Salby M.L. Fundamentals of Atmospheric Physics

550 17

The Middle Atmosphere

meridionally from one radiative environment to another (e.g., from sunlit

regions, where it experiences SW heating, into polar darkness, where LW

cooling prevails). Irreversible heat transfer can then lead to net cooling of

individual parcels (Sec. 3.6), which is manifested in a drift of air to lower 0.

Figure 17.11a shows the horizontal trajectory of an air parcel inside the

polar-night vortex, superposed on the instantaneous distributions of motion

and potential vorticity Q (Sec. 12.5) in a numerical integration. During its

evolution, the vortex is sporadically displaced out of zonal symmetry and dis-

torted by planetary waves. The air parcel shown then passes between different

latitudes and therefore different radiative-equilibrium temperaturesas it orbits

about the displaced vortex. In its thermodynamic state space (Fig. 17.11b), the

parcel's temperature oscillates between excursions of

TRE.

This prevents the

parcel from adjusting to radiative equilibrium, instead trailing behind the lo-

9 v ~ -,

! /,,

l'" T /

""", 9 f

i ~

TM

' i \

4-.

J

Figure

17.11 (a) Distributions of potential vorticity Q and horizontal motion in a two-

dimensional calculation representative of the polar-night vortex (compare Fig. 14.26). The bold

line shows the trajectory of one of an ensemble of air parcels (dots) initialized inside the vortex.

The folding of contours along the edge of the vortex and regions where the Q distribution has

been homogenized by secondary eddies symbolizes horizontal mixing.

(continues)

c:z,

. ,..,,

9

cm

850

84C]

830

820

810

800

790

780

770

760

750

740

730

720

710

700

O(:;0

580

670

660

,,, ,

i,

r l ~ I

_

(b)

I l L I 1

-6 -4 -2

17.3 Air Motion 551

ps

t

ii / ~~

,"

t :I(

,"

20 /

9 .~z.z,.~ I

/" "~ _

/ _

,, ~

30

#" ~-......___.,_.,,~

~'

~ -

40

_ _~...7-

50 ........

60 ~

__ --~ _

9

9 =:==:.-,------ 70 -'------------'--'~:~" Mechanically Forced

--~

~~- --. Unforced .............. -

90-- v --

, I il"~'--'i'~~"'l J 1 , I J I ~ I ~ I , 1 ~ A t 1

0 2 4

6

8 10 12 14 16 18 20 22 24 26

T- YRz (I<)

Figure

17.11

(Continued)

(b) Evolution of the

parcel whose

trajectory is shown in part (a) in

its thermodynamic

state space

(solid line), represented in terms of the

parcel's departure from

local radiative equilibrium. Irreversible heat transfer introduces a hysteresis into the

parcel's state

with each circuit about the displaced vortex, which produces a steady drift of air to lower 0. In

the same calculation, but without planetary waves to maintain the circulation out of

radiative

equilibrium (dotted line), the

parcel lapses into radiative

equilibrium, which brings to a halt

subsequent cooling and descent inside the vortex. After Fusco and Salby (1994), copyright by the

American Geophysical Union.

cal value of

TRE

by a finite temperature difference. The air parcel is therefore

out of thermodynamic equilibrium with its surroundings (Chapter 3). Accord-

ing to the second law, the parcel then experiences irreversible heat transfer,

which introduces a hysteresis into its thermodynamic state with each circuit

about the vortex. Net cooling during successive circuits causes the parcel to

drift across isentropic surfaces toward lower 0 (refer to Fig. 3.6). Following ul-

timately from work performed by planetary waves, net rejection of heat makes

the parcel and the circulation as a whole behave as a radiative refrigerator.

Irreversible heat transfer leads to thermal dissipation of planetary waves

because it destroys large-scale temperature anomalies. Diabatic behavior in-

552 17

The Middle Atmosphere

troduced when the vortex is driven out of zonal symmetry corresponds to

Newtonian cooling (Sec. 8.6), which acts to restore the circulation to radia-

tive equilibrium. Thermal relaxation operates on a timescale of order a week

(Fig. 8.29)~still much longer than the characteristic timescale of advection.

