Introduction
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
e.g.,and references therein. Most gravity wave
sources are located in the troposphere and lower stratosphere. The gravity
waves seen higher up in the stratosphere and mesosphere have therefore mostly
propagated upward from these sources. Some relevant sources are gravity waves
excited by flow over topography (mountain waves) (e.g.,
), gravity waves excited by convection
(e.g., ),
and gravity waves generated by source processes related to strong wind jets,
for example the subtropical jets or the polar jets (e.g.,
, and references therein).
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.,
), turbulent damping (e.g., , and
references therein), and wave saturation and breaking (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, or
. Critical level filtering occurs when during wave
propagation the background wind is not constant and approaches the
ground-relative phase speed cφ of the wave. In this case, due to
Doppler shifting, the intrinsic frequency ω^ and thus the
vertical wavelength λz of the wave approach zero. Thereby the
saturation amplitude of the wave also tends to zero, and the wave will
dissipate completely. For a more detailed discussion see also
and references therein.
One characteristic parameter of atmospheric gravity waves
is E0, the total gravity wave energy per unit mass:
E0=Ekin+Epot,
with Ekin the kinetic and Epot the potential energy
per unit mass. The kinetic energy is given by
Ekin=12u′2‾+v′2‾+w′2‾
and the potential energy Epot by
Epot=12gN2T′T‾2‾.
Here, T‾ is the atmospheric background temperature, g the
gravitational acceleration of the Earth, and N the buoyancy frequency.
Further, u′, v′, w′, and T′ are the perturbation components due to
the gravity wave of the zonal, meridional and vertical wind, as well as the
temperature, respectively. The overbar denotes averaging over one wave period
or multiples of it.
Based on observed spectral characteristics, it is often assumed
that the energy spectrum E(μ,ω^,ϕ)
of wind velocity or temperature perturbations due to gravity waves
takes the form of a separable product of independent functions
e.g.,:
Eμ,ω^,φ=E0A(μ)B(ω^)Φ(ϕ),
with μ=m/m* the ratio of gravity wave vertical wavenumber
m=2π/λz and the characteristic wavenumber m* that separates
the saturated from the unsaturated part of the vertical wavenumber spectrum.
Often, the function A(μ) is approximated as follows:
A(μ)=A0μs1+μs+t,
and B(ω^) is often found to be proportional to
ω^-p:
B(ω^)=B0ω^-p.
A0 and B0 are normalization constants. The function Φ(ϕ)
accounts for the anisotropy of the gravity wave distribution depending on the
horizontal propagation direction ϕ. The parameters s, t, and p are
logarithmic spectral slopes. The spectral slope s describes the unsaturated
part of the vertical wavenumber spectrum (at small m), and t the
saturated part (at large m). While t=3 is usually a very good
approximation, s is not well constrained and is often set to 1. The
spectral slope p describes the shape of the intrinsic frequency spectrum
B(ω^). Often, p is found in the range of approximately
5/3 to 2. It is predicted by linear wave theory, and it is also often
observed, that in the atmosphere the ratio Ekin/Epot is
approximately equal to the spectral slope p, i.e., approximately 5/3 to 2
e.g.,. This means that with the knowledge of
Epot values of Ekin and E0 can be
estimated. For more details see, for example, ,
, , or and
references therein. Experimental tests of this relationship were carried out
in the lower stratosphere, for example, by
(superpressure balloons), and by and
(a combination of Global Positioning System Radio
Occultations (GPS-RO) and radar observations). Another test was carried out
in the mesosphere by (a combination of lidar and radar
observations).
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
Fpx,Fpy=ϱ‾1-f2ω^2u′w′‾,v′w′‾
e.g.,. Fpx and Fpy are
the zonal and meridional momentum flux components, respectively,
ϱ‾ is the atmospheric background density, and f is the
Coriolis parameter. This equation can be rewritten in terms of gravity wave
wavenumbers and temperature amplitude cf.:
Fpx,Fpy=12ϱ‾gN2(k,l)mT^T‾2.
Here, T^ is the temperature amplitude of the gravity wave, (k,l,m)=2πλx-1,λy-1,λz-1 is
the wavenumber vector, consisting of zonal, meridional, and vertical
components, respectively, with λx and λy the apparent
horizontal wavelength in the zonal (x) and meridional (y) directions,
respectively, of a gravity wave with the “true” horizontal wavelength
λh in the direction of wave propagation. This equation was
derived using the linear polarization relations for gravity waves
e.g.,. In Eq. ()
several terms were omitted for simplification. For the gravity waves seen by
infrared (IR) limb sounders, however, neglecting these terms introduces
errors of only a few percent. For details see the discussion in the
supporting information of . Equation ()
can be rewritten for absolute momentum fluxes Fph by introducing the
absolute horizontal wavenumber kh=k2+l2=2π/λh:
Fph=12ϱ‾gN2khmT^T‾2.
Similarly, the potential energy can be rewritten in terms of the gravity wave
temperature amplitude with Epot,max the maximum potential
energy during one wave cycle,
Epot,max=12gN2T^T‾2,
and Epot the potential energy of the wave averaged over one or
more wave cycles:
Epot=14gN2T^T‾2,
which corresponds to Eq. ().
The acceleration or deceleration (X,Y) of the background flow,
in the following for simplification called gravity wave drag,
is given by the vertical gradient of momentum flux:
(X,Y)=-1ϱ‾∂Fpx,Fpy∂z,
with X and Y the drag in the zonal and meridional directions,
respectively, and z the vertical coordinate. For more details see the
review paper by .
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 e.g.,. Further, gravity
wave dissipation drives the meridional circulation in the mesosphere, which
leads to the cold summer mesopause, the coldest region in Earth's atmosphere,
as well as to the relatively warm winter stratopause. In the stratosphere,
gravity wave drag plays an important role, for example for the driving of the
quasi-biennial oscillation (QBO) and semiannual oscillation (SAO) of the
zonal wind in the tropics
e.g.,.
In addition, gravity waves contribute to the Brewer–Dobson circulation in
the stratosphere, particularly to the summertime branch
e.g.,. A tutorial that addresses several
effects of the interaction between gravity waves and the mean background flow
is given in .
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 or and
references therein. At the time of writing, gravity wave parametrization
schemes are still needed even for state-of-the-art high-resolution numerical
weather prediction models e.g.,, and also in the
foreseeable future gravity wave parametrization schemes will still be
required.
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 , ,
, ,
, or . Different from this,
orographic gravity wave parametrizations are dedicated to mountain waves that
are excited by flow over topography, i.e., to a specific source process. Some
examples are , , or
.
There are also attempts to address other specific sources by dedicated
gravity wave parametrizations, for example, gravity waves excited by jets and
fronts , or gravity waves
excited by convective sources
e.g.,.
These schemes were successfully used in GCMs
e.g.,. Another recent development is
so-called stochastic schemes
e.g., which mimic the
observed intermittent nature of gravity wave sources
e.g., in a
simplified fashion.
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
e.g.,.
Therefore comparison with observed global distributions of gravity waves is
important for improving and tuning gravity wave drag schemes. In particular,
observed momentum fluxes allow for a direct comparison with gravity wave drag
schemes.
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
e.g.,, while others
use momentum fluxes
e.g.,.
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 see
also.
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
e.g.,.
This means even distributions of resolved gravity waves need to be validated
against observations. In addition, this climatological data set can be used
for comparison with other observations, for example other satellite data,
superpressure balloons, radiosondes, or ground-based instrumentation. For a
meaningful comparison, however, the respective observational filters of the
different observation techniques have to be taken into account. In
particular, every observation method has its own coverage in gravity wave
wavenumber and frequency space see also. A
detailed discussion of the observational filter of infrared limb sounders has
been given, for example, by .
