Open-Ocean Convection' Observations, Theory, and Models

Home , Free convective layer, Isopycnal, Open ocean convection, Potential density, Shower (precipitation)

OPEN-OCEAN CONVECTION' OBSERVATIONS, THEORY, AND MODELS

John Marshall Friedrich Schott Departmentof Earth,Atmospheric, and Planetary Institut f•ir Meereskunde an der UniversitJt Kiel Sciences Kiel, Germany MassachusettsInstitute of Technology,Cambridge

Abstract. We review what is known about the convec- processis localized in space so that vertical buoyancy tive processin the open ocean,in whichthe propertiesof transfer by upright convectioncan give way to slantwise large volumes of water are changed by intermittent, transfer by baroclinic instability. Moreover, the convec- deep-reachingconvection, u lggczcu '• by w•.tc,'-'•- storms. tive dllU •C;UbLIUI. JIII•, bCi;tlCb •lC; 11UL VC;iy Ulbl. Jill ate 11UIII Observational,laboratory, and modelingstudies reveal a one another.Detailed observationsof the processin the fascinating and complex interplay of convective and Labrador, Greenland, and Mediterranean Seas are de- geostrophicscales, the large-scale circulation of the scribed,which were made possibleby new observing ocean, and the prevailing meteorology. Two aspects technology.When interpreted in terms of underlying make ocean convectioninteresting from a theoretical dynamicsand theory and the contextprovided by labo- point of view. First, the timescalesof the convective ratory and numerical experimentsof rotating convec- processin the ocean are sufficientlylong that it may be tion, great progressin our descriptionand understand- modified by the Earth's rotation; second,the convective ing of the processesat work is being made.

CONTENTS 5. Parameterization of water mass transformation in models ...... 52 Introduction ...... 1 5.1. One-dimensionalrepresentation of 1.1. Backgroundand scope...... 1 plumes ...... 53 1.2. Some preliminaries...... 3 5.2. Geostrophiceddies and the spreading . Observationalbackground ...... 5 phase...... 54 2.1. Phasesand scalesof deep convection...... 5 5.3. Putting it all together ...... 58 2.2. Major ocean convectionsites ...... 6 6. Conclusions and outlook ...... 58 2.3. Meteorologicalforcing ...... 11 . Convective scale ...... 16 3.1. Gravitational instability;"upright" 1. INTRODUCTION convection ...... 17 3.2. Convectionlayer ...... 18 1.1. Backgroundand Scope 3.3. Plume dynamics...... 22 The strongvertical density gradientsof the thermo- 3.4. Observationsof plumes in the ocean...... 26 cline of the ocean inhibit the vertical exchangeof fluid 3.5. Numerical and laboratory studiesof and fluid propertiesbetween the surfaceand the abyss, oceanic convection ...... 31 insulating the deep ocean from variations in surface 3.6. Role of lateral inhomogeneities...... 33 meteorology.However, in a few special regions (see Figure 1) characterizedby weak stratificationand, in 3.7. Complicationsarising from the equation of state of seawater ...... 36 winter, exposedto intense buoyancyloss to the atmosphere,violent and deep-reachingconvection mixes sur- . Dynamicsof mixed patches...... 38 face waters to great depth, settingand maintainingthe 4.1. Observed volumes and water mass properties of the abyss.This paper reviews observa- transformation rates ...... 38 tional, modeling,laboratory, and theoreticalstudies that 4.2. Mixed patchesin numerical and have elucidatedthe physicsof the convectiveprocess laboratory experiments...... 42 and its effect on its larger-scaleenvironment. 4.3. Theoretical considerations ...... 44 In the present climate, open-oceandeep convection 4.4. Restratificationand geostrophic occursonly in the Atlantic Ocean: the Labrador, Green- eddy effects...... 49 land, and MediterraneanSeas (Figure 1), and occasion-

Copyright1999 by the AmericanGeophysical Union. Reviewsof Geophysics,37, 1 / February1999 pages 1-64 8755-12 09/99/98 RG-02 73 9 $15.00 Papernumber 98RG02739 el ß 2 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

•o

26.8 •o

26.6 •O o •6.½ I

40ø 20ø 0ø convectionobserved sections 'Bravo'

Figure 1. The major deep convectionsites of the North Atlantic sector:the Labrador Sea (box a), the GreenlandSea (box b), and the westernMediterranean (box c). Detailed descriptionsand discussionsof the water mass transformationprocess occurring in the three "boxes" are reviewed here. To indicate the preconditionedstate of early winter, the potential densityat a depth of 100 m is shownfor November from the climatologicaldata of Levituset al. [1994b] and Levitusand Boyer[ 1994].Deep-reaching convection has been observedin the shadedregions.

