© K. Hocke et al., Published by EDP Sciences 2025

1 Introduction

The influence of the Moon phase is relatively well known for oceanic tides which show spring tides during New Moon and Full Moon and neap tides during First Quarter Moon and Third Quarter Moon. The beat period of the spring-neap tidal cycle is 14.7653 (solar) days which is half of a lunar synodic month of 29.5306 days (Bartels & Fanselau, 1938). The origin of the spring-neap tidal cycle was explained in detail by Kvale (2006). In a first approximation, the equilibrium tidal theory model can explain the occurence of spring and neap tides. In this model, the gravitational force from the Moon, in combination with the centrifugal force associated with the rotation of the Earth around the center of mass of the Earth-Moon system, produce oceanic bulges on opposite sides of the Earth. The spin of the Earth leads to the effect that an observer at ground passes the two tidal bulges during a lunar day of 24.84120 solar hours which results in a lunar semidiurnal tide of sea level with a period of 12.42060 h. Similarly, the gravitational and centrifugal forces of the Sun produce tidal bulges on the Earth. During New Moon and Full Moon, the tidal bulges induced by the Moon and the Sun are in constructive interference so that an enhancement of the semidiurnal tide can be observed (spring tide). During First Quarter Moon and Third Quarter Moon, the tidal bulges induced by Moon and Sun are orthogonal to each other and a decreased tidal amplitude is observed (neap tide).

In case of the ionosphere, a similar effect can be expected leading to a beat of the tidal amplitude. The lunar semidiurnal tide propagates from the lower atmosphere into the ionosphere where it mainly induces a periodic electric field variation in the dynamo region which generates a lunar semidiurnal variation M₂ in the F region plasma. In the F region, a solar semidiurnal variation S₂ of ionization also exists with a period of 12 h. This solar tide is not induced by gravitational and centrifugal forces as the oceanic tides but by the daily cycle of insolation in the atmosphere as consequence of the solar radiation and the Earth spin. S₂ in the ionosphere depends on the solar semidiurnal tide from below and is a part of the daily cycle of ionization which consists of the diurnal component and its harmonics. The variations M₂ and S₂ combine constructively or destructively depending on their phase difference which possibly depends on the Moon phase. Since the period of M₂ is 12.42060 h and S₂ is 12 h, the beat period of M₂ and S₂ is 1/(1/12 −1/12.42060) h = 14.7653 days. This is the same beat period as in the case of the spring and neap tides of the ocean. Lin et al. (2019) showed the beat of S₂ and M₂ in F₂ peak electron density in the EIA crest region obtained by Global Ionosphere Specification (GIS) based on Gauss-Markov Kalman filter assimilation of slant total electron content (TEC) observed from ground-based global positioning system receivers and space-based radio occultation instrumentations. Around the sudden stratospheric warming (SSW) of January 2009, they got a beat period of 15.13 days for S₂ and M₂. They reported that this would be in agreement with theory. However, we think that the theory of beat oscillations would predict 14.7653 days as explained above.

Beside the M₂ variation, there are also lunar diurnal and terdiurnal variations in the ionosphere (Malin & Chapman, 1970; Hocke et al., 2024a). These lunar daily variations have a beat with the solar diurnal S₂ and solar terdiurnal S₂ variations of TEC respectively, resulting in the same beat period of 14.7653 days as mentioned above.

The influence of the Moon phase on ionospheric electron density has been firstly simulated and discussed by Pedatella & Liu (2013) and Lin et al. (2019) who found that beating between solar and lunar migrating tides reflects on the semidiurnal ionospheric variation. They pointed out that the timing of the SSW and the Moon phase has a strong influence on the semidiurnal ionospheric variation since the lunar ionospheric variation can contribute about 30% of the total ionosphere response to SSWs. Wu et al. (2020) discovered that the arrival time, latitude position, and the intensity of the EIA crest in TEC is modulated by the Moon phase with a period of 14.77 days. This beat period is due to constructive and destructive interference of the solar and lunar semidiurnal tide in the ionosphere which have slightly different frequencies. In addition, the nonlinear interaction of the M₂ tide and the diurnal variation in electron density generates quasi-diurnal and quasi-terdiurnal ionospheric variations which are present in TEC observations, ionosonde data and model simulations (Hocke et al., 2025).

