Temperature profiles derived from Constellation Observing System for Meteorology, Ionosphere and Climate Global Positioning System Radio Occultation satellite constellation data are used to study equatorial gravity wave potential energy associated with waves having vertical wavelengths of less than 7 km and their interaction with the background quasi-biennial oscillation (QBO) wind. The data are binned into grids of size 20° in longitude and 5° in latitude. Results show evidence of vertically propagating convectively generated gravity waves interacting with the background mean flow. Enhancements in potential energy around the descending 0 m s−1 QBO eastward shear phase line are observed. Equatorially trapped Kelvin waves and Mixed Rossby Gravity Waves with zonal wave numbers s ≤ 9 are obtained by bandpass filtering wave number-frequency temperature spectra. Their temporal, spatial and vertical structures, propagation and wave-mean flow interactions are examined with respect to the background mean flow. Equatorial waves observed by COSMIC are compared with those seen in OLR data, with differences discussed.
Wheeler and Kiladis  constructed a tropical climatology of tropospheric source region convectively coupled wave activity using 18 years of Outgoing Longwave Radiation (OLR) data to separate various equatorial waves. A study using Tropical Rainfall Measuring Mission (TRMM) rainfall data observed a similar tropospheric source spectrum [Cho et al., 2004]. A multiyear analysis of stratospheric temperature data observed by the SABER instrument onboard the TIMED satellite isolated various equatorial waves and studied their vertical propagation and interaction with the QBO [Ern et al., 2008].
 The Global Positioning System Radio Occultation (GPS-RO) technique for obtaining temperature profiles below 40 km is now well established. These GPS data are highly accurate and have high vertical resolution, enabling the study of short vertical wavelength global- and regional-scale gravity wave activity [Tsuda et al., 2000; Ratnam et al., 2004; de la Torre et al., 2006; Baumgaertner and McDonald, 2007; Hei et al., 2008; Alexander et al., 2008a]. Previous global GPS temperature observations used GPS/MET or CHAMP satellites but because of their relatively sparse sampling, only seasonal or multiyear phenomena could be studied. These data sets hinted at large perturbations due to irresolvably small waves. Randel and Wu  showed that temperature variances associated with global Kelvin wave activity were two to three times smaller than those associated with higher wave number waves.
 The launch in April 2006 of the six Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) satellites provides an order of magnitude increase in the number of GPS-RO profiles available [Anthes et al., 2008]. In this article, we discuss results of an analysis of COSMIC data by constructing regional, hemispheric and temporal pictures of the tropical UTLS region. The variability and wave mean flow interactions of global-scale equatorially trapped waves and gravity waves are examined. Most of the observed variances of equatorially trapped waves are due to waves with s < 10 [Ern et al., 2008; Hendon and Wheeler, 2008], a spectral region which can be observed using COSMIC GPS-RO data. Small-scale gravity waves are studied using potential energy. Kawatani et al.  analyzed waves appearing in a T106L60 AGCM and related the results to these COSMIC observations.
2. Data Analyses
 Because of the gradual movement of the six COSMIC satellites into their final orbital positions, sufficient data for this study are available from September 2006 onward. The COSMIC version 2.0 dry temperature data product is used, which is derived from the measured refractivity profile by neglecting humidity and as such is accurate above about 10 km in the tropical region. The original COSMIC data are available at 0.1 km vertical resolution but they have an effective vertical resolution on the order of 1 km in the UTLS and stratosphere region. Therefore the original (non-independent) data are interpolated to the approximate real resolution of 1 km.
2.1. Derivation of Potential Energy for Mesoscale Gravity Waves
 Gravity wave energy is the sum of kinetic energy Ek and potential energy Ep terms, with the former only calculable with knowledge of the wind velocities. However, the temperature and wind velocities are coupled to each other via the wave polarization equations. Linear gravity wave theory predicts that the ratio of Ek to Ep is constant and therefore we can consider the total energy of the atmospheric system by studying temperature perturbations alone [Tsuda et al., 2000].
 Potential energy is calculated using two different methods. The first method is the same as used previously with COSMIC [Alexander et al., 2008a], which itself is broadly similar to that used with the previous generation CHAMP GPS-RO satellite [Hei et al., 2008]. The data are binned into grid cells of size 20° longitude × 5° latitude × 7 days, from which the mean background temperature is calculated. There is one cell centered on the equator, with boundaries at 2.5°S and 2.5°N. An individual profile's temperature T is subtracted from and the linear mean is removed using a least squares fitting method. Any missing data points in this profile are linearly interpolated across (which in reality is rarely necessary to do). The data are then Welch windowed to reduce spectral leakage before being 7 km vertically high-pass filtered. The general equation for calculating potential energy Ep is:
where N is the Brunt-Väisälä frequency, g is the gravitational acceleration and all variables except g are functions of height. N2 is calculated from COSMIC derived temperature and pressure. N2 varies from ∼6.5 × 10−4 rad2 s−2 at 20–22 km to 4.5–5.0 × 10−4 rad2 s−2 at 30–32 km.
 The 7 km potential energy Ep7 used here is integrated over a 7 km vertical interval centered on the altitude for which it is calculated, before dividing by seven. This analysis procedure is stepped forward in time by 1 day, therefore consecutive days are not independent in this 7-day averaging.