ally also in the Weddell Sea [see Gordon, 1982]. Con- Geologists speculate about possible North Pacific vection in these regions feeds the thermohaline Deep Water formationin pastclimates (for example,see circulation, the global meridional-overturningcircula- Mammerickx [1985]). There is some evidencefor en- tion of the ocean responsiblefor roughly half of the hancedconvection in the North Pacificat the last glacial polewardheat transportdemanded of the atmosphere- maximum(the •4C age reduction observed by Duplessy et oceansystem [see Macdonald and Wunsch,1996]. Warm, al. [1989], for example). However, the patterns of evi- salty water is drawn poleward, becomesdense in polar dence are contradictory,and as yet, there is no consen- seas,and then sinks to depth and flows equatorward. sus [see Keigwin, 1987; Curry et al., 1988; Boyle, 1992; Water massesmodified by deep convection in these Adkins and Boyle, 1997]. small regionsare taggedwith temperature and salinity In this review we discussthe dynamicsof the water valuescharacteristic of them (togetherwith other tracers masstransformation process itself, and its effect on the suchas tritium from the atomicweapon tests and freons stratification and circulation of its immediate environ- from industrialand householduse), allowingthem to be ment. Some of the relevant fluid mechanics, that of tracked far from their formation region. convectionin "open" domains,is reviewedby Maxworthy 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 3

[1997]. Our scope here is more specificallyoceano- traordinary measuresare taken, only Rayleigh numbers graphic and similar to that of Killworth [1983]. Since in therange 109-10 •6 are attainable in thelaboratory or Killworth's review, however, there has been much in the computer,compared with 1026 in the ocean[see progressin our understandingof the kinematics and Whiteheadet al., 1996]. However, when laboratory and dynamicsof ocean convectionthrough new resultsfrom numerical experimentshave been used in concert and field experiments,through focused laboratory experi- scaledfor comparisonwith the observations,they have ments, and through numerical simulation. We bring led to great insight. things up to date and draw together threads from new It is interestingto note how little the developments observations,theory, and models. that will be describedhere have been influenced by Observationsof the processesinvolved in open-ocean "classicalconvection studies" that trace their lineage deep convectionbegan with the now classicalMediter- back to "Rayleigh-Benard"convection [Rayleigh, 1916; raneanOcean Convection (MEDOC) experimentin the Benard, 1900]. In the ocean the Rayleigh number in Gulf of Lions, northwesternMediterranean [MEDOC convectingregions is many orders of magnitudegreater Group,1970]. Rapid (in a day or so) mixingof the water than the critical value, and the convectionis fully turbu- column down to 2000 rn was observed.Strong vertical lent with transfer properties that do not depend, we currents,of the order of 10 cm s-1 associatedwith believe, on molecular viscositiesand diffusivities(see convective elements were observed for the first time section3.3). Even more importantly,the convectivepro- [Stommelet al., 1971]. Observationsof convectionprior cessin the oceanis localizedin space,making it distinct to MEDOC were limited to descriptionsof hydrostatic from the myriad classicalstudies of convectionrooted in changesand timescalesestimated from changesin the the Rayleigh problem (convectionbetween two plates inventoryof water massproperties. Since MEDOC, and extendinglaterally to _+•). As one might anticipate, particularly in the past decade, new technologieshave edge effectsand baroclinicinstability come to dominate led to different kindsof observationsand deeperinsights the evolvingflow fieldsand, as describedin section4, are into the processesat work. Moored acousticDoppler a distinctiveand controllingfactor in ocean convection. current profilers(ADCPs) were deployedin a convec- Finally, one of the goalsof the researchreviewed here tion regime over a winter period to documentthe three- is to improve the parametric representationof convec- dimensional(3-D) currents occurringin conjunction tion in large-scalemodels used in climate research,in with deepmixing. From a first ADCP experiment,Schott which one cannot,and doesnot wishto, explicitlyresolve and Leaman [1991] determined the existenceof small- the process.Such models are used to studythe general scaleplumes during an intensecooling phase in the Gulf circulation of the ocean and, when coupled to atmo- of Lions convectionregime. The downwardvelocities in sphericmodels, the climate of the Earth. Thus in section theseplumes ranged up to 10cm s -•, andthe horizontal 5 we review progressbeing made in that area. Conclud- plume scalewas only about 1 km. Subsequently,exper- ing remarks are made in section 6. iments in the Greenland Sea [Schottet al., 1993] and again in the Gulf of Lions [Schottet al., 1996] substan- 1.2. Some Preliminaries tiated the existence,scales, and physical role of the The ocean is, in most places and at most times, a plumes.These recent observationsof plumes(reviewed stablystratified fluid driven at its upper surfaceby pat- in detail in section3) have servedto narrow down the terns of momentum and buoyancyflux associatedwith time and space scalesinvolved in water masstransfor- the prevailing winds. The buoyancyforce acting on a mation and the nature of the processesat work. water parcel in a columnis determinedby its anomalyin Along with, and in large part inspired by these new buoyancy: observations, there has been renewed interest in laboratory and numerical studiesof rotating convection[see b = -17(P'/Po) (1) Jones and Marshall, 1993; Maxworthy and Narimousa, 1994]. Two aspectsmake ocean convectioninteresting where !7 is the accelerationdue to gravity and from a theoreticalpoint of view. First, the timescalesof the convectiveprocess in the ocean are sufficientlylong P• -- P -- Pamb that it may be modifiedby the Earth's rotation; second, is the differencein the densityof the particle relative to the convectiveprocess is localizedin spaceso that ver- that of its surroundings,Pamb, and P0 is a constantref- tical buoyancytransfer by upright convectioncan give erencedensity equal to 1000kg m-3. In the ocean, way to slantwisetransfer by baroclinic instability.Labo- complicationsarise becausethe densityof seawatercan ratory and numerical studiesof rotating convectionmo- depend in subtle ways on (potential) temperature O, tivated by the oceanographicproblem have led to ad- salinityS, and pressurep [see l/eronis,1972]: vancesin our understandingof the generalproblem (see section3). Numericalexperiments are presentedin this p - p(O, S, p) (2) review in the same spirit as those in the laboratory exceptthat a numericalfluid is used rather than a real However, often in theoreticalstudies a simplifiedequa- one. Both approacheshave their limitations.Unless ex- tion of state is adopted of the form' 4 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

