Gravity waves are one of the main drivers of atmospheric dynamics. The spatial resolution of most global atmospheric models, however, is too coarse to properly resolve the small scales of gravity waves, which range from tens to a few thousand kilometers horizontally, and from below 1 km to tens of kilometers vertically. Gravity wave source processes involve even smaller scales. Therefore, general circulation models (GCMs) and chemistry climate models (CCMs) usually parametrize the effect of gravity waves on the global circulation. These parametrizations are very simplified. For this reason, comparisons with global observations of gravity waves are needed for an improvement of parametrizations and an alleviation of model biases.

We present a gravity wave climatology based on atmospheric infrared limb
emissions observed by satellite (GRACILE). GRACILE is a global data set of
gravity wave distributions observed in the stratosphere and the mesosphere by
the infrared limb sounding satellite instruments High Resolution Dynamics
Limb Sounder (HIRDLS) and Sounding of the Atmosphere using Broadband Emission
Radiometry (SABER). Typical distributions (zonal averages and global maps) of
gravity wave vertical wavelengths and along-track horizontal wavenumbers are
provided, as well as gravity wave temperature variances, potential energies
and absolute momentum fluxes. This global data set captures the typical
seasonal variations of these parameters, as well as their spatial variations.
The GRACILE data set is suitable for scientific studies, and it can serve for
comparison with other instruments (ground-based, airborne, or other satellite
instruments) and for comparison with gravity wave distributions, both
resolved and parametrized, in GCMs and CCMs. The GRACILE data set is
available as supplementary data at

Our work is focused mainly on the stratosphere
and mesosphere, i.e., on the middle atmosphere in the approximate altitude
range from 20 to 90 km. In this altitude range typical scales of atmospheric
gravity waves are from tens to a few thousand kilometers horizontally and
from a few kilometers to several tens of kilometers vertically

Gravity waves propagate away from their sources. Thereby they redistribute
momentum and energy in the atmosphere, and where they dissipate they can
affect (accelerate or decelerate) the background flow by deposition of
momentum and energy. Dissipation processes include radiative damping (e.g.,

If a gravity wave propagates conservatively upward in a background atmosphere
with constant background wind and temperature, its amplitude will grow
exponentially due to the exponential decrease in atmospheric density with
altitude. At some point, however, the amplitude reaches its saturation limit,
and the wave will start to break. For an overview of the theory of wave
saturation see, for example,

One characteristic parameter of atmospheric gravity waves
is

Based on observed spectral characteristics, it is often assumed
that the energy spectrum

For a conservatively propagating gravity wave, however, the wave energy is
not a conserved quantity. A parameter that is more relevant for the
interaction of gravity waves with the background flow is the vertical flux of
horizontal wave pseudomomentum. In the following, for simplification, we will
call this parameter momentum flux. The momentum flux vector is given by

The acceleration or deceleration

Gravity wave drag plays an important role in the whole middle atmosphere. It
significantly contributes to the wind reversals at the top of the mesospheric
wind jets

Consequently, general circulation models (GCMs) and chemistry climate models
(CCMs) need a realistic representation of gravity wave drag in order to
produce realistic global circulation patterns in the middle atmosphere. The
spatial resolution of these models, however, is usually too coarse to resolve
more than a small fraction of the whole spectrum of gravity waves. Therefore
most global models need gravity wave parametrization schemes (gravity wave
drag schemes); see also

Usually, gravity wave parametrization schemes launch gravity wave momentum flux from a source level and make assumptions about the propagation and dissipation of gravity waves, and thereby the effect (drag) that gravity waves exert on the background flow is simulated.

Traditionally, many global models employ at least two different gravity wave
drag schemes: a nonorographic, and an orographic gravity wave drag scheme.
Nonorographic gravity wave drag schemes usually do not represent specific
gravity wave sources. Often, they assume a fixed source level and a
homogeneous and isotropic launch distribution; i.e., they launch the same
amount of momentum flux in different directions (for example, the four
cardinal directions) at each model grid point. Some examples of such schemes
are the schemes introduced by

There are also attempts to address other specific sources by dedicated
gravity wave parametrizations, for example, gravity waves excited by jets and
fronts

Still, all these schemes are very simplified. They contain tunable parameters
and make simplifying assumptions about the launch distributions, and most
gravity wave drag schemes propagate gravity waves only in the vertical
direction, while in a real atmosphere gravity waves can also propagate
horizontally

