Journalof MarineResearch, 61, 465–489, 2003

Upper ocean controlon the solubility pump of CO 2

byTakamitsu Ito 1 andMichael J. Follows 1

ABSTRACT

Wedevelop and test a theoryfor therelationship of atmospheric pCO2 andthe solubility pump of

CO2 inan abioticocean. The solubility pump depends on thehydrographic structure of theocean and thedegreeof saturation of thewaters. The depth of thermoclinesets the relative volume of warmand coldwaters, which sets the mean solubility of CO 2 intheocean. The degree of saturation depends on thesurfaceresidence time of the waters.

Wedevelop a theorydescribing how atmosphericCO 2 varieswith diapycnal diffusivity and wind stressin asimple,coupled atmosphere-ocean carbon cycle, which builds on established thermocline theory.We consider two limit cases for thermocline circulation: the diffusive thermocline and the ventilatedthermocline. In the limit of a purelydiffusive thermocline (no wind-driven gyres), 1 /3 atmospheric pCO2 increasesin proportionto the depth of thermoclinewhich scales as k , where k isthe diapycnal mixing rate coefŽ cient. In the wind-driven, ventilated thermocline limit, the 1 / 2 ventilatedthermocline theory suggests the thickness of thethermocline varies as we k . Moreover, surfaceresidence times are shorter, and subducted waters are undersaturated. The degree of undersaturationis proportional to the Ekman pumping rate, we k ,formoderate amplitudes of we k . 3 / 2 Hence,atmospheric pCO2 varies as we k formoderate ranges of surface wind stress. Numerical experimentswith an ocean circulation and abiotic carbon cycle model conŽ rm these limit case scalingsand illustrate their combined effect. The numerical experiments suggest that plausible variationsin thewind forcing and diapycnal diffusivity could lead to changesin atmospheric pCO2 ofasmuchas 30ppmv.The deep ocean carbon reservoir is insensitiveto changesin thewind, due to compensationbetween the degree of saturation and the equilibrium carbon concentration. Conse- quently,the sensitivity of atmospheric pCO2 towind-stressforcing is dominated by thechanges in theupper ocean, in direct contrast to the sensitivity to surface properties, such as temperature and alkalinity,which is controlled by thedeep ocean reservoir.

1.Introduction Thepartitioning of carbonbetween oceanic and atmospheric reservoirs and its depen- denceon thecirculation and climate of theoceans has been studied extensively due to the likelyrole of theoceans in modulatingatmospheric CO 2 onglacial-interglacialtimescales

(reviewedby Sigmanand Boyle,2000) andthe current oceanic sink of fossilfuel CO 2 from theatmosphere (e.g. Gruber et al., 1996).While it seems clear that the oceans play a signiŽcant role with regard to bothof theseissues, much remains to beunderstood.

1.Program in Atmospheres, Oceans andClimate, Massachusetts Instituteof Technology, Cambridge, Massachusetts 02139,U.S.A. email:[email protected] 465 466 Journalof MarineResearch [61, 4

Theinventory of carbons in the ocean is largely controlled by two important mecha- nisms:the solubility and biological pumps (Volk and Hoffert, 1985).The solubility pump re ectsthe temperature dependence of solubilityof CO 2 andthermal strati Ž cationof the ocean.Cold deep waters aregenerally enriched in dissolvedinorganic carbon (hereafter, C) inpartdue to theirhigher solubility. For areviewof oceancarbonate system, see Stumm andMorgan (1996). The biological pump involves production and dissolution of organic molecules.Photosynthesis occurs in the euphotic layer, converting inorganic carbon and nutrientsto organic matter. Some organic matter leaves the euphotic layer as sinking particles,and it isremineralized in the oceaninterior. Both solubility and biological pumps tendto increase the deep water C concentration,creating a verticalgradient of C. Boxmodel studies in the 1980 ’ssupportedthe notion of adominantrole for thehigh latitudeoceans in controllingatmospheric pCO2 (Sarmientoand Toggweiler, 1984; Knox andMcElroy, 1984; Siegenthaler and Wenk, 1984), largely through the biological pump. Recentstudies with three-dimensional ocean circulation and biogeochemistry models (Bacastow,1995; Broecker et al., 1999;Archer et al., 2000)suggest that atmospheric pCO2 alsoshows a greatersensitivity to low latitude surface ocean properties than had previouslybeen accepted. Archer et al. (2000)suggest that this might be due to the parameterizationsof subgrid-scalemixing and diapycnal mixing in the ocean. Toggweiler et al. (2003)found that the sensitivity of atmospheric CO 2 tolow latitude surface propertiesin box models depends on the representation of deep water formation, and showedthat the boxmodelscan be sensitiveto low latitudes by an adjustment in theareaof highlatitude surface ocean. Alternatively, Follows et al. (2002),using an idealized general circulationand abiotic carbon cycle model (Fig. 1), showed that the wind-driven circula- tionenhances the sensitivity of atmospheric pCO2 tolow latitude surface properties by creatinga poolof relativelywarm waters intheventilated thermocline which inherit their propertiesfrom themid-latitude surface. The model, which conserves the total amount of carbonin ocean and atmosphere, also illustrated a strongsensitivity of atmospheric pCO2 tothepresence or absence of wind forcing. InFigure 1, we illustrateresults from thatnumerical model, details of which may be foundin Follows et al. (2002).Brie  y,theexperiments are performed with the MIT ocean model conŽ gured in a 60° longitudeby 90 ° latitudebasin at 3 ° 3 3° resolution,with 15 verticallevels. It is overlainby anabioticcarbon cycle model which is coupledto asimple atmosphericreservoir of CO 2.Carbonatechemistry is explicitly solved and the air-sea exchangeof CO 2 isparameterizedwith a uniformgas transfercoef Ž cient.In Follows et al. (2002),we compareexperiments with thermohaline forcing only to those with both thermohalineand wind forcing. The meridional overturning circulation and thermal structureof the model in these two cases is shown in Figure 2. The model resolves the ventilatedthermocline reasonably well. When wind forcing is present, the ocean gyres spin upandthe warm lensof thesubtropical thermocline develops. Though atmospheric pCO2 increasedwith the introduction of the wind forcing, the mean ocean temperature (and therefore,solubility) did not change signi Ž cantly.The increase in atmospheric CO 2 was 2003] Ito& Follows:Solubility pump of CO 2 467

Figure1. Abiotic sector model of ocean-atmosphere carbon cycle: (a) Surface currents and

differencein partial pressure of CO 2 acrossthe sea surface in the sector model without wind

forcing.(b) Surfacecurrents and difference in partial pressure of CO 2 acrossthe seasurface in the sectormodel with strong wind forcing. (c) Difference in zonally averaged C concentration (mol m2 3 )betweenthe model with strong wind forcing and the model with no windforcing.

attributableto thewaters ofthesubtropical thermocline becoming signi Ž cantlyundersatu- rated.The surface currents are slow in the model without wind-forcing (Fig. 1a), the residencetime of water parcels at the surface is long, and the surface ocean is close to equilibriumwith the atmosphere. In the wind-driven model the surface currents are swift (Fig.1b), the air-sea equilibration time scale and the residence time of surface waters are comparable.Waters of theventilated thermocline are signi Ž cantlyundersaturated due to thestrong cooling in thewestern boundary current. Since the thermocline is depletedin C, bymass conservation,carbon must be transferredto theatmosphere. Figure 1c illustrates thedifference in C intheupper ocean between the two cases. Thesenumerical experiments suggested a potentiallysigni Ž cantrole for theventilated thermoclinein modulating atmospheric CO 2 ondecadal and longer timescales, but motivatesthe broad questions: What are the physical controls on the solubility pump of carbonin the oceans? Can we providea generaltheory of itsdependence on wind-stress 468 Journalof MarineResearch [61, 4

