We investigate stratospheric gravity wave observations by the
Atmospheric InfraRed Sounder (AIRS) aboard NASA's Aqua satellite and
the High Resolution Dynamics Limb Sounder (HIRDLS) aboard NASA's
Aura satellite. AIRS operational temperature retrievals are
typically not used for studies of gravity waves, because their vertical and
horizontal resolution is rather limited. This study uses data of a
high-resolution retrieval which provides stratospheric temperature
profiles for each individual satellite footprint. Therefore the
horizontal sampling of the high-resolution retrieval is 9 times
better than that of the operational retrieval. HIRDLS provides 2-D
spectral information of observed gravity waves in terms of
along-track and vertical wavelengths. AIRS as a nadir sounder is
more sensitive to short-horizontal-wavelength gravity waves, and
HIRDLS as a limb sounder is more sensitive to short-vertical-wavelength
gravity waves. Therefore HIRDLS is ideally suited to
complement AIRS observations. A calculated momentum flux factor
indicates that the waves seen by AIRS contribute significantly to
momentum flux, even if the AIRS temperature variance may be small
compared to HIRDLS. The stratospheric wave structures observed by
AIRS and HIRDLS often agree very well. Case studies of a mountain
wave event and a non-orographic wave event demonstrate that the
observed phase structures of AIRS and HIRDLS are also similar. AIRS has a
coarser vertical resolution, which results in an attenuation of the
amplitude and coarser vertical wavelengths than for
HIRDLS. However, AIRS has a much higher horizontal resolution, and
the propagation direction of the waves can be clearly identified in
geographical maps. The horizontal orientation of the phase fronts
can be deduced from AIRS 3-D temperature fields. This is a
restricting factor for gravity wave analyses of limb
measurements. Additionally, temperature variances with respect to
stratospheric gravity wave activity are compared on a statistical
basis. The complete HIRDLS measurement period from January 2005 to
March 2008 is covered. The seasonal and latitudinal distributions of
gravity wave activity as observed by AIRS and HIRDLS agree well. A
strong annual cycle at mid- and high latitudes is found in time
series of gravity wave variances at 42 km, which has its maxima during
wintertime and its minima during summertime. The variability is largest during
austral wintertime at 60∘ S. Variations in the zonal winds at 2.5 hPa are associated
with large variability in gravity wave variances. Altogether,
gravity wave variances of AIRS and HIRDLS are complementary to each other. Large parts of the gravity wave
spectrum are covered by joint observations. This opens up
fascinating vistas for future gravity wave research.
Introduction
By driving the general circulation, the thermal structure and middle-atmosphere chemistry are influenced significantly by atmospheric gravity
waves . The
generation and propagation of gravity waves depend on the sources and
atmospheric conditions. Gravity waves are primarily generated due to
orography, like mountain waves
(; ; ; ), and as a result of deep
convection . Additionally,
gravity waves originate due to body forcing, which comes along with localized
wave dissipation, and wave–wave interaction and due
to wind shear, adjustment of unbalanced flows near jet streams and frontal
systems . Gravity wave source
processes can emit a broad spectrum of waves. For example, it is known that
deep convection excites a broad spectrum of gravity wave phase speeds
e.g.,, as well as a broad range of gravity wave vertical
and, in particular, horizontal wavelengths. There are indications that the
horizontal scales range from several tens to several hundreds of kilometers
e.g.,. Similarly, gravity waves
emitted from jets and fronts cover horizontal wavelengths from less than
100 km to more than 500 km e.g.,and references
therein, and the horizontal scales of mountain waves
cover a range of less than 10 km to several hundred kilometers
e.g.,and references therein. Most global
atmospheric models use gravity wave parameterizations because gravity waves
are small-scale phenomena and cannot be resolved or are only poorly resolved
in the models. Satellite observations are well suited to validate gravity
wave parametrization schemes of general circulation models. In addition,
characteristics of gravity waves can be investigated in global studies with
satellite observations
.
were the first to demonstrate that satellite remote
sensors can observe gravity waves. The number of instruments with
sufficient spatial resolution to observe gravity waves has increased
over the last years. An important limitation of satellite observations
is that each instrument type can only detect a certain part of the
full vertical and horizontal wave number spectrum of gravity
waves. , , and give overviews and comparisons of different observation methods and the range
of detectable vertical and horizontal wavelengths. Advantages and
disadvantages of limb measurements vary in contrast to nadir
instruments. Limb instruments have a good vertical resolution, which
leads to high sensitivity to short-vertical-wavelength waves. However,
the sensitivity for short horizontal wavelengths is reduced due to the
limited horizontal resolution of current limb sounders
. Furthermore, a single measurement track cannot be
used to identify the horizontal propagation direction of the
waves. Nadir instruments observe only gravity waves with long vertical
wavelengths, but the horizontal resolution is better than that of
limb instruments. Given the sensitivity limitations of different atmospheric sounding techniques from satellite, it is evident
that a single technique is not capable of covering the whole spectral range of atmospheric gravity waves. As has been discussed
by, for example, and , combination of different measurement techniques can help to obtain a
more complete picture of the whole spectrum of gravity waves. Still, the range of very short horizontal wavelengths (< 30 km)
and vertical wavelengths around 5–10 km is not covered by these standard satellite measurement techniques and requires other
techniques such as radiosondes or airborne observations e.g.,.
