Wavenumber‐4 spectral component extracted from TIMED/SABER observations

The wavenumber spectral components WN 4 at the mesosphere and low thermosphere (MLT) altitudes (70–10 km) and in the latitude range between ±45° are obtained from temperature data (T) observed by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instruments on board the National Aeronautics and Space Administration (NASA)’s Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics (TIMED) spacecraft during the 11‐year solar period from 2002 to 2012. We analyze in detail these spectral componentsWNk and obtain the main properties of their vertical profiles and global structures. We report that all of the wavenumber spectral components WNk occur mainly around 100 km altitude, and that the most prominent component is the wavenumber spectral component WN 4 structure. Comparing these long duration temperature data with results of previous investigations, we have found that the yearly variation of spectral component WN 4 is similar to that of the eastward propagating non‐migrating diurnal tide with zonal wavenumber 3 (DE3) at the low latitudes, and to that of the semi‐diurnal tide with zonal wavenumber 2 (SE2) at the mid‐latitudes: the amplitudes of the A 4 are larger during boreal summer and autumn at the low‐latitudes; at the mid‐latitudes the amplitudes have a weak peak in March. In addition, the amplitudes of component WN 4 undergo a remarkable short period variation: significant day‐to‐day variation of the spectral amplitudes A 4 occurs primarily in July and September at the low‐latitudes. In summary, we conclude that the non‐migrating tides DE3 and SE2 are likely to be the origins, at the low‐latitudes and the mid‐latitudes in the MLT region, respectively, of the observed wavenumber spectral component WN 4.


Introduction
The mesosphere and low thermosphere (MLT) is an important region coupling the lower and upper parts of the atmosphere. Produced by the gravitational forces of the moon and sun, as well as the thermal action of the sun, the whole atmosphere presents a host of large-scale oscillations (Chapman and Lindzen, 1970). Active atmospheric oscillations in the MLT region, including gravity waves, atmospheric thermal tides, and planetary-scale internal waves, propagate through this region, leading to energy and momentum transportations from lower to higher altitudes.
Recently, lots of space instruments have been used to investigate the atmospheric oscillations at the MLT altitudes. For example, a global measurement of atmospheric tides was obtained by using temperature observations from the Limb Infrared Monitor of the Stratosphere (LIMS) instrument on the Nimbus 7 satellite (Hitchman and Leovy, 1985;Forbes and Wu D, 2006). The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on board NASA's Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite has provided the global structure and climatological (annual and inter-annual variation) characteristics of the large-scale waves and atmospheric temperature tides (e.g., Garcia et al., 2005;Zhang XL et al., 2006;Mukhtarov et al., 2009;Xu JY et al., 2009;Pancheva et al., 2010;John and Kumar, 2011;Gu SY et al., 2013). Previous descriptions of atmospheric tides have been based also on wind measurements from the High Resolution Doppler Imager (HRDI) on board the Upper Atmosphere Research Satellite (UARS) (e.g., Burrage et al., 1995;Khattatov et al., 1997;Huang FT and Reber, 2003). Moreover, global distributions of diurnal and semi-diurnal tides were observed from the Microwave Limb Sounder (MLS) on the UARS (Manson et al., 2002). The wind Imaging Interferometer (WINDII) on the UARS also observed thermospheric wind tidal signatures and equatorial wavenumber 4 density perturbations (McLandress et al., 1994(McLandress et al., , 1996. In addition, TIMED Doppler Interferometer (TIDI) measurements were analyzed for diurnal non-migrating wind tides (e.g., Oberheide et al., 2006;Wu Q et al., 2008;Xu JY et al., 2009).
It was Sagawa et al. (2005) and Immel et al. (2006) who first reported the prominent component in the IMAGE/FUV observation. Lin CH et al. (2007) analyzed electron density from GPS radio occultation measurements of FORMOSAT-3/COSMIC and found that four electron density peaks exist above 250 km. In addition, Wan W et al. (2008) studied the seasonal variation of the component in the total electron content (TEC). Previous researchers have suggested that the prominent longitudinal wavenumber component could be present in almost all the physical parameters of the ionosphere and of the thermosphere, including the F-region airglow , E × B drifts (e.g., Hartman and Heelis, 2007;Kil et al., 2007;Ren ZP et al., 2009), upper thermospheric winds (Häusler and Lühr, 2009), the ion density (Kil et al., 2007), electron density, and the thermospheric zonal wind (Lühr et al., 2007), to name just a few. Furthermore, Oberheide et al. (2011) identified a dominant wavenumber component in the longitude profile of the zonal wind in the MLT region. These authors related the wave pattern to the eastward-propagating non-migrating diurnal tide with zonal wavenumber 3 (DE3) and the eastward-propagating non-migrating semidiurnal tide with zonal wavenumber 2 (SE2). DE3 and SE2 are produced in the troposphere by the release of latent heat Forbes, 2002, 2003) and exhibit four wave peaks when seen from a Sun-Synchronous view.

