Global estimates of gravity wave parameters from GPS radio occultation temperature data

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2010jd013860, 2010 Global estimates of gravity wave parameters from GPS radio occultation temperature data L. Wang 1 and M. J. Alexander 1 Received 12 January 2010; revised 15 July 2010; accepted 19 August 2010; published 10 November [1] Gravity waves (GWs) play critical roles in the global circulation and the temperature and constituent structures in the middle atmosphere. They also play significant roles in the dynamics and transport and mixing processes in the upper troposphere and lower stratosphere and can affect tropospheric weather. Despite significant advances in our understanding of GWS and their effects in different regions of the atmosphere in the past few decades, observational constraints on GW parameters including momentum flux and propagation direction are still sorely lacking. Global Positioning System (GPS) radio occultation (RO) technique provides global, all weather, high vertical resolution temperature profiles in the stratosphere and troposphere. The unprecedentedly large number of combined temperature soundings from the Constellation Observing System for Meteorology, Ionosphere, and Climate and Challenging Minisatellite Payload GPS RO missions allows us to obtain GW perturbations by removing the gravest zonal modes using the wavelet method for each day. We extended the GW analysis method of Alexander et al. (2008) to three dimensions to estimate the complete set of GW parameters (including momentum flux and horizontal propagation direction) from the GW temperature perturbations thus derived. To demonstrate the effectiveness of the analysis, we showed global estimates of GW temperature amplitudes, vertical and horizontal wavelengths, intrinsic frequency, and vertical flux of horizontal momentum in the altitude range of km during December 2006 to February Consistent with many previous studies, GW temperature amplitudes are a maximum in the tropics and are generally larger over land, likely reflecting convection and topography as main GW sources. GW vertical wavelengths are a minimum at equator, likely due to wave refraction, whereas GW horizontal wavelengths are generally longer in the tropics. Most of the waves captured in the analysis of the GPS data are low intrinsic frequency inertia GWs, and the estimated intrinsic frequencies scaled by the Coriolis parameter also show a strong maximum at equator. Enhanced wave fluxes are linked to convection, topography, and storm tracks, among others. As preliminary tests of the analysis in deriving horizontal propagation directions, we compared the GPS estimates with the corresponding estimates from the U.S. high vertical resolution radiosonde data using the conventional Stokes parameters method and we also conducted a separate analysis of the GPS data over the southern Andes in South America. We also showed the first global estimates of GW propagation directions from the GPS data. Finally, the sensitivity of the analysis to the temporal and spatial dimensions of the longitude latitude time cells and the uncertainties of the analysis and possible ways to reduce these uncertainties are discussed. Citation: Wang, L., and M. J. Alexander (2010), Global estimates of gravity wave parameters from GPS radio occultation temperature data, J. Geophys. Res., 115,, doi: /2010jd Introduction 1 Colorado Research Associates Division, NorthWest Research Associates Inc., Boulder, Colorado, USA. Copyright 2010 by the American Geophysical Union /10/2010JD [2] Gravity waves (GWs) are ubiquitous in any atmosphere which has stable density stratification. GWs and their dissipation associated with wave saturation have long been recognized to play an important role in the large scale circulation and the temperature and constituent structures of the middle terrestrial atmosphere. For example, the zonal mean forces associated with GW dissipation are believed to cause the closure of the mesospheric jets and a mean meridional circulation that leads to a warm winter mesopause, a cold summer mesopause, and a reversal of the latitudinal temperature gradient that would have been expected from an atmosphere 1of12

2 in radiative equilibrium [e.g., Houghton, 1978; Lindzen, 1981; Holton, 1982]; GWs contribute to driving the tropical quasi biennial oscillation (QBO) [e.g., Dunkerton, 1997] and semiannual oscillation (SAO) in both the stratosphere and mesosphere [e.g., Sassi et al., 1993; Hamilton et al., 1995; Sassi and Garcia, 1997]; topographic wave drag is believed to slow the westerly winds above the midlatitude tropospheric jet maximum and significantly affect the northern winter climate [e.g., Palmer et al., 1986; McFarlane, 1987; Bacmeister, 1993]; they also play a role in driving the summer hemisphere meridional transport circulation [e.g., Alexander and Rosenlof, 1996] expressed through the downward control principle, and contribute to the formation of the winter stratospheric polar vortex [e.g., Garcia and Boville, 1994]. GWs also affect the tropospheric weather. For example, mountain waves can affect precipitation formation in the troposphere and play a role in boundary layer meteorology [e.g., Smith and Evans, 2007; Smith et al., 2006]. [3] GWs exhibit very broad temporal and spatial scales. Their horizontal wavelengths range from kilometers [e.g., Wang et al., 2006b] to thousands of kilometers [e.g., Vincent and Alexander, 2000], and their periods range from the buoyancy period (which is 5 min in the lower stratosphere) to the inertial period (which is infinite at the equator and one half day at the poles). Thus they generally need to be parameterized in general circulation models used to forecast climate, weather, and stratospheric ozone. Despite significant advances in our understanding of GW characteristics during the past several decades, to date, observational constraints for GW parameterizations are still sorely lacking, especially for GW horizontal propagation directions and vertical fluxes of horizontal momentum. [4] Hodograph analysis and Stokes parameters method (and its variants) [e.g., Eckermann and Vincent, 1989] have been used to derive GW propagation directions and other wave parameters in many previous studies [e.g., Hirota and Niki, 1985; Vincent et al., 1997; Wang et al., 2006a, 2006b]. These methods require, however, both temperature and wind information, which is not available for most satellite data. Ern et al. [2004] used phase differences between adjacent temperature profiles to obtain global estimates of GW horizontal wavelength and