Figure2. Meridional overturning circulation (Sv) and potential temperature ( °C)forthe sector model(a, c) without wind forcing and (b, d) with strong wind forcing (maximum wind-stress 0.2 N m22 ). forcingand diapycnal mixing rates? How mightthe solubility pump respond to climatic change,through changes to these physical properties? Inthis study we seekto understand how the physical structures and processes of the oceancontrol the solubility pump of CO 2.For simplicityand clarity we focuson an abiotic ocean.We developscalings which relate the storage of carbon in the ocean and, thus, atmospheric pCO2 todiapycnal mixing and Ekman pumping rates. We demonstratethat thesescalings accurately predict the behavior of an idealized, three-dimensional, ocean- atmospherecarbon cycle model (Follows et al., 2002).Over areasonablerange of diapycnaldiffusivity and wind-stress, atmospheric pCO2 variesby as much as 30ppmv. Thissuggests a possiblysigni Ž cantrole for thewind-driven gyres in modulating atmo- spheric CO2 ondecadaltimescales, and even with regard to glacial-interglacialchange. It alsoprovides the basis for adeeperunderstanding of the differences between more complexnumerical simulations of theoceans. InSection 2 we reviewthe mass balanceof carbon in a simpli Ž ed,abiotic ocean- atmospheresystem. In Section 3 we brie  yreviewsome relevant aspects of thetheory of 2003] Ito& Follows:Solubility pump of CO 2 469 thermoclinethickness. We outlinethe scaling arguments which relate atmospheric pCO2, diapycnalmixing and Ekman pumping in Section 4, anddemonstrate that these scalings holdtrue in thesetting of thenumerical model. We alsodemonstrate that the upper ocean, andnot the deep oceans, control the sensitivity of atmosphericCO 2 tochangesin surface wind-stress.Finally, we discussthe relevance of thistheory for morerealistic models and for ourunderstanding of thelinks between climate change and biogeochemistry.

2.Partitioning of carbonbetween oceanand atmosphere: Abiotic ocean limit Thehydrographic structure of the oceans, in combination with the alkalinity and bufferingcarbonate chemistry, determines its carbon loading capacity at thermodynamic equilibrium.The thickness of thermoclinecontrols the relative volume of the warm, upper oceansand the cold, deep oceans. For example,a deeperthermocline implies higher ocean heatcontent and lower carbon loading capacity. The ability of theocean to actually achieve thispotential carbon loading is determined by theequilibration state of thewaters which ventilatethe thermocline and the deep ocean. The degree of saturation depends on the competitionbetween the residence time of surfacewater parcels, the surface heat forcing andthe air-sea gas equilibration time scale. The characteristic time scale for air-seaCO 2 equilibrationof themixed layer is on theorder of ayear.If thesurface residence time is muchlonger than a year,the parcel is close to thermodynamic equilibrium with atmo- spheric pCO2. First,we brie  y deŽ nethe ocean-atmosphere carbon balance in the framework ofa 2-boxmodel (Fig. 3). The solubility pump may be understood in terms of the volumes, temperaturesand carbon concentrations of thedeep ocean and the thermocline box. For a closedsystem (neglecting river input and sediment burial), mass balancedictates that atmospheric pCO2 willvary in responseto changesin thevolume and properties of these reservoirs.A statementof mass balancefor thissimpli Ž edocean with a warm, thermocline layer of C concentration, Cth,overlyinga cool,deep ocean layer, with C concentration, Cd, is

at MpCO2 1 VdCd 1 VthCth 5 Ctotal (1)

at where M isthetotal moles of gasesin the atmosphere, and pCO2 isthemixing ratio of

CO2 inthe atmosphere. Vd and Vth arethe volumes of the deep ocean and thermocline, respectively.Note that the upper ocean layer is assumedto be thethermocline and not the surfacemixed layer. Ctotal isthetotal amount of carbonin this closed, atmosphere-ocean system.Hence, from (1),

at pCO2 } 2~VdCd 1 VthCth!. (2)

Assumingthat the thermocline box and the deep ocean box have the same area, the relative volumeof theseboxes is equal to the relative thickness, Vth/Vd 5 h/(H 2 h). The deep at waters representthe leading order control on pCO2 .At thenext order, O(h/H), the 470 Journalof MarineResearch [61, 4

Figure3. Schematic two-box ocean and atmosphere carbon cycle model. The depth of theocean is

setto a constant, H(m).Thetop box is the atmospheric reservoir of CO 2 withits total moles M (mol).The middle box represents thermocline (upper ocean) which is warmwith temperature

Tt h andC concentration Ct h .Thedepth of thermoclineis h(m).Thedeep box represents abyssal

oceanwith is coldwith temperature Td and C concentration Cd .

column C inventorydepends linearly on thethickness of thermocline, h.For example,all elsebeing equal, an increasein the thickness of thermoclineresults in the linear reduction ofthestorage of carbonin theocean.

3.Diffusive and ventilated thermocline Inorder to understand the role of thethermocline as a carbonreservoir, we must Ž rst considerwhat controls its thickness and hydrographic structure. The dynamics of the ocean’sthermoclinehave been extensively studied with two-limit cases for thermocline circulation:the diffusive thermocline and the ventilated thermocline. In a diffusively controlledthermocline, large-scale upwelling of cold waters isbalanced by downward diapycnalmixing of heat. In a ventilatedthermocline, Ekman pumping and surface buoyancygradients dictate upper ocean structure. It is beyond the scope of the present studyto discussthermocline theory in depth.We refer thereader to a reviewby (Pedlosky, 1986)and the paper of (Vallis, 2000) on this topic. The two views of the thermocline, depictedschematically in Figures 4 and5, are not necessarily exclusive. Recent studies haveviewed the thermocline as re  ectinga combinationof theseprocesses (Samelson and Vallis,1997). We Ž ndsomeevidence of thetwo thermocline regimes occurring simulta- 2003] Ito& Follows:Solubility pump of CO 2 471

Figure4. A schematicdiagram for diffusive thermocline in anoceanbasin. neouslyin our numerical simulations when diapycnal diffusivity is suf Ž cientlysmall. Figure2(d) shows some characteristics of anupper, ventilated thermocline overlying an internal,diffusive thermocline. Here we developscalings for thecarbon system in both the diffusive and ventilated thermoclinelimits, and examine these scalings in the context of anumericalmodel which hasboth explicit diapycnal mixing and wind-stress forcing, and thus may be in  uenced by bothmechanisms. Scalingsrelating thermocline depth and diapycnal mixing in a wind-freeocean have beendeveloped and demonstrated to be consistent with basin-scale ocean circulation models(Bryan 1987; Zhang et al., 1999;Marotzke and Scott, 1999; Scott, 2000; Park and Bryan,2000). These studies show that, in the absence of wind forcing, the meridional overturningrate and the depth of thermocline h canbe related to diapycnal diffusivity througha simplescaling relationship. We assumethat the surface buoyancy is prescribed

Figure5. A schematicdiagram for ventilated subtropical thermocline in anoceanbasin. 472 Journalof MarineResearch [61, 4 as Db (innumerical simulations, we userestoring boundary condition with a rapid dampingrate), and also assume that the circulation is in geostrophic and hydrostatic balance.Diapycnal diffusivity is denotedby k (m2/s). Inthis diffusive limit

h } k1/3Db21/3. (3)