The paper is organized as follows: in Sect. the HIRDLS
and SABER instruments are briefly introduced. Then, in
Sect. , we describe how gravity wave temperature
variances, potential energies and momentum fluxes are derived from
temperature altitude profiles observed by HIRDLS and SABER. In addition, we
address the observational limitations of the instruments, and potential error
sources are discussed. In Sect. , we describe how the
data are gridded in preparation of the GRACILE climatological data set, and
what data products are available. In particular, we present examples of
global distributions, a measure of the natural variability, as well as time
series of zonal averages. Finally, Sect. gives a summary of
the paper.
The satellite instruments HIRDLS and SABER
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 CO2
around 15 µm, temperature–pressure profiles of the atmosphere
are derived. In addition, both instruments observe several trace species. In
our study, we use HIRDLS version V006 see also and
SABER version v2.0 data. Detailed information about the HIRDLS instrument,
temperature retrieval and vertical resolution is given, for example, in
, , or
. For SABER, details about the instrument are given,
for example, in or . The SABER
temperature retrieval is described in
.
Characteristics of the HIRDLS and SABER instruments and data sets.
Also given is the coverage used for the GRACILE gravity wave (GW)
climatology.
HIRDLS
SABER
satellite
EOS Aura
TIMED
orbit type
sun-synchronous
precessing
local time at Equator
10:00/22:00
varying
temperature data version used
V006
v2.0
instrument vertical resolution
∼ 1 km
∼ 2 km
GW climatology altitude grid
1 km for zonal averages
1 km for zonal averages
10 km for global maps
10 km for global maps
instrument temporal coverage
January 2005 until March 2008
January 2002, still ongoing at time of writing
GW climatology temporal coverage
March 2005 until February 2008
February 2002 until January 2015
approx. instrument altitude coverage
tropopause to > 80 km
tropopause to > 100 km
GW climatology altitude range
20–50 km
30–90 km
approx. instrument latitude coverage
63∘ S–80∘ N
50∘ S–82∘ N or 82∘ S–50∘ N
GW climatology latitude coverage
62.5∘ S–80∘ N
“even” months: either 50∘ S–80∘ N or 80∘ S–50∘ N
“odd” months: 80∘ S–80∘ N
number of single profiles per day
∼ 6000
∼ 1400
number of profile pairs per day that are
∼ 3500
∼ 400
used for GW momentum fluxes
“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
summarizes some characteristics of both instruments. Also given is the
approximate temporal, latitudinal and altitude coverage of the observations,
as well as the temporal and global coverage provided in our gravity wave
climatology.
While HIRDLS continuously observes the latitude range of about
63∘ S–80∘ N, this is different for SABER: every
∼ 60 days for about 60 days SABER switches between a northward and
southward viewing mode with latitude coverages of
50∘ S–82∘ N and 82∘ S–50∘ N,
respectively. This means that only the latitude range
50∘ S–50∘ N is observed continuously. For the range of
years considered here (2002 until 2015), in February, June, and October the
latitude coverage is always 50∘ S–82∘ N (northward view),
and in April, August and December it is always 82∘ S–50∘ N
(southward view). In the “odd” months (January, March, May, July,
September, and November) SABER switches between northward and southward view.
Consequently, monthly averages of these months have a latitude coverage of
82∘ S–82∘ N. However, latitudes poleward of 50∘
are only observed during part of the month, which may introduce biases into
the gravity wave climatology poleward of 50∘ for those “odd”
months.
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 limb observations of gravity waves
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. . Altitude profiles of the incoming limb
radiances can be measured, for example, by changing the elevation angle of
the line of sight (LOS) of the instrument such that vertical scans through
the atmosphere are performed. The point of the LOS that is closest to the
Earth's surface is the so-called tangent point. In the case of optically thin
emissions, most of the observed radiances have their origin in the vicinity
of the tangent point, both in terms of altitude and in terms of horizontal
position along the LOS. This is due to the exponential decrease in
atmospheric density and, thus, the number of emitting molecules with
altitude. Therefore, temperatures or trace gas mixing ratios that are usually
derived from observed altitude profiles can be attributed to the locations
and altitudes (the “tangent altitudes”) of the tangent points.
Sensitivity function and observational filter
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 and
. Later, pointed out the
importance of differences in the sensitivity of different measurement
techniques for detecting gravity waves, and an analytic expression for the
sensitivity function of limb sounders was derived .
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
λh,AT parallel to the satellite tangent point track
(measurement track) and the apparent horizontal wavelength
λh,LOS parallel to the satellite line of sight (LOS)
could differ from the true horizontal wavelength λh,true
of an observed gravity wave. These differences strongly depend on the
relative orientations of the observed gravity wave, of the LOS, and of the
direction of the tangent point track; however, λh,LOS and
λh,AT will always overestimate
λh,true. Light blue and light orange shaded areas
indicate areas of negative and positive phases, respectively, that would be
obtained by a horizontal section through an idealized plane gravity wave.
Bold brown dots indicate the discrete sampling of this wave by single
altitude profiles observed by the satellite instrument. The horizontal
sampling step is denoted as Δx.
![]()
Sensitivity function
The amplitude response S(kLOS,m) of an altitude profile of
observed limb radiances to an observed sine-shaped gravity wave due to
effects of radiative transfer in the Earth's atmosphere can be written as
follows :
SkLOS,m=1B∂B∂Tγ1/2a2+γ21/4exp-γkLOS24γ2+a2.
Here, m is the vertical wavenumber, and kLOS=2π/λh,LOS the apparent horizontal wavenumber of the
gravity wave in the direction parallel to the LOS of the instrument. In
Fig. an illustration is given showing that the apparent
horizontal wavelength λh,LOS parallel to the LOS, and the
apparent horizontal wavelength λh,AT parallel to the
measurement track, can be quite different from the true horizontal wavelength
λh,true of an observed gravity wave. See also
and . The term
1B∂B∂T in Eq. () is
the linear expansion in temperature T of the blackbody source function B.
The further parameters in Eq. () are γ=1/(2HREarth), a=m/(2REarth)=π/(λzREarth), with REarth the Earth's radius and H the
pressure scale height. See also .
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 (kLOS=0). The resulting temperature amplitude
response of an ideal retrieval ST,ideal(kLOS,m)
can be obtained by calculating the following ratio
:
ST,ideal(kLOS,m)=S(kLOS,m)/S(kLOS=0,m)=exp-γkLOS24(γ2+a2).
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 Δz, caused by the vertical field of view of
the instrument and the retrieval step-width. This smoothing effect can be
accounted for by an additional contribution R(λz)
:
R(λz)=λz22πΔz1-cos2πΔzλz.
Usually, the vertical field of view of the instrument will dominate over the
effect of the retrieval step, and can be set equal to Δz.
The sensitivity ST,real(kLOS,m) of a “real”
temperature retrieval to an observed gravity wave is then given by the
product of R(λz) and ST,ideal(kLOS,m)
such that
ST,real(kLOS,m)=λz22πΔz1-cos2πΔzλz⋅exp-γkLOS24(γ2+a2).
See also , their Eq. (1).
Relevant for our study is the sensitivity SA2(kLOS,m) that
is expected for gravity wave squared temperature amplitudes. This sensitivity
also applies for gravity wave temperature variances, potential energies, or
momentum fluxes. An analytic expression for SA2(kLOS,m) is
obtained by taking the square of ST,real(kLOS,m):
SA2(kLOS,m)=ST,real(kLOS,m)2.
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 SA2(kLOS,m)
is given as function of gravity wave horizontal and vertical wavelengths in
Fig. a for HIRDLS, and in Fig. b for
SABER by assuming vertical resolutions (vertical fields of view of the
instruments) of 1 km for HIRDLS and 2 km for SABER, respectively. It should
be pointed out that the horizontal wavelength relevant for the sensitivity
function is the apparent horizontal wavelength of a gravity wave parallel to
the line-of-sight direction of the satellite instrument
e.g.,. Compared to other global gravity wave
observation techniques, limb sounding covers a quite large range of the
gravity wave spectrum. See also or
.
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 (a) HIRDLS and (b) SABER
using the analytical approximation derived by for the
effects of radiative transfer and an idealized retrieval including the
sensitivity reduction at short vertical wavelengths due to the vertical field
of view of the instruments. (c) and (d) are the same
as (a) and (b), but with the additional suppression of long
vertical wavelengths used for our gravity wave
climatology.
