ATMOSPHERE–OCEAN INTERACTIONS :: LECTURE NOTES

7. The Atmospheric General Circulation

J. S. Wright

jswright@tsinghua.edu.cn

7.1 OVERVIEW

This chapter provides a statistical description of the atmospheric general circulation, includingits mean state and large-scale variability. Evidence for the poleward energy and momentumtransports by the atmosphere is laid out, and the mechanisms behind these transports areexplored. The mean meridional and eddy components of the atmospheric circulation aredescribed, and their relative influences on energy and momentum transport quantified usingreanalysis data. The chapter closes with a synthesis summary of major sources and sinks ofenergy and angular momentum and their roles in driving the atmospheric general circulation.The material in this chapter is by necessity incomplete. We will return to some aspects of theatmospheric general circulation (such as the tropical Walker circulation and the monsoons) inlater chapters, but there are many aspects of the atmospheric general circulation that remainbeyond the scope of this course. A number of useful resources are available for readers seekingadditional details and/or alternative presentations of this material (e.g., Gill, 1982; Holton,1992; Peixoto and Oort, 1992; Hartmann, 1994; Vallis, 2006; Marshall and Plumb, 2008).

7.2 MOTIVATION

The atmospheric general circulation ultimately owes its existence to inhomogeneous heating,which creates temperature gradients. To leading order these gradients are determined bylatitudinal variations in incoming solar radiation. Variations in surface albedo, land–oceandistributions, soil water content, and atmospheric absorption also play important roles. Aswe discussed in Chapter 1 (Figure 1.14), imbalances between net incoming solar radiationand net outgoing longwave radiation at the top of the atmosphere imply the existence of acirculation in the atmosphere and ocean, which has the net effect of fluxing energy from thetropics toward the poles.

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Northward atmospheric energy transportNorthward ocean energy transportTotal northward energy transport

Figure 7.1: Implied energy transports in the atmosphere–ocean system based on the Japanese55-year Reanalysis for 1958–2015 (upper panel) and Climate Forecast System Re-analysis for 1979–2009 (lower panel).

Energy transport in the atmosphere–ocean system can be estimated using the balance

RTOA =∇·~FA +∇·~FO + ∂EAO

∂t, (7.1)

where RTOA is the net radiation balance at the top of the atmosphere (i.e., energy in minusenergy out), ∇ ·~FA is the divergence of the horizontal energy transport in the atmosphere,∇·~FO is the divergence of the horizontal energy transport in the ocean, and ∂EAO

∂t is the changein energy storage in the atmosphere–ocean system. The divergences of horizontal energytransport can be estimated as

∇·~FA = (RTOA −Rsfc)+LH+SH (7.2)

∇·~FO = Rsfc −LH−SH (7.3)

with Rsfc the net (downward) radiation flux at the surface, LH the surface latent heat flux andSH the surface sensible heat flux. If we average over period longer than a year, we can usuallyneglect changes in energy storage. In this case, the total northward energy transport acrossthe latitude ϑ can be calculated as

E (ϑ) =−∫ ϑ

π2

∫ 2π

0RTOAa2 cosϑdλdϑ. (7.4)

Given a gridded data set of vertical energy fluxes, this integral can be approximated as thediscrete sum

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E (ϑ) =−π2∑

j=ϑ

2π∑i=0

Ai j ·RTOA(λi ,ϑ j ), (7.5)

where Ai j is the area of the corresponding grid cell in square meters. The atmospheric andoceanic components of this transport can be similarly estimated by integrating ∇·~FA or ∇·~FO

in place of RTOA.Figure 7.1 shows estimates of these energy transports for two different reanalysis systems,

the Japanese 55-year Reanalysis (JRA-55) and the Climate Forecast System Reanalysis (CFSR).Reanalyses are best estimates of past evolution of the climate system, in which forecastmodel outputs are intelligently blended with relevant observations (taking into account theuncertainties in both) to reconstruct the climate state at specified times. Reanalysis outputsare fundamentally dependent upon their underlying models, and should not be considered‘observations’. The estimates of energy transport shown in Figure 7.1 illustrate some of thesubstantial uncertainties associated with renalysis representations of past climate. JRA-55indicates net energy transport from the southern hemisphere into the northern hemisphere,while CFSR indicates net energy transport from the northern hemisphere into the southernhemisphere. These differences are primarily due to discrepancies in the ocean component:CFSR implies southward zonal mean energy transport in the Southern Hemisphere oceans,while JRA-55 indicates a consistent northward zonal mean energy transport throughout theglobal oceans. These differences may be contributed by several factors, including differencesin the underlying models and the assimilated data. Of particular note, the JRA-55 reanalysisuses observed sea surface temperatures as a prescribed lower boundary condition, while theCFSR reanalysis is based on a coupled atmosphere–ocean reanalysis system. The carefulreader will also note that the JRA-55 data shown in Figure 7.1 covers 1958–2015 while the CFSRdata covers 1979–2009; however, the differences are qualitatively unchanged if the JRA-55climatological mean for 1979–2009 is used instead (not shown).

Although these differences between the JRA-55 and CFSR estimates of poleward energytransport are interesting in their own right, our focus for the remainder of this chapter is onthe atmospheric component of the transport, which is much more consistent between thetwo estimates. Both systems indicate that atmospheric energy transport is southward acrossthe equator, and that zonal mean poleward energy transport in both hemispheres peaks inthe mid-latitude atmosphere near 40∼45. This chapter will explore the mechanisms behindthis distribution of energy transport. Examination of the general circulation of the ocean isdeferred to Chapter 8.

7.3 DESCRIBING THE MEAN STATE

In this chapter, we focus primarily on climatological zonal mean quantities and deviationsfrom them. The climatological mean is a time mean, designated here by an overbar (x) andcalculated as

x = 1

τ

∫ t1

t0

xd t , (7.6)

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pole

W

E

Loss of angular momentum

Gain of angular momentum

Implied momentum transport

Implied energy transport

Energy loss

Energy gain

Figure 7.2: Common paradigms for understanding the effects of the general circulation, whichacts to transport energy and angular momentum poleward from the tropics. Theseparadigms are rooted in the energy budget at the top of the atmosphere (left) andthe angular momentum budget at the surface (right).

where the time interval τ= t1−t0 is the difference between the final and initial times consideredin the average. When calculating or interpreting climatological means it is important toconsider the time period over which the climatology is defined (e.g., 1958–2015 for the upperpanel of Figure 7.1 and 1979–2009 for the lower panel). There is considerable internally-generated variability in the atmosphere and ocean on time scales up to a decade or two (andsometimes even longer). It is therefore advisable to consider a time period τ of at least 20 andoften 30 years when constructing climatological means. On the other hand, in the presence ofexternally-forced climate change (such as anthropogenic global warming), it can sometimesbe useful to allow the climatology to evolve in time. The most useful reference climatologytherefore depends on the problem for which it is intended to serve as a reference. The zonalmean is a spatial average over all longitudes, and is calculated as

[x] = 1

2π

∫ 2π

0xdλ, (7.7)

where λ is longitude in radians. The climatological zonal mean is then the combination ofthese two: the average of a quantity over a time period t0 ≤ τ ≤ t1 and over all longitudes0 ≤λ≤ 2π.