For studies of atmospheric gravity waves, Atmospheric InfraRed Sounder (AIRS) radiance measurements
are suitable. The long-term time series of AIRS radiance
measurements offers the opportunity to study gravity wave occurrence
frequencies and other characteristics climatologically and on a global
scale . AIRS operational
temperature retrievals are typically not used for gravity wave
research. A main drawback is their limited horizontal resolution
related to the cloud-clearing procedure. This procedure facilitates
retrievals in the troposphere by combining radiance measurements of
3 × 3 footprints to reconstruct a single cloud-free
spectrum. This causes a substantial loss of horizontal
resolution. Nevertheless, stratospheric 3-D temperature fields with a
high spatial resolution can be retrieved from AIRS radiances. The AIRS
high-resolution retrieval of provides a temperature
data set which is considered optimal for stratospheric gravity wave
studies. performed a comparison between the AIRS
high-resolution stratospheric temperature retrieval, the AIRS
operational Level 2 data, and the ERA-Interim reanalysis
on the basis of nine measurement years (2003–2011). That study showed
that the AIRS high-resolution retrievals reproduce mean and standard
deviations of ERA-Interim stratospheric temperatures with good
accuracy. Zonal average differences tend to be mostly below ±2 K. used the AIRS high-resolution retrievals to study
interactions of gravity waves with the El Niño–Southern
Oscillation (ENSO). investigated interactions of
gravity waves with the Madden–Julian Oscillation (MJO) using the same
data set. and applied 3-D spectral
analysis techniques to the AIRS high-resolution retrievals, thereby
estimating directional gravity wave momentum flux.
By using the limb sounding technique, the High Resolution Dynamics Limb Sounder (HIRDLS) is sensitive to
short-vertical-wavelength gravity waves and is therefore ideally suited to
complement AIRS observations. HIRDLS temperature observations have
been widely used to study the global distribution of gravity waves. In
particular, absolute gravity wave momentum fluxes are derived from
information about gravity wave vertical and horizontal wavelengths
. Based on these momentum fluxes,
the intermittency in gravity wave global distributions was studied
e.g.,, as well as the interaction of
gravity waves with the background circulation
e.g.,. In addition used HIRDLS
data to compare gravity wave momentum fluxes in models and those
derived from observations. The main advantage of HIRDLS is that 2-D
spectral information of observed gravity waves is provided in terms of
along-track and vertical wavelengths. This information has been
utilized for studying the average spectrum of gravity waves in
different regions e.g.,. We will
use this information here to comprehensively compare AIRS and HIRDLS
gravity wave observations, which is the main aim of our study.
The AIRS and HIRDLS instrument characteristics and the gravity wave
observations are introduced in Sect. . We explain the
detrending method and noise corrections that we used to estimate
gravity wave variances from AIRS and HIRDLS observations. Further,
nadir and limb observation geometries are compared regarding their
sensitivities to gravity horizontal and vertical wavelengths. In
Sect. we present case studies of coincident AIRS and
HIRDLS gravity wave observations and comparisons of time series of
gravity wave variances from AIRS and HIRDLS during 2005 to 2008. In
addition, the influence of the AIRS observational filter is
investigated. In Sect. we will draw conclusions and
give an outlook.
Data and methodsAIRS and HIRDLS observations and temperature retrievals
The Aqua satellite is part of NASA's Earth Observing System and the
first satellite in the A-Train constellation. The flight altitude of
Aqua is 705 km, and it performs in a sun-synchronous polar orbit with
an inclination of 98∘ and a period of 99 min. On board NASA's
Aqua satellite, six instruments are included, and one of them is
AIRS (). Thermal emissions of atmospheric
properties in the nadir and sub-limb geometry are measured by
AIRS. AIRS completes 14.5 orbits per day. At 01:30
(descending orbit) and 13:30 (ascending orbit) local time the
Equator crossing occurs. AIRS has across-track scanning
capabilities. One scan covers 1780 km ground distance with 90
individual footprints. The scans are performed in 2.667 s, and the
along-track distance is 18 km. Granules of 6 min measurement
time, i.e., 135 scans or 12 150 footprints, are accumulated in the AIRS
measurements. A total of 2.9 million radiance spectra are globally detected by
AIRS within 1 day. The measurement coverage of the AIRS instrument
is almost complete since the observations started in September
2002. The analysis of this study is based on measurements during
January 2005 to March 2008, which is the measurement period of HIRDLS.
Aqua carries different instruments, which measure radiation in the
near and mid-infrared and the microwave spectral regions
. Several retrieval
algorithms transform the calibrated radiances into geophysical
quantities . The original resolution of
the AIRS radiance measurements (Level 1 data) is reduced during the
operational retrieval (Level 2 data) by a factor of 3 × 3
(along track × across track). In doing so, the retrievals are
extended into the troposphere and cloud clearing is performed
. Several linear and nonlinear
operations on the infrared and microwave channels are required for the
cloud-clearing algorithm. The algorithm performs on blocks of
3 × 3 AIRS footprints. The clearest field of view in the
3 × 3 block is selected, and a single cloud-cleared infrared
spectrum for the block is computed . Validation of AIRS
operational retrievals for the troposphere provide an accuracy which
is near the anticipated absolute accuracy of 1 K root mean square
over a 1 km layer . A root mean
square deviation of 1.2 and 1.7 K is found in the troposphere and
lower stratosphere, respectively, by comparing AIRS with radiosondes
.
A high-resolution retrieval scheme for stratospheric temperatures
based on AIRS radiance measurements was developed by
. This retrieval scheme provides a temperature
profile for each individual footprint, corresponding to a horizontal
sampling that is 3×3 times better than the operational
retrieval data provided by NASA. While the operational retrievals are
tightly constrained in the stratosphere, the high-resolution retrieval
configuration offers an optimal opportunity for gravity wave analyses,
because spatial resolution and retrieval noise are balanced in the
results by an optimized retrieval configuration. The altitude range of
the retrieval is from 10 to 70 km with a 3 km sampling below 60 km
altitude and 5 km above. In the stratosphere the high-resolution
retrieval has a vertical sampling which is the same as the AIRS operational
retrieval grid. Based on the assumption of hydrostatic equilibrium and
using a given reference pressure from the AIRS operational retrieval at 30 km altitude, the pressure profile is calculated, whereas the
temperature profile is retrieved. In the altitude range between 20 and 60 km
the noise of the high-resolution retrieval is about 1.4 to 2.1 K, and
the total retrieval error, which includes several systematic errors,
is 1.6 to 3.0 K. In this altitude range the retrieval achieves the
most reliable results, which is indicated by the retrieval
diagnostics. There are about 5–6 degrees of freedom for signal in the
retrieved profiles. The vertical resolution varies between 7 km at 20 km altitude and about 15 km at 60 km altitude.
