Lecture 3:
The circulation of the stratosphereand mesosphere
(i)
(ii)
(iii)
(iv)
(v)
(vi)

The observed mean state, and the deduced
meridional circulation
Stratospheric Rossby waves
Rossby waves and the stratospheric circulation
Gravity waves and the mesospheric circulation
Variability of the stratospheric circulation:
wintertime vacillations and polar warmings
Variability of the stratospheric circulation: thetropical quasi-biennial oscillation
FDEPS 2010
Alan Plumb, MIT
Nov 2010

(i) The observed mean state, and the deduced
meridional circulationūJANT̄ūJULT̄ūT̄

JANtropopause

ū

JULT̄

ū

JANT̄

Summer subtropicalstratospheric easterlies
polar night jets(polar vortex edge)

tropospheric jets

ū

JULT̄

ū

JAN

cold tropical tropopause

ū

JULT̄

cold winter polar
stratosphereT̄
warm summer stratopause

cold summer mesopause

warm winter mesopausep (hPa)T̄

Radiative-convective equilibrium (no large-scale heat transport)

JanuaryT̄

cpw̄ ∗ ∂θ = 1 J̄ = −ρΠΠ∂z̄κ T̄w→̄ ∗ ∂T + H∂z1 ̄τ rad T − T e = − τ 1 T̄ − T e radTe∂T̄ + κ T̄ ≃ 10 K km−1H∂zT̄cpw̄ ∗ ∂θ = 1 J̄ = −ρΠΠ∂z̄κ T̄w→̄ ∗ ∂T + H∂z

Te1 ̄τ rad T − T e = − τ 1 T̄ − T e rad∂T̄ + κ T̄ ≃ 10 K km−1H∂z

T̄

Te+90K-50K

0K-5K+100K+25K-10K+35Kcpw̄ ∗ ∂θ = 1 J̄ = −ρΠΠ∂z̄κ T̄→w̄ ∗ ∂T + H∂z

1 ̄τ rad T − T e = − τ 1 T̄ − T e rad∂T̄ + κ T̄ ≃ 10 K km−1H∂z

T̄+90K-50K

5 mm s-10K

1 mm s+25K

Te10 mm s-1-5K10 mm+100Ks-1-10K-1
2 mm s+35K-10.3 mm s-1cpw̄ ∗ ∂θ = 1 J̄ = −ρΠΠ∂z̄κ T̄→w
̄ ∗ ∂T + H∂z

1 ̄τ rad T − T e = − τ 1 T̄ − T e rad∂T̄ + κ T̄ ≃ 10 K km−1H∂zT̄∂11 ∂̄ ∗ = 0a cos ϕ ∂ϕ v̄ ∗ cos ϕ  + ρ ∂z ρw

Te1-10 m s-1
5 mm s-110 mm s-1

10 mm s-10.05 m s-1

0.1 m s-1

1 mm s-1

2 mm s-1
0.3 mm s-1

cpw̄ ∗ ∂θ = 1 J̄ = −ρΠΠ∂z̄κ T̄→w
̄ ∗ ∂T + H∂z

1 ̄τ rad T − T e = − τ 1 T̄ − T e rad∂T̄ + κ T̄ ≃ 10 K km−1H∂zResidual circulation diagnosed
from satellite-derived
temperatures and radiationbudget[Rosenlof, J Geophys Res, 1995]

(ii) Stratospheric Rossby waves

Planetary-scale Rossby waves in winter(spring in southern hemisphere)2006 January 10Geopotential height (m)100 hPa30hPa10hPa

Wave breaking in the stratosphereg −1 ∂θ f + ζ∂pconserved in adiabatic flow
Ertel PV850K[McIntyre & Palmer, Nature, 1983]

1992 September 6
10 hPageopotential
height (m)southern hemisphere
middle stratosphere

10 hParadiative heating(K day-1)

tracer advected with analyzed winds
for 10 days on 850K isentropic surface

midlatitude“surf zone”

vortextropics

O3

ClOvortexO3

ClO

{vortex
filaments

vortexO3ClO

1992 January 28
50 hPageopotential
height (m)northern hemispherelower stratosphere

50 hParadiative heating(K day-1)

tracer advected with analyzed winds
for 10 days on 480K isentropic surface

intrusion

450K

vortex air

intrusionvortexfilament

(iii) Rossby waves and the stratosphericcirculation

Driving the residual circulation∂A + ∇ ⋅ F = dissipationX∂t∂ū − 2Ω sinϕv̄ ∗ = 1 ∇ ⋅ F < 0X∂tρ∂
11 ∂̄ ∗ = 0a cos ϕ ∂ϕ v̄ ∗ cos ϕ  + ρ ∂z ρw∞∂1ρw̄ ∗ = − a cos ϕcos ϕ ∫ ρv̄ ∗ dz
∂ϕz

wave drag pumps flow poleward“downward control” [Haynes
et al, J Atmos Sci, 1981]

7060
50

explicit solutions(1/ρ)∇⋅Fz (km)