7.4 TRANSPORT OF ANGULAR MOMENTUM

Figure 7.2 illustrates two common paradigms for understanding the effects of the generalcirculation. The first is based on the discussion in Section 7.2 above; namely, that the energybudget at the top of the atmosphere implies that the general circulation of the atmosphereand ocean act to transport energy poleward from the tropics. The second is based on theangular momentum budget at the surface, which indicates that the general circulation of the

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Zonal mean angular velocity (uearth + u)

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Angular velocity [m s−1]

Figure 7.3: Zonal mean zonal wind (left) and zonal mean angular velocity (uearth +u; right).Data from the Japanese 55-year Reanalysis.

atmosphere acts to transport angular momentum from the tropics to the poles. The use of thesurface budget rather than the top-of-atmosphere budget in constructing the latter paradigmexplicitly indicates that this angular momentum transport takes place in the atmosphericcomponent of the general circulation (rather than in the coupled atmosphere–ocean system).

Angular momentum per unit mass in the atmosphere consists of two components, a ro-tational component due to the rotation of the Earth around its axis (MΩ = ueartha cosϑ)and a relative component due to atmospheric motion relative to the surface of the Earth(Mr = ua cosϑ):

M = MΩ+Mr =Ωa2 cos2ϑ+ua cosϑ= (uearth +u) a cosϑ. (7.8)

The rotational component of angular velocity uearth =Ωr cosϑ is largest at the equator andsmallest at the poles. Because a À z (particularly in the troposphere), uearth is often ap-proximated as Ωa cosϑ and assumed to be invariant with height. The component due toatmospheric motion u is commonly referred to as the zonal wind.

Figure 7.3 shows distributions of the climatological zonal mean zonal wind ([u

]) and total

atmospheric angular velocity ([uearth +u

]) based on JRA-55. Climatological zonal mean zonal

winds are easterly (westward) in the tropics, particularly near the surface, and westerly (east-ward) in the extratropics. Several important features of the zonal mean zonal wind field areevident, including the trade winds (the region of easterly winds in the tropics and subtropicallower troposphere), the upper tropospheric subtropical jet (the local maxima in westerly windsin the upper troposphere near 30 in each hemisphere), and the mid-latitude storm tracks (thecolumn of westerly winds that extends vertically throughout the troposphere near 40–50 ineach hemisphere).

Easterly and westerly winds are defined relative to a fixed surface, so that easterly zonal windsindicate mean angular momentum smaller than the local component due to Earth’s rotation,while westerly winds indicate mean angular momentum larger than the local componentdue to Earth’s rotation. Accordingly, the effects of friction act to add angular momentum to

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the atmosphere in the tropics (where near-surface winds are easterly), and remove angularmomentum from the atmosphere in the extratropics (where near-surface winds are westerly).This can be understood by noting that the climatological zonal mean angular velocity in theatmosphere is everywhere westerly, in the sense that the Earth’s rotation around its axis is‘westerly’. Friction acting on easterly winds thereby makes the winds ‘more westerly’ and addsangular momentum to the atmosphere. By contrast, friction acting on westerly winds makesthe winds ‘less westerly’ and removes angular momentum from the atmosphere.

The right panel of Figure 7.3 indicates that angular momentum added to the tropical atmo-sphere near the surface is transported poleward primarily in the upper troposphere (note thepoleward distortion of the contours at upper levels). We will examine the mechanisms behindthis transport in the following sections.

Changes in the relative angular momentum per unit mass (Mr = ua cosϑ) can be estimatedby rearranging the zonal momentum equation:

d Mr

d t=− 1

ρ

∂p

∂λ+Fλa cosϑ+ f va cosϑ− f ′w a cosϑ, (7.9)

where f = 2Ωsinϑ and f ′ = 2Ωcosϑ. The first term represents the pressure gradient force inthe zonal direction, the second term represents the effects of friction in the zonal direction,and the final two terms are associated with the Coriolis force. The last term is often neglectedunder the assumption that w ¿ v .

Total angular momentum in the atmosphere can be calculated by integrating Equation 7.8over the entire atmosphere:

⟨M⟩ = a2

g

∫ ps

0

∫ π2

− π2

∫ 2π

0M cosϑdλdϑd p, (7.10)

where a is the radius of the Earth, g is the gravitational constant, λ is longitude in radians,ϑ is latitude in radians, p is pressure, and ps is surface pressure. To the extent that changesin angular momentum storage in the oceans can be neglected (a good approximation, aspure zonal flow in the oceans is restricted to the Antarctic Circumpolar Current), changesin the total angular momentum of the atmosphere are directly related to changes in therotation rate of the solid Earth, and hence to the length of each day. The mean length of dayin January is approximately 8×10−4 s longer than the mean length of day in July, indicating anet redistribution of angular momentum from the solid Earth to the atmosphere in Januaryrelative to July.

Total angular momentum in the atmosphere, oceans, and solid Earth is effectively conserved(neglecting tidal effects due to gravitational interactions with the moon), requiring an equator-ward return transport of angular momentum in the oceans. We will discuss the form of thisreturn transport further in Chapter 8.

7.5 THE MEAN MERIDIONAL CIRCULATION

Although the zonal mean meridional and vertical components of the wind are much smallerthan the zonal mean zonal component of the wind, they are critical for the poleward energyand momentum transports summarized in Figure 7.2. The largest mean meridional winds

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Meridional mass streamfunction

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

Vertical wind [×10−2 Pa s−1]

Figure 7.4: Zonal mean mass streamfunctionΨM (contours; interval 1010 kg s−1) and verticalpressure velocity ω (shading). Data from the Japanese 55-year Reanalysis.

