A Signature of 27 day Solar Rotation in the Concentration of Metallic Ions within the Terrestrial Ionosphere

Figure 1(a) shows the variations in daily mean foEs values in the period 1993–2018 from the ionosonde at Sodankylä, Finland. The observed foEs shows the dominant annual and 11 yr solar cycle variations. The dominant influence on the ionosphere at periods around 27 days is the solar rotation and the corotation of long-lived (meaning lasting several solar rotations) structure in near-Earth interplanetary space and the "lighthouse" effects of similarly long-lived regions of enhanced solar irradiance at relevant wavelengths (Harrison & Lockwood 2020). The period of such variations can vary but is generally close to the Carrington rotation interval of 27.26 days (the period of rotation of the solar photosphere at 26° heliographic latitude, close to the average latitude of sunspots and active regions). The only other period close to this is the lunar orbit period, which generates the sidereal monthly tide component of period 27.55 days. Studies of the power spectra of "geomagnetic tides", caused by the solar and lunar gravitational effects on ionospheric currents, find this component to usually be undetectably small (e.g., Love & Rigler 2014), and the largest effects seen are "13 day" or "semimonthly" variations at period 27.55/2 = 13.78 days, which are strongest in the equatorial electrojet following a stratospheric warming (e.g., Park et al. 2012). Hence we here take variations seen near 27 days to be due to solar rotation. To analyze the short-term variations in Es layers related to the 27 day solar rotation cycle, a sixth-order Butterworth filter has been applied in the time series of foEs. This low-pass temporal filter can separate the long-term and short-term trends of foEs and does not change the temporal phase. The cutoff period is 60 days. The filtered foEs with periods more than 60 days is shown as a dark pink line while the raw data are shown in light pink. In this study, we concentrate on the variability in the short-term periodicities, so we subtract the filtered foEs from the raw data and obtain the residual foEs (δfoEs) with periods less than 60 days, as shown by blue lines.

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To study the short-term periodic oscillations in δfoEs, a Lomb–Scargle spectral analysis (Lomb 1976; Scargle 1982) was conducted. Figure 1(b) shows the normalized Lomb–Scargle periodogram, while the horizontal lines correspond to false-alarm probabilities of 50%, 10%, 1%, and 0.1%. The predominant spectral peaks in the short-term changes of foEs are at periods of approximately 27, 13.5, and 9 days. The 27 day periodicity can also be observed in the daily F10.7 (Figures 1(c) and (d)), the solar wind speed (Figures 1(e) and (f)), and the Dst index (Figures 1(g) and (h)), but the 13.5 day and 9 day periodicities were not found in the F10.7 corresponding to the second and third harmonics of the 27 day solar rotation cycle. Recurrent fast solar wind streams, known as corotating interaction regions (CIRs), originate from persistent coronal holes on successive 27 day solar rotations. (Gosling & Pizzo 1999; Chi et al. 2018). Recurrent geomagnetic activity at the 27 day periodicity is often attributed to CIRs. The periodicities of 13.5 days and 9 days in the geomagnetic activity and the ionosphere are produced by high-speed solar winds from two or three large coronal holes that are persistent and longitudinally separated on successive solar rotation cycles (Vršnak et al. 2007; Lei et al. 2008a). The results indicate that the 9 day, 13.5 day, and 27 day periodic oscillations in Es layers are more likely associated with the variations in recurrent geomagnetic activity and fast solar wind streams than with the solar extreme ultraviolet (EUV) radiation.

