We discuss the global gravity wave (GW) activity expressed by the specific potential energy in the altitude range from 5 km below to 10 km above the tropopause, derived from GPS radio occultation data from CHAMP (2001–2008). The GW analysis is based on vertical detrending of the individual measured temperature profiles by applying a Gaussian filter in two different ways: (i) filtering of the complete temperature profiles and (ii) separate filtering of the profiles for the tropospheric and lower stratospheric parts. The separate filtering method significantly reduces the usually observed wave activity enhancement in the tropopause region which highly depends on the performance of the complete filtering method to reproduce the change in the temperature gradient at the tropopause. We only consider vertical wavelengths less than 10 km. The global mean potential energy in the tropopause region deduced with these different background temperatures will be analyzed, differences will be emphasized and possible error sources of the new method will be considered.
 The broad spectrum of gravity waves (GWs) play an important role for the general atmospheric circulation due to the related transport of energy and momentum between different regions of the atmosphere (e.g., Fritts and Alexander, 2003). The number of observation techniques to detect GWs at different scales are manifold. Direct (radiosondes, rockets) or ground-based remote sensing (lidar, radar) methods are not able to provide global information. Available satellite data give global pictures of vertical and horizontal GW parameters, as e.g., temperature variances, momentum fluxes or (potential) energy, but each seen through an individual observational window depending on the used measurement characteristic [Alexander, 1998; Wu et al., 2006].
 The GPS radio occultation (RO) technique [e.g., Melbourne et al., 1994] is a limb-sounding method sensitive to GWs with small ratios of vertical to horizontal wavelengths λz/λh [Wu et al., 2006].
 The German satellite CHAMP (Challenging Minisatellite Payload) measures about 150–200 globally distributed temperature profiles daily [Wickert et al., 2005]. In addition, since April 2006 COSMIC (Constellation Observing System for Meteorology, Ionosphere and Climate) provides data with a higher temporal and spatial density [Anthes et al., 2008], but nevertheless, CHAMP generates the first global long-term RO data set since May 2001 with a vertical resolution not reachable from any other satellite mission before.
 The restriction of GW analysis to the lower stratosphere or to an altitude range from 1–2 km above the tropopause is caused due to the analyzing method itself, i.e., the demand to determine a temperature background to the corresponding measured temperature profiles. Ideally, the spatial and temporal measurement density is sufficient for the determination of a background temperature by averaging over appropriate latitude/longitude bins and time. The COSMIC data should be suitable for such an approach [Alexander et al., 2008].
 For the CHAMP data, but also for radiosonde measurements another method for the temperature background determination has to be applied. Tsuda et al.  for the GPS/MET (GPS/Meteorology) data (1995–1997), Ratnam et al.  for the CHAMP data from 2001–2003, and Namboothiri et al.  also for the CHAMP data (2001–2005) used a high-pass filter with a cutoff at 10 km to separate a background from each individual RO temperature profile. de la Torre et al.  applied a Gaussian filter to investigate different vertical wavelength ranges. The according filter is applied to the complete temperature profile from the bottom to the top. Usually, this leads to an (artificial) enhancement of GW activity in the tropopause region, depending on how good the filter is able to reproduce the temperature kink at the tropopause.
 In this paper we discuss for the first time the global GW activity derived from CHAMP just below and above the tropopause by applying a new method for the determination of the temperature background. In our approach we separate each temperature profile into a tropospheric (below the tropopause) and stratospheric (above the tropopause) part and deploy a Gaussian filter for each part of the profile. Finally, the temperature background profile is constructed from the two (tropospheric and stratospheric) single background profiles. This method is called the separate method in the following unlike the complete method applying the filter to the complete profile.
 An other wide-used filter technique is the application of a polynomial fit. We did not consider polynomial fits for the vertical detrending here because these techniques allows no direct control about the wavelengths or wavelength ranges that were filtered. But the separate method could be also applied with polynomial fits.
2. Database and Analysis
 The CHAMP mission generates the first long-term GPS RO data set. Beside one complete month of missing data (July 2006) CHAMP delivers continuously temperature profiles since May 2001. We calculate monthly zonal means of GW parameters if at least for 50% of the days per month CHAMP RO data are available.