WN 4
Recently, using data from the HRDI and WINDII instruments on the UARS, Wu Q et al. (2008) and Huang FT and Reber, (2004) found that the zonal wind of DE3 is stronger and occurs primarily between the June solstice and September equinox near the equator, while the meridional wind spectral component is relatively weaker and occurs during the March and September equinoxes. Similar results have been obtained from analysis of data from the TIDI and SABER instruments on board the TIMED satellite (e.g., Oberheide et al., 2006;Chen ZY and Lü DR, 2007;Oberheide and Forbes, 2008). In addition, Bruinsma and Forbes (2010), England et al. (2010), Oberheide et al. (2011) andMiyoshi et al. (2012) demonstrated the importance of the SE2 for generation of the wave-4 structure at the mid-latitudes. Thus, we suggest that the observed annual variation of the spectral component in atmospheric parameters should correspond to that of DE3 and SE2 tides.
Several studies over the last couple of decades have shown that a noticeable longitudinal wavenumber spectrum would be present in the MLT region. Hence, we report results of preliminary studies of the wavenumber spectrum in atmospheric parameter (T) at the MLT altitudes observed by the SABER instruments on board NASA's TIMED spacecraft, which was launched on 7 December 2001. Due to the slow precession of this satellite's orbit, almost complete local time coverage is achieved every 60 days. During the last decade, investigators have studied the climatological (annual and inter-annual variation) characteristics of atmospheric tides and planetary waves by accumulating daily SABER temperature data in a running window of 2 months (60 days) length. In this report, we suggest that SABER data can reveal meteorological (short period variation) characteristics of the large-scale waves in the MLT region, from a new point of view. We use the global observations of atmospheric parameter (T) from TIMED/SABER to study the longitudinal wavenumber spectrums over the mid-low latitudes in the MLT region. Further, we obtain wavenumber spectrums, filtered from the extracted long-period atmospheric parameters, and investigate their vertical profiles and climatological and meteorological characteristic. Our results support the suggestion that the longitudinal wavenumber spectral components may have their origin in the non-migrating tides.
The main purpose of the present work is to investigate the longitudinal wavenumber spectral component of the atmospheric parameter (T) in the MLT region, picked up from the TIMED/SABER observation data sets. Section 2 describes the TIMED/SABER observation data and the analysis methods. In Section 3 we present the analysis of the main wavenumber spectral components and analyze in detail the short period variation of the longitudinal wavenumber spectrum . In Section 4 we compare the short period variation of the main spectrum with data regarding the non-migrating tides. The last section presents our summary and conclusions.

WN k
In this paper, we will analyze variations of the wavenumber spectral components and study in detail the day-to-day variation of the wavenumber-4 spectral component using temperature observations from the SABER instrument on board NASA's TIMED satellite.