TABLE 1. Typical Values of c% and [5s as a Function of of a fluid parcel(as a resultof gravitywaves, turbulence, Potential Temperature O, Salinity S, and Pressurep for or convection)is sufficientlylarge. Thermobariceffects Seawater may be an important factor, particularlyin the Green- land and Weddell Seas. Labrador Greenland Mediterranean Sea Sea Sea The vertical stabilityof the water column is givenby the Brunt-Vfiisfilfifrequency Sl,ll, face Oo,øC 3.4 - 1.4 13.7 N 2= Ob/Oz (4) c•o,x 10-4 K- ] 0.9 0.3 2.0 So, psu 34.83 34.88 38.35 a measureof the frequencyof internal gravitywaves. In [•s, X10-4 Psu-• 7.8 7.9 7.6 stablystratified conditions, N 2 > 0; if N 2 < 0, convec- Depth of 1 km tive overturning ensues.Profiles of N typical of the 0o, øC 2.7 - 1.2 12.8 convectionsites (together with 0 and S) are shownin C•o,X10 -4 K- ] 1.2 0.7 2.3 Figure2. It isuseful to normalizeN byfo= 10-4 S-], a So, psu 34.84 34.89 38.4 typicalvalue of the Coriolisparameter, a measureof the [3s,X 10-4 psu-• 9.0 9.2 8.5 frequencyof inertial waves.We seethat N is positiveat See equation (3). all levels in the column, that N/f falls to about 5 in the deep ocean,but that in the near surfacelayers N/f can exceed100. In the upper kilometer of the ocean,N/f is p = p0[1-- oto(O-- 00) + [3s(S- So)] (3) 30-50, correspondingto a gravitywave period of 30 min where 0% and [•s are thermal expansionand haline or so and a gravitywave phasespeed of a few metersper contractioncoefficients, respectively, and 0o and SO are second. reference temperature and salinities.Typical values of The distance a gravity wave travels in an inertial 0%and [•s are givenin Table 1 as a functionof 0o, So, period, as measuredby the Rossbyradius of deforma- and pressure.To the extent that they can be taken as tion, is given by constant,the governingequations can be entirelyrefor- Lp- NH/fo (S) mulated in terms of a buoyancyvariable and buoyancy forcing.However, particularlyat low temperaturesthe whereH is the depthof the ocean.In the northernNorth thermal expansioncoefficient varies strongly with 0 and Atlantic,L ptakes on a meanvalue of 10km or so[e.g., p; it becomessmaller at lower temperaturesand in- seeEmery et al., 1994].In deepconvection sites where, as creaseswith depth,especially in the GreenlandSea (see a result of recurringconvection, the ambient stratifica- the middle columnof Table 1). The excessacceleration tionis muchreduced, L p is assmall as a fewkilometers of a parcelresulting from the increasein o•with depth, and setsthe scaleof the often vigorousgeostrophic eddy the thermobariceffect (see section3.7), can resultin a field that is commonlyobserved. At scalesgreater than destabilizationof the water column if the displacement L p the Earth'srotation controls the dynamicsand

LABRADOR SEA GREENLAND SEA NW MEDITERRANEAN 0 50 100 N 150 0 50 N 100 0 ( 10'4 S'1 ) 50 N 100 34.0I I 34.5 I S 3 d.0 34.4I 34.6 I 34.8 S 35.0 38.0 38.2 38.4 S 38.6 rn f-•'.... -\, rn .'•...... - ' ½ , "'

lOOO7N - 1000

oooi , I i, .oo: 1.5 2.0 2.5 3.0 (9 3.5 -2.0 -1.0 (9 0 12.5 13.0 13.5 (9 '14.0 27.2 27.4 27.6 27.8 Oe 27.8 27.9 2 .0 28.1 Oe 2 .0 2 .5 29.0 6e 29.5