There are already first attempts to improve gravity wave parametrizations by
comparison with satellite observations. Some comparisons are based on gravity
wave variances or amplitudes

Because these first comparisons have already led to promising results, the
aim of our work is to provide a climatological data set, GRACILE (GRAvity
wave Climatology based on Infrared Limb Emissions observed by satellite), of
gravity wave temperature variances, squared temperature amplitudes, potential
energies, horizontal wavenumbers, vertical wavelengths, and momentum fluxes
based on 3 years (March 2005 until February 2008) of High Resolution Dynamics
Limb Sounder (HIRDLS) observations, and on 13 years (February 2002 until
January 2015) of Sounding of the Atmosphere using Broadband Emission
Radiometry (SABER) observations. Both these instruments are infrared limb
sounders operating on satellites in low Earth orbits. This measurement
technique has the advantage that a comparably large range of the gravity wave
spectrum is covered

Of course, this climatological data set can also be used for comparison with
distributions of gravity waves that are resolved in global models, in order
to find out how realistic these distributions are. It has been shown that
even for high-resolution models gravity wave amplitudes may be
underestimated, and distributions of resolved gravity waves may not be fully
realistic

The paper is organized as follows: in Sect.

Our work is based mainly on data of the satellite instruments HIRDLS and
SABER. Both instruments are infrared (IR) limb sounders operating on
satellites in low Earth orbits. From atmospheric IR limb emissions of CO

Characteristics of the HIRDLS and SABER instruments and data sets. Also given is the coverage used for the GRACILE gravity wave (GW) climatology.

“odd” months: January, March, May, July, September, or November. “even” months: February, April, June, August, October, or December.

HIRDLS observations are available from 22 January 2005 until 17 March 2008,
while SABER observations started on 25 January 2002 and are still ongoing at
the time of writing. However, in order to avoid biases in the GRACILE gravity
wave climatology, we use only full years of data. For HIRDLS, the GRACILE
climatology covers March 2005 until February 2008, and for SABER February
2002 until January 2015. For an overview, Table

While HIRDLS continuously observes the latitude range of about
63

Over the whole period of the SABER mission, the date when SABER switches between northward and southward view has gradually shifted from the middle of the odd months to the beginning of the odd months. The first northward viewing phase of 2017 started even as early as 31 December 2016, i.e., not in January 2017.

Satellite instruments that observe Earth's atmosphere in limb geometry view
toward the Earth's horizon. A schematic of this viewing geometry is given in
Fig.

Limb sounding of optically thin atmospheric emissions is a measurement
technique that is capable of observing small-scale atmospheric fluctuations,
such as gravity waves. This was first reported by

Schematic of the geometry of satellite limb observations. The satellite instrument views toward the Earth's horizon. The point of the instruments' line of sight closest to the Earth's surface is called the tangent point, and the corresponding altitude is the tangent altitude.

Illustration of an example how the apparent horizontal wavelength

The amplitude response

An ideal temperature retrieval (infinitesimal vertical field of view and
infinitesimal retrieval step-width with, at the same time, an infinite
signal-to-noise ratio of the instrument) can compensate for effects of the
vertical wavelength, but has to assume that an observed wave has infinite
horizontal extent (

For a real retrieval, however, there will be a reduction of sensitivity at
short gravity wave vertical wavelengths due to an additional smoothing effect
over an altitude interval

The sensitivity

Relevant for our study is the sensitivity

In our study, we consider the satellite instruments HIRDLS and SABER that
observe infrared limb emissions of atmospheric trace gases. For these
instruments the analytic sensitivity function

Sensitivity of limb sounding instruments to gravity waves as a
function of horizontal and vertical wavelength. Values apply for gravity wave
temperature variances, squared amplitudes, potential energies, or momentum
fluxes and were calculated for

We choose the parameters for the gravity wave analysis in a way that wave
parameters for wavelengths shorter than 25 km are determined. In order to
avoid observed altitude profiles of temperature fluctuations being
contaminated by gravity waves of longer vertical wavelengths, or with
planetary waves, these altitude profiles are high-pass filtered in terms of
vertical wavenumbers

