Geophysical Research Letters

A discussion on the methods of extracting gravity wave perturbations from space-based measurements

Authors


Abstract

[1] The disparities in satellite-based observations of global gravity wave activity are discussed in terms of methods used to extract the gravity wave perturbations from background and the sensitivity of the given satellite to the gravity wave spectrum. The temperature measurements from TIMED/SABER are used to obtain the global gravity wave maps in terms of their potential energies by employing two widely used methods to extract the gravity wave perturbations viz. (1) removal of 0–6 zonal wavenumber large-scale waves and (2) high pass filter with cut-off vertical wavelength at 10 km. The present study for the first time employed these two different methods on the same satellite observations to investigate the sensitivity of global gravity wave patterns and their magnitudes to the methods used to extract them. The results showed significant differences in the gravity wave potential energy magnitudes estimated by employing these two methods. Further, employing the first method on COSMIC-measured temperature profiles, the global gravity wave pattern is estimated and the same is compared with that obtained using SABER observations. This comparison substantiated the assertion that using the same method to extract the gravity wave perturbations from different satellite observations yields the similar global gravity wave pattern. The present study thus provided very useful insights into the observed discrepancies among current global gravity wave patterns and it is envisaged that this is a step forward in unifying the existing methods to extract gravity wave parameters using space-based observations.

1 Introduction

[2] Among the atmospheric waves of various temporal and spatial scales, gravity waves, though confined to shorter scales, are very important in controlling the dynamics of the Earth's middle atmosphere. The momentum and energy carried by gravity waves from lower atmosphere to middle/upper atmosphere play a crucial role in driving the long-term oscillations such as quasi-biennial oscillation and semiannual oscillation in the stratosphere and mesosphere [Antonita et al., 2007, 2008a, 2008b]. In the past, ground-based measurements such as Rocket soundings [e.g., Eckermann et al., 1994], Aircraft/Balloon measurements [Nastrom and Fritts, 1992], Radars [Kumar, 2006, 2007], Lidars [Wilson et al., 1991], and Radiosondes [Wang and Geller, 2003] provided valuable information on gravity waves over various geographical locations. However, ground-based measurements are limited to few geographical locations. Therefore to study gravity wave characteristics over the entire globe, one has to depend wholly on satellite-based observations. This has become highly relevant as precise temperature measurements from space platforms are now available [Preusse et al., 2002; Alexander and Barnet, 2007; John and Kumar, 2012]. Nevertheless, satellite-based measurements too have their limitations and time-to-time evaluation of space-based gravity wave parameters become essential. At this juncture, where there are some contrasting results on global maps of gravity wave activity, it becomes very important to unify the methods to extract the gravity wave information from space-based observations.

[3] Many studies in the past attempted to quantify gravity wave activity by assessing their proxies such as squared temperature amplitudes, wind/temperature variances, and kinetic and potential energies of waves. It was Fetzer and Gille [1994] who pioneered global observations of gravity waves based on LIMS temperature measurements. Wu and Waters [1996] isolated short-scale horizontal perturbations associated with gravity waves in the UARS-MLS temperature fluctuations and obtained high polar values, while Tsuda et al. [2000] extracted short-scale vertical fluctuations associated with gravity waves from GPS/MET data and obtained enhanced values around the equator in the lower stratosphere. However, the zonally averaged gravity wave potential energy showed a secondary maximum over winter hemispheric high latitude in the 30–40 km altitude region. Using HIRDLS temperature measurements, Alexander et al. [2008a] have shown enhanced gravity wave momentum fluxes over higher latitudes as compared to that over the equator. Thus, there exist two sets of global gravity wave maps, one showing high latitude enhancement (with secondary maxima over tropics) and the other showing the equatorial enhancement (with secondary maxima over winter high latitudes). Alexander and Barnet [2007] were the first to discuss these discrepancies in the global gravity wave maps observed by different satellites in details and attributed the observed differences to the observational filter effects. Preusse et al. [2002] also emphasized the importance of sensitivity of the satellite measurements to both vertical and horizontal wavelengths of gravity waves for the intercomparison of gravity wave climatologies obtained from different satellites. However, there are no detailed discussions on methods employed to extract the gravity wave perturbations from the background temperature measurements and also on the magnitudes of gravity wave perturbations, which as mentioned earlier, have been expressed in variety of quantities. Among many, there are two widely used methods for extracting the gravity wave perturbations from space-based observations; they are as follows:

  1. [4] Method 1: extracting the gravity wave-induced fluctuations by subtracting the estimated amplitudes and phases of 0–6 zonal wavenumbers from the instantaneous temperature profiles [Fetzer and Gille, 1994; Preusse et al., 2002; John and Kumar, 2012]

  2. [5] Method 2: extracting the gravity wave-induced fluctuations by high-pass filtering with a cut-off at ~10 km vertical wavelength [Tsuda et al., 2000; Alexander et al., 2008a, 2008b]. However, there are little variations in adopting this method by various researchers.

[6] Interestingly, the global maps of gravity waves obtained using method 1 show relatively high magnitudes of gravity wave proxies as compared to those obtained using method 2. Thus apart from the differences in pattern of global maps of gravity waves, there exists significant disparity in the magnitudes of gravity wave proxies. It becomes very important to address this issue as it has direct implications in the current space-based global gravity wave observations. In this context, the present study discusses the observed disparity in the space-based observations of gravity waves using different satellites in the light of observational filtering effect and the bias induced by the methods used to extract gravity wave perturbations using SABER and COSMIC temperature measurements. So far, methods 1 and 2 are employed on different satellite measurements, for example, method 1 is employed widely to extract the gravity wave perturbations from SABER/HIRDLS temperature measurements, whereas method 2 is employed on COSMIC measurements. There were no attempts to employ both the methods on the same satellite measurements. In the present study, for the first time, we employ methods 1 and 2 on the same satellite measurements and discuss the results. Section 2 gives an overview of the satellite specifications and details of the data used, and section 3 provides the analysis procedure including the gravity wave potential energy formulation. Section 4 presents the results and section 5 gives the discussion and concluding remarks.

2 Data

2.1 TIMED/SABER

[7] SABER is one among the four instruments aboard the NASA satellite—Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED). The SABER instrument is a limb viewing multichannel (1.27–17 µm) infrared radiometer designed to measure the heat emissions by the atmosphere over a broad altitude and spectral range. The spacecraft is positioned in a highly inclined orbit (74°). Over the course of one orbit, SABER observes between about 52°S and 83°N if in a northward-viewing yaw, switching after 60 days to a corresponding southward-viewing yaw. The retrieval algorithm and the accuracy of SABER temperatures are reported by Mertens et al. [2001]. In this study, we make use of the kinetic temperature measurements, version 1.06 of SABER level 2A data.

2.2 COSMIC/FORMOSAT-3

[8] COSMIC/FORMOSAT-3 satellite uses the GPS radio occultation technique for atmospheric and ionospheric research. Detailed description of COSMIC mission, system, satellite and orbital constellations, scientific objectives, and data products can be found in Rocken et al. [2000]. COSMIC data are available from near the surface to 40 km. We have used the version 2.0 wet temperature data for the present study, which is obtained by incorporating the humidity component too. The density of data and spacing of atmospheric profiles have varied during the mission. The effective vertical resolution is of the order of 0.5–1 km in the lower stratosphere and temperature profiles have accuracy better than 0.5 K. Even though their vertical resolution is similar to the limb viewing satellites, their horizontal resolution will be poorer due to the irregular sampling of profiles.

