HIRDLS observations of global gravity wave absolute momentum fluxes: A wavelet based approach

Journal of Atmospheric and Solar-Terrestrial Physics 138-139 (2016) 74–86

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Research paper

HIRDLS observations of global gravity wave absolute momentum fluxes: A wavelet based approach Sherine Rachel John, Karanam Kishore Kumar n Space Physics Laboratory, Vikram Sarabhai Space Centre, Thiruvananthapuram 695022, India

art ic l e i nf o

a b s t r a c t

Article history: Received 7 July 2015 Received in revised form 3 December 2015 Accepted 7 December 2015 Available online 9 December 2015

Using wavelet technique for detection of height varying vertical and horizontal wavelengths of gravity waves, the absolute values of gravity wave momentum fluxes are estimated from High Resolution Dynamics Limb Sounder (HIRDLS) temperature measurements. Two years of temperature measurements (2005 December–2007 November) from HIRDLS onboard EOS-Aura satellite over the globe are used for this purpose. The least square fitting method is employed to extract the 0–6 zonal wavenumber planetary wave amplitudes, which are removed from the instantaneous temperature profiles to extract gravity wave fields. The vertical and horizontal wavelengths of the prominent waves are computed using wavelet and cross correlation techniques respectively. The absolute momentum fluxes are then estimated using prominent gravity wave perturbations and their vertical and horizontal wavelengths. The momentum fluxes obtained from HIRDLS are compared with the fluxes obtained from ground based Rayleigh LIDAR observations over a low latitude station, Gadanki (13.5°N, 79.2°E) and are found to be in good agreement. After validation, the absolute gravity wave momentum fluxes over the entire globe are estimated. It is found that the winter hemisphere has the maximum momentum flux magnitudes over the high latitudes with a secondary maximum over the summer hemispheric low-latitudes. The significance of the present study lies in introducing the wavelet technique for estimating the height varying vertical and horizontal wavelengths of gravity waves and validating space based momentum flux estimations using ground based lidar observations. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Gravity waves Middle atmosphere Momentum fluxes Potential accelerations HIRDLS

1. Introduction The estimation of the vertical flux of horizontal momentum of gravity waves is fundamental to understand their role in controlling the dynamics of the middle atmosphere and has been an active topic of research for several decades. The mean flow acceleration imparted by gravity waves is one of the contributors in driving the long-period atmospheric oscillations such as the Quasi-biennial oscillation (QBO), the Semi-annual oscillation (SAO) in the equatorial middle atmosphere. One of the important parameters associated with gravity waves, which is essential to quantify their interactions with the background atmosphere, is the momentum flux. Realizing the importance of this parameter, several attempts have been made to accurately measure this quantity. Using Doppler radars and other ground based techniques, direct estimation of vertical flux of horizontal momentum of gravity waves have been studied since the early 80's (Vincent and Reid, 1983; Smith and Lyjak, 1985; Fritts and Vincent, 1987; Reid n

Corresponding author. E-mail address: [email protected] (K. Kishore Kumar).

http://dx.doi.org/10.1016/j.jastp.2015.12.004 1364-6826/& 2015 Elsevier Ltd. All rights reserved.

et al., 1988). There have been many studies using ground based as well as satellite based instruments for estimating gravity wave momentum fluxes and their drag in the atmosphere (for instance, Wang and Fritts, 1990; Alexander and Pfister, 1995; Sato and Dunkerton, 1997; Vincent and Alexander, 2000; Fritts and Alexander, 2003; Reid, 2004; Ern et al., 2004; Deepa et al., 2006; Vincent et al., 2007; Alexander et al., 2008; Liu et al., 2009; Alexander et al., 2010; Ern et al., 2011) Over the tropics, there have been a considerable number of studies on gravity wave momentum fluxes and its divergence using ground based remote sensing and in situ observations. At low latitudes, using aircraft measured winds, Alexander and Pfister (1995) computed the vertical fluxes of horizontal momentum over the deep convection and found that there are oppositely oriented momentum fluxes at either side of a possible source region. Sato and Dunkerton (1997) proposed a new method to estimate momentum fluxes using co-spectra of temperature and zonal wind fluctuations. They computed momentum fluxes for Kelvin waves and slowly varying gravity waves and found values in the range 0.02–0.06 m2 s
2 (0.9–2.5 mPa), indicating cancellation of positive and negative momentum fluxes. Vincent and Alexander (2000), using radiosonde observations over the Indian Ocean, reported the

