In this section, we present mean wind circulation in the MLT region over the three radars located at KOT, PAM, and PON. Figure 1 illustrates the time–height plots representing the zonal winds (panels a–c) and meridional winds (panels d–f) over the altitude region of 82–94 km from 1 April to 31 May 2010. Wind contours are constructed from daily mean values, with the solid black line representing the zero wind in zonal and meridional contours. It can be seen that before mid-April, zonal winds are mostly westward for all radars, while the flow is eastward for most observation days after this period. According to Venkateswara Rao et al. (2012), westward winds are stronger than eastward winds within ±9∘ latitude, whereas at ±22∘ eastward winds are stronger. The maximum westward wind is observed to be about 40 m s-1 over KOT at an altitude of 82 km. The maximum eastward wind is in the range of ∼ 25 m s-1 and its occurrence is at around 88, 86, and 94 km over KOT, PAM, and PON, respectively. In general, a similar behavior in the zonal winds is found among the stations, and strong westward winds centered on April 2010 weaken with increasing height. Younger and Mitchell (2006) have shown that westward winds observed during the equinoxes have a maximum of about 30 m s-1, and are located at about 84 km at the Ascension Island equatorial station. The UARS High-Resolution Doppler Imager (HRDI) has also documented the tendency of the speed of westward winds (e.g., Burrage et al., 1996). Figure 1d–f represent the meridional wind for the three radar stations. The major structures produced by the three stations are generally the same. In all three stations southward wind is larger than the northward wind. The maximum southward wind is observed in early April between the 82 and 86 km altitude regions at about ∼ 25 m s-1 over PON. The maximum northward wind is observed over KOT at about ∼ 15 m s-1 between the altitudes of 86 to 92 km. Independent observations of equatorial mean winds at Ascension Island (Hirota, 1978) and other longitudes (Burrage et al., 1996) agree with the general form of the winds. These studies demonstrated that westward winds peak during the equinox while eastward winds peak during the solstice.

A cross-correlation analysis was performed between the three zonal and meridional time series between 82 and 94 km altitudes. This analysis provides a set of time-dependent correlation coefficients of two signals. We found correlation coefficients of 0.68 between KOT and PAM with a lag of zero, 0.65 between KOT and PON, and 0.63 between PON and PAM zonal wind at 86 km, which are significant at the 95 % confidence level. The maximum lag is observed in the altitude range between 90 and 94 km. In the case of meridional wind we observed a time lag of ±5 h. Figures 2 and 3 show the results of the cross-spectral analysis for the zonal and meridional winds. In Fig. 2, the top row (panels a, d, and g) shows the power spectral density of two radars, the middle row (panels b, e, and h) corresponds to the cross-spectral power, and the bottom row (panels c, f, and i) is the coherence spectrum estimated for the 90 km altitude level using the CCS technique. The dashed line in the bottom panels corresponds to the 95 % confidence level. From the figures it can clearly be seen that the zonal and meridional wind power spectra are characterized by a dominant peak at 3–4 and 5–8 days. Furthermore, these peaks appear at all mesospheric heights (82–94 km). Comparing the bottom panels of Figs. 2 and 3 demonstrates that PWs appear in the three radar datasets, and these waves are above the 95 % confidence level. The average coherence is 0.53 between the radars zonal winds and 0.5 between the meridional winds. These coherence plots identify cycles of 3–4 and 5–8 days. In addition, some other PWs (8 and 10–12 days) are also clearly evident; however, they are out of the scope of the present study.