Figure4 illustratesschematically the diffusive thermocline. Downward diffusion of heat balancesthe broad upwelling of cold,deep waters acrossthe basin. Incontrast, other studies have examined the thermocline in an inviscid, wind-driven limit(Luyten et al., 1983).In this limit, the thickness of thethermocline scales with the Ekmanpumping rate

1/2 h } wek . (4)

Figure5 illustratesschematically the bowl of the warm subtropicalthermocline. Wind- forcinginduces Ekman transport and the gyre circulations of theupper ocean, creating a ventilatedthermocline, the properties of which are set by subduction from thesurface waters (e.g.Iselin, 1939; Stommel, 1979; Marshall et al., 1993).In the ventilated thermoclinelimit (where diapycnalmixing is relativelysmall) the subtropical thermocline isformed of warm, carbon-depletedsurface waters advectedinto the interior from the surface. Theseviews of the thermocline, and the scalings and numerical experiments presented here,are particularly relevant to the ocean basins. However, the zonally unblocked AntarcticCircumpolar Current represents an important ocean region with different dynamics.Gnanadesikan (1999) develops a globalview of thermocline thickness, ocean heatcontent and overturning circulation. It is interesting and possible to consider the thermoclinein thecircumpolar channel, but it is beyondthe scope of thisstudy.

4.Carbon scalings and numerical experiments

Inthis section, we outlinescalings for therelationship between atmospheric pCO2 and physicalparameters of an idealized, abiotic ocean and illustrate these scalings using numericalexperiments with the single hemispheric sector ocean model brie  ydescribedin theIntroduction and in more detail by Follows et al. (2002).In all simulations, surface buoyancyis restored to a prescribedmeridional pro Ž lewith a rapid,characteristic time scaleof onemonth. The total carbon inventory of ocean-atmospheresystem, Ctotal, is held constantin all simulations, which allows us to apply the simple carbon mass balance describedin (1). Diapycnal diffusivity and the amplitude of surface wind-stress are varied for sensitivityexperiments. a.Diffusive thermocline Here we examinethe relationship between diapycnal mixing rates and atmospheric pCO2 inthe diffusive thermocline limit. Figure 4 schematicallyillustrates a diffusive 2003] Ito& Follows:Solubility pump of CO 2 473 thermoclinesustained by broad scale upwelling and diapycnal mixing. Likewise, in this case, Cth isdetermined by the balance between the upwelling of deep water and the downwarddiffusion of surface water properties. A prognosticequation for dissolved inorganiccarbon for thisabiotic system can be written

]C DC 1 ¹ · ~uC! 5 ¹ · ~K¹C! 2 . (5) ]t tc where we deŽ ne DC tobe the departure of dissolvedinorganic carbon from thevalue it wouldhave at equilibrium with the overlying atmosphere, were itbrought to thesurface at itscurrenttemperature.

DC 5 C 2 Ceq. (6)

The Ž rst termon the r.h.s. of (5) isthe eddy turbulence  uxterm, and the second term describesthe air-sea CO 2  uxas a dampingtoward the equilibrium value, Ceq. The dampingtimescale, tc,dependson the gas transfer coef Ž cient,the Revelle factor and ionizationfractionation. For amixedlayer of thickness, hml ; 100 m, tc istypicallyabout oneyear (Broecker and Peng, 1974) but will vary with environmental factors. At steadystate, the horizontally averaged surface C mustbe equal to the horizontally averaged Ceq sothat the net, global air-sea CO 2  uxis zero. In an ideal case where the diapycnalmixing can be describedby a uniformdiffusion coef Ž cientand the isopycnals aremostly horizontal, the situation is bestdescribed in terms of thehorizontally-average d carbonbalance equation. For themixed layer,

C~z 5 0! 5 Ceq (7) where C representsthe horizontally-averag ed C concentration.We considerthe horizontal averageof (5), which is a verticaladvection-diffusion equation. We assumethat the verticalvelocity, w,isa constantand the solution can be foundwith appropriate boundary conditions.

z/h C~z! 5 Cdeep 2 @Cdeep 2 C~z 5 0!#e . (8)

Thethickness of diffusive thermocline, h,isdeterminedby h 5 k/w,whichis theratio betweenthe diapycnal diffusivity and the vertical velocity. The top boundary condition comesfrom (7).The bottom boundary condition is setto C(H) 5 Cdeep,andwe assume that H @ h.Thedeep water carbonconcentration, Cdeep,isdetermined by the surface water propertiesat thelocation of deepwater formation,and is assumedto beindependent of k. Integrating(8) verticallywe obtainthe column C inventory,

0 h C~z!dz > H C 2 ~C 2 C~z 5 0!! . (9) E F deep H deep G 2H 474 Journalof MarineResearch [61, 4

Thisrelationship re  ectsthe simpli Ž ed,two-box view suggested by (2).The ocean carbon inventoryis mainly determined by the deep waters becauseof its large volume, as one mightexpect. The impact of the thermocline reservoir enters at the order of O(h/H). Increasingthe depth of thermocline results in anetwarming of the ocean and reduction of thepotential for oceancarbon storage. Combining(3) and(9), the storage of carbonin the ocean can be seento beproportional tothecubed root of thediapycnal diffusion coef Ž cient:

0 E C~z!dz } 2k1/3. (10) 2H

Addingthe constraint of carbonconservation, (1), we seethe relationship of atmospheric pCO2 andthe diapycnal mixing coef Ž cient, k.

at 1/3 pCO2 } k for wek 5 0. (11)

Inthis diffusive thermocline limit, steady-state atmospheric pCO2 ispredictedto vary as thecubedroot of diapycnaldiffusivity. Since the degreeof saturationis independentof k in at this limit, pCO2 issimply controlled by the modulation of the thickness of the warm, carbon-depletedthermocline. The two-dimensional numerical experiments of (Archer et al., 2000)illustrate, in part,this sensitivity to diapycnalmixing rates. i.Numerical experiments of thediffusive thermocline. We mayask whether the relation- shipbetween diapycnal mixing and atmospheric pCO2 predictedin (11) holds in amore complexsetting. To test this we usean ocean general circulation and an abiotic carbon model, conŽ guredin a simple,single-hemisphere basin, and connected to a well-mixed atmosphericreservoir of CO 2.Themodel,as con Ž guredhere, is describedin more detail in (Follows et al., 2002).The total carbon budget of the ocean-atmosphere system is conservedand atmospheric pCO2 adjustswith ocean circulation according to its in  uence ontheoceanic carbon reservoir. C iscarriedas a tracerin the model and air-sea gas transfer coefŽ cientand surface alkalinity are prescribed as spatially uniform values. The model is initializedwith uniform distribution of buoyancyand C,andspun up tosteadystate.

Figure1a showsthe distribution of DpCO2, the pCO2 differencebetween the ocean and atmosphere,in the control spin up ofthemodel where k 5 5 z 1025 m2 s21 and the wind stressis set to zero everywhere. There is a broadtropical and subtropical region of outgassingassociated with the upwelling and warming of cool,carbon rich deep waters.

CO2 isabsorbed from theatmosphere at subpolar latitudes and along the path of the westernboundary current where there is strong cooling of the surface waters. In the absenceof wind forcing, the surface currents and subduction rates are relatively slow, and

DpCO2 hasmoderate values. For thecontrol experiment steady state atmospheric pCO2 is 269ppmv, arbitrarily determined by theimposedtotal ocean-atmosphere budget of carbon.

