From the statistical analysis of the MSTID activity and propagation direction for MSTIDs, we found that MSTIDs frequently propagated southward during daytime, and southwestward during nighttime. This feature is consistent with previous studies (e.g., Kotake et al. 2007; Otsuka et al. 2011, 2013; Tsugawa et al. 2007). In this section, we focus on the solar activity dependnce of the MSTID activity and phase velocity.
MSTID activity
MSTIDs over Japan during the nighttime propagate mostly southwestward. The northwest–southeast alignment of the MSTID wavefront is a preferable condition for the Perkins instability (Perkins 1973). When the normal line to the wavefront of the plasma density perturbations exists between the east and the ionospheric current direction, the plasma density perturbations grow with time through the Perkins instability. Because of the southwestward preference of the nighttime MSTID propagation direction, the Perkins instability is considered to play an important role in generating the nighttime MSTIDs.
Both activity and occurrence rate of nighttime MSTID during 22 years showed clear anticorrelation with solar activity. They were high (low) for low (high) solar activity conditions. This feature was consistent with that reported by previous observations of the nighttime MSTIDs by GPS-TEC (e.g., Saito et al. 2002) and by 630.0-nm airglow images (e.g., Duly et al. 2013; Tsuchiya et al. 2018).
The anticorrelation of the MSTID activity and occurrence rate can be explained by the theory of the Perkins instability. The linear growth rate of the Perkins instability, \({\upgamma }\), is inversely proportional to \(\left\langle {\nu_{in} } \right\rangle\), where \(\left\langle {\nu_{in} } \right\rangle\) is the ion–neutral collision frequency (\(\nu_{in}\)) integrated along the geomagnetic field with a weighting function of the plasma density (Perkins 1973; Hamza 1999). Because \(\nu_{in}\) is proportional to the neutral density, \(\left\langle {\nu_{in} } \right\rangle\) increases with increasing solar activity, and thus \({\upgamma }\) shows anticorrelation with the solar activity.
At midlatitudes, the altitude of the F layer is supported by effective electric fields, \({\varvec{E}}^{*} = {\varvec{E}} + {\varvec{U}} \times {\varvec{B}}\), against the downward gravity-induced diffusion velocity \({\raise0.7ex\hbox{$g$} \!\mathord{\left/ {\vphantom {g {\left\langle \nu \right\rangle }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\left\langle \nu \right\rangle }$}}\), where \({\varvec{E}}\) is the electric field, \({\varvec{U}}\) is the neutral wind, \({\varvec{B}}\) is the geomagnetic field, and \(g\) is the gravitational acceleration. Therefore, \({\upgamma }\) is also proportional to \({\varvec{E}}^{*}\). On average, \({\varvec{U}}\) does not show distinct solar activity dependence (Emmert et al. 2006), but \({\varvec{E}}\) is smaller under low solar activity conditions than under high solar activity conditions (e.g., Fejer 1993; Takami et al. 1996). \({\varvec{E}}\) is a polarization electric field driven through the F-region dynamo (Rishbeth 1971) by \({\varvec{U}}\). Through the F-region dynamo, \({\varvec{E}}\) is generated to satisfy \({\varvec{E}} + {\varvec{U}} \times {\varvec{B}} = 0\), which satisfies the divergence-free conditions of the current, so that the direction of \({\varvec{E}}\) is opposite to \({\varvec{U}} \times {\varvec{B}}\). Under high solar activity conditions, when the height-integrated Pedersen conductivity in the F region is significantly larger than that in the E region, \({\varvec{E}} + {\varvec{U}} \times {\varvec{B}}\) is nearly equal to zero. On the other hand, under low solar activity conditions, the height-integrated Pedersen conductivity in the F region is comparable to that in the E region so that \(\left| {\varvec{E}} \right|\) is smaller than \(\left| {{\varvec{U}} \times {\varvec{B}}} \right|\). Consequently, \({\varvec{E}}^{*} = {\varvec{E}} + {\varvec{U}} \times {\varvec{B}}\) is larger under low solar activity conditions than under high solar activity conditions, so that the growth rate \({\upgamma }\) is larger under low solar activity conditions than under high solar activity conditions. Consequently, the solar activity dependence of the growth rate for the Perkins instability is consistent with that of the observed MSTID activity.
