February
1989
T. Iwasaki,
A Parameterization
Scheme
with
Part
S. Yamada
Two
of Orographic
Different
II: Zonally
Vertical
Averaged
Transformed
and K. Tada
Gravity
Wave
Drag
Partitionings
Budget
Eulerian
29
Analyses
Mean
Based
on
Method
By Toshiki Iwasakil
National Center for Atmospheric Research 2 Boulder, *
Shinichi
Yamada
and Kazumasa
80307
Tada
Japan MeteorologicalAgency, Ote-machi, Chiyoda-ku, Tokyo 100, Japan
(Manuscript received,27 April 1988, in revisedform 15 October 1988
Abstract
The effects of orographic gravity wave drag (GWD) on zonal-mean fields of medium-range forecasts
are analyzed by means of the transformed Eulerian-mean (TEM) method. Results show that the
geostrophic adjustment to GWD behaves very differently between the stratosphere and troposphere.
In the troposphere, both the tropospheric and stratospheric GWDs significantly change EliassenPalm (EP) flux divergence due to large-scale (model-resolvable) waves. The change in the EP flux
divergence is much larger than the net change of tonal wind and GWDs themselves and it is almost
balanced with the change in the Coriolis acceleration term due to meridional flows. Among wave
activities, transient gravity waves resolved in the model are considered to play important roles in the
vertical redistribution of additional wave moments due to GWD.
In the stratosphere, the stratospheric GWD induces a hemispheric single cell meridional circulation.
The vertical motions in this cell cause significant temperature changes. The Coriolis acceleration due
to GWD-induced meridional flows is almost balanced with the GWD itself. In contrast with the
troposphere, EP flux divergence is less affected by GWD.
From the view of Lagrangian-mean meridional circulation, diabatic heating in the tropics and wave,
mean-flowinteraction due to planetary-scale waves have been recognizedmainly to drive a hemispheric
single cell circulation (the so-called Brewer-Dobsoncirculation) in the lower-stratosphere. Our results
indicate that the stratospheric GWD contributes to the maintenance of the single cell circulation as
well. Especially in the midlatitudes of the northern hemisphere, the GWD can be regarded as an
important forcing and considerably enhances lower-stratospheric downward motions in the polar side
of the subtropical jet stream. It might affect significantly the transport of trace constituents in the
stratosphere.
1. Introduction
In Part I by Iwasaki el al. (1989), the effects
of orographic gravity wave drag (GWD) are parameterized in two ways by considering non-hydrostatic
effects. The type A scheme for long waves (wavelength * 100km) distributes the drag forcing
1 Visiting
Scientist
at NCAR
teorological
Agancy
2 The National
Center
sored
by
the
1989,
National
Meteorological
for
Science
on
leave
from
Atmospheric
Foundation.
Society
C
of Japan
the
Research
Japan
Me -
is spon-
mainly to the stratosphere and the type B scheme
for short waves (*10km)
mainly to the lowertroposphere. A combination of these two schemes was
clearlyshown to reduce tonally averagedforecast errors of excessivewesterlies both in the troposphere
and stratosphere. The reduction in forecast errors
suggests that the model without the GWD schemes
underestimates the tropospheric and stratospheric
dissipation of angular momentum.
It is noted that the effects of GWD do not stay
around the forced area but rapidly extend both in
the vertical and horizontal. The followingpoints in
30
Journal
of the Meteorological
Society
of Japan
Vol. 67, No. 1
Part I are of great interest:
• Most of the drag forcing given to the lower
stratosphere (type A) and to the lower troposphere (type B) are rapidly redistributed
throughout the troposphere and reduce tropospheric westerlies north of 40*N.
• Both schemes strengthen tropospheric westerlies south of 40*N, even when the zonal component of GWD is negative.
• The type A scheme significantly changes the
lower-stratospheric temperature while the type
B hardly does.
These findings indicate that the drag forcings are
expected to change zonal-mean fields considerably
through the modification of mean-meridional circulations and wave activities. In this paper, we examine the response of zonal-mean fields by using
the results of forecast experiments with and without
GWD. Particular attempts are made to compare the
responses to type A and B schemes with each other.