momentum flux from the CRISTA (Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere) 2 satellite data. They found enhanced GW fluxes over the Antarctic polar vortex edges and over the Gulf of Mexico and east of Asia in the lower stratosphere in August Alexander et al. [2008] used a similar approach to derive GW horizontal structures from the HIRDLS (High Resolution Dynamics Limb Sounder) satellite data and found similar geographic variability of lower stratospheric GW fluxes in May However, horizontal propagation directions cannot be determined from the CRISTA and HIRDLS measurements, and this results in a correspondingly large uncertainty in horizontal wavelengths and momentum fluxes. Wu and Eckermann [2008] analyzed GW signals from the Aura/MLS (Microwave Limb Sounder) radiance measurements and were able to obtain some GW propagation information from the ascending and descending variance differences by taking advantage of the directional tilting of the Aura MLS weighting functions (which yield a directional sensitivity in response to GWs). Horinouchi and Tsuda [2009] analyzed GW horizontal structures from the COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) radio occultation temperature data by exploiting the clustering of 3 4 COSMIC low Earth orbit (LEO) satellites during the early stage of the mission. In most GW analyses of satellite data to date, GW propagation directions have not been routinely derived. This study introduces a GW analysis method based on the cross wavelet analysis to derive the complete set of GW parameters (including horizontal propagation direction) routinely from the combined COSMIC/CHAMP GPS RO temperature data. To illustrate how the method works, we report the analysis results in the lower stratosphere during December 2006 to February 2007 (and also during June August 2007 for a GW directional analysis over the southern Andes). [5] The paper is organized as follows: Section 2 describes the COSMIC and CHAMP GPS RO data. Section 3 describes the method to derive the complete set of GW parameters from the GPS RO data and presents some initial results of GW temperature amplitudes, vertical and horizontal wavelengths, intrinsic frequencies, and momentum fluxes. Comparison of GW propagation direction estimates from the GPS data and those from the U.S. high resolution radiosonde data using the Stokes parameters method is also given in this section. The current data sampling is a limitation for this method. In addition to documenting the methodology, we also discuss results of sensitivity tests and corresponding uncertainties in the GW properties presented in section 3, and we then summarize these and other uncertainties of the GW analysis in section 4 and discuss how future work using additional GPS measurement will permit improved results. In the end, the Summary and Conclusions are given. 2. Data [6] In this investigation of GWs we use the combined Global Positioning System (GPS) radio occultation (RO) temperature retrievals from the Constellation Observing System for Meteorology Ionosphere and Climate/Formosa Satellite 3 (shortened as COSMIC hereafter) mission [Rocken et al., 2000] and the Challenging Minisatellite Payload (CHAMP) mission. The GPS RO technique was first introduced by Yunck et al. [1988]. It is a space borne remote sensing technique providing accurate, all weather, high vertical resolution profiles of atmospheric variables. As satellites in low Earth orbit (LEO) rise and set relative to the GPS satellites, the GPS receivers on board the LEOs measure the phase delay of the GPS dual frequency radio wave signals which can be converted to the radio wave bending angles. Atmospheric refractivity can be derived from bending angles. In the neutral atmosphere, the refractivity is further reduced to temperature, pressure and water vapor profiles [Anthes et al., 2000]. The GPS/MET mission [Ware et al., 1996] is the first demonstration of the GPS RO technique. Since then, there have been a few follow on GPS experiments including the CHAMP and COSMIC missions. The German CHAMP satellitewaslaunchedinjuly2000withaninclinationangle of The mission provided 200 daily occultations from mid 2000 to late The joint United States and Taiwan COSMIC mission launched six microsatellites into LEO with an inclination angle of 72 in The mission provides daily ROs from 2006 to present (early 2010). 2of12

3 Figure 1. Location map of COSMIC and CHAMP GPS RO soundings on 1 January The small diamonds on the map represent the locations of the COSMIC soundings (1936 in total), whereas the small squares represent the locations of the CHAMP soundings (151 in total). [7] In this study, we analyze the COSMIC and CHAMP Level 2 dry temperature retrievals provided by the COSMIC Data Analysis and Archive Center (CDAAC) of the University Corporation for Atmospheric Research (UCAR). The vertical resolution of the GPS temperature profile is 1 km and the temperature accuracy is sub Kelvin. Since the data qualities of COSMIC and CHAMP retrievals are similar, we combine the data in this analysis to increase data coverage. Figure 1 shows a typical daily location map of the combined COSMIC and CHAMP GPS RO temperature retrievals. The exact distribution of GPS RO soundings is determined by the orbits of the GPS satellites and LEOs. Unlike most polar orbit satellite data (e.g., HIRDLS and AIRS) which have regular orbits, the GPS RO coverage exhibits irregular patterns. As will be described in the next section, we will use this feature to our advantage for GW analysis. Also, the GPS data coverage is not affected by a satellite s yaw cycle as data from some other polar orbit satellites do (e.g., TIMED). The GPS data can reach into very high polar regions routinely, as mentioned by Wang and Alexander [2009]. The combined COSMIC and CHAMP GPS data coverage does not depend on longitude or local times (not shown) but there are more soundings at midlatitudes (with primary peaks at 50 N and 50 S and secondary peaks at 20 N and 20 S) than at equatorial and polar regions. Since temperature retrievals can fail for a number of reasons [Anthes et al., 2000], the number of retrievals is smaller than the number of ROs and there are 1500 and 150 daily temperature profiles available from the COSMIC and CHAMP, respectively. Finally, in addition to the GPS data described above, we also use the U.S. highresolution radiosonde data [Wang et al., 2005] and the NCEP/ NCAR reanalysis data. We will describe the radiosonde data in section 3 when we compare GW propagation direction estimates from the GPS and radiosonde data. 3. Gravity Wave Analysis 3.1. Gravity