Before studying the characteristics of PWs, we checked what periods were dominant in the hourly wind datasets. We used LSP and the new analysis technique of EMD, which is an effective method for adaptively decomposing the signal into different independent frequency components, termed IMFs. The IMFs yield instantaneous frequencies as a function of time, which allows for a precise identification of embedded structures. The time series of hourly zonal wind data at 90 km altitude are shown in Fig. 4 (top left); 10 IMFs can be extracted over KOT, only 8 of which are shown here to characterize the most important components. We investigate the gross characteristics of oscillations for each IMF using LSP analysis to the IMF time series. All IMFs exhibit slow-varying amplitudes and frequencies. The amplitude spectral plots are shown in the right panels of Fig. 4. The 95 % confidence level is shown by a horizontal dashed line. For this figure, the selected altitude is 90 km from the KOT hourly zonal wind dataset. The figure shows that the dominant peaks near semi-diurnal (12 h) and diurnal (24 h) are present in IMF2 and IMF4. IMF7 shows a clear PW period of about 3.5 days, while IMF8 shows a broader range of oscillations with periods ranging from 5 to 8 days and the maximum amplitude occurring at about 6.5 days. The Lomb–Scargle amplitude spectra are shown on the right side of Fig. 4, which reveals components centered at ∼ 3.6 and 6.5 days. The 3.6-day peak is somewhat broad, extending over roughly 3–5 days. Similarly, the 6.5-day wave also shows a broad peak (∼ 5–8.0 days). The EMD technique reveals that some waves with periods that are close to those of diurnal tide are generated due to the interactions of the diurnal tide and PWs, which indicate extensive coupling between the diurnal tide and PWs (Takahashi et al., 2006). In both methods, the PWs in mesospheric altitudes over equatorial radars are clearly seen. The PW periods are observed throughout mesospheric altitudes at all stations, although their amplitudes vary with altitude and from station to station. Similar results are also found at the other radars, indicating that these IMFs are statistically different from noise.

To deduce more information on the dependence of the PWs on height variations in Figs. 5 and 6, we show the mean wind, amplitudes, and phases over the three stations for the observation period. In each figure the top and bottom panels represent the zonal and meridional winds, respectively, as well as the amplitude and phase profiles for each station. The spectral amplitudes and phases were calculated by a LSP analysis within a set time window of 14 days (26 days) in length for the 3.6-day (6.5-day) wave. This window was shifted by a step size of 1 day, and the power spectral amplitude and phase values were estimated. The amplitude and corresponding phase values were considered only when they are > 95 % significant. Mean zonal and meridional winds are also given (curves with solid curves) to show the response of the PWs to background winds. Generally speaking, the 3.6-day zonal amplitudes look similar in all three stations. For example, at KOT and PAM the peaks are as large as 12–14 m s-1 above 90 km. But at Pontianak the zonal 3.6-day amplitudes are smaller and have no prominent peak values. When comparing the 3.6-day wave amplitude with background zonal mean wind, it seems that when there is a westward wind flow, there is also stronger 3.6-day amplitudes. The phase profiles (solid curves with open circles) indicate fairly downward progression in the 82–94 km height range at almost all three stations. KOT, PAM, and PON have vertical wavelengths of 42, 44, and 40 km, respectively. Note that these values are close to those estimated for equatorial regions and the vertical wavelengths are slightly smaller than the theoretical estimates for a 3.6-day wave.

Figure 6 shows the mean vertical profiles of the 6.5-day wave amplitudes and phases observed in the zonal (top panels) and meridional (bottom panels) wind components at the three equatorial stations, together with the mean wind. In the figure, the 6.5-day wave amplitude is shown by solid curves, mean wind is shown by curves with solid circles, and the phase is indicated by curves with open circles. The amplitudes are generally < 10 m s-1 below 90 km altitude levels. The maximum amplitudes (12–14 m s-1) are observed at KOT and PAM radar stations at 94 km of altitude, while moderate amplitudes are observed over the PON radar. Jiang et al. (2008) observed that 6.5-day wave amplitudes were strongest between 84 and 98 km, and the maximum amplitude of ∼ 14.5 m s-1 appeared at 92 km in April–May 2004 using the Wuhan meteor radar. Furthermore, they indicated that the 6.5-day waves near the spring equinox were generally stronger than those in other seasons. A large mesospheric 6.5-day wave was seen during late April and early May 2003 by the SABER instrument aboard the TIMED satellite and the ground-based radar systems (Riggin et al., 2006; Jiang et al., 2008). They mentioned that the 6.5-day wave in the MLT region during April–May 2003 should be regarded as an atmospheric normal mode, which was amplified through sympathetic interaction with the background wind. Takahashi et al. (2006) reported observations of a very strong ∼ 6-day wave with amplitudes reaching ∼ 25 m s-1 present simultaneously in the zonal winds over Cariri (7.4∘ S) and Ascension Island (7.9∘ S). Liu et al. (2004) using the National Center for Atmospheric Research Thermosphere-Ionosphere-Mesosphere Electrodynamics General Circulation Model (TIME-GCM) investigated the structures and seasonal variability in 6.5-day waves. The phase profiles of the 6.5-day wave for zonal and meridional winds for the three radars are shown adjacent to the wind profiles in Fig. 6. Usually there is a downward propagation with time, although upward phase progressions are sometimes observed.