![]()
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 see also. The
resulting sensitivity is given in Fig. c for HIRDLS, and in
Fig. d for SABER. The sensitivities shown in
Fig. c and d are also provided in the GRACILE climatology
together with the distributions of gravity wave parameters. It should however
be pointed out that these sensitivities are just an approximation. The
“true” sensitivity will be similar, but also depends on the details of the
retrieval of temperatures from measured altitude profiles of atmospheric
radiances. These retrieval details can lead to deviations from the idealized
function ST,real(kLOS,m)
.
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 or by
.
Observational filter
The analytic expression for the sensitivity
ST,real(kLOS,m) that combines the effects of
radiative transfer, temperature retrieval and vertical field of view of the
instrument (cf. Figs. a and b) already accounts for a major
part of the overall observational filter of a limb sounding instrument.
However, for the overall observational filter also other effects have to be
taken into account. In particular, details of the wave extraction and wave
analysis will have effect on the wave spectrum contained in the temperature
fluctuations that are attributed to gravity waves. For example, in our case
an additional vertical filter was applied which modifies the sensitivity for
gravity waves (cf. Fig. c and d).
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 e.g.,: to derive momentum
fluxes, the horizontal wavelength of an observed wave has to be determined.
However, as indicated in Fig. , the horizontal sampling
of a wave pattern by different altitude profiles is limited by the horizontal
sampling step Δx. If the sampling step is too coarse, some waves
passing the sensitivity function (cf. Fig. ) may be
undersampled.
According to the Nyquist limit, the shortest horizontal wavelength parallel
to the measurement track that can be resolved by the sampling is
λh,AT,nyq=2Δx. Waves that are undersampled
will undergo spatial aliasing, and their horizontal wavelength will be
overestimated. Accordingly, the gravity wave momentum flux of those waves
will be underestimated as discussed in detail in ; see
also Eq. (). In a correction for these
horizontal aliasing effects was suggested. For this correction, however,
assumptions about the shape of the gravity wave spectrum in a given region
have to be made, and the correction was not applied to the data presented
here. We also did not correct for effects of the sensitivity function.
Aliasing effects and a sensitivity function can be accounted for at a later
stage: as has been shown by , comparisons
between observations and model data can be much improved if all effects of
the observational filter (including aliasing) are taken into account by
simulating the effect of the measurement and applying the simulated
observational filter to the model data.
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 e.g.,.
There are several reasons why this effect is very likely not important for
our results. First, included this effect in their
simulation of the overall observational filter of limb sounders, and the
effect was found to be small for SABER. Second, HIRDLS and SABER momentum
fluxes agree well with CRISTA momentum fluxes. CRISTA momentum fluxes,
however, are unaffected by this effect because CRISTA altitude profiles were
measured almost vertically cf.. Third, for limb
sounders most of the waves that pass the sensitivity function
(cf. Fig. ) without being attenuated too much should have
an aspect ratio λz/λh of smaller than about 0.1,
resulting in a bias of the vertical wavelength of less than ∼ 20 %
for SABER; see also , their Fig. 7. Of course, for
single wave events biases in the observed vertical wavelengths could still
occur. For averaged data, however, these effects should be small.
Background removal
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
e.g.,. Scale
separation in vertical direction works well in the wintertime polar lower
stratosphere where vertical wavelengths of planetary waves are quite long,
while those of gravity waves are usually much shorter. However, this approach
has its shortcomings in the tropics where planetary-scale equatorial wave
modes and gravity waves generally have similar vertical wavelengths (e.g.,
). Another general problem is that, by
introducing a strong low-pass for vertical wavelengths, the remaining
spectral range of gravity waves is considerably narrowed down.
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
and (). This approach aims at
explicitly describing even day-to-day variations of the atmospheric
background due to short-period traveling planetary waves, which is
particularly important for investigating the gravity wave distribution in the
tropics or in the mesosphere, but could also be relevant in the wintertime
polar vortex because of its rapid temporal variations
e.g.,.
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 . Based on these spectra, the
temperature perturbation due to planetary waves with zonal wavenumbers 1–6
and periods longer than about 1–2 days is calculated for the exact location
and time of each observation in each altitude profile, and also subtracted.
In this way, we even account for short-period planetary waves that can have
periods as short as a few days, such as fast Kelvin waves in the tropics
(e.g., ), quasi 2-day waves in the
mesosphere see also, or short-period planetary waves
in the wintertime polar regions (e.g., ). To
remove tides, we utilize the fact that for satellites in slowly precessing
low Earth orbits the ascending and descending nodes, respectively, are at
about fixed local times. For HIRDLS, the local time does not change much
during the mission, while for SABER the orbital plane slowly precesses (a
full cycle is about 120 days). Consequently, tides will appear as stationary
zonal wave patterns if data from ascending and descending nodes are taken
separately. By removing these stationary wave patterns separately for
ascending and descending nodes, tides can easily be removed from the observed
temperature fluctuations e.g.,. In
each altitude profile, we additionally remove the strongest oscillation with
a vertical wavelength of 40 km or longer in order to further suppress
planetary waves, as well as long vertical wavelength gravity waves that are
not covered by our method of determining gravity wave amplitudes. In
addition, at altitudes above 60 km very short vertical wavelength
oscillations in SABER altitude profiles are removed by a low pass with a
cutoff vertical wavelength of 5 km in order to remove oscillations that are
presumably caused by minor retrieval artifacts in the mesopause region. On
average, gravity wave vertical wavelengths are relatively long at these
altitudes. Therefore, the effect of this additional filtering on the overall
distribution of gravity waves should be small.
Method for determining gravity wave amplitudes, phases, and vertical wavelengths
The resulting altitude profiles of temperature residuals are analyzed with a
two-step method introduced by . First, the whole
altitude profile is analyzed by the maximum entropy method (MEM;
) for identifying all vertical wavelengths present in
the profile. In the second step, in a sliding 10 km vertical window
amplitudes and phases are fitted by a sinusoidal fit for all vertical
wavelengths found by the MEM. For each altitude, the results are sorted
according to the largest (second largest, and so on) amplitude. In the
current paper, we further consider the strongest component only. This
assumption is also often used for other methods of analyzing temperature
altitude profiles with the aim of deriving gravity wave momentum fluxes
e.g.,. As discussed in the next subsection
(Sect. ), this assumption is a good approximation because
higher-order gravity waves do not contribute much to the overall gravity wave
temperature variance.
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. c and d. The combination of MEM and
sinusoidal fits, in short MEM/HA (HA for harmonic analysis), combines the
advantages of addressing a relatively wide part of the vertical wavelength
range and a fixed analysis window length. The latter is important, for
instance, when investigating regions of wind shear where the vertical
wavelength is refracted and strong gradients in wave amplitude are expected.
Latitude–altitude cross sections of SABER zonal-average gravity
wave temperature variances times 2 (a–d), gravity wave squared
amplitudes of single altitude profiles (e–h), and gravity wave
squared amplitudes of pairs of altitude profiles utilized for determination
of absolute momentum fluxes (i–l). Values are for average
January (a ,e, i), April (b, f, j),
July (c, g, k), and October (d, h, l). Overplotted
winds are from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is
20 m s-1.
![]()
Same as Fig. but for the HIRDLS
instrument.
![]()
Latitude–altitude cross sections of gravity wave potential energies
calculated following Eq. () from gravity wave
temperature variances obtained directly after background removal. SABER
variances are shown in the upper row, and HIRDLS variances in the lower row.
Values are for average January (a, e), April (b, f),
July (c, g), and October (d, h). Overplotted winds are
from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is
20 m s-1.
![]()
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 (a, e), April (b, f),
July (c, g), and October (d, h). Overplotted temperatures
are from the SPARC climatology . The
contour line increment is 10 K.