Wavelet analysis (Torrence & Compo 1998) can determine the dominant periodicities and show how the magnitude of these fluctuations varies in time. Figure 2 shows the results of the wavelet analysis of foEs from the Sodankylä ionosonde. Figure 2(a) shows the daily mean original foEs (black lines in the top panel), and the reconstructed time series of foEs from the wavelet transform (green lines in the bottom panel). The reconstruction of the time series using the wavelet transform has an rms error (RMSE) of 0.05 MHz. The wavelet spectrum in Figure 2(b) shows a band of the significant annual variation in foEs. The variations of 0.5, 1, 2, 3, and 4 MHz are contoured. The cross-hatched regions on either edge indicate where edge effects become important. In addition to the seasonal, semiannual, and annual variations, the oscillations near the periods of 13.5 and 27 days become more evident at solar maximum (2000–2003 and 2011–2014) than at solar minimum. This is confirmed by the average power spectrum of foEs (Figure 2(c)), which shows the peaks at 13.5 and 27 days. The power at 27 days is significantly above the 95% confidence level represented by a dashed line. Figure 2(d) shows the relationship between the oscillations at periods near 27 days including its subharmonics of 13.5 days and the geomagnetic activity Dst index. The scaled-averaged wavelet power is the weighted sum of the wavelet power spectrum over a certain period to give a measure of the average variance versus time as proposed by Torrence & Compo (1998). The scaled-averaged power is defined as the weighted sum of the wavelet power spectrum over scales s₁ to s₂:

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$$\begin{eqnarray}&&{\overline{{W}_{n}}}^{2}=\displaystyle \frac{{\delta }_{j}{\delta }_{t}}{{C}_{\delta }}\sum _{j={j}_{1}}^{{j}_{2}}\displaystyle \frac{{\left|{W}_{n}({s}_{j})\right|}^{2}}{{s}_{j}}\end{eqnarray} \tag{ 1 }$$

where δ_j and δ_t are the empirical factors for scale averaging, and C_δ is the empirical reconstruction factor. j₁ and j₂ represent scales in a certain band over which wavelet power is calculated. The scale-averaged wavelet power can be used to study the changes in amplitude of wavelet power of one frequency over a scale range. The weighted scaled-averaged wavelet power spectrum of foEs between 13.5 and 27 days (actually 12–30 days) is shown as a black line. It shows a clear correlation between 12 and 30 day power of foEs and the periodic changes in the 27 day smoothed daily minimum Dst index (red line) over the solar cycles. An upper limit of 30 days ensures that solar rotation periods (centered on the Carrington period of 27.26 days) are always captured. However, often there are two "sectors" of toward and away (from the Sun) heliospheric field polarity, which means that solar rotation effects often give periodicities of around 13.5 days, which are captured by using the lower limit of 12 days. At some times (particularly sunspot maximum) there can be three or four (or even more) sectors, and the higher-frequency harmonics of the solar rotation frequency that they generate will not be captured by this band. The hourly Dst index is represented by the pink dots. The Dst index is an important parameter to quantify the disturbance of the geomagnetic field in a magnetic storm (Shen et al. 2017). Note that Dst is increasingly negative for enhanced geomagnetic activity. During solar maximum, the 12–30 day power of foEs is significantly above the 95% level, along with the occurrence of the intense geomagnetic storms (indicated by Dst_min ≤ −100 nT). Although there is some evidence for "active longitudes" in solar active regions, persistent solar longitudinal structure is weak and so F10.7, like other electromagnetic emissions (at EUV, UV, and infrared radiation/visible wavelengths) shows almost no periodicities that are harmonics of the solar rotation period. On the other hand the sector structure of the interplanetary magnetic field (with sectors of field pointing toward and away from the Sun) means that harmonic periods at frequencies near 13.5 and 9 days are much stronger. Hence it is not surprising that they are seen in solar wind speed and the Dst geomagnetic response. That they are seen strongly in the foEs response is therefore significant and implies a strong influence of the solar wind. Note that a lunar tidal effect would be dominant at around 13.5 days with much weaker lines at 27 and 9 days, and this is inconsistent with the foES spectrum shown in Figure 1(b).

Many researchers have studied the time lag between the response of the ionospheric F-layer and geomagnetic activity (Zhang & Holt 2008; Ren et al. 2018). The time lag of the response of different ionospheric parameters to the 27 day solar rotation cycle ranges from 0 to 3 days. The time lag of the 27 day variation in Es layers from the Sodankylä ionosonde in response to the geomagnetic activity is investigated as shown in Figure 3. Figure 3(a) shows the cross-correlation function between the 12–30 day wavelet power of foEs and the 27 day smoothed daily minimum Dst index as a function of time lag during 1993–2018. The correlation coefficient with a time lag ranging from −15 to 15 days is analyzed. The maximum cross-correlation is −0.433 at a time lag of 11 hr. The correlation becomes lower before and after this time lag. This reveals that the ionospheric time delay of Es layers at altitudes of 90–130 km to the geomagnetic activity Dst index is approximately 11 hr. For the maximum cross-correlation, its density scatter plot and a scatter plot of the 27 day smoothed daily minimum Dst versus the 12–30 day wavelet power are shown in Figures 3(b) and (c). The observations in the density scatter plot were binned in 1.0 (Dst) × 0.005 MHz² (wavelet power).

