where  denotes the mean value, and , , s, and  denote the amplitudes, phases of different tidal components, wave numbers, and longitudes, respectively. A window of 24 hours is used in this least square fitting. The amplitudes and phases of these components are obtained from the least square fitting which is further used to derive the temporal behaviour of the winds for a particular tidal component over a given location. The reconstructed winds for all the tidal components are shown in Figure 5 along with the model winds (black solid line) for six representative nights. For each of the nights, different tidal components are identified by different colours, and the sum of these amplitudes and A0 is shown in the black dash-dot-dot-dot line. A good comparison between the magnitudes of WACCM-X wind and the resultant amplitudes as obtained from equation 1, serves as a validation of the analysis of the least square fit. It can be seen that the diurnal component (magenta dotted line) shows larger magnitude, whereas the amplitudes of other three components, quarter-diurnal (QDT, red long-dashed line), terdiurnal (blue dashed line), and semidiurnal (teal dash-dot line) show comparable magnitudes with each other. The effect of aliasing can arise in the higher-order tidal amplitudes when two tidal components possess the same zonal wave numbers. In our analysis, the model simulation produces continuous data with an hour cadence. Therefore, there is no issue on sampling of the data. Further, we separated the wave numbers of different tidal periodicities using the least square fitting. Therefore, the effect of aliasing will not reflect in the obtained amplitudes of different tides. As the migrating component of diurnal and semi-diurnal tides have larger magnitude, they can be aliased into higher-order tides with same wave numbers with greater magnitudes (Moudden and Forbes, 2013). However, the amplitudes of wave numbers 1 and 2 in QDTs and terdiurnal tides appear very small. We have also used a 7h filter to remove the contribution of higher-order tides which we have also discussed in later. The amplitudes of QDTs obtained after 7h filtering remain the same as calculated from equation 1. The result further verifies that the obtained amplitudes do not contain the effect of aliasing in the higher-order tides.
Broadly, the winds are poleward and equatorward in the daytime and nighttime, respectively, as seen in the strong diurnal component. The amplitudes and phases of different tidal components contribute differently to the resultant variations of meridional winds. The subtle variations in the winds can be due to the influence of higher-order tidal contributions. For example, the winds are poleward in the daytime, but due to the opposite phase of other tidal components, a double-humped structure can be seen in the model wind during daytime. After sunset, the winds turn equatorward. On occasions, the meridional winds reverse their direction from equatorward to poleward after sunset (Figure 5). The shaded regions of Figure 5 indicate the duration when the reversal in meridional winds can be seen. On such occasions, we can see that the magnitudes of the QDT vary concurrently with the winds thereby, it is likely responsible for causing the reversal in the meridional winds. The magnitude of the winds after post-sunset reversal gets even stronger when the phases of the other three tidal components match one another. For example, on the day of year 7 (Figure 5d), we see a larger increase in the magnitude of winds during post-sunset time, and interestingly, quarter-diurnal, terdiurnal, and semidiurnal tides seem to be occurring in phase. Figure 6 shows the reconstructed winds while QDT has not been considered in the reconstruction. A clear difference can be seen, especially in the wind variation during post-sunset hours. When the QDT is absent, the reversal in winds is not being generated and the winds show the usual variation of poleward to equatorward.
Figure 5: Four tidal components obtained by the least square fitting in the WACCM-X simulated meridional wind output for 6 sample days. The shaded regions indicate the post-sunset hours when the reversal in meridional winds can be seen. The changes in wind magnitudes are calculated from minimum (Vmin) and maximum (Vmax) wind values during such reversals.
Figure 6: Only difference with Figure 5 is that QDT has not been taken while reconstructing the winds. The post-sunset winds do not show reversal clearly without the inclusion of QDT.
 
We have also verified the amplitude of higher-order tides by analysing the WACCM-X simulated winds using a 7h band-pass filter (Moudden and Forbes, 2013; Gong et al., 2023). The least square fitting method was applied after processing the winds of a given location by a 7h band-pass filter. The 7h band-pass filter diminishes the contribution arising from semi-diurnal and diurnal tides, which predominantly contribute to the meridional wind variation. The effect of aliasing, if any, due to these tides will also be reduced using this technique (Moudden and Forbes, 2013). The amplitude of QDTs obtained using this calculation aligns with the result obtained by the earlier-mentioned method, wherein the wave number and the corresponding tidal periodicities were used. This demonstrates that the higher-order tides do not contain the aliasing effect in the analysis as carried out in this study.
 