On the other hand, for the daytime MSTID, the occurrence rate showed anticorrelation of the solar activity, whereas the solar activity dependence of MSTID activity was weak. Since most of the daytime MSTIDs propagate equatorward, the daytime MSTIDs are thought to be caused by GWs propagating in the thermosphere. The plasma in the F region moves along the geomagnetic field lines through the ion–neutral collisions because the ion motion across the geomagnetic field line is restricted owing to the ion gyrofrequency being much higher than the ion–neutral collision frequency, and the current in the F region does not produce polarization electric fields due to the high conductivity in the daytime E region. GWs propagating equatorward and upward have larger amplitudes of neutral particle oscillation, parallel to the geomagnetic field lines, and thus induce larger plasma density perturbations in the ionosphere compared with GWs propagating in other directions (Hooke 1968). This directivity of the ion motion to the neutral particle oscillation caused by GWs could be responsible for the preference of the equatorward propagation for the daytime MSTIDs.
To maintain the kinetic energy of the upward propagating GWs, the decrease in the neutral density in the thermosphere causes an increase in the amplitude of the GWs. Bowman (1992) have suggested that the amplified GWs may be responsible for spread F, which is also a plasma density disturbance in the ionosphere. Due to this effect, the MSITD activity could increase with decreasing solar activity. However, the daytime MSTID activity obtained in this study did not show distinct solar activity dependence, suggesting that the daytime MSTID over Japan could not be caused by GWs propagating from the lower atmosphere directly. Vadas (2007) has shown that the effect of viscosity on the GWs increases with decreasing solar activity because the neutral density decreases with decreasing solar activity. Because the viscosity of the neutral atmosphere reduces amplitude of GWs, the MSTID activity could be suppressed under low solar activity conditions. The combination of these opposite effects may cause indistinct solar activity dependence of the daytime MSTID activity. On the other hand, owing to the high viscosity, GWs may dissipate and create horizontal body forces by deopsiting momentum into the background atmosphere, such that secondary GWs may be generated (Vadas and Liu 2009). The seocndary GWs could be generated frequently under low solar activity conditions because of the low neutral density. High occurrence of the secondary GWs under low solar activity conditoins may be responsible for the anticorrelation of the daytime MSTID occurrence rate with solar activity.
Phase velocity of MSTIDs
Daytime MSTID was found to occur most frequently in winter. This feature was consistent with MSTIDs in different regions (e.g., Kotake et al. 2006; Otsuka et al. 2011). Miyoshi et al. (2018) successfully reproduced MSTIDs generated by upward propagating GWs that are spontaneously generated in the global atmosphere–ionosphere coupled model, and showed that the daytime MSTID was more active in winter than in summer. According to the dispersion relation for GW, the vertical wave number (\(m\)) of GW is expressed as
$$ m^{2} = \frac{{N^{2} }}{{\left( {c - U} \right)^{2} }} - k^{2} - \frac{1}{{4H^{2} }}, $$
(1)
where \(k\) and \(c\) are the horizontal wave number and horizontal phase speed of the gravity wave, respectively, \(N\) is the Brunt–Väisälä frequency, and \(H\) is the scale height of the neutral atmosphere. Background neutral wind (\(U\)) also affects the vertical wave number (\(m\)). From the dispersion relation, it was found that \(m\) was larger when \(\left( {c - U} \right)^{2}\) was smaller.