([v]) are about 1 m s−1, a factor 10 smaller than the largest mean zonal winds (

[u

]) and a factor

100 larger than the largest mean vertical winds ([w

]). Climatological mean deviations from

purely zonal flow can be described by the meridional mass streamfunction, which is definedas the integrated north–south transport above a given pressure p:

ΨM = 2πa cosϑ

g

∫ p

0[v]d p. (7.11)

The mass streamfunction has units of kg s−1, and the flow of mass between any two streamlinesis equal to the difference between the streamlines. It is self-evident from the Equation 7.11that the zonal mean meridional flow can be retrieved from the vertical gradient of the massstreamfunction:

[v] = g

2πa cosϑ

∂ΨM

∂p. (7.12)

By conservation of mass, the zonal mean vertical pressure velocity can also be retrieved as thezonal gradient of the mass streamfunction:

[ω] =− g

2πa cosϑ

∂ΨM

∂ϑ. (7.13)

In fluid dynamics, the definition of the streamfunction relies on the flow being non-divergent.This requirement is satisfied for the global atmosphere in steady state, but is not necessarilysatisfied for short time periods or sub-regions of the atmosphere.

Figure 7.4 shows the climatological zonal mean meridional mass streamfunction and verticalvelocity based on JRA-55. Several key features of the mean meridional circulation are evident.

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Figure 7.5: Northward fluxes of zonal momentum (upper panel) and temperature relative toglobal mean temperature at each level (lower panel) by the climatological zonalmean meridional circulation. Data from the Japanese 55-year Reanalysis.

The largest of these is the overturning circulation associated with the tropical Hadley cell, withascending motion (ω< 0) near the equator and descending motion (ω> 0) in the subtropicsof both hemispheres. The Hadley cell is a thermodynamically direct overturning circulation,in the sense that it transports energy from a warmer area to a colder area. The Hadley cell isbracketed in both hemispheres by the mid-latitude Ferrell cells. Overturning in each Ferrellcell is opposite to that in the Hadley cell in the same hemisphere, with mean upward motionover the high mid-latitudes and mean downward motion over the low mid-latitudes. TheFerrell cells are therefore thermodynamically indirect, with energy transport from a colderarea to a warmer area. This seemingly counterintuitive transport is a consequence of strongpoleward energy transport by eddies (deviations from the zonal mean) in this region. Eddiesare discussed in Section 7.7. The Ferrell cells are much weaker than the Hadley cells. We willsee later in this chapter that the mean meridional circulation is a minor component of the totalenergy transport in mid-latitudes, and in fact that net energy transport by the mean meridionalcirculation is toward the equator rather than toward the poles. On the poleward flanks of theFerrel cells we find even weaker thermodynamically direct overturning circulations calledpolar cells. The polar cell in the northern hemisphere is only visible in Figure 7.4 via thedistribution of vertical wind (ascending motion near 60N and descending motion over higherlatitudes, as the mass flow in the climatological mean mass streamfunction is less than theminimum contour level.

Figure 7.5 shows northward fluxes of zonal momentum and heat by the climatologicalzonal mean meridional circulation. The lower tropospheric source of angular momentum is

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evident, as the mean meridional circulation fluxes angular momentum into the intertropicalconvergence zone. This momentum is then transported upward in the ascending branch ofthe Hadley cell and advected poleward in the upper troposphere. Both the Hadley cell andthe Ferrell cells flux momentum into the subtropical jets (southward advection of westwardmomentum is negative). The temperature fluxes indicate that the mean meridional circulationacts to transport warm air primarily equatorward in the lower troposphere, with a muchweaker return flow in the upper troposphere. Here we have defined heat transport based

on the temperature anomaly relative to the global mean at each level ([v][

T −⟨T ⟩]

) rather

than the absolute temperature, as this approach better highlights the net cooling or warmingimpacts of temperature advection by the mean meridional circulation. The transport of heatby the mean meridional circulation shown in Figure 7.5 appears to contradict the polewardenergy transport shown in Figure 7.1, indicating that the poleward energy transport must beaccomplished either by (1) transport of energy in a different form or (2) transport of energyin elements of the atmospheric circulation that are not represented in this time mean zonalmean framework. The answer, as it turns out: a little of both.

7.6 THE ATMOSPHERIC ENERGY CYCLE

An understanding of the atmospheric energy budget requires a return to the concept of diabaticheating, discussed previously in Chapter 4. Changes in the energy content of a column ofatmosphere can be represented by the conceptual equation

∂Ea

∂t= Rnet +SH+LP+TR, (7.14)

where Rnet is the net absorption of longwave and shortwave radiation by the atmosphere (totalabsorption minus total emission), SH is sensible heating of the atmosphere via contact with thesurface (communicated upward via turbulence, as discussed in Chapter 6), LP is the net latentheating of the atmosphere by conversion of water vapor into precipitation (condensationminus re-evaporation), and TR is convergence or divergence of energy into the atmosphericcolumn. With the exception of TR, all of the terms on the right-hand side of Equation 7.14 arediabatic. Note that LP is typically not equal to the latent heat flux at the surface (LH, which isdependent on the local surface evaporation rate), as the water vapor that condenses to formprecipitation within the column may have evaporated elsewhere. This is important to keepin mind when comparing this energy budget to the inferred transport shown in Figure 7.1,which is based on the surface latent heat flux and therefore implicitly includes water vaporredistribution in its estimate of northward energy transport.

Figure 7.6 shows the climatological zonal mean atmospheric energy balance under steadystate conditions (i.e., assuming that ∂Ea

∂t = 0). Outside of the polar regions, both Rnet and SH areapproximately invariant with latitude, although SH tends to be slightly larger in regions witha greater zonal mean ratio of land to ocean. Variations of energy transport with latitude aretherefore dominated by variations in LP. Steady state energy transport is divergent (negative)only in the deep tropics, where energy gains due to LP and SH outweigh energy losses dueto Rnet, and convergent (positive) everywhere else. This distribution again implies energytransport from the tropics poleward to middle and high latitudes.

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LP SH Radiation Transport

Figure 7.6: Zonal mean atmospheric energy balance. Data from the Japanese 55-year Reanaly-sis.

