ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus GmbHGöttingen, Germany10.5194/angeo-33-483-2015Driving of the SAO by gravity waves as observed from satelliteErnM.m.ern@fz-juelich.dehttps://orcid.org/0000-0002-8565-2125PreusseP.RieseM.https://orcid.org/0000-0001-6398-6493Institut für Energie- und Klimaforschung – Stratosphäre (IEK–7),
Forschungszentrum Jülich GmbH, 52425 Jülich, GermanyM. Ern (m.ern@fz-juelich.de)29April201533448350410October20142April20157April2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/33/483/2015/angeo-33-483-2015.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/33/483/2015/angeo-33-483-2015.pdf
It is known that atmospheric dynamics in the tropical stratosphere have an
influence on higher altitudes and latitudes as well as on surface weather
and climate. In the tropics, the dynamics are governed by an interplay of the
quasi-biennial oscillation (QBO) and semiannual oscillation (SAO) of the
zonal wind. The QBO is dominant in the lower and middle stratosphere, and the
SAO in the upper stratosphere/lower mesosphere. For both QBO and SAO the
driving by atmospheric waves plays an important role. In particular, the role
of gravity waves is still not well understood.
In our study we use observations of the High Resolution
Dynamics Limb Sounder (HIRDLS) satellite instrument to derive gravity wave momentum fluxes and
gravity wave drag in order to investigate the interaction of gravity waves
with the SAO. These observations are compared with the ERA-Interim
reanalysis. Usually, QBO westward winds are much stronger than QBO eastward
winds. Therefore, mainly gravity waves with westward-directed phase speeds
are filtered out through critical-level filtering already below the
stratopause region. Accordingly, HIRDLS observations show that gravity waves
contribute to the SAO momentum budget mainly during eastward wind shear, and
not much during westward wind shear. These findings confirm theoretical
expectations and are qualitatively in good agreement with ERA-Interim and
other modeling studies. In ERA-Interim most of the westward SAO driving is
due to planetary waves, likely of extratropical origin. Still, we find in
both observations and ERA-Interim that sometimes westward-propagating gravity
waves may contribute to the westward driving of the SAO. Four characteristic
cases of atmospheric background conditions are identified. The forcings of
the SAO in these cases are discussed in detail, supported by gravity wave
spectra observed by HIRDLS. In particular, we find that the gravity wave
forcing of the SAO cannot be explained by critical-level filtering alone;
gravity wave saturation without critical levels being reached is also
important.
Meteorology and atmospheric dynamics (general circulation; middle atmosphere dynamics; waves and tides)Introduction
In the tropical stratosphere and lower mesosphere, the zonal
wind is dominated by an interplay of the quasi-biennial oscillation (QBO) in
the lower and middle stratosphere and the semiannual oscillation (SAO) in the
upper stratosphere/lower mesosphere. The QBO has an average period of
28 months. Usually the QBO winds are asymmetric with a strong westward
wind phase (as strong as about -40 m s-1) and much weaker eastward winds
(only about 20 m s-1 at maximum). The SAO has a period of 6 months, and
both eastward and westward winds can be quite strong: about -60 to
-20 m s-1 for westward wind, and about 20 to 40 m s-1 for eastward wind e.g.,and references
therein. More details about QBO
and SAO can be found in and references therein.
The QBO and the SAO are important processes in atmospheric dynamics. Both QBO
and SAO have an effect on the tracer transport in the stratosphere
e.g.,.
Further, the QBO has an effect on the stability of the polar vortex
e.g.,, and there are indications that both QBO and
SAO have an influence on the timing of sudden stratospheric warmings
e.g.,. It has been found that the QBO has an effect on
the weather and climate in the lower atmosphere and even at the surface
e.g.,.
Because of their importance, the tropics have been the focus of previous measurement campaigns and
will be the topic of future ones
e.g.,.
In addition, modeling efforts are currently underway to improve the
representation of the tropics and, in particular, the QBO in weather and
climate models
e.g.,.
With a more realistic model representation of the QBO, potentially the
coupling toward higher latitudes and even seasonal weather prediction might
be improved e.g.,.
Both QBO and SAO filter the spectrum of waves that propagate upward. This
filtering of waves is relevant for the formation of circulation patterns at
higher altitudes. For example, the pre-filtered wave spectrum is likely
responsible for the formation of a QBO and an SAO in the tropical mesopause
region see alsoand references
therein.
It has also been found that the QBO and the SAO interact with each other. For
example, the QBO and SAO periods are often synchronized
e.g.,, and it has been
suggested that the eastward phase of the SAO can initiate an eastward phase
of the QBO e.g.,.
It was proposed by and
that the QBO is a wave-driven circulation. The wave
driving by planetary waves alone is, however, not sufficient, and it has been
concluded that most of the wave driving is contributed by mesoscale gravity
waves e.g.,. This is
also in agreement with direct observations of the QBO driving by gravity
waves .
Similarly, the wind reversal of the SAO from westward to eastward winds is
likely driven by gravity waves and (to a minor extent) by planetary waves, for
example equatorially trapped Kelvin waves. Different from this, the wind
reversal from SAO eastward to westward wind is assumed to be mainly driven by
horizontal advection and meridional momentum transport of extratropical
planetary waves
e.g.,.
Therefore the descent of the SAO westward wind phase with time is usually
much steeper than the descent of the SAO eastward wind phase, which is mainly driven
by vertically propagating waves. In particular, several studies
suggest that the filtering of the spectrum of upward-propagating waves by the
QBO has a strong influence on the SAO winds
e.g.,. This wave-filtering effect of the QBO (mainly critical-level filtering) is also seen in
observed gravity wave momentum flux spectra .
A number of general circulation models (GCMs) and chemistry–climate models
(CCMs) are able to simulate an SAO. In most simulations, the SAO is driven by
a combination of resolved waves and parameterization of subgrid-scale gravity
waves e.g.,. In some
simulations, the SAO is driven alone by gravity waves and planetary waves
explicitly resolved by the model e.g.,.
The role of the different terms in the tropical momentum balance,
in particular the role of gravity wave drag,
is, however, strongly dependent on the model setup and
model resolution
e.g.,.
This shows that there is still large uncertainty about details of the
forcing of the SAO.
To obtain a more realistic QBO and SAO in GCMs/CCMs, an improvement in the
parameterized gravity wave drag is required. Up to now most observational
estimates of the gravity wave contribution to the SAO momentum budget have
been from ground-based stations
e.g.,. In order to constrain
gravity wave parameterizations, however, global observations (from satellite)
are needed e.g.,.
Several previous studies based on global satellite observations indicate that
the gravity wave distribution in the tropics interacts with the QBO and SAO
winds
e.g.,.
These studies were, however, limited to gravity wave variances or squared
amplitudes. It was only recently that information
about gravity wave momentum fluxes, gravity wave drag, and detailed spectral
information were obtained for the QBO by . For the
SAO, the direct estimation of gravity wave drag from global observations is
still an open issue. Further, spectral information about the gravity waves
that contribute to the SAO can help to improve our physical understanding of
the wave dynamics in the tropics.
In our study we use satellite observations of gravity waves by the High
Resolution Dynamics Limb Sounder (HIRDLS) instrument to investigate how
gravity waves contribute to the driving of the SAO. In
Sect. some information about the HIRDLS instrument is
given, as well as descriptions of how gravity waves are extracted from the temperature
observations and how gravity wave momentum fluxes and drag are derived. In
Sect. we determine the SAO momentum budget from the
European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim
reanalysis. In Sect. it is shown how HIRDLS gravity wave
variances and momentum fluxes are modulated by the SAO. Further, gravity wave
drag is calculated from the momentum fluxes and compared to the SAO momentum
budget in ERA-Interim. The driving of the SAO by gravity waves is discussed
in detail for four characteristic cases in Sect. . In
Sect. this discussion is supported by presenting
gravity wave spectra that are determined from the observations. Finally, in
Sect. the results are summarized and discussed.
Data and methodsSatellite data and related gravity wave diagnostics
Our study is based on temperature observations of the HIRDLS satellite
instrument and the gravity wave momentum fluxes that are estimated from these
observations. In the following, some information about the HIRDLS instrument
is given, and the procedure to derive gravity wave momentum fluxes and drag
is introduced.
The HIRDLS instrument
The HIRDLS instrument observes atmospheric limb emissions of CO2 at
15 µm in the infrared. From these observations, altitude profiles of
atmospheric temperature are derived, as well as several trace species. HIRDLS
is onboard the EOS-Aura satellite, and temperature observations are available
from January 2005 until March 2008. The altitude range covered is from the
tropopause region to the upper mesosphere. The vertical resolution of the
observed temperature altitude profiles is close to the vertical field of view
of the instrument (about 1 km). The HIRDLS horizontal sampling distance
between consecutive altitude profiles is about 90 km.
More information about the HIRDLS instrument and temperature retrieval is
given, for example, in and
. In our study we use HIRDLS V006 temperatures
see also.
Extraction of gravity waves, and estimation of gravity wave
momentum flux and drag
To investigate the role of gravity waves in the forcing of the SAO we derive
gravity wave variances, momentum fluxes and drag from HIRDLS temperature
observations. All time series presented later in our work are averages over
the latitude band 10∘ S–10∘ N and over 7 days
with a time step of 3 days. This provides both good statistics and a time
resolution that is sufficient to sample the rapid circulation changes that
are associated with the SAO.