In order to further investigate these waves, a band-pass filtering analysis of the horizontal winds in each height grid was carried out. The dominance of the 3.6-day wave periodicity is also clearly evident in the filtered time series of all three radars as shown in Fig. 7. In this figure, we considered step sizes of 2 km between the heights of 82 and 94 km. The data at the three sites were subjected to an elliptical band-pass filter with cutoff periods of 3.0–4.0 days. The figure clearly shows the time variations in the occurrence of the 3.6-day wave, with the KOT amplitudes being larger than those of the other two radars. The largest wave activity, with amplitudes of ∼ 16 m s-1, occurred at 92 km in the zonal wind during 1–15 April and 20 April–10 May over KOT. While the zonal and meridional wind components have similar amplitudes near the equator, the zonal 3.6-day wave amplitudes are larger than the meridional wind amplitudes. This is consistent with the other measurements.

Next, we perform a similar analysis with the 6.5-day oscillations. Figure 8 illustrates the features of the 6.5-day oscillations at different heights from 82 to 94 km. The zonal and meridional wind dataset was subjected to a band-pass filter of 5–8 days width. The amplitude of the oscillations at KOT reached ∼ 16 m s-1 at 88–94 km and lasted for 2 to 3 cycles in the 21-day interval spanning 22 April to 12 May 2010. It is interesting to note that the 6.5-day zonal wind oscillations at KOT, PAM, and PON were almost in phase during this period. The PAM and PON zonal winds showed common oscillation features during the intervals 1–14 April and 20 April–12 May 2010. The KOT zonal wind showed larger amplitudes than the other equatorial sites. The filter analysis determined that 6.5-day waves have a period of about 6–7.5 days, with the maximum wave amplitude occurring at 6.5 days. The zonal 6.5-day amplitudes are generally slightly stronger than the meridional amplitudes in all radar observations.

In this section, we investigate the possible temporal modulation of 3.6 and 6.5-day waves throughout the observation period through wavelet analysis. Figures 9 and 10 show the 3.6 and 6.5-day periodicities at three different height levels (86, 90, and 94 km) over three different radars. Wavelet analysis was applied to the dataset for the period 1 April–31 May 2010 for constructing the contours. Specifically, the commonly used Morlet wavelet function was used which better captures the time-varying nature periodicities. The details of this method can be found in Torrence and Compo (1998). In the figures, the 3.6- and 6.5-day periods are marked by white dotted lines.

In Fig. 9 we illustrate the 3.6-day zonal spectral intensities observed at 86, 90, and 94 km for the three radars. It is evident that during the observation period, a large burst of wave activity with a period of about 3.6 days occurred at all altitude levels. The wave period extended 2–5 days but the maximum intensity was near 3.6 days. The black line in the plots indicates areas with 95 % confidence level. The white dotted line indicates the 3.6-day wave period. From the figure, the wave intensity at higher altitudes appears to be slightly larger than that at the lower altitude levels. Figure 9d shows wider periods oscillating at 2–7 day periods. The 3.6-day wave amplitudes at PON have slightly smaller amplitudes compared to the other two radars.

To deduce more information on the time–height variations and dependence of the 6.5-day wave, we show the amplitudes at the three radars at 86, 90, and 94 km in Fig. 10. The 6.5-day peak is somewhat broad, ranging over 5–8 days at some heights and 5–10 days at other levels. The wave amplitude increases with altitude and reaches a maximum of about 22 K at mesospheric altitudes for all three radars. The 6.5-day oscillation has a broad spectral peak extending over several days at 90 and 94 km of altitude at KOT. The maximum amplitude of ∼ 24 K is observed over KOT at altitudes of around 94 km. The temporal localization oscillations using wavelet analysis shows strong 6.5-day waves during the observation period. During the observation period, the maximum amplitudes show differences between the measurements and thus make the wave activity out of phase at these locations (Kishore et al., 2005).