Figure 2. Climatologicalprofiles of potential temperature,salinity, potential density,and Brunt-Vfiisfilfi frequencyfrom the convectionsites shown in Figure1. (a) LabradorSea, station Bravo. (b) GreenlandSea, near 75øN,5øW. (c) Gulf of Lions,near 42øN,5øE. 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 5 geostrophicbalance pertains. On scalesmuch smaller thanm p, however,balanced dynamics break down (see Marshallet al. [1997a]for a discussionof the breakdown of the hydrostaticapproximation). The surface layers of the ocean are stirred by the winds and undergo a regular cycle of convectionand restratificationin responseto the annual cycleof buoyancyfluxes at the seasurface (see the detaileddiscussion in section2.3). The buoyancyflux is expressedin terms of heat and fresh water fluxes as

= -- -- • + po[3sS(E- P) (6) Po Cw whereCw is the heat capacity of water (3900 J rg -1 K-•), • is the surfaceheat loss,and E - P representsthe net freshwater flux (evaporationminus precipitation). The magnitudeof the buoyancyflux 03 plays an important role in the developmentof dynamicalideas presented in this review; it has units of meters squared per second cubed,that of a velocitytimes an acceleration.Over the interior of the ocean basin, heat fluxesrise to perhaps 100W m-2 in winter,and E - P is perhaps1 m yr-•, implyinga buoyancyflux of --•10-8 m2 s-3. For stratification typicalof the upper regionsof the main thermocline, mixed layers do not reach great depth when ex- Figure 3. Schematicdiagram of the three phasesof open- posedto buoyancyloss of thesemagnitudes, perhaps to oceandeep convection:(a) preconditioning,(b) deep convec- severalhundred meters or so (seethe contoursof winter tion, and (c) lateral exchangeand spreading.Buoyancy flux mixed-layerdepth in the North Atlantic presented by throughthe sea surfaceis representedby curly arrows,and the underlyingstratification/outcrops is shownby continuouslines Marshallet al. [1993]).At the convectionsites shaded in The volume of fluid mixed by convectionis shaded. Figure 1, however,the stratificationis sufficientlyweak, N/f • 5-10, and the buoyancyforcing is sufficiently strong,often greater than 10 -7 m2 s -3, correspondingto schematicallyin Figure 3: "preconditioning" on the heatfluxes as high as 1000 W m-2, thatconvection may large-scale(order of 100 km), "deep convection"occur- reach much greater depths, sometimesgreater than 2 ring in localized,intense plumes (on scalesof the order km. This review is concernedwith the dynamicalpro- of 1 km), and "lateral exchange"between the convection cessesthat occurin thesespecial regions, which resultin site and the ambient fluid through advectiveprocesses the transformationof the propertiesof large volumesof (on a scale of a few tens of kilometers). The last two fluid and set the propertiesof the abyssalocean. phasesare not necessarilysequential and often occur In section2 we review the observationalbackground; concurrently. eachconvection site hasits own specialcharacter, but we During preconditioning(Figure 3a) the gyre-scale emphasizecommon aspects that are indicativeof m•ch- cycloniccirculation with its "doming"isopycnals, brings anism. In section 3 we discussthe convectiveprocess weakly stratifiedwaters of the interior closeto the sur- itself, and in section4 we discussthe dynamicsof the face. The potential density at a depth of 100 m in a resulting homogeneousvolumes of water. Finally, in Novemberclimatology is contouredin Figure 1, showing section5, we discusshow one might parameterize the the preconditionedstate over the North Atlantic. Buoy- water masstransformation process in large-scalemodels. ancyforcing associatedwith the prevailingmeteorology then triggersconvection. As the winter seasonsets in, vigorousbuoyancy loss erodes the near-surfacestratifi- 2. OBSERVATIONAL BACKGROUND cation of the cyclonicdome, over an area of perhaps several hundred kilometers across,exposing the very 2.1. Phasesand Scalesof Deep Convection weakly stratified water mass beneath directly to the Observationsof deep convectionin the northwestern surfaceforcing [Swallow and Caston,1973]. Subsequent Mediterranean,the most intensivelystudied site (see, cooling events may then initiate deep convection in for example,the MEDOC Group[1970], Gascard [1978], which a substantialpart of the fluid columnoverturns in and Schottand Leaman [1991]),suggest that the convec- numerousplumes (Figure 3b) that distributethe dense tive processis intermittent and involvesa hierarchyof surface water in the vertical. The plumes have a hori- scales.Three phasescan be identifiedand are sketched zontal scale of the order of their lateral scale, -<1 km, 6 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