The retrieval setup of the AIRS high-resolution retrieval
distinguishes between day- and nighttime conditions. The Juelich Rapid
Spectral Simulation Code (JURASSIC) model is used
for radiative transfer calculations. This model assumes local
thermodynamic equilibrium (LTE), which restricts the study of daytime
measurements to the 15 µm channels. The 4.3 µm channels are
affected in the daytime by non-LTE effects due to solar excitation of CO2
molecules . Non-LTE effects are not noticed in
nighttime measurements of AIRS. Therefore the nighttime retrieval uses both
wavebands. Lower retrieval noise and better vertical resolution of the
nighttime retrievals than the daytime retrievals is the
consequence. The data in this study were split into day- and nighttime,
depending on the solar zenith angle, and only the nighttime data were used. The retrievals consider values
larger than 108∘ as nighttime data. Note that especially
throughout polar summer at high latitudes this restriction leads to
data gaps.
HIRDLS is a 21-channel
infrared limb-scanning radiometer aboard NASA's Aura satellite
, which is part of the A-Train constellation of NASA satellites, too. Therefore AIRS and HIRDLS cross the same
geographic locations within a few minutes. Aura was launched on 15
July 2004 in a sun-synchronous polar orbit. Aura has an inclination of
98∘ at a flight altitude of 705 km. During launch, HIRDLS was damaged and it was not possible to scan in azimuth, which would have given 3-D
capabilities . Instead, the line of sight of HIRDLS is fixed to an azimuth of -47∘ with respect to the orbit plane, resulting
in a latitudinal coverage of about 63∘ S to
80∘ N. In order to resolve the issues that were caused by this damage, extensive corrections to the processing algorithms have been
performed . Along-track distances between subsequent altitude
profiles are down to only 100 km because the line of sight of HIRDLS
is fixed. This remarkably fine along-track sampling offers a great
opportunity for the analysis of gravity waves. Measurements of thermal emissions with
1 km vertical resolution are made in four channels on the long-wave side of the 15 µm
bands, from which the temperature is retrieved as a function of pressure . The fractional cover-up of
HIRDLS's field of view induces perturbations of the measured atmospheric limb
radiances, which have been eliminated . Temperature
retrievals are provided for January 2005 to March 2008. HIRDLS
measures in an altitude range between the tropopause region and the
upper mesosphere on a pressure grid with 121 levels. The vertical field of view of the instrument is 1 km, which is
achieved as vertical resolution between 13 and 60 km from the measured temperature–altitude
profiles . Our analysis uses retrieval products
obtained with NASA processing software. HIRDLS temperature
retrievals are carefully validated. Comparisons between HIRDLS and
SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) and between HIRDLS and ECMWF (European Centre for
Medium-Range Weather Forecasts) temperatures indicate that HIRDLS has a
warm bias at the tropical tropopause. In the stratosphere HIRDLS
temperatures are within 1 K of ECMWF temperatures, within 1–2 K of
Microwave Limb Sounder temperatures, and within 2 K of lidar
temperatures .
Removal of background signals to extract gravity wave
information
This paper partly focuses on statistical comparisons of temperature
variances related to stratospheric gravity wave activity. The total
variance (σtot2) of the satellite temperature measurements typically consists of three components: the variance of gravity
waves (σgw2), of background signals (σbg2), and
of noise (σnoise2).
σtot2=σgw2+σbg2+σnoise2
To eliminate the background signals from the temperature measurements
and to receive gravity wave signals, a detrending procedure is
necessary. Large-scale latitudinal temperature gradients and planetary
wave activity are linked with the background signals. For AIRS a local detrending method is applied, whereas a global detrending method has
been used for HIRDLS. Both methods are standard methods that have been optimized for each instrument. The removal of
background signals in AIRS temperature measurements follows the
detrending method described by , , and
. A fourth-order polynomial fit in the across-track
direction is used in this method for defining the
background. Perturbations are calculated by subtracting the polynomial
fit from the raw brightness temperature data. Here we transferred the
method to temperature retrievals and applied the fit independently for
each altitude. Note that this procedure tends to suppress wave fronts which are parallel to the across-track direction, but only if the
wave patterns cover most of the AIRS measurement track. Small-scale wave patterns of gravity waves with short along-track wavelengths
are typically not affected. This effect can possibly be
reduced if the background is smoothed along-track. However, in the case of
extreme latitudinal gradients in the temperature fields, e.g., at the
polar vortex edge, other problems can be introduced by smoothing. Therefore
along-track smoothing was not considered here.
The background removal applied to HIRDLS temperatures comprises
several steps. For a fixed latitude and altitude, the data set is
subdivided into overlapping time windows of 31 days length. For these
31-day time windows, the zonal mean temperature and trend are removed,
and 2-D spectra in longitude and time are estimated. By
back-transformation of these spectra for the spectral components
exceeding an amplitude threshold, the contribution of planetary waves
with zonal wave numbers up to 6 and periods as short as about 1.4 days
is calculated for the precise location and time of each HIRDLS
observation and subtracted. Further, the altitude profiles are
vertically filtered in order to remove oscillations with vertical
wavelengths longer than about 25 km. The whole procedure is described
in more detail in . At the end of the procedure
quasi-stationary zonal wave numbers 0–4 are subtracted to remove the
significant tidal modes, thereby distinguishing ascending and descending orbits . The final altitude profiles of
temperature fluctuations thus obtained are traced back to mesoscale
gravity waves.