TIMED Observations
Since late January 2002, the SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) instrument on the Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) satellite has provided global temperature (T) observations for the latitudes range 50°N-50°S from the lower stratosphere to the lower thermosphere (20-120 km). These data provide an unprecedented opportunity for studying in detail the climatological characteristics of the longitudinal wavenumber spectral components in coupling the lower and upper atmosphere. Over a period of approximately 60 days, as the TIMED satellite both ascends and descends through orbital nodes, SABER is able to collect data sampled at almost a full 24 hours of local solar time. Figure 1 presents a local time (LT) series during a 7-year interval taken on the ascending (red dots) and descending (blue dots) orbit nodes at the equatorial latitude and at the 100 km altitude.
The TIMED/SABER observations are downloaded from the Web site: http://saber.gats-inc.com/. More details about the instrument and recent results are given by Killeen et al., (2006) and Remsberg et al. (2008).
In the present study, we analyze Saber data, version 2, from both ascending and descending orbital nodes in the altitude range between 70 and 110 km and the latitude range between 45°N and 45°S, collected during 2002-2012.

Wavenumber Spectrums Analysis
We have developed a technique to decompose the atmospheric waves of different longitudinal wavenumbers, based on wavenumber spectral analysis. Using this technique, we express daily temperature data by the composition of their wavenumber spectral components , where is the daily average of temperature ( ); indicates LT and denotes the integer day numbers (UT days); is the longitude and indicates altitude; denotes latitude; denotes the longitudinal wavenumber; and and are the amplitudes and phases of the spectral components , respectively: The top plot of Figure 2 is an example of the temperature data from July 31, 2004, at the equatorial latitude ( ) and at the altitude of 100 km, represented as a distribution of longitude . For a single-fit-using equation, we use a horizontal grid spacing of 15 or 16 orbits a latitude cycle to extract the spectral components. The bottom plot of Figure 2 presents the deduced wavenumber spectral amplitudes from the top temperature data, represented as a wavenumber distribution . It is obvious in Figure 2 that wave number 4 ( ) dominates the wavenumber spectral components in temperature ( ). As suggested by previous research, the components are the strongest spectrum components in the MLT region as well as in the thermosphere and ionosphere (e.g., Sagawa et al., 2005;Immel et al., 2006;Wan W et al., 2008;Liu HX et al., 2009). Hence, among these wavenumber spectral components, we are mainly interested in the wave number 4 ( )

Results
SABER\TIMED observations provide the daily temperature data analyzed here; these data have horizontal and vertical resolution of 2.5° latitude by 2 km height. In addition, for each local time and each day number , the amplitudes of the wavenumber spectral components are then derived from the daily temperature data. Figure 3 shows the mean distribution of the amplitudes of the main wavenumber spectral components, which are further averaged among different years (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012), as a distribution in the plane of latitude vs height. From top to bottom and from left to right the plots refer the wavenumber , respectively. It is also obvious in Figure 3, as well as in Figure 2, that the wavenumber spectral component is quite remarkable among the different spectrum components in temperature ( ).

Wavenumber Spectral Components
It should be noticed that the wavenumber components in temperature present the convergent tendency, that is, wavenumber spectral amplitudes decrease as the wavenumber increases, as shown in Figure 3. In addition, the wavenumber component are obvious, as illustrated in the bottom left plot of Figure 3. The wavenumber spectral amplitudes are a little larger, as seen in the top right plot of Figure 3, which would be consistent with the of the total electron content (TEC) in the EIA region (Mu WF et al., 2010).
As seen in the top plots of Figure 3, the wavenumber component is strongest at the altitudes range from 84 to 90 km around the equator; it is stronger at ±30°. The amplitudes at high-mid latitudes are larger than that at low-latitude. The amplitudes of the second wavenumber component are largest at 85 km along the equator. Next, the wavenumber component is strong from 100 to 110 km at mid-low latitudes in the northern hemi- sphere. As shown in the bottom left plots of Figure 3, the wavenumber component is stable and strong around 100 km altitude and at the low-latitudes; i.e., the amplitude may reach to 1.2 K, and the (relatively weak -it may reach only to 0.8 K) peak amplitude occurs at 80-90 km. The wavenumber components and are weaker in the MLT region.
Hence, among these wavenumber spectral components, we are mainly interested in the wavenumber component . The meteorological (short period variation) characteristics of the wavenumber spectral component will be presented in the next section.