Here weseekto understand the sensitivity of atmospheric pCO2 tosmall changes in the 2003] Ito& Follows:Solubility pump of CO 2 475

Figure6. Steady state sensitivity of thermocline depth, dT ,todiapycnal mixing rate in the sector

modelin the diffusive thermocline limit (no wind forcing). Simulated thermocline depth, dT , is diagnosedfrom the steady state temperature Ž eldfollowing Park and Bryan (2000). The steady statethermocline depth scales with the cubed root of the diapycnal diffusivity, consistent with the scalingtheory. physicalparameters. The sector model is integratedto newsteady states for arangeof k spanningover two orders of magnitude but with the same buoyancy boundary conditions asthecontrol run. Simulatedtemperature Ž elds conŽ rm thecubedroot dependence of thermoclinedepth to diapycnaldiffusivity. Figure 6 showsthe relationship between k andthe simulated thermoclinedepth, dT,whichis diagnosedfrom themodeled Ž eldsfollowing the de Ž nition ofParkand Bryan (2000).

top T 2 T zdz E ~ bottom! bottom dT~x, y! 5 (12) top ~T 2 T !dz E bottom bottom

InFigure 6, thevalues of dT areobtained from zonalaverages at 30N.

Figure7 showsthe relationship between the steady atmospheric pCO2 and k. The result isinexcellentagreement with the scaling analysis of (11)with atmospheric pCO2 varying as k1/3. 476 Journalof MarineResearch [61, 4

Figure7. Steady state sensitivity of atmospheric pCO2 todiapycnalmixing rate in the sector model inthe diffusive thermocline limit (no wind forcing). Each dot in the plot represents simulations withdifferent diapycnal diffusivity, and the line is theleast square Ž ttothesepoints. Diapycnal

diffusivities, k,arevaried over two orders of magnitude.The steady state atmospheric pCO2 scales withthe cubed root of the diapycnal diffusivity, and the modeled sensitivity is in an excellent agreementwith the simple theory.

Thesector model supports the qualitative and quantitative predictions of the scaling. Sincethe simulated upper ocean currents are weak without the surface wind-stress forcing (Fig.2), the surface buoyancy distribution is close to the prescribed meridional pro Ž le, thoughthere is asmalldeparture in our simulations, and its magnitude increases with k. However,the deviations of thesurface buoyancy from theprescribed value are very small for areasonablerange of k,andthesensitivity of atmosphericCO 2 islargelydetermined by thevolume (or thickness)of the thermocline which scales as k1/3. b.The ventilated thermocline Inthe previous section we developeda simplescaling that successfully predicts the relationshipbetween diapycnal mixing and atmospheric pCO2,inanabiotic ocean in the absenceof windforcing. What is thein  uenceof windforcing on the carbon inventory of theocean and atmospheric CO 2?Themagnitude of thecarbon reservoir in theventilated thermoclineis a functionof thevolume of thermoclinewaters andtheir carbon content — see (2). Theoryand numerical models have shown that in aclosedbasin, thermocline thickness 2003] Ito& Follows:Solubility pump of CO 2 477

Figure8. A schematicdiagram for ventilated subtropical thermocline in an ocean basin. In

subtropicalgyre, we consider an idealizedpath of thewestern boundary current. dx isthe width of

thewestern boundary current, and Lx isthe width of thebasin. Northward  owhasthe velocity of 2 1 v (m s )from(0, 0) to(0, y0 ),thenit separates from the coast and moves toward ( x0 , y0 ) with thevelocity of u (m s21 ).

(or volume,assuming constant surface area) variesas the square root of theamplitude of thewind-stress forcing, t (Luyten et al., 1983):

1/2 Vt } h } wek . (13) Inan inviscid, wind-driven ocean, the thermocline waters areformed in the subduction regionsfrom wherethey are advected into the interior. As illustratedin Figure1, surface currentsare considerably swifter inthe wind-driven ocean. The residencetime of waters in themixed layer is, therefore, shorter and water parcels may be subducted while still far from equilibriumwith the atmosphere. For thewind-driven ocean we mustalso evaluate theimpact of this short residence time on thesaturation state and carbon concentration in thesubducted thermocline waters. i.What sets the C ofthe abiotic, ventilated thermocline? Figure8 depictsidealized pathwaysof water parcels in the subtropical and subpolar gyres of the northern ocean basins.In the subtropics, a waterparcel travels northward in the western boundary current, separatingfrom thewestern boundary at y 5 y0 wherethe curl of thewind stress vanishes. Thewater travels eastward to the point ( x0, y0)whereit is subductedbeneath the surface layer.After subduction,the water parcel is no longer in contact with the atmosphere, so 478 Journalof MarineResearch [61, 4 carbonis conserved, and it travels downward and southward along the trajectory indicated byadashedline. Such trajectories can be calculatedfrom thesurface wind stress explicitly (Luyten et al., 1983).Hence, for theabiotic case, the carbon stored in the subtropical thermoclineis determinedby the C concentrationat the point of subduction. We Ž rst considerthe carbonbalance in themixedlayer by integrating(5) verticallyfrom thesurface to thebase of themixed layer. For simplicity,we assumea prescribed,constant mixedlayer depth of hml.Consideringthe  uxbalanceat the base of themixed layer, we Ž ndan equation for thesurface carbon balance.

DC w DC 1 ` ~C 2 Cent! 5 2 (14) Dt hml tc where D/Dt isthe total derivative following a parcelincluding the effect of horizontal advection.Vertical advection is representedby theentrainment term on thel.h.s. of (14), whichis active only when the water is upwelling. ` is 1 if w ispositive (upwelling); 0 elsewhere(downwelling) as itisinthesubtropical gyres. Cent representsthe concentration justbelow the base of mixedlayer. We rewrite(14) in terms of DC using(6), and Ž nd an expressionfor thechange in the carbon disequilibrium, DC,followinga water parcelas it movesaround the surface ocean:

DDC w DC DCeq 1 ` ~C 2 Cent! 5 2 2 . (15) Dt hml tc Dt

Theair-sea gas transfer term is expressed as a dampingtoward equilibrium or an exponentialdecay of DC.We haveadditional forcing on ther.h.s., which is expressedas thechange of Ceq followingthe water parcel, DCeq/Dt, re ectingchanges in temperature, salinityor alkalinityof thewater parcel during its transit. This Lagrangian framework is derivedin more detail, including a treatmentof biological in  uences,by Follows and Williams(2003). Here, we assumethat alkalinity and salinity of waters areuniform in spaceand time, and Ceq variesonly with atmospheric pCO2 andsea-surface temperature. We alsoassume a steady,well-mixed atmosphere. The prescribed SST distributionis a functionof latitudeonly. Thus we maytake an idealized view in which Ceq varies only withlatitude.

DCeq ]Ceq ]Ceq 5 1 u · ¹ C , v . (16) Dt ]t H H eq ]y

Combining(15) and (16), we Ž nd a simpliŽ edequation for theevolution of DC.