It is difficult and always some kind of trade-off to distinguish in
observations between planetary waves and gravity waves. Therefore for both
AIRS and HIRDLS a minor contribution of the background variances is
caused by gravity waves, depending on the method of background
removal. For AIRS, the background may contain minor contributions of
gravity waves with long horizontal wavelength, while for HIRDLS the
background will contain minor contributions due to gravity waves with
long vertical wavelengths. Still, at most latitudes the background
variances will be dominated by global-scale waves. The variances are
calculated from the fluctuations relative to a zonal average for a
fixed altitude and latitude ±0.5∘. Figure shows latitudinal time series of the
AIRS and HIRDLS background variances during the measurement period
between 2005 and 2008 at 42 km altitude. The overall structure of the background signals in
both data sets is rather similar. An annual cycle at high latitudes is
detected which has its maxima during wintertime and its minima during summertime. The maximum in both data sets is up to 270 K2 around
50 to 60∘ N/S. The activity of planetary waves is
weaker in the Southern Hemisphere winter, and in the Southern
Hemisphere the polar vortex is more invariant than in the
Northern Hemisphere e.g.,. This is represented by the
background variances, which are larger in Northern Hemisphere winter
than in Southern Hemisphere winter.
Time series of monthly mean temperature background
variances for measurements between 2005 and 2008 at 42 km
altitude. (a) AIRS high-resolution retrieval. (b) HIRDLS
operational retrieval. Data gaps in AIRS data (white areas) are
related to the restriction to nighttime measurements.
Estimation of retrieval noise
Temperature variances are notably affected by noise if long time spans
or large areas are analyzed. Therefore it is fundamental to carefully
characterize retrieval noise. For AIRS the noise was estimated
directly from the measurements using the method of ,
following the approach of .
presented a generic technique for noise estimation developed for image
analysis. Individual noise estimates are obtained for each AIRS
granule and each altitude. The temperature data are convolved with a
3 × 3 pixel filter mask which eliminates image structures. The
variance of the filtered data is calculated, which gives an
approximation of the noise. Note that it is possible to misinterpret plane waves with very short
horizontal wavelengths as noise with the method
of , because thin lines are eventually recognized as
noise. However, based on inspection of the data, we concluded that this
issue does not affect our analysis.
Figure shows global mean noise estimates for the
temperature measurements of AIRS and HIRDLS on individual days. The
noise estimate for AIRS is about 1.0 K at 24 km altitude and
increases to 2.2 K at 55 km altitude. Seasonal differences of 10 %
are found, with lowest values in January and highest values in
July. Noise profiles for April and October are similar and located in
between. These direct noise estimates from the temperature data agree
well with the estimated retrieval noise, which is about 1.4 to 2.1 K
in the altitude range between 20 and 60 km
. Gravity wave variances of AIRS are corrected by
subtracting the squared noise estimate from the temperature
variances. For HIRDLS both a measured and a predicted precision are
provided. The predicted precision corresponds to the expected
uncertainty of the retrievals based on uncertainty of the input
parameters. This includes not only the radiance noise but also other
parameters, e.g., forward-model errors . The theoretically estimated temperature
precision of HIRDLS has no seasonal variability and is about 0.6 to
1.7 K, increasing with altitude (see
Fig. ). When the noise estimate of HIRDLS and AIRS is compared, the values of HIRDLS are quite low, and therefore noise is
not corrected for in our HIRDLS analysis.
Estimated global mean noise profiles for AIRS (a) and
HIRDLS (b).
Sensitivity functions of AIRS and HIRDLS
Each type of current satellite instruments can detect only a certain
part of the full vertical and horizontal wave number spectrum of
gravity waves, which is determined by its observational filter
.
For AIRS the sensitivity to vertical and horizontal wavelengths was determined using an approach similar to . In the vertical
direction, temperature profiles representing wave perturbations have been convolved with the averaging kernel functions of the retrieval
to take into account the smoothing effects. In the horizontal direction, the polynomial fit detrending method has been applied to simulated
wave perturbations in the across-track direction in order to quantify the potential filtering of large-scale features. In both cases, the
sensitivity to the given wavelengths was determined by calculating the ratio of the variances of the filtered and unfiltered perturbation
data. Here we varied the wave phases over all possible values when we calculated the variances.
The sensitivity function of the current generation of limb sounders is really two-dimensional
and the sensitivity for horizontal, and vertical wavelengths cannot be
estimated independently. The calculation of the HIRDLS sensitivity
function follows the approach of and , with additional
vertical filtering being applied. This additional filtering was added
because in the analysis by gravity wave amplitudes are
determined in sliding windows of 10 km vertical extent. Amplitudes
with vertical wavelengths longer than 25 km cannot be reliably
determined from those windows, and therefore only vertical wavelengths
up to 25 km are used in the vertical analysis of altitude
profiles. This vertical analysis is a two-step approach utilizing the
maximum-entropy method for identifying the dominant vertical
oscillations, followed by a harmonic analysis (MEM/HA). For more
details see . As a secondary aspect, the vertical filtering
will further reduce contamination by planetary waves in the polar
vortex. These waves usually have long vertical wavelengths of around
40 km or longer.
Figure illustrates the sensitivity functions for AIRS
and HIRDLS for gravity wave temperature variances. Only waves with
horizontal wavelength longer than 20 km can propagate from the
troposphere into the stratosphere ; therefore the
horizontal wavelength in the plots are cut below 20 km. The
sensitivity of AIRS exceeds the 20 % level for vertical wavelengths
longer than 15 km and horizontal wavelengths shorter than
1280 km. Highest sensitivity is found for long vertical and short
horizontal wavelengths, as expected for a nadir sounder. In contrast,
the observational filter of HIRDLS shows the typical picture for limb
sounders with high sensitivity for short vertical and long horizontal
wavelengths. The 20 % level of sensitivity is exceeded for vertical
wavelengths longer than 2 km and shorter than 39 km and for
horizontal wavelengths longer than 140 km. The horizontal wavelengths
considered in the HIRDLS sensitivity function are the wavelengths
along the line of sight of the satellite. The true wavelength is
usually shorter than this projection. Therefore limb sounders can
detect gravity waves with even shorter horizontal wavelength than
suggested by the sensitivity function. When assuming that horizontal wave
vectors of observed gravity waves are randomly distributed, the
average horizontal wave number is underestimated by a factor of
2, giving a rough measure of how much shorter observed true
horizontal wavelengths could be on average. Similar values for HIRDLS are found by .