Extraction of gravity waves
In order to extract gravity waves from satellite temperature observations
we follow the procedure described in
.
In the first step, from observed temperature altitude profiles the zonal-mean
background temperature is subtracted, as well as stationary and traveling
global-scale waves of zonal wave numbers 1–6. In particular, Kelvin waves in
the tropics, which can have very short periods of only a few
days e.g.,, are also removed. The
strongest tidal modes are removed by subtracting quasi-stationary zonal
wave numbers 0–4 separately for ascending and descending parts of the
satellite orbits see also.
The result after this first step are altitude profiles of residual
temperatures that can be attributed to mesoscale gravity waves. The strongest
vertical wave structures in these altitude profiles are determined by a
two-stage method called MEM/HA, which is described in detail in
. The result is vertical profiles of wave amplitudes,
vertical wavelengths and vertical phases of the strongest gravity waves for
each altitude profile of residual temperatures. In our study, these gravity
wave parameters are determined in windows of 10 km vertical extent
see also. In this way a large vertical
wavelength range of 2–25 km is covered by the analysis.
Estimation of absolute momentum fluxes
The absolute momentum flux Fph carried by an observed gravity wave is
calculated using the following equation :
Fph=12ϱ0λzλhgN2T^T2.
In this equation λh and λz are the horizontal and vertical
wavelength of the gravity wave, ϱ0 is the atmospheric density, g
the gravity acceleration, N the buoyancy frequency, T^ the
temperature amplitude of the wave, and T the atmospheric background
temperature.
The horizontal wavelength of a gravity wave is determined from pairs of
altitude profiles. Like in , we assume that the same wave
is observed in two consecutive altitude profiles of a given satellite
measurement track (profile pairs) if the vertical wavelengths in these
altitude profiles differ by no more than 40 %. In the tropics this is the
case for about 60–70 % of all profile pairs. The HIRDLS along-track
sampling time step is about 10–15 s on average. Therefore, it can be
assumed that a gravity wave is observed quasi-instantaneously by two
consecutive altitude profiles see also. The horizontal
wavelength of the observed gravity wave is estimated from the shift of the
vertical phase of the wave between the two altitude profiles see
also.
This horizontal wavelength is, however, only the projection of the true
horizontal wavelength of the gravity wave on the satellite measurement track,
and is therefore always an overestimation. See also the discussion in
.
Because the spatial orientation of the observed gravity wave cannot be
determined from a single satellite measurement track, no directional
information is available, and the momentum fluxes are only absolute (total)
momentum fluxes. See also the detailed discussion in .
The uncertainty of these total momentum fluxes is large, at least a factor of
2. Two main error sources are uncertainties in the horizontal wavelength
and the sensitivity of the instrument for the detection of gravity waves.
This sensitivity decreases close to the detection limits at short horizontal
and short vertical wavelengths. Satellite instruments observing in
limb-viewing geometry can only detect gravity waves with horizontal
wavelengths > 100–200 km see
also, and therefore
observe only part of the momentum flux of the whole spectrum of gravity waves
e.g.,. Further, the vertical resolution
of an instrument limits the range of vertical wavelengths that can be
detected. Therefore HIRDLS is sensitive only to gravity waves with vertical
wavelengths > 2 km. For a more detailed error discussion see also
and .
Estimation of total (absolute) gravity wave drag
The total (absolute) drag XY by gravity waves on the background flow can be
calculated from vertical gradients of total (absolute) momentum flux:
XY=-1ϱ0∂Fph∂z,
with z the vertical coordinate.
Because the total momentum flux Fph is only an absolute value, the total
drag XY calculated from its vertical gradient also contains no
directional information. Like total momentum fluxes, total gravity wave drag
has large uncertainties, at least a factor of 2. The net gravity wave drag
that is exerted on the background flow could even be zero in regions of
non-zero total drag if the drag due to the single gravity waves in a certain
region cancels out see
also.
This lack of directional information can, however, often be overcome. For
example, for the case of a wind reversal at the top of a strong wind jet, it
can be assumed that the momentum flux distribution below the wind reversal is
dominated by gravity waves propagating opposite to the wind direction in the
jet e.g.,. If these waves, while
propagating upward, encounter the wind reversal at the top of the jet, they
will dissipate more strongly because they either encounter critical wind
levels or their propagation conditions become less favorable
(intrinsic frequencies and thus critical amplitudes for the onset of wave
breaking are reduced). For such cases the resulting net drag will then be
close to equal to the total drag and will be opposite to the prevailing wind
direction in the jet see also. Cases where the
assumption of a prevalent direction of the total gravity wave drag observed
from satellite led to meaningful results are, for example, the reversal of
the summertime mesospheric jet or the gravity wave
driving of the QBO .
In our current study the situation is sometimes more complicated because the
spectrum of gravity waves that reaches the stratopause region and contributes
to the driving of the SAO is pre-filtered by the QBO in the lower and middle
stratosphere. This is discussed in detail in
Sects. –.
ERA-Interim and the TEM zonal momentum budget
As mentioned in the Introduction, the contribution of gravity waves in the
tropical momentum budget of the SAO is not well known and differs between
different simulations. Therefore, one of the main goals of our study is to
provide some guidance for global models regarding the role of gravity waves
in the SAO momentum budget. For this purpose, realistic background winds are
required for the period and altitude range considered. Previous studies
have shown that zonal winds in the tropics provided by ECMWF are in good
agreement with observations
e.g.,. In particular,
there is qualitatively good agreement between the QBO-related gravity wave
drag variations derived from the ECMWF ERA-Interim reanalysis and those
derived from satellite observations . Therefore we use
ERA-Interim also for studying the role of gravity waves in the driving of the
SAO. More information about ERA-Interim can be found in .
For our study, ERA-Interim data are interpolated on a horizontal
longitude/latitude grid of 1 ∘×1 ∘ resolution. The
vertical resolution is about 1.4 km. Further, we use all available time
steps (00:00, 06:00, 12:00 and 18:00 GMT) to avoid biases by diurnal cycle
effects see also.
The different terms of the ERA-Interim momentum budget are calculated for
each of the 6 h time steps. In order to match the temporal resolution of our
HIRDLS gravity wave data, 7-day averages are calculated from these single
estimates every 3 days (see also Sect. ). Finally,
latitudinal averages are calculated over the tropical latitude band
10∘ S–10∘ N.
As detailed in , the transformed Eulerian mean (TEM)
momentum budget of the zonal-mean zonal wind can be written as follows:
∂u‾∂t+v‾*u‾cosΦΦacosΦ-f+w‾*u‾z=X‾PW+X‾GW,
with u‾ the zonal-mean zonal wind, ∂u‾/∂t its tendency, and v‾* and
w‾* the TEM meridional and vertical wind, respectively. Further,
f is the Coriolis frequency, a the Earth's radius, and Φ the
geographic latitude. X‾PW and X‾GW are the
zonal-mean zonal wave drag due to planetary waves and gravity waves,
respectively. Subscripts Φ and z stand for differentiation in
meridional and vertical direction, respectively, and overbars indicate zonal
averages.
In the following, the momentum terms involving v‾* and
w‾* will be called “meridional advection term” and “vertical
advection term”, respectively.
Altitude–time cross sections of the 10∘ S–10∘ N
average
(a) ERA-Interim zonal wind in m s-1,
and the following
terms of the ERA-Interim
tropical momentum budget in m s-1 d-1:
(b) zonal wind tendency ∂u‾/∂t,
(c) planetary wave drag from
EP flux divergence including zonal wave numbers 1–20, and
(d) missing drag
that is attributed to gravity waves.
Contour lines represent the zonal wind from (a). The bold solid line
is the zero wind line.
Dashed (solid) lines indicate westward (eastward) wind.
Contour interval is 20 m s-1.
Generally, the drag of resolved waves X‾res can be
calculated from the divergence of the Eliassen–Palm flux (EP flux).
The meridional (F(Φ)) and vertical component (F(z)) of the EP
flux can be expressed as follows:
F(Φ)=ϱ0acosΦv′Θ′‾Θ‾zu‾z-u′v′‾,F(z)=ϱ0acosΦf-(u‾cosΦ)ΦacosΦv′Θ′‾Θ‾z-u′w′‾.
The divergence of EP flux is given by
∇⋅F=1acosΦ∂∂ΦF(Φ)cosΦ+∂∂zF(z),
and the zonal-mean drag of resolved waves is
X‾res=1ϱ0acosΦ∇⋅F.
Generally, both planetary waves and gravity waves contribute to the
overall drag of resolved waves.
In our work, we use the drag of waves with zonal wave numbers k= 1–20 that
are explicitly resolved in ERA-Interim (i.e., only the larger-scale resolved
waves) as an estimate for the drag of planetary waves
X‾PW in Eq. ():
X‾PW=X‾res(k≤20).
See also .
Usually, in models the contribution of gravity waves (X‾GW)
comprises the contribution of all resolved waves with higher zonal
wave numbers (for example, k> 20), gravity wave drag
X‾param
that is simulated by dedicated parameterizations
(in the case of ERA-Interim just by Rayleigh friction),
and the remaining imbalance X‾imbalance in the momentum budget
that is introduced, for example, by data assimilation.
