FDEPS 2012, Lecture 3

Rossby waves and thestratospheric Brewer-Dobson
circulation
Ted Shepherd
Department of Meteorology
University of Reading• Rotating, stratified geofluids are characterized by waves(especially Rossby and inertia-gravity)– Waves transfer angular momentum and energy– For the atmosphere, energy can be radiated to space
but the angular momentum budget is closed• The middle atmosphere is (mainly) dynamically stable,
so forced by waves and damped by radiation– Circulation is mechanically driven: a refrigerator• The zonal (axisymmetric) flow filters the angularmomentum transfer, inducing differential torques– Feedback on zonal flow is wave-mean interaction– The two-way interaction provides mechanisms for
global-scale teleconnections• Often the torques act as a drag, but not always– Super-rotation is certainly possible• ‘Eliassen adjustment’: The instantaneous zonal-mean
response to an imposed torque or radiative heating
involves a residual circulation to maintain thermal-windbalance: case shown here is for a negative torque(arrows depict the induced circulation)
Zonal wind tendencyTemperature tendency

Shepherd (2000 JASTP)

• In the extratropics, persistent torques lead todownward ‘burrowing’ of the mean meridional
circulation; negative torque ⇒ poleward flow

ddrduτ = (ru) = u + r
dt
dt
dt
0

Radiative cooling and surface
drag, which are relaxational,‘accommodate’ the circulation(u is absolute velocity)
Initial wind tendency

Initial circulation

Final circulation

Zonally symmetric calculations from Haynes et al. (1991 JAS)• In the stratosphere, the small thermal inertia means
temperatures follow the Sun: warm at the summer poleand cold at the winter pole
• Thermal wind balance implies eastward (westerly) flow inthe winter hemisphere, and westward flow in the summer
hemisphere
Observed temperature (left) and zonal wind (right) for January (CIRA)

Shepherd (2003 Chem. Rev.)• When the flow is westerly, planetary-scale Rossby
waves can propagate into the stratosphere (Charney &Drazin 1961 JGR), where they break in a hemisphericwide ‘surf zone’ (McIntyre & Palmer 1983 Nature)
PV on 850 K isentropic surface• This behaviour was argued
to be that of a nonlinear
critical layer (see below)
Critical layers occur wherethe wave phase speed
equals the flow speed

McIntyre & Palmer (1987 Nature)• The “surf zone” in the Canadian Middle Atmosphere
Model, a realistic climate simulation model– 30-day particle advection at 1000 K (approx 35 km)• Where the waves break, they exert a torque from theangular momentum transfer

Ngan & Shepherd (1999 JAS)• For Rossby waves, the momentum deposition is always
negative. For barotropic dynamics, it is easy to show thatr∂u∂=−u'v' = v'q' = ∇ • F∂t∂y( )where q is potential vorticity (PV) and F is EP flux
• An analogous relation holds for stratified flow (Dickinson1969 JAS; Andrews & McIntyre 1976 JAS), although thezonal-wind response is then non-local (Eliassen 1951
Astrophys. Norv.)• Breaking Rossby waves mix PV downgradient, hence
the induced torque is negative• N.B. In the stratosphere, PV mixing cannot happen
spontaneously• Wave-induced torques drive a middle atmospherecirculation with a strong seasonal dependence– Mainly from Rossby waves in the stratosphere– Mainly from gravity waves in the mesosphere

CMAM results from Beagley et al. (1997 Atmos.-Ocean)• This is the origin of the stratospheric “Brewer-Dobsoncirculation”, which cools the tropics and warms the poles

Mainly operates
in the winterhemisphere
The circulation isthermally
indirect: a‘refrigerator’

Holton et al. (1995 Rev. Geophys.)• The BDC raises and cools the tropical tropopause,and lowers and warms the extratropical tropopause

Positive forcing(anti-Rossbywaves)
Control case
Negative forcing(Rossby waves)

GCM calculations by Thuburn & Craig (2000 JAS)• The seasonal variation in the BDC leads to aseasonal variation in lower stratospheric temperature• Tropical temperatures are lowest in boreal winter,when the tropical upwelling is the strongest
MSU Channel 4temperature(approx 100hPa)

Yulaeva, Holton & Wallace (1994 JAS)

Compensation
between tropics
and extratropics
suggests theinfluence of theBDC

• The seasonal cycle in tropical tropopause temperaturecauses a seasonal cycle in dehydration, which isimprinted on the water vapour entering the stratosphere:
the “water vapour tape recorder” (Mote et al. 1996 JGR)

Mote et al. (1998 JGR)• Tropical tropopause temperature also controls
stratospheric water vapour on interannual timescales
Figure showsinterannualanomalies in the“tropical taperecorder” asseen in HALOE
measurementsfrom the UARS
satellite

