\(A=A_0+\sum_{s=-4}^5\sum_{i=0}^3A_iSin(\frac{2\pi}{T_i}t+sλ+ϕ_i),\ T_i=6,8,12,24\dots\dots\dots..(1)\)
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.