TROPICAL BOUNDARY LAYER EQUILIBRIUM IN THE LAST ICE AGE - Alan Betts

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. D2, PAGES 2529-2534, FEBRUARY 20, 1992

TROPICAL BOUNDARY LAYER EQUILIBRIUM IN THE LAST ICE AGE

Alan K. Betts

AtmosphericResearchM, iddlebury,Vermont W. Ridgway

AppliedResearchCorporationL,andover,Maryland

Abstract. A radiative-convectivbeoundarylayer from the oceansto the continentailce sheetsproducesa

modelis usedto assessthe effectof changingseasurface correspondingreverse displacementof air. The first

temperaturep, ressurew, ind speed,and the energyexport approximationt,he pressureat the currentsea level, is

fromthetropicsontheboundarylayerequilibriumequivalent howeverunchangedbecausethemassof air displacedby the potentialtemperature. It remainsdifficult to reconcilethe ice approximatelyequalsthemassof air whichreplacesthe observationthsatduringthelastglacialmaximum(18,000yr evaporatedseawater. (There are small correctionsw: ater

BP) thesnowlineonthetropicalmountainsfell 950 m, while expandasbout10%onfreezingb,utthisisoffsetbythefact

thetropicalseasurfacetemperaturefsell only 1-2 K.

thatthe densityof air changesa similaramountbetweensea

levelandthepressureandtemperaturoenthe continentailce

1. Introduction

sheets.) The fall of thesnowlineonthetropicalmountainshas

led to extensivedebateduringthe lastfew years[ Rind and

Peteet, 1985; Broecker, 1989; Rind, 1990]. The fall of

The tropicalclimateduringthe lastglacialmaximum snowlineis too large to be explainedby the small fall of

(18,000yr B.P.) raisesmanyfascinatingquestions.Here we SSTsin the tropics[Rindand Peteet,1985]. However,the

shall try to reconstructf,rom a few key observations, heightof the freezingleveldoesnotdependsimplyon SST.

plausibleconditionsfor thetropicaloceanicboundarylayer, It dependson the thermalstructureabovethe surfacein the using the simple one-dimensionaml odel of Betts and lower troposphere. The vertical structureof the present

Ridgway [1989], abbreviatedBR89. It is believed that tropicalatmosphereis controlledby a balanceof radiative tropicalseasurfacetemperature(sSST) wereat themost2 K and convectiveprocessesT. he warm SSTsare maintained

lower than at present,the bestestimatebeingonly 1.4 K lower [Climate:Long-RangeInvestigationM, apping,and Prediction(CLIMAP), 1981]. Thesesmallfallsof SSTin the

primarilyby a balanceof theincomingsolarradiationandthe surface evaporation. An unstablevertical structureis maintainedby a comparablenet longwavecoolingof the

tropicsare in apparentconflictwith the largefalls in the atmosphere.The atmospheritchermalbalanceis maintained

snowline on the tropical mountainsfor which the best whenthe watervaporevaporatedat thesurfaceis condensed

estimaties950_+50m [seeRindandPeteet1,985].Forthe and precipitatedout from deep convectivesystems. The

sameepochthe fall of sealevel in the tropicsdueto the convectiveresponseto destabilizationis so fast that the

accumulationof water in the high-latitudeice sheetswas resultingverticalstructurein thetropicsis alwaysveryclose about120 m, and atmospheriCcO2 was about195 ppm, to a moist equilibriumstructureand a little unstablewith [Rind, 1987], in comparisonwith its presentvalueof 330 respect to the wet adiabatic lapse rate in the lower

ppm.

troposphere[Riehl, 1979; Betts, 1982; Xu and Emanuel,

1.1. Discussion ,

1989]. Air ascendsinto cumulonimbuscloudsfrom a moist subcloudlayer, reachingsaturationat cloudbaseabout60

mbar above the surface. The moist adiabat is the

The fall of sea level is consistenwt ith the large

redistribution in water from the oceans to the ice sheets. It

impliesa longperiodof enhanceedvaporatiofnromthewarm tropicaol cean'spolewardadvectioanndprecipitatioanssnow on the continents. The evaporationof 120 m of water correspondtso a surfacelatentheatflux of 10 W m-2 for

thermodynamipcathfollowedby sucha saturatedair parcel as it ascendsadiabaticallywith condensation.Each wet adiabat is conventionallylabeled by 0?, the equivalent potential temperature,which is the maximum potential temperaturereachedby the parcelas it ascendsto the upper troposphereand condensesout all its water vapor. The

1000 years! This is small, but it may be a significant perturbatioonf thetropicalenergybudget(seebelow). This

fall of sealevelwill produceanincreasien thepressuraet

the new lower sea surface because the redistribution of water

equilibriumvalueof 0Enearthesurfaceovertheoceansthus determines the moist adiabatic ascent path and the equilibriumverticalthermalstructureof thetropics.We have no reasonto believe on eithertheoreticalgroundsor from

climate model simulations [Rind, 1987] that this tight

convectivecouplingbetween0E and atmosphericstructure

Copyright1992 by the AmericanGeophysicaUl nion.