Further insight can be gained by looking at the vertical distribution of energy and its trans-port by the mean meridional circulation. Figure 7.7 shows the vertical distribution of moiststatic energy (MSE) and its components at the equator, as well as the northward flux of MSEby the mean meridional circulation within the tropics and subtropics (30S–30N). MSE isdefined as the sum of potential energy (PE = g z), sensible heat (SH = cv T ) and latent energy(LE = Lv q):

MSE = g z + cv T +Lv q. (7.15)

Potential energy represents the gravitational potential of air, and increases monotonically withheight. Under hydrostatic balance, this distribution of gravitational potential is balanced bythe vertical pressure gradient. Sensible heat is thermal energy of air, and decreases slightlywith height. Integrating through the entire atmosphere, we have:

PE =∫ p0

0g zdp =

∫ ∞

0

(− 1

ρ

d p

d z

)pdz =

∫ p0

0

p

ρdp

SH =∫ p0

0cv T dp =

∫ p0

0cv

p

ρRddp = cv

Rd

∫ p0

0

p

ρdp,

where we have assumed hydrostatic balance (g =− 1ρ

d pd z ) and made the approximation that

sea level is a constant pressure surface (i.e., that∫ p0

0 zdp ≈ ∫ ∞0 pdz). These assumptions are

satisfied to leading order for the Earth’s atmosphere, constraining the ratio of potential energyto sensible heat to be roughly Rd

cv∼ 0.4 — in effect, a large fraction of the thermal energy is tied

up in holding the atmosphere up against the effects of gravity. The qualitative relationship

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Vertical Energy Distribution

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Figure 7.7: Vertical profiles of moist static energy and its components along the equator (centerpanel), and transport of moist static energy by the mean meridional circulationin the tropics and subtropics of the Southern Hemisphere (left) and NorthernHemisphere (right). Data from the Japanese 55-year Reanalysis.

between potential energy and sensible heat can be further illustrated by the expression forhydrostatic pressure at a given altitude (Equation 2.5), which shows that pressure is inverselyrelated to the scale height H = Rd T

g . All other things being equal, a colder atmosphere ismore concentrated near the surface than a warmer atmosphere, and therefore has a smallerpotential energy.

Figure 7.8 shows the vertically integrated northward transport of MSE and its componentterms (PE, SH, LE) by the mean meridional circulation. The mean transport of sensibleheat is equatorward in the tropics, as indicated by Figure 7.5. The mean transport of latentenergy is also equatorward; however, the net transport of MSE in the tropics and subtropicsis poleward, consistent with the sign of the inferred energy transport in Figure 7.1. Thisis due to large poleward transports of potential energy, which more than compensate theequatorward fluxes of sensible heat and latent energy. Referring back to Figure 7.7, north–south fluxes of latent energy are largest near the surface, where water vapor is large. Themean meridional circulation in this part of the tropical atmosphere is equatorward, into theintertropical convergence zone. Fluxes of sensible heat are also largest near the surface, inthe lower tropospheric equatorward branch of the Hadley cell, but are also relatively largealoft, in the upper tropospheric poleward branch. Thus, there is substantial compensationbetween the lower tropospheric and upper tropospheric fluxes of sensible heat. Fluxes ofpotential energy are effectively zero near the surface, but are of a similar magnitude to fluxesof sensible heat in the upper troposphere. Essentially, the poleward transport of potentialenergy and sensible heat in the upper troposphere overwhelms the equatorward transportof latent energy and sensible heat in the lower troposphere, even though the equatorwardcomponent of sensible heat transport is slightly larger than the poleward component.

A clearer picture of this energy cycle emerges from the zonal mean distribution of diabatic

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Inferred total energy transportInferred atmospheric energy transportPotential energyLatent energySensible heatMoist static energy

Figure 7.8: Vertically-integrated northward transport of moist static energy and its components(see text) by the mean meridional circulation. Data from the Japanese 55-yearReanalysis.

heating (Figure 7.9; see also Figure 4.7). Horizontal gradients in surface temperature andsurface pressure cause convergence in the deep tropics, driving the lower tropospheric equa-torward branch of the overturning cell. Evaporation and sensible heating in the surface layerduring this equatorward flow (the latter is evident as diabatic heating in the lower tropospherein Figure 7.9) ultimately flux large amounts of warm, moist air into the intertropical conver-gence zone. Warm, moist air is light relative to its environment (Chapter 4). This convergenceof warm, moist air therefore feeds convective instability within the convergence zone, driv-ing time mean upward motion. Upward motion results in adiabatic cooling, which causescondensation and latent heating. Latent heating drives further upward motion, and rein-forces the meridional density gradients (virtual potential temperature contours in Figure 7.9;see also Equation 4.18) that drive convergence toward the tropics in the lower troposphereand divergence from the tropics in the upper troposphere. In effect, deep convection in theintertropical convergence zone takes latent energy and sensible heat from the lower tropo-sphere and converts them to potential energy via upward motion. This potential energy isthen transported poleward in the upper troposphere and removed slowly by radiative cooling.Upon returning the surface, relatively cool, dry air re-enters the equatorward branch of theoverturning circulation, where it again gains heat and moisture as it flows toward the tropics.This picture of the atmospheric circulation, with heating near the surface and in the tropicsand cooling aloft and near the poles, is sometimes referred to as the ‘atmospheric heat engine’.

Although this heat engine perspective helps to reconcile the expectation of poleward netenergy transport (Figure 7.1) with the observation of equatorward heat transport in the tropics(Figure 7.5), Figure 7.8 shows that poleward energy transport of MSE by the mean meridional

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Diabatic heating rate [K day−1]

Figure 7.9: Climatological zonal mean diabatic heating (shading) and virtual potential temper-ature (contours). Data from the Japanese 55-year Reanalysis.

circulation overestimates inferred atmospheric energy transport in the tropics. Moreover,poleward transport of MSE by the mean meridional circulation substantially underestimatesatmospheric energy transport in the mid-latitudes (and even has the wrong sign in the South-ern Hemisphere mid-latitudes). To complete our description of the atmospheric circulation,we must also consider the role of eddies.

7.7 THE ROLE OF EDDIES

Eddies encompass all motions that deviate from the climatological zonal mean, and canbe conveniently classified into two main types. Transient eddies are temporary deviationsfrom the time mean (x ′ = x −x). Transient eddies include weather fluctuations, and may also(depending on the definition of the time mean) include seasonal phenomena like monsoonsand interannual phenomena like the atmospheric response to the El Niño–Southern Oscilla-tion. Stationary eddies are time-mean deviations from the zonal mean (x∗ = x − [

x]). Major

stationary eddies are associated with topographic effects (such as the Tibetan Plateau) andzonal sea surface temperature gradients (such as those associated with the Gulf Stream orKuroshio). The total time mean meridional flux of a quantity x can then be calculated as[

v x]= [

v][

x]+ [

v∗x∗]+[v ′x ′

](7.16)

where the first term represents the flux by the mean meridional circulation, the second termrepresents the flux by stationary eddies, and the final term represents fluxes by transienteddies. The second and third terms are often collected together as the total eddy flux. Notethat Equation 7.16 omits cross-terms. This omission is appropriate assuming that the time

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e [h

Pa]

Northward momentum flux by eddies

30

20

10

0

10

20

30

Zona

l mom

entu

m fl

ux [m

2 s−

1 ]

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

700

800

900

1000

Pre

ssur

e [h

Pa]

Northward heat flux by eddies

15

10

5

0

5

10

15

Hea

t flu

x [K

m s−

1 ]

Figure 7.10: Climatological zonal mean northward fluxes of zonal momentum (upper panel)and heat (lower panel) by eddies. Data from the Climate Forecast System Reanaly-sis.

mean transport and time mean terms are calculated over the same time period (see alsodiscussion of Reynolds averaging in Section 6.3.3), but is invalid for examining variability inthe transport over shorter time periods.