Wavenumber-4 Spectral Component
In this paper, we focus on wavenumber spectral component in the atmospheric parameter ( ). For lack of daily temperature data, previous research into annual and inter-annual temperature variation focused on analysis of the climatological characteristics of the wavenumber components. Now, we reverse that approach by taking the component for example, presenting its climatological (annual and inter-annual variation) and meteorological (short period variation) characteristics by using the now-plentiful daily temperature data. Figures 4 and Figure 5 show the yearly variations of the component ; Figures 6 and 8  2012 each year, are illustrated in Figure 4. As can be seen in Figure 4, as well as in the left bottom plot of Figure 3, the wavenumber spectral amplitudes present a remarkable annual variation at the low-latitudes: is larger in J-months (May, June, July and August), i.e., the spectral amplitudes may reach 6 K in August, as shown in the third-row plot of  In order to analyze, in detail, the day-to-day variations of the wavenumber spectral components in the MLT region, as well as to compare the annual variation of the wavenumber spectral component with results of previous research, the component is smoothed with a running window of 1-month. Similar to Figures 4 and 5, Figures 6a 6b, 8a, and 8b show the wavenumber spectral component at 100 km and along the equator; i. e., the amplitude and the phase , respectively. As illustrated in Figure 6a, the spectral component are strong at the low latitudes during the period of boreal summer to autumn, and present a weak peak in March at the mid-latitudes. Obviously, the yearly variation of the wavenumber spectral component at the low-latitudes is highly dependent upon the nonmigrating tide DE3; this observation agrees with previous studies (e.g., Wu Q et al., 2008;Friedman et al., 2009;Oberheide et al., 2011). Additionally, the peak of the wavenumber spectral component in summer is obviously divided into two peaks. For instance, the spectral amplitudes are larger in July and Septem-

Lat (°)
A k z φ k = 1, 2, 3, 4, 5, 6  ber. Additionally, a weak peak of the occurs in March at the mid-latitudes, which matches the variation of SE2 at the MLT altitudes (Pancheva et al., 2010;Oberheide et al., 2011). As to Figure 6b, the spectral phases are stable when the corresponding amplitude is strong enough (i.e., in a J-month), but it is much noisier when amplitudes are weaker. This phenomenon is similar to the variation of DE3 in the MLT region ). In addition, as shown in Figure 6b, the spectral phases have a cycle of about two months.
As seen in Figure 8a, the spectral amplitudes along the equator are larger above 100 km altitude; and in April, June, and July; i.e., we observe that the amplitude reaches 4 K in July 2008 at 100 km. In addition, as illustrated in Figure 8b, the spectral phases are stable at the MLT altitudes, especially in J-months. The wave length along the equator is about 30 km, as shown in Figure 8b.

WN 4
In this work, the day-to-day variation of the wavenumber spectral component is represented by the difference between suc- cessive daily averages, smoothed with a running window of 1-month, of the daily component. This day-to-day variation of the smoothed average wavenumber spectral component is shown in Figures 7a, 7b, 9a, and 9b; i.e., the amplitude and the phase , respectively. As seen in Figure 7a, the amplitudes of the day-to-day variation are also obvious in J-months and at the lowlatitudes. We report that the day-to-day variation has peak amplitudes in September at the low-latitudes in the southern hemisphere. Also, as Figure 9a indicates, the day-to-day variation of the wavenumber spectral component is most remarkable around 100 km along the equator.