Since GWD schemes significantly influence tonal
means of not only tonal wind but also temperature, consistent analysis of the angular momentum
transport and heat transport is desired. The representation based on the Lagrangian-mean meridional circulation is more suitable to reform the budget analysis than the representation based on the
Eulerian-mean. Because periodic waves without
drift motions, which never cause net heat and momentum transports, produce Eulerian-mean flows
(see for example, Matsuno, 1980), we use the transformed Eulerian-mean (TEM) method which approximates the Lagrangian-mean circulation (Andrews and McIntyre, 1976). In the TEM, the tendency of the zonal wind is reasonably separated into
the Coriolis acceleration due to net mean-meridional
motion and the wave activity (EP flux divergence)
and the adiabatic terms of thermodynamic equation are dominated by mean-meridional advections
(Dunkerton, 1978). As to the response to stratospheric drag forcings, Palmer et al. (1986, hereafter
referred to as PSS) proposed a simple model based
on a 2-dimensional linear solution. It will be compared to our full analyses based on the forecast experiments.
2. TEM diagnosis procedure
Dynamically consistent forecast fields produced
by NWP models allow us to diagnose tonal means
using fully primitive TEM equations without a
geostrophic approximation. FollowingDunkerton et
al.(1981) and Andrews et al.(1983), the TEM tonal
momentum and thermodynamic equations are written in a log-pressure spherical coordinate as follows:
and
Variables are listed in the Appendix. The overbars and primes denote zonal means and deviations from the zonal means, respectively. The subscripts of z and * indicate partial derivatives. The
ADV*(u) represents the advective tendency of zonal
wind due to the residual circulation including the
Coriolis acceleration. Here, the Eliassen-Palm flux
divergence DF denotes the wave, mean-flow interaction only of the model-resolvable waves and the
interaction of parameterized subgrid-scale gravity
waves is represented as an external forcing XGWD*
The external forcing X denotes horizontal and vertical diffusionsin the free atmosphere.
In order to get physical insights into the impacts
of the GWD schemes, we decompose the difference
between the two forecasts with and without GWD
into each term of equations (1) and (2). Integrating these equations with time and dividing by the
forecast period t, we have
February
1989
T. Iwasaki,
S. Yamada
where * and [ ] indicate differencesbetween
two forecastsand time-averagedtendencies[A]=
from common initial conditions, we used the relations of *u(0)=0 and *(0)=0.
These equations
relate the changes in the tonal wind and in the potential temperature at forecast time t with the averaged tendencies of TEM. In order to reduce numerical errors, we take the full forecast period of t=8
days and composite 3 cases. The time-averaged tendenciesare evaluated from field variables with a time
intervalof 24 hoursbut for [XGWD]
with the interval of 6 hours. These analyses may be subjected
to time-sampling errors, vertical-interpolation errors
and finite-differenceerrors. Hence, the dissipation
term (Loss) is defined to assess these errors as follows:
If the errors and changes in the external forcings
(except for GWD) are negligibly small, the term of
Lossbecomes equal to the parameterized GWD. The
change in the external forcing (vertical and horizontal diffusion) [*X] is thought to be much less than
the numerical error in the TEM analyses, at least in
the free atmosphere. Hence, its effects are neglected
in the discussions below.
3. Results
3.1 Meridional circulation induced by the parameterized GWD
The upper panel of Figure 1 shows the difference
in the mass streamfunction between run A and control run C, i. e., (A-C), where the mass streamfunctions are calculated from integrating residual vertical velocities,as given by definition (8), with respect
to latitude. In the stratosphere of the Northern
Hemisphere, the type A scheme induces a meridional circulation with a single-cellstructure, whose
ascending, poleward and descending flows are located in low, mid- and high latitudes, respectively.
In the troposphere, the residual circulation induced
by the type A scheme is roughly separable into two
cells. South of 40*N, flows form a direct cell whose
stream lines almost close at the lower boundary. In
the northern cell, a number of stream lines do not
close and the mass stream function does not become
and K. Tada
31
zero at the lowest level. This roughly indicates
that
the latitudinal
distribution
of surface pressure of run
A becomes
considerably
different
from that of the
control run as the forecast
period
t progresses.
In
the conventional
Eulerian-mean
analysis,
the difference in the mass streamfunction
at each latitude *
holds
where *P is the difference in tonally averaged surface pressure between two forecasts with and without GWD. In fact, the zonally averaged surface pressure predicted by the run A is about 10mb more
than the control run in high latitudes at t=8 days.