![]()
Latitude–altitude cross sections of gravity wave temperature variances, squared amplitudes and potential energies
The upper row of Fig. shows latitude–altitude
cross sections of zonal-average gravity wave temperature variances for
average January, April, July, and October determined from 13 years of SABER
data (February 2002 until January 2015). This time interval was used for all
SABER latitude–altitude cross sections shown in our study. Temperature
variances were multiplied by a factor of 2 to make them directly comparable
to zonally averaged squared amplitudes that are also shown in
Fig. . (Averaged over one wave period, the variance
due to a perfect sine wave is 0.5 times its amplitude squared.) The
climatological cross sections shown in the first row of
Fig. represent the gravity wave temperature
variances obtained directly after the removal of the atmospheric background
state as described in Sect. , i.e., before the MEM/HA and
the 10 km vertical windowing are applied. Overplotted contour lines
represent the zonal-average zonal wind of the Stratosphere-troposphere
Processes And their Role in Climate (SPARC, A core project of the World
Climate Research Programme) climatology for the respective month see
also.
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
e.g.,.
The second row in Fig. shows the corresponding
squared amplitudes for the strongest wave component obtained by applying the
MEM/HA and 10 km vertical windowing. The distributions are almost the same
as for gravity wave temperature variances times a factor of 2; only absolute
values are somewhat reduced for squared amplitudes. This reduction is caused
by the fact that we consider only the strongest wave component at each
altitude and neglect smaller amplitude waves that will also exist
e.g.,. However, the contribution of those
higher-order small-amplitude waves to both squared amplitudes and momentum
fluxes is usually small, and their distribution is easily biased by
instrument noise and other instrument effects.
As detailed in Sect. , gravity wave horizontal
wavelengths and thus absolute momentum fluxes can only be determined from
pairs of altitude profiles that have a short enough sampling distance and at
the same time match in their gravity wave vertical wavelength (i.e.,
presumably observe the same gravity wave). As discussed in
, there are currently two different approaches of
treating those altitude profiles that do not match in their vertical
wavelength. The first method uses a cospectral analysis for determining
squared temperature amplitudes see, for
example,. In the case of non-matching vertical
wavelengths, this method returns small values of squared amplitudes and,
correspondingly, small gravity wave momentum fluxes, even for cases when
gravity waves in both altitude profiles of a pair have considerable
amplitudes. In our work, we follow the second method mentioned in
see also, for
example,: in the case of matching vertical
wavelengths, it is assumed that meaningful values of horizontal wavelengths
can be deduced, and the average gravity wave amplitude of both profiles is
used. If, however, the vertical wavelengths do not match, it is assumed that
no horizontal wavelength information can be derived, and this pair of
altitude profiles is just not considered for calculating gravity wave
momentum fluxes.
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.
and provide evidence supporting this assumption:
the third row in Fig. shows gravity wave squared
amplitudes of those pairs of altitude profiles that are considered suitable
for the determination of momentum fluxes (i.e., those pairs of altitude
profiles with matching gravity wave vertical wavelength and at the same time
short enough horizontal sampling distance; see also
Sect. below). As can be seen from
Fig. , squared amplitudes considering all altitude
profiles are almost exactly the same as the squared amplitudes of the pairs
of altitude profiles used for momentum flux determination. This indicates
that these “suitable” pairs should be still representative for the global
distribution of gravity waves, because the whole number of single profiles
and the reduced number of matching pairs of altitude profiles, and thus also
the non-selected pairs, have almost the same distribution and magnitude of
gravity wave squared amplitudes.
Figure shows the same as
Fig. but for the HIRDLS instrument and the
corresponding 3-year time period (March 2005 until February 2008). This time
interval was used for all HIRDLS latitude–altitude cross sections shown in
our study. SABER and HIRDLS distributions are very similar. Even the absolute
values are in good agreement. Minor differences may arise from differences in
the viewing geometries (different line-of-sight directions and different
vertical fields of view), or from (minor) differences in the “real”
instrument sensitivity functions caused by differences in the temperature
retrieval.
Once gravity wave temperature variances or squared amplitudes are available,
the determination of potential energies is straightforward by applying
Eq. () for gravity wave temperature variances, or
Eq. () for squared amplitudes. Similar to
Fig. a–d, Fig. a–d
show zonal-average cross sections of gravity wave potential energies
calculated from SABER temperature variances for the average months of
January, April, July, and October. Figure e–h
show the same but for the HIRDLS instrument. As must be the case, the basic
features of the distributions displayed in
Fig. are the same as in
Figs. and . Also
available as part of the GRACILE gravity wave climatology are zonal-average
distributions for the other average calendar months. All gravity wave
potential energy values given in the climatology are calculated directly from
temperature variances using Eq. (). This means that no
10 km vertical window is applied, and values represent averages over a full
wave cycle.
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
http://saber.gats-inc.com/temp_errors.php. Similar values are also
found in , their Table 1. For higher altitudes (lower
part of the table) errors are increased because the retrieval has to account
for non-LTE effects, involving additional uncertainties. Values in the lower
part of the table are taken from Table 2 in . Values
in parentheses apply for cold summer mesopause conditions.
altitude
standard deviation
variance
(km)
(K)
(K2)
15
0.3
0.09
20
0.3
0.09
30
0.3
0.09
40
0.6
0.36
50
0.6
0.36
60
0.7
0.49
70
1.0
1.00
80
1.8 (2.7)
3.3 (7.3)
85
2.2 (5.4)
4.9 (29.2)
90
3.6 (8.9)
13.0 (79.3)
95
5.4 (10.3)
29.2 (106.1)
100
6.7 (8.9)
44.9 (79.3)
Error considerations
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
for HIRDLS and are also provided for each HIRDLS
altitude profile together with the temperature data. Therefore, it is
possible to compare HIRDLS random errors directly with the estimated gravity
wave temperature variances. For SABER, the temperature precision was
estimated by , and values are also given on the SABER
website at http://saber.gats-inc.com/temp_errors.php, last access:
18 April 2018. In Table we have summarized these
SABER precision estimates. In Table , temperature
standard deviations, as well as variances (standard deviations squared), are
given for “normal” midlatitude conditions, as well as for conditions of a
cold summer mesopause.
In order to find out whether random errors may affect the determination of
gravity wave temperature variances or amplitudes,
Fig. shows zonal-average cross sections of the
ratio of temperature precision squared (random error variances) to gravity
wave temperature variances after background removal for the average months of
January (left column), April (second column), July (third column), and
October (right column). The upper row is for SABER, and the lower row for
HIRDLS. Overplotted contour lines in Fig. represent
temperatures for the respective month taken from the SPARC climatology
.
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∘ S for the months of November until February (around austral
summer), and north of 50∘ N for the months of May until August
(around boreal summer). For the respective winter hemisphere and latitudes
equatorward of 40∘, “normal” random error variances are assumed. In
order to avoid jumps in the random error variances, a smooth transition is
introduced between cold summer mesopause values poleward of 50∘ in
the respective summer hemisphere and “normal” values starting at
40∘. For all other months “normal” random error variances are
assumed for SABER.
For HIRDLS the precision (random error) predicted by the retrieval algorithm
is provided together with each retrieved temperature profile. As stated in
, these theoretical values should be an upper estimate
because the temperature precision estimated directly from retrieved HIRDLS
temperature profiles in regions of low atmospheric variability (“measured
precision”) is better than the theoretical estimate by about a factor of 2
over a larger altitude range their Fig. 5.1.3.
Determining the “measured precision” is possible only in regions where
little atmospheric variability, in particular little activity of gravity
waves, is expected. Therefore, for the HIRDLS values shown in
Fig. , as well as for the values provided together
with the gravity wave climatology, we used values of the predicted HIRDLS
precision (standard deviation) divided by 2 in order to approximately match
the measured precision 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. , gravity wave temperature
variances usually are well above the noise level. There are only two
exceptions: the summertime high latitudes in the lower and middle
stratosphere, and the cold summer mesopause region. In particular, in the
summer mesopause region considerable biases should be expected. In this
region, the temperature precision is about 7 K, which corresponds to about
50 % of the estimated variances in Fig. a and c.