It should also be pointed out that due to the limitations by the sensitivity
function limb scanning satellite instruments are able to observe only part of
the whole spectrum of gravity waves that is present in the atmosphere. Due to
this limitation a large fraction, if not most, of the overall gravity wave
momentum fluxes is therefore not visible for limb scanning satellite
instruments. A strategy to overcome the limitations of a single measurement
technique would be, for example, a combination of complimentary measurement
techniques as proposed by

The analytic expression for the sensitivity

Further, if multiple altitude profiles are combined for the wave analysis,
for example for deriving gravity wave momentum fluxes, limitations of the
spatial sampling of an instrument that lead to an undersampling of the
horizontal structure of an observed gravity wave (aliasing) also have to be
considered

According to the Nyquist limit, the shortest horizontal wavelength parallel
to the measurement track that can be resolved by the sampling is

Aliasing effects and a sensitivity function can be accounted for at a later
stage: as has been shown by

Another effect of the observational filter that has recently been discussed
is that observed altitude profiles usually are not perfectly vertical and
will therefore partly sample the horizontal structure of an observed gravity
wave while performing an altitude scan. This can lead to biases in the
observed vertical wavelength for gravity waves of short horizontal
wavelengths

There are several reasons why this effect is very likely not important for
our results. First,

The first step in any analysis of gravity waves from observations is the separation of the measured quantity into an atmospheric background and the fluctuations due to gravity waves. Particularly, temperature altitude profiles observed from satellites will contain contributions of both planetary waves with large horizontal scales and of gravity waves with much smaller horizontal scales. One of the major challenges of methods for removing the atmospheric background state from observed temperature altitude profiles is therefore to effectively separate the fluctuations due to planetary waves (which are usually much larger in amplitude) from those of gravity waves. Usually, this separation is done via a separation of scales, either vertically or horizontally. In the case of time series observed by ground-based stations, temporal filtering of time series is also frequently applied to extract the gravity wave signal.

Scale separation in vertical direction is usually performed by filtering
observed altitude profiles vertically. One method is to use polynomial fits
in the vertical direction as an estimate for the atmospheric background and
subtract this background from an altitude profile to obtain the fluctuations
that are attributed to gravity waves. Another method is vertical filtering of
single altitude profiles by introducing a low-pass filter for vertical
wavelengths and attributing only fluctuations with vertical wavelengths
shorter than about 10 km to gravity waves

Different from this, much of the vertical wavelength spectrum of gravity
waves can be preserved if scale separation in the horizontal direction is
utilized. Our approach of horizontal scale separation was introduced in

The procedure utilized in our study for extracting small-scale temperature
fluctuations due to gravity waves from observed altitude profiles requires
several steps. First, the zonal-average background temperature is subtracted
from each altitude profile of observed temperature. To estimate the
contribution of planetary waves we calculate 2-D spectra in longitude and
time for overlapping time windows of 31-day length and a set of fixed
latitudes and altitudes

The resulting altitude profiles of temperature residuals are analyzed with a
two-step method introduced by

Since the MEM is performed on the whole profile, we trust also wavelengths
larger than the sliding window but not larger than approximately 25 km;
therefore the filtering of removing all waves of 40 km and longer is
applied. The resulting sensitivity functions combining both radiative
transfer and retrieval effect as well as the vertical wavelength filtering
are presented in Fig.

Latitude–altitude cross sections of SABER zonal-average gravity
wave temperature variances times 2

Same as Fig.

Latitude–altitude cross sections of gravity wave potential energies
calculated following Eq. (

Zonal-average cross sections of the ratio of SABER (upper) and
HIRDLS (lower) temperature precision squared (random error variances) to
gravity wave temperature variances after background removal. Values are for
average January

The upper row of Fig.

The dominant climatological features are an overall increase in gravity wave
temperature variances with altitude, which is expected due to the decrease in
atmospheric density with altitude. Further, temperature variances are
particularly enhanced in the polar region during wintertime, which is caused
by strong activity of orographic and polar-jet-related gravity wave sources.
In addition, the strong background wind offers favorable propagation
conditions (increased saturation amplitudes) for gravity waves propagating
opposite to the background winds. Another enhancement of temperature
variances is seen in the summertime subtropics, which is mainly caused by
gravity waves excited by convective sources and favorable propagation
conditions in the subtropical jets. These features are qualitatively in good
agreement with several previous studies

The second row in Fig.