-0.8

40

5-0.
-0.3

30
-0.0-1-2-3-4-620

χ∗-510− 2Ω sinϕρv̄ ∗ = ∇ ⋅ F∂χρv̄ ∗ = − ∗∂z∞1χ∗ = −∫ ∇ ⋅ F dz
2Ω sin ϕ z

00latitude

30

60

9060

90

7060
50
40

-0.8
-0.5

-0.3

30
-1-3-2-5-6-8-7-10-9-1120-4-0.0-12

 wave drag must
penetrate into tropics toexplain tropical upwellingz (km)-1.0100030latitude1992 September 610 hPa
geopotential
height (m)southern hemisphere
middle stratosphere

10 hParadiative heating(K day-1)

strongest downwelling / radiative
cooling at edge of vortex

1-10 m s-1
5 mm s-1

10 mm s-1

10 mm s-1
0.05 m s-1

0.1 m s-1

1 mm s-1

2 mm s-1
0.3 mm s-1

Rossby wave drag can accountfor circulation in stratosphere,
but not mesosphereneed gravity wave drag inmesosphere(iv) Gravity waves and the mesosphericcirculation

Internal gravity wavesz(km)6040200-1000100200

2 −2u′w′ ∼ 1 m s
1 ∇ ⋅ F ≃ 1 ∂ ρu ′ w ′→ ρρ ∂z−2
∼ 1 × 10−4ms−1∼ 10 ms day→ v̄ ∗ ∼ 1 ms

−1−1

[Vincent & Reid, J Atmos Sci, 1983]solstice circulation
Eastward gravity waves produce
eastward force – pump flow
equatorward

Westward gravity waves produce drag –pump flow poleward

(v) Variability of the stratospheric circulation: wintertime
vacillations and polar warmings

warm

Variability of North Poletemperatures
Monthly mean T, 30 hPa

High degree of variability inwinter (in spring in S Hem)
i.e., during seasons ofstrong wave activity

coldpolar Twave 1wave2[Labitzke, J Geophys Res, 1981]

Major warming Jan 200910 hPa

WARM

COOL

Polar warming as a response towave amplification[Matsuno, J. Atmos. Sci., 1971]

stage 1 (conservative):∇ ⋅ F = − ∂A∂t→ forms critical layer
stage 2 (no further growth, dissipative)∇ ⋅ F = dissipation

Why do waves amplify?

COOLWARM

Vacillations in simple models(Holton & Mass, J. Atmos. Sci. , 1976)
amplitude
thresholdTruncated quasi-linear modelon midlatitude β − planeū = Uzsin ly→ linear calculation for wave
→ ∇ ⋅ F → ∂ū/∂t|φ ′ |ūVacillations in GCMs [Scott& Polvani, Geophys Res
Lett, 2004]
steady thermal forcing of
Rossby wave
variability supressed intropospherevacillations stratospheric in
originū60o N, z, tVacillations in GCMs [Scott& Polvani, Geophys Res
Lett, 2004]
steady thermal forcing of
Rossby wave
variability supressed intropospherevacillations stratospheric inorigin
ū60o N, z, t∇⋅FF z 200hPa)

(vi) Variability of the stratospheric circulation: thetropical quasi-biennial oscillation

Equatorial winds(monthly mean anomalies)

Irregular period around 27 months
Downward migration of westerlies and easterlies
Confined (mostly) within about 10 degrees of equator

Can be produced by 2 upward propagating waves ofopposite zonal phase speed:

“QBO” in the lab

subcritical forcing

“QBO” in the lab

supercritical forcing

References
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Anderson, J. G., Brune W. H., Proffitt1989: Ozone Destruction byChlorine Radicals Within the Antarctic Vortex: The Spatial andTemporal Evolution of ClO-O3 Anticorrelation Based on in Situ ER-2
Data, J. Geophys. Res., 94, 11465-11479
K. Labitzke, 1981: Stratospheric-Mesospheric MidwinterDisturbances: A Summary of Observed Characteristics, J. Geophys.
Res, 86, 9665-9678
Mahlman, J. D., Umscheid, L. J., 1984: Dynamics of the middle
atmosphere: Successes and problems of the GFDL "SKYHI" generalcirculation model, Terra Scientific Publishing Company, 501-525 pp.
McIntyre, M. E., Palmer, T.N., 1983: Breaking planetary waves int thestratosphere, Nature, 305, 593-600
Naujokat, B., 1981: Long-Term Variations in the Stratosphere of theNorthern Hemisphere During the Last Two Sunspot Cycles, J.
Geophys. Res., 86, 9811-9816

References
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●Plumb, R. A., 2002: Stratospheric Transport, J. Met. Soc. Japan, 80,793-809
Plumb, R. A., 2007: Tracer interrelationships in the stratosphere, Rev.
Geophys., Vol. 45, RG4005, 1-33
Rosenlof, 1995: Seasonal cycle of the residual mean meridional
circulation in the stratosphere, J. Geophys. Res., 100, 5173-5191
Waugh, D. W., Plumb, R. A., Atkinson, R. J., Schoeberl, M. R., Lait, L.
R., Newman, P. A., Loewenstein, M., Toohey, D. W., Avallone, L. M.,
Webster, C. R., May, R. D., 1994: Transport out of the lower
stratospheric Arctic vortex by Rossby wave breaking, J. Geophys.
Res., 99, 1089-1105
NCEP,
http://www.cpc.noaa.gov/
Atmosphere and Ocean in a Laboratory,
http://www.gfd-dennou.org/library/gfd_exp/index.htm