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seasonal and inter-annual variability of gravity waves in the lower stratosphere. These authors followed a similar method as Sato and Dunkerton (1997) to estimate momentum fluxes of gravity waves. But the values they obtained were 4–50 times higher than that of Sato and Dunkerton (1997). Deepa et al. (2006) reported momentum fluxes of gravity waves and the mean flow acceleration over Gadanki (13.5 °N, 79.2 °E) using Rayleigh lidar observations. The momentum flux of observed prominent gravity waves was 0.05–0.1 m2 s
2 (1–2 mPa) below 45 km and 0.1–0.2 m2 s
2 (0.05–0.1 mPa) above this altitude. These authors observed good agreement between the estimated and observed mean flow accelerations. Antonita et al. (2007), in a similar study, using Rayleigh lidar temperature measurements over Gadanki and rocketsonde wind observations over Thumba (8.5°N, 77°E) found momentum fluxes in the range 0.2–0.5 m2 s
2 (0.3–0.7 mPa) in the 30–60 km altitude region. Antonita et al. (2008a) also quantified the role of gravity waves in driving the stratospheric QBO using Rayleigh lidar temperature measurements over Gadanki and NCEP/NCAR reanalysis winds. This study revealed that the contribution of gravity waves towards the westerly phase of the QBO varies from  10% to 60% while that during the easterly phase from 10% to 30%. Using a two-dimensional numerical model, Dunkerton (1997) emphasized the role of gravity waves in driving the QBO. However, this study didn’t provide quantitative assessment of gravity waves contribution towards the observed acceleration in the QBO regime. Ern and Preusse (2009) quantified the role of Kelvin waves in driving the QBO. This study concluded that the Kelvin waves contribute about 20–35% of the expected total wave forcing and indicated that rest of the forcing may be from gravity waves. Further, an attempt was made to derive the gravity wave effect on the QBO using ERA Interim reanalysis data and satellite observations of gravity waves (Ern et al., 2014). Very recently, Kim and Chun (2015a) studied the contributions of the equatorial waves to the QBO using Hadley Centre Global Environment Model version 2 (HadGEM2). These authors used gravity wave parameterization that couples its source spectrum to the convection. Kim and Chun (2015b) reported the momentum forcing of the QBO by equatorial waves using reanalysis data. Antonita et al. (2008b) using meteor wind radar observations of gravity wave momentum fluxes, studied their forcing towards mesospheric semiannual oscillation. In addition, based on satellite data, the forcing of the SAO by gravity waves was discussed by Ern et al. (2015). Thus over the tropical locations, there have been many studies on different aspects of gravity waves and their momentum fluxes/mean flow accelerations. Over the extra-tropics, Tsuda et al. (1990) using MU radar winds over Japan (35°N, 136°E) have shown that the zonal momentum flux induced by gravity waves has the eastward and the westward maxima in July–August and December–February, respectively. Typical accelerations at 70 km altitude range from 7 to 13 m/s/day and from
8 to
11 m/s/day in summer and winter respectively. Another study using MU radar observations reported gravity wave momentum fluxes in the range of  0.1 to 0.3 m2 s
2 (2–6 mPa) in the lower stratospheric region (Fritts et al., 1990). From the same location, Gavrilov et al. (2000) observed typical momentum flux values for internal gravity waves with strong interannual variability. They also observed that the mean wave momentum flux is directed to the east in the summer and to the west in the winter, opposite to the mean wind direction in the middle atmosphere. In high resolution general circulation models also, the convectively generated gravity waves are parameterized (Chun and Baik, 1998, 2002). There have been several attempts in the past to improve the convective gravity wave drag parameterization (Song and Chun, 2008; Choi and Chun, 2011). Using the super pressure balloon experiments over the winter polar vortices of both hemispheres in 2002 and 2005, Vincent

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et al. (2007) reported gravity wave momentum fluxes. The magnitude of momentum fluxes were clearly different in both hemispheres, with mean values of 3.4 mPa observed in the southern hemisphere compared to 2.6 mPa in the northern hemisphere. The values were least over the North pole whereas it was substantially high near the Antarctic peninsula (  10 mPa). They also found that 2/3 of the momentum fluxes over the Antarctic is due to waves of orographical origin. Hertzog et al. (2008) also reported gravity wave information using super balloon observations over the Antarctica and the Southern Ocean. These authors reported significant momentum flux by non-orographic gravity waves equatorward of 60°S where maximum momentum flux is observed from satellite. This study focused on those gravity wave parameters that are relevant to their parameterization in the global models. Even though there have been several studies from ground based instruments at different geographical locations on various aspects of gravity wave momentum fluxes and mean-flow accelerations, global aspects of gravity waves have been emerging from satellite based observations. Using satellite based temperature measurements, there have been considerable amount of studies on global gravity wave momentum fluxes. However, satellite retrievals also pose limitations in terms of desired horizontal and vertical resolutions and observational filter effect (Alexander, 1998).There is also an inherent disadvantage in space based gravity wave momentum flux from current infrared limb-scanning instruments as only the absolute values of momentum fluxes can be retrieved. This is because one cannot deduce the propagation direction of gravity waves and hence the direction of momentum fluxes (Ern et al., 2004). Ern et al. (2004) using CRISTA temperature measurements obtained global maps of gravity wave momentum flux in the lower stratosphere, which showed high degree of variability across the globe. The maximum values of momentum flux are observed over the high latitudes/poles during winter. A comparison with the results of Warner and McIntyre GW parameterization scheme was carried out and the absolute values of momentum fluxes derived from CRISTA are found to be 2–4 times higher. Alexander et al. (2008) also reported gravity wave momentum flux using HIRDLS temperature measurements employing a technique that determines co-varying wave temperature amplitude in adjacent temperature profile pairs, wave vertical wavelength as a function of height using S-transforms and the horizontal wave number along the line joining each profile pair. This method allowed a local estimate of magnitude of gravity wave momentum flux which showed largest magnitudes over the high latitudes in the southern hemisphere in the month of May and smaller but significant values over the summer subtropical latitudes. Wright and Gille (2011) using HIRDLS temperature measurements quantified gravity wave momentum fluxes over monsoon regions across the globe during the years 2005–2007. Alexander et al. (2010) reviewed the recent studies on gravity waves and their effects in stratospheric resolving climate models. This article also reviewed the recent observations and analysis methods to retrieve the global gravity wave momentum fluxes. Very recently, Geller et al. (2013) compared the gravity wave momentum fluxes estimated using space based observations with climate models. This study is the first detailed attempt to quantitatively compare gravity wave momentum flux form climate models with observations. This study reported that satellite observations compare well with model outputs at 20 km whereas at 50 km the former magnitudes are smaller as compared to later magnitudes. These authors also observed that satellite derived momentum fluxes fall off very rapidly as compared to that derived using climate models. However, overall an encouraging agreement was observed between models and satellite derived momentum fluxes. One of the most important missing elements in these studies is

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an attempt to validate gravity wave momentum flux derived from satellite observations using ground based observations. However, there were few attempts in the past to validate the space based gravity wave momentum fluxes using radiosonde (Geller et al. 2013) and super pressure balloons (Hertzog et al., 2012). In this regard, a study has been carried out with a central objective to establish global gravity wave momentum flux in the stratosphere using two years of HIRDLS temperature measurements during 2006–2007. In the present study, satellite based momentum flux observations are compared with ground based LIDAR observations over a low latitude station, Gadanki (13.5°N, 79.2°E). We use wavelet based technique to infer the vertical wavelength of observed gravity waves as a function of height. The ground validation and wavelet based estimations of vertical wavelengths are relatively new aspects as compared to earlier studies. Section 2 describes the different datasets used in the present study. Section 3 discusses the methodologies adopted, Section 4 gives the synthetic work for evaluating the adopted methodology, Section 5 discusses the results and Section 6 provides the summary.