As detailed in Sect.

Regarding average momentum fluxes calculated in a certain region, the first
method will result in much lower average values than the second method. The
second method inherently assumes that the matching pairs are representative
for the average momentum flux in this region. Figs.

Figure

Once gravity wave temperature variances or squared amplitudes are available,
the determination of potential energies is straightforward by applying
Eq. (

SABER temperature precision (random error) for different altitudes.
Values in the upper part of the table are for local thermal equilibrium (LTE)
conditions and are taken from Table 2 at

Gravity waves appear as temperature fluctuations in observed altitude
profiles. Accordingly, systematic errors of the temperature retrieval are
removed by the separation into gravity wave fluctuation and background. This
holds both for constant offsets as well as for offsets slowly varying with
geolocation (e.g., offsets dependent on altitude or latitude). Different from
this, measurement noise leads to random temperature fluctuations that will
affect the estimation of gravity wave temperature variances and squared
amplitudes. Estimates of the temperature precision are given, for example, by

In order to find out whether random errors may affect the determination of
gravity wave temperature variances or amplitudes,
Fig.

Cross sections for each average calendar month are provided as part of the
GRACILE gravity wave climatology. For the climatology, SABER random error
variances for cold mesopause conditions are adopted for those latitudes and
months when these conditions are approximately expected, i.e., south of
50

For HIRDLS the precision (random error) predicted by the retrieval algorithm
is provided together with each retrieved temperature profile. As stated in

Error estimates are, of course, uncertain to some degree and we here compare zonal mean values of gravity wave temperature variances, which are averages over strong and weak gravity wave events. Therefore even in regions where on average the fraction of noise is very small, noise may still influence the results via the weak events to some degree. On the other hand, we are using the strongest component only, which suppresses noise in the presence of a real wave.

As can be seen from Fig.

The results shown in the lower row of Fig.

As mentioned in Sect.

From limb sounding instruments with only one single measurement track, the
horizontal wavelength along the orbital track can be estimated from the phase
differences

Latitude–altitude cross sections of zonal-average percentages of
short-distance pairs of altitude profiles used for determining absolute
momentum fluxes (i.e., with matching vertical wavelengths) with respect to
the total number of short-distance pairs of altitude profiles. Shown are
multi-year averages for SABER and HIRDLS for the months of
January

Latitude–altitude cross sections of zonal-average gravity wave
vertical wavelengths from single altitude profiles. Values are in kilometers.
Shown are multi-year averages for SABER

Latitude–altitude cross sections of zonal-average gravity wave
horizontal wavenumbers

Latitude–altitude cross sections of zonal-average gravity wave
absolute momentum fluxes in mPa. Shown are multi-year averages for
SABER

Same as Fig.

Current-day limb sounders can observe waves which have shorter horizontal
wavelengths than properly resolved by the sampling distance along the orbit
track. In spite of this undersampling of short horizontal wavelength waves,
average values of horizontal wavelengths are still meaningful if the sampling
distance for such pairs of altitude profiles is shorter than about 300 km

Apart from horizontal sampling considerations, a gravity wave has to be
observed quasi-instantaneously in order to avoid phase progression due to the
wave frequency

We assume that the same wave is observed in both profiles of a short-distance
pair, if the vertical wavelengths of the strongest gravity wave observed at a
given altitude in these two profiles agree within 40 %, i.e., about the
error margin of the vertical wavelength determination by the MEM/HA method

Pairs of altitude profiles with non-matching vertical wavelengths are
disregarded. In this way, about 40 % of all pairs that are potentially
useful for determining momentum fluxes are omitted. Nevertheless, the
distributions of gravity wave squared amplitudes are almost the same for
single profiles and the pairs suitable for calculating momentum fluxes (cf.
Sect.

From pairs of altitude profiles, however, only 2-D information is provided. In particular, the propagation direction of an observed gravity wave remains unknown, and only absolute gravity wave momentum fluxes can be determined from single-track limb sounders like HIRDLS and SABER.

Vertical wavelengths and horizontal wavenumbers are needed to determine gravity wave momentum fluxes. Therefore, next we will investigate zonal-average cross sections of these parameters. Further, these distributions can be useful for comparison with the distributions that are obtained for gravity waves that are resolved by high-resolution atmospheric models.