As air relaxes toward radiative equilibrium, temperature anomalies associated

with the wave field collapse, and with them so does eddy motion. Momentum

carried by planetary waves is then transferred to the zonal-mean flow.

Planetary waves also experience mechanical dissipation when the polar-

night vortex is subjected to quasi-horizontal mixing, which destroys large-scale

motion anomalies. Such behavior is evident in Fig. 17.11a from the folding

of tracer contours along the edge of the vortex and in regions where the dis-

tribution of Q has been homogenized. Those features neighbor the critical

line of stationary planetary waves (see Fig. 14.23), where large eddy displace-

ments overturn the distribution of Q and render the local motion dynamically

unstable (Sec. 16.4). Air is then wound up in secondary eddies that cascade

large-scale tracer structure to small dimensions, where it is eventually ab-

sorbed by diffusion. Secondary eddies generated through instability produce

an irreversible dispersion of air along isentropic surfaces, because advection

operates much faster than diabatic processes. Under amplified conditions, dis-

persive eddy motions can entrain and mix low-latitude air well into the body

of the vortex. Like thermal dissipation, mechanical dissipation of planetary

waves acts to maintain the Arctic polar-night vortex warmer and weaker than

the radiative-equilibrium circulation.

Weaker planetary waves in the Southern Hemisphere introduce smaller

meridional displacements and hence smaller departures of individual parcels

from local radiative equilibrium. The Antarctic polar-night vortex also expe-

riences anomalous radiative cooling at high latitudes through exchange with

the underlying surface. The Antarctic plateau, which is as high as 700 mb, is

much colder than the surrounding maritime region. Radiative exchange be-

tween the cold surface and the lower stratosphere in the 9.6-~m band of

Ozone represents anomalous cooling not experienced by the Arctic vortex. To-

gether, these factors leave the Antarctic polar-night vortex colder and closer

to radiative equilibrium than its counterpart over the Arctic. The foregoing

considerations then imply that the Antarctic vortex should possess a weaker

meridional circulation and reduced transfer of ozone out of its photochemical

source region.

Even though the actual circulation is more complex, it is convenient to

consider motion two-dimensionally in terms of the zonal-mean circulation

- (~, 9, ~). This representation is especially useful in light of the numer-

ous chemical species that must be accounted for in stratospheric photochem-

istry. Within this framework, zonal-mean distributions of motion and chemi-

cal species interact with the wave field. Wave fluxes of momentum, heat, and

chemical mixing ratio enter the equations governing zonal-mean properties

(see, e.g., Andrews

et al.,

1987), analogous to the convergence of eddy momen-

17.4

Sudden Stratospheric

Warmings 553

tum flux appearing in the zonal-mean budget (14.5). Transfers of momentum

accompanying dissipation of planetary waves then force the zonal-mean flow

by exerting an eddy drag. Deceleration of the zonal-mean flow must be at-

tended by a change in zonal-mean thermal structure to maintain thermal wind

balance. Wave dissipation thus drives the circulation out of radiative equilib-

rium, which in turn forces a mean meridional circulation like the one inferred

earlier from Lagrangian considerations.

The zonal-mean circulation in Fig. 17.9 was calculated in this manner. In

the lower stratosphere, it consists of two equator-to-pole Hadley cells that

transport ozone-rich air from the photochemical source region in the tropics

to extratropical regions. Meridional transport and subsequent downwelling

explain the large column abundances observed at high latitudes (Fig. 1.19).

Most active when planetary waves are amplified, that transport also explains

the strong seasonality of total ozone (Fig. 1.18). Maximum values of ~o3

appear during late winter and spring, just following the period of strongest

planetary wave activity.