DDC DC ]Ceq 1 5 2v . (17) Dt tc ]y

Here, we assumethat the entrainment term is zerosince Ekman pumping is downwardin thesubtropical gyre. Also, the meridional velocity, v,andthe gradient, ]Ceq/] y, are 2003] Ito& Follows:Solubility pump of CO 2 479 assumedto be constant.This expression (17) can be integrated analytically following the trajectoryof the water parcelin the surface mixed layer, from aninitial location in the tropicsto the point of subduction.The pathway in thesurface consists of twoparts; (1) the westernboundary current, and (2) theinterior gyre circulation. For simplicity,we assume thatthe western boundary current is purely meridional with velocity v andthe interior trajectoryis purely zonal to the point of subduction,( x0, y0),withvelocity u,asdepicted in Figure 8. Thegeneral solution for (17)is

]Ceq DC~x~t!, y~t!! 5 DC~t 5 0!e2t/tc 1 ~vt ! ~e2t/tc 2 1! (18) c ]y where t isthetime since the parcel started its transit through the western boundary current system at ( x, y) 5 (0,0)withinitial carbon anomaly DC(t 5 0). The Ž rst termrepresents the in uenceof the initial condition, which exponentially decays with time. The second termrepresents the solubility change associated with the meridional advection of awater parcel.We de Ž nethetimeinterval in whichthe parceltransits from (0,0) to(0, y0) as t0 [ y0/v,andthe transit time from (0, y0) to ( x0, y0) as t1 [ x0/u.For thisidealized pathway we Ž ndan expression for thecarbon anomaly (local disequilibrium) at the location of subduction,( x, y) 5 ( x0, y0).Weapply(18) separately to two intervals, from (0,0) to(0, y0),andfrom (0, y0) to ( x0, y0).Thecombined result is

]Ceq DC~x , y ! 5 DC~t 5 0!e2t0/tc 1 ~vt ! ~e2t0/tc 2 1! e2t1/tc. (19) 0 0 F c ]y G

DC( x0, y0)isthe degree of saturationat the location of thesubduction. Subduction may occurin various longitudes, and x0 canhave a rangeover the longitudinal width of the basin,suggesting that the magnitude of DC( x0, y0)isthe greatest near the western boundary,and exponentially decreases eastward. When water masses subduct into the thermocline, C isconserved following the parcel in this abiotic limit and in absence of diapycnalmixing. Thus, the carbon concentration of the ventilated thermocline can be expressedas C( x0, y0) 5 Ceq( x0, y0) 1 DC( x0, y0), where Ceq( x0, y0)isafunctionof localtemperature, salinity and alkalinity. We examinetwo limits of thesolution (19): the slowtransport limit where the transit time of the water parcel through the western boundarycurrent system is comparable to theair-sea equilibration timescale, and the fast transportlimit where the transit is very fast relative to air-seaequilibration. ii.Weak wind forcing and slow transport. If thewind-stress curl is suf Ž cientlyweak the transittime along the western boundary current system is much longer than the timescale 2 t0/t c for air-seaequilibration of pCO2; t0 @ tc.Inthis case, we assume e ! 1 and DC( x0, y0)becomesindependent of the initial condition. (19) simpli Ž es to

]Ceq DC~x , y ! , 2 ~vt ! e2t1/tc t @ t . (20) 0 0 F c ]y G 0 c 480 Journalof MarineResearch [61, 4

Inthis limit, the water parcel resides in the surface long enough to “forget” the initial disequilibriumat thebeginning of its boundary current transit. The form of(20)suggests that DC( x0, y0)isproportional to the product of v, tc, and ]Ceq/] y.Inthe boundary current, v ispositive (northward), tc,isset by thegas exchange coef Ž cientand carbonate chemistry,and ]Ceq/] y dependson the relationship of solubilityto temperature and the

SSTdistribution.Solubility decreases with temperature, ]Ceq/]T , 0,andthe meridional temperaturegradient, ]T/] y,isnegative in thenorthernhemisphere, ]T/] y , 0. Using the chain rule, ]Ceq/] y 5 (]Ceq/]T ) (]T/] y) . 0, thus we Ž ndapositivegradient of Ceq in thenorthern hemisphere. Thedisequilibrium at thepoint of subduction is controlledby thecompetition between integratedforcing (i.e. cooling) along the trajectory of thewater parcel and the damping effectof air-seagas exchange. Cooling along the boundary current is associated with the downstreamuptake of CO 2. Air-sea CO2  uxlagsthe air-seaheat  uxduetothedifference intimescalesbetween gas exchange and heat exchange. An intensi Ž cationof theboundary currentenhances undersaturation of theparcel due to the rapid cooling and its associated solubilityincreases. An increasein gas exchange timescale also enhances the disequilib- rium, DC,becauseof thegreater lag between the cooling and the CO 2 uptake,see (18). Assumingthat the western boundary current is passively closing the interior gyre circulation, v,issimply proportional to the subtropical Ekman pumping rate, wek. ConsideringSverdrup ’sequation(see Chapter1 and2 ofPedlosky(1996) for reference), thenorthward velocity in the boundary current is

f Lx wek v 5 (21) b dx H where dx isthewidth of the western boundary current, Lx isthelongitudinal width of the basin.The speed of the boundary current, v,isdetermined by the Ekman pumping rate. Thus,from (20),the C oftheventilated thermocline varies linearly with Ekman pumping inthisslow transport regime:

Cth 5 C~x0, y0! } 2wek t0 @ tc. (22)

Combiningthe dependencies of thermocline thickness, (13), and subducted carbon concentration,(22), on Ekman pumping, and enforcing conservation of carbon in the ocean-atmospheresystem, (2), we Ž ndfor thisslow transport (weak wind stress) limit,the dependenceof atmospheric pCO2 onthe subtropical Ekman pumping:

at 3/2 pCO2 } wek for t0 @ tc (23) iii.Strong wind forcing and rapid transport. Inthe limit of strongwind forcing, the transit ofthewaterparcel from tropicsto subduction is fast relative to theair-seaCO 2 exchange, t0 ! tc, and 2003] Ito& Follows:Solubility pump of CO 2 481

]Ceq DC~x , y ! , DC~0! 2 y e2t1/tc t ! t . (24) 0 0 F 0 ]y G 0 c Becauseof therapid advection, C islargelyunchanged by theair-sea exchange of carbon whichis too slow. The parcel also undergoes signi Ž cantcooling, so is considerably undersaturatedat the point of subduction and largely re  ectsthe initial condition at the beginningof thewestern boundary current transit:

Cth 5 C~x0, y0! , C~0, 0! t0 ! tc. (25) Inthis limit, assuming that C(0,0 )isindependent of the wind forcing, the budget of carbonin the ventilated thermocline, VthCth,ismodulatedonly by variations in thermo- 1/ 2 clinethickness, which varies as wek following(13) (Luyten et al., 1983).An increase in windforcing increases the depth of the thermocline and increases the volume of warm thermoclinewaters. Hence the ocean carbon budget is decreased and atmospheric pCO2 increases.Combining (2), (13) and (25), the steady state atmospheric pCO2 isproportional tothesquare-root of Ekman pumping in the strong wind limit.

at 1/2 pCO2 } wek for t0 ! tc (26)

Anincrease in thewind stress deepens the ventilated thermocline, and the increase in the volumeof warm, thermoclinewater decreases ocean carbon inventory, which results in an increasein atmospheric pCO2. Theslow and rapidtransport regimes are separated at acriticaltimescale where a surface waterparcel reaches local equilibrium with overlying atmospheric pCO2 undercurrent physicalconditions. This is on the order of one year. For theocean ’ssubtropicalgyres, withdimension ( y0 ; 3000km),the critical western boundary current speed marking the regimeshift is thereforeabout 0.1 m s 21,whichis ofsimilarorder to themean speed of the presentGulf stream or Kuroshio.