4. Discussion:

In the previous section, we have discussed the post-sunset enhancement in electron density as obtained from WACCM-X over low-latitudes which agrees well with enhancements in the OI 630.0 nm nightglow emissions after sunset (Figure 1). The spectral analysis and least square fit indicate the contribution of tidal components in the meridional wind variation obtained from WACCM-X. The least square fit provides the amplitude and phase information of different tidal components such as diurnal, semi-diurnal, terdiurnal, and quarter-diurnal, which depicts a picture that helps in understanding the tidal contribution to the meridional wind variation. The top panel (panel a) of Figure 7 shows the amplitude variation of four tidal components during the period from January to March. The amplitudes of diurnal tides can be seen to be larger as compared to the other three components, which show reasonably similar amplitudes, as also mentioned above for a few days. The quarter-diurnal tides have been shown to be responsible for the reversal of post-sunset hour meridional winds, as demonstrated for a few days, as shown in Figure 5. The variations in phase and amplitude of the higher-order tides, such as terdiurnal and quarter-diurnal are depicted in the panels b and c of Figure 7, respectively. The phases of QDTs coincide with the time of wind reversal, and the amplitudes of QDTs are also larger when the model shows an increase in the electron density. This is in simultaneity with the time when a maximum in poleward wind magnitudes occurs in the post-sunset hours. The bottom panel (panel d) of Figure 7 shows the changes in wind magnitudes from those at the time of the abatement of equatorward wind (Vmin, as shown in Figure 5d) and its peak value after that reversal (Vmax, as shown in Figure 5d). Depending on the amplitude and phase of QDT, the change in wind magnitude shows day-to-day variations (Figure 7). For example, the reduction/absence in wind reversal can be seen, as shaded with light blue colour, with the simultaneous reduction in amplitude of QDT. Besides, an increase in the amplitude of QDT and significant changes in wind magnitudes are seen, as shaded in salmon colour. Reference lines are drawn in Figure 7 (panels c and d) for the amplitude of QDT and magnitude of wind reversal at the values 16 and 25 ms-1, respectively. It can be seen that whenever the magnitudes of wind reversal exceed 25 ms-1, the amplitudes of QDTs are greater than 16 ms-1, and the times of peak phase values are seen to be around or before midnight. As discussed earlier, the time of the phases of different tides is also important. When the peaks in the phases of different periodicities, such as QDTs, terdiunal, and semidiurnal tides align in time, there can be further amplification in the wind magnitudes. For instance, we have seen a larger magnitude in wind reversal on DOY 7 due to the synchronization of phases of these three tidal components (Figure 5d). Such phase matching of these three tidal components is also seen for days 14 and 17. As the phases of QDTs are seen to be shifted beyond midnight towards the end of March, no reversal in winds in the post-sunset hours is observed. In this way, the amplitudes and phases of different tidal components, such as quarter-diurnal, terdiurnal, and semidiurnal tides, come out as important factors for the occurrence of reversal in the post-sunset wind, with the QDTs as the major contributor.
Figure 7: The amplitudes of different tides are shown in panel (a) for different days from January to March as obtained from the WACCM-X simulated meridional winds. Panels (b) and (c) show the phases and amplitudes of the quarter-diurnal and terdiurnal tidal components for the same duration, respectively. The bottom panel (d) depicts the change in wind magnitude after the post-sunset reversal in the wind. The shaded regions with salmon colour indicate the presence of wind reversal, and the magnitude of wind reversal can be seen to correspond with the amplitude of QDT. The blue shaded regions indicate the days when reversals were not seen, and the amplitudes of QDT were small. Reference lines have been marked for magnitude of wind reversal and maximum amplitude of QDT at the values of 25 and 16 ms-1, respectively. The phase of QDT, a reference line marked at 24 LT, also plays an important role. Whenever the magnitudes of wind reversal are greater than 25 ms-1, on most occasions, the amplitudes of QDT are greater than 16 ms-1 and phases are present at pre-midnight time.
 