AIRS (a) and HIRDLS (b) observational filters
indicate the sensitivity of temperature variances to gravity waves
with different horizontal and vertical wavelengths. The black
lines show a momentum flux factor (see text for details).
Supposing the same relative potential temperature amplitudes for two
waves with different values of horizontal and vertical wavelengths,
waves with short horizontal and long vertical wavelength can
potentially carry more gravity wave momentum flux. We calculated a
momentum flux factor M(kh,m), which gives a rough estimate of how much
waves of different horizontal and vertical wave numbers kh and m
could possibly contribute to momentum flux,
Fph=M(kh,m)×T^T2,
for a given normalized wave amplitude T^/T. Following
, the momentum flux factor is calculated according to
3Mkh,m=12ρgN2khmAB,A=1-ω^2N2×1+1m212H-gcs22-14×1+fmω^212H-gcs221/2,5B=Θ^/Θ¯2/T^/T¯2,
with density ρ, gravity acceleration g, buoyancy frequency N,
intrinsic frequency ω^, scale height H, sound speed cs,
Coriolis parameter f, and potential temperature Θ. The black
contour lines shown in both panels of Fig. indicate
the normalized momentum flux factor, M′(kh,m)=M(kh,m)/Mmax,
which is normalized by the maximum value Mmax that occurs in the
range of horizontal and vertical wavelengths shown. The normalized
momentum flux factor can attain values between near 0 and 1. Of course
the normalized momentum flux factor is just a scaling factor that does
not provide information about the relative occurrence rate of waves
with given horizontal and vertical wavelengths in the atmosphere.
Here we give an example of the importance of the momentum flux factor
in interpreting the AIRS and HIRDLS gravity wave
observations. When assuming that HIRDLS observes a gravity wave with
600 km horizontal wavelength and 6 km vertical wavelength (which is
well within its sensitivity range), the corresponding normalized
momentum flux factor is 0.02. Further, assuming that AIRS observes a
gravity wave with 200 km horizontal wavelength and 30 km vertical
wavelength, the corresponding normalized momentum flux factor is
0.26. The gravity wave observed by AIRS would contribute a factor 10
more momentum flux than HIRDLS if both had the same amplitude.
Comparison of AIRS and HIRDLS gravity wave observationsCase studies of individual wave events
Following , in this section individual gravity wave
events in the AIRS data are compared with HIRDLS observations at the
same location and at a similar time. Overpass times of the same
geographic locations are within minutes of each other for AIRS and HIRDLS, because
both are members of the A-Train constellation of NASA satellites. However, based
on their different viewing geometries, AIRS as a nadir sounder and
HIRDLS as a limb sounder with fixed azimuth angle of -47∘, the
times where AIRS and HIRDLS see the same geographic locations differ
by about 100 min. The gravity wave patterns can change substantially
on timescales of 100 min, in particular in the case of gravity waves from non-orographic sources with
high frequencies and fast group velocities. The phase
structure of mountain waves is more likely invariant in a 100 min
interval than that of waves from other sources, because they are
stationary relative to the ground. Mountain waves are therefore best
suited for a direct comparison of AIRS and HIRDLS data. Additionally to the effect due to the local time differences between the
two data sets a second effect due to the considered data has to be taken into account. For AIRS only the descending node is considered
(only nighttime data), while for HIRDLS both ascending and descending nodes are considered (daytime data and nighttime data are averaged).
This may have some effect in the tropics where a diurnal cycle in the gravity wave sources is expected, but should not have much effect in
the polar vortex region during wintertime. We
analyzed several gravity wave events from different sources, which are
observed by both AIRS and HIRDLS. Figures and show
temperature perturbation maps of the AIRS operational retrieval and
the AIRS high-resolution retrieval, as well as HIRDLS measurement
locations at 30 and 42 km altitude. In
Figs. and the corresponding vertical
cross sections of the AIRS operational retrieval, the AIRS
high-resolution retrieval, and HIRDLS are presented. The AIRS
measurements have been linearly interpolated to the HIRDLS track for
this comparison.
Temperature perturbations from AIRS retrievals on 29
September 2006 at about 03:00 UTC at 30 km (a, c) and 42 km (b, d) for
a mountain wave event near Tierra del Fuego. (a, b) AIRS
operational retrieval. (c, d) AIRS high-resolution
retrieval. Black circles indicate the locations of HIRDLS
profiles.
Vertical cross sections of temperature perturbations on 29
September 2006 at about 03:00 UTC for a mountain wave event derived from
the AIRS operational retrieval (a), the AIRS high-resolution
retrieval (b), and HIRDLS (c).
The first case shows a mountain wave event at Tierra del Fuego, South
America, on 29 September 2006 (Figs. and ). This case was also investigated by
, but a different analysis of the HIRDLS data is used
in this study. The results found by are reproduced
successfully. The vertical maps and cross sections of the temperature
perturbations from the AIRS high-resolution retrieval and HIRDLS agree
well in amplitude and phase structure of the mountain wave
event. attributed remaining small differences in the vertical phase structure of the observed waves to the different vertical
resolution of both instruments. Note that the AIRS operational
retrieval also shows this event, but the retrieved wave amplitudes are
significantly lower. The vertical resolution of the operational
retrieval is also significantly degraded compared with the
high-resolution retrieval above 40–45 km. attributed this to
stronger smoothing constraints in the operational retrieval.
The second case study shows a non-orographic wave event over the
southern Indian Ocean on 8 August 2007
(Figs. and ), which was likely initiated by jet or
storm sources. Figure shows in the
upper panel (a) a zonal average of the horizontal wind of ERA-Interim and
in the lower panels (b, c) the horizontal winds at 243 hPa (about 10 km) and
13.9 hPa (about 30 km). In the zonal average of the horizontal wind
the jets at the upper troposphere lower stratosphere and in the polar
stratosphere are clearly seen. The maps at 243 and 13.9 hPa show
the polar front jet, too. The exit region of the jets, where gravity
wave generation is common, is located at the position of the wave
event. Figure shows 8.1 µm
brightness temperature measurements of AIRS, which cover a spectral window region and are sensitive to surface or cloud emissions.