2. Data 2.1. Aura/HIRDLS The NASA Earth Observing System (EOS) Aura satellite was launched on 15 July 2004, with the High Resolution Dynamics Limb Sounder (HIRDLS) as one of its instruments. Useful data from this instrument has been obtained for the period 2005 January to 2007 December. HIRDLS is a multi-channel infrared limb scanning radiometer having 21 channels covering the spectral range 6.12 mm to 17.76 mm. Its height coverage is from 8 to 80 km with separate temperature profiles for both day and night from pole to pole and its latitudinal coverage lies between 62°S to 85°N. In the present study, we have taken temperature observations in the height domain of 20–60 km between the latitudes 60°S and 80°N. More details of the experiment, technical specifications and instrument features can be found in Gille et al. (2008). Overview and characterization of the retrievals of temperature, pressure and other constituents along with their algorithm details are given by Khosravi et al. (2009). After its launch, due to an obstruction in the optical aperture, the mission went through some initial glitches as the signals received at the detectors were contaminated by the blockage. But the retrieval algorithm has been later corrected and incorporated to obtain reliable data. The impact of the blockage on HIRDLS radiances and the correction scheme to remove its contribution to the measured signal is described by Gille et al. (2008). We use HIRDLS measured temperature profile (level 2, version v2.04.09) data for our analysis for two years from 2005 December to 2007 November. The random error of the temperature has been calculated to be between 0.5 K at 20 km and  1 K at 60 km (Yan et al., 2010). Barnett et al. (2008) compared the HIRDLS retrievals with that of COSMIC measurements with emphasis on fine vertical structures and found good agreement between the two. The vertical resolution is  1 km. The horizontal spacing between profiles is  75 to 100 km, which varies from one altitude to other. The satellite is capable of resolving gravity waves having  200 km or greater horizontal wavelength in a very favorable viewing geometry given the observational filter/visibility filter. It may capture smaller wavelengths right from 75 km, but they may be undersampled at times due to the horizontal resolution of the satellite. Owing to the finer spacing of profiles of HIRDLS when compared to other limb viewing satellites like TIMED/SABER, HIRDLS may be capable of better resolving the shorter horizontal wavelengths. Wright et al. (2011) compared the HIRDLS, COSMIC and SABER observations of stratospheric gravity wave induced perturbations.

These authors reported that the gravity wave induced perturbations agrees fairly well among these three satellite observations. 2.2. Rayleigh LIDAR at Gadanki Gravity wave momentum fluxes are estimated using temperature observations of Rayleigh LIDAR at Gadanki for two months, March and November 2007, to compare with momentum fluxes obtained from HIRDLS observations. The LIDAR measurements are obtained as a part of five year long Middle Atmospheric Dynamic (MIDAS) campaign. The details of MIDAS programme along with its objectives can be found in detail in Ramkumar et al. (2006). The Gadanki LIDAR employs an Nd: YAG laser, operated at 532 nm, as the transmitter. The pulse energy is 0.4 J and pulse width is 7 ns. The LIDAR is operated with an altitude resolution of 300m and a pulse repetition frequency of 20 Hz. The system provides backscattered signals, which are integrated over 5000 transmitted pulses, corresponding to an averaging of 250 s in time. More details and technical specifications of the LIDAR are described by Deepa et al. (2006). Estimation of temperature from LIDAR data and the sources of errors are explained in detail by Parameswaran et al. (2000). The statistical error due to signal variance is 1 K in the lower altitudes (27–50 km) and it increases with altitude (2.5K at 65 km). Due to this reason, we have taken measurements from 27 to 60 km which is required for the present study. Inter comparison of estimated gravity wave momentum fluxes is carried out between LIDAR and HIRDLS.

3. Methodology 3.1. Extraction of gravity wave induced fluctuations and momentum flux from HIRDLS observed temperature profiles The primary temperature data used for the present study are obtained from HIRDLS as it provides the best vertical and horizontal resolutions so far available from an infrared limb sounder in space. The day-to-day temperature measurements from HIRDLS are taken for two years from 2005 December to 2007 November and profiles are gridded into 5°  10° grids over the globe for each day. Using this gridded dataset, the amplitude and phases of 0–6 zonal wavenumber planetary waves are estimated using leastsquare fit technique and the same are removed from the instantaneous temperature profiles falling into appropriate grids. By carrying out the background removal separately for ascending and descending modes of HIRDLS, the effects of diurnal tides on the obtained gravity wave perturbations are minimized (Preusse et al., 2001). Further details on the background removal method for extracting gravity wave induced fluctuations can be found in John and Kumar (2012). After obtaining gravity wave induced perturbations, these profiles are further processed to estimate momentum fluxes. The absolute values of momentum flux of gravity waves are calculated ω k by making use of N = m (Ern et al., 2004; Deepa et al., 2006; Alexander et al., 2008; Ern et al., 2011), where ω is the intrinsic frequency of the gravity wave, N the Brunt Vaisala frequency, k is the horizontal and m is the vertical wave vector. The gravity wave momentum flux is given by 2

F=

1 k ⎛⎜ g ⎞⎟2 ⎛ T ′ ⎞ ⎜ ⎟ ρ 2 m ⎝ N⎠ ⎝ T ⎠

(1)