Figure 7.10 shows the time mean northward transports of momentum and heat by ed-dies. Both transient and stationary eddies are included. Eddies act to flux momentum intothe mid-latitude storm tracks and flux heat from the subtropics toward the poles. The rea-sons for these fluxes are illustrated for the Northern Hemisphere in Figure 7.11. Polewardflow in mid-latitudes experiences a Coriolis acceleration, so that the streamlines are tiltedsouthwest–northeast. Equatorward flow likewise experiences a Coriolis acceleration, so thatthe streamlines are very nearly north–south. The zonal wind anomaly in the northward branchof the flow is positive (eastward) relative to the background flow, while the zonal wind anomalyin the southward branch of the flow is negative (westward). This configuration results in anet northward transport of zonal momentum. Eddy heat transport depends on the differ-ence in temperature between the northward and southward branches of the flow. Owingto the procedures by which mid-latitude eddies form, temperature waves associated withmid-latitude eddies tend to be displaced westward relative to the accompanying pressurewaves. Air flowing toward the north is therefore warm relative to air flowing south, resulting ina net northward heat transport. This westward displacement of the temperature waves relativeto the pressure waves is largest near the surface, so that eddy heat transport maximizes in thelower troposphere. A full description of mid-latitude eddy formation and the mechanismsbehind the relative displacement of the temperature and pressure waves is beyond the scope

14

north

WARM

COLD

WARM

streamline

isotherm

H

L

Figure 7.11: Schematic illustration showing how mid-latitude eddies in the Northern Hemi-sphere provide northward fluxes of angular momentum, heat, and moisture.

of this chapter.Figure 7.12 shows time mean transports of zonal momentum, heat, and moisture by station-

ary eddies. Comparison with Figure 7.10 indicates that the bulk of the north–south transportof momentum and heat by eddies is accomplished by transient eddies, particularly in themid-latitudes. Stationary eddy fluxes in the mid-latitudes are of the same sign as total eddyfluxes, indicating that stationary eddies typically amplify the transport of momentum and heatby transient eddies. In the mid-latitudes, the magnitude of heat transport by stationary eddiesonly approaches that by transient eddies during Northern Hemisphere winter (Section 7.9). Anotable exception to the dominance of transient eddies in the total eddy flux occurs in thetropics, where stationary eddies act to flux heat and moisture out of the tropics and into thesubtropics (opposing the mean meridional circulation). These stationary eddy transportsoccur in the low-level anticyclonic circulations associated with the subtropical highs (Fig-ure 7.13), which are located over the subtropical oceans in the North and South Atlantic, Northand South Pacific, and South Indian oceans. Strong evaporation on the eastward and equa-torward flanks of these circulations feeds precipitation on the westward and poleward flanks.In addition to the subtropical highs, other major stationary eddies include the subpolar lows(low-level cyclonic circulations located over the Bering Strait, Labrador Sea, and certain partsof the Southern Ocean) and topographically-forced deviations in the zonal flow associatedwith the Tibetan Plateau and major mountain chains.

Not all deviations from the zonal mean contribute substantially to the time mean meridionaltransports of energy and angular momentum. For example, the tropical overturning Walkercirculation, with rising motion over the tropical continents and sinking motion over thetropical oceans, primarily redistributes energy in longitude. The Walker circulation plays animportant role in coupled atmosphere–ocean interactions in the tropics, including the ElNiño–Southern Oscillation, and will be discussed further in Chapter 9. Other deviations fromthe climatological zonal mean, such as monsoon systems, contribute to meridional transports

15

90°S 60°S 30°S 0° 30°N 60°N 90°N

100200300400500600700800900

1000

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ssur

e [h

Pa]

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30

20

10

0

10

20

30

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l mom

entu

m fl

ux [m

2 s−

1 ]

90°S 60°S 30°S 0° 30°N 60°N 90°N

100200300400500600700800900

1000

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ssur

e [h

Pa]

Northward heat flux by eddies

15

10

5

0

5

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15

Hea

t flu

x [K

m s−

1 ]

90°S 60°S 30°S 0° 30°N 60°N 90°N

100200300400500600700800900

1000

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ssur

e [h

Pa]

Northward water vapor flux by eddies

54321

012345

Wat

er v

apor

flux

[g k

g−1

m s−

1 ]

Figure 7.12: Climatological zonal mean northward fluxes of zonal momentum (upper panel),heat (middle panel), and moisture (lower panel) by stationary eddies. Data fromthe Climate Forecast System Reanalysis.

60°E 120°E 180° 120°W 60°W90°S

60°S

30°S

0°

30°N

60°N

90°N

980 985 990 995 1000 1005 1010 1015 1020 1025 1030 1035 1040Pressure at mean sea level [hPa]

60°E 120°E 180°E 120°W 60°W90°S

60°S

30°S

0°

30°N

60°N

90°N

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

Evaporation minus precipitation [mm d−1]

Figure 7.13: Climatological mean distributions of mean sea level pressure (left panel), evapo-ration minus precipitation (right panel), and 850 hPa winds (streamlines). Datafrom the Climate Forecast System Reanalysis.

16

of energy and angular momentum in certain seasons but substantial compensations in theannual cycle mean that this systems make only minor contributions to the climatologicalzonal mean. The monsoon systems will be discussed in detail in Chapter 11.

7.8 VORTICITY

Vorticity is a measure of the spin in the motion of a fluid, and is tightly related to angularmomentum. Vorticity can be calculated as the curl of the vector velocity:

ζ= i(∂v

∂z− ∂w

∂y

)+ j

(∂w

∂x− ∂u

∂z

)+k

(∂v

∂x− ∂u

∂y

)(7.17)

where ζ is referred to as the relative vorticity because the wind vector u = (u, v, w) is definedrelative to the surface of the Earth. For large-scale motion in the atmosphere and ocean,for which L À H (see Section 5.4.1), the radial (vertical) component of vorticity is the mostimportant for describing the two-dimensional (horizontal) flow. We therefore often reduce therelative vorticity to its radial component:

ζ= ∂v

∂x− ∂u

∂y. (7.18)

Relative vorticity can be understood by imagining a paddle wheel embedded in the horizontalflow, perpendicular to the surface. If the fluid flow would cause the paddle wheel to rotate,then the relative vorticity is non-zero.