In the TEM analysis, the difference in mass streamfunctions does not correspond exactly to the surface
pressure difference, because residual velocities add
heat flux terms to Eulerian-mean velocities (e.g.,
Trenberth,1987). However,the [*(50*N,
xsurface)]
calculated from the surface pressure differenceswith
the relation (14) is comparable with (strictly a little less than) [*x(50*N, 850mb)] calculated from
residual velocities. Even in the TEM analysis, a
considerable part of non-zero differencesin the mass
streamfunctions in lower levels comes from the surface pressure difference.
The lower panel of Figure 1 shows the response
of residual circulations to the type B scheme. In
the stratosphere, the type B scheme hardly affects
the flow. Of course, the type B scheme does not directly force the stratospheric circulation but significantly modifies stratospheric planetary-scale waves
through the wave propagation in a medium-range
time scale as shown in the Part I. However, their
wave, mean-flow interactions seem still too weak
to change the mean-meridional circulations in the
stratosphere. In the troposphere, the type B scheme
induces two cell circulations as does the type A
scheme. In the northern cell, open stream lines,
corresponding to the latitudinal redistribution of
zonally averaged surface pressure, appear as well.
The tropospheric circulation induced by the type B
scheme is rather weaker than that by the type A
scheme. It seems to be due to the fact that the
surface gravity wave stress generated by the type B
scheme is smaller (see section 4.1 of Part I)
Here, we note that the ensemble means of forecasts within a medium-range time scale are not close
to an equilibrium state of the model atmosphere, but
are in transition from the initial climate (the ensemble mean of initial conditions) to the model climate. If the forecast period t is much longer than a
medium-range time scale, *P(t) must be saturated
at a surface pressure difference between two model
32
Journal
climates
with
for a long term
and
without
average, *p(t)t
GWD
of the Meteorological
schemes.
in the right
Hence,
hand
side
of the relation (14) approaches zero and most stream
lines are expected to close at the lower boundary. In
this sense, the open cell structure in the response of
the meridional circulation should be regarded as a
reflection of the transition stage from the ensemble
mean of initial values (actual climate) to the model
climate.
3.2 Angular momentum balance
According to Eq. (10), the tonal wind change
u(t) due to GWD is decomposed into the* contributions of mean-meridional motion [*ADV*(u)],
wave driving (EP flux divergence) [DF]
and
forcing itself [XGWD]The mean-meridional term
is dominated by the Coriolis acceleration
*
Society
of Japan
Vol.67,
No.1
In the northern-hemispheric stratosphere, the
[*ADV* (u)] due to the type A becomes positive,
since this scheme induces poleward flows as shown
in the previous subsection. In the lower troposphere, both schemes change [*ADV* (u)] in their
signs around 40*N, reflecting the two-cell structure
in the GWD-induced residual circulation, i, e., poleward flows in the north and equatorward flows in
the south.
Figure 2 shows the differences in Eliassen-Palm
flux divergence [*DF] between two runs with and
without GWD together with the difference in the
flux vectors [*F] by arrows. Both type A and
B schemes increase EP flux in the high-latitude
lower troposphere. This additional flux converges
and reduces westerlies throughout the whole troposphere north of 40*N. As shown later, the flux
Fig. 1. Meridional cross sections of GWD-induced residual circulation. Mass streamfunctions are averaged
during the whole forecast period of 8 days and composited for three cases. Contour interval is 2*109
kg/s and negative areas are shaded. (top: for run A minus control run, bottom: for run B minus control
run)
February
1989
T. Iwasaki,
S. Yamada
and K. Tada
33
convergencebalancesmostlywith Coriolisaccelera- to seriously affect this TEM analysis. At the 70
tion due to GWD inducedmeridionalmotion. Be- mb level, the change in the Coriolis acceleration
tween30*and 40*N,EP flux divergenceinducedby (*[*ADV*(u)]) highly compensates for the drag
GWDis positiveand enhancestroposphericwester- forcing [XGWD]and then net tendency *u(t)t is very
lies. Thus, modelresolvablewavesplay important small compared to these two terms. North of 30N,
rolesin the troposphericredistributionof drag forc- the drag forcings prevail against the change in the
ings producedin the parameterization.