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Figure 4 corresponds to Figure 3 but uses the Ap geomagnetic index instead of Dst: it shows the correlation between the oscillations at periods of 12–30 days in Es layers from the Sodankylä ionosonde and the magnetic activity Ap index during 1993–2018. The cross-correlation function between the 12–30 day wavelet power of foEs and the 27 day smoothed daily Ap index as a function of time lag is shown in Figure 4(a). The maximum cross-correlation is 0.402 at a time lag of 25 hr. The different time lags are consistent with the different responses of Dst and Ap indices to the interplanetary magnetic field (IMF) (Davis et al. 1997; McPherron et al. 2004; Adebesin 2016). The Dst index shows a decrease several hours after the southward turnings of the IMF (Lockwood et al. 2016a), while the Ap index shows a rise around the time of the southward turnings. The time delay between these two geomagnetic activity indices is approximately 14 hr, based on the analyses of the maximum cross-correlations in Figures 3 and 4. The density scatter plot and scatter plot of the 27 day smoothed daily mean Ap versus the 12–30 day wavelet power for the maximum cross-correlation are shown in Figures 4(b) and (c). The observations in the density scatter plot were binned in 0.6 (Ap) × 0.005 MHz² (wavelet power).

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Figure 5 shows the results of the wavelet analysis of foEs at Slough (51.5°N, 0.6°W) during the period 1957–1995. The Dst index is available from 1957, therefore the ionosonde data before 1957 are not investigated. The reconstruction of the time series using the wavelet transform has an RMSE of 0.03 MHz. The annual, semiannual, and quasi-seasonal variations are apparent in the wavelet spectrum of foEs in Figure 5(b). However, the 13.5 day and 27 day periodic oscillations in foEs at Slough are not as significant as those at Sodankylä. In Figure 5(c), the peaks at periods of 13.5 and 27 days are both below the 95% confidence level (dashed line). The correlation between the 12–30 day wavelet power and the daily Dst index is not evident as shown in Figure 5(d).

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The global observations of Es layers can be derived from the amplitude scintillation S4 index from GNSS RO signals. Yu et al. (2020) have derived the global foEs from the COSMIC S4max data during 2006–2014. To investigate the global 27 day oscillations in Es layers and compare with the ground-based observations by ionosondes, the foEs data derived from the COSMIC during 2006–2014 are analyzed. The top panel in Figure 6 shows the foEs along the 60°N–90°N latitude band derived from the COSMIC S4max data. The green line in the bottom panel shows the reconstructed data from the wavelet transform. The reconstruction of time series has an RMSE of 0.01 MHz. Figure 6(b) shows the wavelet spectrum of foEs with enhancements of oscillations at the annual, semiannual, seasonal, 27 day, and 13.5 day periods. The strong fluctuations at periods of 13.5 and 27 days can also be found in the average power spectrum in Figure 6(c), and are at the 95% confidence level (dashed line). A significant 27 day oscillation in Es layers can be found at the high-latitude Sodankylä ionosonde (Figure 2), but not at the midlatitude Slough ionosonde (Figure 5). This indicates that the 13.5 day and 27 day oscillations related to the 27 day solar rotation cycle are dependent on the latitude.