In our case, the overall contribution of gravity waves can be written as
X‾GW=X‾res(k>20)+X‾param+X‾imbalance.
In the ECMWF model, the contribution X‾res(k>20),
attributed to gravity waves resolved by the model, severely underestimates
the contribution of gravity waves in the real atmosphere, and the
distribution of resolved waves of high zonal wave number in the tropics is
not very realistic e.g.,.
Further, X‾param and X‾imbalance
are not standard model output and are therefore not known. For this reason,
we follow an approach similar to the one presented in
and estimate the contribution
X‾GW in Eq. () indirectly. This is
done by calculating X‾GW in Eq. ()
as “missing drag” from all the other terms in the ERA-Interim momentum
budget, thereby assuming that all other contributions in
Eq. () are known and realistic see
also. Given a good underlying model and by assimilating a
considerable amount of data, this missing drag can be assumed to be the
contribution of gravity wave drag in the zonal momentum budget
e.g.,. Even if the missing drag
should no longer be fully reliable in the stratopause region (for example,
because only few data are available for the data assimilation), the missing
drag can be used as a proxy for gravity wave drag, and its relative
variations should still contain valuable information.
The SAO momentum budget in ERA-Interim
Altitude–time cross sections of the ERA-Interim zonal wind and the different
terms of the tropical momentum budget in the altitude range 30–60 km are
shown in Fig. . As mentioned before, all values in these time
series are 7-day averages, additionally averaged over the latitude band
10∘ S–10∘ N. The time series covers the period from January
2005 until June 2008.
Figure a shows the zonal-mean zonal wind, which displays a
pronounced semiannual oscillation pattern, centered at about 47 km
altitude. During the course of a calendar year, a strong westward wind phase
is followed by an eastward wind phase, a weaker westward wind phase, and,
again, an eastward wind phase. There is, however, considerable interannual
variability in the strength of the different wind phases, as well as the
exact timing and altitude of their maxima. A longer time series of tropical
winds can be found, for example, in , and an investigation
of the relative strength of different SAO cycles has been carried out, for
example, by . In particular,
argue that activity of Rossby waves at northern
latitudes is responsible for the finding that the first SAO cycle of a
year is often stronger. At altitudes below 40 km the zonal wind is dominated by
the QBO.
Figure b shows the wind tendency
∂u‾/∂t. Usually the zones of eastward (i.e.,
positive) wind tendency are tilted, meaning they descend in altitude with
time. This characteristic behavior is typical for wind reversals that are
driven by upward-propagating waves
e.g.,. Different from
this, zones of westward (i.e., negative) wind shear are almost vertical. This
indicates that SAO wind reversals from eastward to westward wind are likely
not driven by dissipation of upward-propagating waves that have their sources
in the tropical troposphere. In the period considered, there is, however, one
exception to this rule: the westward shear zone in mid-2006 descends in
altitude with time, which suggests that (as an exception) this wind reversal
is mainly driven by upward-propagating tropical waves.
Even though fewer and fewer data are assimilated in ERA-Interim at increasing
altitude, the SAO zonal winds should be quite reliable
e.g.,. Consequently, the
zonal wind tendency ∂u‾/∂t, which is determined
directly from u‾, should also be quite reliable.
In ECMWF data planetary waves are quite realistic in the lower stratosphere
.
Although the quality of the planetary waves in ECMWF
somewhat decreases toward higher altitudes
,
it can be assumed that the main features of planetary wave driving are
captured by ERA-Interim at stratopause heights.
ERA-Interim planetary wave drag for zonal wave numbers k= 1–20 derived from
the EP flux divergence is shown in Fig. c. Satellite
observations suggest that eastward-directed planetary wave drag of vertically
propagating Kelvin waves (the strongest eastward-propagating equatorial
planetary wave mode) should be small at the stratopause
e.g.,. This is also indicated in
the ERA-Interim planetary wave drag: eastward planetary wave drag is mostly
weak. Except for sporadic events, it is usually weaker than 0.5 m s-1 d-1.
Westward planetary wave drag, however, is usually quite strong during early
winter of both hemispheres (June/July and November/December), and it reaches
values as high as -2 m s-1 d-1 (occasionally even -4 m s-1 d-1). These
bursts of strong planetary wave drag are likely not caused by vertically
propagating equatorially trapped waves, because these bursts do not show the
characteristic descent in altitude with time that is typical for
wave–mean-flow interaction by critical-level filtering of upward-propagating
waves. Instead, the strong planetary wave drag events occur simultaneously
over a large altitude range. This indicates that these events are likely
caused by horizontal transport of wave momentum of extratropical waves from
the polar jets, as has been proposed by several authors
e.g.,. These strong bursts of
planetary wave drag are in good correspondence with the periods of strong
westward (negative) zonal wind tendency in Fig. b, and are
therefore likely the main driver of the wind reversal from SAO eastward to
SAO westward winds.
One exception is mid-2006: during this period the westward-directed
planetary wave drag is less pronounced.
The missing drag in the ERA-Interim momentum budget is displayed in
Fig. d. This missing drag is the sum of wind tendency
(Fig. b) and advection terms minus planetary wave drag
(Fig. c). For a discussion of the ERA-Interim advection terms
see Appendix . Even if the magnitude of the missing drag may
not be fully realistic, relative variations can provide some information
about the contribution of gravity waves in the SAO momentum budget.
Planetary wave drag alone is almost sufficient to explain the negative (i.e.,
westward) wind tendencies in Fig. b. Since other
contributions of negative drag are much weaker, the missing drag
(Fig. d) is dominated by the meridional advection term, which
is the strongest positive contribution in the ERA-Interim momentum budget
(see Appendix ). Gravity waves are therefore expected to
contribute mainly to the SAO wind reversals from westward to eastward winds.
Westward (i.e., negative) gravity wave drag (i.e., missing drag) is usually
much weaker and found only sometimes during westward wind shear (for example
in mid-2006), or in the lower part of the SAO westward wind jets during
December/January.
Gravity waves observed from satellite and the SAO momentum budget
We now investigate how observed gravity waves are modulated by the SAO, and
whether observed absolute gravity wave momentum fluxes and gravity wave drag
are in agreement with the theoretical picture of the driving of the SAO. In
particular, it is expected that eastward wave driving of the SAO should be
dominated by upward-propagating gravity waves, while westward driving is
expected to arise from extratropical planetary waves
e.g.,.
Altitude–time cross sections of averages over the
latitude band 10∘ S–10∘ N.
(a) HIRDLS gravity wave
squared temperature amplitudes determined in 10 km
vertical windows
from
the HIRDLS altitude profiles.
Values were divided by 2 to be comparable to gravity wave variances.
Units in (a) are dB(K2).
(b) HIRDLS
total gravity wave momentum fluxes in mPa
from a gravity wave analysis using a 10 km vertical window covering
vertical wavelengths < 25 km, and
(c) total gravity wave drag obtained from vertical gradients of the
HIRDLS momentum fluxes shown in (b).
For comparison,
ERA-Interim
(d)∂u/∂t and
(e) planetary wave drag (k= 1–20)
are repeated from Fig. 1b and c, respectively.
Units in (c–e) are m s-1 d-1.
Contour lines indicate the zonal wind:
westward wind is dashed,
and the bold contour line indicates zero wind.
Contour increment is 20 m s-1.
Gravity wave squared amplitudes
Figure a shows an altitude–time cross section of gravity wave
squared temperature amplitudes of the strongest gravity waves found in the
individual altitude profiles in the latitude band
10∘ S–10∘ N using a MEM/HA vertical analysis with a 10 km
vertical window (see Sect. ). Squared amplitudes were
divided by 2 to make the values directly comparable to gravity wave
temperature variances. For a comparison of gravity wave squared amplitudes
and variances see Appendix .
From Fig. a, we find that gravity wave squared amplitudes are
considerably stronger during SAO westward wind than during eastward wind.
This is likely an effect of wave filtering by the QBO: the red shaded area in Fig. d shows the range of ground-based
wave phase speeds that would encounter critical levels due to the QBO winds
in the altitude range 18–40 km. As can be seen from
Fig. d, this range is asymmetric with respect to zero
wind. This is the case because the amplitude of the QBO westward phase (about
-40 m s-1) is much stronger than the amplitude of the QBO eastward
phase (about 10 m s-1). Consequently, a much larger range of
westward-directed gravity wave phase speeds (phase speed range from 0 to
-40 m s-1) will be filtered out by the QBO at altitudes below
40 km. Therefore gravity wave amplitudes and variances are reduced during
SAO eastward winds, even though propagation conditions for gravity waves with
westward-directed phase speeds would be favorable due to increased intrinsic
phase speeds and thereby increased saturation amplitudes see
also.
Time series at 47 km
(about the center altitude of the SAO)
for the period January 2005 until June 2008.
All parameters are averages over the latitude band
10∘ S–10∘ N.
(a) The zonal-average zonal wind from ERA-Interim in m s-1
and
(b) the ERA-Interim zonal momentum budget terms:
∂u‾/∂t (black dashed),
0.5 times the sum of meridional and vertical advection terms (blue),
0.5 times missing drag (red),
and
planetary wave drag for zonal wave numbers 1–20 (green).