Coriolis acceleration and contribute to the reduction
Figure 3 shows contributions of [*ADV*(u)], in westerliesas suggested by Tanaka and Yamanaka
[*DF] and [XGWD]to net changesin tonal mo- (1985). South of 30*N, the Coriolis term prevails
mentumtendency *u(t)tof Eq. (10)due to the type against the drag forcing and accelerates the westA scheme at 70mb and 700mb levels. In midlatitudes, the type A scheme produces the largest
drag forcing around 70mb. Since the quantity [Loss]
calculated by the definition (12) is almost equal to
[XGWD],numerical errors and [*X] do not seem
erlies. The EP flux divergence due to large-scale
waves is hardly changed by the inclusion of the type
A scheme except for north of 70*N. At the 700mb,
the change in the EP flux divergence [*DF] and in
Coriolis acceleration [*ADV* (u)] are much larger
Fig. 2. Meridional cross sections of GWD-induced Eliassen-Palm fluxes (arrows) and their divergences
(contours) averaged during 8 days and composited for three cases. The magnitudes of flux intensities
are shown by arrows at the lower left corner of the figure (units: kg/sec2). Contour interval of flux
divergence is 0.5m/(sec*day) and negative (deceleration) areas are shaded. (top: for run A minus
control run, bottom: for run B minus control run)
34
Journal
of the Meteorological
Society
of Japan
Vol.67, No.1
Fig. 3. Contributions
of eachtermin Eq. (10)to the nettendencychangein mean zonalwind *u(t)t
due
to thetypeA schemeat 70mb(top)and 700mb(bottom).Thetimeperiodt is thefullforecastlength
of 8 days. The [Loss]definedby Eq. (12)is alsoshownto indicatenumericalerrors. Heavysolid,
thin solid,broken,chainand dottedlinesindicate *u(t)t[*ADV*(u)],[xGWD],
[*DF] and [Loss],
respectively.
[verticalunit: m/(sec*day)]
Fig.
4.
Same
as Figure
3, except
than GWD [XGWD]
and almostbalanceeachother.
Both terms changein sign around40*N.The [*DF]
dominatesa little over the [*ADV*(u)] in all latitudes and the net tendency *u(t)tbecomespositive
(negative)south (north) of 40*N.
Figure 4 showsthe contributionsto the net tendency change *u(t)tin the type B scheme. In the
stratosphere,the type B schemehardly changeseither the Coriolisaccelerationor the EP flux divergence. In the troposphere,the EP flux divergence
and Coriolisaccelerationterm strongly respondto
the type B scheme. Even at the level of 700mb,
where large GWD forcingsare distributed by the
type B scheme, these two terms becomelarger in
for type
B scheme.
magnitude than the drag forcings. Both terms
change in sign around 40*N and compensate for each
other as well, as observed in the case of incorporating the type A scheme.
3.3 Heat balance
Since the zonally averaged diabatic heating rate
Q in the model are hardly affected by the introduction of GWD schemes at least within a mediumrange time scale, temperature differences between
two forecasts with and without GWD schemes are
considered to be adiabatically induced'. Figure 5
shows the meridional cross sections of the advection
term [*ADV* (*)] in the thermodynamic equation
(11). The eddy term [*EDDY (*)] is found to be
February
much
less
1989
than
T. Iwasaki,
the
heat
advection
due
S. Yamada
to residual
velocities. The difference between [*ADV* (*)] and
net temperature change shown in Figure 12 of Part I
may arise from numerical errors in the TEM diagnosis. A comparison between [*ADV* (*)] and the net
temperature change confirms that significant temperature changes are induced in the lower stratosphere by the heat advection due to the residual
flow, i.e., heatings around (50*N,200mb) and coolings around (30*N, 100mb). From further decor
position of the advection term, the vertical component appears to be dominant in these stratospheric
temperature changes.
As is well-known, the representation of heat balance in the TEM is very differentfrom that in a conventional Eulerian-mean diagnosis whereeddy terms
and K. Tada
35
play important roles in heat transports in midlatitudes. In this TEM analysis, the finding that
vertical advections are dominant in GWD-induced
temperature change is also consistent with the concept on the stratospheric thermal balance in terms
of the Lagrangian-mean circulation. Then, we can
straightforwardly understand the relation of heat
transport to the meridional circulation.
4.