Updated from Randel et al. (2004 JAS)• Radiosonde observations reveal variations in the BDC
associated with El Niño
Regression of DJF
temperature onto
Nino 3.4 index
These stratosphericfeatures must be
dynamically driven

Free & Seidel (2009JGR)• The Brewer-Dobson circulation was originally inferredfrom observations of water vapour and ozone– Dryness of stratosphere implies tropical entry– Ozone distribution implies poleward motion
March2004
OSIRISozone

Shaw & Shepherd (2008 Nature Geosci.)• Transport by the BDC explains the seasonal andinterhemispheric differences in ozone

TOMS total ozone
data (1985-1997)

Figure courtesy ofVitali Fioletov,
Environment
Canada• The seasonal cycle of stratospheric variability implies aseasonal cycle in the Brewer-Dobson circulation– Midlatitude column ozone anomalies build up throughwinter and spring, and decay photochemically during
the quiescent summer (several-month timescale)

TOMS total ozone, from Fioletov & Shepherd (2003 GRL)

Polar temperatures at 30 hPa (approx 25 km)• Forcing of planetary Rossby waves is stronger in theNH than in the SH, so the Arctic winter is warmer andmore variable than the Antarctic (summer is quiet)
1979-1997

1955-2000

Yoden, Taguchi & Naito (2002 JMSJ)• Response of polar temperatures to increasing wave forcing
h0 in a mechanistic model reveals complex dynamics

Yoden, Taguchi & Naito (2002 JMSJ)• Observations suggest that the upward EP flux depends
in part on the state of the stratosphere– This challenges the accepted paradigm
Correlation between k=1 variability
in troposphere and stratosphere

Perlwitz & Harnik (2003 J Clim)• Variations in the upward wave forcing (“winter heat flux”,proportional to vertical EP flux) are associated withvariations in polar downwelling, hence in polar vortex
strength and in polar ozone abundance
There is acontinuoustransition
between thetwohemispheres

Adapted fromWeber et al.
(2003 GRL)• This inter-annual variability in the polar downwelling ismost pronounced in the NH, and leads to decadal
timescale changes in ozone

WMO (2011)• For the Arctic, anomalies in transport and in(temperature-induced) chemical loss act in phaseand contribute equally to the observed ozone
variability (while chlorine loading is high)Tegtmeier et al. (2008 GRL)• In addition to the “deep” branch of the BDC driven byplanetary-wave drag, there is also a “shallow” branch forwhich synoptic-scale wave drag is important

Plumb (2002 JMSJ)• Synoptic-scale
waves arepresumably a major
contributor to theobserved outflow
just above thetropical tropopause,
which occurs yearround
Seen in airborne
lidar measurements
after Mt Pinatubo
eruption
Grant et al.
(1994 JGR)• The importance of synoptic-scale Rossby waves to the
BDC may seem surprising, but the drag from synopticscale waves extends continuously into the subtropicallower stratosphere
Annual meanobserved EP
flux and flux
divergencefrom ERA-40
Tropopause
shown withthick line
Randel, Garcia & Wu
(2008 JAS)

LC1

LC2

The subtropicalsynoptic-scaleRossby wave drag isunderstood to arisefrom the nonlinear
breaking of growing
baroclinic waves
Simmons & Hoskins(1978 JAS)
Edmon, Hoskins &McIntyre (1980 JAS)
Thorncroft, Hoskins& McIntyre (1993QJRMS)• The breaking of synoptic-scale Rossby waves on the flank of
the jet is a fundamental phenomenon, which is responsible
for the maintenance of eddy-driven jets

Vallis (2006)• Just as with stationary planetary waves, the breaking ofsynoptic-scale waves occurs in nonlinear critical layers– The subtropical critical layer in the upper troposphere,
and the midlatitude critical layer in the middletroposphere– Here for northern winter; northern summer is similar

Randel & Held (1991 JAS)• Don’t you see zonal wave 5-6 ‘cat’s eyes’ here at 21 km inthe NH?
Figure courtesyof Dirk
Offermann,
University ofWuppertal

Shepherd (2000JASTP)

Summary• Rossby waves propagate from the troposphere into thestratosphere and provide a negative torque where theydissipate (‘Eliassen-Palm flux convergence’)– The waves generally dissipate by breaking sideways innonlinear critical layers• Negative torques drive poleward flow: the origin of the‘Brewer-Dobson circulation’ important for chemical species• Planetary waves propagate deep into the stratosphere
during the winter season, and drive polar downwelling• Synoptic-scale waves propagate into the subtropical lower
stratosphere year-round, and drive a shallow branch of theBDC– The tropical upwelling undergoes year-to-year
variations

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.
• Edmon, H. J., Hoskins, B. J., McIntyre, M. E., 1980:
Eliassen-Palm cross sections for the troposphere, J. Atmos.
Sci., 37, 2600-2616.
• Fioletov, V. E., Shepherd, T. G., 2003: Seasonal
persistence of midlatitude total ozone anomalies, Geophys.
Res. Lett., 30, 1417, 4pp.
• Free, M., Seidel, D. J., 2009: Observed El Nino Southern
Oscillation temperature signal in the stratosphere, J.
Geophys. Res., 114, D23108.