 Calculation of Ep7 by integration degrades the vertical resolution. The second method calculates potential energy independently at each height but still uses 7 km vertical high-pass filtering. Calculation of an individual profile's potential energy at each height is meaningless because a full wave cycle does not exist. If sufficient profiles are available, it can be assumed that all wave phases pass through a constant height and therefore taking the mean at each height over some time period provides a physically meaningful result. As a result of the orbital inclination of the COSMIC satellites, the equatorial region has the lowest amount of profiles which in the worst case is as low as ∼30 per month in each 20° × 5° grid cell but is usually twice this. Thus 1 month of data are used to obtain the 1 km vertically independent potential energy Ep1 profiles. In this instance, Ep1 are integrated in time instead of height so all variables in equation (1) except g become functions of time. Calculation of Ep1 is useful despite the decreased temporal resolution because it allows the study of small-scale vertical changes, which are smeared out in the calculation of Ep7. These effects include the tropopause and the QBO u = 0 m s−1 descending phase line, across which the potential energy changes markedly.
 The Ep7 consists of waves with ∼2 km < λz < 7 km and periods less than about 10 days. Waves with long horizontal wavelengths λx and longer periods are part of the background temperature in each grid cell. This results in the removal of most global-scale waves meaning that the majority of the Ep7 is due to mesoscale gravity waves. There are probably minor contributions to Ep7 from high phase speed cx Kelvin waves, although these waves generally have large vertical wavelength λz. MRGWs may also contribute to the Ep7, although they generally have small temperature amplitudes.
 A larger part of the wave spectrum is included in Ep1 because of the longer data averaging interval. Slower cx Kelvin waves with periods of less than 30 days contribute to the total Ep1, resulting in a more pronounced QBO variability (see section 3.1 below). Despite this, Ep1 is still mainly a result of small-scale gravity waves [Randel and Wu, 2005; Ern et al., 2008].
 Definition of the background temperature is an important problem because it will affect all subsequent calculations of potential energy. Testing reveals that changing the temporal resolution of the grid cells to 5 days results in too few profiles, whereas calculating over longer timescales acts to smear out small-scale effects, so 7 days is a good compromise for calculating potential energy [Alexander et al., 2008a]. The Ep7 and Ep1 recalculated using potential temperature θ result in similar UTLS values to those calculated using T (not shown), despite the shallower tropopause gradient in θ. Polynomial fitting functions of different order can also be used to obtain T′ [Vincent and Alexander, 2000; Zhang et al., 2004], but this results in larger tropical UTLS potential energy values when compared with the COSMIC method detailed above (which itself probably overestimates the potential energy somewhat because of the sharp cold point tropopause structure [Alexander et al., 2008a]).
 The precision of the COSMIC refractivity is 0.7% at 30 km but <0.2% between 10 and 20 km [Schreiner et al., 2007]. The accuracy of the COSMIC derived temperature is better than 0.5 K. Uncertainties in an individual profile's 7 km vertically averaged Ep7 is about 25%, which reduces to ∼10% after 7-day grid cell averaging. The seasonal averages, to be discussed below, have uncertainties of <5%. For the 1 km height independent monthly averaged Ep1, the uncertainty is also <5%.
 The COSMIC results are compared with NCEP zonal wind reanalysis data [Kalnay et al., 1996], which are averaged over the appropriate temporal and spatial domains and are provided below 10 hPa (∼31–32 km). The results are also compared with OLR data, which are often used as a proxy for deep convective activity (e.g., Wheeler and Kiladis ; Alexander et al. [2008b]). These 2.5° × 2.5° data are averaged over the appropriate space and time domains.
2.2. s − ω Spectra and Hovmöller Analysis for the Global-Scale Wave Modes
 Equatorially trapped waves, their propagation and mean flow interactions are studied using Hovmöller diagrams of the temperature perturbations T′. The COSMIC temperature data at each height are initially divided into their symmetric and antisymmetric components about the equator. Gridded data which are a function of latitude ψ may be decomposed into symmetric and antisymmetric components, where their sum equals the original data field. The symmetric component T′S(ψ) is:
and the antisymmetric component T′A(ψ) is:
 Anticipating the structure of the tropical Ep1 in section 3.2, the raw temperature data are binned into separate Northern Hemisphere (between 0.5°N and 10°N) and Southern Hemisphere (between 0.5°S and 10°S) grid cells with temporal resolution 1 day and longitude width of 20°. The 1-day resolution is possible because of the larger latitude range and it allows the study of short period waves such as MRGWs, which have ground based periods of <5 days. On the other hand, averaging the temperature perturbations over this longitude and latitude range degrades the spatial resolution by changing the exact GPS-RO profile's coordinates to that of the average bin coordinates. This adds some noise to low s waves and attenuates the signal of higher s waves.
 The zonal mean daily temperature is removed to form T′ at each height and for each day. These T′ are the average residual temperature in each grid cell and are not from single COSMIC profiles. The data analysis period is 96 days, stepped forward in time by 32 days. A Welch window is applied in time to this 96-day data set to minimize spectral leakage.
 Waves are extracted using space-time spectral analysis [Hayashi, 1971, 1982] separately on the symmetric and antisymmetric components. This analysis is appropriate for data which are cyclical in longitude with a finite time and was applied to OLR data [Wheeler and Kiladis, 1999], TRMM [Cho et al., 2004], CHAMP GPS-RO T′ for Kelvin wave analysis [Randel and Wu, 2005] and SABER data [Ern et al., 2008]. In summary, at a fixed latitude, complex FFTs of T′ in longitude provide Fourier coefficients for input into further FFTs in time. The wave number-frequency s − ω spectrum is thus obtained. The data are then bandpass filtered in s − ω space in order to extract specific waves (as discussed below). The 20° longitude grid resolution of COSMIC allows the study of waves with s ≤ 9. After bandpassing, reverse FFTs are applied to the coefficients so that Hovmöller diagrams can be constructed. In order to minimize signal suppression, only data from the middle 32 days of each 96-day block are used for Hovmöller analysis.