Lunar M₂ wind amplitudes from 40–50 m/s can occur in the dynamo region during northern hemispheric winter and SSWs (Pedatella et al., 2014). Particularly, the equatorial ionosphere is disturbed due to the SSW-induced amplification of the lunar tide (Yamazaki et al., 2012, 2017). The amplification of the M₂ variation is due to favorable vertical propagation conditions for the lunar tide (Pekeris resonance) on its way through the middle atmosphere (Forbes & Zhang, 2012). In the dynamo region at 100–110 km altitude, the M₂ tide generates electric field variations which are mapped along the magnetic field from the E region to the F region. In the E region where the ion lifetime is small (fast dissociative recombination of molecular ions and electrons), plasma transport plays a minor role and the tide-induced plasma variations are small. In the F region, the ion lifetime is much larger than in the E region because of slow radiative recombination of atomic ions and electrons at high altitudes (Hargreaves, 1992). Thus, the tide-induced electric field variations which are mapped to the F region induce considerable F region plasma variations because of the $\vec{E}\times \vec{B}$ plasma drift. Periodic electrodynamic lifting of the equatorial F region plasma is associated with the projected electric field variations of the lunar tide (Yamazaki & Richmond, 2013; Pedatella et al., 2014).

Similarly as the lunar semidiurnal tide, the solar tides generate periodic electrodynamic lifting of the equatorial F region plasma but with slightly different periods than the lunar variations. Thus, a beat of lunar and solar daily variations can be expected in the F region plasma. The aim of the present study is to characterize the average beat of solar and lunar daily variations in the ionosphere and to study the average influence of the Moon phase on the daily TEC variations. For this sake, we analyse the long-term time series of TEC as observed by the worldwide network of GNSS ground receivers from June 1998 to October 2024.

Section 2 describes the GNSS dataset, the spectral analysis and the data filtering. Section 3 presents the results, and discussion and conclusions are given in Sections 4 and 5, respectively.

2 Data and data analysis

2.1 Ionospheric total electron content (TEC)

The worldwide network of Global Navigation Satellite System (GNSS) ground receivers for the radio signals of the GNSS satellites monitors TEC. The International GNSS Service (IGS) provides world maps of vertical TEC with a time resolution of 2 h and a spatial resolution of 5° in longitude and 2.5° in latitude since June 1998. The present study analyses the TEC data from June 1998 to October 2024. Hernández-Pajares et al. (2009) described the calculation and the error assessment of these TEC maps which have a relative error of TEC less than 20% compared to coincident satellite altimeter observations, even over data sparse regions such as the oceans. The TEC maps of IGS are appropriate for the analysis of lunar tides in ionospheric TEC (Pedatella et al., 2014; Hocke et al., 2024a).

2.2 Data analysis

The data analysis of the present study is based on Fast Fourier Transform (FFT) spectral analysis and digital filtering. At first, the time series of TEC in Southern China at the grid point 25° N latitude and 110° E longitude is analysed for the occurrence of lunar and solar daily variations. We selected this grid point because the lunar influence is strong in Southern China which is below the equatorial ionization anomaly (EIA). In addition, this region is well covered by GNSS receivers, so that the TEC maps should have a high quality in this region.

The FFT spectrum is calculated from the selected time series of TEC from 1998 to 2024. A Hamming window and zero padding to the data segment were applied. The zero padding extended the data segment by a factor of 5 in order to have a highly resolved frequency grid for a good matching of the lunar tidal frequencies. Since a Hamming window and zero padding are decreasing the FFT amplitude spectrum, we performed a calibration of the FFT amplitude spectrum by means of artificial sine waves with known amplitudes.