Flow in the atmosphere and ocean is said to be cyclonic if the spin indicated by the relativevorticity is oriented in the same direction as the Earth’s rotation, and anticyclonic if the spinindicated by the relative vorticity is oriented in the opposite direction of Earth’s rotation. Theeasiest way to determine whether the spin in the fluid is oriented in the same direction as theEarth’s rotation is to compare the sign of the relative vorticity ζ to the sign of the planetaryvorticity f . The flow is cyclonic if the signs of ζ and f are the same, and anticyclonic if thesigns of ζ and f are opposite.

The evident correspondence between ζ and f motivates the definition of absolute vorticity,which is defined as the sum of these two terms:

η= f +ζ≈ 2Ωsinϑ+ ∂v

∂x− ∂u

∂y. (7.19)

The absolute vorticity η is equal to the curl of the absolute velocity, in which the rotation of theEarth around its axis is included. Absolute vorticity is conserved for frictionless flow, providedthe fluid parcel retains its shape.

Suppose a parcel with an initial relative vorticity ζ= 0 is displaced in the north–south direc-tion while maintaining its shape. The absolute vorticity η is conserved for this perturbation,but the planetary vorticity would change, requiring that the relative vorticity change in theopposite direction. Figure 7.14 shows a schematic illustration of this process in the NorthernHemisphere. For a northward displacement, f increases and ζ< 0, indicating anticyclonic flow.For a southward displacement, f increases and ζ> 0, indicating cyclonic flow. In other words,a northward displacement induces an anticyclonic anomaly and a southward displacement

17

'0

'N

'S

north

0 = f0

0 = + fN

0 = + fS

fN > f0 > fS

< 0

> 0

= 0

Figure 7.14: Schematic illustration of a Rossby wave, which propagates westward relative tothe background flow.

induces a cyclonic anomaly. Both types of anomaly tend to reduce the displacement to theeast and enhance the displacement to the west, so that the disturbance tends to propagatetoward the west. This type of disturbance is called a Rossby wave. Rossby waves propagatewestward relative to the background flow at a phase speed

c =−βL2

4π2 (7.20)

where L is the wavelength of the disturbance and β = ∂ f∂ϑ is the north–south derivative of

planetary vorticity. Stationary Rossby waves are Rossby waves for which the wave length L =2π

pU/β, where U is the background flow (in this case c =−U ). Stationary Rossby waves can only

exist within a westerly (eastward) background flow. Rossby waves with wavelengths shorterthan the stationary wavelength propagate eastward with respect to the surface but westwardwith respect to the background flow. Rossby waves with wavelengths longer than the stationarywavelength propagate westward with respect to both the surface and the background flow.

Figure 7.15 shows an example of a stationary Rossby wave in the climatological NorthernHemisphere winter mean 500 hPa geopotential height field. This wave has a wavenumberof 2∼3, with clear northward displacements over the Atlantic and Pacific Oceans (associatedwith the thermodynamic effects of the Gulf Stream and Kuroshio, respectively) and a weakernorthward displacement over Asia (associated with the mechanical effects of the TibetanPlateau). Transient Rossby waves are also frequently observed in the atmosphere, and playimportant roles in weather patterns and eddy transports of heat, moisture and momentum(see also Section 7.7).

The requirement that a parcel maintains its shape makes absolute vorticity conservationawkward to apply in practice, and motivates the definition of potential vorticity:

18

DJF 500 hPa Geopotential Height

5.0

5.1

5.2

5.3

5.4

5.5

5.6

5.7

5.8

5.9

6.0

Geopote

nti

al H

eig

ht

[km

]

Figure 7.15: A stationary Rossby wave in the 500 hPa geopotential height field during NorthernHemisphere winter. Data from the Climate Forecast System Reanalysis.

PV = η

ρ·∇θ, (7.21)

where ρ is density and θ is potential temperature. Focusing again on the radial component(the potential vorticity of the horizontal flow), Equation 7.21 reduces to

PV = η

ρ

∂θ

∂z=−ηg

∂θ

∂p, (7.22)

where the latter equality is based on an assumption of hydrostatic balance. Potential vorticity isconserved in the absence of sources or sinks (i.e., frictional effects on the flow and/or changesin θ due to diabatic heating). We will discuss potential vorticity further in Chapter 8.

7.9 THE SEASONAL CYCLE

Figure 7.16 shows climatological zonal mean zonal wind for the solstice seasons (winter /summer). The westerly jets are stronger in the winter hemisphere, because the meridionaltemperature gradients are sharper during winter. Seasonal jets (and particularly the summerjet) are stronger in the southern hemisphere because temperature contours are more zonal(limiting meanders in the jet) and frictional dissipation is weaker (because of the land–oceandistribution in each hemisphere). The seasonal polar night jets are also visible near 100 hPa inthe winter hemisphere. The polar night jet (also known as the polar vortex) is also strongerin the southern hemisphere than in the northern hemisphere. Air inside the wintertimestratospheric polar vortex is largely isolated from the air in the mid-latitude stratosphere,and can get cold enough to form polar stratospheric clouds, particularly in the SouthernHemisphere.

19

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

700

800

900

1000

Pre

ssur

e [h

Pa]

January zonal mean zonal wind

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

700

800

900

1000

Pre

ssur

e [h

Pa]

July zonal mean zonal wind

30 24 18 12 6 0 6 12 18 24 30

Zonal wind [m s−1]

Figure 7.16: Climatological zonal mean zonal wind in January (left) and July (right). Data fromthe Japanese 55-year Reanalysis.

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

700

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900

1000

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ssur

e [h

Pa]

January meridional mass streamfunction

90°S 60°S 30°S 0° 30°N 60°N 90°N

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200

300

400

500

600

700

800

900

1000

Pre

ssur

e [h

Pa]

July meridional mass streamfunction

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

Vertical wind [×10−2 Pa s−1]

Figure 7.17: Climatological zonal mean meridional mass streamfunction (contours) and ver-tical pressure velocity (shading) in January (left) and July (right). Data from theJapanese 55-year Reanalysis.