Inbrief summary: Atmospheric pCO2 dependson the wind-driven ocean circulation throughits control on thevolume of the ventilated thermocline and through its control on thesaturation state of subductedwaters. For relativelyweak wind forcing, pCO2 re ects 3/ 2 bothof thesein  uencesand scales as wek .For strongEkman pumping rates, the western boundarycurrent becomes very swift andthe saturation state of thewaters ofthe ventilated thermoclineno longerdepends on theresidence time of surfacewater parcels. In this fast 1/ 2 transportlimit, pCO2 scales with wek . iv.Wind-driven gyre: Numerical experiments. Dothe scalings for theventilated thermo- clinehold up in the numerical sector model? Figure 1b shows DpCO2,theair-sea difference,in a wind-drivenintegration of the model. In that case the maximum wind- stressis set to 0.2 N m 2 2 withdiapycnal diffusivity of 5 z 1025 m2 s21. As noted in (Follows et al., 2002),upwelling and outgassing are now con Ž nedto thetropics, and the subtropicalair-sea  uxchanges sign relative to the case with thermohaline forcing only. 482 Journalof MarineResearch [61, 4

Figure9. The relationship between the wind stress amplitude and the atmospheric pCO2 calculated bythe idealized GCM. Scalings(23), (26) are in excellent agreement with the modeled sensitivities.Horizontal axis represents nondimensionalized magnitudes of Ekmanpumping. The

case we k 5 1 (non 2 dim)corresponds to the simulation with the westerly wind-stress maximum of 0.2 N m22 .Spatialpattern of wind stress is prescribed, and its amplitudes are varied. The

verticalaxis is the difference in pCO2 betweenthe run withwind amplitude, t,andthe controlrun (no wind, t 5 0).

Thewestern boundary current, which is rapidlylosing heat, becomes undersaturated with

CO2.Theundersaturated water drives the downstream oceanic uptake of carbonfrom the atmosphereas predictedby thesimple theory. This is consistent with the observed uptake ofcarbon by the subtropical gyres (Takahashi et al., 1997)and more realistic models (Follows et al., 1996).The region of netocean outgassing near the intergyre boundary at mid-latitudesis due to the cyclonic circulation of the subpolar gyre feeding carbon rich subpolarwaters towarmer mid-latitudes. at We usethe numerical model to Ž ndthesteady state pCO2 for arangein amplitude of thewind stress forcing. t,themaximum wind-stress, was variedfrom 0.1N m 22 to 0.4 N m22 keepingthe spatial pattern the same. Though the theory is developed for an inviscidocean, a Ž nitediapycnal mixing rate of 10 25 m2 s21 was imposed.Total ocean andatmosphere carbon was conserved.The results of the individual experiments are depictedin Figure9 alongside the theoretical predictions for theslow, (23), and fast, (26), transportregimes, assuming the critical maximum wind-stress to be at 0.2 N m 22. The numericalmodel results are clearly consistent with the predicted scalings: When the wind 22 3/2 stressforcing is weaker than 0.2 N m ,atmospheric pCO2 scales as t . At maximum 2003] Ito& Follows:Solubility pump of CO 2 483

Figure10. Change in zonally averaged C concentrationin the sector model for moderateand strong windexperiments ( t 5 0.1 N m22 and t 5 0.2 N m22 ,respectively)with respect to the model withoutwind-forcing. Increasing wind stress forcing leads to decreasing carbon concentration and inventoryin the ventilated thermocline. Note that the deep ocean carbon concentration changes verylittle. (a) moderate —nowind,(b) strong —no wind.

22 windstress of around0.2 N m ,thesensitivity of atmospheric pCO2 becomesweaker in thenumerical experiments, suggesting a convergencewith the idealized value of t1/2. c.Upper ocean control Figure10 illustratesthe sensitivity of theoceanic reservoirs of carbonto changes in the Ekmanpumping. With increasing wind stress, ventilated thermocline C decreasesdue to theshorter residence time of water parcelsat thesurface and increasing undersaturation at thepointof subduction.In contrast there is verylittle change in thedeep ocean C (Fig. 10). at Theupper ocean controls the sensitivity of pCO2 towind-stress in strongcontrast to the sensitivityto surfaceproperties, such as temperature,which is controlledby thelarge deep oceanreservoir. Whydoes the deep ocean carbon reservoir show such a smallchange in C? The deep waters doindeedbecome increasingly undersaturated as thewind-stress forcing increases sincethe shorter surface residence time also impacts the subpolar region (Fig. 11). In the deepocean, however, the enhanced undersaturation, DC,isalmost completely compen- at satedby the increase in Ceq,thesaturation C,dueto the increase in pCO2 . Globally, changesin ocean C arebuffered, stabilizing the ocean-atmosphere carbon partitioning — see,for example(Bolin and Eriksson, 1959).

Asimpleocean and atmosphere box model illustrates the compensation of Ceq and DC whichmust hold for theglobal ocean. We de Ž netheglobal mean ocean C concentration

C 5 (VdCd 1 VthCth)/(Vd 1 Vth)(see Fig.3). From thisand (1) we mayrelate C and at at pCO2 throughmass balance.They must obey, MpCO2 1 VC 5 constant,where M is the numberof molesof gasin the atmosphere, and V 5 Vd 1 Vth isthetotal volume of the ocean.Consider small perturbations in atmospheric pCO2 andmean ocean C concentra- tion. 484 Journalof MarineResearch [61, 4

Figure11. Zonally averaged saturation state, DC (mmol kg21 ),ofthe sector model for cases (a) withoutwind forcing, (b) moderate wind forcing, and (c)strong wind forcing. Both upper and deep oceanbecome increasingly undersaturated as windstress increases due to the decreasing surface residencetime which prevents full equilibration with the atmosphere. However, the undersatura- tionof thelarge deep ocean reservoir is largelycompensated by bufferingand the increase in the saturatedconcentration. Hence deep ocean C isstabilized and insensitiveto changesin windstress forcing(Fig. 10).

at MdpCO2 1 VdC 5 0. (27)

Following(6), a perturbationin C mustbe thesum of perturbationsin Ceq and DC in the abioticlimit.

dC 5 dCeq 1 dDC. (28) Combining(28) with the de Ž nitionof the Revelle or buffer factor (Bolin and Eriksson, at at 1959), (dpCO2 /pCO2 )/(dCeq/Ceq) 5 Bu ; O(10) we Ž ndanexpressionfor thechange inglobalmean C:

C eq at dC 5 at dpCO2 1 dDC. (29) S Bu pCO2 D Combining(29) with the linearizedmass balance(27) we canevaluate the sensitivity of the oceanmean carbon concentration, C,tothesaturation state, DC: 2003] Ito& Follows:Solubility pump of CO 2 485