3 Method of Analysis

3.1 Extraction of Gravity Wave Perturbations From Satellite Measurements

[9] The most commonly employed methods for extracting wave-induced fluctuations are long-term and short-term averaging methods, polynomial fitting, various types of high, low, and band pass filters, and so on, each of which has its own limitations. In the present study, we use two widely used methods to extract gravity wave-induced fluctuations as mentioned in section 1. For method 1, we have gridded the data into 5° × 20° (latitude × longitude) grids over the globe and then amplitude and phase of 0–6 zonal wave number components are estimated. The amplitude and phases are then used to construct the planetary waves, which are subtracted from the instantaneous profiles falling into the respective grids, thus providing the fluctuations due to gravity waves alone. By detrending the ascending and descending orbits of the satellite separately, we also accounted for the effects of tides as discussed by Preusse et al. [2002]. We follow the method proposed by Preusse et al. [2002] to extract the gravity wave perturbations. However, we use least-squares method to extract 0–6 zonal wavenumber planetary wave information rather than the Kalman filter method. For more details and validation of the present method, readers are referred to John and Kumar [2012]. However, there seems to be planetary wave leakage over winter high latitudes in the global maps reported by John and Kumar [2012], which show very high magnitudes over winter high latitudes. To implement method 2, we have averaged the data in 5° × 20° × 7 (latitude × longitude × days) grids. The instantaneous temperature profiles falling in to appropriate grid are then subtracted from the mean profile of corresponding grid and the perturbation profile thus obtained is high-pass filtered with cut-off vertical wavelength of 10 km [Tsuda et al., 2000; Alexander et al., 2008a, 2008b]. In the present study, we use both the methods to extract gravity wave activity in terms their potential energy using the SABER and COSMIC temperature measurements.

3.2 Potential Energy of Gravity Waves

[10] The potential energy per unit mass, Ep of gravity waves in the atmosphere, which is a measure of gravity wave intensity, is defined as [Wilson et al., 1991]

display math

where g(z) is the acceleration due to gravity, T0(z) is the mean temperature at an altitude z, T′(z) is the temperature fluctuation of the instantaneous temperature profile about the mean temperature T0(z), and N(z) is the Brunt-Väisälä frequency.

4 Results

[11] SABER temperature measurements during the boreal summer of 2007 are chosen for the present study. The data are arranged into grids of 5° × 20° (latitude × longitude) for the extraction of planetary waves and subsequent gravity wave-induced fluctuations, as discussed in the section 3.1. Using the method discussed in section 3.2, the gravity potential energies are estimated for each instantaneous profile and are grouped into 5° × 10° grids over the globe. Gravity wave potential energy is calculated in the height region from 20 to 40 km and the same is averaged to obtain the stratospheric gravity wave activity. The potential energies are then averaged for June-July-August 2007 over the globe. Figure 1a shows the global map of gravity wave potential energy in the stratosphere (20–40 km) obtained from SABER temperature measurements using method 1 for extracting the gravity wave perturbation for the boreal summer. One of the most striking observations from this map is a maximum in potential energy magnitudes at Southern Hemispheric high latitudes, especially over the southernmost tip of the South America. A secondary peak in gravity wave activity can be noticed over the Northern Hemispheric tropical region. However, there are significant differences in the primary and secondary peak magnitudes. The global gravity wave maps reported by Preusse et al. [2009] were depicted as temperature squared amplitudes in logarithmic scale (in dB), whereas it is represented as potential energy in the present study. However, the temperature variances associated with gravity waves can be converted into potential energy for typical values of mean temperature and Brunt-Väisälä frequency in the stratosphere. The conversion of temperature variance to dB scale is given by Fetzer and Gille [1994] as dB = 10 log10(T2). The global gravity wave map at 28 km for the month of July reported by Preusse et al. [2009] indicates that the primary peak exists over the Southern Hemisphere high latitudes with the gravity wave variance of the order of ~15 dB, which corresponds to potential energy of ~31 J/kg (by assuming background temperature as ~250 K and N as 0.02 Hz). Thus, the magnitude of gravity wave potential energy observed in the present study is comparable with those reported by the earlier studies using method 1 for estimating gravity wave perturbations. As the global gravity wave activity in the stratosphere depicted in the Figure 1a shows high latitude/polar highs in the present study, it is important to discuss whether there are sources of gravity waves over these regions. The sources for gravity waves over the poles were reported by Sato [2000] and sources in the South Pole by Li et al. [2009]. The major sources discussed by these authors are topography, polar night jets, and wave breaking in the polar vortex. It is observed that high latitudes and poles show maximum gravity wave activity around the region where the polar night jet is situated [Sato, 2000]. Zülicke and Peters [2007] showed that pole ward propagating Rossby waves break in the vicinity of tropospheric jets resulting in the generation of stratospheric Inertio-gravity waves.