(c) Comparison of
observed HIRDLS gravity wave drag at 46 km (black)
and
absolute values of
several ERA-Interim terms at 47 km
averaged vertically over 10 km:
∂u‾/∂t (black dashed),
planetary wave drag (green), and
0.5 times missing drag (red).
(d) Range of ground-based phase speeds (red shaded)
that are filtered out by the QBO in the altitude range 18–40 km.
(e) ERA-Interim zonal wind at the altitude levels
z1= 41 km (black)
and z2= 51 km (red).
Months of four characteristic background wind situations are
indicated by blue hatched bands.
In all panels
periods of strong westward (eastward) wind shear are indicated by gray
(orange) shading.
Times when the zonal wind at 47 km is zero are marked by brown vertical
lines.
Different from this, eastward-propagating gravity waves with ground-based
phase speeds exceeding the maximum eastward QBO wind of only 10–20 m s-1
are not filtered out by the QBO and can reach the stratopause region. During
phases of SAO westward wind these waves find favorable propagation conditions
(increased critical amplitudes because background wind and phase speed of the
waves are opposite). Consequently, we find large variances and amplitudes of
likely eastward-propagating gravity waves during SAO westward wind phases,
much higher than gravity wave variances and amplitudes during SAO eastward
winds.
Gravity wave momentum flux
The altitude–time distribution of absolute values of HIRDLS gravity wave
momentum fluxes estimated as described in Sect. is
displayed in Fig. b. The values are given in millipascal on
a linear scale. As already indicated by the enhanced gravity wave variances
during phases of SAO westward winds, gravity momentum fluxes are also much
stronger during westward winds than during eastward winds. Again, this is an
effect of the filtering of the spectrum of upward-propagating gravity waves
by the QBO in the stratosphere.
In the absence of wave dissipation, gravity wave momentum flux would be a
conserved quantity. Different from this, in Fig. b momentum
flux decreases continuously with altitude, indicating that there is always
some dissipation of gravity waves at almost all altitudes and during most of
the time. Another important finding is that the momentum flux maxima during
SAO westward wind phases have a characteristic triangular (sawtooth-like)
shape: the shape of these maxima follows the downward propagation of the
zones of strong eastward wind tendencies with time. This indicates that the
gravity waves dissipate and interact with the background winds. Similar
effects have been observed before for Kelvin wave momentum fluxes during QBO
eastward wind shear e.g.,, for gravity wave
momentum fluxes during both eastward and westward wind shear of the QBO
, and for the wind reversal from mesospheric
westward to eastward winds in the summer hemisphere at midlatitudes
.
Gravity wave drag
Figure c shows altitude–time cross sections of absolute
(total) gravity wave drag calculated from vertical gradients of absolute
momentum fluxes. Around the stratopause gravity wave drag varies between
about zero and somewhat above 1 m s-1 d-1. As expected, gravity wave drag
usually maximizes during eastward-directed (i.e., positive) vertical shear of the
zonal wind. This is particularly the case during December, January and
February in each year, i.e., when the eastward shear is strongest.
As mentioned above, the spectrum of upward-propagating gravity waves has been
filtered by the QBO before reaching the stratopause region, and usually
westward-propagating gravity waves will undergo stronger filtering.
Particularly for SAO westward wind phases it can therefore be assumed that
the gravity wave distribution is dominated by waves propagating eastward,
i.e., opposite to the SAO background wind. During eastward wind shear the
propagation conditions of eastward-propagating waves become worse, and they
will undergo stronger dissipation. Therefore the direction of gravity wave
drag during eastward wind shear should be eastward.
This means, there is clear observational evidence that upward-propagating
gravity waves contribute strongly to the reversal from SAO westward to SAO
eastward winds. This also agrees well with the fact that the zones of
eastward wind shear propagate downward with time.
During westward (i.e., negative) vertical shear of the zonal wind gravity wave
drag is usually much weaker. Given the fact that eastward-propagating gravity
waves should dominate the gravity wave momentum flux spectrum in the
stratopause region, it is difficult to tell whether the gravity wave drag
during westward shear is directed westward or eastward. Only in May and June
2006, at altitudes above 50 km, an enhancement of observed gravity wave
drag follows closely the negative vertical shear of the zonal wind. Together
with the fact that ERA-Interim missing (i.e., gravity wave) drag in this region is
negative (see also Fig. d), this indicates that the
observed gravity wave drag should also be negative (westward). Moreover, the
exceptional descent of the zone of westward wind shear with time in mid-2006
seems to be mainly driven by dissipation of westward-propagating gravity
waves.
For comparison with the satellite observations, Fig. d shows
the zonal wind tendency ∂u‾/∂t in ERA-Interim, and
Fig. f shows the planetary wave drag in ERA-Interim
calculated from the EP flux divergence of resolved waves with zonal
wave numbers 1–20.
By comparing Fig. c–e we find that negative (i.e., westward)
values of ERA-Interim zonal wind tendency match very well with ERA-Interim
planetary wave drag. Both the tendency and planetary wave drag show enhanced
values in very short bursts that cover larger
altitude regions in nearly vertical bands. At the same time, observed absolute gravity wave drag is
usually small.
During periods when the zonal wind tendency is positive (i.e., directed eastward),
however, the situation is reversed: the tendency shows maxima that descend in
altitude with time. These maxima coincide with enhanced observed absolute
gravity wave drag, while planetary wave drag is weak at the same time.
This indicates that SAO wind reversals from eastward to westward wind
(westward tendency) are mainly driven by planetary waves (likely of
extratropical origin), while the wind reversals from SAO westward wind to SAO
eastward wind (eastward tendency) are mainly driven by eastward-propagating
gravity waves of tropical origin.
However, there are also exceptions. For example, the eastward to westward
wind reversal in mid-2006 seems to be mainly driven by westward-propagating
gravity waves. Further, negative values of gravity wave drag in ERA-Interim
(see Fig. d) might indicate that the
dissipation of westward-propagating gravity waves could also be important on other occasions (for
example, in the lower part of the SAO westward jet in December–February).
It should also be noted that the increases in observed gravity wave drag
usually coincide with the ERA-Interim zonal wind shear zones.
This means that the observed gravity wave drag is in reasonable agreement
with the pattern that would be expected from wind filtering of the wave
spectrum by the ERA-Interim SAO winds.
In addition to previous findings
e.g.,, this is another
indication that the SAO winds in ERA-Interim are quite realistic, at least in
their basic features.
Time series in the stratopause region
The timing of the different terms in the SAO momentum budget is investigated
in more detail for an altitude of 47 km, i.e., about the center altitude of
the SAO. Figure a shows the zonal-mean wind at this
altitude. The characteristic SAO pattern of alternating eastward and westward
winds can be clearly identified with the stronger westward phase (i.e., phase
of negative wind) at the beginning of each year, and with a weaker one in the
middle of each year. Periods of eastward (westward) wind tendency are
indicated by orange (gray) shading in each of
Fig. a–e. In addition, the times of zero wind are
marked by brown vertical lines.
Figure b shows the different terms in the ERA-Interim
momentum budget. The black-dotted curve is the tendency of the zonal wind
(∂u‾/∂t), the green line is the drag due to
resolved planetary waves with zonal wave numbers 1–20, the blue line is the
sum of the meridional and the vertical advection terms, and the red line is
the gravity wave drag (missing drag) in the ERA-Interim momentum budget.
Because both advection term and gravity wave drag are much stronger, they
have been multiplied by 0.5 to make them better comparable to the other
terms. Please note that the advection term and gravity wave drag are on different
sides of Eq. () and partly compensate for each other.
Again, we find that most of the eastward wind tendency in ERA-Interim can be
explained by gravity wave drag, and most of the westward wind tendency by
planetary waves. Sometimes strong westward wind tendency results in strong
negative peaks in the time series. These peaks often coincide with strong
bursts of negative (i.e., westward-directed) planetary wave drag.
Negative gravity wave drag during westward wind tendencies is usually weak.
Only in mid-2006, and in the period December 2006 until January 2007, are there
also stronger events of negative (i.e., westward) gravity wave drag. Other
instances of stronger negative gravity wave drag seen in
Fig. d, for example at the beginning of the years 2005, 2006
and 2008, are at lower altitudes and therefore do not show up in the time
series at 47 km altitude.
In Fig. c HIRDLS observations are compared with
ERA-Interim. In order to account for a minor observational filter effect, we
compare the HIRDLS time series from 46 km with the ERA-Interim time series
at 47 km see also. In Fig. c
the black solid line shows the total gravity wave drag at 46 km derived
from HIRDLS observations.
Absolute values of the following ERA-Interim momentum terms at 47 km
altitude are also displayed: zonal wind tendency (black dotted), planetary
wave drag (green), and missing (gravity wave) drag (red). For better
comparison, the ERA-Interim terms were smoothed vertically by a 10 km
running mean and averaged over the latitude band 10∘ S–10∘ N
after taking the absolute values. The vertical smoothing is applied to
account for the 10 km vertical window of our HIRDLS gravity wave analysis.
Again, gravity wave drag from ERA-Interim is multiplied by 0.5 for better
comparison.