For investigation of the beating the lunar and solar daily variations, we filtered the TEC series with a digital non-recursive, finite impulse response bandpass filter. Zero-phase filtering is ensured by processing the time series in forward and reverse directions. The filter uses a Hamming window. The number of filter coefficients corresponds to a time window of three times the central period, so that the bandpass filter has a fast response time to temporal changes in the data series. The bandpass for the semidiurnal variation is open for both, the S₂ and the M₂ variation, and the bandpass cut-off frequencies are at 1.8 and 2.2 cycles per day (cpd). Further details about the bandpass filtering are provided by Studer et al. (2012). For the diurnal variation, the bandpass cut-off frequencies are at 0.8 and 1.2 cpd. For the terdiurnal variation, the bandpass cut-off frequencies are at 2.7 and 3.3 cpd.

The envelope of the amplitude of the filtered TEC series is mainly modulated by periods of the solar cycle, the annual cycle (and its harmonics), and the beat period of solar and lunar tides (14.7653 days) as a FFT spectral analysis of the envelope amplitude time series shows. The spectral analysis is performed in the same manner as above.

There are two possibilities to study the influence of the Moon phase on TEC. For the single grid point in Southern China, we can sort and bin the filtered TEC series with respect to lunar days from 0 (New Moon) to 29.5306 (New Moon again). Lunar day 14.7653 stands for Full Moon.

The other possibility is to analyse the amplitude and phase of the FFT spectrum (of the filtered envelope series) at the beat period 14.7653 days. This analysis can be easily made for each grid point worldwide, so that we can derive world maps of the average amplitude and phase of the beat effect. We did this analysis for characterization of the beat of the semidiurnal TEC variation worldwide. We define the phase of the FFT spectrum by calculation of the phase difference between the FFT component and the phase of a cosine wave with maxima at New Moon and Full Moon. Thus, phase 0° means that the tide maximum appears at New Moon or Full Moon. Phase 180° means that the tide maximum is at First Quarter Moon (or Third Quarter Moon). The New Moon dates are computed by means of a reference date (New Moon at Greenwich (UK) on 2025-01-29, 12:36 UTC (Espenak, 2025)), and the New Moon phase is repeated in average with a period of 29.5306 days.

3 Results

The FFT amplitude spectrum of TEC is determined for Southern China (25°N latitude, 110°E longitude) using the TEC series of the time interval from June 1998 to October 2024. Figure 1 shows spectral peaks at the frequencies 1 cpd, 2 cpd, and 3 cpd which belong to the solar diurnal, semidiurnal and terdiurnal variations of TEC respectively. On the left hand side of these solar daily variation components there are the spectral peaks of the lunar diurnal, semidiurnal, and terdiurnal variation. The red dashed lines are exactly drawn at the expected frequencies of M₂ − S₁, M₂, and M₂ + S₁, which are (24/12.4206 − 1) cpd, 24/12.4206 cpd, and (24/12.4206 + 1) cpd, respectively. We can see that these frequencies exactly match to the spectral peak positions of the three lunar daily variations of TEC.

Figure 1 FFT amplitude spectra of TEC (blue line) in Southern China (25 °N latitude, 110°E longitude) for the time interval from 1998 to 2024. The red dashed lines indicate the lunar diurnal variation M2 − 1 cpd, the lunar semidiurnal variation M2, and the lunar terdiurnal variation M2 + 1 cpd. The spectral peaks of the solar daily variations S1, S2, and S3 are at 1 cpd, 2 cpd, and 3 cpd respectively. The magenta line denotes the 95% confidence level.

There are also some other spectral lines in Figure 1, e.g., a spectral line occurs at M₂ − 1/(27.55 days) (small line left to M₂ line). This small spectral peak indicates the modulation of the M₂ variation by the anomalistic month (variable Earth-Moon distance due to eccentricity of the Moon orbit). The M₂ variation of TEC is maximal about three days after perigee transit of the Moon (Hocke, 2025). In the present study, we only consider the beat of S₂ and M₂ but one has to keep in mind that other spectral peaks also contribute to the observed variations. The anomalistic month may generate a perigean spring tide which is strongest when the Moon is at its perigee and when M₂ and S₂ interfere constructively. According to Figure 1, this anomalistic month or eccentricity variation is about 0.25 TECU.