]C 1 5 1 2 at , 0.2. (30) ]DC MBu pCO2 1 1 1 VCeq 2

Thisrelationship tells us that,in the globally averaged, steady state, a changein saturation state, dDC, must belargely compensated by a correspondingchange in the saturation carbonconcentration, dCeq dueto increasing atmospheric pCO2.Hencethe resulting change in C ismoderate. dC ; 0.2dDC. Theeffect of undersaturation due to intense surface currents is mediated by the compensatingincrease in Ceq.Inthe three-dimensional, sector ocean model we Ž nd a signiŽ cantdecrease in upperocean C dueto increased wind forcing. However, the global constraint,(30), is facilitated by compensation between Ceq and DC inthe large deep oceanreservoir. It is the warm, upperocean waters whichdominate the sensitivity of atmospheric pCO2 tochanges in wind-stress in contrast to the more widely considered sensitivityto changes in surface properties (e.g., temperature or alkalinity) which is controlledby thecold high latitudes and deep ocean reservoir. d.Combined effects of windand diapycnal mixing: Numerical experiments Possiblyin the ocean, and certainly in ocean circulation models, the thermocline structureis signi Ž cantly in uencedby both wind and diapycnal mixing. Using the numericalmodel, we mapout the sensitivity of atmospheric pCO2 tothe combined effects ofdiapycnalmixing and wind-stress forcing in theidealized, abiotic sector model (Fig. 12). Theeffects of diapycnaldiffusion and wind-driven circulation are competitive. When diapycnaldiffusivity is large,atmospheric pCO2 isless sensitive to the variations in the windstress forcing. In this case, the upper ocean is mainly dominated by the diffusive thermocline.In contrast, when diapycnal diffusivity is suf Ž cientlysmall ( k ; 1025 m2 s21), theventilated thermocline and wind-stress forcing dominate the sensitivity of atmospheric pCO2.Scalings(23) and (26) are in excellentagreement with the numerical simulations in thelimiting regimes. The idealized scalings discussed in the previous sections correspond totheaxes of theplot in Figure12. Ingeneral, increasing either wind-stress amplitude or diapycnal mixing rates increases atmosphericCO 2 overmost of the explored parameter space. In the case of diapycnal mixing,this is dueto anincreasein thevolume of warm waters anda decreasein the mean oceansolubility of CO 2.Inthe case of wind forcing, it is due to the combination of the deepeningof theventilated thermocline and the increasing undersaturation of thermocline waters asthe transit time through the western boundary current system becomes short relativeto air-sea gas exchange times. These model results suggest that, over reasonable rangesof variability in these parameters, atmospheric pCO2 couldvary by as much as 30 ppmv. 486 Journalof MarineResearch [61, 4

Figure12. Steady state atmospheric pCO2 asa functionof diapycnal diffusivity and wind-stress forcingamplitude. Horizontal axis is the nondimensionalize dEkmanpumping, and vertical axis is the 13 powerof diapycnaldiffusivity.

5.Summary and discussion We havedeveloped a generaltheory for thesolubility pump of carbon in an abiotic ocean with a Ž xedalkalinity. For aclosedocean-atmosphere system, atmospheric pCO2 variesinversely with the oceanicbudget. The oceanic budget of carbonis controlledby the thermalstructure of the ocean which largely dictates the effective carbon loading if all water masseswere saturatedat the point of subduction.This is modulatedby thedegree of saturationof the subducted waters. Hence, for thissystem, atmospheric pCO2 varieswith the productof thermocline thickness and thermocline dissolved inorganic carbon concentration. For asimple,single-basin ocean, without wind forcing, the surface residence times are longand subducted waters areclose to equilibriumwith the overlying atmosphere. Hence pCO2 varieswith the volume of warm waters orthermocline thickness which, in this limit, scales with k1/3:thediapycnal mixing coef Ž cientto theone third power. For aninviscid 1/ 2 oceanwith wind forcing the thickness of thesubtropical thermocline scales as wek , the squareroot of the Ekman pumping rate. Surface ocean currents are swift, subduction occursbefore waters haveequilibrated with the overlying atmosphere and the ventilated thermoclineis undersaturated.Over awiderange of Ekmanpumping rates, the degree of 2/3 undersaturationscales linearly with wek.Henceatmospheric pCO2 varies as wek . Dissolvedinorganic carbon in theventilated thermocline, Cth,isreduced as thewind-stress 2003] Ito& Follows:Solubility pump of CO 2 487 forcing(and undersaturation) increases. These scalings accurately predict the sensitivities ofan ocean model of intermediate complexity: The MIT ocean model con Ž guredin a single hemispherebasin, with abiotic carbon cycle and a coupledatmospheric CO 2 reservoir. Incontrast to the response to other physical in  uences,the sensitivity to wind-stress changesis facilitatedby the upper ocean, and not the large carbon reservoir of thedeep oceans.Classical box models of theocean carbon cycle infer a dominantrole for thelarge, deepocean reservoir and high latitude oceans in modulatingthe solubility pump, and thus atmospheric pCO2.Thesensitivity to surface properties, e.g. temperature and alkalinity, is controlledby thehigh latitudes through the deep ocean reservoir. The subtropical oceans andventilated thermocline dominate the sensitivity of atmospheric pCO2 tochanges in surfacewind-stress in abiotic carbon cycle models. The intense, wind-driven circulation stronglyaffects the saturation state of both upper oceans and abyss. Increasing wind-stress leadsto increased undersaturation, a decreasedocean carbon budget, and an increase in atmospheric pCO2.However,changes in atmospheric pCO2,andequilibrium C, compen- satethose in the saturation state in the deep ocean. As aresult,the deep ocean carbon loading is largelyunchanged by the variations in the wind-stress. The change in atmospheric pCO2 is attributableto changes in the subtropical, upper ocean saturation state and carbon budget. Thetheory and models suggest a dominantand signi Ž cantrole for theupper ocean in modulatingthe response of atmospheric pCO2 tochangesin the wind stress forcing, as has occurredin past climate changes. Doubling the wind-stress leads to an increase in atmospheric pCO2 ofas much as 30 ppmv in this model. Interestingly, this infers a mechanismwhich would increase atmosphericCO 2 duringglacial climates where hemi- spherictemperature gradients and mid-latitude westerlies would likely be increased. Thisstudy used highly idealized models to betterunderstand aspects of a verycomplex system.Some of thesimplifying assumptions are signi Ž cantand the subject of continuing study.Notably, here we havefocused on the impact of changes in wind stress on the physicalstructure of theocean. We havenot discussed the sensitivity of thegas transfer coefŽ cientin orderto facilitateno-wind experiments and to focuson otheraspects of the physicaldependence. However, this is the subject of an ongoing study. Here we have focusedon anabioticocean and neglected biological in  uences.Of courseit islikely that thebiological pumps are also sensitive to changes in wind stress forcing (Boyle, 1986; 1988)and diapycnal mixing. We expectthat an approach based on theone used here will alsoprovide insight into the biological pumps and particularly their response in the subtropicaloceans, to changes in climate and physical forcing. One further limitation of thisstudy is the focus on dynamics related to ocean basins. The important region of the AntarcticCircumpolar Current and the Southern Ocean are controlled by different, or modiŽ eddynamics. We arestudying this regime separately, but ultimately a global synthesismust emerge.

Acknowledgments. TIisthankful to the Geophysical Fluid Dynamics Program at Woods Hole OceanographicInstitution since this work started during the GFD summerschool in 2001. MJF is gratefulfor support from NSF (OCE-0136609).Two anonymousreviewers and R. Williams provideduseful suggestions which improved the manuscript. 488 Journalof MarineResearch [61, 4

REFERENCES Archer,D. E.,A. Winguth,W. Broecker,R. Pierrehumbert,M. Tobisand R. Jacob.2000.