Of course, by taking the absolute value and by averaging vertically over the
different ERA-Interim terms, significant information is lost. Still, in
Fig. c, there is an overall correspondence between
enhancements of absolute zonal wind tendency and absolute planetary wave drag
during periods of negative wind tendency, as well as between the relative
variations in absolute zonal wind tendency and absolute ERA-Interim gravity
wave drag during periods of positive wind tendency. There is also reasonable
correspondence between the relative variations in ERA-Interim and HIRDLS
absolute gravity wave drag. The correlation coefficient between absolute
ERA-Interim and HIRDLS gravity wave drag is 0.77, which is highly
significant, given the high number of data points (around 380; effectively
only around 160 due to overlapping bins).
In addition, for both HIRDLS and ERA-Interim the integral over the gravity
wave drag peak in the beginning of each year is larger than the integral over
the peak in the middle of each year. This is qualitatively in good agreement
with the fact that usually the westward wind phase in the beginning of each
year is stronger, and more gravity wave drag is required for the wind
reversal to eastward wind. This indicates that relative variations in
ERA-Interim gravity wave drag might still contain useful information at
47 km altitude.
Absolute values of ERA-Interim gravity wave drag, however, are usually much
higher: at least a factor of 2, and sometimes a factor of 4. Even though
HIRDLS observes only part of the whole spectrum of gravity waves (only
horizontal wavelengths > 100–200 km), this difference is probably too
high to be explained by observational filter effects alone. This is further
supported by several modeling studies that obtain much weaker gravity wave
drag than ERA-Interim
e.g.,.
In Fig. d the range of zonal wind speeds in the
altitude range 18–40 km is indicated by an area shaded in red. This is
about the range of ground-based zonal phase speeds that should be removed
from the spectrum of all gravity waves via critical-level filtering by the
QBO winds. Because the westward wind phase of the QBO is much stronger,
usually westward phase speeds as strong as -40 m s-1 are removed from the
spectrum. On the other hand, almost all eastward-propagating gravity waves
with phase speeds higher than about 10 m s-1 should still be contained in
the gravity wave spectrum entering the altitude range where the SAO is
observed.
One exception is the period April until July 2006. In this period only
westward-propagating gravity waves with phase speeds that are less negative
than -10 m s-1 are filtered out by the QBO. It can therefore be expected
that more westward-directed gravity wave momentum flux is available for the
driving of the SAO than during other periods. In addition, during this period
the drag due to planetary waves is comparably weak (see
Fig. c). This probably explains why in mid-2006 exceptionally
a downward-propagating westward shear zone develops. This shear zone is
likely driven by westward-propagating gravity waves originating from the
tropics, and not by planetary waves from the extratropics like the other
westward wind reversals in ERA-Interim in the period 2005 until mid-2008. This expected enhancement of westward gravity wave drag is clearly seen
in the HIRDLS absolute gravity wave drag shown in Fig. c;
however it is only weakly indicated in Fig. c because the
westward gravity wave drag maximizes at altitudes higher than 46 km.
Possibly, the stronger than usual westward gravity wave drag also contributes
to the fact that westward SAO winds in mid-2006 are somewhat stronger than in
the middle of the other years in the period considered in our study.
Of course, it should be emphasized that the situation in mid-2006 is an
exceptional event. Even if a longer period of over 10 years (2002–2012) is
considered, this is the only event of this strength. This indicates that such
events are likely not important from a climatological point of view. Still,
from this event we can learn more about the effect of the QBO on the driving
of the SAO.
Discussion of four characteristic cases
In the following, we want to obtain a better qualitative understanding of the
dissipation of gravity waves in the stratopause region. With this improved
physical understanding, we will be able to identify the most relevant
processes that should be included in global models for simulating a realistic
SAO. Therefore, in this section, we will qualitatively discuss characteristic
situations of the atmospheric background and the gravity wave dissipation
that may result from this. Some evidence for this understanding will be
presented in Sect. by discussing observed gravity
wave spectra. During all of these considerations we will focus on the zonal
direction only (zonal winds and zonally propagating gravity waves), because
meridionally propagating gravity waves will not contribute much to the
SAO.
Figure e
shows the SAO winds at 41 km (“level 1”, black curve)
and 51 km altitude (“level 2”, red curve). There are four basic cases that can be identified:
negative (i.e., westward) vertical shear of the zonal wind
between levels 1 and 2 – zonal wind at level 1 is negative (i.e., westward);
positive (i.e., eastward) vertical shear of the zonal wind
between levels 1 and 2 – zonal wind at level 1 is negative (i.e., westward);
negative (i.e., westward) vertical shear of the zonal wind
between levels 1 and 2 – zonal wind at level 1 is positive (i.e., eastward);
positive (i.e., eastward) vertical shear of the zonal wind
between levels 1 and 2 – zonal wind at level 1 is positive (i.e., eastward).
Here, “positive” and “negative” shear refer to the average
vertical shear considering the whole altitude range between
level 1 and level 2.
Four months approximately matching these characteristic cases are indicated
in Fig. e by blue hatched rectangles:
(a) January 2006, (b) March 2006, (c) June 2006, and (d) May 2007.
Zonal wind altitude profiles for these months are shown later in
Fig.
(see Sect. ).
However, before addressing these real-world situations,
we will qualitatively discuss “idealized” cases.
The “idealized” situation of these four cases is illustrated in
Fig. with a schematic picture for each case. In
each of Fig. a–d, the x axis indicates the zonal
wind speed u and the gravity wave ground-based phase speed cφ.
The y axis is the vertical coordinate z, and it also stands for the
strength of gravity wave momentum flux, indicated by the vertical extent of
the blue hatched rectangles. Two altitude levels are highlighted as z1 and
z2. Level z1 is assumed to be situated directly on top of the region
dominated by the QBO, while z2 is assumed to be situated in the altitude
region dominated by the SAO. (In our work we assume the levels
z1= 41 km and z2= 51 km.) The zonal wind vertical profile
between the levels z1 and z2 is indicated by a red line. For
simplification, it is assumed that the zonal wind changes monotonously with
altitude, i.e., has a constant vertical gradient. The range of gravity wave
phase speeds that is assumed to be filtered out by the QBO at altitudes
z<z1 is marked by two vertical green dashed lines.
Schematic illustration of four characteristic cases how
gravity wave drag contributions in the SAO momentum budget are generated.
Two altitude levels are considered. The level z1 is
located below the SAO-related wind shear, and the level z2 above it.
The red lines indicate simplified vertical profiles of the zonal background
wind u.
The blue hatched boxes indicate the amount of gravity wave momentum flux
at the two levels with MFw (MFe) the momentum flux for
westward (eastward) ground-based phase speed Cφ.
It is assumed that there is no momentum flux at ground-based phase speeds
located between the
green dashed vertical lines, because this phase speed range
has been removed through critical-level filtering by the
QBO at altitudes z<z1.
The four cases are
(a) westward vertical shear of the zonal wind,
u(z1)< 0 and u(z2)< 0;
(b) eastward wind shear, u(z1)< 0 and u(z2)> 0;
(c) westward wind shear, u(z1)> 0 and u(z2)< 0; and
(d) eastward wind shear, u(z1)> 0 and u(z2)> 0.
Zonal wind altitude profiles averaged over
10∘ S–10∘ N and 1 month for
(a) January 2006, (b) March 2006,
(c) June 2006, and (d) May 2007.
These four situations roughly represent the four cases introduced
in Fig. 4.
The zonal wind (blue) and the zonal wind smoothed by
a 10 km vertical running mean (green) are shown in the above.
The red vertical bars indicate the average zonal wind and the altitude
ranges for which gravity wave momentum flux spectra are calculated.
These altitude ranges are centered at z1= 41 km and z2= 51 km
(horizontal dashed lines).
The amount of eastward-directed (MFe) and westward-directed (MFw) gravity
wave momentum fluxes on the levels z1 and z2 is qualitatively indicated
by blue hatched rectangles. The extent of the rectangles in the x direction
gives the range of gravity wave phase speeds, while the extent in the
y direction is a measure for the amount of momentum flux at a given phase
speed. Figure a and b are for westward-directed
zonal wind at the lower altitude level (u(z1)< 0), resulting in enhanced
momentum flux MFe(z1) and reduced MFw(z1). Different from this,
Fig. c and d represent cases of u(z1)> 0,
resulting in reduced MFe(z1) and enhanced MFw(z1). Consequently, this
dependency on the background wind means that the direction of QBO winds
(i.e., the QBO phase) at z=z1 has a strong influence on the amount of
eastward and westward-directed momentum fluxes at this altitude.
One of the limiting factors of momentum flux is wave saturation. Due to the
decrease in air density, the amplitude of a conservatively propagating
gravity wave grows exponentially with altitude. At some point, however, the
amplitude cannot grow further and reaches its saturation limit, and thereafter the wave
starts to dissipate. The saturation amplitude (T^sat) is
proportional to the difference between ground-based phase speed and
background wind. In the following, we only consider the zonal direction,
because this the only direction that is relevant for the driving of the SAO. In this
case, the saturation amplitude is given by
T^sat=TgN|cφ-u‾|.
See also Eq. (10) in .