In the mesosphere, the meridional circulation is transformed into a pole-

to-pole cell, with air passing from the radiatively heated summer hemisphere

to the radiatively cooled winter hemisphere. Despite the distribution of net

heating (Fig. 8.27), the summer mesosphere is actually colder than the win-

ter hemisphere (Fig. 1.7), which is only weakly illuminated. Like the winter

stratosphere, the mesosphere is driven out of radiative equilibrium by me-

chanical disturbances that propagate up from below. Planetary waves play a

role at these altitudes, but gravity waves are thought to be the primary agent

responsible for driving the mesosphere out of radiative equilibrium. This con-

clusion is supported by the fact that, unlike the stratosphere, both hemispheres

of the mesosphere are far from radiative equilibrium. Westward-propagating

gravity waves can propagate through westerlies of the winter stratosphere with-

out encountering a critical level (Sec. 14.3.4), whereas eastward-propagating

gravity waves can do the same in the summer stratosphere. Upon reaching

mesospheric heights, gravity waves excited in the troposphere have amplified

sufficiently to break (Fig. 14.25). Momentum carried by the waves is then

transferred to the zonal-mean flow, which, on being decelerated, alters the

thermal structure to maintain thermal wind balance.

17.4 Sudden Stratospheric Warmings

Occasionally during northern winter, the circulation becomes highly disturbed.

Accompanied by a marked amplification of planetary waves, the disturbed

motion is characterized by a marked deceleration of zonal-mean westerlies or

even a reversal into zonal-mean easterlies. At the same time, temperatures

over the polar cap increase sharply~by as much as 50 K, so the dark winter

pole actually becomes warmer than the illuminated tropics. This dramatic

554

17

The Middle Atmosphere

sequence of events takes place in just a few days and is known as a

sudden

stratospheric warming.

A stratospheric warming is under way on the day shown in Fig. 1.10a.

Zonal-mean wind on the same day (Fig. 17.12b) has reversed across much

of the winter hemisphere at 30 mb and above. Zonal-mean temperature

(Fig. 17.12a) is anomalously warm from 70 mb upward. Polar temperatures

there are some 40 K warmer than climatological values (Fig. 1.7) and exceed

those over the equator, so the meridional temperature gradient is reversed.

These dramatic changes in the zonal-mean circulation result from the absorp-

tion of planetary waves, which have amplified and transmit upward anoma-

lously strong momentum flux.

Even though it is formally defined in terms of zonal-mean properties, the

stratospheric warming is actually a phenomenon that is inherently zonally

asymmetric. Figure 1.10a reveals that zonal-mean deceleration on this day

really follows from a marked displacement of the cyclonic low out of zonal

symmetry and its replacement over the polar cap by an anticyclonic high that

E

W

n"

W

n~

_ f

. 250

-

10

50-

_-.-------2

100

- ~

5oo

----____ ~~

.

_

250

1000 " I

0 10 20 30 40 50 60 60 80

LATITUDE (Degs)

Figure 17.12 Zonal-mean (a) temperature (K).

(continues)

90

17.4

Sudden Stratospheric Warmings

555

E

v

w

oc

w

n-

I \

I X

I A

I

|

i -22.1 i

l

I

X\ . i

..I

25 / / I I I I

/ I I I

r /

/

I // I

I

5 ! ! I I ~, / I 1 I'

I I t" I

i/

I I /I I . ... i i

10 ~ " ~ ,1 1~"

\ I /

\ x / 0

50

100

500 L-- .... \ \ \

1000

0 10

20 30 40 50 60 60 80 90

LATITUDE (Degs)

Figure 17.12

(Continued)

(b) zonal wind (m s -1) on March 4, 1984, during a stratospheric

sudden warming (compare Fig. 1.10a).

has built in from midlatitudes. This asymmetric flow pattern corresponds to

an amplification of planetary wavenumber 1. It permits air to flow freely be-

tween tropical and extratropical regions---on the timescale of a day, rather

than on the much longer timescale of the zonal-mean meridional circulation.

Figure 17.13 shows the distributions of potential vorticity and motion near 10

mb on the same day. The cyclonic vortex has been displaced well off the pole

and has undergone a complex distortion, with high-latitude air (blue) being

drawn equatorward around the anticyclone that has invaded the polar cap.

Large eddy displacements have overturned the potential vorticity distribution

[e.g., near (135~176 to make

aQ/ay

< o. That motion is then dynami-

cally unstable (Sec. 16.2), so the planetary wave field breaks (Mclntyre and

Palmer, 1983).