3. Potential Energy of Mesoscale Gravity Waves
3.1. Zonal Mean Conditions
 The zonal mean stratospheric 7-day averaged 7 km vertical Ep7 between 2.5°S and 2.5°N is plotted in Figure 1a, along with the zonal mean zonal wind from the NCEP reanalysis. The Ep7 at for example 26 km consists of data from 23–29 km inclusive. The equivalent monthly averaged 1 km independent Ep1 is shown for comparison in Figure 1b with the same color scale. These potential energy results are based on one bin centered on the equator.
 There is overall agreement between the two methods of calculating potential energy. The Figure 1aEp7 shows fluctuations on the order of a week or two, which can be linked back to the influence of changes in deep convective activity (i.e., the gravity wave generator) in certain regions of the tropics, mainly in the Eastern Hemisphere. These are not visible in the monthly calculations of Ep1 (Figure 1b). The magnitude of the potential energy from July to November 2007 between 26 km and 30 km is slightly different between Figures 1a and 1b. The 7 km vertical integration smoothes out Ep7, resulting in values about 0.3–0.6 J kg−1 lower than the 1 km height independent Ep1, even though both are 7 km vertically high-pass filtered. As discussed above, Ep1 consists of a wider spectrum of waves and a small amount of equatorially trapped wave information, so in general it should be slightly larger. In the region below 22 km before May 2007, Ep7 of 5.0 J kg−1 is quasi-periodically observed, but in the monthly mean Ep1 these are 3.5–4.4 J kg−1 because Ep7 are affected by the sharp cold point tropopause and are likely to overestimate the true atmospheric potential energy.
 The downward movement of the u = 0 m s−1 phase line associated with westward QBO shear is evident, from 30 km in September 2006 to 21 km by June 2007. This decrease in the altitude at which the winds switch from eastward to westward corresponds to a decrease in the Ep7 as eastward propagating gravity waves are critically filtered out at lower levels by the background wind. The Ep1 at the 0 m s−1 westward shear phase line is 2.0–3.2 J kg−1 (Figure 1b). Wave filtering continues above the wind reversal as increasingly strong westward winds are encountered, so that by the height of the −20 m s−1 phase line, Ep1 is 1.1–1.7 J kg−1.
 Westward winds are observed throughout the lower and middle stratosphere from June 2007 to November 2007, allowing eastward travelling gravity waves to propagate vertically through this entire region. The 32 km Ep1 more than doubles from 0.5–0.8 J kg−1 in April 2007 to 1.7–2.0 J kg−1 in August 2007 as low speed waves begin to encounter their critical level. This pattern of increased Ep1 decreases through time in response to the descending eastward shear.
 During the eastward shear phase from August 2007 onward, the stratospheric Ep1 shows a band like structure around the 0 m s−1 phase line. The Ep1 shows a decrease with height along this phase line, from ∼4.0 J kg−1 at 22 km in March 2008 to ∼2.5 J kg−1 at 31 km in August 2007. Wave amplitudes increase with altitude because of the decreasing density and as such temperature variance increases with altitude along the eastward shear 0 m s−1 phase line [Randel and Wu, 2005; Ern et al., 2008]. Some reduction of wave amplitude and thus potential energy at the highest altitudes is a result of the Welch data windowing used here. de la Torre et al.  constructed a CHAMP climatology from 2001 until 2006 and separated waves into two bands before calculating the Ep: λz < 4 km and 4 km < λz < 10 km, both of which had maximum eastward shear related Ep at 21–25 km and decreasing values up to about 30 km.
 The increase in Ep7 and Ep1 observed around the descending eastward QBO shear u = 0 m s−1 phase line from August 2007 onward may be due to some inter-related processes. Firstly, temperature variance varies as ∼ ∣ − c∣−1 so for a wave spectrum symmetrically distributed around 0 m s−1, variance will increase close to the 0 m s−1 line [Randel and Wu, 2005]. An observational filtering effect of COSMIC may also explain the increase in potential energy. COSMIC is more likely to observe gravity waves with slower vertical group velocity cgz. Since cgz decreases close to a critical level, the waves themselves are more likely to be observed [Alexander, 1998; Alexander and Barnet, 2007]. Doppler shifting of waves' λz into or out of the bandpass filtering region may also occur. So a certain wave may be visible at some heights and not others, depending upon the background wind profile and the wave's parameters. QBO related changes in gravity wave variance were also noted in SABER data, where a different analysis procedure meant that no bias due to global-scale waves (s < 6) existed [Krebsbach and Preusse, 2007; Ern et al., 2008].
3.2. Seasonal Changes in Potential Energy
 The seasonal structure of equatorial Ep7 (calculated from the grid cell between 2.5°S and 2.5°N) varies with height and longitude as well as with the background mean winds, as illustrated in Figure 2. The seasonal mean OLR is plotted below each panel as a function of longitude. A clear relation between deep convective activity (low OLR) and large UTLS Ep7 is observed. For example, in MAM 2007 (Figure 2b), Ep7 exceeding 5.0 J kg−1 are observed from 0–40°E, 70–140°E and around 300°E. These longitudes correspond directly to low OLR values above Africa, Indonesia and South America respectively. The UTLS Ep7 show hemispheric differences in JJA 2007 (Figure 2c), with Eastern Hemisphere Ep7 of 5.0 J kg−1 and Western Hemisphere Ep7 of 3.5–4.5 J kg−1.