Discussion
From the above analysis of data from the TIMED satellite over a range of the atmospheric parameter ( ), we conclude that the most prominent feature of the wavenumber spectrum is the fourpeaked longitudinal structure ( ). The observed yearly variation of the spectral component in Figures 3 and 4 were almost fully emulated by DE3 at the low-latitudes and by SE2 at the  Similarly, the analysis demonstrates that DE3 is intimately connected at low latitudes with the longitudinal distribution, by topography and land-sea difference, of the predominant wavenumber, which is wavenumber 4. (e.g., Pancheva et al., 2010;Oberheide et al., 2009Oberheide et al., , 2011. As suggested by previous studies, the longitudinal wavenumber spectral component in the ionospheric F region may originate from longitudinal modulation of the latitudinal symmetric modes; the main contributing tide is believed to be the DE3 tide . Comparing our work with the above results, we note that the yearly variation of the spectral component is completely consistent with that in the temperature fluctuations of DE3 at the low latitudes. Moreover, observational evidence supports the hypothesis that SE2 may be an important source of the wavenumber-4 structure at the mid-latitude in the ionosphere and thermosphere (e.g., Oberheide et al., 2007;Forbes et al., 2008;Hagan et al., 2009;England et al., 2010;Häusler et al., 2010;Oberheide et al., 2011;WN 4 Pancheva and Mukhtarov, 2012;Chang LC et al., 2013). Our results above suggest that the mid-latitude peak of the spectral component may correspond to the SE2 tide at the middle latitudes.
Hence, we suggest that the wavenumber spectrum is determined primarily by the DE3 tide at the low-latitudes and by the SE2 tide at the mid-latitudes. In addition, the abundant observation data available from the TIMED satellite have allowed analysis of the local time (LT) variations of the wavenumber spectral phases at the MLT altitudes. Statistical analysis of these data finds that the phases of the component are regular when the amplitudes are strong. Figure 10 shows two examples of the average phases , represented as a distribution of LT. The top plot of Figure 10 presents the phases at the altitude of 100 km along the equator in the J-months (May, June, July and August); the bottom plot presents phases in March at the 110 km altitude at 30ºN latitude. As seen in Figure 10, in an LT period the phase variation is obviously linear. We suppose that the wavenumber component may originate mainly from the longitudinal modulation of one single mode. In addition, as illustrated in the top and bottom   Figure 10, the estimated period of 24 LT and 12 LT, respectively, demonstrate that the single mode should be a diurnal tide and a semi-diurnal tide, which exhibit four wave peaks when seen from a Sun-Synchronous view.

Summary and Conclusions
In the present work, TIMED\SABER observation data have been used to obtain longitudinal wavenumber spectral components of the atmospheric parameter ( ) and to investigate the wavenumber-4 spectral component at the MLT altitudes (70-110 km). We report that the most prominent wavenumber spectral component is the component . The main results are outlined as follows: (1) The variations of the wavenumber spectral components in Temperature (T) are observed to be strong in the MLT region and at the low-latitudes. Among the components, is strongest; is second-strongest.
is stronger around 100 km altitude and at the low-latitudes. The wavenumber spectral amplitudes A 1 are larger along the equator and at mid-latitudes in the altitude range of 80-90 km. (2) Using long duration temperature data, the climatological (annual and inter-annual variation) characteristics of the wavenumber spectral component are presented. The yearly variations imply the possibility that the component in temperature is dependent at the low latitudes primarily on the diurnal, eastward, wavenumber 3 nonmigrating tide DE3, and on the semi-diurnal, eastward, wavenumber 2 nonmigrating tide SE2 at the mid-latitudes. In addition, we find that the wavenumber spectral component undergoes a remarkable short period variation: the peak spectral amplitude A 4 in temperature occurs primarily in boreal summer and autumn at the low-latitudes and above 100 km altitudes. From the above results, we conclude that the climatological characteristic of the wavenumber spectral components is consistent with that of the non-migrating tides in temperature. In addition, the meteorological characteristic of the wavenumber spectral component shows two peak amplitudes during the boreal summer and autumn, i.e., July and September, which may originate from the longitudinal modulation of the DE3 tide at the lowlatitudes and shows a weak peak amplitude in March, which may originate from the longitudinal modulation of the SE2 tide at the mid-latitudes. Thus, we suggest that the non-migrating tides DE3 and SE2 should be acknowledged as the origins of the observed longitudinal wavenumber spectral component at, respectively, the low-and the mid-latitudes in the MLT region.

Acknowledgments
The TIMED/SABER temperature observations were provided through the website http://saber.gats-inc.com. The present work is supported by National Science Foundation of China (41604138,