Low brightness temperatures indicate the presence of high clouds associated with a storm system in the study area, which could also be
a source for the gravity wave event.
The temperature perturbation maps show that the HIRDLS track is at the
edge and catches mostly the western part of the wave
event. Nevertheless, the vertical cross sections of the AIRS
high-resolution and HIRDLS retrievals show a similar structure, with
larger amplitudes in HIRDLS and slightly larger vertical wavelengths
in AIRS. The coarser vertical resolution of AIRS is obvious in the
vertical cross section and results in an attenuation of the amplitudes
and coarser vertical structures than for HIRDLS. This effect
increases with altitude, which can be attributed to decreasing
vertical resolution of the AIRS retrieval with height. The observed phase shift with altitude is expected, because of the time difference
between AIRS and HIRDLS measurements of 100 min and the non-orographic source of the gravity waves. A comparison
between the AIRS operational and high-resolution retrieval shows a
severe attenuation of the amplitude of the wave event and the coarser
horizontal resolution of the operational data. These case studies
illustrate that despite the rather different sensitivity functions
AIRS and HIRDLS are capable of observing gravity waves from the same
sources in individual events.
Same as Fig. but for a
non-orographic gravity wave event over the southern Indian Ocean
on 8 August 2007 at about 17:00 UTC.
Same as Fig. but for a
non-orographic gravity wave event over the southern Indian Ocean
on 8 August 2007 at about 17:00 UTC.
Time series of gravity wave variances
This section focuses on time series of gravity wave variance of AIRS
and HIRDLS at about 30 and 42 km altitude during January 2005 to
March 2008. The temporal development and latitudinal structure of the
gravity wave variance at 30 km is shown in
Fig. and at 42 km in
Fig. . A detailed picture
for four selected latitudes at 42 km is given by
Fig. . Additionally, in all figures
the zonal mean wind of ERA-Interim at the chosen altitude is
shown. Latitudes 44∘ N and 47∘ S in
Fig. are chosen, because they are the
maximum and minimum latitudes, which are completely covered by AIRS
measurements. We found that the seasonal cycle is captured very well
in the AIRS and HIRDLS data sets and the structure is rather
similar. Apart from the wintertime maxima in the polar regions,
gravity wave variance between 50∘ S and 50∘ N is usually
between 0.1 and 0.5 K2 (30 km) and 0.5 and 2 K2 (42 km) for
AIRS high-resolution retrieval and between 1 and 2 K2 (30 km) and
2 and 5 K2 (42 km) for HIRDLS. In the subtropics a weaker annual
cycle with maxima during summertime and minima during wintertime is
found. These summertime maxima have been observed before
e.g.,, and they have been
attributed to stronger activity of deep convective sources during
summer e.g.,. Additionally, a major effect
is the modulation of wave amplitudes by the background winds. We found
an annual cycle at high latitudes, which has its maxima during wintertime and its minima during summertime. The highest values are found
at the polar vortex in the Southern Hemisphere with values up to
9 K2 for AIRS high-resolution retrieval and up to 29 K2 for
HIRDLS. Between December 2006 and February 2007 a double-peaked maximum at
44∘ N is seen in AIRS high-resolution retrieval and HIRDLS. The second peak in both data sets could be related to a strong
warming in the beginning of January 2007 . The enlarged peak in the HIRDLS data is mainly caused by
short-vertical- and long-horizontal-wavelength waves that are not visible for AIRS. This becomes clear if Fig. is
compared to Fig. . The HIRDLS data which are filtered with the AIRS sensitivity
function show a strongly reduced second peak which is more similar to the AIRS time series. AIRS
high-resolution retrievals detected a double-peaked maximum between December 2005 and February 2006 at 44∘ N, which is not seen in HIRDLS at
this latitude but somewhat further north. The same behavior was found by in zonal mean momentum flux measurements of
HIRDLS. In January 2006 a major
sudden stratospheric warming (SSW) occurred and the double-peak
structure is likely related to the SSW. In the high-resolution
retrieval of AIRS it could be seen, with a small delay, that the
gravity wave activity is strengthening after the SSW when the zonal
wind increases again. For an overview of gravity wave activity in the
Northern Hemisphere polar region during recent winters see
. discussed gravity wave activity
located at Southern Hemisphere orographic hotspots and their
correlation with background winds in more detail.
(a) Zonal average of horizontal wind of ERA-Interim for a
non-orographic gravity wave event over the southern Indian Ocean
on 8 August 2007 at 18:00 UTC. (b, c) Horizontal wind maps of
ERA-Interim. The white box indicates the region covered in
Figs. and .
8.1 µm brightness temperature measurements of AIRS for a
non-orographic gravity wave event over the southern Indian Ocean
on 8 August 2007. Low brightness temperatures indicate the
presence of high clouds associated with a storm system in the study area.
Comparing zonal winds at 2.5 hPa (about 42 km) and stratospheric
gravity wave variances a strong correlation can be found for both AIRS
and HIRDLS. The largest gravity wave variances occur in mid- to
high-latitude regions where stratospheric zonal mean winds are
∼ 25 m s-1 or greater. At 44∘ N and 47∘ S the
maxima during wintertime correspond with strong westerly zonal winds,
up to 110 m s-1 at 47∘ S. At 20∘ N and 20∘ S
maxima during summertime match well with strong easterly zonal
winds. It is often observed that gravity wave activity is amplified in
the presence of strong background winds
e.g.,. If the phase speeds of gravity
waves are opposite to the background wind their saturation amplitudes
are enlarged. An additional effect is that the vertical wavelength of
these gravity waves is Doppler-shifted towards longer vertical
wavelengths, which are better visible in particular for AIRS. A more
detailed discussion of this effect can be found, for example, in
and . This also means that
long-vertical-wavelength gravity waves are preferentially found in regions of strong
background winds. This is the likely reason why in
Fig. the patterns of AIRS
gravity wave variances match the distribution of the background winds
somewhat better than the HIRDLS variances.