Therefore, gravity wave temperature variances and squared amplitudes,
potential energies, and momentum fluxes will be high-biased. This has already
been pointed out by : in this region their wave analysis
showed phase differences between pairs of altitude profiles that were
indicative of an enhanced noise level.
The results shown in the lower row of Fig. confirm
the results of . By assuming that the HIRDLS precision
is better by a factor of 2 than the predicted precision, it is avoided that
the ratio shown in Fig. , lower row, exceeds the
value of 1. This should not be possible because our values of “gravity wave
temperature variances” should contain the contributions of both gravity
waves (i.e., true atmospheric variability) and measurement noise. Further, it
is unlikely that the HIRDLS precision should be much worse than the SABER
precision, which would be the case if we would assume the predicted precision
without division by 2.
Estimation of gravity wave absolute momentum fluxes
Method
As mentioned in Sect. , the results of the MEM/HA
method are altitude profiles of gravity wave amplitudes, vertical wavelengths
and phases. To estimate gravity wave momentum fluxes, the horizontal
wavelength λh of an observed gravity wave has to be
estimated (see Eq. ).
From limb sounding instruments with only one single measurement track, the
horizontal wavelength along the orbital track can be estimated from the phase
differences dϕ between subsequent altitude profiles at fixed altitude
levels , provided that the same wave event is observed in
both altitude profiles:
λh,AT=2πΔxdϕ,
with Δx the along-track sampling step.
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 (a, e), April (b, f), July (c, g), and
October (d, h). Overplotted winds are from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is
20 m s-1.
![]()
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 (a–d) and
HIRDLS (e–h) for the months of January (a, e),
April (b, f), July (c, g), and October (d, h).
Overplotted winds are from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is
20 m s-1.
![]()
Latitude–altitude cross sections of zonal-average gravity wave
horizontal wavenumbers kh/(2π) (i.e., average reciprocal horizontal
wavelengths) from those pairs of altitude profiles that are also used to
calculate momentum fluxes. Values are in 10-3 km-1. Shown are
multi-year averages for SABER (a–d) and HIRDLS (e–h) for
the months of January (a, e), April (b, f),
July (c, g), and October (d, h). Overplotted winds are
from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is 20 m s-1.
![]()
Latitude–altitude cross sections of zonal-average gravity wave
absolute momentum fluxes in mPa. Shown are multi-year averages for
SABER (a–d) and HIRDLS (e–h) for the months of
January (a, e), April (b, f), July (c, g), and
October (d, h). Overplotted winds are from the SPARC climatology
. Westward
(eastward) winds are indicated by dashed (solid) contour lines. The zero wind
line is bold solid. The contour line increment is
20 m s-1.
![]()
Same as Fig. but for gravity wave
absolute momentum flux in
m2 s-2.
![]()
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
e.g.,. Both HIRDLS and SABER perform
altitude scans of the atmosphere, first top–down, then bottom–up, and so
on. For SABER this leads to a roughly triangular scan and varying distance
for different altitudes: in the stratosphere and mesosphere the distance
between two consecutive scans is less than 300 km for a pair of
top–down/bottom–up scans and larger than 600 km for a pair of
bottom–up/top–down scans. Only the shorter distance is used. For HIRDLS the
distance between two consecutive scans is about 90 km in both cases.
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 ω. However, this is not a limiting factor because for
HIRDLS and SABER the time needed to observe a short-distance pair of altitude
profiles is 1 min or less, i.e., much shorter than
the the period given by the buoyancy frequency N.
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
see also. This is the case for about
60 % of all short-distance pairs. Latitude–altitude cross sections of
zonal-average percentages of “used pairs” (i.e., those short-distance pairs
with matching vertical wavelengths) relative to the number of “potentially
useful pairs” (i.e., the total number of short-distance pairs) are given in
Fig. for SABER (upper) and HIRDLS
(lower) for the climatological average months of January, April, July, and
October.
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. and Figs.
and ). This strongly indicates that the
“suitable” pairs are still representative for the global distribution of
gravity waves.
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.
Latitude–altitude cross sections of vertical wavelengths and horizontal wavenumbers
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.
Vertical wavelengths
Figure shows latitude–altitude cross sections
of zonal-average gravity wave vertical wavelengths determined from all single
altitude profiles. The different columns in
Fig. represent the different average calendar
months of (from left to right) January, April, July, and October. For SABER
(upper), averages are determined from the period February 2002 until January
2015, and for HIRDLS (lower) from the period March 2005 until February 2008.
There are two main features that shape the zonal-average distribution of
vertical wavelengths. (See also the discussion in .)
First, there is a general increase in vertical wavelengths with altitude.
This is as expected, because for mid-frequency gravity waves the gravity wave
saturation amplitude T^sat is proportional to the
vertical wavelength λz of the wave e.g.,:
T^sat=T‾N2gλz2π.
As mentioned earlier, the amplitude of a conservatively propagating gravity
wave will increase with altitude because of the decrease in atmospheric
density with altitude. Due to their smaller saturation amplitude, short
vertical wavelength gravity waves will therefore saturate at lower altitudes,
such that, with increasing altitude, long vertical wavelength gravity waves
will more and more dominate the global distribution
e.g.,.
At low altitudes, it is therefore expected that vertical wavelengths will be
shorter on average. This is also seen in Fig.
for both HIRDLS and SABER. However, at low altitudes vertical wavelengths for
HIRDLS are usually even shorter than for SABER, except inside the jet
streams. This effect is caused by the narrower HIRDLS vertical field of view
that allows HIRDLS to detect also somewhat shorter vertical wavelength
gravity waves than SABER (for the HIRDLS and SABER sensitivity functions see
also 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 and references therein.
As expected, this effect is seen in Fig for
both instruments. In regions where vertical wavelengths are quite long, we find that HIRDLS vertical
wavelengths can be even somewhat longer than SABER values. This could be an
effect of the characteristics of the “real” HIRDLS and SABER sensitivity
functions including radiative transfer and temperature retrieval which will
deviate from the theoretical sensitivity functions shown in
Fig. (cf. Sect. ). These deviations
can be quite substantial, as has been shown, for example, by
. Apart from these systematic differences, the
uncertainty of our vertical wavelength determination by the MEM/HA method is
about 20 % as has been estimated by .
Horizontal wavenumbers
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. ,
Fig. shows zonal-average distributions of
kh/(2π), i.e., reciprocal horizontal wavelengths, for SABER (upper) and
HIRDLS (lower). Again, the different columns represent different calendar
months. Please note that horizontal wavenumbers derived from HIRDLS and SABER
will be low biased because only the apparent horizontal wavelength
λh,%AT in the direction parallel to the satellite
measurement track can be estimated (see also Fig. ).
The most salient feature of the zonal-average distribution of kh/(2π) is
reduced values at low latitudes. This effect is caused by the fact that in
the tropics the Coriolis parameter is smaller; i.e., there is more space
between the two limitations of the Coriolis parameter and the buoyancy
frequency and longer horizontal wavelength gravity waves can exist. For a
more detailed discussion see also , their Sect. 3.3.
Similar reductions of horizontal wavenumbers at low latitudes have been
found, for example, by using radiosonde data, i.e., a
different measurement technique.
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. and the
discussion in .
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 see also.
Partly, however, this reduction in horizontal wavenumbers may also be caused
by physical reasons.
If observed temperature variances are dominated by noise, it is expected that
the corresponding horizontal wavenumber kh,noise in a region is
given by
kh,noise2π=14Δx
with Δx the horizontal sampling step-width of the instrument along
the measurement track . For HIRDLS, the sampling step is
approximately 90 km. Accordingly, we expect
kh,noise/(2π)≈2.8×10-3 km-1. For SABER,
Δx is in the range of about 180 to 300 km, depending on altitude.
Accordingly, we expect kh,noise/(2π) in the range between
1.4×10-3 km-1 at 30 km altitude and 0.8×10-3 km-1 at 90 km altitude.