Wave Temperature Perturbations [8] The extraction of GW perturbations, i.e., the removal of the background, is crucial to any GW analysis. Many previous GPS GW studies estimated GW temperature perturbations by applying a vertical wavelength (l z ) filter directly to individual GPS temperature profiles [Tsuda et al., 2000, 2004; Ratnam et al., 2004a, 2004b; de la Torre et al., 2006a, 2006b; Baumgaertner and McDonald, 2007]. In fact, large scale waves such as Kelvin waves can have similar l z as GWs [e.g., Holton et al., 2001]. Therefore, filtering temperature profiles with respect to l z alone does not clearly separate global scale waves and GW signals. The combined COSMIC and CHAMP data provide many more daily profiles than previous GPS missions, thus giving us the opportunity to define the background temperatures on the basis of horizontal scale and to separate the GWs from the globalscale waves on this basis. [9] Following closely Wang and Alexander [2009], we obtain GW perturbations by first interpolating each raw temperature profile to a regular 200 m vertical resolution (which is oversampling for the GPS data) between 8 and 38 km altitude. We then bin the profiles within each day to a longitude and latitude resolution. The S transform is subsequently performed as a function of longitude for each latitude and each altitude, giving zonal wave number 0 6asa function of longitude. Note that the S transform is a continuous wavelet like analysis [Stockwell et al., 1996] that uses an absolute phase reference, and the longitudinal integral of the transform recovers the Fourier transform. We then reconstruct zonal wave numbers 0 6 to define the largescale temperature variation. This large scale temperature variation, interpolated back to the position of each original profile, is subtracted leaving perturbations with horizontal fluctuations shorter than wave number 6. Since the GPS RO data have relatively sparse coverage poleward of 70 where planetary waves could be undersampled, there could be planetary wave residuals in GW perturbations thus derived at high latitudes. We have tested the sensitivity of the analysis results using different cutoff zonal wave numbers ranging from 3 to 10 (whenever the data spatial coverage allows this) and have found that the main results reported here remain largely the same. Note that Alexander et al. [2008] used a similar procedure to derive GW perturbations from the HIRDLS temperature data. [10] Figure 2 shows one example of raw temperature profiles and background and perturbation profiles obtained using the above procedure. Wavelike structures are clearly seen in the perturbation profile. Note that this procedure to derive GW background profiles neglects the time variations of large scale waves within one day Gravity Wave Temperature Amplitudes and Vertical Wavelengths [11] We estimate GW temperature amplitude T and vertical wavelength l z corresponding to the dominant mode at each height by computing the S transform in altitude for each temperature perturbation profile. We determine the dominant mode from the spectral peak in the vertical temperature spectrum at each height in the wavelet analysis. Our analysis can resolve GWs with vertical scales no shorter than twice the vertical resolution of the GPS data ( 1 km). In practice, the limited height range of the profiles means we cannot resolve GWs of ultralong vertical scales, nor waves with scales very close to the Nyquist vertical wavelength, so we limit our analysis to vertical scales between 4 and 15 km. 3of12

4 Figure 2. (a) Raw (black) and background (red) temperature profiles (10 35 km) of one sounding sampled at (33.54 N, W) on 1 January (b) Corresponding gravity wave temperature perturbation profile. [12] Figure 3 shows the contoured map of December 2006 to February 2007 seasonal mean T and energy weighted l z averaged in the altitude range of km. Note that the time period studied here coincides with that of Horinouchi and Tsuda [2009]. Many colocated soundings occurred during this period of time due to the clustering of COSMIC LEOs, which could benefit the analysis of GW horizontal structures in this study, as will be described in the next subsection. The original estimates of T and l z are gridded using a resolution of 15 in both longitude and latitude using all the available data. The values of T range from 0.2 to 1.1 K. In general, T maximizes at low latitudes where convective activity is believed to be the strongest. It also exhibits some land sea contrast with enhancement over the continents, indicating the possible role of topography (which is recognized as another major source of GWs). The latitudinal variation of T and the land sea contrast are consistent with earlier studies of GWs from GPS and other data sets [e.g., Tsuda et al., 2000; Wang and Geller, 2003; Alexander et al., 2008]. The value of T is slightly smaller than what is reported in Figure 4 of Alexander et al. [2008], though the latter corresponds to monthly mean values (May 2006) and for a different altitude range (20 30 km). Note that most previous GW studies analyzed GW variances (i.e., rms temperature perturbations) or potential energy density Pe. We report T instead of Pe because we will use T to calculate momentum flux as will be discussed later in this section. Pe of the dominant mode is related to T by the following formula [13] The dominant l z is 5 8 km, and l z generally displays the opposite latitudinal pattern in comparison to T. These results are generally consistent with the results from the HIRDLS analysis [Alexander et al., 2008]. The longer vertical wavelengths at midlatitude and high latitudes could be related to the stronger winds in the upper troposphere in these regions. Pe ¼ g2 2N 2 T 0 2; =T ð1þ where g is gravity, N is the Brunt Väisälä frequency, and T is the background temperature. For a typical N of 0.02 s 1 and T of 200 mph K in the lower stratosphere, a T of 1 K corresponds to a Pe of 3 Jkg 1. Note that the Pe inferred from T reported here cannot be compared directly with potential energy densities reported in previous GPS GW studies [e.g., Tsuda et al., 2000] because in essence the latter calculated the spectral sum of Pe for all the available vertical scales contained in their GW perturbations instead of only for the dominant mode as done in this analysis. Figure 3. Contoured map of December January February (a) seasonal mean gravity wave dominant temperature amplitude and (b) vertical wavelength averaged in the altitude range of km from the combined COSMIC and CHAMP GPS RO data. 4of12