up toward the surfaceso that they can be readily and directly exposedto intense surfaceforcing. This latter condition is favored by cyclonic circulation associated with density surface, which "dome up" to the surface (see Figures3a and 1). Whether and when deep convectionthen occursde- pendson the seasonaldevelopment of the surfacebuoyancy flux with respectto the initial stratificationat the beginningof the winter period and on the role of lateral .eddies advection.Not only is the integral buoyancysupply im- (..,10 km) portant, but so is its timing. An integral buoyancyloss that may have resultedin deep convectionwhen concen- Figure 4. Lateral scalesof the key phenomenain the water trated in a few intensewinter stormsmay not yield deep masstransformation process: the mixed patch on the precon- mixed layers if distributed evenly over the winter ditioned scale created by plumes together with eddies that months. In the latter case, lateral advection may have orchestratethe exchangeof fluid and propertiesbetween the time to draw stratifiedwater into the potential convec- mixedpatch and the stratifiedfluid of the periphery.The fluid being mixed is shaded;the stratifiedfluid is unshaded. tion site from the periphery and stabilizeit. It is perhapsnot surprising,then, that as the instru- mental record of the interior ocean lengthens,it is be- withvertical velocities of up to 10 cm s-• [Schottand comingclear that deep-water formation is not a steady Leaman, 1991;Schott et al., 1996]. In concertthe plumes state processthat recurs every year with certainty and are thought to rapidly mix propertiesover the precon- regularity.The intensityof convectionshows great vari- ditioned site, forming a deep "mixed patch" rangingin ability from one year to the next and from one decadeto scale from several tens of kilometers to >100 km in another [seeDickson et al., 1996]. diameter.(The MEDOC Group [1970] calledthe mixed We now briefly review the main featuresof the three patch a "chimney,"a name that is still in commonuse major open-oceanconvection regimes: the Mediterra- today. However, the analogy between a deep mixed nean, Greenland and Labrador Seas. patch and a chimneyis misleadingbecause, as we shall 2.2.1. Labrador Sea. The cycloniccirculation of see,there is very little vertical massflux within the patch. the Labrador near-surfacecirculation is set by the West For this reasonwe prefer not to usethe name chimney.) Greenland Current and the Labrador Current, shallow Withthe cessation ofstrong forcing, or if thecooling currents carrying cold, low-salinity water around the continuesfor manydays, the predominantlyvertical heat LabradorSea (Figure 5). Below,higher-salinity Irminger transfer on the convectivescale gives way to horizontal Sea Water enters in the north on a cyclonicpath, as is transfer associatedwith eddying on geostrophicscales indicated schematicallyin Figure 5. The doming of the [Gascard,1978] as the mixed patch laterally exchanges upper layer, as expressedin the topographyof the {ro = fluid with its surroundings(see Figure 3c). Individual 27.5 surface,is also shownin Figure 5. In the southeast, eddiestend to organizethe convectedwater in to coher- the northwesternloop of the North Atlantic Current ent lensesin geostrophicbalance. The mixed fluid dis- transportswarm water past the exit of the Labrador Sea. perses under the influence of gravity and rotation, It is associatedwith a deepening of the (ro -- 27.5 spreadingout at its neutrallybuoyant level and leading, isopycnalof some 300 m toward the southeast,and it on a timescaleof weeks to months,to the disintegration occasionallysheds eddies that leave their water mass of the mixed patch and reoccupationof the convection propertiesin the region.Below 3000 m the deepwestern siteby the stratifiedfluid of the periphery.The hierarchy boundarycurrent (DWBC), suppliedin the main by of processesand scalesinvolved in the water masstrans- Denmark Strait overflow waters, passesthrough the formation processare summarizedin Figure 4. Labrador Sea steeredby topography. The stratificationof the preconditionedstate is three- 2.2. Major Ocean ConvectionSites layered(a verticalprofile at oceanweather ship Bravo is The observationssuggest that there are certain fea- shown in Figure 2a, and a salinity sectionis shown in tures and conditionsthat predisposea region to deep- Figure 6). The surfacelayer is fresh,perhaps the result reaching convection.First, there must be strong atmo- of lateral eddy transport from the shallow boundary sphericforcing because of thermal and/or haline surface currentson the periphery (see section4.4). Below, at fluxes.Thus open-oceanregions adjacent to boundaries --•200-700 m, Irminger Sea Water causesa weak interim are favored, where cold and dry winds from land or ice temperatureand salinitymaximum (Figure 2a), stronger surfacesblow over water, inducing large sensibleheat, in the northernthan the southernLabrador Sea (Figure latent heat and moisture fluxes. Second, the stratifica- 6). Underneath, down to 2000 m, there is a layer of tion beneath the surface-mixed layer must be weak near-homogeneousLabrador Sea Water (LSW), formed (madeweak perhaps by previousconvection). And third, in previouswinter convection,which recirculatesin the the weakly stratified underlyingwaters must be brought westernbasin (Figure 6). The bottom is coveredby cold 37, 1 /REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 7

64 • --

60 ø

ISW Figure 5. Circulation schematic showing the cycloniccirculation and preconditioningof the Labrador Sea convectionregime. The depth of B the (ro = 27.5 isopycnalin the early winter is contoured in meters. The warm circulation branches of the North Atlantic Current and 55 ø Irminger Sea Water (ISW), and the near-surface, cold, and fresh East/West Greenland and Labrador Currentsare also indicated.The posi- 150 tion of Bravo is labeled "B." It is important to 200 emphasizethat this is a circulationschematic; in reality, the circulationis highly time dependent and comprisesa vigorouseddy field on the de- 400 formation radius (---7 km). 50"