Because the temperature amplitude enters Eq. () in a quadratic
way, T^sat is also limiting the momentum flux of a gravity
wave. Overall, the momentum flux of a saturated gravity wave is proportional
to the third power of |cφ-u‾|see Eqs. 1
and 4 in, which shows the importance of the background
winds. For the special case of a critical wind level
(cφ=u‾), the critical amplitude becomes zero, and the
wave dissipates completely. However, saturation and wave dissipation can also occur without critical wind levels being
reached. For a review on
saturation effects of gravity waves see, for example, .
Considering the whole spectrum of gravity waves in a given propagation
direction (in our case either eastward or westward), the gravity waves
propagating into this direction can attain larger amplitudes and thereby
carry more momentum if the intrinsic phase speed |cφ-u‾| and thus the saturation amplitude is high.
Therefore, for the scheme in Fig. 4, we assume that, at a given altitude
level, the overall momentum flux for a given propagation direction can be higher if
the difference |cφ-u‾| is high. This is particularly
the case when background wind and ground-based phase speed have opposite
directions.
Further, gravity wave observations show that gravity wave momentum fluxes
continuously decrease with altitude e.g.,. Therefore,
we assume in Fig. that gravity wave momentum flux
at the higher altitude level z2 should always be lower than at the lower
altitude level z1.
Of course, the use of rectangles for the shape of the gravity wave spectrum
is just an illustration, and the “true” gravity wave spectrum will have a
much more complicated shape, depending on the details of the gravity wave
sources and the gravity wave dissipation at altitudes below
z1. For example, the study by indicates that there
could be an asymmetry of the gravity wave spectrum in the tropopause region,
with much stronger momentum fluxes at eastward-directed gravity wave phase
speeds. If this is the case, it would be expected that, on average, the forcing
in the stratopause region should be directed even more prevailingly eastward
than already expected from the stronger filtering of westward-propagating
gravity waves by the QBO. Consideration of such effects is, however, beyond the
scope of our study. The very simplified scheme proposed here is only intended
to explain the very basic mechanisms leading to the observed effects. In
particular, there is still considerable uncertainty about the shape of
the momentum flux spectrum of convective gravity waves see
also.
Based on our very simplified assumptions, implications for gravity wave drag
will now be discussed separately for each of the four cases introduced at the
beginning of this section.
Case (a), January 2006: u(z1)<0, ∂u/∂z<0
At the level z1 the momentum flux MFe(z1) of gravity waves with
eastward-directed phase speed is high because |cφ-u‾|
is high. At the same time the momentum flux MFw(z1) of gravity waves with
westward-directed phase speed is comparably low because |cφ-u‾| is low (see Fig. a).
With increasing altitude, propagation conditions for gravity waves with
eastward-directed phase speeds become more favorable because, for those waves,
|cφ-u‾| and thus T^sat increases
with altitude. Because the waves already have large amplitudes at z=z1, it is
nevertheless expected that, at some point, a considerable part of them will reach
their saturation amplitude and start to dissipate, even though their
intrinsic phase speeds are high and they do not encounter critical wind
levels. Due to the fact that MFe(z1) ≫ MFw(z1), the resulting net
gravity wave drag will be strongly positive (i.e., eastward).
This wave saturation effect should happen preferentially at high altitudes
(close to z2) because it depends on the amplitude growth of the gravity
waves with altitude. Indeed, such strong values of gravity wave drag are seen
in Fig. c in HIRDLS observations at altitudes above about
45 km during January 2006 and other situations matching case (a). In these
cases we also find strongly positive values of ERA-Interim missing drag (see
Fig. d).
Still, from Fig. d there are also indications for weak
negative (i.e., westward-directed) gravity wave drag at low altitudes (between
about 40 and 45 km) during periods matching the conditions of case (a),
for example during January 2006 and January 2007. This finding could be
realistic, because in case (a), for gravity waves with westward-directed
phase speeds, the difference |cφ-u‾| reduces with
altitude, leading to lowered saturation amplitudes and enhanced dissipation.
Part of these gravity waves will even encounter critical levels where
|cφ-u‾|=0. Although MFe(z1) ≫ MFw(z1), at
low altitudes the dissipation of westward-propagating gravity waves might
still dominate and lead to slightly negative gravity wave drag.
Overall, there is strong indication that the driving of the SAO cannot be
understood alone from critical-level filtering of gravity waves
between the two levels z1 and z2.
It is very likely that gravity wave saturation without
critical levels being reached also plays an important role.
Otherwise the strong values of eastward gravity wave drag
that always occur in case (a) at high altitudes (close to z2)
cannot be explained.
This will be further discussed in Sect. ,
and more observational evidence will be presented.
0$}?>Case (b), March 2006: u(z1)<0, ∂u/∂z>0
Like in case (a), the momentum flux MFe(z1) is high and MFw(z1) is low
(see Fig. b). With increasing altitude the
propagation conditions become worse (better) for gravity waves with eastward
(westward-) directed phase speeds as |cφ-u‾| decreases
(increases). Since at z=z1 MFe(z1) ≫ MFw(z1), the resulting
net gravity wave drag should therefore clearly be positive (directed
eastward).
0$, $\partial u/\partial z<0$}?>Case (c), June 2006: u(z1)>0, ∂u/∂z<0
In case (c) the momentum flux MFw(z1) is high, and MFe(z1) is low,
because |cφ-u‾| is high for westward-propagating
gravity waves, and low for eastward-propagating gravity waves (see
Fig. c). With increasing altitude the propagation
conditions become worse (better) for gravity waves with westward- (eastward-)
directed phase speeds as |cφ-u‾| decreases
(increases). Although the phase speed spectrum of westward gravity waves is
more strongly filtered by the QBO, and only waves with high ground-based
phase speeds are remaining, the resulting net gravity wave drag should be
negative (directed westward).
Because usually westward-directed momentum fluxes are partly filtered out by
the QBO, it would be expected that the resulting net gravity wave drag is
weaker than, for example, in case (a). This is also indicated in
Fig. c for a fixed altitude of 47 km.
0$, $\partial u/\partial z>0$}?>Case (d), May 2007: u(z1)>0, ∂u/∂z>0
At the level z1 the momentum flux MFe(z1) of gravity waves with
eastward-directed phase speed is low because |cφ-u‾|
is low. At the same time, the momentum flux MFw(z1) of gravity waves with
westward-directed phase speed is high because |cφ-u‾|
is high (see Fig. d). However, the phase speed range
of MFw is strongly reduced due to filtering of the gravity wave spectrum by
the QBO at altitudes z<z1. With increasing altitude the difference
|cφ-u‾| is increased for gravity waves with
westward-directed phase speeds, resulting in only little westward-directed
gravity wave drag. At the same time, |cφ-u‾| is
reduced for gravity waves with eastward-directed phase speeds. Nevertheless,
this results in only little gravity wave drag, because MFe(z1) is already
low at z=z1. In particular, during the period considered in our study,
eastward wind phases of the SAO are usually weaker than westward wind phases.
Therefore, the vertical gradient ∂u/∂z, and also the
resulting (net) gravity wave drag, will only be weak in
case (d).
Gravity wave spectra in the four characteristic cases
We now discuss gravity wave momentum flux spectra observed by HIRDLS for
conditions roughly corresponding to the four cases introduced in
Sect. . In particular, an interesting question is whether
there is any evidence of gravity wave saturation effects without critical
levels being reached. If this is the case, this might have important
implications for the representation of gravity waves in global models, either
resolved or parameterized.
HIRDLS gravity
wave momentum flux spectra for the four cases illustrated
in Fig. 4.
Upper row (a–c): January 2006,
westward vertical shear of the zonal wind, u(z1)< 0 and u(z2)< 0;
second row (d–f): March 2006,
eastward wind shear, u(z1)< 0 and u(z2)> 0;
third row (g–i): June 2006,
westward wind shear, u(z1)> 0 and u(z2)< 0; and
lower row (j–l): May 2007,
eastward wind shear, u(z1)> 0 and u(z2)> 0.
The left column (a, d, g, j) shows spectra for 41 km altitude, and
the middle column (b, e, h, k) for 51 km altitude.
These altitudes correspond to the lower and upper levels z1 and z2, respectively, in Fig. 4.
The right column (c, f, i, l)
shows the differences between the spectra at 41 km
and the spectra at 51 km altitude.
As already mentioned, the situations of cases (a)–(d) are
roughly matched in (a) January 2006, (b) March 2006, (c) June 2006, and (d) May 2007, respectively.
Vertical profiles of the zonal wind for these months are shown in
Fig. (blue curves). Of course, the zonal wind
vertical profiles in Fig. only on average
match the idealized assumption made in Sect. of a linear
increase or decrease in the zonal wind with altitude. Nevertheless, the
change in the background winds on average, and the corresponding change in
observed gravity wave momentum flux spectra, will provide further insight into
details of the forcing of the SAO.
From single observations of gravity wave momentum flux, the average gravity
wave spectrum in a certain region can be recovered see
also. For example, momentum flux as function of
horizontal and vertical wave number can be determined by sorting the single
observed momentum fluxes into bins in the plane of horizontal and vertical
wave numbers see also.
The determination of the HIRDLS gravity wave momentum flux spectra shown in
Fig. is very similar to that in
. The different rows in
Fig. correspond to the different cases
described in Sect. .