Time series of monthly temperature variances due to gravity
waves between 2005 and 2008 at 30 km altitude. (a) AIRS
operational retrieval. (b) AIRS high-resolution
retrieval. (c) HIRDLS. Contour lines indicate zonal mean wind
from ERA-Interim. Please note the different color bar ranges.
Same as Fig.
but for 42 km.
The values of the operational retrieval are a factor of 2 lower if
they are compared to the AIRS high-resolution retrieval. At
44∘ N no double peak related to the SSW is seen in AIRS
operational retrieval values between December 2005 and February 2006 and December 2006 and February 2007. At 20∘ N and 20∘ S
gravity wave variances during
wintertime are not increasing, which is seen in both the AIRS
high-resolution retrieval and in the HIRDLS data. Obviously, the AIRS
high-resolution retrieval is more suitable for the analysis of gravity
waves than the AIRS operational retrieval due to the better horizontal
resolution and improved vertical resolution.
Influence of sensitivity functions on gravity wave
variances
As we conducted a full spectral analysis of the HIRDLS data, we are
able to apply the AIRS sensitivity functions to the HIRDLS data in
order to estimate the fraction of variances that is actually observed
by both instruments. For this procedure horizontal and vertical
wavelengths of the gravity waves are required. From the HIRDLS
measurement track consecutive altitude profiles, which observe the
same gravity wave, are used to determine horizontal wavelengths. This
approach has been used before to estimate gravity wave momentum fluxes
from satellite data e.g.,. The average sampling
distance between these consecutive altitude profiles is 90 km, and
the profiles are observed within only about 15 s. Therefore often
the same gravity wave should be observed in consecutive profiles, and
due to the short sampling times the wave field should not change due
to the oscillation frequency of the wave. The horizontal structure of
the wave is responsible for phase differences. Nevertheless, to ensure
that in successive profiles the same gravity wave is looked at, only
waves with the vertical wavelengths differing by no more than 40 %
in the two profiles of a pair are selected. The fraction of selected
pairs with respect to the total number of possible pairs is thereby
reduced to about 60–70 % at low latitudes, and to about 50–60 %
at high latitudes. Gravity wave variances due to the strongest gravity
wave components in all single profiles without pair selection and of
the selected pairs are almost exactly the same. Therefore the selected
pairs are considered to be representative for the global distribution
of all gravity waves. However, there will always be an angle α
between the horizontal wave vector of the gravity waves kGW
and the sampling track of the satellite. The observed horizontal
wave number kobs will therefore underestimate kGW by a
factor cos(α), and the horizontal wavelength will be
overestimated by a factor 1/cos(α).
Time series of monthly mean gravity wave variances for
measurements between 2005 and 2008 at 42 km altitude and
different latitudes (see plot titles). Orange dash-dotted lines: AIRS operational
retrieval. Red dashed lines: AIRS high-resolution retrieval. Blue lines:
HIRDLS. Black dotted lines indicate zonal mean winds at 2.5 hPa
from ERA-Interim.
Time series of gravity wave variances at 42 km altitude
and different latitudes (see plot titles). Red dash-dotted lines: AIRS
high-resolution retrieval. Blue lines: HIRDLS. Orange dashed lines: HIRDLS
with MEM/HA. Cyan dotted lines: HIRDLS filtered with AIRS sensitivity
function. Note that filtered HIRDLS data are scaled by a factor of
5.
Figure
illustrates the influence of the observational filter of AIRS to the
HIRDLS gravity wave variances by showing HIRDLS gravity wave variances
with and without the AIRS observational filter being
applied. Additionally, gravity wave variances of the AIRS
high-resolution retrieval are shown. Plotted are time series of the
gravity wave variance at 42 km altitude for the same latitudes as in
Sect. from HIRDLS, HIRDLS with MEM/HA,
AIRS high-resolution retrieval and HIRDLS filtered with AIRS
sensitivity function. Note that for a better identification the
results from HIRDLS filtered data sets were scaled by a factor of
5. The HIRDLS gravity wave variance is significantly reduced after the
AIRS observational filter is applied. HIRDLS filtered with AIRS
sensitivity function reproduces at the maximum 8 % at 47∘ S
and at the minimum 3 % at 20∘ N of the HIRDLS gravity wave
variance. Values of HIRDLS including the AIRS observational filter are
considerably lower than values directly from the AIRS high-resolution
retrieval. This confirms that there is only small spectral overlap of
the HIRDLS and AIRS sensitivity functions and points to an
under-representation of small horizontal-scale waves in HIRDLS data
compared with AIRS. Still, relative variations are very similar, and
some structures seen in AIRS became visible in HIRDLS gravity wave
variances after including AIRS observational filter. At 44∘ N
the filtered HIRDLS gravity wave variances show the double-peak
structure between December 2005 and February 2006, which is not seen in
unfiltered data. The gravity wave activity is strengthening after the
SSW when the zonal wind increases again in both filtered HIRDLS
gravity wave variances. This is also seen in AIRS, albeit somewhat
delayed. Between December 2005 and February 2006 and between December 2006 and February 2007 the filtered HIRDLS
gravity wave variances are more gradually decreasing with time at
44∘ N after the peak value than in the unfiltered HIRDLS gravity
wave variances. This behavior is very similar to the AIRS gravity
wave variances. The analysis confirms that AIRS and HIRDLS gravity
wave measurements can be considered complementary to each other,
because they observe different sections of the gravity wave
spectrum. The relative variations in all time series are similar,
which indicates that these variations are induced by similar physical
processes (e.g., wind effects and source mechanisms). Therefore it
might be possible to transfer directional information obtained for
AIRS to HIRDLS observations.