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Figure 7 shows the weighted scaled-averaged wavelet power spectrum of foEs derived from the COSMIC S4max data at different latitude bands during 2006–2014. The 12–30 day (mainly 13.5 day and 27 day) oscillations at high latitudes in the Northern and Southern Hemispheres have a power of 0.02–0.06 MHz² above the 95% confidence line. The 12–30 day power at high latitudes is stronger than that at midlatitudes and low latitudes. The overall spectrum is consistent with the results from ground-based ionosondes, in which the Es layers present a more significant 27 day oscillation at the high latitude of the Sodankylä ionosonde than at the midlatitude Slough ionosonde. However, there are differences in the temporal behavior shown in Figure 2(b). For the Sodankylä data (Figure 2(b)) the peaks for periods near 27 days occur primarily at sunspot maximum. A similar but smaller solar-cycle dependence is present for the COSMIC data. The high-latitude peaks in the 12–30 day power of foEs are a summer phenomenon: for the Northern Hemisphere they are midway through each calendar year and in the Southern Hemisphere they are near its start, which is consistent with a summer maximum of high-latitude Es layers in previous studies (Kirkwood & Nilsson 2000).

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Figure 8 shows the global map of the scale-averaged wavelet power of foEs at periods of 12–30 days from COSMIC in a 10° × 10° grid during the period 2006–2014. The geomagnetic latitude contours of 60°, 70°, and 80° are represented by red (blue) lines in the Northern (Southern) Hemisphere. The geomagnetic equator is also plotted as a yellow line. The 12–30 day scale-averaged wavelet power of foEs is strong at high latitudes in both hemispheres, indicating that the 13.5 day and 27 day oscillations in Es layers dominate the high-latitude regions. The auroral-type Es layers were found to occur at high latitudes, and are associated with magnetic and auroral activities (Hunsucker & Owren 1962). At high latitudes, the wind shear effect is not as efficient as at midlatitudes (Gubenko et al. 2018; Yu et al. 2019a). Therefore, the auroral Es layers are thought to be caused by magnetic-field-aligned plasma irregularities (Kirkwood & Nilsson 2000). The two-stream and gradient-drift instabilities occur in the auroral region accompanied by strong electric fields (Gubenko et al. 2018). The formation of midlatitude Es layers is mainly controlled by wind shear, and it is modulated less by the 27 day solar rotation. The weak 12–30 day power is visible at midlatitudes between 15° and 45°. In addition, due to the effect of Lorentz forcing on the ion convergence of Es plasma, the weak Es layers form troughs along the 70°N–80°N and 60°S–70°S geomagnetic latitude bands (Yu et al. 2019a), and thus present weak 12–30 day oscillations. Another interesting feature is the relatively strong 12–30 day wavelet power of Es layers near the magnetic equator. The formation of the equatorial Es layers is attributed to the magnetic-field-aligned irregularities associated with the equatorial electrojet. The formations of auroral and equatorial Es layers are both associated with an intense current flow, which is found to increase with intense magnetic activities (Whitehead 1970). The auroral and equatorial Es layers with 13.5 day and 27 day periodic oscillations are both modulated by the solar rotation cycles through magnetic activity. In addition, 16 ground-based ionosonde stations, which have at least five years of continuous manually-scaled data at the same period as COSMIC RO data during 2006–2014, are further used to study the 27 day oscillations in Es layers on a global scale. The circles represent the locations of 16 ionosondes used in the wavelet spectrum analysis, with the size of these symbols denoting the 12–30 day wavelet power. It should be noted that the signals of 13.5 day and 27 day periodicities are more clearly identified from the ionosonde observations than the COSMIC satellites. The 12–30 day power of Es layers from ionosondes is generally larger than that from satellites. The details of foEs data from 16 ionosonde stations and the 12–30 day power are listed in order of decreasing north latitude in Table 1.

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Figure 9 shows the percentage of the scale-averaged wavelet power of foEs at periods of 12–30 days from COSMIC in a 10° × 10° grid during the period 2006–2014. The global map of wavelet power shows a significant enhancement within low-latitude and high-latitude bands. The 12–30 day oscillations account for 10%–14% of all variations in foEs at low latitude and high latitude. The 12–30 day power of foEs is 4%–10% at midlatitudes. This reveals that the 13.5 day and 27 day periodic oscillations in the Es layers are evident at low latitudes and high latitudes, but are not significant at midlatitudes. The wavelet spectral results of 16 ground-based ionosonde stations present a consistent result, with the percentage of the 12–30 day power represented by the size of the circles on the map.

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