2.2. Data Analysis
 According to the linear theory of GWs [see, e.g., Nappo, 2002; Fritts and Alexander, 2003] the measured temperature profile T(z) is expanded into a background temperature (z) and a perturbation T′(z) which can also be considered as a fluctuation:
The background is assumed to be steady, the fluctuations are much smaller than the background and the fluctuations should not affect the background. Usually, the fluctuations are addressed to GWs, but this depends strongly on the measuring method (observational window) and the background separation approach.
 For the determination of the background profile (z) a non-recursive Gaussian low-pass filter with a cutoff at 10 km was constructed whereas the cutoff height determines the number of the filter weights [Schönwiese, 2006]. To avoid missing data at the beginning and the end of the background profile due to the application of the centered filter weights, the filtering was applied for the complete profile, starting/ending at the altitude z1/zn (n: number of profile data). Accordingly missing values below the first (z1) and above the last (zn) measured profile altitude were linearly extrapolated using the first and last 4 km intervals.
 By subtracting (z) from T(z) (equation (1)) the resulting T′(z) profile is then high-pass filtered with a cutoff at 10 km, i.e., the detrended T′ structure only contains vertical wavelengths less than 10 km. This statement, of course, is only valid for an ideal filter.
 In a next step the temperature variance T′2 was integrated using a sliding window with a width of 2 km and a step size of 200 m equivalent to the vertical resolution of the CHAMP profiles [Tsuda et al., 2000].
The mean temperature variance can also be considered as a measure of GW activity. But, with the background temperature (z) the squared buoyancy frequency N2(z) can be calculated:
and finally the specific potential energy Ep as another parameter for the characterization of gravity wave activity here is given by:
g and cp denote the acceleration of gravity and the specific heat capacity of air at constant pressure, respectively.
 The direct determination of total wave energy, i.e., the sum of potential (Ep) and kinetic energy (Ek), is not possible with the RO technique because only temperature profiles are available. However, according to the linear theory of GWs the ratio of Ek/Ep is constant providing an opportunity to estimate also the total wave energy [Fritts and Alexander, 2003].
3.1. The New Approach
 The analysis technique described above is applied to each individual CHAMP temperature profile in two ways. First, we dispose the method on the complete temperature profile, which is the hitherto approach. This is demonstrated for the background temperature on the left profile in Figure 1a. The large deviation between the measured temperature profile and the determined background in the tropopause region is remarkable.
 The profile in the center of Figure 1a demonstrates the new approach: The profile was considered as composed of two parts separated by the lapse rate tropopause (LRT) [World Meteorological Organisation, 1957]. Only the LRT altitude occurs in both profiles. Therefore, for the resulting background temperature (Figure 1a, right curve) at the LRT altitude the temperature with the smallest difference to the measured profile was taken.
Figure 1b shows the resulting normalized temperature fluctuations T′/ in percent demonstrating the differences between the two methods. At about ±3 km around the LRT both methods deliver the same normalized temperature fluctuations.
 Finally, the potential energy Ep for that example is shown in Figure 1c. One can clearly see the significant reduction of Ep in the tropopause region derived with the separate method in comparison with the complete method.
 For the application of the separate method for each individual temperature profile the first LRT was determined using an algorithm described by Schmidt et al. . Multiple tropopauses [Schmidt et al., 2006] were also considered and the separation border was chosen as the mean of the first and last LRT. The results look similar (not shown here) to those derived with the first LRT only. If no LRT could be determined for both, the complete and separate method, the according profile was rejected (about 0.8% of all profiles).
3.2. Global GW Activity
 The zonal mean normalized temperature fluctuations, the temperature variance, and the potential energy derived from CHAMP with the complete and separate method and for the time period May 2001–February 2008 are presented in Figure 2. We show the selected GW parameters as an average relative to the first LRT height. The methodical advances of a tropopause based consideration are given by Birner .
 The differences between the complete and separate methods are apparent. The complete method (Figures 2a, 2c, and 2e) disallows a detailed evaluation of the GW parameters in a ±2–3 km band around the tropopause. The separate method in that altitude range reduces the wave parameters significantly and globally.
 The lower stratospheric Ep maximum (Figure 2f) is located in the tropics with highest values 3 km above the equatorial tropopause. In the upper troposphere the extra-tropical maximum Ep is observed between 30°–60° on the southern hemisphere (SH) and 30°–80° on the northern hemisphere (NH) in the altitude range 3–5 km below the LRT. This is the region just below the (climatological) location of the subtropical and polar jet streams. The broader upper tropospheric latitude band of Ep and the higher Ep values just above the LRT at the NH are linked to the stronger variability of the polar jet stream there [Holton, 2004]. The tropical upper tropospheric Ep maximum is located 2–3 km below the tropopause. Here, convective processes play a major role.