Figure 1.

Global map of gravity wave potential energy in the stratosphere (20–40 km) during boreal summer estimated using (a) method 1 and (b) method 2.

[12] After estimating the global map of gravity waves using method 1, we have estimated the same using method 2 as described in section 1. Figure 1b shows the global map of gravity wave potential energy same as that of Figure 1a but obtained using method 2. One can notice the striking difference in these two maps. The magnitudes of gravity wave potential energy estimated using method 1 is approximately four times more as compared to that obtained using method 2. However, both the maps show two regions exhibiting relatively high gravity wave activity, one over Southern Hemispheric high latitudes and another over Northern Hemispheric tropics. These two methods also captured the localized high gravity wave activity near southernmost tip of the South America. The magnitude of secondary peak over Northern Hemispheric tropics is comparable with that of Figure 1a, but over Southern Hemispheric high latitude, the potential energy magnitudes significantly differ. Thus, the global gravity wave activity estimated using two different methods shows significant differences, especially in the potential energy magnitudes. Most of the earlier studies, which are based on SABER measurements, used method 1, whereas COSMIC-based studies employed method 2. Thus, the method used to extract the gravity wave perturbations seems to be the primary reason for observed differences in stratospheric global gravity wave maps reported in earlier studies. To further strengthen this assertion, we have estimated the global map of gravity wave using COSMIC measurements of temperature by employing method 1. Figure 2 shows the global map of gravity wave in the stratosphere (20–40 km) during boreal summer. It is very interesting to note that the gravity wave activity pattern looks very similar to Figure 1a, which also employs method 1. However, SABER measurements are relatively higher in magnitude than that of COSMIC measurements. Thus by employing methods 1 and 2 on the same satellite measurements, we have brought out the importance of background removal procedure for space-based gravity wave studies.

Figure 2.

Same as Figure 1(a) but estimated using COSMIC observations.

5 Discussion and Concluding Remarks

[13] Alexander and Barnet [2007] were first to discuss discrepancies in the global gravity wave maps observed by different satellites in details and attributed the observed differences to the observational filter effects. On the other hand, the present study shows that the global gravity wave maps do depend on the method used to extract the gravity wave fluctuations. However, one cannot rule out the observational filter effects described by Alexander [1998]. The following paragraphs discuss these two aspects in details.

  • 1.Differences in the methods used for extracting the gravity wave fluctuations

[14] The methods used to deduce gravity wave-induced fluctuations in different studies vary from mean trend removal to polynomial fits and filters as discussed in section 1. Each of these methods has its own disadvantages and biases. For example, in polynomial fitting, the fitted polynomial serves as the background and the difference between the polynomial fit and the instantaneous profile gives the gravity wave-induced fluctuations. Depending on the order of the polynomial chosen, several harmonics of the wave will be suppressed. Thus, the polynomial fitting method is subjective to the order used. Filters of various kinds are also commonly employed (high pass, low pass, and band pass) to obtain the gravity wave perturbations. In the present study, we used high pass filter with 10 km cut-off in vertical wavelength. This method has two disadvantages, (1) in addition to gravity waves, equatorial waves that have similar wavelengths will also add on to the tropical high in the potential energy maps. Over the mid and high altitudes also, there is a possibility that planetary wave having wavelengths <10 km can contaminate the gravity wave perturbations and (2) the gravity waves with vertical wavelengths >10 km, which are dominant over the mid/high latitude, will be completely suppressed. In the present study, one can notice the differences in the magnitudes of gravity wave potential energy estimated using SABER observations by employing methods 1 and 2 (refer to Figures 1a and 1b), especially over Southern Hemispheric high latitudes. Method 2, which restricts the gravity wave spectrum in the vertical wavelength domain, heavily underestimates the potential energies estimated from the same satellite observations by employing method 1. However, one should also discuss the disadvantages of method 1, if any. Method 1, which removes the planetary waves with 0–6 wavenumbers, allows all the vertical wavelengths resolved by the satellite and hence represents more realistic gravity wave spectrum in the vertical domain. In this method, spatial structure having wavenumber >6 can leak into the gravity wave filed. For example, planetary waves emanating from the troposphere can break near the polar vortex and the debris of these waves can reflect in the gravity wave field derived using method 1. One more possibility is that the breaking waves near the polar vortex initiating a deep helical tongue of potential vorticity extruded from the polar vortex as reported by the Polvani and Saravanan [2000] using global primitive equation model. This tongue is often observed to roll up into deep isolated columns, which can appear as small horizontal-scale gravity wave structures in the analysis using method 1. Very recently, Yan et al. [2010] reported that large-scale fluctuation structures, which are inconsistent with gravity waves, can be retained in the analysis similar to method 1 in the present study. Further, these authors used an along-track temperature filter to remove these large-scale structures. Thus, the discrepancies in the results from the preceding space-based studies of gravity waves may be explained in the light of the method used for the extraction of gravity wave-induced perturbations. Hence, a uniform method for extracting the gravity wave perturbations is need of the hour to compare the results obtained using various satellites. However, as discussed earlier, each satellite has its own constraints in observing the entire spectrum of gravity waves actually present in the atmosphere. Due to these constraints, apart from differences in the methods followed to extract the gravity wave perturbations, there can be additional differences in the observed global maps of gravity waves observed by different satellites, which is discussed in the following section.

