FDEPS 2012, Lecture 5

Gravity waves and stratospheremesosphere coupling
Ted Shepherd
Department of Meteorology
University of Reading• Flow over topography induces high pressure on theupwind side and low pressure on the downwind side
– Leads to a downstream force on the Earth– An opposite drag force on the atmosphere is implied• Atmospheric angular momentum covaries with the length ofday due to this momentum exchange– But where does this drag occur?
Sawyer (1958) argued
the displacement ofstreamlines would
decrease with altitude(see figure), implying
momentum flux
convergence at lowlevels

• But we know that mountains and other sources (e.g.
convection) can force internal gravity waves, which canpropagate to great heights– What happens to the momentum?

http://www.metvuw.com/

Vertical temperature profiles observed by Rayleigh lidar
Sequence of(< 30-min avg)
profiles (offsetby 10 K) atEureka, Canada
Dashed lines
show adiabatic
lapse rate
From Whiteway& Carswell(1994 JAS)

Start with disturbance zonal momentum equation∂u'∂u '∂u∂p'ρ0+ ρ0 u+ ρ0 w '=−∂t∂x∂z∂xAssumeThen∂u '∂u 'u'∝exp[ik(x −ct)],= −c∂t∂x∂u '∂u ∂p '
ρ0 ( u −c )+ ρ0 w ' +=0∂x
∂z ∂x
∂∂u
⇔ [ ρ0 ( u −c ) u ' +p ' ] = −ρ0 w '∂x∂z∂∂u⇔[L] [L] =0 =−ρ0 [ ρ0 (u −c )u' w ' + p' w ']∂x∂zTherefore

p'w' =−ρ0 (u −c)u'w'

But p ' w ' > 0
andfor upward propagating GWs, hencesgn(c −u) =sgn(u'w')

c > u ⇒ positive momentum forcing

c < u ⇒ negative momentum forcing• In both cases the waves act to drag the flow towards theirphase speed where they dissipate– This is not always a “drag”; it can be an acceleration• In the absence of transience and dissipation, there is nomomentum flux convergence and ρ0 u ' w ' is constant withheight– This is the Eliassen-Palm theorem (1961)

• In the mesosphere, gravity-wave drag is important for
driving the meridional overturning circulation

Plumb(2002JMSJ)• Downward control: in the steady limit, the TEM
vertical velocity (related to diabatic vertical velocity) is1∂ ∞ ρF c o s φw =−dz∫a ρ c o s φ ∂φ z 2 Ωsin φ*• For gravity waves, this simplifies to1∂ c o s φ u ' w ' w =−
a c o s φ ∂φ  2 Ωs in φ *or integrated over the (north) polar cap,

∫φπ/2cos φu' w 'w a cos φdφ=2 Ωs in φ*

• Positive momentum flux drives polar upwelling,
negative momentum flux drives polar downwelling• The seasonal variation in stratospheric winds controls
the spectrum of gravity waves reaching the mesosphere(where they reach large amplitudes and break)– Gravity waves are dissipated at critical levels (c=U)• The result is a negative torque in the winter hemisphere,
and a positive torque in the summer hemisphere
Gravity
waves dragthe zonalflow
towards
their phasespeed(Eliassen &Palm 1961)
McLandress (1998 JASTP)• The gravity-wave drag is so strong that it reverses thewinter-to-summer-pole temperature gradient in the uppermesosphere• Summer mesopause is the coldest region on Earth!
• Reversal of winds above implies the gravity-wave
induced torques are acting to accelerate the flow

Cold summer mesopause

Shepherd (2003 Chem. Rev.)• Wave-induced torques drive a middle atmospherecirculation with a strong seasonal dependence– Mainly from Rossby waves in the stratosphere — the‘Brewer-Dobson circulation’ (BDC)– Mainly from gravity waves in the mesosphere

CMAM results from Beagley et al. (1997 Atmos.-Ocean)• The same gravity-wave filtering mechanism operates
on shorter timescales too• Stratospheric Sudden Warmings act to cool the polarmesosphere (Holton 1983 JAS), seen here in the
CMAM-DAS response to the 2002 Antarctic SSW– Forecast ensemble shows response is deterministic
10 hPa SP T

0.1 hPa SP TT (hits - misses)

Ren, Polavarapu & Shepherd (2008 GRL)• The SSW is associated with a huge change in thezonal winds, shown here at 60°S

Hits
(withSSW)

Misses(noSSW)

