the dip equator and from the EIA crest for all the days included in this study. The scintillation index at the EIA crest is usually higher compared with that from the dip equator.
In the text

	Figure S3: (a) – (c) are the unfiltered sTEC corresponding to the Δ sTEC events shown Figure 3 d-f, respectively, in the main article file. The lower panels (d – f) show S4 index during the corresponding event displayed in the upper panel. Large amplitude wave structures in Δ sTEC are coincident with elevated S4 index.
In the text

Figure S4: The left panels show scatter plots of S4 indices obtained from IPP tracks over the EIA crest vs. (a) Doppler PSSR (c) Maximum FFT peak at EIA crest (e) Mean FFT peak at EIA crest. The right panels are scatter plots of S4 indices obtained from IPP tracks over the dip equator vs. (b) Doppler PSSR (d) Maximum FFT peak at dip equator (f) Mean FFT peak at dip equator. The linear correlation indices are shown in the plots. All available data, regardless of the occurrence of plasma bubbles or spectral peaks ≥ 1 TECU, are included in the plots.

In the text

	Figure S5: Scatter plots and linear correlation indices of (a) Plasma bubble depth vs. S4 indices from the EIA crest. (b) S4 indices from the dip equator vs. S4 indices from the EIA crest.
In the text

	Figure S6: Same as Figure 10a in the main article file.
In the text

	Figure S7: Same as Figure 10b in the main article file.
In the text

	Figure S8: Same as Figure 11a in the main article file.
In the text

	Figure S9: Same as Figure 11b in the main article file.
In the text

Figure S10: (a) Figure 11a from the main article file and (b) Figure 13 from the main article file (with the horizontal axis cropped). The arrowed positions, numbered 1 – 4, show periodic structures in the HF Doppler spectrogram that match the crests of the waveform in the bottom figure. Apart from the tilt of the numbered structures in the HF Doppler spectrogram, the periodic structures in the upper plot and the crests of the waveform in the lower plot show a one-to-one correspondence.

In the text