46 60 o 50 ø 40 ø W •.• cold,fresh .,,•• warm,salty ß station"Bravo" ,.-,,,--,,• ISW= IrmingerSea Water depthof 60 :--- 27.5 convectionobserved, 1978 .... w .. AR7 section

and relativelyfresh Denmark Strait OverflowWater that lateral extent of the convectionregime during the con- circulatescyclonically around the Labrador Sea, leaning vectiveprocess itself, at the height of winter. The central againstthe deep topographicslope. At 2500-3200 m an Labrador Sea is ice-free in winter, and so ice and brine intermediatesalinity maximum (also apparent in Figure releaseprobably do not play a primary role in the gen- 6 far out into the Atlantic) is indicativeof water from the eration of deep convection.However, the ice plays an Gibbs Fracture Zone with Eastern Basin Mediterranean indirectrole becauseit is carriedinto the precondition- Water admixtures. ing cyclonicflow, either from the East Greenland Cur- Deep convectionin the central Labrador Sea in late rent or through the Barents Sea, and may modify the winter has been deducedfrom the continuoushydro- preconditioningstability (Figure 6). graphic observationsof weather ship Bravo [Lazier, The water massesentering the upper part of the 1973] and observedin the shadedregion in Figure 5 by DWBC suggesta secondLabrador Sea source, located Clarke and Gascard [1983]. The "products"of deep in the vicinityof the southwesternmargin [Pickart, 1992]. convectionare evident in Figure 7, which showsdata Its high anthropogenictracer content relative to LSW from a hydrographicsection taken during summer1990, suggeststhat this water mass drains into the DWBC running through Bravo, across the Labrador Sea to more quicklythan the LSW, where it forms the shallow- Greenland. We see an extensivemixed patch of fluid est layer. Direct evidencefor its formation, however,has extendingdown to a depth of 2 km, presumablystirred not yet been found. by convectionin the previouswinter, but "capped"at the Water masses formed in the Labrador Sea can be surfaceby a shallow stratified layer of a few hundred traced in to the North Atlantic at depths down to meters in depth. However, little is known about the 2000 m. The salinityminimum created in Labrador Sea 8 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

Atlantis II, Jan-April 1964, Salinity ..... : ..... : ß :..: : : :. •

,•ß : •34.,92.•: ):••.s••'•, •.98: •: • •, :: : 1 ooo

2000 ,': ß . . 34.94i. ' ' 3494'•" ::: :: ' • ' ":: ' ß , .'

3000 . ,:.' ! Figure 6. (top) Salinity distribution and ' 2 Q .... • • ' -- 34.92• ' /' I (bottom) Brunt-Vfiisfilfifrequency, N along 4000 •_•,. ß , ?.•,2 . , , , '. -,•-. %-I a sectionmade by Atlantis II in February 46øW 42 ø 38 ø 34 ø 1964,running from the exit of the Labrador Sea to the central North Atlantic (as BuoyancyFrequency (x 10-4 s -1) marked in Figure 1). The sectionreveals a minimum of salinity and stability in the depth range 1100-1800 m, a consequence g• ".,.: :::.: :"• i' i: •'-•ø'•..'T'ø?-i i •1[ i .•:'•':• i :_ of Labrador Sea convection. ;,•-.-•.'.:•' .•'.10._•• ß ' ' 20'-- ' '-• ' ...... 1000

•.2000 • ...."7"'-•. 1•)' ß ' ' .10.---',•.._.r•;. •.'. 10q -' ß . ' ' ß ' ' 10 ..: • ß .- ß