Where ρ is background atmospheric density, g is acceleration due to gravity, T′ is amplitude of gravity wave and T is the local background atmospheric temperature. T′ will correspond to the amplitude of gravity wave which has the horizontal and vertical

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wave vectors k and m, respectively. Thus for estimation of gravity wave momentum flux, it is required to find out the vertical and horizontal wavelengths of the most prominent gravity waves observed by the satellite. To achieve this, gravity wave induced perturbation profiles are subjected to wavelet analysis to obtain height resolved vertical wavelength information. The consecutive profiles along the satellite path are then used to estimate the vertical and horizontal wavelengths as discussed in Ern et al. (2004) and Alexander et al. (2008). However, Ern et al. (2004) employed a combination of harmonic analysis and maximum entropy methods (MEM-HA) to extract height resolved vertical wavelength and Alexander et al. (2008) employed S-transform for this purpose. In the present study, we use Morlet wavelet to extract height resolved vertical and horizontal wavelengths. The Morlet wavelet is basically a sinusoid modulated by a Gaussian, which is widely used in geophysical applications for analyzing localized variations of spectral power within a time series. The vertical profiles of gravity wave induced temperature perturbations with 1 km height resolution are subjected to wavelet analysis in the present study. The perturbations profiles useful for the present study are in the height domain of 20–60 km. We have padded the perturbation profiles with zeros in 10–20 km and 60– 70 km height region to minimize the edge effects. The present analysis procedure thus is able to resolve gravity waves in the vertical wavelength domain of 2–40 km in 20–60 km height region. However, due to variable width of a wavelet function (wider for longer wavelengths and narrower for shorter wavelength), the results have good/poor height and poor/good wavenumber resolution for short/long wavelengths. As mentioned earlier, wavelet analysis provides the height-wavelength information of gravity wave perturbations and the same is used to derive the horizontal wavelengths by using cross spectrum technique. The horizontal resolution of HIRDLS is 75–100 km. However, it varies from one altitude to other due to slanted scan pattern. We have taken separation distance between the two adjacent profiles at each individual height levels to estimate the horizontal wavelengths. Ern et al. (2004) deduced the horizontal wavelength from two adjacent profiles by assuming that these profiles belong to the same gravity wave. By calculating the phase difference between the two adjacent profiles, the horizontal wavelength is estimated as the distance between the two profiles is known. These authors limited their horizontal wavelength estimations to those adjacent profiles having the vertical wavelength difference below 6 km. Alexander et al. (2008) employed the S-transform to obtain height resolved vertical wavelength information. Subsequently, co-spectrum was computed for adjacent S-transformed profiles to obtain the wave amplitude, vertical and horizontal wavelengths of the largest amplitude wave present in both profiles. Wright and Gille (2011) also used similar method to estimate the gravity wave momentum fluxes. We adopt the co-spectrum technique similar to Alexander et al. (2008) in the present study. It is to be remembered that the estimated horizontal wavelength is along the satellite track. This is one of the limitations of satellite based gravity wave momentum flux estimations. Further, the momentum flux formulation by Ern et al. (2004) is based on the linear theory of internal GWs under simple background condition, considering exclusively the upwardpropagation assumption. In the real atmosphere, where background wind and stability change with height, the assumption applied to the linear theory can be violated. Recently, Kim et al. (2012) discussed the impact of downward propagating gravity waves on their momentum flux estimation. These authors, using numerical simulations, showed that the downward propagating gravity waves contribute about 4.5–8.2% of that from upward propagating waves to net momentum flux. So by assuming only upward propagating waves there could be errors in the estimated momentum flux. However this error is relatively smaller

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compared to the errors arising from other limitations discussed earlier. 3.2. Momentum flux from LIDAR observations over Gadanki In order to validate gravity wave momentum fluxes estimated from satellite observations, ground based temperature measurements using LIDAR observations over Gadanki are used. Continuous measurements of temperature for 6–8 h with 4 min temporal and 300 m height resolution in 20–65 km height region during night-time are used for the present study. The mean removed temperature profiles are used to estimate gravity wave momentum flux using Eq. (1), except for the fact that k is replaced by

ω N

m

(where

ω is the intrinsic frequency of gravity waves). How-

ever, in the present study we use Doppler shifted frequency (as we are observing from the ground) rather than intrinsic frequency to derive gravity wave momentum fluxes using lidar observations. The anticipated errors in momentum flux calculations for not using the intrinsic frequencies are discussed in Section 5.1. More details on momentum flux estimations using lidar observations can be found in Antonita et al. (2007).

4. Gravity wave parameter extraction using wavelet and cross spectral approach As discussed in the methodology Section 3.1, HIRDLS temperature measurements are extensively used to estimate gravity wave momentum flux in this study. To evaluate the present method, we generated a test signal as discussed by Alexander et al. (2008). Three gravity wave signals with different vertical and horizontal wavelengths are simulated. The signals are multiplied with three different weighting functions such that they peak at different height regions. The following are the equations used to simulate gravity wave signals,

S1 = 10* exp ⎡⎣ (z−20)2 /ln2/(20 km)2⎤⎦ * sin ( 2πm1z + φ1) S2 = exp [(z−35)/7]* sin ( 2πm2 z + φ2 ) S3 = 5* sin ( 2πm3 z + φ3 ) Where m is the vertical wave number, z is the altitude and φ is the phase. For simulations, we used vertical wave numbers of m1 ¼ 0.5, m2 ¼0.2 and m3 ¼0.1 corresponding to vertical wavelengths of 2, 5 and 10 km respectively and phases φ1 ¼ π/2, φ2 ¼ π and φ3 ¼ 3π/2 corresponding to horizontal wavelength of 400,200 and 133 km respectively (assuming 100 km as the separation between the profiles). Table 1 shows gravity wave parameters used in the simulations. The vertical resolution for simulations is taken as 0.25 km. After simulating gravity waves with abovementioned specifications, all the three signals are added to get the composite signal. Fig. 1(a) shows the height-space section of simulated gravity waves. The x-axis designated as profile number in Fig. 1(a), represents the spatial coordinate. This figure thus represents the temperature fluctuations caused primarily by three gravity waves. Fig. 1(b) shows one of the height profiles of temperature Table 1 Gravity wave simulation parameters. Parameter