Discussion
4.1 Geostrophic adjustment to the ageostrophy induced by GWD schemes
The above analyses lead us to the following physical picture on the geostrophic adjustment of the
zonal mean fields to the ageostrophy induced by the
parameterized GWD. Figure 6 shows a schematic
Fig. 5. Meridional cross sections of [*ADV* (*)] with contour interval of 0.5K/day. Shaded areas are
negative. (top: for run A minus control run, bottom: for run B minus control run)
36
Journal
Stratospheric
Tropospheric
of the Meteorological
response
response
and
Society of Japan
to stratospheric
both
to tropospheric
to stratospheric
Vol.67, No.1
GWD
GWD
GWD
Fig. 6. Schematic diagram of geostrophic adjustments to GWD in tonal-mean fields. Broken lines connect
mainly balanced terms.
diagram of the angular momentum balance associated with the GWD in the stratosphere (top) and
the troposphere (bottom). In the stratosphere, the
zonal-mean fields respond only to stratospheric drag
forcings (type A). As was shown in Section 3.2, the
zonal component of the type A GWD is almost
balanced with the change in the Coriolis acceleration. Although planetary-scale waves are significantly modified by both the type A and B schemes,
the change in wave, mean-flow interactions of these
waves (EP flux divergence) contribute little to the
net change in the zonal wind except for north of
70*N. In the case of the type A scheme, the EP flux
divergence seems to be relatively important north
of 70*N. However, numerical errors (the difference
between [XGWD]and [Loss]) become so large in
high latitudes that detailed discussions on momentum balance should be left untouched. The heat
advections due to mean-vertical motion change the
temperature distributions in the lower stratosphere
so as to achieve thermal wind balance to the change
in the vertical shear.
In contrast, in the troposphere, the EP flux divergence plays an important role in geostrophic adjustment to both the stratospheric and tropospheric
forcings. In the case of run A, the major portion
of the drag forcings generated in the stratosphere is
rapidly transmitted to the troposphere and change
the tropospheric mean tonal flow, as discussed in
Part I. This vertical transfer of momentum seems to
be made mainly not through the mean-meridional
circulation but through the vertical propagation of
waves. This is seen from the fact that the contribution of mean meridional circulation to *u(t)t is
very different in sign from the net tendency change
which is positive (negative) south (north) of 40*N
as shown in the previous section, but that it almost
has the same sign as the change in the EP flux divergence. The rapid vertical transfer of momentum
implies that the group velocitiesof waveswhich contribute to the momentum transfer are much faster
than those of Rossby waves. They must be gravity waves resolved in the model. As mentioned in
Section 2.1 of Part I, stationary gravity waves cannot effectivelytransfer momentum owing to inertial
effects. Hence, transient gravity waves, which can
easily interact with mean flows, may transfer most
of the momentum given to the stratosphere by the
type A scheme back to the troposphere. Simultaneously, mean-meridionalflowsmay change so that the
mass field may geostrophically adjust to changes in
the tropospheric tonal wind field. Tropospheric drag
produced by the type A schemeis less effectiveto the
tropospheric flow fields. Special experiments omit-
February
1989
T. Iwasaki,
S. Yamada
and K. Tada
37
Fig. 7. EP flux (arrows) and its divergence (contours) of run A averaged for the forecast period of 8 days
and composited for three cases. The magnitudes of flux intensities are shown by the arrows at the
lower left corner of the figure. Contour interval is 5m/(sec.day) and negative areas are shaded.
ting the tropospheric component of the type A drag
(below 300mb) have similar tropospheric momentum balance to the run A. Thus, the change in tropospheric flows due to the type A scheme is considered to result mostly from the stratospheric component. In run B, the drag forcing generated mainly in
the lowertroposphere may be redistributed throughout the troposphere by model-resolvable waves as
well. Consequently, impacts of both the type A and
B schemes on the tropospheric zonal wind become
rather barotropic even though the vertical partitionings of drag forcings are not vertically uniform.
As to the response of tonal-mean fields to stratospheric drag forcings, a simple solution based on a
2-dimensional linear model was attempted by PSS.
Since this was solved as an initial value problem,
it can be directly compared to the impacts on forecasts. Their solution can almost describe the stratospheric response analyzed in this work. However,
their solution is insufficient to describe the tropospheric response, because it neglects changes in the
EP flux divergence which is shown to be significantly larger in this analysis. Another shortcoming
arises from the lower boundary condition of *x=0.