Figure a, d, g, and j (left column in
Fig. ) show momentum flux spectra at the
altitude z1= 41 km, and
Fig. b, e, h, and k (middle column in
Fig. ) show spectra at z2= 51 km. For
both the left and the middle column, a logarithmic momentum flux scale is used. The
right column (Fig. c, f, i, and l) shows, on
a linear momentum flux scale, the difference between the spectra in the left
and middle column. The spectra in the right column therefore provide
information about the part of the wave spectrum that has dissipated between
the altitudes z1 and z2. Of course, our analysis uses a 10 km
vertical window, and all spectra shown in
Fig. represent only average conditions for
altitude ranges of 10 km. Therefore, they will only on average match the
four idealized cases. The vertical intervals and average zonal winds that
correspond to the spectra in Fig. are
marked in Fig. by red vertical bars that are
centered at the altitude levels z1= 41 km and z2= 51 km,
respectively.
Case (a), January 2006: u(z1)<0, ∂u/∂z<0
The situation of case (a) is approximately matched during January 2006. The
corresponding spectra are shown in
Fig. a–c. The reduction of momentum fluxes
shown in Fig. c peaks at vertical
wavelengths λz> 10 km, i.e., at intrinsic phase speeds
c^φ> 30 m s-1 (c^φ=Nλz/(2π)). While the reduction of momentum fluxes at low phase
speeds could be due to critical-level filtering of gravity waves with
westward phase speeds, significant reduction of momentum fluxes is also found
at vertical wavelengths > 20 km, i.e., intrinsic phase speeds
> 60 m s-1. The latter cannot be explained by critical-level
filtering of westward phase speeds. Obviously gravity waves with high
intrinsic eastward phase speeds also dissipate and possibly reach their saturation
amplitude.
This is further evidence that, in case (a) close to the level z2 in the
upper part of the SAO region, gravity wave drag should be strongly positive
(i.e., eastward) (see also Fig. d). In addition, this indicates
that, even though the vertical gradient of the zonal wind between the levels
z1 and z2 is strongly negative on average, eastward-propagating gravity
waves reach saturation (because these waves have quite high amplitudes and
strong momentum fluxes). This will be even more likely the case for
situations like in Fig. a when the local
vertical gradient of the zonal wind weakens or reverses close to z2. While
saturation and dissipation of eastward-propagating gravity waves will
strongly dominate at high altitudes, at low levels (close to z1)
dissipation of westward-propagating gravity waves could still result in
slightly negative (i.e., westward-directed) net gravity wave drag, which is also
indicated in Fig. d. Further, the involvement of such high
intrinsic phase speeds shows that the background winds should be quite
strong. This indicates that the quite strong ERA-Interim winds during January
2006 (stronger than -60 m s-1 at 47 km altitude) might be realistic.
0$}?>Case (b), March 2006: u(z1)<0, ∂u/∂z>0
Background conditions matching case (b) are found during approximately March
2006, and the corresponding spectra are shown in
Fig. d–f. Compared to case (a), the
reduction of momentum fluxes (Fig. f) is now
shifted toward lower intrinsic phase speeds. Not much reduction is found at
vertical wavelengths > 15 km (intrinsic phase speeds
> 45 m s-1), and the peak reduction is at vertical wavelengths
< 10 km, i.e., intrinsic phase speeds < 30 m s-1. This is in
good agreement with the assumption that mainly gravity waves with eastward
phase speeds undergo critical-level filtering, and gravity waves with
westward-directed phase speeds should not contribute much. Accordingly, the
resulting net drag should be positive (i.e., eastward), which is in good
agreement with ERA-Interim during March 2006 in the altitude range
40–50 km (see Fig. d).
0$, $\partial u/\partial z<0$}?>Case (c), June 2006: u(z1)>0, ∂u/∂z<0
The situation of case (c) is approximately matched during June 2006. The
corresponding spectra are displayed in
Fig. g–i. In case (c), the spectral
distribution of the momentum flux difference between lower and upper level
(Fig. i) is qualitatively very similar to
case (b) (Fig. f). Absolute values are,
however, somewhat reduced. Accordingly, this indicates that mainly gravity
waves with westward phase speeds should undergo critical-level filtering, and
gravity waves with eastward-directed phase speeds should not contribute much.
In particular, Fig. i does not indicate a
strong reduction of momentum fluxes at long vertical wavelengths (i.e., high
intrinsic phase speeds), which would be an indication of saturation and
dissipation of eastward-propagating gravity waves like in
Fig. c (case (a)). The resulting net drag
should therefore be negative (i.e., westward), which is also indicated in
ERA-Interim during June 2006 in the altitude range 45–50 km (see
Fig. d). In the observations peak values of drag during June
2006 are at somewhat higher altitudes (between 50 and 55 km; see
Fig. c). Although momentum flux differences in
Fig. i are somewhat reduced compared to
Fig. c and f, still considerable drag is
seen during June 2006 in Fig. c. The likely reason for this is the shift
of peak drag toward higher altitudes: due to the decreased atmospheric
density at higher altitudes, even a smaller amount of momentum flux can
produce significant drag.
0$, $\partial u/\partial z>0$}?>Case (d), May 2007: u(z1)>0, ∂u/∂z>0
Conditions matching case (d) are found, for example, during May 2007. The
corresponding spectra are shown in
Fig. j–l. The reduction of momentum
fluxes (Fig. l) is very weak compared to all
other cases. Accordingly, only little gravity wave drag is observed in
Fig. c. Further, ERA-Interim shows only weak drag during May
2007 (see Fig. d).
Conclusions
In our study we have investigated the momentum budget of the semiannual
oscillation of the zonal wind (SAO) in the tropical latitude band
10∘ S–10∘ N for the period January 2005 until mid-2008. The main
focus was on the contribution of gravity waves that is not easily accessible
and is subject to large uncertainties in both observations and modeling
studies.
Temperature observations of the High Resolution Dynamics Limb Sounder
(HIRDLS) satellite instrument were used to derive absolute values of gravity
wave momentum flux, as well as total (absolute) gravity wave drag from
momentum flux vertical gradients. These values of gravity wave drag were
compared to the different terms in the momentum budget of the ERA-Interim
reanalysis of the European Centre for Medium-Range Weather Forecasts (ECMWF),
in particular to the zonal wind tendency and the missing drag. It is
assumed that this missing drag can be attributed to the gravity wave
contribution in the momentum budget.
Based on our measurements and gravity wave theory we infer a consistent
picture of the SAO. Our findings confirm the general assumption that gravity
waves should mainly contribute to the SAO momentum budget during eastward
wind shear. This is compatible with the filtering of the spectrum of upward-propagating waves by the QBO in the lower and middle stratosphere
e.g.,.
Background winds during QBO westward phases are usually much stronger than
during eastward phases, and gravity waves with ground-based phase speeds
between about -40 and 10 m s-1 tend to be filtered out by QBO wind
before entering the upper stratosphere. This means that a large part of the
spectrum of waves with westward-directed (i.e., negative) phase speeds is
filtered out. Accordingly, we find that observed gravity wave variances and
momentum fluxes are much stronger during SAO westward winds, which provide
favorable propagation conditions for gravity waves with eastward-directed
phase speeds. These waves are much less affected by the QBO than gravity
waves with westward-directed phase speeds. The dissipation of gravity waves
with eastward-directed phase speeds strongly contributes to the SAO momentum
budget during SAO eastward wind shear, and in ERA-Interim, zones of SAO
eastward wind shear propagate downward with time, as would be expected for
wave-driven wind reversals.
These situations of eastward wind shear (∂u/∂z>0) prevail
during much of the time of significant SAO gravity wave forcing, and they are
discussed in more detail with the introduction of the two characteristic cases (b) and (d) in Sect. .
These two cases differ in their direction of the zonal wind at an altitude
level of z=z1 located directly below the altitude region dominated by the
SAO. The zonal wind at this altitude has a strong influence on the amount of
eastward-directed gravity wave momentum flux that is available for driving
the SAO. In particular, the gravity wave driving of the SAO is much stronger
if the zonal wind at z=z1 is westward. Consequently, the direction and
strength of the QBO winds (i.e., the QBO phase) at z=z1 plays an important
role in the driving of the SAO.
During eastward wind shear, peak values of observed HIRDLS gravity wave drag
are about 1 m s-1 d-1. This is qualitatively in good agreement with several
modeling studies
e.g.,. Observed
values are, however, somewhat lower, which may be explained by the fact that
the observed drag represents an average over an altitude range of 10 km.
In addition, our method may underestimate momentum fluxes. Further, HIRDLS
observes only part of the whole spectrum of gravity waves, and therefore only
part of the gravity wave drag. The missing drag in ERA-Interim is
significantly higher than in the observations and in the other modeling
studies. A likely reason for this is that the meridional advection is somewhat too
strong in ERA-Interim. Nevertheless, relative variations in the missing drag
in ERA-Interim provide some information, and there is good agreement between
relative variations in observed gravity wave drag and relative variations in
absolute values of ERA-Interim missing drag.
During westward wind shear, gravity wave drag is usually weaker in both
observations and ERA-Interim, and in the ERA-Interim momentum budget the
westward-directed (i.e., negative) zonal wind tendency is mainly balanced by
planetary wave drag. This planetary wave drag is likely of extratropical
origin because zones of westward-directed SAO wind tendency are almost
vertical and do not gradually propagate downward with time, as would be
expected for wind reversals that are mainly driven by purely vertically
propagating waves.