As we can see in Fig. , for SABER these values
are approximately reached in the summer mesopause region, and at high
latitudes of the summer hemisphere in the middle stratosphere. Similarly, for
HIRDLS values close to kh,noise/(2π) are reached also at high
latitudes of the summer hemisphere in the lower and middle stratosphere. As
can be seen from Fig. , in the same regions we find
an enhanced ratio of measurement noise estimates to gravity wave temperature
variances. This finding indicates that, indeed, in these regions gravity wave
distributions will be generally affected by measurement noise. Consequently,
also horizontal wavenumbers and vertical wavelengths, as well as absolute
momentum fluxes, in these regions will not be very reliable.
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 λh,AT of a gravity wave in
the direction parallel to the measurement track can be determined, which will
usually overestimate the true horizontal wavelength of the wave (see also
Fig. ). More discussion of this effect is given, for
example, in , , or
. Estimates by that are based on 3-D
temperature data of the nadir scanning Atmospheric Infrared Sounder (AIRS)
satellite instrument indicate a low bias of along-track horizontal
wavenumbers by a factor between 1.5 and around 2, which is qualitatively in
good agreement with values estimated by . Generally,
however, it is difficult to provide more reliable estimates of this
uncertainty.
Latitude–altitude cross sections of absolute momentum fluxes
Latitude–altitude cross sections of SABER and HIRDLS zonal-average gravity
wave absolute momentum fluxes are shown in
Fig. . Distributions represent the average
calendar months of January, April, July, and October. Averages for SABER
(upper) are over 13 years (February 2002 until January 2015), and for HIRDLS
(lower) over 3 years (March 2005 until February 2008). It should be noted
that, in our work, gravity wave momentum fluxes are generally calculated as
averages over values obtained point by point from pairs of altitude profiles
with their individual values of gravity wave amplitudes, vertical
wavelengths, and horizontal wavenumbers. Consequently, these average momentum
fluxes will be different from values that would be obtained by just combining
average values of gravity wave amplitudes, vertical wavelengths, and
horizontal wavenumbers like those previously shown, for example, in
Figs. , ,
, and .
Like for gravity wave temperature variances or squared amplitudes (see
Sect. ), enhancements of momentum fluxes are seen in the
wintertime polar regions, and in the summertime subtropics. In contrast to
temperature variances and squared amplitudes, however, there is a general
decrease in momentum fluxes with altitude, which indicates that there is an
overall dissipation of gravity waves with altitude. This observed decrease,
however, is stronger than that usually found in GCMs/CCMs
, which is an issue that is still not fully understood.
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 shows the same as
Fig. but in units of m2 s-2, i.e.,
following Eq. () but without the factor
ϱ‾. These values are also shown because they are useful for
comparison with, for example, radars that determine gravity wave momentum
fluxes from observed wind fluctuations. Without the density factor, momentum
fluxes gradually increase with altitude, similar to gravity wave potential
energies, temperature variances, or temperature squared amplitudes.
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. ). Accordingly, the better HIRDLS
along-track sampling will lead to reduced aliasing effects compared to SABER
and result in higher momentum fluxes.
Error considerations
As already indicated by the uncertainty of the horizontal wavelengths
entering Eq. () (cf. Sect. ), the
uncertainty of HIRDLS and SABER absolute momentum fluxes is large, at least a
factor of 2. A more detailed error discussion is given in
. However, due to the large uncertainties involved, it
does not make much sense to provide a more sophisticated discussion of
errors, here.
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
e.g.,.
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. ). In particular,
uncertainties can be considerably reduced if effects of the observational
filter are simulated and included in comparisons with model data
e.g.,.
As pointed out by , the following main
effects have to be taken into account for comparisons between measurements
and models: (a) sensitivity of the instrument for an observed gravity wave in
dependence of the vertical wavelength and the apparent horizontal wavelength
λh,LOS along the instrument line of sight, (b) projection
of the horizontal wavelength on the tangent point track, (c) the effect of
aliasing due to horizontal undersampling of waves, (d) the vertically slanted
sampling path for calculating the observed vertical wavelength, (e) selection
criteria for pairs of altitude profiles for the calculation of momentum
fluxes.
Global distributions and natural variability
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.
Parameters available
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. ), gravity wave squared amplitudes, horizontal
wavenumbers divided by 2π, and absolute momentum fluxes are provided.
Temperature variances and squared amplitudes are given in K2, and momentum
fluxes are given in Pa, as well as in m2 s-2, i.e., without the
density factor. Vertical wavelengths and horizontal wavenumbers divided by
2π are given in km and km-1, respectively. To obtain climatological
data sets, we interpolate the data of the single altitude profiles and of the
“suitable” pairs on regular grids, resulting in climatological global
distributions, as well as climatological latitude–altitude cross sections.
Further, time series of monthly zonal averages are provided for some
parameters. More details and some examples are given in the following
subsections. A full list of parameters available in the GRACILE gravity wave
climatology, as well as a short description, are given in
Tables and . The data are
provided in Network Common Data Format (NetCDF) in the climatology data file
available at the PANGAEA open-access world data center under
10.1594/PANGAEA.879658.
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 -999. In addition to the climatological
distributions listed in the table, also distributions of maximum and minimum
monthly values are given. These distributions are named “_clim_max” and
“_clim_min” (instead of just “_clim”).
parameter name
unit
array type
description
lat_grid_zav_XX
degrees
1-D
latitude coordinate for zonal-average cross sections
z_grid_zav_XX
km
1-D
altitude coordinate for zonal-average cross sections
gwmf_zav_clim_XX_Pa
Pa
3-D (lat, z, month)
climatological zonal-average gravity wave momentum fluxes
(12 average calendar months)
gwmf_zav_clim_XX_m2s2
m2 s-2
3-D (lat, z, month)
same but in units of m2 s-2 climatological zonal-average gravity wave
gw_temp_var_zav_clim_XX
K2
3-D (lat, z, month)
temperature variances (12 average calendar months)
gw_temp_ampsq_single_zav_clim_XX
K2
3-D (lat, z, month)
climatological zonal-average gravity wave squared amplitudes of single
altitude profiles (12 average calendar months)
gw_temp_ampsq_mfpairs_zav_clim_XX
K2
3-D (lat, z, month)
climatological zonal-average gravity wave squared amplitudes of pairs
that are used to estimate momentum fluxes (12 average calendar months)
gw_Epot_single_var_zav_clim_XX
J kg-1
3-D (lat, z, month)
climatological zonal-average gravity wave potential energies
calculated from variances based on single altitude profiles of residual
temperatures (12 average calendar months)
gw_Lz_single_zav_clim_XX
km
3-D (lat, z, month)
climatological zonal-average gravity wave vertical wavelengths
calculated from single altitude profiles (12 average calendar months)
gw_kh_mfpairs_zav_clim_XX
km-1
3-D (lat, z, month)
climatological zonal-average gravity wave horizontal wavenumbers
divided by 2π calculated from those pairs of altitude profiles that are
used to estimate momentum fluxes (12 average calendar months)
Gridding of climatological global distributions
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∘ longitude × 5∘ latitude, and average values are
attributed to the center longitude and latitude of each bin. The longitude
and latitude steps used for the bin centers are 5 and 2.5∘,
respectively, i.e., the bins are overlapping. According to the fewer data
available, for SABER larger bins of 30∘ longitude times 20∘
latitude, and longitude and latitude steps of 10 and 5∘,
respectively, were chosen.
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. but for 3-year averages
of the HIRDLS instrument at 30 km
altitude.
![]()
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 (a, b, c) and
HIRDLS (d, e, f) for average global maps of gravity wave
temperature variances (a, d), squared amplitudes (b, e),
and absolute momentum fluxes (c, f). Overplotted winds are from the
SPARC climatology .
Westward (eastward) winds are indicated by dashed (solid) contour lines. The
zero wind line is bold solid. The contour line increment is
20 m s-1.
![]()
Global distributions of SABER 13-year average gravity wave vertical
wavelengths (a, d, g, j), horizontal wavenumbers
kh/(2π) (b, e, h, k), and squared
amplitudes (c, f, i, l) for different calendar months at 30 km
altitude.