At the left side of Figure 1, the noise reaches an amplitude of 0.1 TECU. The 95% confidence limit is at two times the noise which is about 0.2 TECU. Thus, the spectral peaks of the lunar and solar daily variations are significant more than 95% since their amplitudes are larger than 0.2 TECU. Compared to the semiannual oscillation (SAO) of TEC which is about 5.6 TECU, the lunar daily variations of TEC (diurnal and semidiurnal components) are about 0.8 TECU in Figure 1 which is 14% of the strong SAO variation. Thus, the lunar daily variations of TEC should be taken into account at low geomagnetic latitudes (as in Fig. 1), while the lunar influence on TEC could be neglected at middle and high geomagnetic latitudes.

The frequency difference between the solar semidiurnal peak and the lunar semidiurnal peak is 2 cpd − M₂ = (2 − 24/12.4206) cpd. This frequency difference is the beat frequency of the solar and lunar semidiurnal oscillation, and it corresponds to a beat period of 14.7653 days which is half of a lunar synodic month. The same beat period is also present for the solar and lunar diurnal variation and the solar and lunar terdiurnal variation.

The next step is that the long-term time series of TEC in Southern China is filtered for the semidiurnal variation with a bandpass from 1.8 cpd to 2.2 cpd. That means, the filtered series will contain both oscillations the lunar semidiurnal variation and the solar semidiurnal variation. Then, we analyse and discuss the modulations of the envelope of the semidiurnal amplitude by means of a FFT spectrum which is shown in Figure 2. It is obvious that the semidiurnal amplitude is modulated by the solar cycle and the annual oscillation and its harmonics. Comparable to the strength of the modulation amplitudes due to the seasonal variations, we find a spectral peak at the frequency (2 − 24/12.4206) cpd which correspond to the beat period of 14.7653 days (red dashed line on the right hand side of Fig. 2). A similar analysis is performed later for all grid points of the worldwide TEC maps of IGS and the amplitudes and phases of the FFT component at the beat frequency will be evaluated.

Figure 2 FFT spectrum of amplitude envelope of the semidiurnal variation of TEC (bandpass 1.8–2.2 cpd) in Southern China (blue line). The envelope is modulated by periods of the solar cycle, seasonal variations (annual oscillation AO, semiannual oscillation SAO and further harmonics). The beat of the lunar and solar semidiurnal variation generates a spectral peak at the beat frequency 2 cpd − M2 (equal to a period of 14.7653 days or half of a lunar synodic month). The magenta line denotes the 95% confidence level.

As mentioned in the previous section, another possibility is to evaluate the filtered time series of the semidiurnal TEC variation in Southern China by means of sorting and binning the envelope amplitude values as function of Moon phase (lunar cycle from 0 to 29.5306 lunar days). Figure 3 shows the result. The semidiurnal amplitude is maximal at 2–3 days after New Moon (lunar day 0) and again 2–3 days after Full Moon (lunar day 14.7653). The thick black line shows the result averaged for all seasons. The maximal amplitude is about 5.1 TECU and the minimal amplitude is about 3.6 TECU that means the modulation is about ±0.75 TECU which agrees well with the FFT spectrum amplitude of about 0.8 TECU at the beat frequency 2 − M₂ in Figure 2. The influence of the Moon phase on the semidiurnal amplitude is quite similar in each season.

Figure 3 Amplitude of the semidiurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all TEC data in Southern China from 1998 to 2024. The colored lines show the results for the different seasons.