 For the discussion of the zonal monthly mean potential energy in different altitude regions Figure 3 shows Ep values deduced with the separate method averaged over three heights ranges: between the LRT and 5 km below (a), between the LRT and 5 km above (b), and between 5–10 km above the tropopause (c).
 The NH extra-tropical (>40°N) upper tropospheric mean Ep exhibits a maximum during summer with values of about 8–10 J/kg reaching also the polar zone. The mid-latitude summer maximum indicate that convection contributes to that enhancement. On the other side, the polar Ep summer maximum suggests an increase of GW activity due to the northward shift of the polar jet stream during summer. Between 30°N–40°N the maximum is observed between December and February. This is just the time and location where the subtropical jet stream has the maximum.
 At the SH the upper tropospheric maximum values are concentrated between 30°S–60°S with a not so clear annual cycle as a result of the different geographical conditions on both hemispheres, i.e., the different distribution of the land-sea masses.
 In the lower stratosphere (Figures 3b and 3c) the mean maximum Ep values are observed in the tropics during NH winter. This is in agreement with previous studies [e.g., de la Torre et al., 2006]. In the tropical 5–10 km interval above the tropopause a roughly 2 year cycle of the maximum potential energy is identified leading directly to the quasi-biennial oscillation (QBO). As already discussed in former studies [de la Torre et al., 2006; Namboothiri et al., 2008], also Kelvin waves or other equatorial trapped waves could make a contribution to the GW analysis in the tropics leading to the QBO-like pattern.
 An interesting feature is the extra-tropical Ep maximum which shifts from the summer (Figure 3b) to the winter months (Figure 3c). The latter is again in agreement with previous investigations [e.g., de la Torre et al., 2006].
3.3. Error Discussion
 Generally, the GW analysis (section 2.2) offers at several points possibilities to influence the final Ep distribution, not only in the tropopause region.
 The determination of the relative temperature variance in equation (4) is one example. The usage of the direct non-averaged temperature variance T′2 instead of the integrated variance (equation (2)) leads to a sharp, global distributed Ep maximum (10–12 J/kg) 400–600 m above the LRT for the separate method (not shown here). However, the application of the integrated temperature variance for the separate method leads to a more uniform Ep distribution close to the tropopause (Figure 2f).
 From a physical point of view, it seems reasonable to assume that in the absence of specific mechanisms, as critical layers, wave amplitudes and finally Ep just below and above the tropopause should not change significantly.
 By application of equation (2) the width of the sliding window also affects the potential energy distribution. This is denoted by the slightly discontinuity in the temperature variance and Ep distribution (Figures 2d and 2f). Overestimation or underestimation of Ep, especially in the tropopause region are possible consequences.
 The separate method introduced here provides another opportunity to control the Ep output at the tropopause. To avoid data lost at the beginning and end of the filtered profiles due to the application of central filter weights, the measured temperature profile is extrapolated beyond the first (last) data point using the data of the first (last) 4 km interval (section 2). The choice of the interval length slightly influences the final Ep distribution at the LRT (not shown here).
 Therefore, the requirement for a statistical quantification of the overall under or overestimation of wave activity at the tropopause is crucial.
 This study has shown the GW activity expressed by the specific potential energy from GPS RO measurements (CHAMP) for the time interval May 2001 to February 2008. We introduced a new method for the temperature background determination in the tropopause region. The new method reduces the (artificial) enhancement of wave potential energy in the tropopause region significantly and enables a detailed discussion of the spatial and temporal distribution of Ep.
 It should be noted that the separate method demonstrates an improvement in the determination of realistic GW activity in the tropopause region compared with the complete method, but the question for the ‘real’ GW activity in that region is still open. Also the separate method introduced here exhibit scope for the Ep distribution in the tropopause region depending on the used filtering procedure and temperature variance.
 To solve this problem only satellite measurements with a suitable temporal and spatial resolution can bring any effort. The COSMIC constellation, together with existing and upcoming RO missions, could be a first step.
 The authors would like to thank the CHAMP team for providing the RO data and orbits. We would also like to thank the anonymous referees for helpful comments and suggestions.