![]()
Global distributions of HIRDLS 3-year average gravity wave vertical
wavelengths (a, d, g, j), horizontal wavenumbers
kh/(2π) (b, e, h, k), and squared
amplitudes (c, f, i, l) for different calendar months at 30 km
altitude.
![]()
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∘ S and 50∘ N indicate that only
latitudes equatorward of 50∘ are continuously covered by
SABER.
![]()
Time series of monthly zonal-average gravity wave absolute momentum
fluxes at 30 km altitude for (a) HIRDLS and (b) SABER, as
well as for SABER at (c) 50 km and (d) 70 km altitude.
Values are in mPa on logarithmic
scales.
![]()
Same as Fig. but for gravity
wave potential energy in J kg-1 on logarithmic
scales.
![]()
Absolute gravity wave momentum fluxes
As an example, climatological distributions of gravity wave absolute momentum
fluxes are shown in Figs.
and for SABER and HIRDLS, respectively, at an
altitude of 30 km for each average calendar month.
Although the averages for SABER and HIRDLS are based on a different number of
years for averaging, the distributions shown in
Figs. and ,
respectively, are very similar with enhanced values in the wintertime polar
vortex and with the characteristic longitudinal structure in the summertime
subtropics that is caused by the characteristic distribution of convective
gravity wave sources. In the Southern Hemisphere, during the months of April
to October the region of the Southern Andes and the Antarctic Peninsula
stands out. This region is known as a pronounced source of mountain waves
e.g.,. Of course, due to the better sampling
of the HIRDLS instrument, for HIRDLS a finer longitude/latitude binning of
the data is possible, allowing for a better horizontal resolution of the
global distribution.
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. shows zonal-average cross
sections of the average number of data points that enter the
longitude/latitude bins used for gridding the global distributions for the
typical month of January. The upper row is for SABER, and the lower row for
HIRDLS. The left column displays the number of data points obtained for
gravity wave temperature variances (i.e., before applying the 10 km vertical
window of the MEM/HA method). As can be seen, the number of data points is
generally still quite high. Please note that SABER uses larger long/lat bins,
resulting in a quite high number of data points per bin at mid and low
latitudes. During January, however, SABER covers high latitudes only during
part of the month, and the number of data points per long/lat bin is strongly
reduced.
The middle column of Fig. shows the average number
of data points per long/lat bin obtained for gravity wave amplitudes of
single altitude profiles. This number is basically the same as in the left
column, with the exception that for HIRDLS the numbers are strongly reduced
at low latitudes and low altitudes. This is the case because at these
altitudes a number of altitude profiles have to be omitted in the tropics
because limb radiances are cloud contaminated. Please note that for vertical
profiles of gravity wave amplitudes the 10 km vertical window is used.
This means, for example, that for values displayed at an altitude of 20 km
HIRDLS observations of altitudes as low as 15 km are utilized. Consequently,
global distributions at 20 km will be less reliable and contain data gaps.
Therefore, in the GRACILE climatology global distributions are only provided
at 30 km and above. Zonal averages for HIRDLS are considered more robust and
are provided starting from 20 km as the lowest altitude. Still, at altitudes
close to 20 km zonal averages could be biased. For SABER, in order to avoid
effects of cloud-contaminated radiances, we generally provide only values at
altitudes of 30 km and above.
In the right column of Fig. the average number of
data points per long/lat bin used for obtaining gravity wave absolute
momentum fluxes is shown, i.e., the number of “suitable” pairs. As
mentioned in Sect. , the number of data points is
strongly reduced for momentum fluxes. First, because only around 60 % of
pairs match in their vertical wavelengths, and, second, for SABER only every
second pair has a short enough along-track sampling distance to be used for
the determination of momentum fluxes. Particularly at high latitudes the
SABER average distributions in the “odd” months, i.e., when the SABER
viewing geometry changes between northward view and southward view, will
therefore not be very robust.
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∘ S and 80∘ N. For SABER
those enhancements are located around 50∘ S and 80∘ N for
northward viewing periods, and around 80∘ S and 50∘ N for
southward viewing periods. During January, SABER switches between northward
and southward view. Therefore, in Fig. for SABER
enhancements of the measurement density occur at 80∘ S,
50∘ S, 50∘ N, and 80∘ N. However, because SABER
observes high latitudes only during part of the month, the measurement
density at high latitudes is generally reduced and the enhancements at
80∘ S and 80∘ N are not well visible in
Fig. .
Gravity wave vertical wavelengths and horizontal wavenumbers
As another example, Fig. shows, at an
altitude of 30 km, average horizontal distributions of gravity wave vertical
wavelengths (left column), gravity wave horizontal wavenumbers kh/(2π)
(middle column), and gravity wave squared amplitudes for the SABER
instrument. The different rows in Fig.
represent the different calendar months (from top to bottom) of January,
April, July, and October. Again, horizontal wavenumbers represent those pairs
of altitude profiles that are also used to calculate gravity wave momentum
fluxes. Vertical wavelengths and squared amplitudes were derived from all
single altitude profiles. Figure shows the
same as Fig. but for the HIRDLS instrument.
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. ). In addition, the horizontal wavenumber distribution
displays several enhancements of high wavenumbers that are related to
specific gravity wave source regions.
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. , horizontal wavenumbers are close to the
value kh,noise in regions of the respective summer hemisphere
where gravity wave squared amplitudes (right column) are quite low. Again,
this indicates that gravity wave parameters in these regions will not be very
reliable.
Natural variability: minimum and maximum distributions
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 2π. These
maximum and minimum global maps are also part of the GRACILE climatology, but
are not shown. They are provided for the same altitudes as the average global
maps. It should however be pointed out that these maximum and minimum
distributions should not be interpreted as “characteristic” global
distributions because features may just shift from year to year in the
monthly global distributions, thereby producing patterns in the
climatological maximum and minimum distributions that are not seen in single
years. Such shifts are more likely to occur in the longitudinal direction,
for example by shifts in the position of stationary planetary waves that
modulate gravity wave activity at high latitudes during wintertime.
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.
and . The meridional resolution and latitude step of those
cross sections is according to the grid used for the global maps: a
resolution of 20∘ and a step-width of 5∘ for SABER, and a
resolution of 5∘ and a step-width of 2.5∘ for HIRDLS. As a
measure of natural variability, also for zonal averages maximum and minimum
values are provided together with the “climatological average”.
An example of this variability is shown in Fig.
for absolute momentum fluxes and each climatological calendar month at 30 km
altitude. The black solid and red solid lines are for SABER and HIRDLS,
respectively, and represent the “climatological average”, while the
corresponding shaded envelopes indicate the range of natural variability of
the monthly zonal-average values for the respective calendar month. The
borders of these envelopes represent the maximum or minimum monthly
zonal-average value, respectively, that is attained in the multi-year data
sets of HIRDLS and SABER, respectively, for a given calendar month.
The latitude range between the two vertical lines at 50∘ S and
50∘ N indicates the latitude range that is continuously observed by
SABER. Consequently, SABER values poleward of these lines will be less robust
and less representative of typical conditions during the respective month.
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 . However,
the distributions in represent a fewer number of years
and just the months of January and July.
Considering an overall error of momentum fluxes of a factor of 2 or more
(cf. Sect. ), in Fig. there
is an overall agreement between the SABER and HIRDLS distributions, even
though HIRDLS covers a shorter time period of only 3 years. There are still
some offsets between SABER and HIRDLS that are mostly in the range 20 to
30 %. These offsets may be related to differences in the viewing
geometries of the instruments, differences in the sampling, as well as
differences in the “real” sensitivity functions of the instruments, or the
different numbers of years covered.
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∘ N are
closer to October conditions, i.e., somewhat enhanced with respect to average
September conditions (cf. Fig i and j). Average
September conditions at high northern latitudes will be better represented by
HIRDLS because HIRDLS covers high northern latitudes during the whole month.