That is, the zonal mean of surface pressure is unchanged. This condition implies equatorial winds in
the troposphere, which are the returning flowsof the
stratospheric poleward winds. They explained that
the tropospheric westerlieswere decelerated through
the Coriolis effects due to these returning equatorial flows. However, the surface pressure is different between run A and the control run. Therefore, our results differ from PSS's solution in the
lower-tropospheric meridional flows and their Coriolis accelerations. The lower boundary condition of
x=0 is not appropriate for the initial value prob*
lem.
4.2 Role of the type A GWD in the lower stratospheric and tropospheric general circulation
The Lagrangian-mean flows form a Hadley-like
single cell circulation (the so-called Brewer-Dobson
circulation) in a hemispheric lower stratosphere and
troposphere, as was clearly shown by Kida (1977,
1983). It has been recognized that this structure is
maintained not only by diabatic heating, but also by
wave, mean-flowinteractions. Pfeffer (1987) showed
that the EP flux divergence due to large-scale waves
significantly contributes to the formation of the single cell circulation especially in high latitudes.
Of course, neither numerical experiments by Kida
nor observational analyses by Pfeffer included effects
of subgrid-scale gravity waves. However,as shownin
Section 3.1, the type A GWD considerably enhances
the single cell structure in the stratosphere. Here,
wecompare the role of subgrid-scale gravity wavesto
the role of large-scale waves. Figure 7 shows the EP
flux divergence of run A. It is found that large-scale
waves do not produce large EP flux convergencedeceleration in the mid-latitudinal stratosphere where
the large GWD is produced. In this region, the
GWD seems to be relatively important. In fact, systematic forecast errors of lower-stratospheric temperature are significantly reduced by incorporating
the GWD scheme. On the other hand, in higher latitudes, the GWD becomes small because the excita-
38
Journal
Fig.
8.
in the
Schematic
mid-latitude
diagram
lower
showing
of the Meteorological
how
effects
of GWD
Society of Japan
influence
the
distribution
Vol.67, No.1
of trace
constituents
stratosphere.
tion of gravity waves is rather inactive due to weaker
westerlies in the lower troposphere. Planetary-scale
waves, which may have larger coherence length and
are more easily propagated in the horizontal than
gravity waves, are thought to act more effectively
on the mean flow in higher latitudes. Therefore, it
seems that diabatic beatings, wave, mean-flow interactions of large-scale waves and subgrid-scale gravity waves contribute to the maintenance of the lowerstratospheric single cell circulation in different ways.
.3 Effects of GWD on Me dower-stratosphere tracer
4
transports
It is well-known that some stratospheric trace constituents have very asymmetric distributions and
annual marches between the southern and northern hemispheres.
Atmospheric circulations associated with the earth's orography are believed to
be one of the major causes of these asymmetries.
Among them, the roles of planetary-scale waves in
meridional circulations and eddy diffusions of stratospheric species have interested many authors. From
the above discussion, we can expect that GWD also
plays an important role in the stratospheric tracer
transport especially in the mid-latitudes.
As was symbolically represented by Holton
(1980), in the Lagrangian-mean framework, stratospheric tracers are mainly transported in the vertical by advections due to mean-motions, while in
the horizontal by eddy diffusion. In the case of
ozone, the distribution in the lower stratosphere is
primarily determined by dynamical effects, because
its chemicallifetime is very long, except in the tropics. Between 300mb and 100mb levels, the atmosphere is stable (as a part of the stratosphere) on
the polar side of the subtropical jet stream, while it
is rather convective (as a part of the troposphere) on
the equatorial side. At this altitude in mid-latitudes,
the ozone mixing ratio is increased by the downward
advection of ozone-rich air from the upper stratosphere but decreased by horizontal mixing with the
ozone-poor tropospheric air from lower latitudes on
isentropic surfaces. Figure 1 shows that the type A
GWD significantly enhance the lower-stratospheric
downward motion in the Northern Hemisphere. It
must increase the ozone mixing ratio at least below
the 100mb level in mid-latitudes (just north of the
jet stream).
Next, we point out that the levelof the tropopause
is also important for the distribution of trace constituents. In the troposphere, vertical diffusion coefficients become noticeably larger than those in
February
1989
T. Iwasaki,
S. Yamada
the stratosphere and dominate vertical transports
of constituents. Then, mixing ratios of constituents
sharply change around the tropopause. As is wellknown, total ozone amounts (vertically integrated
ozone mass) are much larger on the polar side of the
subtropical jet stream than on the equatorial side,
reflecting the difference in the tropopause height.