Neutral winds in the thermosphere are produced due to a balance between the pressure gradient force and ion drag. The pressure gradient forces are caused by the solar extreme ultraviolet (EUV) heating of the thermosphere. Therefore, the neutral winds in the thermosphere blow poleward during daytime and equatorward during nighttime. Regarding seasonal variation of the neutral winds in the thermosphere, the winds blow from the summer hemisphere to the winter hemisphere because the thermospheric temperature is higher in summer hemisphere than in winter hemisphere due to the difference in the solar zenith angle between summer and winter hemispheres. Consequently, the thermospheric winds during the daytime blow poleward, and are larger in winter than in summer. Such a feature can be seen in the seasonal variation of the thermospheric winds measured by the Middle and Upper atmosphere (MU) radar in Japan (Kawamura et al. 2000). For the GWs propagating equatorward, the background winds blow in the direction opposite to the GW propagation, and are larger in winter than in summer. Therefore, \(\left( {c - U} \right)^{2}\) is larger in winter than in summer. According to the dispersion relationship for GW, the vertical wave number is expected to be larger in summer than in winter, and hence, the vertical wavelength could be larger in winter than in summer. Due to the high viscosity and thermal conductivity in the thermosphere, GWs in the thermosphere are dissipated (Pitteway and Hines 1963). In particular, the GWs with shorter vertical wavelengths could likely be attenuated and dissipated, but the GWs with longer wavelengths could propagate for long distances while maintaining the amplitude of the oscillation. Considering the dissipation of GWs, it is expected that the GWs in the thermosphere could be attenuated in summer because the vertical wavelength is shorter, and could propagate for long distances in winter. This scenario can explain our statistical result, which shows that the daytime MSTIDs occur most frequently in winter.
Regarding solar activity dependence, our results showed that the average phase velocity of the daytime MSTIDs was larger under low solar activity conditions than under high solar activity conditions. This dependence of the phase velocity on solar activity is attributed to the dependence of distribution of the phase velocity occurrence rate on solar activity. Under high solar activity conditions, the phase velocities of daytime MSTID are distributed widely between 20 and 200 m/s, and their maximum occurrence is at 130 m/s. On the other hand, under low solar activity conditions, the phase velocities tend to be confined to a range between 100 and 200 m/s. The occurrence rate of the phase velocity between 20 and 100 m/s is lower under low solar activity conditions than under high solar activity conditions. The low occurrence rate of low phase velocity of daytime MSTIDs in the low solar activity could be explained in terms of the dissipation of GWs in the low solar activity. According to the dispersion relation for GW, the GWs with slow phase velocity (small c in Eq. (1)) could have larger vertical wave number (m) or shorter vertical wavelength. The GWs with short vertical wavelengths are likely to dissipate, and only GWs with longer vertical wavelengths could survive in the thermosphere. Because viscosity is larger when the neutral density is small, the dissipation of GWs due to viscosity could occur under low solar activity conditions (Vadas 2007). Our results suggest that under low solar activity conditions, GWs with slow phase velocity tend to be attenuated in the thermosphere, and the daytime MSTIDs are mostly caused by GWs with higher phase velocity although the daytime MSTIDs under high solar activity are caused by GWs with various phase velocities up to approximately 200 m/s. From Fig. 8, it can be seen that the occurrence rate of the higher phase velocity (100–200 m/s) increases with decreasing solar activity. This may be caused by an increase in the secondary GWs generated by dissipation of the primary GWs in the thermosphere, where the neutral density is low under low solar activity conditions, as discussed in the previous subsection.
Since GWs in the thermosphere are considered to propagate from the lower atmosphere, seasonal variation of GW activity in the thermosphere may be affected by that of GWs in the lower atmosphere. Murayama et al. (1994) reported annual variation of the GWs in the lower stratosphere, observed by the MU radar in Japan, and showed that GW kinetic energy is maximized in winter. They have suggested that the GW kinetic energy in the stratosphere over Japan is high when the subtropical jet stream at approximately 12-km altitude is strong. Satellite observations have revealed the global distribution of the GW activity in the stratosphere (Tsuda et al. 2000; Jiang et al. 2004), and have shown that the GW activity is highest in winter in both northern and southern hemispheres. Using the Atmospheric Infrared Sounder (AIRS) aboard NASA's Aqua satellite, Hoffmann et al. (2013), who have investigated the global distribution of hotspots of stratospheric GWs, have shown that most of the hotspots were related to the orographic GWs. High GW activity in the stratosphere in winter may be related to the high GW activity in the thermosphere, resulting in high MSTID activity during the daytime in winter. However, using the MU radar in Japan, Tsuda et al. (1990) reported that seasonal variation of GW kinetic energy in the mesosphere (65–85 km) showed maxima in both summer and winter, and minima during equinox. Further study of the vertical propagation of GWs from the lower atmosphere to the thermosphere may be needed to understand the underlying mechanisms for seasonal variation of the GWs in the thermosphere and daytime MSTIDs.