Analogously to Figure 3, the beat of the other lunar and solar daily variations can be determined. Figure 4 shows the result for the diurnal variation. The thick black line shows maxima of the diurnal amplitude 2–3 days after New Moon and Full Moon. However, the colored lines of the seasons show some deviations from the mean behaviour. Figure 5 shows the result for the terdiurnal variation. In difference to the semidiurnal and diurnal amplitude, the influence of the Moon phase is not so clear for the terdiurnal amplitude. The result is a bit similar if we only take the daytime data of the terdiurnal amplitude series. The thick black line shows maxima of the diurnal amplitude 2–3 days after New Moon and Full Moon. However, the colored lines of the seasons show some deviations from the mean behavior.

Figure 4 Amplitude of the diurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all TEC data in Southern China from 1998 to 2024. The colored lines show the results for the different seasons.

Figure 5 Amplitude of the terdiurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all daytime TEC data (solar zenith angle SZA < 90°) in Southern China from 1998 to 2024. The colored lines show the daytime results for the different seasons.

In the following, the influence of the Moon on the semidiurnal TEC amplitude is derived worldwide using the FFT amplitude and phase values at the beat frequency of the solar and lunar semidiurnal oscillation. The FFT is independently computed for each grid point by using the filtered envelope amplitude series at each grid point. Figure 6 shows the modulation amplitude. Strong modulations of the semidiurnal variations occur around the EIA at low latitudes. This important result is in agreement with the study by Wu et al. (2020) who found a strong dependence of the EIA crest’s position, arrival time and strength on the lunar phase. Small beat amplitude values are obtained along with the geomagnetic equator in Figure 6, which agrees with the relatively small M₂ amplitude in TEC along the geomagnetic equator (Hocke et al., 2025). In the northern hemisphere, there is a longitudinal variation showing three yellow peaks above the Pacific, the Atlantic, and China.

Figure 6 Beat amplitude of the semidiurnal variation of TEC (FFT amplitude at period 14.7653 days) for the time from 1998 to 2024. The red line denotes the geomagnetic equator. The magenta cross denotes the location in Southern China (25°N latitude, 110°E longitude) which we analysed in the previous figures.

Figure 7 shows the Moon phase of the maximal semidiurnal amplitude. Light brownish colors as in Southern China (red cross) correspond to a maximal amplitude a few days after New Moon or Full Moon. The phase is 55.7° at the red cross which corresponds to 2.3 lunar days after New Moon or Full Moon. This value agrees with the maxima positions in Figure 3. Over Florida and the western Atlantic, the maximum is reached at First Quarter Moon. We only show the phase values at beat amplitudes greater than 0.17 TECU since the phase determination is unreliable for signals with a small amplitude. In total, one can say that the maximum of the semidiurnal amplitude at the EIA occurs a few days after New Moon or Full Moon.

Figure 7 Moon phase of maximal semidiurnal amplitude of TEC. Maximum at New Moon (or Full Moon) is at phase 0°, maximum at First Quarter Moon (or Third Quarter Moon) is at 180°. Light brownish colors (e.g., at location of red cross) means that the maximum occurs a few lunar days after New Moon or Full Moon. The white areas are regions where the beat amplitude is too small (<0.17 TECU). The magenta line denotes the geomagnetic equator. The red cross denotes the location in Southern China (25°N latitude, 110°E longitude) which we analysed in the Figures 1–5.

4 Discussion

The analysis of the GNSS TEC data of IGS showed that the Moon phase has an influence on the diurnal, semidiurnal, and terdiurnal variation of TEC. The three daily variations show the same beat frequency of the solar and lunar spectral component which are close together. The beat period is 14.7653 days which is equal to the beat period of oceanic tides leading to spring and neap tides. While in case of oceanic tides the interplay between the gravitational potentials from the Sun and the Moon is important, the situation for the modulation of the solar and lunar daily variations of TEC is different. We assume that the changing phase is different between the solar semidiurnal wind tide and the lunar semidiurnal wind tide in the ionospheric dynamo region (100–110 km altitude) is most important. In the dynamo region, a constructive interference of the solar and lunar wind tide would induce a larger electric field variation which is mapped into the equatorial F region where the associated plasma drift variation generates larger semidiurnal variations of electron density, particularly in the EIA region.