3000

4000 ' ' ' ' ' ' 10• 46øW 42 ø 38 ø 34 ø

convectioncan be seensliding down from approximately resemblesthe Labrador Sea of the beginning of the 1200 to 1800 m alongthe extentof the sectionin Figure century[see LabSea Group, 1998]. 6. Towardthe east,salinity increases as a resultof the 2.2.2. Greenland Sea. The Greenland Sea has as- influence of Mediterranean waters. The core of the pects in common with other convectingseas but also salinityminimum is markedby low stabilityof only about differsbecause of the importantrole of ice in precondi- N • 5f and correspondinglylow potential vorticity tioning.The warm water branchof the cycloniccircula- [Talleyand McCartney,1982]. tion in the GreenlandSea (Figure8) is composedof the Finally,it shouldbe emphasizedthat the propertiesof northward flow of warm, saline Atlantic Water in the Labrador Sea Water are far from constant[see Lazier, Norwegian-AtlanticCurrent that sendsbranches west- 1988, 1995; Dicksonet al., 1996]. It appearsthat LSW ward into the interior and then continuesas the Spits- was cold and fresh at the start of the century,character- bergen Current through Fram Strait into the Arctic isticof the then prevailingcold conditions.After warm- Ocean. The southward flow of cold, fresh water out of ing throughthe 1930s,LSW reachedits twentiethcen- the Arctic Ocean is carried by the East Greenland Cur- tury extremein the early 1970s.Since then we haveseen rent, which sendsan eastwardbranch out into the inte- increasinglyintense winters, and the O-S trajectoryof rior, the Jan Mayen Current alongthe Jan Mayen Ridge, LSW has moved toward colder, fresher conditions,yet and a second branch further south, the East Iceland nearly without change in potential density!The early Current.The cycloniccirculation is associatedwith dom- 1990spresented us with, once again,wonderfully deep ing indicatedin Figure 8 by the depth of the •o - 27.9 convection,which appears now to be on the wane(mixed surface;it risesfrom >200 m at the peripheryto <50 m layersonly reacheda few hundredmeters in the winter in the central Greenland Sea. The stratification in the of 1998).At the end of the twentiethcentury the system center(Figure 2b) is three-layered:on top, thereis a thin 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 9 layer of Arctic SurfaceWater originatingfrom the East 26 24 23 22 21 20 19 18 17 16 15 14 13 12 10 Greenland Current. Underneath, a layer of Atlantic Intermediate Water existssupplied from the southeast, below which residesthe weakly stratified Greenland Sea Deep Water, the product of previousconvection events. The role of ice appearsto be decisivein the precon- •'-•1500 ditioning of Greenland Sea convection:in early winter the ice first spreadseastward across the central Green- land Sea, and brine rejectionunder the ice increasesthe 2500 surface layer density [Roach et al., 1993]. The mixed layer under the ice coolsto the freezing temperature of -1.9øC anddeepens by about1 m d-• [Schottet al., 3500 55o 56o 57o 58o 59o 60øN 1993] to about 150 m in mid-January.Later in the winter 26 24 23 22 21 20 19 18 17 16 15 14 13 12 10 season,typically late January,the ice formsa wedge(the

Is Odden [Vinje, 1977; Wadhamset al., 1996]) extending 500, far out toward the northeast,and enclosingan ice-free bay, the "Nord Bukta" (Figure 8). This ice-free bay is thought to be largely a result of southwardice export that is due to strongnortherly winds [Visbeck et al., 1995]. Preconditioning continues through February with mixed-layerdeepening in the Nord Bukta, to 300-400 m, induced by strong winds that blow over the ice. Finally, typicallyin March, preconditioningis far enough advancedthat deep convectionin the Nord Bukta may developwhen the meteorologicalconditions are favor- 55o 56o 57o 60ON able. However, during the past decade,deep convective 26 24 23 22 21 20 19 18 17 16 15 14 13 12 10 activityin the Greenland Seawas weak, so this sequence of eventsis based on the evidenceof only a few occur- 5OO rences.The lateral scaleof deep, mixed regimesin the Greenland Sea appearsto be coupled to that of the Is Odden. Only once, in 1988, has a mixed patch been ?--1500 observed[Sandyen et al., 1991] when the Is Odden was closed. When observations of convection were available in the past decade, convection went down only to 2500 --•1500-mdepth [Rudelset al., 1989; Schottet al., 1993]. However, tracer evidence[Smethie et al., 1986] indicates that deepwater (>2000 m) ventilationof the Greenland 35OO Sea from the surface must have occurred at previous 55o 56o 57o 58o 59o 60øN times. Figure 7. Sectionsof (top) potential temperature,(middle) 2.2.3. NorthwesternMediterranean. The cyclonic salinity,and (bottom) potentialdensity along the sectionin the circulation around the northwestern Mediterranean ba- Labrador Sea marked in Figure 5. Data from R/V Dawson, sin, marked schematicallyin Figure 9, originates as July 1990. Courtesyof Bedford Institute of Oceanography(A. boundarycurrents on both sidesof Corsica[Astraldi and Clarke, personalcommunication). Gasparini,1992] and followsthe topographywestward as the Northern Mediterranean Current, feeding into the Catalan Current east of Spain.South of the dome there Water (WMDW). The cycloniccirculation of the region is sluggisheastward flow, marked by the BalearesFront is indicatedby the doming of the tro = 28.8 isopycnalas during part of the year [Millot, 1987]. derived from historical data (Figure 9). The cyclonic The water mass distribution in the western Mediter- circulation has maximum transport in winter and is raneancomprises three layers(Figure 2c). At the surface thoughtto be largelydriven by the curl of the wind stress the water is of modified Atlantic type, originatingfrom [e.g., Heburn, 1987]. The winter transport maximum the inflow through the Strait of Gibraltar. At 150- to could also be a consequenceof widespread cooling, 500-m depth a warm, salty layer is found, Levantine inducing density gradients that enhance the baroclinic IntermediateWater (LIW). LIW is formed by shallow cyclonic flow. Similarly, enhanced coastal fresh water convection in the eastern Mediterranean Basin and then input in late winter can further enhance density gradi- slowly propagatesinto the western basin through the ents and thence cyclonic flow. There are two strong, Strait of Sicily. Below the LIW layer, the basin is filled cold, dry offshorewinds in winter: the tramontaneorig- with near-homogeneousWestern Mediterranean Deep inating from the Pyrenees to the northwest, and the 10 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