5 3.3. Gravity Wave Horizontal Wavelength and Intrinsic Frequency [14] GW intrinsic frequency ( ^!) can be derived from the hodograph analysis or the Stokes parameters method and its variants [e.g., Hirota and Niki, 1985; Eckermann and Vincent, 1989; Vincent et al., 1997; Wang et al., 2006a, 2006b] when wind profiles are available. In the radiosonde analysis [e.g., Wang et al., 2005], GW horizontal wavelengths (l H ) can be estimated indirectly from the GW dispersion relation once ^! and vertical wavelengths are already derived. [15] When only temperature profiles are available (as in the case of most satellite observations), adjacent soundings can be analyzed together to deduce the horizontal structure of GWs. For example, Ern et al. [2004] estimated l H from CRISTA (Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere) temperature profiles by using the phase difference between adjacent profiles using the maximum entropy method and harmonic analysis technique and related the phase difference to the magnitude of GW horizontal wave number k H, k H ¼ D ij Dr ij ; where D ij is the phase difference between two adjacent profiles, and Dr ij is the distance between the two profiles. Due to the coarse horizontal resolution of CRISTA, large alias errors due to wave undersampling occurred. As discussed in detail in the study by Ern et al. [2004], the above approach gives an underestimate of k H. Alexander et al. [2008] used a similar approach to estimate k H from the HIRDLS temperature profiles, but used the cross S transform to determine D ij. The horizontal resolution of HIRDLS temperature profiles is much better than CRISTA, especially along the orbit track, so the problem of GW undersampling, is lessened in the HIRDLS analysis. Results from both of these analyses showed longer horizontal wavelength near the equator and shorter horizontal wavelength at high latitudes, but the sampling patterns did not allow determination of wave propagation direction. Note that this observed variation in k H with latitude is beneficial for our analysis in the tropics because of the sampling variations shown in Figure 1. [16] Wada et al. [1999] analyzed equatorial inertia GWs from the TOGA COARE IOP radiosonde data and used the cross spectral analysis technique to estimate l H. Ratnam et al. [2006] used a cross correlative analysis to estimate horizontal propagation direction F and l H of equatorial GWs observed in radiosonde profiles during the CPEA campaign, and Evan and Alexander [2008] used a similar procedure with TWP ICE radiosondes. Since these had both temperature and wind profiles, they compared estimates of F from cross correlative analysis and hodography analysis and found them consistent within the uncertainty error. [17] The large number of combined COSMIC and CHAMP daily profiles and the nearly isotropic horizontal resolution of the GPS data (Figure 1) provide a good opportunity to study GW horizontal structures with a global perspective. We derive global information on GW horizontal wave number vector (k, l) from the GPS data by calculating the phase differences between adjacent soundings using the cross ð2þ S transform analysis. A monochromatic GW sampled by a GPS temperature profile can be expressed by T ¼ T 0 cosðkx þ ly þ mz!tþ ¼ T 0 cosðþ; where (x, y, z) is the profile location, t is time, (k, l, m) is the three dimensional wave number vector, w is the groundbased frequency, and is the phase information contained in the vertical profile. Hence, kx þ ly þ mz!t ¼ : It follows that the phase difference between two adjacent GPS profiles i and j at the same altitude is D ij ¼ k x i x j þ lyi y j! ti t j ð5þ if the two profiles are sampling the same wave, where D ij i j. Note that D ij can be obtained from the cross S transform analysis [Wang et al., 2006a, 2006b; Alexander et al., 2008] if the wave is not undersampled. Wave undersampling occurs when the distance between two profiles is equal to or greater than l H /(2 cos ), where l H is the horizontal wavelength of the wave and is the angle between the wave propagation direction and the line connecting the two profiles. Let n be the number of soundings in a group sampling the same wave at different locations and at different times. We calculate all the possible combinations of D ij between each pair of profiles in the group. Thus we have C n (which is the total number of possible pairs among the n soundings (from combinatorial mathematics, C n ¼ n! 2! ðn 2Þ!, e.g., C 4 =6,C 3 = 3.)) profile pairs and C n linear equations for (k, l, w). If n = 3, we have a linear problem to solve for (k, l, w). If n 4, we have an overdetermined linear problem which we can solve for (k, l, w) using the least squares fitting algorithm. If we neglect the time variation in (5), we get D ij ¼ k x i x j þ lyi y j : ð6þ Thus we have an overdetermined linear problem which we can solve for (k, l) using the least squares fitting algorithm if n 3. The horizontal wavelength l H is related to K (k, l)by H ¼ 2 j~kj : To derive horizontal wavelength l H, we partition the GPS RO data into hr longitude latitude time cells. For each cell with n 3, we identify the dominant vertical wavelength (i.e., the vertical wavelength corresponding to the spectral peak) at each altitude from all the available soundings in the cell. We then use (6) and (7) to determine the horizontal wave vector. Figure 4 shows global estimates of the DJF seasonal mean of l H (specifically we calculate the seasonal mean of ~K first and then use (7) to obtain the seasonal mean of l H ) in the altitude range of 17.5 to 22.5 km. For each cell, the seasonal mean is calculated from the mean (weighted by T 2 ) of all the available data within that cell. Note that the latitudinal range of Figure 4 is slightly smaller than that of Figure 3. We exclude the results for the cells north of 75 N or south of 75 S because the GPS data coverage is too sparse in these regions to obtain reliable statistics for l H and the other wave parameters to be discussed later in this section. ð3þ ð4þ ð7þ 5of12