We have investigated the post-sunset enhancement in electron density, which follows the reversal in meridional winds after sunset for January to March as obtained from WACCM-X simulations. Out of a total of 90 days from January to March, we have found such reversal in winds on 39 days during post-sunset times in the WACCM-X simulation. The amplitude of different tidal components, as well as the superposition of those components, were calculated and compared with the change in wind magnitudes after the reversal. As can be seen, the broad meridional wind pattern follows the diurnal tidal component. Therefore, we removed the contribution of the large background diurnal component. The changes in wind magnitudes have been calculated considering the contribution of quarter-diurnal, terdiurnal, and semi-diurnal components only, which are shown to be responsible for the reversal in wind. The changes in amplitude of different tidal components have been calculated between the time of Vmin and Vmax (as shown in Figure 5d). Figure 8 shows the relation between the changes in amplitude of the (a) quarter-diurnal, (b) terdiurnal, and (c) semidiurnal tides with the changes in wind magnitudes wherein the diurnal contribution has been subtracted. The amplitudes of QDT show a clear positive relation with the change in wind magnitude, whereas the other tidal components contribute at small magnitudes. Collectively, when the phases of these tides match, they also give rise to larger changes in the wind magnitudes. Therefore, based on the detailed analysis and results as depicted in Figures 5, 6, 7, and 8a, it can be concluded that the magnitudes of quarter-diurnal tide play a major role in the reversal of meridional winds as seen during post-sunset hours.
Figure 8: The x-axis depicts the change in wind magnitude during the post-sunset wind reversal obtained by subtracting the contribution of diurnal tide amplitudes. The change in tidal components during the wind reversal period is depicted on the y-axis. Different panels show variations in the changes in amplitudes of different tides with the change in wind magnitudes. The quarter-diurnal tide shows the best correlation with the wind reversal.
The diurnal variation in tides is clearly seen in the broad picture of meridional wind variation. Typically, winds are poleward and equatorward during the day and nighttime, respectively (Figure 5). The small-scale variations are seen due to other tidal components, such as, semi-diurnal, terdiurnal, and quarter-diurnal. Higher-order tides, such as terdiurnal and quarter-diurnal, have been investigated at lower thermosphere altitudes using the temperature and wind data obtained from both measurements and models (Moudden and Forbes, 2013; Guharay et al., 2018; Jacobi et al., 2017; Pancheva et al., 2021). In a recent work, the climatological mean amplitude of QDTs has been shown to be comparable with semi-diurnal and terdiurnal in the thermospheric altitude of around 250 km as measured by incoherent scatter radar over Arecibo (Gong et al., 2023). The quarter-diurnal and terdiurnal tides in the upper atmospheric altitudes can be generated in different ways. Both the migrating and non-migrating tides can play a significant role here. However, thermal excitation by the solar heating and non-linear wave-wave interaction can generate the higher-order tides of different wavenumbers in the middle and upper atmosphere (Xu et al., 2012, 2014; Moudden and Forbes, 2013; Geißler et al., 2020). Although the amplitude of these higher-order tides is significantly small compared to diurnal tides, they nonetheless seem to play an important role in the dynamics of the thermosphere, especially in the post-sunset hours. Here, we show that the QDTs are more effective in causing the reversal in meridional winds after sunset, which has not been reported so far, to the best of our knowledge.

5. Summary:

The OI 630.0 nm nightglow emission brightness typically shows a monotonic decrease after sunset. On many occasions, an enhancement in emissions has been observed during post-sunset hours as measured by HiTIES over Mt. Abu, a low-latitude location in India. In a comprehensive and detailed investigation, the presence of poleward wind has been shown to be responsible for such enhancement in emissions at low latitudes as the poleward winds bring down the plasma to lower altitudes (Saha et al., 2021). The cause of such reversal in the usually equatorward winds at post-sunset hours has been examined in this study. In order to address the optical observations, free-running WACCM-X simulations have been carried out for a three-month duration, which also showed an increase in electron density during post-sunset hours on many occasions in the altitudinal region of 250 km, as also shown in the digisonde measurements in our earlier study (Saha et al., 2021). The WACCM-X simulations show a reversal of equatorward wind coincident with the time of enhancement in electron density, which serves as an independent confirmation of our observations reported earlier (Saha et al., 2021). In the present work, the variations of meridional winds obtained from WACCM-X have been analysed to understand the cause of such reversals during the post-sunset time. Different tidal periodicities, such as diurnal, semidiurnal, terdiurnal, and quarter-diurnal, are fitted using least square method, which reveals very interesting information on the amplitudes and phases of each of the components and their association with the direction of the meridional wind. The phase and amplitude of higher-order tides play a crucial role in the nighttime thermospheric dynamics. Whenever the amplitudes of higher-order tides fall in the same phase, the magnitudes of wind reversal get enhanced. Thereby, a strong tidal contribution has been found to be the cause behind the poleward reversal of meridional winds after sunset, which causes an increase in electron density as well as enhancement in OI 630.0 nm emission. Especially, QDTs play the dominant role in the variation of meridional wind. This also explains why such reversals in winds do not occur on all the nights in a given season.  Thus, the redline OI 630.0 nm emission enhancements in the post-sunset time can also serve as an indicator of the reversal of winds and the existence of the strength of the higher-order tides at that time.

6. Acknowledgement:

The nighttime optical data, used in this study, has been obtained by the Physical Research Laboratory, Ahmedabad, India. This work is supported by the Department of Space, Government of India. FL was supported by NASA Contract 80GSFC18C0061 to the University of Colorado, Boulder, USA.

7. Open Research:

The data used to represent the figures in this work can be accessed from https://osf.io/gteq9/. A netCDF file containing all the relevant WACCM-X simulated data used in this study is available at the following link: https://doi.org/10.5281/zenodo.8400600.

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