Figure

There are two main features that shape the zonal-average distribution of
vertical wavelengths. (See also the discussion in

At low altitudes, it is therefore expected that vertical wavelengths will be
shorter on average. This is also seen in Fig.

The second effect that shapes the zonal-average distribution of vertical
wavelengths is that vertical wavelengths are particularly increased when the
background wind is strong. Gravity waves propagating in the direction
opposite to the background wind will be Doppler-shifted toward longer
vertical wavelengths. These waves can attain larger saturation amplitudes,
and will therefore dominate the gravity wave spectrum in these regions. See
also the discussion in

As expected, this effect is seen in Fig

Different from vertical wavelengths, horizontal wavelengths can attain quite
large values of a few thousand kilometers. Showing average horizontal
wavelengths would therefore overemphasize those values that do not contribute
much to average momentum fluxes and that therefore are not representative for
the average distribution of gravity wave momentum fluxes. This is why in the
following we choose to present average horizontal wavenumbers in terms of
reciprocal horizontal wavelengths, similar to in

Similarly to Fig.

The most salient feature of the zonal-average distribution of

The main difference between the horizontal wavenumber distributions of HIRDLS
and SABER is that, on average, SABER horizontal wavenumbers are generally
lower than those estimated for HIRDLS. Likely reason is the coarser SABER
horizontal sampling along-track, which will lead to stronger aliasing of
horizontal wavelengths that is caused by an undersampling of the short
horizontal wavelength part of the gravity wave spectrum. For a further
discussion of aliasing effects see Sect.

There is also a decrease in horizontal wavenumbers with altitude. This is
most obvious for the SABER instrument that covers a larger altitude range.
Partly, this decrease may be caused by the SABER sampling distance that
increases with increasing altitude for the short-distance pairs of altitude
profiles that are only considered here

If observed temperature variances are dominated by noise, it is expected that
the corresponding horizontal wavenumber

As we can see in Fig.

Apart from this, horizontal wavenumbers of limb sounders with only a single
measurement track are generally low-biased, which is one of the main error
sources when calculating absolute gravity wave momentum fluxes. Only the
apparent horizontal wavelength

Latitude–altitude cross sections of SABER and HIRDLS zonal-average gravity
wave absolute momentum fluxes are shown in
Fig.

Like for gravity wave temperature variances or squared amplitudes (see
Sect.

Sometimes observed vertical gradients of absolute momentum fluxes can provide
useful information about the effect of gravity waves on the background winds.
This is the case when gravity waves encounter critical levels in regions of
strong vertical gradients of the background wind, or when those strong
vertical gradients lead to enhanced breaking of gravity waves
(e.g.,

Figure

Generally, HIRDLS values of gravity wave momentum flux are somewhat higher in
the polar vortices. One possible reason is that in these regions average
horizontal wavelengths are relatively short
(cf. Fig.

As already indicated by the uncertainty of the horizontal wavelengths
entering Eq. (

From the 2-D information available from single-track limb sounders like
HIRDLS or SABER it is only possible to provide estimates of absolute gravity
wave momentum fluxes. Directional information can only be obtained from
multiple (i.e., three or more) soundings of the same wave providing 3-D
information

Generally, uncertainties in gravity wave parametrizations and in our
understanding of the effect of gravity waves in the atmosphere are still
quite large. Therefore, in spite of their large uncertainties, absolute
momentum fluxes have been used and will continue to be very useful for
improving global models by providing a better understanding of gravity wave
effects, as well as by providing better constraints for gravity wave
parametrizations (see also Sect.

As pointed out by

In the previous sections latitude–altitude cross sections of gravity wave temperature variances, squared amplitudes, potential energies, vertical wavelengths, horizontal wavenumbers, and momentum fluxes were already presented. In this section, we describe how the data were gridded from observed altitude profiles into global maps and zonal-average cross sections, and which data sets are available in the GRACILE gravity wave climatology.

Based on single altitude profiles, the data available are gravity wave
temperature variances, gravity wave squared amplitudes and potential
energies, as well as vertical wavelengths. For the “suitable” pairs of
altitude profiles that are used for calculating momentum fluxes (cf.
Sect.