Still, we find exceptions where gravity waves may exert westward-directed
drag in the SAO momentum budget. One of these exceptions is found during a
period of westward-directed wind shear (∂u/∂z< 0); this
is discussed in our characteristic case (c): in a time window during May and
June 2006, the QBO filtering of waves with westward-directed phase speeds is
less effective, and the drag due to planetary waves is found to be comparably weak
in ERA-Interim. During this period the ERA-Interim missing drag is
negative (westward). At the same time, absolute gravity wave drag observed by
HIRDLS is high, and the zone of westward-directed SAO wind shear
exceptionally shows a downward propagation with time. Other cases of
westward-directed gravity wave drag might be during December and January in several
years at altitudes 40–45 km (in the lower part of the SAO altitude
region), as indicated in the ERA-Interim missing drag. It is, however, not
clear whether this finding is very reliable.
In Sect. , another characteristic case (case (a)) is
introduced, which addresses the situation of westward-directed wind at
z=z1 and westward-directed wind shear (∂u/∂z< 0). In
this case, likely wave saturation of eastward-propagating gravity waves
results in strong eastward-directed gravity wave drag, although the overall
wind shear is westward, considering a larger altitude range. Case (a) is
somewhat different from our other characteristic cases (b)–(d), because the
intrinsic phase speeds of the dissipating eastward-propagating waves are
high and critical wind levels are not being reached. This situation often
occurs during January and may be important for the onset of SAO wind
reversals from westward to eastward winds at high altitudes.
It is also notable that the location and timing of the shear zones of the
ERA-Interim zonal wind reasonably well match the enhancements of observed
gravity wave drag. In addition to previous studies
e.g.,, this is another
indication that the ERA-Interim zonal wind in the stratopause region should
be realistic in its basic features. Of course, the fact that ERA-Interim
winds in the tropics are quite reasonable is a merit of the data assimilation
scheme. Even though the model physics in the stratopause region is
oversimplified (use of Rayleigh friction and strong damping of resolved
waves above about 40 km altitude instead of a dedicated gravity wave
parameterization scheme) quite reliable winds are simulated in the tropical
stratopause region.
Free-running global models, however, cannot benefit from data assimilation
and require a realistic representation of the most relevant physical processes.
As has become apparent during our study, critical-level filtering of
gravity waves is not sufficient for simulating a realistic SAO.
Additionally, wave saturation processes without critical levels being reached
play an important role and have to be parameterized in a realistic way.
This implies that a realistic wave saturation scheme is required for
the gravity waves explicitly resolved in the model.
There are even indications that, depending on the model setup,
data assimilation of lower atmospheric data is not always able to
overcompensate the effect of an unrealistic gravity wave parameterization
e.g.,,
which underlines the importance
of including realistic physical processes in the models.
Overall, our study for the first time provides direct observational evidence
from global observations of gravity waves that, indeed, gravity waves
contribute strongly to the eastward wind reversals of the SAO but only
weakly to the westward wind reversals, as would be expected from theoretical
considerations. However, there are also exceptions when westward-directed
gravity wave drag is important. Obviously, the momentum budget of the SAO is
somewhat more complicated than expected. The findings of our study therefore
provide important information and can give some experimental guidance to
model studies and simulations of the SAO.
Of course, one of the drawbacks of our study is that the direction of gravity
wave momentum fluxes cannot be directly inferred from the satellite
observations. This is the case because information is provided only for the
vertical direction and the direction along the satellite measurement track,
i.e., only 2-D information is available for investigating the observed gravity
waves. Therefore, there is still some uncertainty about the direction and
magnitude of net gravity wave drag in general. This limitation could be
overcome, for example, by the infrared limb-imaging technique, giving full 3-D
information about the observed gravity waves by additionally providing
observations for the direction across the satellite measurement track. For a
more detailed discussion of this measurement technique and its capabilities
see, for example, or
.
Another approach for improving the representation of the SAO in global models
would be a more systematic monitoring of temperatures and winds in the
stratopause region, or even the mesosphere. In particular, global
observations of winds in the stratopause region are sparse see
also. Including such observations in the assimilation
schemes of operational meteorological analyses, or in reanalyses, would
improve their winds in this altitude region. These improved winds, in turn,
could then serve as a reference for free-running global models and help to
improve model physics, resulting in an improved simulated
SAO.
Discussion of the advection terms in the ERA-Interim momentum budget
Altitude–time cross sections of the
following
terms of the ERA-Interim
tropical momentum budget in m s-1 d-1:
(a) vertical advection term,
(b) meridional advection term, and
(c) missing drag
that is attributed to gravity waves (see also Fig. 1d).
All values are averages over the latitude band 10∘ S–10∘ N.
Contour lines represent the zonal wind. The bold solid line
is the zero wind line.
Dashed (solid) lines indicate westward (eastward) wind.
Contour interval is 20 m s-1.
Figure a shows the vertical advection term of ERA-Interim.
The main contributions of vertical advection are directed westward
(up to -2 m s-1 d-1),
and they occur usually in the period December/January.
There is also another event of strong westward forcing in mid-2006.
Eastward forcing is usually weak.
The meridional advection term is shown in Fig. b. The forcing
due to meridional advection is directed eastward and mainly occurs in the
westward wind phases of the SAO. In addition, meridional advection strongly
increases at altitudes above about 55 km. In the altitude range considered
in our study the contribution of meridional advection can be as strong as
about 5 m s-1 d-1.
Compared to other model simulations of the SAO, the advection terms in
ERA-Interim are quite strong. In other simulations typical values in the
stratopause region are of the order 2.5 m s-1 d-1 and less, i.e., considerably
weaker e.g.,.
Therefore the advection terms in ERA-Interim might not be fully realistic.
Still, the relative variations should provide some information about the
momentum budget in the stratopause region. At higher altitudes (above
55 km), however, meridional advection seems to be no longer reliable.
The missing drag in the ERA-Interim momentum budget is shown in
Fig. c (see also Fig. d). Obviously, the
advection terms are the main contributions in the ERA-Interim missing drag.
This means that, like the advection terms, the missing drag will not be fully
realistic; however it still may provide useful information from its relative
variations.
Comparison of gravity wave variances and squared amplitudes
Altitude–time cross sections of HIRDLS gravity wave
(a) temperature variances (no vertical window applied), and
(b) squared temperature amplitudes determined in 10 km
vertical windows
from
the HIRDLS altitude profiles.
Values in (b) were divided by 2 to be comparable to the variances in (a).
Units in (a) and (b) are dB(K2).
Values in (a) and (b) are averages over the
latitude band 10∘ S–10∘ N.
Contour lines indicate the zonal wind:
westward wind is dashed,
and the bold contour line indicates zero wind.
Contour increment is 20 m s-1.
Figure a shows an altitude–time cross section of HIRDLS
temperature variances due to gravity waves, directly after removal of the
large-scale atmospheric background temperatures (the first step as described
in Sect. ). All HIRDLS altitude profiles in the latitude
band 10∘ S–10∘ N are considered. The variances are given in
dB(K2), i.e., on a logarithmic scale. For comparison,
Fig. b replicates Fig. a and shows gravity wave
squared amplitudes of the strongest gravity waves found in each altitude
profile in the latitude band 10∘ S–10∘ N using a MEM/HA
vertical analysis with a 10 km vertical window (see
Sect. ). Squared amplitudes were divided by 2 to make the
values directly comparable to the variances shown in Fig. a.
We find that the distributions of variances and squared amplitudes are very
similar. Obviously, even though a 10 km vertical window was applied for
the determination of wave amplitudes, the squared amplitudes capture the
basic features of the interaction of the gravity wave distribution with the
SAO winds. Values in Fig. b are only slightly lower than in
Fig. a (about 1.5 dB, i.e., 30 %; please note that the
color scale in Fig. b has been shifted). One reason for the
slightly reduced values is an averaging effect of the 10 km vertical
window. In addition, part of the gravity wave variance is carried by weaker
waves that are neglected in our study. For the calculation of gravity wave
momentum fluxes, only pairs of altitude profiles with matching vertical
wavelengths are considered (see also Sect. ). The
distribution for squared amplitudes times 0.5 of these pairs looks almost
exactly the same as in Fig. b (both in absolute values and
relative variations) and is therefore not shown. The good agreement between
gravity wave variances and squared amplitudes demonstrates that, in spite of
the vertical averaging effect, gravity wave amplitudes determined in a
10 km vertical window are well suited for study of the interaction of the
gravity wave distribution with the SAO winds.
Acknowledgements
We are grateful to ECMWF (http://www.ecmwf.int) for providing the
ERA-Interim data. Further, we would like to thank NASA for making HIRDLS data
available via their web page
http://disc.sci.gsfc.nasa.gov/Aura/data-holdings/HIRDLS/index.shtml.
Very helpful comments from the two anonymous reviewers are gratefully
acknowledged.The article processing charges for
this open-access publication were covered by a Research
Centre of the Helmholtz Association.The topical editor C. Jacobi thanks two anonymous referees for
help in evaluating this paper.
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