Iwasaki and Kaneto (1984) showed that the altitude of the tropopause primarily determines the
seasonal variation of total ozone amounts in midlatitudes. In the control run without GWD schemes,
the tropopause height in mid-latitudes (northern
side of the subtropical jet stream) cannot be maintained realistically, but it becomes higher with the
forecast period because cooling biases in the lower
stratosphere reduce static stability just above the
tropopause. These errors are clearly reduced by incorporating the type A GWD. Therefore, subgridscale gravity-wavedrags are thought to affect significantly the distribution of trace constituents through
the lowering of the tropopause. The stratospheric
temperature change is induced mainly by mean vertical heat advections as discussed in Section 3.3.
Thus, we can say that the GWD enhances the
downward Lagrangian motion on the polar side of
the subtropical jet stream and affects the distributions of lower-stratospheric trace constituents in
two ways; i,e., enhancements of vertical advective
transports and loweringthe polar tropopause (suppressing vertical diffusion) as schematically shown
in Figure 8. In the case of ozone, both effects must
contribute to the increase of total amounts in midlatitudes. The vertical residual velocities w* averaged north of 40*N is about -0.5mm/sec (downward) at 100mb in run A and run AB. It is comparable with values estimated under the assumption
of radiative-advective balance (e.g., Murgatroyd and
Singleton, 1961 and Gille et al. 1987). On the
other hand, the vertical velocity of the control run
at the same level is almost zero. Of course, this
model might produce downward motion through
wave, mean-flow interactions of large-scale waves, if
the forecast period were extended and the model
reached its equilibrium stage. In the model climate of the control run, however, the cooling bias
would be more apparent than in the forecast in the
mid-latitude lower stratosphere and the downward
motion would still be slower compared to the actual climate. Therefore, the stratospheric GWD
is thought to be very important for the forecast
and climate simulation of conservative stratospheric
species, such as water vapor, ozone and so on.
5. Conclusions
The TEM analyses of the impacts on the type A
and B GWD schemes are summarized as follows;
• In the stratosphere: The type A schemeinduces
and K. Tada
39
a single-cellresidual circulation with its upward
branch on the equatorial side and the downward
branch on the polar side of the subtropical jet
stream. The Coriolis acceleration due to the
meridional flow of this cell highly compensates
for the drag forcing. Net change in the tonal
wind is almost explained by the sum of these
two terms. The heat advection due to the vertical motion in this cellroughly accounts for the
temperature change induced by the GWD. The
type B scheme induces less residual flowsin the
stratosphere.
Inthe troposphere: Both schemes change the
EP flux divergence of model-resolvable waves.
These changes are much larger than the accelerations due to the drag forcings themselvesand
highly compensate for the Coriolis acceleration.
Most of the drag forcing given to the stratosphere (type A) and to the lower troposphere
(type B) may be rapidly redistributed throughout the troposphere through the momentum
transport by the transient gravity waves (phase
speed C*0) resolved in the model.
The response of zonal-mean fields to the type A
GWD has been compared to the simple solution obtained by PSS. The stratospheric response agrees
well with their solution. However, PSS's solution is
insufficient to represent the tropospheric response.
Deficiency arises from (i) the shortcomings associated with the lower boundary condition and (ii) the
neglect of eddy effects. In particular, even zonalmean (two-dimensional) models should include the
effects of GWD-induced large-scale eddies in the troposphere.
The stratospheric GWD contributes to the maintenance of a lower-stratospheric single-cell circulation (in the sense of Lagrangian-mean) as well as
diabatic heating and wave, mean-flow interactions
of planetary-scale waves. The GWD is relatively
important in the mid-latitudes. The changes in
the meridional circulation by the GWD are thought
to influence tracer transports in the lower stratosphere through the enhancement of vertical advection and the suppression of vertical diffusionaround
the tropopause north of the subtropical jet stream.
The asymmetric distributions of trace constituents
and their annual marches between the southern and
northern hemispheres is due partly to the excitation
of gravity waves by subgrid-scale orography.
Acknowledgments
Numerical calculations of both parts in this study
were carried out at the Numerical Prediction Division of the Japan Meteorological Agency. The authors wish to express their sincere thanks to Drs. K.