Wave 1 Wave 2 Wave 3

Vertical wavelength (km) 2 Horizontal wavelength (km) 400 Maximizing Height (km) 21

5 200 53

10 133 Equal amplitude at all heights

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Fig. 1. (a) Simulated height-space section of gravity wave field using three monochromatic waves as described in Section 4, (b) A typical height profile of simulated gravity wave temperature perturbation, (c) Morlet wavelet spectrum of the simulated gravity waves and (d) cross spectrum of adjacent profiles of the extracted gravity waves from wavelet spectrum.

perturbations, which is used for the wavelet analysis. The signature of all the three simulated waves can be noticed in this profile. Fig. 1(c) shows wavelet spectrum of temperature height profile shown in Fig. 1(b). The wavelet spectrum clearly shows presence of three simulated waves at respective altitudes and wavenumbers. Thus Morlet wavelet provides reliable information on height resolved vertical wavelengths as demonstrated in Fig. 1 (c). The wavelet analysis is carried out on all the six simulated profiles of temperature perturbations. The adjacent height profiles of the retrieved temperature perturbations from wavelet analysis are then used to estimate cross spectrum. Fig. 1(d) shows cross

spectrum of three simulated gravity waves. The height profiles of three simulated wave perturbations are extracted at each time step and then cross spectrum is estimated using two adjacent profiles of each simulated wave. All the three cross spectra peak at respective vertical wavenumbers used in simulations as shown in Fig. 1(d). The phase at the peak amplitude of the cross spectrum is used to estimate the horizontal wavenumber through the relation k¼ Δφ/Δr, where Δr is the separation between two adjacent profiles. It is noted that the horizontal wave numbers used for the simulations are retrieved back using this relation. Thus Fig. 1 demonstrates the method adopted in the present study to retrieve

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height resolved vertical and horizontal wavelengths using Morelet wavelets.

5. Results and discussion 5.1. Validation of HIRDLS measured momentum flux using LIDAR observations over Gadanki There have been attempts to compare gravity wave momentum fluxes estimated using satellite observations with model outputs but not with ground based measurements (Ern et al., 2004). The gravity wave momentum flux obtained from satellite based observations and ground based measurements are compared in the present study. Ground based lidar observations over a low latitude station, Gadanki, are used for this purpose. Earlier studies on gravity waves over Gadanki showed a semiannual variation in gravity wave momentum fluxes with equinoctial maxima (Ramkumar et al., 2006). Keeping this in view, we have estimated momentum flux profiles during the months of March and November 2007 (as September month has very few lidar observations due to clouds, we have chosen November 2007) using the procedure described in Section 3.2. However, before we embark on estimation of momentum fluxes from Lidar for comparison with satellite observations, we have to ensure that gravity waves observed from the two platforms fall in the same range, otherwise the comparison make no sense. Previous studies by Deepa et al. (2006) and Antonita et al. (2007) over Gadanki reported prominent gravity wave periods ranging from 0.5–3 h and 2–4 h respectively. The vertical wavelengths of gravity waves observed over this region are in the 12 to 14 km range as reported by Ern et al. (2004). Using the dispersion relation for mid-frequency gravity wave approximation and assuming brunt vaisala frequency of 0.017 Hz for the stratosphere, we have theoretically estimated the horizontal wavelengths for gravity waves with ground based periodicity ranging from 0.5–6 h and the vertical wavelengths ranging from 1 to 30 km and results are shown in Fig. 2. The horizontal wavelengths for gravity wave periodicities 2–4 h and vertical wavelengths 12–14 km is highlighted by a rectangular box in this figure. Since the horizontal wavelengths are in the range of 400–1000 km, this can be detected and resolved by HIRDLS (Preusse et al. 2002). Thus it is confirmed that the Lidar at Gadanki and HIRDLS can see a similar spectrum of gravity waves and hence the comparison is meaningful. Fig. 3(a) and (b) shows height time sections of mean removed temperature fluctuations from lidar observations on two selected

Fig. 2. Theoretically estimated horizontal wavelengths for gravity waves with periodicity from 0.5 to 6 h and vertical wavelengths from 1 to 30 km using gravity wave dispersion relation.