 The UTLS Ep7 calculated here is not a true measure of the atmospheric potential energy. Because of the sharp cold point tropopause in the tropical regions (at about 17 km altitude), artificial increases in temperature variance result in enhanced Ep7 values. Large temperature variances and Ep7 derived using θ, in order to minimize cold-point tropopause effects, are also observed (results not shown). Some increase in Ep7 around the tropopause makes sense qualitatively, because deep convection is a strong source of gravity waves and larger scale waves. These waves induce temperature perturbations from the background mean, resulting in larger Ep7 above deep convection.
 Stratospheric Ep7 above about 22 km are not affected by this cold-point tropopause problem. The seasonal averages of DJF and MAM show that the Ep7 at around 30 km altitude are fairly constant in longitude. This is because the background wind profile below 30 km filters out of most of the convective gravity waves. In contrast, the JJA (Figure 2c) and SON (Figure 2d) 30 km Ep7 show longitudinal differences. During these seasons, only westward propagating gravity waves in the Eastern Hemisphere are filtered out below 30 km. This leaves all of the eastward propagating components. An illustration of longitudinal differences is apparent during SON, when 23–29 km Ep7 is 1.5–2.5 J kg−1 in the Eastern Hemisphere, coincident with deep convective activity. Above the Pacific Ocean, Ep7 is <1.5 J kg−1. COSMIC may be observing high speed convectively generated gravity waves at 23–29 km which are propagating nearly vertically in the Eastern Hemisphere.
3.3. Spatial Distribution of Potential Energy in the Tropics
3.3.1. April and September 2007
 The changes in stratospheric potential energy above and below the 0 m s−1 zonal wind line are investigated by using the 1 km height independent Ep1 monthly averages. The equatorial zonal mean zonal wind is 0 m s−1 at 22–24 km during April 2007 and −30 m s−1 at 30 km (Figure 1). In September 2007, the zonal wind is westward throughout the entire stratosphere. Different wave filtering effects can be expected to occur during these conditions and are observed in the COSMIC data. The two months of April 2007 and September 2007 are shown in Figure 3 at four separate heights: (a, e) 15 km, (b, f) 22 km, (c, g) 26 km and (d, h) 32 km. The NCEP zonal winds are provided at specific pressure levels [Kalnay et al., 1996], so they are converted to altitude, the closest of which is plotted in each case. In order to resolve Ep1 details, the color scales are different at each height but consistent between months.
 During April 2007, the upper tropospheric mean zonal winds at 100 hPa are close to 0 m s−1 (Figure 3a). Monthly mean low OLR (indicative of deep convection) occur above South America, Africa, the Indonesian region and the Western Pacific. The convectively coupled gravity waves generated should be detectable as large Ep1 directly above these high cloud tops because little wave filtering by the background mean flow can occur, as is often observed at 15 km and other upper tropospheric heights (not shown). A region of large Ep1 is detected above the equatorial Eastern Pacific away from convection. This may be due to lateral forcing by extra-tropical Rossby wave energy because this a region of upper tropospheric eastward winds, although using COSMIC data alone this cannot be proven.
 An interesting feature is observed at 22 km (Figure 3b), where Ep1 at ±10° are often larger than the equatorial Ep1. This phenomenon can be seen in the Pacific and Indian Ocean regions. Because of the background critical level filtering occurring below, the 22 km Ep1 is likely to consist of waves with fast ground based horizontal phase speeds cx > 0 as well as all cx < 0 waves. By 26 km (Figure 3c), the only waves which are not filtered are those with large ∣cx∣ which propagate nearly vertically. There is essentially no convective relation with Ep1 at 32 km (Figure 3d). The equatorial wave structures have vanished because of lower level filtering. The background wind profile between 26 km and 32 km is one of increasingly strong westward winds which filter out nearly all of the waves with λz < 7 km. It is possible that other waves such as fast Kelvin waves still exist at 32 km but these are not revealed in the filtered Ep1 distributions.
 The September 2007 Ep1 are significantly different from April 2007 due to the background QBO phase, which is entirely westward in the stratosphere. There is also a different convective source distribution, with the lowest OLR indicating the presence of the Asian monsoon. During September, deep convective activity occurs above the Bay of Bengal and the northern Indonesian region, although this does not always coincide with enhanced Ep1 at 15 km (Figure 3e). Other regions of large Ep1 at 10°S–15°S occur above Peru, Western Africa and the central Indian Ocean.
 Equatorial symmetry in Ep1 is observed at 22 km (Figure 3f) and 26 km (Figure 3g) in the Atlantic sector. Ep1 exceeds 2.0 J kg−1 at several places at both 10°N and 10°S at 22 km. The largest Ep1 at 26 km occur above Africa. Filtering of slow cx < 0 waves occurs below 22 km, leaving only fast cx < 0 and all of the cx > 0 components. Increasingly strong westward winds between 22 km and 26 km remove even more of the faster cx < 0 waves.
 The September 2007 32 km Ep1 (Figure 3h) is below 3.0 J kg−1 and shows a strong correspondence with deep convection which is mainly due to cx > 0 waves. The lower speed cx > 0 waves are beginning to encounter their critical level as the background zonal wind approaches the 0 m s−1 line. This, along with the increased likelihood of detecting slower velocity waves, accounts for the large Ep1.