Ninomiya and T. Kitade and the staff members of
40
Journal
of the Meteorological
the Numerical Prediction Division for their continuous encouragements. In particular, Mr. M. Kudo,
Mr. K. Kurihara and Dr. H. Nakamura gave us
useful suggestions on the characteristics of gravity
waves. This report was completed while one of the
authors (T. I.) visited the National Center of Atmospheric Research (NCAR) with partial support from
the National Oceanic and Atmospheric Administration under NA85AAG02575.He had several stimulating discussions with the scientists of NCAR. He
is very grateful to Dr. A. Kasahara for arranging
the visit to NCAR, his critical reading and valuable
comments on this manuscript. Comments and discussions with Profs. J. Wallace and J. Holton and
Drs. N. McFarlane, B. A. Boville, M. D. Yamanaka
and two anonymous reviewers are appreciated. We
are pleased to acknowledge Miss R. Bailey for her
skillful typesetting.
Appendix
List of symbols
a
earth's radius
Coriolis*parameter
g
gravitational acceleration
z(=-H ln p/ps) altitude in log-pressure
coordinate
H
scale height (=7000m)
ps
reference surface pressure
(=1000mb)
* latitude
u
zonal wind component
meridional wind
v
component
w
vertical wind component
potential temperature
*
air density*0
(=-*sexp(-z/H))
*s
x
Q
x
reference surface air density
external forcing
external heating
mass streamfunction
References
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February
1989
T. Iwasaki,
S. Yamada
and
K. Tada
41
二種 類 の垂 直配 分 を考 え る地 形性 重力波 ドラ ッグのパ ラメ リゼ ーシ ョン
第 二部
TEM
法 に よ る帯 状平 均場 の解 析
岩 崎俊 樹1・山 田慎一 ・多 田一正
(気象庁 ・数値予報課)
中 期 予 報 ・帯 状 平 均 場 に及 ぼ す 重 力 波 ドラ ッ グ (GWD)
用 い て 解 析 す る。 そ の 結 果 は 、 GWD
の 影 響 を transformed
Eulerian-mean
method
を
に 対 す る地 衡 風 調 節 の 機 構 が 対 流 圏 と成 層 圏 で は 大 き く異 な る こ と
を 示 して い る 。
対 流 圏 の 場 合 は 、 GWD
を 成 層 圏 と対 流 圏 の ど ち ら に 与 え て も、 大 規 模 (model
フ ラ ッ ク ス が 著 し く変 化 す る。 GWD
る Elissen-Palm
(EP)
の 変 化 や GWD
よ り も大 き く、 コ リオ リ加 速 項 の 変 化 とバ ラ ン ス し て い る。 波 の 活 動 度 の う ち で も、 非 定
常 の 重 力 波 が 、 GWD
に よ る EP
resolvable な) 波 動 に よ
フ ラ ッ ク ス の 発 散 の 変 化 は 、帯 状 風
に 関 係 した 運 動 量 の 鉛 直 再 配 分 に 重 要 な 役 割 を 果 た して い る と考 え られ る。
成 層 圏 の 場 合 は 、 成 層 圏 に 与 え た ドラ ッ グ が 単 一 細 胞 型 の 循 環 を 誘 起 す る。 この 循 環 の 鉛 直 運 動 は 有 意
な 気 温 変 化 を も た らす 。 ま た 、 この 循 環 に よ る コ リオ リ加 速 は ほ ぼ GWD
場 合 と は対 照 的 に 、 EP
とバ ラ ン ス して い る 。 対 流 圏 の
フ ラ ッ ク ス 発 散 の 変 化 は小 さ い。
ラ グ ラ ン ジ ュ的 平 均 子 午 面 循 環 の 見 地 か ら は 、 熱 帯 に お け る非 断 熱 加 熱 と大 規 模 波 動 ・平 均 流 相 互 作 用
が 、 下 部 成 層 圏 に お け る単 一 細 胞 循 環
(い わ ゆ る Brewer-Dobson
た 。 我 々 の 解 析 結 果 は 、 成 層 圏 に お け る GWD
循 環)
を維 持 して い る と考 え られ て き
も単 一 細 胞 循 環 の維 持 に貢 献 し て い る事 を示 して い る。 特
に 北 半 球 中 緯 度 で は重 要 な 駆 動 力 で あ る 。 ま た そ れ は 成 層 圏 に お け る微 量 成 分 輸 送 に も大 き な影 響 を与 え
て い る と推 察 され る 。
1米国立 大 気科 学研 究 セ ン ター ・滞 在 研究 員