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days in the month of May 2007. These days are chosen as the wave features are very prominently seen on these days. Each scan is separated by 12 min time interval and height resolution is 300 m. These height-time sections clearly show the upward propagation of gravity waves in the stratosphere with peak amplitudes of  5 K. In Fig. 3(a), gravity wave propagation is predominantly seen in the upper stratosphere whereas in Fig. 3(b) it is seen in the lower stratosphere with the clear downward phase propagation indicating the upward energy propagation. These temperature fluctuations are then used to estimate height profiles of gravity wave momentum fluxes after transforming them into frequency domain using Fourier analysis. In the present analysis, we use ground based frequencies of gravity waves to estimate their momentum flux using formulation discussed in Section 3.2. However, one should use intrinsic frequencies to compute gravity momentum fluxes. The estimation of intrinsic frequency requires background wind information in the direction of wave propagation. The wind measurements as well as direction of wave propagation are not available during the present observations. However by assuming typical horizontal wavelengths ( 1000 km) over Gadanki in the present and previous studies and background wind in the direction of wave propagation (  20 m s
1), we estimated the intrinsic periods for observed periodicities (0.5–4 h). By using typical values for N (0.02 Hz), temperature amplitude (2K) and background temperature (250 K), we estimated expected errors in gravity wave momentum fluxes for not accounting for the Doppler shift of observed frequencies. The observed periods in the present study mostly varied from 0.5 to 4 h and the mean error is around  20% for 1000 km horizontal wavelength and is around  57% for 500 km horizontal wavelength. With these limitations, we have estimated gravity wave momentum flux from lidar observations. Fig. 4(a) and (b) depicts the mean height profiles of gravity wave momentum flux estimated using space based HIRDLS and ground based Lidar observations over Gadanki for the months of March and November, 2007 respectively. We have not compared gravity wave momentum flux case by case as measurements of HIRDLS and Lidar are not coincident in time of the day. The momentum fluxes are multiplied by atmospheric density derived using SABER measurements and presented in mPa (milli Pascal). The horizontal bars represent the standard deviation of the data. In the month of March 2007, we have 10 days of lidar observations whereas 15 days of observations were available in the month of November 2007. HIRDLS observations were available for more than 20 days in each month. The observed gravity wave momentum fluxes are in agreement with the previously reported values over Gadanki by Deepa et al. (2006) which were in the range of 0.05–0.1 m2 s
2 (1–2 mPa) below 45 km and 0.1–0.2 m2 s
2 (0.05–0.1 mPa) above this altitude. Keeping in view that HIRDLS and lidar employ entirely different techniques for temperature measurements, gravity wave momentum fluxes estimated using these two independent techniques compare very well as shown in Fig. 4. We also do not expect a one-to-one correspondence in the momentum flux magnitudes as we know the limitation of satellite based measurements. However, the orders of magnitude are in excellent agreement. Apart from magnitudes, altitudinal variation of gravity wave momentum fluxes is in good agreement between the two. Thus in terms of magnitude as well as in terms of altitudinal variation, both lidar and HIRDLS momentum fluxes compare well. However, the comparison shown in Fig. 4 is dominated by the altitudinal structure of density profile. An attempt is also made to compare the momentum flux profiles without multiplying them by density profiles (figure not shown). These profiles also showed good agreement between LIDAR and HIRDLS measurements. As mentioned earlier, comparison of gravity wave momentum flux measured by space and ground

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Fig. 3. (a) & (b) The height time sections of mean removed temperature perturbation from the lidar observations over Gadanki on two typical days in May 2007.

based observations provided much needed validation for space based momentum flux estimations. However, one has to remember that the comparison shown here is for monthly mean momentum fluxes and there may be notable differences if we compare case by case depending on the direction of propagation of gravity waves with respect to satellite track, which is the cause for under/over estimation of momentum flux by satellite based observations. 5.2. Global maps of absolute momentum fluxes of gravity waves

from HIRDLS After validating HIRDLS measurements, global maps of the absolute momentum fluxes of gravity waves are estimated. Before discussing gravity wave momentum fluxes, we discuss some of gravity wave parameters derived using HIRDLS observations. Fig. 5 (a–c) shows the monthly mean global distribution of gravity wave temperature variance (after removing 0–6 planetary wave contribution), wavelet variances of leading gravity wave component and co-spectral variances respectively at 35 km altitude for the

Fig. 4. The monthly mean height profiles of gravity wave momentum fluxes estimated using HIRDLS and LIDAR over Gadanki for (a) March 2007 and (b) November 2007.

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Fig. 5. Monthly mean global distribution of (a) gravity wave temperature variance (after removing the 1–6 planetary wave contribution), (b) wavelet variances of leading gravity wave component, (c) co-spectral variance for the month of January 2007 at 35 km. Figures (d–f) are also same as figures (a–c) but for the month of July 2007.

month of January 2007. From these figures, it is evident that gravity wave activity is relatively higher over the 60–70°N latitudes. A secondary peak can be seen in gravity wave activity over 10–20°S latitudes. The maximum gravity wave variance observed in Fig. 5(a) is around  16 K2 and it is  10 K2 in Fig. 5(b) which represent the leading gravity wave variance. Further, the maximum co-spectrum variance is found to be 4 K2 from Fig. 5(c). It can be noticed that  37.5% of variance is lost while selecting the leading gravity wave component. A total variance of 75% is lost from observed total gravity wave variance to co-spectrum variance. Fig. 5(d–f) are also same as Fig. 5(a–c) but for the month of July. The gravity wave activity shows its maximum over 50–60°S in the month of July. From these figures, it is evident that 40% of gravity wave variance is lost while selecting the leading gravity wave component. In this case, a total variance of  80% is lost from total gravity wave variance (Fig. 5(d)) to co-spectrum variance (Fig. 5(f)).However, it is noticed that the loss of gravity wave variance changes from one height to other as well as from one month to the other. The reduction of variances between top and middle panels is caused by considering only the strongest wave component in each altitude profile. This reduction is similar to the reductions reported by Ern et al. (2014, 2015). The reduction between middle and bottom panels is also expected and a property of the co-spectral method, which is known to provide lower

estimates of variances and momentum fluxes (Geller et al., 2013). The gravity wave parameters depicted in the Fig. 5(a–f) are estimated for the year 2006 also for studying the interannual variability. The latitude–altitude distribution of all the parameters exhibited similar pattern. However, there were notable differences in their magnitudes. Over the Northern hemispheric high latitudes, the gravity wave variances are larger in January 2006 than that during January 2007. However, over the Southern hemispheric high latitudes the gravity wave variances are larger in July 2007 than that during July 2006. Fig. 6(a–b) shows the global distribution of vertical and horizontal wavelengths of observed gravity waves at 35 km altitudes for the month of January. The cross section of vertical wavelength clearly indicates the dominance of longer vertical wavelengths in the range of 20–30 km over the jet regions and relatively shorter wavelengths in the range of 10–15 km over the equator. The horizontal wavelengths are not showing any preferential occurrences except over the 20–40°S latitudes, where relatively shorter horizontal wavelengths are observed. Fig. 6(c–d) is also same as Fig. 6 (a–b) but for the month of July. The global distribution of vertical wavelength shows the similar features as that of the month of January except that relatively shorter vertical wavelengths are observed over 50–60°S, where relatively large gravity wave activity is observed. Further, the global maps of horizontal

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Fig. 6. Global distribution of gravity wave parameters (a) vertical wavelength and (b) horizontal wavelength at 35 km altitude for the month of January. Figures (c–d) are also same as figures (a–b) but for the month of July 2007.