6 the details of l H zonal asymmetries are comparatively more sensitive to the cell dimensions (not shown). Similarly, the geographic variability of ^!/f does not depend significantly on either the temporal or spatial dimensions of the cells. The magnitudes of ^!/f do not depend significantly on the temporal dimension of the cells either, but they increase by 5% when the shorter spatial dimension of 10 is used (not shown) Gravity Wave Momentum Flux [20] Vertical flux of horizontal momentum (F px, F py ) (or simply put, momentum flux) is a very important GW parameter which is related directly to the GW induced force on the background wind (X ; Y ) Figure 4. Same as Figure 3 but for the horizontal wavelength. Note that the results for cells north of 75 N or south of 75 S are not shown here due to insufficient numbers of valid cells available for this analysis in these regions (see text for details). It is evident that l H generally decreases with increasing latitude, despite exhibiting certain degree of zonal asymmetries. Such a latitudinal dependence of l H is consistent with many previous studies [Ern et al., 2004; Wang et al., 2005; Alexander et al., 2008]. Quantitatively, the estimates of l H from the GPS RO data are longer than the regional radiosonde results [Wang et al., 2005] but are shorter than the HIRDLS results [Alexander et al., 2008]. The different temporal and spatial coverages and resolutions of the data, the different years and seasons of the analyses, and the details of analysis methods could all contribute to the differences in the estimates. Note that in theory we would prefer the temporal and spatial dimensions of the cells to be as small as possible, but due to the limited temporal and spatial coverage of the GPS data, in practice these dimensions have to be large enough so that there can be sufficient number of valid cells (i.e., those with at least three soundings inside them to allow for the derivation of GW horizontal structure characteristics as mentioned above) available to obtain global estimates of wave parameters. [18] With all the wave number components (k, l, m) determined, we can derive other important wave parameters such as intrinsic frequency ^!, phase speed, and group velocity from the GW dispersion relation. For example, Figure 5 shows the global estimate of ^!/f where f is the Coriolis parameter. It is evident that ^!/f maximizes at the equator and it ranges between 1.05 and Therefore most of the waves captured by our analysis of the GPS RO data are lowintrinsic frequency inertio GWs. We also note that the latitudinal variation of ^!/f is consistent with radiosonde analysis [Wang et al., 2005] which also focused on low intrinsic frequency inertio GWs. [19] We have done sensitivity tests of the analysis using different temporal dimensions (including 2, 3, 4, 6, 8, 12, and 24 h) and slightly different spatial dimensions (including 15 and 10 ) for the longitude latitude time cells and have found that the magnitudes of l H are not very sensitive to these temporal dimensions chosen but l H is generally shorter (by 20%) when the shorter 10 spatial dimension is chosen (not shown). In addition, the latitudinal dependence of l H is not sensitive to the temporal and spatial dimensions chosen X ; Y F px; F py : ð8þ Using GW polarization relations, Ern et al. [2004] related (F px, F py ) to temperature amplitude T for a monochromatic wave, which under low intrinsic frequency approximation can be reduced to F px ; F py ðk; lþ g 2 T 0 2 ¼ ; ð9þ 2m N T where is the background density, and T is the background temperature. With (N,, T) calculated directly from the GPS RO data, and (k, l, m, ^!, T ) for the dominant wave already determined as described in previous subsections, we can calculate momentum flux components using the above formula. [21] Figure 6 shows the global estimates of momentum flux magnitudes averaged in the altitude range of km during December 2006 to February The magnitudes of momentum fluxes are generally similar to previous studies [Ern et al., 2004; Alexander et al., 2008]. Note that Figure 6 shows several prominent hot spots for wave fluxes and we can interpret most of the geographic variability of wave fluxes exhibited in the plot by the proximity of the regions of elevated fluxes with possible GW source regions in the lower atmosphere. GW fluxes were very strong over the Amazon in South America, regions where strong convective activity occurs [e.g., Pfister et al., 1993]. GW fluxes were also strong over Scandinavia, reflecting the possible excitation of GWs due to flow over topography there [e.g., Dörnbrack and Figure 5. Same as Figure 4 but for the intrinsic frequency scaled by the absolute value of Coriolis parameter. 6of12

7 Figure 6. Same as Figure 4 but for the magnitude of momentum flux. Leutbecher, 2001; Eckermann et al., 2007]. The enhancement of GW fluxes over the northwestern Atlantic and the coasts along the northeastern U.S. and eastern Canada could be due to enhanced activity in the vicinity of the storm track in that region during the winter season [e.g., Wu and Zhang, 2004]. It is worth noting that Figure 6 also suggests a possible link between El Niño Southern Oscillation (ENSO) and the geographic variability of GW fluxes in the lower stratosphere. DJF corresponds to the mature phase of an El Niño episode (though a relatively weak one). During the mature phase of an ENSO event, the western tropical Pacific is abnormally cold and dry whereas the central and eastern tropical Pacific is abnormally warm and wet and has enhanced convective activity. This seems to be consistent with the observations of subdued GW fluxes over the western tropical Pacific and relatively enhanced GW fluxes over the eastern tropical Pacific. A link between interannual variability of GW variances in the tropics and ENSO has been reported by Wang and Geller [2003]. We will explore in further detail possible links between the geographic variability of GW activity and different ENSO phases (as indicated in Figure 6) using additional years of data in future studies. Note that the momentum flux distributions do not directly match patterns in convection as indicated by regions of low outgoing longwave radiation. Detailed modeling studies are needed to establish more definite and concrete links between enhanced wave fluxes and GW source regions. [22] Similar to the sensitivity test results for both l H and ^!