Atmospheric pCO2 sensitivityto thebiological pump in the ocean. Global Biogeochem. Cycles, 14, 1219–1230. Bacastow,R. B.1995.The effect of temperaturechange of the warmsurface waters of theoceans on

atmosphericCO 2 .GlobalBiogeochem. Cycles, 10, 319–334. Bolin,B. andE. Eriksson.1959. Changes in the carbon dioxide content of theatmosphere and sea dueto fossil fuel combustion, in Distributionof Matterin the Sea and Atmosphere, B. Bolin,ed., RockefellerInst. Press, NY, 130 –142. Boyle,E. A.1986.Deep ocean circulation, preformed nutrients, and atmospheric carbon dioxide: Theoriesand evidence from oceanic sediments, in Mesozoicand Cenozoic Oceans, Geodynamics Series, 15, AGU, 49 –59. 1988.The role of vertical chemical fractionation in controlling late Quaternary atmospheric carbondioxide. J. Geophys.Res., 93, 15701–15714. Broecker,W. S.andT.H.Peng.1974. Gas exchange rates between air and sea.Tellus, 26, 21–35. 1982.Tracers in the Sea, Eldigio Press, Lamont-Dohe rtyObservatory of Columbia University, 1 –689. 1993.Greenhouse Puzzles, Eldigio Press, Lamont-Doherty Observatory of ColumbiaUniver- sity, 1–251. Broecker,W. S.,J. Lynch-Stieglitz,D. Archer,M. Hoffmann,E. Maier-Reimer,O. Marchal,T. Stockerand N. Gruber.1999. How strongis theHarvardton-Bear constraint? Global Biogeochem. Cycles, 13, 817–820. Bryan,F. 1987.Parameter sensitivity of primitiveequation ocean general circulation models. J. Phys. Oceanogr., 17, 970–985. DOE. 1994.Handbook of Methodsfor the Analysisof theVarious Parameters of the Carbon Dioxide Systemin Sea Water, Version 2, A.G.Dicksonand C. Goyet,eds., ORNL/ CDIAC-74,1 –22. Follows,M. J.,T.Itoand J. Marotzke.2002. The wind-driven, subtropical gyres and the solubility

pump of CO2 .GlobalBiogeochem. Cycles, 16, 1113,doi:10.1029/ 2001GB001786. Follows,M. J.,R.G.Williamsand J. C.Marshall.1996. The solubility pump in thesubtropical gyre oftheNorth Atlantic. J. Mar.Res., 54, 605– 630.

Follows,M. J.andR. G.Williams.2003. Mechanisms controlling the air-sea  ux of CO2 in the North AtlanticOcean, in OceanCarbon Cycle and Climate, T. Oguzand M. Follows,eds., NATO ASI volume(submitted). Gent,P. R.andJ. C.McWilliams.1990. Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr., 20, 150–155. Gnanadesikan,A. 1999.A simple,predictive model for the structure of the oceanic pycnocline. Science, 283, 2077–2079. Goyet,C. andA. Poisson.1989. New determinationof carbonicacid dissociation constants in sea wateras afunctionof temperatureand salinity. Deep-Sea Res., 36, 1635–1654. Gruber,N., J. L.Sarmientoand T. F.Stocker.1996. An improved method for detecting anthropo-

genic CO2 intheocean. Global Biogeochem. Cycles, 10, 809–837. Iselin, C. O’D.1939.The in  uenceof vertical and lateral turbulence on thecharacteristics of waters atmid-depths.Trans. Amer. Geophys. Union, 20, 414–417.

Knox,F. andM. B.McElroy.1984. Changes in atmosphericCO 2 : In uenceof themarine biota at highlatitude. J. Geophys.Res., 89, 4629–4637. Ledwell,J. R.,A. J.Watsonand C. S.Law. 1993.Evidence for slow mixing across the pycnocline froman openocean tracer-release experiment. Nature, 364, 231–246. Luyten,J. R.,J.Pedloskyand H. Stommel.1983. The ventilation thermocline. J. Phys.Oceanogr., 13, 292–309. Marotzke,J. andJ. R.Scott.1999. Convective mixing and the thermohaline circulation. J. Phys. Oceanogr., 29, 2962–2970. 2003] Ito& Follows:Solubility pump of CO 2 489

Marshall,J. C.,A. J.G.Nurserand R. G.Williams.1993. Inferring the subduction rate and period overthe North Atlantic. J. Phys.Oceanogr., 23, 1315–1329. Marshall et al. 1997a.Hydrostatic, quasi-hydrostatic, and non-hydrostatic ocean modeling. J. Geophys.Res., 102(C3), 5733–5752. Marshall et al. 1997b. A Ž nite-volume,incompressible Navier Stokes model for studies of theocean onparallelcomputers. J. Geophys.Res., 102(C3), 5753–5766. McKinley,G., M. Followsand J. C.Marshall.2000. Interannual variability of the air-sea  ux of oxygenin the North Atlantic. Geophys. Res. Lett., 27, 2933–2936. Park,Y. G.andK. Bryan.2000. Comparison of thermally driven circulations from a depth- coordinatemodel and an isopycnal layer model, Part I. Scalinglaw sensitivity to vertical diffusivity.J. Phys.Oceanogr., 30, 590–605. Pedlosky,J. 1986.Thermocline theories, in GeneralCirculation of the Ocean, H. G.I.Abardaneland W.R.Young,eds., Springer-Verlag, NY, 55 –101. 1996.Ocean Circulation Theory, Springer-Verlag, NY, Roy,R. N.,L.N.Roy,K. M.Vogel,C. Portermoore,T. Pearson,C. E.Good,F. J.Milleroand D.M. Campbell.1993. Determination of the ionization constants of carbonic acid in sea water in salinities5 to45andtemperatures 0 to45 °C.Mar.Chem., 44, 245–267. Samelson,R. andG. K.Vallis.1997. Large-scale circulation with small diapycnal diffusivity: the two-thermoclinelimit. J. Mar.Res., 55, 223–275. Sarmiento,J. L.andJ. R.Toggweiler.1984. A newmodel for the role of theoceans in determining

atmospheric pCO2 . Nature, 308, 620–624. Scott,J. R.2000.The roles of mixing,geothermal heating, and surface buoyancy forcing in ocean meridionaloverturning dynamics, Ph.D. Thesis, Massachusetts Institute of Technology.

Siegenthaler,U. andT. Wenk.1984. Rapid atmospheric CO 2 variationsand ocean circulation. Nature, 308, 624–626. Sigman,D. M.andE. A.Boyle.2000. Glacial-interglacial variations in atmosphericcarbon dioxide. Nature, 407, 819–928. Stommel,H. 1979.Determination of watermassproperties of waterpumped down from the Ekman layerto the geostrophic  owbelow. Proc. Nat. Acad. Sci. U.S., 76, 3051–3055. Stumm,W. andJ. J.Morgan.1996. Aquatic Chemistry, 3rd Edition, John Wiley and Sons, NY, 1022pp. Takahashi,T., R. A.Feely,R. F.Weiss,R. H.Wanninkhof,D. W.Chipman,S. C.Sutherlandand

T.T.Takahashi.1997. Global Air-Sea Flux of CO 2 :Anestimate based on measurementsof sea-air

pCO2 difference.Proc. Nat. Acad. Sci., 94, 8292– 8299. Toggweiler,J. R.,A.Gnanadesikan,S. Carson,R. Murnaneand J. L. Sarmiento.2003. Representa- tionof the carbon cycle in box models and GCMs: 1.Solubility pump. Global Biogeochem. Cycles, 17(1), 1026,doi: 10.1029/ 2001GB001401. Vallis,G. K.2000.Large-scale circulation and production of strati Ž cation:Effects of wind, geometry,and diffusion. J. Phys.Oceanogr., 30, 933–954. Volk,T. andM. I.Hoffert.1985. Ocean carbon pumps: analysis of relativestrength and ef Ž ciencies

inocean driven atmospheric CO 2 changes, in TheCarbon Cycle and Atmospheric CO 2 : Natural VariationsArchean to Present,E. T.Sandquistand W.S.Broecker,eds., AGU, Washington,D.C., 99–110. Weiss,R. F.1974.Carbon dioxide in waterand sea water: The solubility of anon-idealgas. Mar. Chem., 2, 203–215. Zhang,J., R.W.Schmittand R. X.Huang.1999. The relative in  uenceof diapycnal mixing and hydrologicforcing on the stability of the thermohaline circulation. J. Phys.Oceanogr., 29, 1096–1108.

Received: 4February,2003; revised: 16June,2003.