wouldbe any differentover the warmoceansin the glacial

Papernumber91JD02974.

period. On a given0e wetadiabatt,hefreezinglevel(which we canexpecto be associatecdloselywiththesnowlinei)s

0148-0227/92/91JD-02974505.00

at a fixedpressures, othattheheightof thesnowline(above

2529

2530

BettsandRidgway:TropicalBoundaryLayerDuringLastIce Age

the presentsea level) is essentiallyconstantunless0?. section1.2. There are three ways to producea drop in

changes.Thusa dropof the snowlineof 950 m requiresa subcloudlayer0?.:a dropof temperatur(eATo),a fall of

largedropof 0E(? 14K, seebelow)in thelow-leveal irover moisture(Aqo)o, r anincreaseof surfacepressur(eApo).The

thetropicaloceanss, othatthewhole troposphersehiftsto a couplingbetweenthelow levelair temperaturaendmoisture

coolertemperatureT. he low-level0?.is in turna functionof and the SST, surfacepressure,and wind are discussedin

low-levelpressuret,emperaturea,ndhumidity.

section 2.

Figure 1 summarizesthe physicalprocesseasndthe simplifiedmoistthermodynamicassociatewdithconvection 1.2. Relationshipof Low- Level 0Fto

in the tropicson a pressure-temperatudrieagram. Air from Heightof FreezingLevel

the subcloudlayerriseswith condensatioinn cumulonimbus

For thewetadiabaticatmosphersehownin Figure1,

cloudsto reach thermal equilibriumbelow the tropical it is straightforwartdo computethe dropof freezinglevel

tropopause(the schematicon the left). A horizontaline with 0?.. This is shownin Figure2 asa dashedline. We

marks the currentfreezing level in the midtroposphere. havetakenthepresent-daeyquilibriumvalueof 0?.as346.9

Temperatureh, umidity,and pressurein the subcloudlayer K, correspondintgo theboundarylayerequilibriumsolution

determine cloud base and the ascent wet adiabat. Below by BR89 overan SST of 300 K, with a surfacepressuroef

cloud base,the fall of temperaturewith heightis the dry 1012mbaranda surfacewindspeedof 6.7 m sq. Thewet

adiabatilcapserateof-9.7K km'l. Theslopindgryadiabats adiabatis thesimplestreferencestructure.However,thereis

in the subcloud layer are lines of constantpotential evidencethat below the freezinglevel, the tropical

temperature0,. Abovecloudbase,themoistadiabaticlapse atmospheries moreunstableandcloserto a secondreference:

rate is less,about -5 K km'?. As cloudair amendsfrom thewetvirtualadiaba[tBetts1, 982,1985;Xu andEmanuel,

cloud base to the upper tropospherei,t is warmedby 1989;13ettsandBarrio,1991]. This wet virtualadiabatis the

condensatiofnrom a dry potentialtemperaturoef 0 to the neutraldensityadiabatfor reversiblemoist ascentwhere

value0e, indicatedby the dottedline. This is thedefinition liquidwaterloadingis consideredT. hesolidlinein Figure

of the equivalentpotentialtemperatureof a par,el. For a 2 showsthe dependencoef thefall of thefreezinglevelon

par,el in the subcloudlayer this asymptoticvalueof 0?. is the wet virtualadiabathrougha given0Eat a cloudbase

givenby [Betts,1982]

height of 950 mbar. For the wet adiabaticreference

atmospher(edashedline)thefreezinglevelcorrespondintog

0?. -- 0 exp(2.67q]T*)

(1) the zeroline for 0E=346.9K is 5114m, whilefor thecooler

wet virtual adiabaticatmosphere(solidline) the zero line

where0 ispotentiatel mperaturqei,smixingratio,andT* is correspondtso 4685 m. The presentsnowlinevaluesarein

temperatureat the lifting condensatiolnevel (cloudbase). betweena, round4800 m. A dropof 950+50m in freezing

As the ascentwet adiabatfallsto lowervaluesof 0?. level (zF)thencorrespondtos a fall of 0, to 333.7_+0.7 K,

and the atmospheregetscooler,the heightof the freezing if the tropical atmospherehas a wet adiabaticstructure

level (0? C level) also falls, as shown. This is discussedin (dashedline),and332.1_+0.7 K, if thetropicaal tmosphere

Tropopouse

Outflow '

reezng Level

p

61

950 ClouBdase

1012mb

?eeoo ? ?

".... Equivalent

Wet ?...... Potential Temp.

A(-d5iKakbm'"a.t.

I

II' Cond.e.nsati6n

, ,

8 D-ry9d.7iaKbkatm

O?C qo A

o

Fig. 1. Schematicshowingthedependencoef thewetadiabatandfreezinglevelonchangeisn near-surfacaeir temperaturep,ressurea, ndhumidity.

BettsandRidgway:TropicalBoundaryLayerDuringLastIce Age

2531

200

. -200

_z -400 WET VIRTUA

N

ADIABA?T/

Izi

(OEV) /'/

t_?.-600

'//' WET_AO!ABAT

u_ // o -800

(OE)

.-J

:

, -950 +_ 50m

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