Zonal-average cross sections of gravity wave parameters provided in
the GRACILE gravity wave climatology data file. In the parameter names “XX”
is to be replaced by either “SABER” or “HIRDLS”. Grid points not covered
by data are flagged with

In order to obtain global distributions, for a fixed altitude the data of the
single months are distributed into a set of longitude latitude bins, and
averaged. For HIRDLS, the extent of these bins is
15

A monthly mean value assigned to a gridbox equals the total of all values within this gridbox divided by the number of all data points within the gridbox. Each “paired observation” is treated as a new data point, and the center coordinates between the two single observations that contribute to this paired observation are taken as the new coordinates for the pair, i.e., we assign new coordinates in latitude, longitude and time to the pair. In this way, ambiguities are avoided at the cost of creating a new set of coordinates.

In this way, we obtain monthly global maps. To obtain the “typical” global distribution for each calendar month, these global maps are averaged separately for each calendar month. For SABER, 13 years of data are averaged (February 2002 until January 2015), and for HIRDLS, 3 years (March 2005 until February 2008). In the GRACILE gravity wave climatology, average global maps are provided from 30 to 90 km in steps of 10 km for SABER, and from 30 to 50 km in steps of 10 km for HIRDLS.

Global distributions of gravity wave absolute momentum fluxes at 30 km altitude. Shown are 13-year averages for SABER for each calendar month.

Same as Fig.

Latitude–altitude cross sections of the number of values per
long/lat bin used for global maps, zonally averaged for the average month of
January. Shown are multi-year averages for SABER

Global distributions of SABER 13-year average gravity wave vertical
wavelengths

Global distributions of HIRDLS 3-year average gravity wave vertical
wavelengths

Zonal-average gravity wave momentum fluxes at 30 km altitude. Shown
are climatological averages for each calendar month (solid lines), as well as
shaded envelopes that indicate the range of natural variability during the
respective time period considered. SABER values are in black, and HIRDLS
values are in red. The climatological averages are 13-year averages for
SABER, and 3-year averages for HIRDLS, separately for each calendar month.
Vertical lines at 50

Time series of monthly zonal-average gravity wave absolute momentum
fluxes at 30 km altitude for

Same as Fig.

As an example, climatological distributions of gravity wave absolute momentum
fluxes are shown in Figs.

Although the averages for SABER and HIRDLS are based on a different number of
years for averaging, the distributions shown in
Figs.

Next, we discuss the statistics of data points that are used for creating global maps of different gravity wave parameters. The number of data points available for the longitude/latitude bins depends on the bin size, the temporal coverage, as well as on the process of pair selection for calculating momentum fluxes.

As an example, Fig.

The middle column of Fig.

In the right column of Fig.

It should be noted that the satellite sampling geometry leads to local
enhancements of the measurement density at the northernmost and southernmost
latitudes of the global coverage. For HIRDLS, this leads to an enhanced
measurement density at around 63

As another example, Fig.

As expected, vertical wavelengths are longest at mid and high latitudes where the background wind is strongest, particularly in January at high northern latitudes, and in July at high southern latitudes.

Similarly, low horizontal wavenumbers are generally found at low latitudes
but for different physical reasons (see the discussion in
Sect.

For example, horizontal wavenumbers are enhanced over the Southern Andes and
the Antarctic Peninsula, a region that is known for strong activity of
mountain waves. Further, in the summer hemisphere subtropics enhanced
horizontal wavenumbers are found in those regions that are known for deep
convection as a strong source of gravity waves (see also

As was already indicated in the zonal averages displayed in
Fig.

In order to provide an envelope of the natural variability, we also calculate
for each grid point the maximum and minimum values that are attained on
monthly average. These values are also given as global maps for each calendar
month for all parameters supplied, i.e., gravity wave temperature variances,
squared amplitudes, potential energies, and momentum fluxes, as well as
vertical wavelengths and horizontal wavenumbers divided by

In our work, zonal averages for each month are obtained by zonally averaging
the values of the grid points in the monthly global maps. Climatological
latitude–altitude cross sections for different parameters, i.e., averages
over multiple years, were already shown in Sects.

An example of this variability is shown in Fig.

The latitude range between the two vertical lines at 50

As expected, the zonal averages display a maximum at wintertime high
latitudes, related to the polar vortex, and another maximum in the summertime
subtropics that is caused by convectively generated gravity waves. These
distributions are similar to those shown in

Considering an overall error of momentum fluxes of a factor of 2 or more
(cf. Sect.