Fig. 7. Altitude–latitude cross sections of zonal mean (a) gravity wave variance, (b) leading gravity wave component's variance derived using wavelet analysis, (c) co-spectral variance, (d) vertical wavelength, (e) horizontal wavelength, (f) vertical derivative of gravity wave variance and (g) vertical derivative of co-spectral variance for the month of July 2007.

wavelength shows relatively shorter wavelengths over 40–60°N during the month of July. However, relatively large horizontal wavelengths are observed over 55°S latitudes. A band of relatively

larger horizontal wavelengths can be noticed over the equator. However, they are not distinctly different from the high latitude magnitudes. Over the equator, where the satellite path is near

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Fig. 8. (a–l) Global maps of zonal mean gravity wave absolute momentum fluxes in the 20–60 km height region obtained by averaging two years of monthly mean momentum fluxes using HIRDLS observations during December 2005–November 2007. The maps are arranged as panels representing four seasons, namely winter (Dec–Jan– Feb), Vernal Equinox (Mar–Apr–May), summer (Jun–Jul–Aug) and Autumnal Equinox (Sep–Oct–Nov) with respect to the NH.

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meridional, there is a chance of over estimation of horizontal wavelengths. The reasons for observed range of both horizontal and vertical wavelengths may be attributed to the source characteristics of the gravity waves, limitation of satellite based gravity wave observations and the selective filtering by the background winds as discussed earlier. Fig. 7(a–g) shows the altitude–latitude cross sections of zonal mean gravity wave variance, leading gravity wave component's variance derived using wavelet analysis, cospectral variance, vertical wavelength, horizontal wavelength, vertical derivative of gravity wave variance and vertical derivative of co-spectral variance respectively for the month of July. The cross sections of all the variances show their maximum over southern hemispheric high latitudes with a secondary peak over Northern hemispheric sub-tropics. The altitude profiles of variance show sharp gradient at around 40–45 km. The vertical wavelength profiles show the decreasing magnitudes with altitude, whereas horizontal wavelength profiles show little variation with altitude. However, the estimation of vertical wavelength and variance may be affected below 30 km and above 50 km region due to the zeropadding below 20 km and above 60 km. Overall, the vertical derivative of gravity wave variances shows increasing magnitudes with altitude (positive gradient). However, the vertical derivative of co-spectral variance shows decreasing magnitude with altitude (negative gradient) above 45 km over those region where primary and secondary peaks in gravity wave activity is observed. Usually, the gravity wave amplitudes should increase with altitude owing to conservation of momentum, which should yield the positive vertical gradients in their variances. However, if wave breaking takes place then there may be chances of negative vertical gradients as shown in Fig. 7(g). Thus Figs. 5–7 show the gravity wave parameters retrieved using the HIRDLS observations. These quantities are then used to estimate gravity wave momentum flux using the Relation (1). Fig. 8(a–l) shows global maps of the zonal mean absolute gravity wave momentum fluxes in the 20–60 km height region. Each map represents a monthly mean generated by averaging two years of observations during December 2005–November 2007. The maps are arranged as panels representing four seasons, namely Winter (Dec–Feb), Vernal Equinox (Mar–May), Summer (Jun–Aug) and Autumnal Equinox (Sep–Nov) with respect to the Northern Hemisphere (NH). The maps are limited to 60° in the South due to the limitation of the satellite which covers only NH pole completely. The height is restricted to below 60 km as the noise in the measurements above 60 km is prominent in HIRDLS. As the magnitudes of estimated gravity wave momentum fluxes range 4– 5 orders (in Pascal units), we use logarithmic values for better representation. As mentioned earlier, the results below 30 km and above  50 km in Figs. 7 and 8 may be affected by the zero padding applied below 20 km and above 60 km. The global pattern of momentum flux shown in Fig. 8 is very similar to those obtained in previous studies (Alexander et al., 2008; Ern et al., 2011; Geller et al., 2013). In general, the winter hemispheric high latitudes show the maximum gravity wave momentum flux with the secondary maximum over the summer hemispheric low-latitudes. During boreal winter, gravity wave momentum fluxes show their maximum over the NH high latitudes. A secondary maximum is observed over the SH low latitudes. A reversed pattern can be observed during austral winter. However, gravity wave momentum fluxes are stronger over the SH high latitudes as compared to that over the NH high latitudes during respective winters. During the equinoxes, distribution of momentum fluxes makes transition from the high to low latitudes. The observed pattern of the absolute gravity wave momentum fluxes in Fig. 8 is very consistent with earlier reported climatologies (Geller et al., 2013). However, there are differences in magnitudes. At 20 km altitude, Geller et al. (2013) reported the maximum absolute gravity wave