Summary and conclusions
In this study we compared temperature variances of AIRS and HIRDLS to
evaluate the relationship of their stratospheric gravity wave
observations. Our analyses are performed on the HIRDLS operational
retrievals, AIRS operational retrievals, and a dedicated AIRS
high-resolution data set. AIRS (nadir) and HIRDLS (limb) have different measurement geometries, and therefore they have opposite
sensitivities to horizontal and vertical wavelengths, which is shown
by their sensitivity functions. However, a comparison of individual
orographic and non-orographic gravity wave events showed that
stratospheric wave structures of AIRS and HIRDLS agree very well,
which is consistent with earlier work of . With
respect to the AIRS high-resolution retrievals, the case studies
demonstrate that AIRS and HIRDLS agree generally well in amplitude and
phase structure for a mountain wave event and a non-orographic wave
event. AIRS has coarser vertical resolution, which results in an
attenuation of the amplitude and coarser vertical structures than for
HIRDLS, which is much more evident for the AIRS operational
retrieval. However, AIRS has a much higher horizontal resolution, and
the propagation direction of the wave can be clearly identified in
geographical maps of the wave events. The horizontal orientation of
the phase fronts can be deduced from AIRS 3-D temperature fields. This
is a restricting factor for gravity wave analyses of current limb
measurements.
A comparison of time series of gravity wave variances of AIRS and
HIRDLS revealed that HIRDLS gravity wave variances show an offset due
to regular background activity of gravity waves and are typically
about a factor of 3–5 larger than for AIRS. This is attributed to the
different measurement geometries and the limitation to long vertical
wavelengths for AIRS in particular. We calculated a momentum flux
factor, which gives a rough estimate of how much waves of given
horizontal and vertical wavelengths and amplitude contribute to
momentum flux if they exist in the real atmosphere. It indicates that
the waves with short horizontal and long vertical wavelengths seen by
AIRS contribute significantly to momentum flux, even if the AIRS
temperature variance may be small compared to HIRDLS. Despite this
systematic difference, the seasonal and latitudinal distributions of
stratospheric gravity wave activity found in both data sets are rather
similar. Overall, these variations are related to the well-known
seasonal patterns of gravity wave activity with summertime maxima in
the subtropics and wintertime maxima at high latitudes
e.g.,. Several sources of
gravity waves can produce these maxima. The summertime
maxima in the subtropics occur because of the stronger
activity of deep convective sources during summer. Gravity wave variances show great
enhancement in the winter hemisphere over mid- and high latitudes where
the polar night jet is strongest , and due to
strong mountain wave activity . The seasonal
distribution of stratospheric gravity wave activity found in this
study agrees well with other satellite climatologies based on limb
measurements e.g.,. The gravity wave variances
agree qualitatively well with the AIRS climatology of ,
which is based on 15 µm radiance measurements, and of
, which is based on 4.3 µm brightness
temperature variances.
compared HIRDLS, COSMIC, and SABER detections of
stratospheric gravity waves during the years 2006–2007 and concluded
that, when allowing for their different vertical resolution
capabilities, the three instruments reproduce each other's results for
magnitude and vertical scale of perturbations to within their
resolution limits in approximately 50 % of the cases. In a second study
investigated whether the dissimilar results of many
gravity wave studies are primarily of instrumental or methodological
origin. Their analysis is located around the southern Andes and Drake
Passage with different gravity-wave-resolving instruments. Their
results show important similarities and differences. Limb sounder
measurements show high intercorrelation between any instrument
pair. AIRS and radiosonde observations tend to be uncorrelated or
anticorrelated with the other data sets, suggesting very different
behavior of the wave field in the different spectral regimes accessed
by each instrument. Evidence of wave dissipation is seen and varies
strongly with season. A first combination of nadir instrument (AIRS) and limb instrument (MLS) observations was done by
, who analyzed the wave momentum flux and the full 3-D direction of propagation for a mountain wave case study
over the Andes. In contrast to these three studies, we focus on a
global statistical comparison of a nadir instrument (AIRS) and a limb
instrument (HIRDLS) over a measurement period of 3 years. The data
sets of AIRS and HIRDLS are found to be complementary to each
other. AIRS primarily observes only the short-horizontal- and
long-vertical-wavelength waves, and HIRDLS primarily observes only the
long-horizontal- and short-vertical-wavelength waves. To address the
differences between the AIRS and HIRDLS distribution in terms of the different
sensitivity functions, a simple approach of filtering HIRDLS data with
the AIRS sensitivity function was used. Still, relative
variations are very similar, and some structures seen in AIRS became
visible in HIRDLS gravity wave variances after including the AIRS
sensitivity function. Of course, not all differences can be explained
by this simple approach, but it might be possible to transfer
directional information obtained for AIRS to HIRDLS observations for
case studies.
In summary, despite the different sensitivity function, AIRS and
HIRDLS are capable of observing gravity waves from the same sources in
individual events, and their relative distributions of gravity wave
variances agree well. The analysis confirms that AIRS and HIRDLS
observe largely different sections of the gravity wave spectrum, but
they complement each other, and thus larger parts of the gravity
wave spectrum can be observed. Combining the observations would be a
great chance for gravity wave research in the future.
Data availability
AIRS and HIRDLS data are distributed by the NASA
Goddard Earth Sciences Data Information and Services Center (GES
DISC; https://disc.gsfc.nasa.gov/). ERA-Interim data were obtained from the European Centre for
Medium-Range Weather Forecasts (ECMWF; http://apps.ecmwf.int/datasets/data/interim-full-daily/).
Author contributions
All authors contributed to the design of the study
and provided input to the manuscript. The data for the study were
processed by CIM, and additionally she produced all figures and
drafted the text. The 3-D AIRS retrieval scheme was developed and the
3-D AIRS data used were produced by LH and MJA. ME produced the HIRDLS
data set used. QTT provided the HIRDLS observational filter data.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
The work by Manfred Ern was partly supported by Deutsche
Forschungsgemeinschaft (DFG) grant no. PR 919/4-1 (MS-GWaves/SV).
The article processing charges for this open-access publication were covered
by a Research Centre of the Helmholtz Association.
Edited by: Markus Rapp
Reviewed by: Marvin A. Geller and two anonymous referees
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