/f, the geographic variability of momentum flux magnitudes is generally not sensitive to the temporal and spatial dimensions of the cells chosen but on the average the magnitudes ofmomentumfluxesincreaseby 32% when the spatial dimension of the cells decreases from 15 to 10 (not shown). Finally note that this analysis can yield height dependent estimates of momentum flux components but we caution against calculating GW forcing directly from the momentum flux estimates from this analysis using (8). The reason is that we obtain GW parameter estimates for the most dominant GW mode at each height in this analysis but we are not necessarily dealing with the same GW mode at each height Gravity Wave Horizontal Propagation Direction [23] The knowledge of GW horizontal propagation direction F is crucial to ray tracing observed GW events to their sources in the lower atmosphere, but this parameter is not routinely derived in most satellite GW studies so far (as mentioned in the Introduction). Actually it is straightforward to calculate F in our analysis from the derived horizontal wave number components (k, l), i.e., F = arctan (l, k). To test the effectiveness of our analysis in estimating F from the GPS data, we compare the GPS results with the U.S. highresolution radiosonde analysis using the conventional Stokes parameters method. Note that both the GPS RO directional analysis described here and the Stokes parameters analysis of radiosonde data give estimates of intrinsic propagation directions. They are therefore directly comparable. The U.S. high resolution radiosonde data (The U.S. high resolution radiosonde data are available from the following URL: ftp:// atmos.sparc.sunysb.edu/pub/sparc/hres/.) have been used for GW analysis in several previous studies [Wang and Geller, 2003; Wang et al., 2005; and Gong et al., 2008]. The radiosonde data have been described in detail in these previous studies so we describe the data only briefly here. The radiosondes are launched over more than 90 stations covering Alaska, contiguous U.S., Hawaii, the Caribbean, and part of the western tropical Pacific. In general twice daily (at 0000 and 1200 UTC) wind and temperature soundings are available for each station with a vertical resolution of 30 meters. [24] The left column of Figure 7 shows the estimates of F from the radiosonde data which are grouped in three different regions: Alaska, contiguous U.S. and the Caribbean, and part of the western tropical Pacific. As in Figures 3 6, the analysis is for the period December 2006 to February Note that although overall the radiosonde data have more than 90 stations, as mentioned earlier, data from only 63 stations are available for the time period examined here. Following Wang and Geller [2003] and Gong et al. [2008], we first interpolate the raw data linearly to a regular vertical resolution of 30 meters and then obtain GW temperature and wind perturbations by removing second order polynomial fits from the interpolated data in the altitude range of km. We then derive GW propagation directions using the Stokes parameters method. The right column of Figure 7 shows the corresponding estimates of F from the GPS data. To get the estimate of F for each station from the GPS data, soundings in a h longitude latitude time cell centered around that station are used to evaluate k and l using (6). Note that we use a finer cell for this analysis than that used in the global analysis (Figures 4 6) to limit overlap of the cells surrounding each radiosonde stations. Each arrow reported in Figure 7 represents the direction corresponding to the peak in the angular distribution (with an interval of 15 ) of wave energies for that location (in the case of the radiosonde analysis) or cell (in the case of the GPS analysis). The tail point of each arrow in Figure 7 represents the location of the corresponding radiosonde station and the arrow length is taken be a fixed but arbitrary value. Since the distances between adjacent radiosonde stations are generally smaller than the spatial dimension of the longitude latitude cells chosen here, the estimates from the GPS data at adjacent stations may not be completely independent. [25] The two analyses show more agreement in the contiguous U.S. and Caribbean than in Alaska and western tropical Pacific. Some of the differences in the two estimates could be due to the different spatial and time samplings of the GPS and radiosonde data. Also, bear in mind that the radio- 7of12

8 Figure 7. December 2006 to February 2007 seasonal mean gravity wave propagation directions in the altitude range of km over (a) Alaska, (b) contiguous U.S. and Caribbean, and (c) part of the western tropical Pacific from the U.S. high vertical resolution radiosonde data. (d, e, and f) Corresponding propagation direction estimates from the GPS data. The tail point of each arrow in Figure 7 represents the location of each radiosonde station. The radiosonde estimates are derived from the Stokes parameters method, whereas the GPS results are obtained from the method introduced in this study. For clarity, westward and eastward directions are plotted using blue and red arrows, respectively. Each arrow has the same arbitrary length. See text for further details. sonde analysis uses both wind and temperature information over each individual radiosonde station whereas the GPS analysis uses only temperature information of soundings around that radiosonde station. Furthermore the Stokes parameters method gives a Fourier spectrally averaged estimate for all the available GW modes (i.e., with vertical wavelengths ranging from 60 meters up to 6.9 km) whereas the GPS analysis gives the estimate for the dominant mode at each height for the altitude range considered ( km) among modes with vertical wavelength ranging from 4 to 15 km and height dependent results are combined to determine the final angular distribution of wave energies which is reported in the right column of Figure 7. [26] As another test of the effectiveness of the method in deriving F, we have conducted a separate analysis over the southern Andes during June August Similar to previous analysis, for each grid point in the longitude latitude grid (47.5 S 22.5 S, 75 W 65 W, with a resolution of 5 ), we use a h longitude latitude time cell centered around each grid point. Given the comparatively large cell dimension (which is needed to ensure that there are enough data points falling into each cell to obtain estimates) relative to the grid resolution, the results of adjacent grid points in this analysis are not totally independent. We choose the Southern Hemisphere winter season for this analysis because the prevailing tropospheric zonal winds were stron- 8of12

