Introduction
Atmospheric gravity waves (hereafter: GWs) propagate vertically and
horizontally from their tropospheric source regions to the mesosphere and
lower thermosphere (MLT, 80–100 km), which is a main region of GW breaking
and hence associated with the deposition of GW momentum and energy. Thus, GWs
are responsible for the vertical coupling between different atmospheric
layers. Vertical propagation of GWs is in principle only possible if the
waves move against the mean flow and do not reach any critical levels where
they are filtered by the background wind.
Dynamical processes like momentum deposition by breaking GWs lead to changes
of the temperature and wind field. Based on the quasi-geostrophic transformed
Eulerian-mean (TEM) equations on a beta-plane see,
e.g.,, the momentum balance in zonal direction is given as
∂u∂t-f⋅v=1ρ0∇⋅F+X≡Du.
Here, u and v are the zonally averaged zonal wind velocity and residual
mean meridional circulation, t is time, and f=2Ωsinϕ is the
Coriolis frequency, which includes the rotation rate of the Earth Ω and
the latitude ϕ. Note that for simplicity, mean values are denoted
without overbars in the text. The Eliassen–Palm flux divergence ∇⋅F per temporal mean density ρ0 represents together with X
the zonal GW drag Du, which is the GW momentum deposition into the zonal
wind field, i.e., a zonal force per unit mass on the zonal-mean flow. The
Eliassen–Palm flux F contains contributions from both planetary
waves as well as small-scale GWs, and X represents all further
contributions to the mean zonal force per unit mass associated with GWs and
other small-scale disturbances.
For a steady-state atmosphere with vanishing time derivatives, which is the
case, e.g., during the solstices, the zonal momentum balance in the
extratropical MLT is primarily given between the zonal mean GW forcing and
the zonal mean Coriolis force as for instance described by
. For summer conditions planetary waves play a minor role
in the mesosphere because tropospheric excited planetary waves cannot
propagate up to mesospheric heights due to the Charney–Drazin criterion
. Hence, F is primarily determined by the
contribution from GWs. Consequently, the summer momentum balance in zonal
direction is between the mean flow acceleration due to the divergence of the
GW momentum flux and the negative Coriolis acceleration of the mean
meridional wind:
-f⋅v≈Du=-1ρ0⋅∂(ρu′w′)∂z.
Here, u′w′ and ρ are the temporal mean vertical flux of zonal momentum
and the temporal mean density at 1 km above and below a reference height
with a temporal mean density ρ0. During wintertime, however, planetary
waves can propagate into the mesosphere and contribute to F such
that the relation given in Eq. () is not fulfilled
seefor more details.
Based on Eq. () it is obvious that the vertical
divergence of the vertical flux of zonal momentum that is imposed by
breaking GWs on the mean background flow drives the residual meridional
summer-to-winter-pole circulation. Subsequently, for reasons of mass
conservation, this meridional flow needs to be balanced, which leads to a
residual upwelling and hence adiabatic cooling over the summer pole as well
as a residual downwelling and adiabatic warming over the winter pole. This
results in very low temperatures in the summer mesopause and the existence of
the warm winter stratopause e.g.,.
This chain of causality has first been introduced by, e.g.,
and is described in detail by, e.g.,
, , and . First
and most realizations of this mechanism are based on parametrization in
models . For reviews we refer the reader to
, who give a general description, to
, who give an overview on the current status of GW
effects in atmospheric models and observations, and to a recently published
first comparison between GW absolute momentum fluxes from climate models,
high-resolution models, and fluxes derived from global satellite observations
.
Based on the technique by , first direct observations
of the upper mesospheric momentum balance were performed, e.g., by
with the Buckland Park MF radar near Adelaide. However,
they only focussed on some selected case studies for few days throughout the
year. Another case study of GW flux measurements using MF radar
interferometry was presented by at Saskatoon. These
authors could not find a balance between zonal GW deceleration and Coriolis
acceleration, probably owing to their limited time series of only 17 days.
Later, studied the stratospheric vertical momentum flux,
variance and drag of the background wind with the MU radar and found
evidence for a strong interaction between inertio-GWs and the background wind
field in summer and winter.
A further attempt to evaluate the momentum balance in the mesosphere has been
presented by . They used horizontal winds from two MF
radars near Adelaide, Australia, and Christchurch, New Zealand, in connection
with satellite temperatures in order to resolve the momentum equations
appropriate for large-scale fluid flow on a sphere. Caused by the limitations
of data availability and vertical extent, and using additional theoretical
assumptions they estimated and discussed the mean momentum balance for only
1 month at an altitude of 80 km.