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.,
).
This effect is mainly seen in January and February poleward of about
40∘ N (see Fig. a and b).
There is also a large range of variability in March for SABER, but not for
HIRDLS (see Fig. c). This effect is caused by
the single year of 2011. In this year, there was an exceptionally strong and
stable polar vortex with far above-average activity of gravity waves for this
month e.g.,.
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 -999. Also provided are
approximate sensitivity functions. The latitude–altitude grid is the same as
for the parameters listed in
Table .
parameter name
unit
array type
description
n_bin_temp_var_zav_clim_XX
number
3-D (lat, z, month)
zonal-average number of data points falling into lat/long bins used for
global maps of gravity wave temperature variances (single profiles)
(12 average calendar months)
n_bin_temp_ampsq_single_zav_clim_XX
number
3-D (lat, z, month)
same, but numbers refer to gravity wave squared amplitudes
(single profiles) (12 average calendar months)
n_bin_pair_shortdx_zav_clim_XX
number
3-D (lat, z, month)
same, but numbers refer to pairs of consecutive gravity wave
squared amplitude profiles that have horizontal separations short
enough to be potentially used for calculating gravity wave momentum
fluxes (12 average calendar months)
n_bin_pair_gwmf_zav_clim_XX
number
3-D (lat, z, month)
same, but numbers refer to pairs of consecutive gravity wave
squared amplitude profiles that are finally used for calculating
gravity wave momentum fluxes (12 average calendar months)
ratio_T_precsq_gw_temp_var_zav_clim_XX
ratio
3-D (lat, z, month)
ratio of estimated temperature precision squared to gravity wave
temperature variances (12 average calendar months)
lh_grid
km
1-D
horizontal wavelength coordinate for sensitivity function
lz_grid
km
1-D
vertical wavelength coordinate for sensitivity function
sens_fct_XX
fraction
2-D (lh, lz)
approximate sensitivity function for the gravity wave parameters
provided as function of gravity wave horizontal and vertical wavelengths,
values are relative sensitivity, i.e., between about 0 and 1
(see also Fig. c and d)
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 -999. The latitude–altitude grid is
the same as for the parameters listed in
Table .
parameter name
unit
array type
description
time_grid_zav_series_XX
years
1-D
continuous time coordinate (years) with the cross section attributed
to the middle of the months (HIRDLS: 36 months, SABER 156 months)
time_grid_zav_series_XX_iso
ISO8601
1-D
continuous time coordinate in ISO8601 format with the cross section
attributed to the 15th 23:59:59 UT of each month (HIRDLS: 36 months,
SABER 156 months)
year_grid_zav_series_XX
year
1-D
year of the particular month (HIRDLS: 36 months, SABER 156 months)
month_grid_zav_series_XX
month
1-D
month in the particular year (January = 1, … December = 12)
(HIRDLS: 36 months, SABER 156 months)
gwmf_zav_series_XX_Pa
Pa
3-D (lat, z, month)
time series of monthly zonal-average gravity wave momentum fluxes
(HIRDLS: 36 months, SABER 156 months)
gwmf_zav_series_XX_m2s2
m2 s-2
3-D (lat, z, month)
same, but in units of m2 s-2
gw_temp_var_zav_series_XX
K2
3-D (lat, z, month)
time series of monthly zonal-average gravity wave temperature
variances (HIRDLS: 36 months, SABER 156 months)
gw_temp_ampsq_single_zav_series_XX
K2
3-D (lat, z, month)
time series of monthly zonal-average gravity wave squared amplitudes
of single altitude profiles (HIRDLS: 36 months, SABER 156 months)
gw_temp_ampsq_mfpairs_zav_series_XX
K2
3-D (lat, z, month)
time series of monthly zonal-average gravity wave squared amplitudes
of pairs that are used to estimate momentum fluxes
(HIRDLS: 36 months, SABER 156 months)
gw_Epot_single_var_zav_series_XX
J kg-1
3-D (lat, z, month)
time series of monthly zonal-average gravity wave potential energies
calculated from variances based on single altitude profiles of residual
temperatures (HIRDLS: 36 months, SABER 156 months)
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 -999. In
addition to the climatological distributions listed in the table, also
distributions of maximum and minimum monthly values are given. These
distributions are named “_clim_max” and “_clim_min” (instead of just
“_clim”).
parameter name
unit
array type
description
lon_grid_map_XX
degrees
1-D
longitude coordinate for global maps
lat_grid_map_XX
degrees
1-D
latitude coordinate for global maps
z_grid_map_XX
km
1-D
altitude coordinate for global maps
gwmf_map_clim_XX_Pa
Pa
4-D (lon, lat, z, month)
climatological global maps of gravity wave momentum fluxes
(12 average calendar months)
gwmf_map_clim_XX_m2s2
m2 s-2
4-D (lon, lat, z, month)
same, but in units of m2 s-2
gw_temp_var_map_clim_XX
K2
4-D (lon, lat, z, month)
climatological global maps of gravity wave temperature variances
(12 average calendar months)
gw_temp_ampsq_single_map_clim_XX
K2
4-D (lon, lat, z, month)
climatological global maps of gravity wave squared amplitudes
of single altitude profiles (12 average calendar months)
gw_temp_ampsq_mfpairs_map_clim_XX
K2
4-D (lon, lat, z, month)
climatological global maps of gravity wave squared amplitudes
of pairs that are used to estimate momentum fluxes
(12 average calendar months)
gw_Epot_single_var_map_clim_XX
J kg-1
4-D (lon, lat, z, month)
climatological global maps of gravity wave potential energies
calculated from variances based on single altitude profiles of
residual temperatures (12 average calendar months)
gw_Lz_single_map_clim_XX
km
4-D (lon, lat, z, month)
climatological global maps of gravity wave vertical wavelengths
calculated from single altitude profiles of residual temperatures
(12 average calendar months)
gw_kh_mfpairs_map_clim_XX
km-1
4-D (lon, lat, z, month)
climatological global maps of gravity wave horizontal wavenumbers
divided by 2π calculated for those pairs of altitude profiles that are
used to estimate momentum fluxes (12 average calendar months)
Time series of monthly zonal averages
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. for absolute gravity wave momentum
fluxes. Figure a and b show absolute
gravity wave momentum fluxes for HIRDLS and SABER, respectively, at 30 km
altitude.
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 ∼ 20 % and have been discussed before in
Sects. and . These differences, however,
cannot be taken as a measure of the overall uncertainty of the values shown.
As has been pointed out by , the uncertainty of momentum
flux estimates is much larger (about a factor of 2, or even more). The
largest uncertainties are expected in the summertime lowermost stratosphere,
and in the cold summer mesopause region (see also Sect. ).
In addition to the time series at 30 km,
Fig. c and d show SABER absolute gravity
wave momentum fluxes at 50 km (Fig. c)
and 70 km altitude (Fig. d). At altitudes
of 30 and 50 km the seasonal variations are dominated by a winter maximum at
high latitudes and a summer maximum in the subtropics. The wintertime maximum
is related to the polar vortex, and the summertime maximum is caused by
gravity waves that are excited by deep convection in the subtropics. For
comparison, Fig. shows the same as
Fig. but for gravity wave potential
energies. Also in Fig. the alternating
pattern of maxima at wintertime high latitudes and in the summertime
subtropics is evident.
This alternating pattern changes between 50 and 70 km. The subtropical
maximum is shifted poleward, likely an effect of meridional propagation of
gravity waves e.g.,.
In addition, the wintertime maximum that is related to the polar vortex
weakens considerably. This leads to a semiannual rather than an annual
variation of gravity wave absolute momentum fluxes at mid and high latitudes.
These effects have been reported before by , or
.
Weaker variations are related to the QBO and the SAO
(e.g., ). In
addition, there is a weak quasi-decadal variation see
also. Similar quasi-decadal variations are also found in
gravity wave energy densities observed by radiosondes .
These variations might be correlated with the 11-year solar cycle, however,
much longer data sets would be needed for an in-depth investigation of this
effect.