Secondary eddies that amplify in the region of instability bring about an ir-

reversible rearrangement of air. Midlatitude air (red) drawn poleward spins

up anticyclonically to conserve potential vorticity. It then forms easterly flow

556 17 The Middle Atmosphere

over the polar cap that prevails in the zonal mean (Fig. 17.12). At the same

time, polar air drawn equatorward degenerates into small anomalies of cy-

clonic vorticity that are only suggested in the analyzed distribution of Q.3 The

foregoing behavior resembles an expanded critical layer that engulfs much of

the hemisphere when the wave field amplifies and overturns the Q distribution

(compare Fig. 14.26).

Motions during a stratospheric warming bring about a major rearrange-

ment of air and chemical species. Ozone then flows freely from its site of

chemical production at low latitude to middle and high latitudes. Air advected

poleward moves approximately along isentropic surfaces. In the lower strato-

sphere, where the ozone column is concentrated, isentropic surfaces slope

downward toward the pole, so air descends as it streams poleward. On a longer

timescale, poleward-moving air also experiences radiative cooling, which in-

troduces a net downward displacement across isentropic surfaces. These are

the same mechanisms responsible for generating the Brewer-Dobson circu-

lation, which is temporarily accelerated due to the exaggerated meridional

displacements accompanying a stratospheric warming.

Ozone-rich air advected poleward descends and undergoes compression,

which increases the absolute concentration

/903

and magnifies the column

abundance of ozone. Stratospheric warmings are often accompanied by a

marked increase of total ozone at high latitudes. Figure 17.14 shows the dis-

tributions of 2~o3 and 400 K isentropic motion on February 25, 1984, when

the zonal-mean flow was reversed down to 70 mb. A tongue of enhanced to-

tal ozone (~o3 > 500 DU) coincides with the cross-polar flow, where air from

lower latitudes has descended and experienced compression. In the Eastern

Hemisphere, air that has been displaced equatorward leads to anomalously

low Xo3.

Stratospheric warmings occur primarily in the Northern Hemisphere, where

planetary waves are strong. However, behavior like that described here invari-

ably closes the winter season of both hemispheres. Spring witnesses a weaken-

ing of the equatorward temperature gradient that supports strong zonal flow.

Circumpolar westerlies then collapse in the

final warming

and are eventually

replaced during summer by circumpolar easterlies.

3The

Q distribution must be derived from meteorological analyses, which have limited ability

to resolve such features because they are based largely on temperature observations.

Figure

17.13 Distributions of potential vorticity Q and horizontal motion on the 850 K

isentropic surface (near 10 mb) for March 4, 1984. High-Q polar air (blue), which marks the

polar-night vortex, has been displaced off the pole by a large-amplitude planetary wave and

has undergone pronounced distortion, with secondary eddies appearing along its tail. Low-Q air

from equatorward (red), which is advected into the polar cap, spins up anticyclonically to form a

reversed circulation, with easterly circumpolar flow at high latitudes (compare Fig. 14.26).

17.5 The Quasi-Biennial Oscillation 557

17.5 The Quasi-Biennial Oscillation

The circulation in the tropics is also chiefly zonal. However, it is modified

importantly by interannual variations. Figure 17.15 shows zonal wind averaged

over equatorial stations as a function of time and height. An oscillation of 26 to

28 months prevails over seasonal variations at heights of 15 to 30 km. Known

as the

quasi-biennial oscillation

(QBO), this variation is seen to descend with

time in an alternating series of easterlies and westerlies that attain speeds

of 20 to 30 m s -1. At higher levels, the QBO gives way to the semi-annual

oscillation, which is a harmonic of the seasonal cycle. The QBO is symmetric

about the equator and is confined to latitudes of less than about 15 ~ .

Even though it is nearly periodic, the QBO is not a harmonic of the sea-

sonal cycle. Therefore, it cannot be explained simply in terms of seasonality

that is imparted to the lower stratosphere from other regions. Latent heating

in the troposphere contains no preferred period on timescales of the QBO.

Likewise, diabatic heating in the equatorial stratosphere is unable to explain

the oscillation (Wallace, 1967). This leaves momentum transfer. During the

westerly phase of the QBO, air over the equator moves faster than the earth,

so the specific angular momentum exceeds that found at other latitudes. This

rules out horizontal advection of zonal-mean momentum as an explanation.