Momentum balance results of were based on two different
simplifications derived from the full momentum equation in zonal direction
using WACCM3 model results for December conditions. Whereas the results of
both methods were comparable in the Southern Hemisphere (summer), differences
occurred mainly in the Northern Hemisphere (winter). Based on the model
findings, ground-based lidar wind measurements as well as winds calculated
from 61 days of TIDI measurements were used for an indirect estimation of the
GW forcing.
In contrast to the extensive method presented by
resolving the complete momentum equations and to the indirect method proposed
by to estimate the GW forcing, we use in our present study
a direct way to estimate the momentum balance from measurements with the
Saura MF Doppler radar (hereafter: SMF radar) at polar latitudes
. This article is organized as follows: in
Sect. the SMF radar and the used experimental data are
introduced briefly. The annual variation of the mesospheric momentum balance
as given in Eq. () is then checked and discussed in
Sect. on the basis of 3 years of observations, i.e.,
from 2009 to 2011. With seasonal mean vertical profiles for summer and winter
the balancing quantities are regarded quantitatively including their SDs (standard
deviations). Conclusions are given in
Sect. .
Height–time cross sections of the 3-year mean zonal GW drag Du and negative
Coriolis acceleration -f⋅v from the SMF radar for 2009 through 2011.
Zero contour lines are indicated by black solid lines. Contours of negative and
positive values are shown with intervals of 100 m s-1 day-1 with
dotted white and black lines, respectively. The GW drag values are averages
over 20 days, shifted by 10 days. The Coriolis acceleration is calculated
as averages over 7 days, shifted by 1 day.
![]()
Observational data
The database for the present study consists of observations
with the unique, narrow beam SMF radar that is located on the
northern Norwegian island of Andøya (69∘ N, 16∘ E). The
benefit of this radar is continuous high-quality measurements over a broad
height range with high temporal and vertical resolution during all seasons.
The SMF radar transmits and receives electromagnetic signals with a Mills
Cross antenna of 29 crossed dipoles at a frequency of 3.17 MHz
seefor details. Two coplanar tilted radar beams are
transmitted successively in different spatial directions with a fixed
off-zenith angle of 6.8∘. For any pair of opposite radar beams, the
radial wind velocity is measured within 2 min. That means the measurement
for four spatial directions (two coplanar beam measurements perpendicular to
each other) takes 4 min. This is the temporal resolution for the analysis of
the zonal (u) and the meridional wind (v), which are determined from the
measured radial wind velocity seefor details of the wind
analysis. This radar configuration has been used since the
middle of 2007. Vertically, the SMF radar observations range from about 60 to
100 km with a vertical resolution of 1 km.
GW momentum fluxes are determined from the radial wind velocity variations of
the coplanar radar beams by applying the method by .
The implementation of this method and the application of data selection
criteria for obtaining statistically meaningful momentum flux results has
been done according to . For validating the mesospheric
momentum balance, the vertical GW momentum flux divergence Du is
calculated using density values from the NRLMSISE-00 empirical atmospheric
model , which are available daily with an altitude
resolution of 1 km.
Verification of the momentum balance
Mean annual variation
The summer mesospheric momentum balance as theoretically expected from
Eq. () is now checked on the basis of the
experimental data from the SMF radar. Figure shows the mean
annual variation of zonal GW drag Du and negative Coriolis acceleration of
the mean meridional wind -f⋅v between 70 and 100 km altitude for
3 years (2009 through 2011). Consistent with the calculations of the
vertical flux of zonal momentum u′w′ and of the meridional wind v in
, the zonal GW drag is shown as running averages over 20
days, which are shifted by 10 days, and the Coriolis acceleration is shown as
running averages over 7 days, which are shifted by 1 day. With these
averaging intervals the high temporal variability of the wind field is taken
into account and the momentum flux is calculated for a sufficiently long time
span in order to obtain reliable values see,
e.g.,.
It is noticeable that both quantities have an almost homogeneous and
comparable structure during summer, but more heterogeneous and differing
patterns during winter. As described in Sect. , the
contribution from both planetary waves and GWs to the mesospheric momentum
balance depends on the season. During summer the influence of planetary waves
is minor such that the momentum balance as given in
Eq. () is quantitatively fulfilled, i.e., from end of
May until middle of August. Du and -f⋅v vary predominantly
around 0 m s-1 day-1 below 78 km, have positive values with
maxima of about 120 m s-1 day-1 between 78 and 93 km, and are
predominantly negative above. Further, the observed mean characteristics of
the MLT dynamics agree reasonably well with the zonal-mean behavior as for
instance discussed in .