Other differences are related to different temporal coverages at high
latitudes. For example, SABER samples high northern latitudes only in late
September. Therefore SABER momentum fluxes poleward of 50

The largest variability, as seen by the widened envelopes, is seen at high
northern latitudes during winter and early spring. This variability is
related to sudden stratospheric warmings that introduce a strong variability
of the polar vortex, and thus of zonal-average gravity wave activity (e.g.,

There is also a large range of variability in March for SABER, but not for
HIRDLS (see Fig.

Additional diagnostics for climatological zonal-average gravity wave
parameters provided in the GRACILE gravity wave climatology data file. In the
parameter names “XX” is to be replaced by either “SABER” or “HIRDLS”.
Grid points not covered by data are flagged with

Time series of gravity wave parameter zonal-average cross sections
provided in the GRACILE gravity wave climatology data file. In the parameter
names “XX” is to be replaced by either “SABER” or “HIRDLS”. Grid points
not covered by data are flagged with

Global maps of parameters provided
in the GRACILE gravity wave climatology data file.
In the parameter names “XX” is to be replaced by either “SABER” or
“HIRDLS”. Grid points not covered by data are flagged with

In addition to the climatological multi-year average months that were
discussed before, in the GRACILE climatology we also provide time series of
monthly zonal averages for several gravity wave parameters. These time series
span 13 years for SABER and 3 years for HIRDLS. An example is shown in
Fig.

As already indicated in the climatological (multi-year average) zonal-average
cross sections and the climatological global distributions, HIRDLS momentum
fluxes are somewhat higher than SABER values in austral winter at high
southern latitudes, and somewhat lower at lower latitudes. These systematic
offsets are usually on the order of

In addition to the time series at 30 km,
Fig.

This alternating pattern changes between 50 and 70 km. The subtropical
maximum is shifted poleward, likely an effect of meridional propagation of
gravity waves

Weaker variations are related to the QBO and the SAO
(e.g.,

The GRACILE gravity wave data set is publicly available and
can be downloaded from the PANGAEA open-access world data center at

The satellite data used in our study are open access. HIRDLS data are freely
available from the NASA Goddard Earth Sciences Data and Information Services
Center (GES DISC) at

The SPARC temperature and zonal wind climatology is freely available at

In this paper the
global climatology GRACILE (

The GRACILE climatology consists of global maps and zonal averages for average calendar months. For HIRDLS, these averages were calculated over the 3-year period March 2005 until February 2008. For SABER, averages were calculated over the 13-year period February 2002 until January 2015. For these distributions also an envelope of minimum and maximum distributions is provided, which represents the natural variability during the time periods used for averaging. In particular, at high northern latitudes this variability can be quite strong, depending on the occurrence of sudden stratospheric warmings during boreal winters. Since it is desirable for global models not only to simulate reasonable average distributions, but also a reasonable range of natural variability, these max/min envelopes are useful for comparison with the ranges simulated by global models. To further illustrate the natural variability during the time periods considered, we also provide time series of monthly zonal averages for all parameters.

In the paper several examples of the provided data sets are given, and the main features of the distributions are briefly discussed. In addition, an error discussion is performed that gives information where the derived parameters may be less reliable. Further, some statistics are provided for the selection of pairs of altitude profiles that are used for the estimation of absolute gravity wave momentum fluxes.

Also given are approximate HIRDLS and SABER sensitivity functions for the
observed gravity wave parameters. As has been pointed out in several previous
studies, this sensitivity function has to be taken into account for
meaningful comparisons with other observations

One of the main limitations of the GRACILE climatology is that only absolute
momentum fluxes are available because the HIRDLS and SABER measurement tracks
provide only 2-D information. For estimating the direction of momentum fluxes
or net momentum fluxes real 3-D information from multiple soundings of the
same wave either by different instruments

The authors declare that they have no conflict of interest.

This work was partly supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project PR 919/4–1 (MS–GWaves/SV) which is part of the DFG researchers group FOR 1898 (MS–GWaves), as well as by the DFG project ER 474/3–1 (TigerUC) which is part of the DFG priority program SPP–1788 “Dynamic Earth”.

We thank NASA for making HIRDLS level 2 data freely available via the NASA
Goddard Earth Sciences Data and Information Services Center (GES DISC) at