3.3.2. January 2007 and January 2008
 The January 2007 and January 2008 Ep1 are discussed to allow comparison with the model results of Kawatani et al. . Although the convective source distribution is similar for both months, the stratospheric Ep1 is different due to the changed QBO structure. In January 2007, the QBO is in its westward shear phase with the 0 m s−1 line at 24 km, while 1 year later, the QBO is in its eastward shear phase with the 0 m s−1 line at 25 km (see Figure 1).
Figure 4 shows the Ep1, zonal wind and OLR during January 2007 and January 2008. The deep convective regions are centered south of the equator, but even so, the January 2007 Ep1 at 22 km (Figure 4b) and 26 km (Figure 4c) are still approximately equally distributed about the equator. Larger Ep1 is generally observed close to the three deep convective regions, especially at 26 km, at which altitude most of the waves with low ∣cx∣ are filtered out.
 With the complete reversal of the QBO phase by January 2008, the lower stratospheric Ep1 show significant differences to those observed a year earlier. The monthly mean OLR during both years is similar, resulting in similar Ep1 at 15 km (Figures 4a and 4e). Ep1 exceeding 4.2 J kg−1 are visible from the Indian Ocean through to the Western Pacific, as well as above South America around 20°S.
 There are larger Ep1 at 22 km during January 2007 (Figure 4b) than January 2008 (Figure 4f), especially above the equator. The situation is reversed at 26 km, where Ep1 exceeds 4.0 J kg−1 in the Western and Eastern Pacific during January 2008 (Figure 4g). Eastward propagating waves are being filtered out around this altitude as the background wind profile approaches 0 m s−1, whereas the 26 km altitude in January 2007 (Figure 4c) is above the 0 m s−1 phase line, with a lot of the waves removed at lower altitudes. Both of the 32 km altitude regions generally have low Ep1 values of under 1.0 J kg−1, although small regions of Ep1 up to 2.0 J kg−1 are visible west of South America and above Northern Australia in January 2008 (Figure 4h).
4. Global-Scale Equatorial Wave Characteristics
 The analysis of the spatial, temporal and vertical changes in Ep1 in section 3 shows the filtering of mesoscale gravity waves by the changing background QBO wind structure. It is also useful to isolate global-scale equatorially trapped waves and observe their spatial and temporal variability and interaction with the QBO. Large-scale zonally averaged observational features of QBO wave filtering were reported previously using CHAMP [Tsuda et al., 2004; Randel and Wu, 2005]. CHAMP also enabled Kelvin waves with zonal wave numbers 1 and 2 to be extracted using a sine wave fitting function [Tsai et al., 2004; Tsuda et al., 2006]. Higher frequencies and wave numbers can be studied using COSMIC. As with measurements made by other instruments, the stratospheric equatorial waves observed by COSMIC have been ‘pre-filtered’ by the background winds and also because large λz waves propagate faster therefore are less likely to be captured (e.g., Ern et al. ; Hendon and Wheeler ).
 Kelvin waves are filtered in the symmetric component between s = 1 and s = 9, while MRGWs are extracted from the antisymmetric component. Wheeler and Kiladis  used the equivalent depth he filtering region of 8 m < he < 90 m for upper tropospheric OLR data, which Ern et al.  defined as the slow cx Kelvin wave band (from cx = , cx < 30 m s−1). Stratospheric Kelvin waves have a wider range of periods than upper tropospheric Kelvin waves, from the ultra-fast (periods of 3–4 days) to the ultra-slow (periods of 25–30 days). Therefore in addition to the slow wave band, Ern et al.  defined a fast cx Kelvin wave band for 90 m < he < 2000 m for the study of SABER data primarily in the stratosphere between 20 km and 50 km (although SABER measurements are available below 100 km). A fast cx Kelvin wave band is also used here with the COSMIC data, although after considering the power spectra and altitude range of COSMIC, this band is restricted to 90 m < he < 240 m. The slow filter using equivalent depths of 8 m < he < 90 m corresponds theoretically to waves with 2.3 km < λz < 7.6 km for a stratospheric N2 = 6 × 10−4 rad2 s−2. This λz filtering range is similar to that used for extracting gravity waves and studying their potential energy (section 3). The fast cx Kelvin wave band of 90 m < he < 240 m encompasses the region of 7.6 km < λz < 12.5 km. An he of 90 m corresponds to cx = 30 m s−1, which exceeds the QBO speed for the majority of the time. Fast Kelvin waves with he > 90 m exhibit a much weaker modulation of temperature variance than slower waves [Ern et al., 2008], although they are still important and interact strongly with the background mean flow at higher altitudes (e.g., Salby et al. ; Garcia et al. ). Because of the 20° longitude COSMIC temperature data binning, the filtering is for ∣s∣ ≤ 9 and for ground based periods greater than 2 days.
4.1. s − ω Spectra
 The s − ω spectra are obtained using the method outlined in section 2.2 and are shown for COSMIC at 16 km and 22 km in Figure 5 by making a composite of 96 day spectral blocks from 13 September 2006 to 26 January 2008. The data blocks are Welch windowed in time and stepped forward by 32 days. This minimizes the suppression of waves with periods of less than 32 days, which is about the maximum expected period of the waves of interest [Wheeler and Kiladis, 1999; Ern et al., 2008]. Symmetric and antisymmetric OLR and TRMM source spectra are red, so in order to observe the waves in those data sets, the results must be divided by a background spectrum [Wheeler and Kiladis, 1999; Cho et al., 2004; Hendon and Wheeler, 2008]. This is not necessary to do for temperature data because the waves are clearly apparent in the original s − ω spectra [Ern et al., 2008]. Various dispersion curves for a range of equivalent depths are overplotted in Figure 5 [Andrews et al., 1987].