The QBO is thought to be driven mechanically by vertically propagating

waves that transfer momentum upward from the troposphere. The particular

waves involved remain a matter of some discussion, but there is no debate

over their origin. Unsteady latent heating inside tropical convection excites a

spectrum of wave activity, much of which propagates vertically into the middle

atmosphere. Upon being absorbed, that wave activity transfers momentum to

the zonal-mean flow, which is thereby accelerated toward the phase speeds of

individual waves.

As illustrated in Fig. 17.16, eastward- and westward-propagating waves have

transmission and absorption characteristics that differ between easterly and

westerly layers of the QBO (e.g., as controlled by their intrinsic frequencies;

Sec. 14.6). These differences allow wave absorption to establish a westerly

critical line, where the zonal flow matches the phase speed and therefore

absorbs westerly waves, flanked aloft by an easterly critical line, where the

zonal flow matches the phase speed and therefore absorbs easterly waves.

Transfers of westerly and easterly momentum at those sites of wave absorption

Figure 17.14 Total

ozone

~O3 and horizontal motion on the 400 K isentropic surface in the

Northern Hemisphere on February 25, 1984, during a stratospheric warming when zonal flow

was disturbed down to 70 mb. A tongue of enhanced Xo3 coincides with cross-polar flow be-

tween longitudes of 150~ and 30~ where air descends along isentropic surfaces and undergoes

compression. Air displaced equatorward in the Eastern Hemisphere ascends isentropically and

undergoes expansion to introduce anomalously low ~o3-

558 17 The Middle Atmosphere

-'o

o o o o o ~

~"

.c,- ,- .i

'~o o o

.c ,,-

N

UJ

o o IR

o o o o .l~o o

{

.tO o o o o o o o

m o

, o

o o o

~o

. j,-

~

o o'--o 0 o o

," Ol

tO kO

r'. 0

to~ ~ ,-

Figure 17.15 Monthly mean zonal wind (m s -1) averaged over equatorial rawinsonde stations.

Updated from Naujokat (1986); courtesy of B. Naujokat (Free U. Berlin).

(continues)

then cause both critical lines to descend (Lindzen and Holton, 1968; Holton

and Lindzen, 1972), as is observed in Fig. 17.15.

The tropical QBO has an extratropical counterpart. During years when

equatorial winds are easterly, the polar-night vortex is warmer and more dis-

turbed than during years when equatorial winds are westerly (Labitzke, 1982;

Holton and Tan, 1982). Owing to the close relationship between ozone and

17.5 The Quasi-Biennial Oscillation

559

~o o o o g

nmO

0 0 0 0 0

*- O4 ~'3 I,-. 0

a= ~--

I~'~'~'i~' ~' ~ ' ~

0 0 C C 8

--..-.~. -~'~ __

.... ~- k~ 0

~--- s

...

...... ~ ..-

,,,,,,,,

._

.

y ~,~,~

I',,-

) '.. :::

x\\~ x'~

...... Ni~; .

,'," ,',' :,,

9 ~ .. ,

--

e.o o ~~ ~,_

,,,

g

,,-, ,,-

C~- 0 0 0 0 0

,,i

i"

mO

e- ,r,.

~ ~ .....

..... ,~~-~,_ ,_

O)

v--

Ot

v--

t,.

,fo

v-

t--

cO

v--

Figure 17.15

(Continued)

disturbances to the circumpolar vortex, similar interannual variability is man-

ifested by total ozone in extratropical regions. For instance, interannual vari-

ations of Antarctic Eo3 (see Fig. 17.23 later in this chapter) are strongly cor-

related with equatorial winds (Garcia and Solomon, 1987). The extratropical

QBO appears to result from a repositioning of the critical line for planetary

waves in relation to the polar-night vortex. During the easterly phase of the

QBO, the critical line advances into the winter hemisphere, where it introduces

large eddy displacements of the vortex (Fig. 17.17a). Conversely, the critical

Salby M.L. Fundamentals of Atmospheric Physics

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