9 direction, both eastward and westward propagations were identified while in the meridional direction, northward propagation was dominant. It is difficult to directly compare the results from this analysis with those from Horinouchi and Tsuda [2009] because the former are reported on regular grids whereas the latter correspond to locations of those quasi linearly aligned GPS RO soundings. [28] Note that the analyses of F (Figures 7 9) can be sensitive to the dimensions of the cells. The global estimates of F (Figure 9) are also generally sensitive to both the temporal ^ and and spatial dimensions of the cells, more than lh,!/f, momentum flux magnitudes, especially in the Northern Hemisphere. The sensitivity of F to cell dimensions is particularly evident when comparing Figures 7 and 9 over Alaska where nearly opposite propagation direction estimates were obtained. The region over the Southern Ocean and south of 50 S is an exception, where the propagation direction estimates are fairly insensitive to cell dimensions if the temporal dimension is 4 h or longer (not shown). Presumably, these limitations may be substantially reduced if GPS RO sampling improves in the future. 4. Discussion Figure 8. June August 2007 seasonal mean gravity wave propagation directions over the southern Andes. The underlying filled contour shows the topography of the region. As in Figure 7, westward and eastward directions are plotted using blue and red arrows, respectively, and each arrow has the same arbitrary length. ger than during other seasons in this region so we expect larger topographic GW excitations with more uniform wave propagation directions. Figure 8 shows that GWs generally propagate westward over the southern Andes in the lower stratosphere. This is consistent with the characteristics of mountain waves which are expected to propagate upwind and orthogonal to the orientation of the main topography. [27] As in Figures 3 6, Figure 9 shows the global estimates of F in the altitude range of km during December 2006 to February Note that the altitude range is slightly different from the one used in the analysis in Figure 7 and the longitude latitude cell dimension is instead of Figure 9 shows a first global estimate of GW horizontal propagation directions from satellite data. Overall, F are more uniformly distributed in the Southern Hemisphere (mostly westward), especially over the Southern Ocean, than in the Northern Hemisphere. This could be due to the comparatively strong and steady zonal winds in the Southern Hemisphere. The distribution of F is more complex in the Northern Hemisphere, though it is discernible that more GWs propagate westward at midlatitudes than eastward. Horinouchi and Tsuda [2009] obtained GW horizontal propagation direction statistics in the Northern Hemisphere during the same season and they found that in the zonal [29] In this analysis, we assume the existence of a dominant GW mode in each longitude latitude time cell at each height when deriving GW horizontal wave number components and momentum flux components. In practice, GWs are often found to be intermittent and localized [e.g., Fritts and Alexander, 2003]. To reduce uncertainties due to the violation of this assumption, we will need to reduce the dimension of each longitude latitude time cell (which evidently requires denser data coverage) and to set threshold wave amplitude for the existence of dominant GW modes. Also, it is conceivable that sometimes multiple wave modes with different vertical wavelengths could coexist in a single longitude latitude time cell. The analysis will need to be extended to deal with such a scenario in the future. [30] Evidently, uncertainty of the analysis can also arise if the GPS data do not have sufficient coverage within a given cell (i.e., the wave in that cell is undersampled). To reduce the Figure 9. Same as Figure 4 but for the horizontal propagation direction. Westward and eastward directions are plotted using blue and red arrows, respectively, and each arrow has the same arbitrary length, as in Figures 7 and 8. 9 of 12

10 Figure 10. Same as Figure 4 but for the (a) number of valid cells and (b) mean sounding distance in each cell. alias due to wave undersampling, we should choose the spatial dimension of each cell to be a fraction of l H and the temporal dimension of each cell to be a fraction of the wave period. As reported from previous studies [e.g., Ern et al., 2004; Wang et al., 2005; Alexander et al., 2008], GWs generally have longer periods and longer horizontal wavelengths in the tropics, so the spatial and temporal dimensions of cells could be set relatively larger. In contrast, both the spatial and temporal dimensions of cells need to be reduced at higher latitudes. In the current analysis, for simplicity, we use a constant longitude latitude time cell throughout the globe. To aid the interpretation of the analysis results reported here, we show in Figure 10 the number of valid cells (i.e., those with at least three soundings so that characteristics of GW horizontal structures can be derived) and the average sounding distance within each cell for Figures 3 6 and 9. Similar to the geographic distribution of the number of daily GPS soundings described in section 2, the number of valid cells has primary peaks at 50 N and 50 S and secondary peaks at 20 N and 20 S. In contrast, there are few valid cells in high polar regions. Therefore, the statistical significance of the results shown in Figures 3 6 and 9 is comparatively the best at midlatitudes. [31] The estimate of momentum flux is subject to errors due to potential aliasing effects of wave undersampling. In previous studies with CRISTA and HIRDLS [Ern et al., 2004; Alexander et al., 2008], adjacent profiles were obtained nearly simultaneously in time and the authors use the scalar form of the medium frequency approximation to (9) to derive momentum flux magnitude. In these earlier studies, undersampling always leads to underestimates of the horizontal wave number and momentum flux. For GPS sampling, there will also be time differences between adjacent profiles that can sometimes be substantial fractions of the wave period. Since we neglect the time difference in sampling in this analysis (6), undersampling could lead to either underestimates or overestimates of horizontal wave number and momentum flux. In future work if we use the full equation (5), undersampling would consistently lead to underestimates of k, l, and w and underestimates of momentum flux. [32] GPS RO measurements are limited by the line of sight integration of the limb viewing technique to resolve only GWs with horizontal wavelengths of a few hundred km or longer. In fact, as shown in Figures 4 5, most of the waves captured in our analysis are low intrinsic frequency and long horizontal wavelength inertia GWs. Shorter horizontal scale GWs are expected to carry a significant fraction of the total momentum flux [Fritts and Alexander, 2003], so the inherent limitation of the GPS measurements will likely underestimate the GW momentum flux in the real atmosphere. [33] In addition to COSMIC and CHAMP, there are currently several other satellite missions (e.g., German s GRACE and TerraSAR X; EUMETSAT s GRAS/MetOp A) in operation which also provide GPS RO data. Furthermore, more GPS RO missions have been scheduled for launch in the near future (e.g., German s TanDEM X). In future studies of GWs using GPS RO data, all these data can be combined to increase the data coverage, which can help reduce the analysis uncertainties significantly. Also, with more data available, we can use the complete formula (5) to derive k, l, and ground based frequency simultaneously (although our sensitivity tests seem to suggest that the improvement of analysis due to the consideration of the time variation of GW modes is likely to be smaller than that from choosing a finer spatial dimension for the cells made possible by the increased data coverage in the future). 