 While Kelvin waves dominate the symmetric s − ω spectra with similar magnitude at both 16 km and 22 km, the shape and region covered by the equivalent depths (and hence phase velocities) are different. The Kelvin waves' spectral peak moves to higher frequencies and equivalent depths in the stratosphere. Significantly less variance is associated with waves having he < 25 m (cx ∼ 16 m s−1) at 22 km than at 16 km. This result is expected, because higher frequency Kelvin waves with larger cgz and λz can propagate into the stratosphere more easily [Salby et al., 1984; Hendon and Wheeler, 2008]. The majority of Kelvin wave variance is contained in waves having s ≤ 5. The antisymmetric spectra at 16 km and 22 km show that most of the variance is associated with MRGWs having s > −5. The MRGWs also shift to higher he in the stratosphere, where they are in the region 8 m < he < 90 m.
 The westward propagating n = 1 equatorial Rossby (ER) waves are weakly visible in the 16 km symmetric spectra but have negligible variance at 22 km, consistent with previous observations that ER waves are primarily tropospheric [Kiladis and Wheeler, 1995; Hendon and Wheeler, 2008; Sridharan et al., 2008]. While they display some height coherence in Hovmöller diagrams, the ER waves generally have amplitudes of less than 0.5 K which is similar to the uncertainty of the COSMIC temperature measurements and so are not discussed further.
 Some variance associated with eastward propagating n = 0 Equatorial Inertia Gravity Waves (EIGWs) in the antisymmetric s − ω spectra is noted. While the n = 0 EIGWs are weakly resolvable, the resultant vertical structure has little height consistency, suggestive of noisy data. The filtering reveals that these waves are not of sufficient amplitude nor do they exhibit much height coherence to allow further consideration.
4.2. Hovmöller Diagrams
 Hovmöller (longitude-time) diagrams are often used to investigate the zonal and temporal propagation of specific wave components [Shiotani et al., 1997; Wheeler and Kiladis, 1999; Tsai et al., 2004; Randel and Wu, 2005]. The Hovmöller diagram for 8 m < he < 90 m slow cx Kelvin waves at 22 km during 2007 is illustrated in Figure 6. The zonal winds at 22 km are eastward before mid-May and westward afterward. Global-scale s = 1, 2 Kelvin waves dominate the diagram, consistent with Figure 5c. For these waves, variability in amplitude is apparent throughout the year, with maximum amplitudes of about 2.4–3.0 K in the Eastern Hemisphere. Especially large wave activity occurs during November. Dominant periods are around 10–20 days, with s = 1 waves generally having longer periods than s = 2 waves. The ground based phase speeds cx are ∼15–30 m s−1. These slow Kelvin wave parameters are similar to those observed with the CHAMP GPS-RO satellite, where amplitudes of up to 2.0 K were also noted [Tsai et al., 2004; Randel and Wu, 2005]. Higher wave number Kelvin waves are also visible in Figure 6. These waves have periods of about 5 days, are mostly s = 3 or s = 4, have maximum amplitudes of about 2.0 K and cx for the dominant s are ∼20–30 m s−1. These results are consistent with previous s = 4 observations [Holton et al., 2001].
 The equivalent fast cx Kelvin waves at 22 km are illustrated in Figure 7 and incorporate waves with 30 m s−1 < cx < 50 m s−1. These waves have amplitudes <1.2 K, which is usually less than the slow Kelvin waves' amplitudes. Most of these fast waves are either s = 1 or s = 2 with periods of less than about 10 days. Amplitudes of the fast band Kelvin waves in the upper troposphere are often less than 0.6 K (not shown), consistent with the results of Figure 5. Larger λz waves propagate faster which may influence observation of these waves.
 The 22 km MRGW filtered COSMIC T′ are displayed in Figure 8. These waves are visible in the unfiltered antisymmetric data, but there could be some spectral noise contamination by gravity waves in this band filter [Ern et al., 2008]. Wave packet like behavior of the MRGWs is apparent, with amplitudes sometimes exceeding 1.2 K for four wave cycles. In general, these freely propagating MRGWs do not circumnavigate the globe while maintaining their amplitudes. The MRGW wave packets propagate eastward, while the individual phases propagate westward. A sudden decrease in amplitude of the MRGWs occurs after mid-May 2007. This coincides with the descent of the QBO 0 m s−1 line below 22 km, after which the winds at this altitude are westward. This illustrates the removal of most of the westward propagating MRGWs by the background mean flow. There is no clear longitudinal preference for MRGWs prior to June 2007. There is a large amount of 22 km MRGW activity above Africa and the Indian Ocean between February and May 2007, and large MRGW activity above the Atlantic Ocean in April and May 2007. MRGW periods are around 3–5 days with s > −5, resulting in cx of ∼20–30 m s−1, similar to that reported by Yanai and Maruyama .