momentum flux using HIRDLS as
1.7(log10 Pa) over the southern hemispheric high latitudes during the month of July. The present results show it to be
1 (log10 Pa). Alexander et al. (2008) reported the absolute gravity wave momentum flux for the month of May, 2006. The maximum magnitudes observed by these authors during the month of May was
2.5 (log10 Pa) over the southern hemispheric high latitudes. In the present study, we observe
2 (log10 Pa) over the same region and period. Thus the absolute gravity wave momentum fluxes reported in the present study are comparable in both magnitude and global pattern with those reported earlier. However, there are notable discrepancies in the observed magnitude, which can be attributed to the methods used to derive the temperature perturbations (after removing the planetary scale waves), the vertical and horizontal wavelengths of gravity waves. Using HIRDLS observations Geller et al. (2013) showed difference in gravity wave momentum flux magnitudes estimated using MEM-HA and S-transform techniques. Wright et al. (2015) discussed the limitations of S-transform in estimating the gravity wave induced temperature perturbations. Thus the methods used to estimate the gravity wave induced perturbations introduce discrepancies in the gravity wave momentum flux estimates. As the absolute global gravity wave momentum flux in the stratosphere depicted in Fig. 8 shows winter 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 planetary wave breaking in the polar vortex. It is observed that the high latitudes and the poles show maximum gravity wave activity around the region where the polar night jet is situated (Sato, 2000; John and Kumar, 2012). Zülicke and Peters (2007), showed that poleward propagating Rossby waves break in the vicinity of tropospheric jets resulting in the generation of stratospheric inertiogravity waves. A secondary maximum observed over the low latitudes in the summer hemisphere can be due to the large convective activity taking place over these regions during this season (Alexander and Pfister, 1995). Thus Fig. 8 depicts the monthly variation of global gravity wave momentum fluxes in the stratosphere. Two years of global gravity wave momentum fluxes are used to study the interannual variation over the high latitudes and equator (figure not shown). It is observed that gravity wave momentum fluxes exhibit annual oscillations over the high latitudes with peak amplitudes during the winter season and semiannual oscillation especially in the 50–60 km height region over the equator with two comparable peaks during vernal and autumnal equinoxes. The SAO in gravity wave momentum fluxes over the low latitudes was reported by Antonita et al. (2007) using lidar observations over Gadanki. These authors also quantified gravity wave forcing towards SAO. Further, the SAO in the stratospheric winds, temperature and ozone over low latitudes was reported by Kumar et al. (2011). Very recently, Ern et al. (2015) by making use of HIRDLS measurements derived gravity wave momentum fluxes and drag in order to investigate the interaction of gravity waves with the SAO. These authors emphatically showed that gravity waves contribute to the SAO momentum budget mainly during eastward wind shear, and not much during westward wind shear. Thus the present observations of SAO in gravity wave momentum fluxes over the equatorial latitude are consistent with the earlier results. Unfortunately, due to lack of sufficient data from HIRDLS, we cannot investigate the signature of QBO in gravity wave momentum fluxes. However, Ern et al. (2011, 2014) and John and Kumar (2012) reported the QBO in gravity wave momentum fluxes and potential energies respectively.

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Following the calculation of the absolute momentum fluxes of gravity waves, one can estimate the potential acceleration of these waves. The calculation of acceleration imparted by gravity waves is described in detail by Fritts and Alexander (2003). In the present study, only the absolute values of acceleration known as potential acceleration can be calculated assuming that those gravity waves propagate opposite to the winds (Ern et al., 2011). The primary purpose of assessing mean-flow accelerations due to gravity waves from observations is due to its significance in their parameterization in general circulation models. The assessment of model outputs of gravity wave induced acceleration with observations and providing feedback to the model based on the differences between the two will help in improving gravity wave parameterization schemes in the global models. However, sign and direction of gravity wave drag cannot be distinguished from the present calculation, which are essential to understand impacts of gravity waves on large-scale circulation. It is envisaged that the future space based observations of gravity waves can resolve these issues so that their impact on middle atmospheric dynamics can be studied quantitatively.

6. Summary Two years of temperature measurements (2005 December– 2007 November) from HIRDLS onboard EOS-Aura satellite are used to estimate the absolute momentum fluxes of gravity waves over the globe. The capability of HIRDLS to detect and resolve gravity waves is investigated in this study using gravity wave simulations. The least square fitting is employed to estimate 0–6 zonal wavenumber planetary wave amplitudes and the same is subtracted from the instantaneous profiles to extract gravity wave fields from HIRDLS measured temperature profiles. The wavelet and cross spectrum technique is then used on temperature perturbations from consecutive profiles for estimation of the vertical and the horizontal wavelengths of gravity waves respectively. Gravity wave momentum fluxes are calculated using temperature perturbations, the vertical and the horizontal wavelength of observed gravity waves. Gravity wave momentum fluxes obtained from satellite measurements are compared with that obtained from ground based Rayleigh lidar over a low latitude station, Gadanki. The range of prominent horizontal and vertical wavelengths at Gadanki is generated using observed gravity wave periods and dispersion relation. It is ensured that both lidar and HIRDLS can observe the same spectrum of gravity waves. The comparison of gravity wave momentum fluxes measured using HIRDLS and lidar are in good agreement. However, we used Doppler shifted frequency rather than the intrinsic frequency of gravity waves to estimate their momentum fluxes using lidar observations as there were no middle atmospheric wind observations over the observational site. However, even having the wind information would not be sufficient to estimate intrinsic frequencies as one should know the direction of propagation of gravity waves. Global maps of the absolute momentum fluxes, the horizontal and the vertical wavelengths and cross spectral amplitudes are constructed. After validating space based gravity wave momentum fluxes, their monthly mean latitude-height sections are constructed using two years of observations. It is found that the winter hemisphere has the maximum absolute momentum flux magnitudes over the high latitudes with a secondary maximum over the summer hemispheric low latitudes. During the equinoctial months, the transition of high momentum fluxes from winter hemisphere to summer hemisphere is observed. The two year time-series of momentum flux are used to study their interannual variability. It is observed that over the high-latitudes, gravity wave momentum flux exhibits annual oscillations in both the

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hemispheres and over equator they show semiannual oscillation. Thus the present study discussed space based gravity wave momentum flux observations, which can have implications in assessing the global model outputs and providing feedback for better gravity wave parameterization schemes.

Acknowledgments Sherine Rachel John is thankful to ISRO for providing Research Fellowship for her work. The authors are thankful to the AURA/ HIRDLS team for the freely downloadable data and to NARL, Gadanki, for the Lidar data during the MIDAS period used in this study.

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