5. Summary and Conclusions [34] We introduce a GW analysis method based on the cross wavelet analysis to derive the complete set of GW parameters from the GPS RO temperature retrievals. Following closely Wang and Alexander [2009], we derive GW perturbations from the combined COSMIC and CHAMP GPS RO data for each day by removing zonal modes 0 6. We derive the GW temperature amplitude T and vertical wavelength l z for the dominant mode at each height using the S transform. [35] To obtain global estimates of GW horizontal wavelengths, intrinsic frequencies, and momentum fluxes, we partition the daily COSMIC and CHAMP GPS RO data into hr longitude latitude time cells. For each cell, we identify the dominant vertical wavelength at each altitude from all the available soundings in that cell. We then calculate the phase differences between all the available pairs of soundings in the cell at the dominant vertical wavelength. If there are at least three soundings in the cell, with phase differences determined, we solve a overdetermined linear problem (6) for horizontal wave number vector (k, l) from which we can obtain GW horizontal propagation direction F and horizontal wavelength l H. With T, l z, and (k, l) derived, 10 of 12

11 we estimate intrinsic frequency ^! using GW dispersion relation and vertical fluxes of GW horizontal momentum using (9). [36] As a demonstration of the analysis method, we present global estimates of the December 2006 to February 2007 seasonal mean T, l z, l H, ^!/f, and momentum flux magnitude averaged in the altitude range of km. It is evident that most of the waves captured in this analysis of the GPS RO data were low intrinsic frequency inertia GWs. Consistent with previous studies [e.g., Tsuda et al., 2000; Wang and Geller, 2003], GW temperature amplitudes were generally larger at low latitudes and over the lands, reflecting the excitation of GWs by convection and topography (Figure 4). Also consistent with previous studies [e.g., Alexander et al., 2008], GW vertical wavelengths were shorter in the tropics than at midlatitude and high latitude, possibly due to wave refraction. GW horizontal wavelengths decreased with increasing latitudes (Figure 5), being consistent with several previous studies [Ern et al., 2004; Wang et al., 2005; and Alexander et al., 2008]. Intrinsic frequencies scaled by the Coriolis parameter were larger at the Equator (Figure 6), being consistent with radiosonde analysis [Wang et al., 2005]. The magnitude of GW momentum flux derived in this study (Figure 6) is generally in line with momentum flux estimates from other studies using different data [Ern et al., 2004; Alexander et al., 2008]. We interpret most of the geographic variability of wave fluxes exhibited in Figure 6 by the proximity of the regions of elevated fluxes with possible GW source regions in the lower atmosphere. In particular, we have found possible evidence of impacts of ENSO on the geographic distribution of lower stratospheric GW fluxes. [37] We conduct two tests to assess the horizontal propagation direction estimates from the GPS RO data. In one test, we compare the GPS results with GW propagation direction estimates from the U.S. high vertical resolution radiosonde data using the conventional Stokes parameters method (Figure 7). The two analyses show more agreement in the contiguous U.S. and Caribbean than in Alaska and western tropical Pacific. As another test of the effectiveness of the analysis method in obtaining GW propagation directions, we conduct a separate analysis of the GPS data over the southern Andes in South America (47.5 S 22.5 S, 75 W 65 W) during June August 2007 and find that the propagation direction estimates are generally consistent with the theoretical expectation of mountain wave propagation directions, i.e., upwind and orthogonal to the orientation of topography (Figure 8). We also report the first global estimates of GW horizontal propagation directions from the satellite data (Figure 9). [38] We discuss the uncertainties of estimates for horizontal wave vector (and other related wave parameters) using the analysis method. One primary cause for uncertainties arises from the limited spatial and temporal coverage of the combined COSMIC and CHAMP GPS RO data which, despite being a great leap forward in comparison to previous GPS missions, is still a far cry from the optimal coverage needed for this type of analysis (though the GPS RO data coverage is expected to improve when soundings from other existing and future GPS missions are included for GW analysis in future studies). Due to the limited sampling, we evaluate the horizontal wave vector using (6) which neglects time variation of wave phase. Another limitation of the method is the assumption of the existence of a dominant monochromatic wave in each longitude latitude time cell at a given height. We can extend the analysis in future studies to include the consideration of secondary spectral peaks when they exist. [39] Finally, we note that the GW analysis method introduced in this study is not limited to GPS RO data. It can be applied directly to other observational data and high resolution analysis/reanalysis and simulation data for GW analysis, if those data have sufficient spatial and temporal resolution. [40] Acknowledgments. This research was supported by the Climate and Large Scale Dynamics Program of the National Science Foundation grant ATM We would like to thank Marvin Geller for providing the U.S. high resolution radiosonde data. L.W. would like to thank Ralph Millif for helpful discussions on El Niño Southern Oscillation. References Alexander, M. J., and K. H. Rosenlof (1996), Nonstationary gravity wave forcing of the stratospheric zonal mean wind, J. Geophys. Res., 101(D18), 23,465 23,474, doi: /96jd Alexander, M. J., et al. (2008), Global estimates of gravity wave momentum flux from High Resolution Dynamics Limb Sounder (HIRDLS) observations, J. Geophys. 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