20

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

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900

1000

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ssur

e [h

Pa]

January northward heat flux by eddies

90°S 60°S 30°S 0° 30°N 60°N 90°N

100

200

300

400

500

600

700

800

900

1000

Pre

ssur

e [h

Pa]

July northward heat flux by eddies

15 10 5 0 5 10 15

Heat flux [K m s−1]

Figure 7.18: Climatological zonal mean eddy heat fluxes in January (left) and July (right). Datafrom the Climate Forecast System Reanalysis.

Figure 7.17 shows climatological zonal mean meridional mass streamfunction for the solsticeseasons. The ascending branch of the Hadley cell shifts into the summer hemisphere, witha strong cross-equatorial return flow into the winter hemisphere in the upper troposphere.The solstice seasons are therefore characterized by strong energy transport from the summerhemisphere into the winter hemisphere. The Ferrell and polar cells are likewise stronger in thewinter hemisphere, and are less variable in the Southern Hemisphere than in the NorthernHemisphere.

Figure 7.18 shows the climatological zonal mean northward heat transport by eddies duringthe solstice seasons. Like the mean meridional circulation, eddy heat transport is strongestin the winter hemisphere. This reflects the effects of multiple factors. First, eddy activityin the storm tracks is larger during winter, as might be expected given the greater supply ofmomentum fluxed into the subtropical jet by the cross-equatorial mean meridional circulation(see also Section 7.10). Second, as mentioned above, the meridional temperature gradientsare sharper in the winter hemisphere, so that the temperature difference between northwardflows and southward flows in eddies is larger during winter. The seasonality of eddy fluxes ofangular momentum is qualitatively similar, due to the seasonal variations of the subtropicalupper tropospheric jet.

7.10 SYNTHESIS AND EXTENSIONS

Figure 7.19 shows the zonal mean distribution of vertically-integrated momentum flux con-vergence. This distribution illustrates the key features of the angular momentum paradigmfor understanding the atmospheric general circulation. The effects of the mean meridionalcirculation are strongest in the tropics, where friction acting to dissipate the lower tropo-spheric easterly trade winds represents a flux of angular momentum from the surface to the

21

90°S 60°S 30°S 0° 30°N 60°N 90°N2.0

1.5

1.0

0.5

0.0

0.5

1.0

1.5

2.0

Zona

l mom

entu

m fl

ux c

onve

rgen

ce [m

s−

2]

Atmospheric zonal momentum flux convergence

TotalMMCEddy

Figure 7.19: Vertically-integrated momentum flux convergence, including contributions by themean meridional circulation (dashed) and eddies (dotted). Data from the ClimateForecast System Reanalysis.

atmosphere. This angular momentum is transported to the upper troposphere via convectivemotion in the intertropical convergence zone, and then fed into the subtropical upper tropo-spheric westerly jets via Coriolis acceleration on the poleward flow (Figure 7.20). Eddies thenflux this angular momentum out of the subtropical jets and into the extratropical storm tracks,where it is returned to the surface by frictional dissipation (Figure 7.21). This process occursvia a cascade of kinetic energy to smaller and smaller turbulent scales, as discussed in Chapter6.

Rather than summarizing the energy paradigm per se, we will instead briefly discuss someuseful extensions to this perspective. Suppose we redefine total potential energy as thegravitational potential energy plus the sensible heat (i.e., the dry static energy s = cv T + g z). Itis evident from the arguments discussed in Section 7.6 that most of this energy is unavailablefor conversion to kinetic energy (winds) under adiabatic (or approximately adiabatic) flow. Ina classic paper, Lorenz (1955) showed that the minimum possible potential energy that canbe attained adiabatically by a fixed mass of atmosphere within a fixed domain is associatedwith the redistribution of mass that results in a purely horizontal density stratification (i.e.,pressure, density, temperature and geopotential height contours coincide exactly). We candefine the available potential energy as the difference between the total potential energy andthis minimum total potential energy. This available potential energy is the part of the potentialenergy that is available for conversion to kinetic energy. As such, it is clear that the only way allof the available potential energy can be converted to kinetic energy is in producing a purelybarotropic flow.

The concept of available potential energy is particularly useful when applied to the global

22

N

SE

EQUATOR

aW W

E E

flux of angular momentum into tropical atmosphere

poleward flux of angular momentum

S

NE

EQUATOR

Figure 7.20: Schematic illustration showing how the mean meridional circulation fluxes angu-lar momentum into the subtropical jets.

aW W

W WE E

flux of angular momentum into tropical atmosphere

poleward flux of angular momentum

return flux of angular momentum out of

midlatitude atmosphere

return flux of angular momentum out of

midlatitude atmosphere

eddieseddies

Figure 7.21: Schematic illustration showing how eddies flux angular momentum out of thesubtropical jet and into the mid-latitude storm tracks, where it is dissipated byturbulence and surface friction.

23

where rq ¼ −g−1 ∂p∂q is the isentropic density, the

overline indicates a time and zonal average, andthe prime a departure from such a temporal andzonal average (i.e., f ′¼ f − f ). The first term onthe right-hand side is the mass transport by thezonal and timemean circulation and is in the samedirection as the Eulerian mean circulation. Thesecond term is the mass transport by the eddiesand dominates the isentropic mass transport inmid-latitudes. This eddy mass transport is similarto the Stoke's drift in shallow water waves (7).The circulation on isentropic surfaces is similar tothe transformed Eulerian mean circulation inwhich a residual circulation is computed by ac-counting for the eddy mass transport (8–10). Be-cause the potential temperature of an air parcel isapproximately conserved in the free troposphere inthe absence of condensation, the isentropic circula-tion is more indicative of the parcel trajectories thanthe circulation obtained through Eulerian averaging.

A key issue when discussing the isentropiccirculation lies in that the entropy of moist air isnot uniquely defined (11). Indeed, the specific en-tropy of water vapor can be specified only towithin an additive constant. As a consequence, theentropy of moist air can be known only up to thisconstant multiplied by the water concentration. Totest whether this has an impact on the averagedcirculation, we computed the circulation by usingthe equivalent potential temperature, qe, to define

isentropic surfaces (11). The equivalent potentialtemperature is conserved for reversible adiabatictransformations, including phase transitions. Incontrast to the potential temperature, it includes acontribution from the latent heat content of watervapor and can be roughly approximated byqe ∼ qþ Lv

Cpq, with Lv the latent heat of vaporiza-

tion and q the water vapor concentration. Both qand qe define two distinct sets of isentropic sur-faces, and correspond to a correct definition of thethermodynamic entropy. We refer here loosely to“dry” isentropes as surfaces of constant potentialtemperature and to “moist” isentropes as surfacesof constant equivalent potential temperature. Thestream function onmoist isentropes,Yqeðqe; fÞ, isdefined by

Yqeðqe0 ,fÞ

¼ 1t ∫

t

0 ∫2p

0 ∫psurf

0Hðqe0− qeÞva cos f

dpgdldt ð4Þ

Figure 1, B and C, compares the stream functionson dry and moist isentropes. Although qualita-tively similar, the two circulations differ substan-tially in that the total mass transport on moistisentropes is approximately twice that on dry is-entropes. This difference is present in both hemi-spheres and throughout the entire year.