We got the result that the average behavior of the Moon influence on TEC is an increase of the amplitudes of the three lunar daily TEC variations 2–3 days after New Moon and Full Moon. It is best seen for the beat of the solar and lunar semidiurnal oscillation of TEC. The modulation strength is about ±0.75 TECU for the semidiurnal variation in Southern China and at some other places of the EIA region. This strong modulation is due to the strong M₂ variation in TEC along the EIA (Wu et al., 2020; Hocke et al., 2025). We find that the long-term time series of GNSS TEC maps since 1998 is very valuable for studies of lunar daily oscillations. In spite of performing the analysis separately for each grid point of the TEC maps, we obtain coherent world maps of beat amplitude and phase. Further, the results agree with past related studies on lunar variations in TEC (Wu et al., 2020; Hocke et al., 2024a, 2025). The lunar variations in TEC are strongest along the EIA where the electric field variations induced by the Moon lead to a periodic electrodynamical lifting of the equatorial ionospheric plasma. The strong meridional horizontal gradients of ionization at the EIA are a further explanation that the lunar-induced plasma transport processes are most obvious at the EIA.

A detailed explanation for the phase behaviour of the beat of S₂ and M₂ is difficult since the phase of the solar semidiurnal tide and the lunar semidiurnal tide is changing when the tides propagates upward from their excitation regions in the troposphere and stratosphere. The beat of S₂ and M₂ may even play a stronger role in extreme situations as the ionospheric response to SSWs (Pedatella & Liu, 2013; Lin et al., 2019). A statistical study of the ionospheric response to SSWs showed that there is often a variable delay between the SSW event onset and the increased semidiurnal variation in the ionosphere (Hocke et al., 2024b). The delay might be small when S₂ and M₂ are in phase at the onset time of the SSW and large when S₂ and M₂ are in antiphase.

Figure 7 shows the Moon phase of the maximal semidiurnal amplitude. Generally, the maximum is reached 2–3 days after New Moon or Full Moon, with some exceptions outside of the EIA region and also in the EIA region over the West Atlantic in the northern hemisphere. Possibly, the phase difference of S₂ and M₂ shows some variations with longitude and latitude. It is more surprising that mean characteristics of the Moon phase influence on daily TEC variations are existing since the vertical phase progression of lunar and solar atmospheric tides is quite complex and modulated by seasonal variations, the solar cycle, and other factors such as nonmigrating tides. An open question is how far the daily EUV variations in the rotating Earth’s atmosphere contribute to S₁, S₂, and S₃. Particularly in case of S₁ it is likely that the phase difference between the solar diurnal variation and the lunar diurnal variation of TEC is not only depending on the solar diurnal tide from below but also on the diurnal EUV variation at ionospheric heights. Even for numerical simulations it might be difficult to separate between TEC contributions from the upward propagating solar diurnal tide and those from the diurnal EUV variation in the rotating ionosphere.

5 Conclusions

The average influence of the Moon phase on ionospheric TEC is derived from TEC maps of the International GNSS Service IGS from 1998 to 2024. At low latitudes, we find three spectral lines in the TEC spectra having frequencies of the lunar variations at M₂ − 1 cpd (diurnal), M₂ (semidiurnal), and M₂ + 1 cpd (terdiurnal) where cpd stands for cycles per day and M₂ is the lunar semidiurnal variation with a period of 12.4206 hours. These lunar variation lines are close to the spectral lines of the solar diurnal, semidiurnal and terdiurnal variations, so that a beat of the solar and lunar oscillations occurs with a frequency of 2 − M₂ which corresponds to a beat period of 14.7653 days (half of a lunar synodic month). In the modulation spectrum of the semidiurnal amplitude envelope, a significant spectral peak is at 1/14.7653 cpd and is about 0.8 TECU (TEC Units) in Southern China which is comparable to the strength of the seasonal modulation of the semidiurnal amplitude. The composite analysis shows that the maximal semidiurnal TEC amplitude is reached 2–3 days after New Moon (or Full Moon). The influence of the Moon phase on the diurnal and terdiurnal amplitudes is similar but less clear as for the semidiurnal amplitude. The world map of the semidiurnal beat amplitude is presented. It shows increased beat amplitudes in the EIA region. The maximal semidiurnal amplitude at low latitudes mostly occurs a few days after New Moon or Full Moon. In the West Atlantic of the northern hemisphere, the maximal semidiurnal amplitude appears at First Quarter Moon. We conclude that the beat of lunar and solar daily variations is certainly important for space weather, and an inclusion of the Moon in space weather models is desirable as already suggested by Forbes & Zhang (2012) and Zhang et al. (2014).