 The slow band Kelvin waves at 16 km between January and June 2007 do not reveal clear convective coupling (Figure 9a). Most of the Kelvin waves have s ≤ 3. The amplitudes at 16 km are generally weaker than at 22km (Figure 6) and there is not clear correspondence of waves between these two altitudes. The corresponding Kelvin waves visible in the OLR data are displayed in Figure 9b. The OLR data are filtered over the same he and s range as the COSMIC data. Longer period Kelvin waves are more apparent in the OLR filtered data than in COSMIC at 16 km. This is because the dominant OLR Kelvin wave he is smaller than that for COSMIC Kelvin waves (as confirmed by the OLR s − ω spectra: not shown). There is not often a clear relationship between the COSMIC 16 km T′ and OLR Kelvin waves. OLR measurements are not from a specific height, but rather include data from cloud tops which may be at for instance 10 km or 18 km altitude. This may contribute to the difference between the results. There may also be tropospheric wave filtering effects to consider. Kawatani et al.  used a T106L60 AGCM to observe the propagation of equatorially trapped waves and their correspondence with OLR source regions. They found that two-monthly mean vertical energy flux is positive above ∼300 hPa, implying wave generation at altitudes up to 300 hPa. Thus wave filtering has already occurred well below 16 km, which may explain the differences between the Kelvin waves observed independently in the OLR and COSMIC data sets.
 MRGWs at 16 km usually have amplitudes of <0.6 K and are also not often coincident with MRGWs observed in the OLR data (not shown). It is likely that tropospheric filtering, including hemispheric differences due to the Walker circulation, is occurring here as well [Kawatani et al., 2008].
4.3. Vertical Wave Propagation
 The waves observed in the COSMIC data at 22 km are also visible at neighboring heights. In order to investigate their vertical structure, monthly longitude-height plots of temperature variance are displayed in Figure 10 for the slow Kelvin waves and Figure 11 for the MRGWs during 2007.
 The slow Kelvin waves' variance shows significant monthly variability both around the tropopause (∼17 km) and in the lower stratosphere (LS). There is not always clear convective coupling with Kelvin wave activity. Kelvin waves show some tendency to increase in amplitude between 16 km and 20 km toward the east from February to May 2007 (Figures 10b – 10e), illustrating that the Kelvin waves move to higher altitudes as they propagate eastward. During these months, UTLS winds are light, with speeds of less than about ∣10∣ m s−1, which is less than the slow cx band Kelvin wave cx (∼10–30 m s−1). Kelvin wave activity is largely suppressed during September and October 2007 (Figures 10i and 10j). Large Eastern Hemisphere Kelvin wave activity noted at 22 km during November and December 2007 (Figure 6) is apparent as increased temperature variance throughout the UTLS region, where it reaches 3.0–4.0 K2.
 As observed in the MRGW Hovmöller diagram at 22 km (Figure 8), a significant decrease in amplitude occurs after June 2007. The vertical profiles of MRGW band temperature variance in Figure 11 show that this is related to filtering by the background winds. Large variances occur in the stratosphere during the eastward QBO phase before May 2007 (Figures 11a – 11e) and sometimes show eastward phase tilt with height. Very low LS temperature variances are observed during the rest of 2007 as a result of the westward winds. Around the tropopause region from September 2007 onward (Figures 11i – 11l), more MRGW variance is present in the Western Hemisphere where the Walker circulation is eastward, than in the Eastern Hemisphere where it is westward. It is possible that many of the MRGWs generated by convection in the Eastern Hemisphere are critically filtered out by the westward Walker circulation winds.
 Wave mean flow interactions are visible in both the mesoscale gravity wave Ep1 analysis of section 3 and the global equatorially trapped wave analysis of section 4. While most of the spatial and altitude variability of Ep1 is due to gravity waves, equatorially trapped waves with s < 9 and periods less than 30 days may contribute slightly to the total. There is often a coincidence between convection and large potential energy (e.g., Figure 3h). Some of the observed stratospheric equatorial waves appear freely propagating and may have been excited by random large-scale convection and so are not necessarily directly convectively coupled [Salby and Garcia, 1987].
 Large 22 km Ep1 occurs during April 2007 (Figure 3b), often with larger values at ±10° than on the equator. While Kelvin wave activity is present at 22 km (Figures 6 and 7), the amplitudes are relatively small when compared with other months because of some lower level critical level interactions and filtering. MRGWs are also visible between South America and the Indian Ocean (300°E and 100°E), with some small activity above the Central Pacific in early April (Figure 8). The MRGWs may explain some of the larger Ep1 observed at ±10° during this time.
 The September 2007 22 km Ep1 (Figure 3f) and the equatorially trapped wave amplitudes and locations are different to April. MRGWs are of much smaller amplitude in September due to lower level filtering (Figure 8), while the Kelvin wave amplitudes are very small throughout the entire UTLS region (Figure 10i). However, Kelvin waves are equatorially symmetric and cannot explain the larger Ep1 at ±10° (Figure 3f). It is therefore not clear what waves are contributing to this Ep1. The Asian monsoon is active during September but is not associated with large Ep1 at this altitude (although it is by 32 km, see Figure 3h, so there are small-scale gravity waves being generated by this monsoonal convection).
 The observations of individual waves and their vertical structure suggests that some of the lower stratospheric zonal mean Ep1 below the 0 m s−1 line observed in Figure 1b before June 2007 is due to temperature perturbations of MRGWs, which are then removed by the westward winds above. The marked increase in Kelvin wave amplitudes during November and December 2007 may account for a small part of the increase in lower stratospheric Ep1 in Figure 1b although it is important to stress that irresolvably small gravity waves still contribute most of the total Ep1 observed during this time.