The discrepancy between the two circulationscan be understood by looking at the joint dis-

tribution, M(qe, q), of the meridional mass trans-port at a given latitude f. To obtain this distribution,we sorted the meridional mass flux a cos fvd l dp

gby the value of q and qe and integrated over time.Figure 2 shows the joint distribution obtainedfrom theNCEP-NCARReanalysis at 40°N duringDecember, January, and February, averaged be-tween 1970 and 2004. By definition, the equivalentpotential temperature is larger than the potentialtemperature, qe > q, so the distribution is 0 be-low the diagonal qe = q. In addition, the watercontent is roughly proportional to the differenceq ≈ Cp

L ðqe− qÞ, so that the further a parcel isabove the diagonal, the higher its water content.The maximum amount of water vapor in an airparcel rapidly decreases with temperature due tothe Clausius-Clapeyron relationship. The masstransport distribution becomes narrower in theupper-right corner of Fig. 2: This portion of thegraph corresponds to upper tropospheric air parcelswith low temperature and therefore low water va-por. The stream function at a given latitudeYq andYqe can be obtained by integrating the jointdistribution M(qe, q) over selected portions of thedomain. The mass transport between two dryisentropes q1 and q2 is given by the integral

DYq ¼ Yqðq2, fÞ−Yqðq1, fÞ¼ ∫

q2

q1∫∞

0Mðqe, qÞdqedq ð5Þ

Fig. 1. The global mean circulation from the NCEP-NCAR Reanalysis. (A)Stream function on pressure surfaces Yp. (B) Same as (A) for the streamfunction on dry isentropes Yq. (C) Same as (A) for the stream function onmoist isentropesYqe. Contour interval is 2.5 × 1010 kg s−1. Solid contours arepositive values of the stream function and correspond to northward flow at lowlevels, whereas dashed contours are negative values of the stream functionand correspond to southward flow at low levels. In (B) and (C), the thin solidline and two dotted black lines show the 50, 10, and 90 percentiles,respectively, of the surface potential or surface equivalent potential temper-ature distributions.

22 AUGUST 2008 VOL 321 SCIENCE www.sciencemag.org1076

REPORTS

on

Oct

ober

7, 2

011

www.

scie

ncem

ag.o

rgDo

wnlo

aded

from

Figure 7.22: Mean meridional circulation in (a) pressure coordinates and (b) potential tem-perature coordinates based on the NCEP–NCAR reanalysis. From Pauluis et al.(2008).

atmosphere (which is a fixed mass of atmosphere within a fixed domain). Consider again thezonal mean distributions of net incoming solar radiation and outgoing longwave radiationshown in Figure 1.14, from which the energy transports shown in Figure 7.1 are derived. Zonalinhomogeneities in absorbed solar radiation are continually creating available potential energy(via surface sensible and latent heat fluxes, via direct solar heating of clouds in the intertropicalconvergence zone, etc.), increasing the baroclinicity and moving the atmosphere away from itsminimum potential energy state. The balancing flux of outgoing longwave radiation is muchmore evenly distributed in latitude because it reflects the constant tendency of the atmosphereto relax toward the minimum potential energy state, even though it never reaches it. Thisrelaxation occurs via the conversion of potential energy to kinetic energy, where that kineticenergy constitutes the general circulation of the atmosphere. Kinetic energy associated withconvective motion accounts for only about 2% of the total kinetic energy in the atmosphere,with the remaining 98% driven by horizontal heating gradients; however, despite its relativelysmall proportion, convective motion is critical for maintaining the atmospheric circulation.

Finally, we return to the zonal mean distribution of diabatic heating shown in Figure 7.9. Toleading order, diabatic heating corresponds to upward mass flux (across potential temperaturesurfaces) and diabatic cooling corresponds to downward mass flux. The basic structure ofthe mean meridional circulation can therefore be retrieved from the zonal mean distributionof diabatic heating shown in Figure 7.9. The Hadley cell overturning (with rising motionin the subtropics and sinking motion in the subtropics) is particularly apparent, while thesmall centers of diabatic heating in mid-latitudes provide hints of the rising branches of theFerrell and polar cells. The overriding impression, however, is of a single global overturningcirculation with rising motion in the tropics and sinking motion in high latitudes, equatorwardmotion near the surface and poleward motion in the upper troposphere. It is worth notingthat defining the meridional mass streamfunction with vertical motion defined in termsof potential temperature rather than in terms of pressure yields exactly this type of global

24

overturning circulation, with rising motion in the tropics, poleward motion aloft, sinking overhigh latitudes, and equatorward flow near the surface (Figure 7.22). Pauluis et al. (2008) furthershowed that these changes are even more pronounced if the mass streamfunction is definedin terms of equivalent potential temperature rather than dry potential temperature, yieldingsymmetric overturning circulations with mass transports that are more than twice as large asin the dry potential temperature case! In essence, this revised perspective helps to reconcileand eliminate the artificial distinctions between eddies and the mean meridional circulation.See recent work by Laliberté et al. (2015) for a particularly nice application of this approach.

REFERENCES

Gill, A. E. (1982), Atmosphere–Ocean Dynamics, 662 pp., Academic Press, London, U.K.

Hartmann, D. L. (1994), Global Physical Climatology, 411 pp., Academic Press, San Diego, CA, USA.

Holton, J. R. (1992), An Introduction to Dynamic Meteorology, 3rd ed., 511 pp., Academic Press, London, U.K.

Laliberté, F., et al. (2015), Constrained work output of the moist atmospheric heat engine in a warming climate,Science, 347, 540–543.

Lorenz, E. N. (1955), Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167.

Marshall, J., and R. A. Plumb (2008), Atmosphere, ocean, and climate dynamics: An introductory text, 319 pp.,Elsevier Academic Press, Boston.

Pauluis, O., A. Czaja, and R. Korty (2008), The global atmospheric circulation on moist isentropes, Science, 321,1075–1078.

Peixoto, J. P., and A. H. Oort (1992), Physics of climate, 520 pp., Springer–Verlag, New York.

Vallis, G. K. (2006), Atmospheric and Oceanic Fluid Dynamics, 745 pp., Cambridge University Press, Cambridge,U.K.

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