In contrast, the winter season is mainly dominated by the presence of
planetary waves, which disturb the propagation of GWs see,
e.g.,. This additional influence of the
planetary waves on the momentum balance is not considered by the SMF radar
observations in this study. Hence, the winter zonal GW drag from
Fig. no longer balances the negative Coriolis
acceleration of the mean meridional wind. Both quantities vary strongly in
height and time with positive and negative maxima of similar magnitudes as in
summer. Thereby, Du shows no clear pattern whereas -f⋅v is
predominantly positive above 80 km and negative beneath for end of September
through April. During May and from middle of August through middle of September, -f⋅v is negative over the whole shown altitude range.
Note that as described in , extreme values at the
lowermost and uppermost heights may be less reliable when compared to values
in the central altitude domain (between ∼ 75 and 95 km) because they are
calculated from a lower number of radial wind values. Additionally,
especially the values between about 70 and 80 km in winter have higher
SDs than in the other heights and seasons.
Vertical profiles (left) of 3-month mean zonal wind u (blue),
vertical flux of zonal GW momentum u′w′ (black), zonal GW drag Du (red)
and negative Coriolis acceleration of the mean meridional wind -f⋅v
(dashed green) from SMF radar measurements in summer 2010. Horizontal lines denote
the SD of each quantity at each height and are plotted every 2 km
for simplicity. The scatter plot of -f⋅v and Du (right) including the
SDs for 71 to 92 km altitude under specification of the correlation
coefficient R and the number of values N. See text for further information.
![]()
Mean vertical profiles in summer and winter
In the following, the findings from the height–time cross sections for summer
and winter are discussed on the basis of 3-month mean vertical profiles
for June through August 2010 (JJA) and December 2010 through February 2011
(DJF). These results stress the aforementioned magnitudes and errors
quantitatively for exemplary periods. The data are calculated on the basis of
running averages over 10 days, which are shifted by 1 day for a consistent
error estimation of all quantities. The left panels of
Figs. and show the mean
vertical profiles of zonal wind u, vertical flux of zonal GW momentum
u′w′, zonal GW drag Du, and negative Coriolis acceleration of the mean
meridional wind -f⋅v as well as their corresponding SDs for JJA and DJF. The vertical profiles are complemented by scatter
plots (right panels) describing the correlation between -f⋅v and
Du.
The 3-month mean values of u and u′w′ for summer 2010 in
Fig. show the well-known GW-mean flow interaction,
which was for instance discussed in detail also for this radar by
. Thus, zonal wind and vertical flux of zonal GW momentum
are oppositely directed and reverse both in sign around 90 km. That means
u is westward directed with magnitudes of approximately -35 m s-1
below 90 km and it is eastward directed above with maxima around
10 m s-1. Simultaneously u′w′ reverses from positive values
(∼ 3 m2 s-2) below 90 km to negative values (up to
-6 m2 s-2) above. The SDs of both quantities vary
according to their magnitudes in the particular altitudes. Hence, the
SD of u varies between about ±7 m s-1 below
90 km and ±2–3 m s-1 above. The corresponding values for u′w′
increase with height from ±1 m2 s-2 to about
±5 m2 s-2 in the whole shown altitude range. Overall, these
SDs are relatively small owing to the strong and stable GWs
in summer.
The mean vertical profiles of zonal GW drag Du and negative Coriolis
acceleration of the mean meridional wind -f⋅v for summer 2010 both
cover values between ±20 m s-1 day-1 below 80 km and
maximize in about 60 to 70 m s-1 day-1 between 82 and 92 km.
This is the altitude range where GW drag maximizes owing to increased GW
breaking and hence momentum deposition on the background atmosphere. Above
92 km, Du varies strongly (between ±120 m s-1 day-1) and
has negative values above 96 km as observed in the 3-year mean
height–time cross sections in Fig. . The Coriolis
acceleration of the mean meridional wind also reverses to negative values
above 93 km, but only in the order of -40 m s-1 day-1. Note
that overall Du varies more strongly over the whole shown altitude range than
-f⋅v owing to the vertical derivative of u′w′ entering this
quantity.
Same as Fig. , but for winter 2010/2011.