Reference 2• Grant, B. W., Browell, E. V., Fishman, J., Brackett, V. G.,
Veiga, R. E., Nganga, D., Minga, A., Cros, B., Butler, C. F.,Fenn, M. A., Long, C. S., Stowe, L. L., 1994: Aerosolassociated changes in tropical stratospheric ozone following
the eruption of Mount Pinatubo, Journal of GeophysicalResearch, 99, 8197-8211.
• Haynes, P. H., Marks, C. J., McIntyre, M. E., Shepherd, T.
G., Shine, K. P., 1991: On the Downward Control ofExtratropical Diabatic Circulations by Eddy-Induced Mean
Zonal Forces, J. Atmos. Sci., 48, 651-678.
• Holton, J. R., Hayens, P. H., McIntyre, M. E., Douglass, A.
R., Rood, R, B., Pfister, L.: Stratosphere-troposphereexchange, Rev. Geophys., 1995, 33, 4, 403-439.

Reference 3• Mote, P. W., Dunkerton, T. J., McIntyre, M. E., Ray, E. A.,
Haynes, P. H., Russell, J. M. III., 1998: Vertical velocity,vertical diffusion, and dilution by midlatitude air in thetropical lower stratosphere, J. Geophys. Res., 1998, 103,
D8, 8651-8666.
• Ngan, K., Shepherd, T. G., 1999: A Closer Look at Chaotic
Advection in the Stratosphere. Part I: Geometric Structure,J. Atmos. Sci., 56, 4134-4152.
• Perlwitz, J., Harnik, N., 2003: Observational Evidence of aStratospheric Influence on the Troposphere by Planetary
Wave Reflection, J. Climate, 16, 3011–3026.
• Plumb, R. A., 2002: Stratospheric transport., J. Meteor. Soc.
Japan, 80, 793-809.

Reference 4• Randel, W. J., Held, I. M., 1991: Phase Speed Spectra ofTransient Eddy Fluxes and Critical Layer Absorption, J.
Atmos. Sci., 48, 688–697.
• Randel, W. J., Wu, F., Oltmans, S. J., Rosenlof, K.,
Nedoluha G. E., 2004: Interannual Changes ofStratospheric Water Vapor and Correlations with TropicalTropopause Temperatures, J. Atmos. Sci., 61, 2133–2148.
• Randel, W. J., Garcia, R., Wu, F., 2008: DynamicalBalances and Tropical Stratospheric Upwelling, J. Atmos.
Sci., 65, 3584–3595.
• Shaw, T. A., Shepherd, T. G., 2008: Atmospheric science:
Raising the roof, Nature Geoscience, 1, 12-13.
• Shepherd, T. G., 2000: The middle atmosphere, J. Atmos.
Sol.-Terr. Phys., 62, 1587-1601 .

Reference 5• Simmons, A., Hoskins, B., 1978: The life-cycles of somenonlinear baroclinic waves. J. Atmos. Sci., 35, 414-432.
• Tegtmeier, S., Rex, M., Wohltmann, I., Kru¨ger, K., 2008:
Relative importance of dynamical and chemical
contributions to Arctic wintertime ozone, Geophys. Res.
Lett., 35, L17801.
• Thorncroft, C. D., Hoskins, B. J., McIntyre, M. E., 1993: Twoparadigms of baroclinic-wave life-cycle behaviour, Q. J. R.
Meteorol. Soc., 119, 17–55.
• Thuburn, J., Craig, G. C., 2000: Stratospheric Influence on
Tropopause Height: The Radiative Constraint, J. Atmos.
Sci., 57, 17–28.
• Vallis, G. K., 2006: Atmospheric and Oceanic FluidDynamics, Cambridge University Press, 770pp..

Reference 6• Weber, M., Dhomse, S., Wittrock, F., Richter, A.,
Sinnhuber, B.-M., Burrows, J. P., 2003:, Dynamical controlof NH and SH winter/spring total ozone from GOME
observations in 1995–2002, Geophys. Res. Lett., 30, 11,1583.
• WMO, 2011: Scientific Assessment of Ozone Depletion:
2010, World Meteorological Organization, 516pp.
• Yoden, S., Taguchi, M., Naito, Y., 2002: Numerical studies
on time variations of the troposphere-stratosphere coupledsystem, J. Meteor. Soc. Japan., 80, 811-830.
• Yulaeva, E., Holton, J. R., 1994: On the cause of theannual cycle in tropical lower-stratospheric temperatures, J.
Atmos. Sci., 51, 169-174.