 The CHAMP GPS-RO satellite has been operational since 2001, allowing its multiyear results to be compared with COSMIC. de la Torre et al.  showed the stratospheric modulation of zonal mean Ep, with maximum values for waves with λz < 10 km of about 8.0 J kg−1. Waves with 4 km < λz < 10 km resulted in large Ep below the 0 m s−1 phase line during the QBO eastward shear phase, similar to that observed with COSMIC (Figure 1b). Direct comparison with the magnitude of Ep7 is complicated because of different definitions of the background mean and different spatial and temporal averaging (which is necessary because of the smaller CHAMP data rate), but the general structure of the zonal mean potential energy is consistent. When the CHAMP data were used to construct latitude/longitude potential energy plots [Ratnam et al., 2004], significant differences to those obtained by COSMIC are found (Figures 3 and 4). This is most likely due to the lower CHAMP data rate rendering many waves irresolvable.
 SABER was used to study equatorially trapped stratospheric waves equatorward of 14° using Kalman filtering and a 31 day window over a 4-year period [Ern et al., 2008]. SABER has a ∼2 km vertical resolution and can measure waves with s < 7. A similar LS ω − s spectrum to that obtained with COSMIC was found, although the SABER waves are more clearly visible above the background because of the longer data averaging period. The temperature variance of various equatorially trapped waves was examined. A larger Kelvin wave signal existed during the QBO westward phase than during the QBO eastward phase. Slow band Kelvin wave variance in the LS was 0.5–1.0 K2 during QBO westward winds and <0.2 K2 during QBO eastward winds. This is often slightly less than the COSMIC slow Kelvin wave 20–24 km variances of 0.8–4.0 K2 between June and December 2007 (QBO westward winds, Figure 10), although monthly and hemispheric variability of the COSMIC results is significant. The COSMIC data set is not yet long enough to form a climatology, but from January to March 2007 in weakly eastward winds (<10 m s−1), 20–24 km variances of ∼0.4–2.0 K2 are observed, which is usually somewhat lower than during westward winds. The SABER results of Ern et al.  revealed about a factor of 5 decrease in Kelvin wave variance during QBO eastward winds.
 Variances of MRGWs observed by SABER at 20–24 km were <0.2 K2 during eastward winds and <0.05 K2 during westward winds [Ern et al., 2008]. COSMIC observes variances of ∼0.1–0.5 K2 during the eastward winds at 20–24 km from January to May 2007 (Figure 11), although as with the Kelvin wave results, the variances are highly variable between altitude, longitude and month. In the westward wind period from June 2007 onward, variances of <0.1 K2 are usually observed between 20 km and 24 km. While the variances of Kelvin waves and MRGWs obtained by COSMIC are larger than those obtained by SABER, the general pattern is consistent. Differences from the SABER variance results may be due to the different analysis methods employed, the shorter duration of the COSMIC data set, and the different sampling rate and locations of COSMIC.
 COSMIC derived temperature data are used to investigate the spatial and temporal variability of gravity waves, via the study of potential energy, in order to examine convective waves and wave mean flow filtering effects. Global-scale equatorially trapped Kelvin waves and Mixed Rossby Gravity Waves over a range of equivalent depths are studied separately.
 Potential energy is calculated using grid cells of size 20° in longitude by 5° in latitude. Seasonal hemispheric differences in gravity wave potential energy are observed, with larger values occurring around the tropopause above deep convective activity and also in the Eastern Hemisphere stratosphere during SON 2007 at which time the background winds are westward throughout the entire height region. Monthly averaged 1 km height independent Ep1 show differences in potential energy depending upon the QBO phase and the location of convection. Large Ep1 are visible directly above deep convection at altitudes, which are close to the QBO 0 m s−1 phase line. This Ep1 is probably primarily due to convectively generated gravity waves propagating nearly vertically.
 The wave mean flow interaction of specific equatorially trapped waves is investigated during 2007 by studying the temperature perturbations of eastward propagating Kelvin waves and westward propagating MRGWs. Kelvin waves are filtered over the equivalent depth interval 8 m < he < 90 m for the slow band and 90 m < he < 240 m for the fast band, while MRGWs are filtered over the range 8 m < he < 90 m only. Observations show the eastward propagating wave packet nature of MRGWs during periods of eastward background winds. The majority of the observed Kelvin waves have zonal wave numbers less than 5. The Kelvin waves at 22 km appear freely propagating. Comparisons between 16 km COSMIC slow band Kelvin waves and OLR slow band Kelvin waves show little clear relationship. This may be due to lower level filtering and the fact that OLR are not at a constant height. There is large variability in Kelvin wave and MRGW activity between months in 2007. MRGWs are filtered out in the westward QBO phase and also in the Eastern Hemisphere where the tropospheric Walker circulation is westward.
 Temperature data obtained from the COSMIC GPS-RO satellite constellation are a powerful tool for investigating global-scale wave dynamics and smaller scale gravity wave mean flow interactions in the equatorial UTLS region and in the future will enable long term monitoring of these waves.
 This research was undertaken while one of the authors (S.P.A.) was in receipt of a Japan Society for the Promotion of Sciences (JSPS) post-doctoral fellowship. This study was supported in part by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) through a Grant-in-Aid for Scientific Research (19403009) and the Kyoto University Active Geosphere Investigation (KAGI) for the 21st century COE program. COSMIC data were obtained from the COSMIC Data Analysis and Archive Center (CDAAC). NCEP zonal wind and uninterpolated OLR data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their Web site at http://www.cdc.noaa.gov/. We wish to thank Prof. Kaoru Sato for useful discussions and advice. The valuable comments of two anonymous reviewers are highly appreciated.