![]()
The SD of -f⋅v is relatively small below 80 km
(about ±8 m s-1 day-1) when compared to that of Du
(±20 m s-1 day-1). Between 82 and 90 km, both quantities
have comparable SDs of about
±45 m s-1 day-1. Above 90 km, the SDs
become again smaller for -f⋅v, but much bigger for Du according
to the magnitudes of these quantities. These exemplary summer vertical
profiles of both quantities from the SMF radar measurements agree
quantitatively very well to each other and prove that the summer momentum
balance as given in Eq. () is fulfilled in the MLT
region. Additionally, the corresponding scatter plot of Du versus -f⋅v for the values from 71 to 92 km altitude illustrates the very good
correlation of both quantities. The diagram covers the same scale range as
the vertical profiles. The values show a highly significant correlation with
a correlation coefficient of 0.91. For comparison only, the 1 : 1 line is
added.
In Fig. the vertical profiles of u, u′w′, Du,
and -f⋅v as well as the scatter plot of Du versus -f⋅v are shown for winter 2010/2011. As mentioned before, GW propagation is
disturbed during the winter season due to the dominance of other kinds of
waves like primarily planetary waves. This means that for the momentum
balance contributions from planetary waves and GWs need to be taken into
account. Consequently, Eq. (), which covers only the
influence of GWs, is not fulfilled. The 3-month mean vertical profiles of
zonal wind and vertical flux of zonal momentum do not show an anticorrelation
as observed during summer. That is, while u has weak positive values of
∼ 10 m s-1 maximum over the whole shown altitude range, u′w′ is
positive below 89 km and predominantly negative above with magnitudes of
±5 m2 s-2.
The winter zonal GW drag and negative Coriolis acceleration of the mean
meridional wind differ more strongly from each other than in summer. The vertical
profiles have predominantly negative values below 75 km and positive values
above with exception of Du being again negative between 92 and 97 km. In
the central altitude domain, the magnitudes are mainly up to
∼ 100 m2 s-2 for Du and up to ∼ 40 m2 s-2 for
-f⋅v, respectively. The corresponding scatter plot of Du versus
-f⋅v for 71 to 92 km clearly demonstrates the strongly scattering
values that have a low correlation coefficient of 0.51 only. Overall, all
quantities vary more strongly over the whole regarded altitude range in winter
than in summer and have higher SDs. Note that the estimated
magnitudes are comparable to the findings of , who showed
results from May on the Southern Hemisphere that correspond to early winter
values in the Northern Hemisphere.
Conclusions and outlook
Summarizing the findings of the present work, the momentum balance has been
verified quantitatively for the first time from local SMF radar observations
in the polar summer MLT when GWs play the major role in the mesospheric
dynamics. During winter, planetary waves contribute additionally to the
momentum balance and can filter GWs. As the planetary wave contribution is
not considered by the present investigations using the SMF radar
measurements, the momentum balance including GW contributions only is
fulfilled in summer but does not exist in winter. These results have clearly
been shown from 3-year mean annual cycles of zonal GW drag and Coriolis
acceleration of the mean meridional wind. Three-month mean vertical profiles
and scatter plots for summer 2010 (JJA) and winter 2010/2011 (DJF) of these
quantities, complemented by zonal wind and vertical flux of zonal GW
momentum, complete the investigations and take the SDs into
account. In summer, a distinct GW-mean flow interaction can be observed with
anticorrelated vertical profiles of zonal wind and vertical flux of zonal
momentum. At the same time, zonal GW drag and negative Coriolis acceleration
of the mean meridional wind have enhanced and comparable magnitudes in the
altitude range between 82 and 92 km, where GW breaking and hence momentum
deposition on the background atmosphere increase. In contrast, during winter
these quantities vary strongly in magnitudes over the altitude range from 70
to 100 km. Zonal wind and vertical flux of zonal momentum reveal no
anticorrelation as observed in summer, and the momentum balance requires the
information of both GW and planetary wave contributions. The stronger
variability during the more disturbed winter conditions also leads to higher
SDs of the investigated quantities than in summer. In future studies, the momentum balance should also be estimated and
discussed for similar radar instruments at other latitudes, like the MF radar
at the midlatitude site Juliusruh see, e.g.,. This
would allow the definition of the time and height range where the mainly
GW-determined momentum balance is fulfilled for different latitudes. Also the
latitudinal dependence of the GW drag strength could be proven. Furthermore,
the experimental results should be compared qualitatively and quantitatively
to model simulations in order to deepen the understanding of the
experimentally determined findings.