  • 2.Differences in the sensitivity of each satellite technique to the gravity wave spectrum

[15] The satellite sensitivity to the gravity wave spectrum is also an important factor in interpreting the observed global maps of gravity wave activity, which primarily depends on two factors, (1) the weighting function used for retrieving the temperature from the measured line of sight radiance and the (2) spatial (both vertical and horizontal) sampling of the geophysical parameter. Preusse et al. [2002] reported the sensitivity of limb viewers to the gravity wave spectrum and concluded that horizontal wavelengths >200 km and vertical wavelengths >5 km can be detected by the limb viewers such as CRISTA and SABER. As COSMIC uses radio occultation technique, the distance between consecutive profiles over the globe varies largely. But, occultations over a period of time (say a few hours) will give profiles nearby which will be capable of deciphering gravity waves with larger horizontal wavelengths and longer periods. More details on the weighting function and horizontal and vertical resolutions of various satellites are provided by Alexander and Barnet [2007]. In the present study, the global gravity wave map estimated from SABER and COSMIC measurements shows similar pattern with noted difference in the magnitude as shown in Figures 1a and 2, which can be attributed to the sensitivity of the satellite to the given gravity wave spectrum. As mentioned earlier, the sensitivity of the satellite depends on the weighting functions and radiative transfer models adopted for retrieving the geophysical parameter. However, the sensitivity of the satellite seems to be the secondary as compared to the methods used to extract the gravity wave perturbations in explaining the observed differences in the global maps of gravity waves. Thus for the first time, two widely used methods for extracting the gravity wave fluctuations are employed on the same satellite observations, which provided useful insights into the space-based gravity wave observations. The following are the two important outcomes of the present study:

[16] 2.1. Most of the differences observed in the global maps of gravity wave potential energy can be attributed to the method adopted for separating the gravity wave fields from the background. In the present study, a difference of ~15 J/kg is noticed between methods 1 and 2 over southernmost tip of the South America where maximum gravity wave potential energy is observed.

[17] 2.2. If same method is used for extracting the global gravity wave activity using two different satellites, the global pattern seen by the two satellite is very similar with notable differences in magnitudes, which is attributed to the sensitivity of the satellite to the given gravity wave spectrum. In the present study, a difference of ~5–6 J/kg is observed between SABER and COSMIC derived gravity wave potential energies over southernmost tip of the South America.

Acknowledgments

[18] Sherine Rachel John is grateful to ISRO for providing research fellowship for her work. The authors are thankful to the TIMED/SABER and COSMIC/FORMOSAT-3 team for processing the data and making it available and freely downloadable.

[19] The Editor thanks Ding-Yi Wang and two anonymous reviewers for their assistance in evaluating this paper.

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