Ren et al. (2008 GRL)GW
momentumflux

GW drag• The dramatic zonal
wind changes
associated with theSSW alter thefiltering of thegravity-wave (GW)
spectrum, leading toa positive GWDanomaly (hencecooling) in the polarmesosphere
Thick=hits
Thin=misses
Ren et al. (2008 GRL)• The mesospheric response to extended recoveries fromNH SSWs in the free-running CMAM seems quite realistic

Hitchcock & Shepherd (JAS, in press)

• Evolution of CMAM polar-cap temperature anomalies can be
attributed to different wave forcings via Eliassen adjustment

Hitchcock & Shepherd (JAS, in press)

The 2006 SSW in observations and models
CMAM-DAS
did not
assimilate
mesosphericobservations,
yet doesbetter thanthe twooperationalsystemsFigurecourtesyof Gloria
Manney,NASA JPL• When CMAM isnudged toreanalyses in thestratosphere, themesosphere
reproduces theobservations
very well• Information
propagates
upward throughwave fluxes

McLandress et al.
(JAS, submitted)

• Removing either the orographic and/or the nonorographic gravity-wave drag changes temperaturesat 0.05 hPa (70 km) during the extended recovery
phase– There is a nonlinear coupling between orographic
and non-orographic gravity-wave dragMcLandress et al. (JAS, submitted)

• Outside the period of the SSW, orographic GWD isresponsible for limiting the upper stratospheric winds andthus limiting the polar descent induced by non-orographic
GWD, which acts to bring down high values of COMcLandress et al. (JAS, submitted)

• The very low summer mesopause temperatures lead tothe formation of Polar Mesospheric Clouds (PMCs)• The onset of the PMC season is highly variable in theSH, much less so in the NH

Karlsson et al. (2011 JGR)• This behaviour is due to the lateness of the SH polarvortex breakdown, which provides a source of variability
in SH mesopause temperatures in early summer throughthe same gravity-wave filtering mechanism
Late PMC onset
Early PMC onset

Karlsson et al. (2011 JGR)• Late vortex breakdowns filter more eastwardpropagating gravity waves– Reduces positive torque in upper mesosphere– Reduces polar upwelling and cooling– Delays onset of PMCs

Karlsson et al. (2011 JGR)• The ozone hole has led toa delay in SH vortex
breakdown by about 3weeks (bottom)• The previous reasoning
based on gravity-wave
filtering would imply awarming of the upper
mesosphere in late spring• CMAM simulations of theozone hole show thiseffect (top), but also awidespread mesosphericcooling during summer
Lossow, McLandress,
Jonsson & Shepherd (2012• Analysis shows that theTEM vertical velocity (wbar star) induced byresolved wave drag(red) acts generally
against that induced by
GWD (blue), andcompletely dominates
the upper mesosphereresponse in earlysummer (bottom)• Arises from in-situ
baroclinic instability
Lossow, McLandress,
Jonsson & Shepherd (2012JASTP)

However, climate models tend to have a systematic
bias towards a too-late Antarctic vortex breakup– This would affect the timing of stratospheremesosphere coupling relative to the PMC season

Butchart et al. (2011 JGR)The SH jet has a maximum around 60°S
– At this latitude band, the surface is represented entirely
as ocean in the models, hence no orographic GWD!

OGWDinCMAM
McLandress, Shepherd,Polavarapu & Beagley(2012 JAS)• When CMAM is run in data assimilation mode, increments
imply missing drag at these latitudes, which descends fromthe upper stratosphere as the zero wind line descends (left)• There is other evidence for the role of OGWD at theselatitudes• An ad hoc inclusion of extra OGWD in this latitude belt
substantially reduces the zonal-wind bias in CMAM (right)