Acknowledgments

We thank Yosuke Yamazaki for advices about the modulations of daily TEC variations. We thank the International GNSS Service (IGS) and all contributors for maintaining the worldwide GNSS receiver network. The TEC maps of the IGS are freely available at CDDIS, NASA’s archive of space geodesy data (https://cddis.nasa.gov/). The TEC maps are a product of IGS (Hernández-Pajares et al., 2009). Planetary ephemeris data courtesy of Espenak (2025). Open access funding is provided by University of Bern and swissuniversities. We thank the reviewers and the editor for many improvements of the article. The editor thanks Jaroslav Urbář and an anonymous reviewer for their assistance in evaluating this paper.

References

All Figures

Figure 1 FFT amplitude spectra of TEC (blue line) in Southern China (25 °N latitude, 110°E longitude) for the time interval from 1998 to 2024. The red dashed lines indicate the lunar diurnal variation M2 − 1 cpd, the lunar semidiurnal variation M2, and the lunar terdiurnal variation M2 + 1 cpd. The spectral peaks of the solar daily variations S1, S2, and S3 are at 1 cpd, 2 cpd, and 3 cpd respectively. The magenta line denotes the 95% confidence level.

In the text

Figure 2 FFT spectrum of amplitude envelope of the semidiurnal variation of TEC (bandpass 1.8–2.2 cpd) in Southern China (blue line). The envelope is modulated by periods of the solar cycle, seasonal variations (annual oscillation AO, semiannual oscillation SAO and further harmonics). The beat of the lunar and solar semidiurnal variation generates a spectral peak at the beat frequency 2 cpd − M2 (equal to a period of 14.7653 days or half of a lunar synodic month). The magenta line denotes the 95% confidence level.

In the text

	Figure 3 Amplitude of the semidiurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all TEC data in Southern China from 1998 to 2024. The colored lines show the results for the different seasons.
In the text

	Figure 4 Amplitude of the diurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all TEC data in Southern China from 1998 to 2024. The colored lines show the results for the different seasons.
In the text

Figure 5 Amplitude of the terdiurnal variation of TEC as function of the Moon phase. New Moon is at lunar day 0, Full Moon is at lunar day 14.7653 days. The lunar cycle ends at lunar day 29.5306. The thick black line shows the dependence on the Moon phase for all daytime TEC data (solar zenith angle SZA < 90°) in Southern China from 1998 to 2024. The colored lines show the daytime results for the different seasons.

In the text

	Figure 6 Beat amplitude of the semidiurnal variation of TEC (FFT amplitude at period 14.7653 days) for the time from 1998 to 2024. The red line denotes the geomagnetic equator. The magenta cross denotes the location in Southern China (25°N latitude, 110°E longitude) which we analysed in the previous figures.
In the text

Figure 7 Moon phase of maximal semidiurnal amplitude of TEC. Maximum at New Moon (or Full Moon) is at phase 0°, maximum at First Quarter Moon (or Third Quarter Moon) is at 180°. Light brownish colors (e.g., at location of red cross) means that the maximum occurs a few lunar days after New Moon or Full Moon. The white areas are regions where the beat amplitude is too small (<0.17 TECU). The magenta line denotes the geomagnetic equator. The red cross denotes the location in Southern China (25°N latitude, 110°E longitude) which we analysed in the Figures 1–5.

In the text