Zonal windincrementsfrom data
assimilation

McLandress, Shepherd, Polavarapu & Beagley (2012 JAS)• Pole-to-pole interhemispheric coupling?
– OSIRIS observations of PMCs at the summer
mesopause (after the onset period) show anapparent correlation between PMC size andtemperatures in the winter polar lower stratosphereKarlsson et al. (2007 GRL)• Simulations withthe extended
CMAM show asimilar correlation
pattern to the obs(associating PMC
radius with lowtemperature)
Here the twohemispheres arecombined, 19
years of model
dataBlack lines
indicate summer
mesopause
Karlsson, McLandress & Shepherd (JASTP 2009)• The interhemisphericcoupling comesfrom GWD• Plots show
GWD response
to positive
winterhemisphere EP
flux anomalies
in CMAM• Response is
upwards andsideways• Karlsson et al.
(JASTP 2009)Summary• Internal gravity waves can transfer momentum to greatheights and exert a “drag force” (which can be positive)
where they dissipate• This drag force controls the thermal structure of themesosphere (e.g. cold summer mesopause)• The momentum transfer is filtered by winds in thestratosphere, providing a mechanism for stratospheremesosphere coupling on a variety of timescales, mostprominantly in polar regions– Warm stratosphere implies cold mesosphere• In this way, the behaviour of the mesosphere is “slaved”
to that of the stratosphere through gravity-wave drag• Models are able to capture this process very well

Reference 1• Beagley, S. R., de Grandpre, J., Koshyk, J. N., McFarlane,N. A., Shepherd, T. G., 1997: Radiative-dynamical
climatology of the first-generation Canadian Middle
Atmosphere Model, Atmosphere-Ocean, 35, 293-331.
• Butchart, N., Cionni, I., Eyring, V., Shepherd, T. G., Waugh,
D. W., Akiyoshi, H., Austin, J., Bruhl, C., Chipperfield, M. P.,
Cordero, E., Dameris, M., Deckert R., Dhomse, S., Frith, S.
M., Garcia, R. R., Gettelman, A., Giorgetta, M. A., Kinnison,
D. E., Li, F., Mancini, E., McLandress, C., Pawson, S., Pitari,G., Plummer, D. A., Rozanov, E., Sassi, F., Scinocca, J. F.,
Shibata, K., Steil, B., Tian, W., 2010: Chemistry--Climate
Model Simulations of Twenty-First Century Stratospheric
Climate and Circulation Changes, J. Clim., 23, 5349-5374.
• Eliassen, A., Palm, E., 1961: On the transfer of energy instationary mountain waves., Geofys. Publ., 22, 3, 1-23.

Reference 2• Hitchcock, P., Shepherd, T. G.: Zonal mean dynamics ofextended recoveries from stratospheric sudden warmings,J. Atmos. Sci., in press.
• Karlsson, B., Kornich, H., Gumbel, J., 2007: Evidence forinterhemispheric stratosphere-mesosphere coupling derived
from noctilucent cloud properties, Geophys. Res. Lett., 34,L16806.
• Karlsson, B., McLandress, C., Shepherd, T. G., 2009: Interhemispheric mesospheric coupling in a comprehensive
middle atmosphere model, J. Atmos. Sol.-Terr. Phys., 71,518-530.

Reference 3• Karlsson, B., Randall, C. E., Shepherd, T. G., Harvey, V.
L., Lumpe, J., Nielsen, K., Bailey, S. M., Hervig, M., Russell
III, J. M., 2011: On the seasonal onset of polarmesospheric clouds and the breakdown of thestratospheric polar vortex in the Southern Hemisphere, J.
Geophys. Res., 116, D18107.
• Lossow, S., McLandress, C., Jonsson, A. I., Shepherd, T.
G., 2012: Influence of the Antarctic ozone hole on the polar
mesopause region as simulated by the Canadian Middle
Atmosphere Model, J. Atmos. Sol.-Terr. Phys., 74, 111–123.
• McLandress, C., 1998: On the importance of gravity waves
in the middle atmosphere and their parameterization ingeneral circulation models, J. Atmos. Sol.-Terr. Phys., 60,1357–1383.

Reference 4• McLandress et al, J. Atmos. Sci.,submitted.
• McLandress, C., Shepherd, T. G., Polavarapu, S., Beagley,S. R.,2012: Is Missing Orographic Gravity Wave Drag near
60°S the Cause of the Stratospheric Zonal Wind Biases in
Chemistry-Climate Models?, J. Atmos. Sci, 69, 802-818.
• Plumb, R. A., 2002: Stratospheric transport. J. Meteor. Soc.
Japan, 80, 793-809.
• Ren, S., Polavarapu, S. M., Shepherd, T. G., 2008: Verticalpropagation of information in a middle atmosphere dataassimilation system by gravity-wave drag feedbacks,Geophys. Res. Lett., 35, L06804, 5pp.
• Whiteway, J. A., Carswell, A. I., 1994: Rayleigh lidar
observations of thermal structure and gravity wave activity
in the high Arctic during a stratospheric warming, J. Atmos.
Sci., 51, 3122-3136.