80øN 40øW 30 ø 20 ø 10 ø 0 o 10 ø 20 ø 30øE

75 ø :,

70 ø

20' W 10 ø 0 o 10OE

cold fresh -- ,.._ warm,salty , depth of 6e=27.9 ...... ice edge (March '89) convection 1989 ß GSM station

Figure 8. Schematicof the circulationof the Greenland Sea, showingthe warm water flow of the Norwegian Atlantic Current and its recirculation,and cold water flowsof the East Greenland Current and Jan Mayen Current that constitutethe cycloniccirculation. Doming is indicatedby the depth of isopycnalo% = 27.9, and the Is Odden is markedby the positionof the ice edge (dotted) in March 1989 (see text for details)."GSM" is the location of repeated moored deployments.

mistral, blowing out of the Rhone valley. The center of tion event [Leaman and Schott,1991], which was in the the preconditioningdome (Figure 9) lies directlyin the processof being "capped"(see section4.4) when the path of the mistral,and tramontaneoutbursts can reach mid-Februarymistral triggereddeep convectiona sec- there also.An additionalfactor that might help localize ond time. Figure 10 showsthe doming in the density the preconditioneddome may be the generationof Tay- distributionalong a meridionalsection through the Gulf lor columnsover the "Rhone fan," a topographicfeature of Lions during preconditioningof winter 1991-1992 protruding from the continentalslope far out in to the convectionand the homogeneouspatch throughoutthe Gulf of Lions [Hogg,1973]. upper 1500 m after the onset of deep convectionin Typically,the integratedheat lossover the courseof February 1992. The near-surfacedensity gradients at the winter has erasedthe buoyancyof the surfacelayer by northern and southernlimits of the patch indicate the about mid-February. The horizontal extent of mixed presenceof a rim current around it [Schottet al., 1996], patchesfor 1969, 1987,and 1992are markedin Figure 9. as is discussed in section 4.4. They were all observedduring the secondhalf of Feb- Convectionto somewhatshallower depths occasion- ruary. However, in 1987 an earlier strong mistral on ally occursin the elongateddome to the eastof the Gulf January10-11 had alreadyinduced a first deep convec- of Lions, as was recentlyreported by Sparnocchiaet al. 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott:OPEN-OCEAN CONVECTION ß 11

43 ø ':':':'::ß ---•1 --•'.. --"•'.!" ' ....'"'::'....•.. '•"...... "" __.__.__/'

,.• '-:',..:.:""....• ,•.f.'•'•Z.;-g•o 7.?•_ •...•,•.•• - • • -4L--/ • / / ":':::::::::::::::::::::::::::::::::::::::::::::::: .....' ..... ' i!i!:.i::...•..,. i. •t• oO• •_ '• • / _,_- '--':'::i:!:.'.:i:i:i:i:i:i:!:i:ii:i:i:i:i:i:i:i:i:i:!:i:i:i:i.'.::i::.'i:i..' '

42"

.... .,.., • ...... ' :: 41 ø ...... ,

3 ø E 4 ø 5 ø 6 ø 7 ø 8 ø 10 ø A2 J

16 - 21 Feb '69 5ø E-section 1991/92 eT6 extents...... of17- 23 Feb '87 preconditioning:I,,,--=-,,iCorsica transport array I•-L7,. ADCP-triangle convectioneeeeeee 18-regime' 22 Feb '92 depthof 6e=28.8 le,A;3.•'•••42ON, 5OE

Figure 9. Circulationand convectionconditions of the northwesternMediterranean. Shownare depthsof the isopycnalsurface cr o = 28.8kg m-3 (courtesyG. Krahmann)for thebeginning of winter,indicating the cyclonicdoming; the resultingboundary circulation by schematiccurrent vectors,including the weaker offshore branchingto the southwest;and extents of deep mixed patchesas observedin February 1969 (dashed),1987 (large dots), and 1992(circled small dots). Also markedare positionsof the triangulararray of mooredADCP stations(see alsoinset) and of the repeated5øE section.

[1995]. Reanalyzingdata from the MEDOC 1969 exper- estimated using climatologicalformulae and measure- iment, they determineddeep mixing down to 1200 m in mentsof seasurface temperature and cloudcover. In the the Ligurian Sea, southeastof Nice, and from moored central Labrador Sea these standard observations were instrumentsfound convectiondepths between 500 and available for several decadesfrom weather ship Bravo, 800 m in the winter of 1991-1992. until it was withdrawn in 1974. Since then, time series of Interannual variability of convectionin the Gulf of even a minimal set of meteorologicalparameters have Lions has been observed since the first convection ex- rarely been available,with the notable exceptionof the periments:1969, the year of the first MEDOC experi- LabradorSea Deep ConvectionExperiment [see LabSea ment [MEDOC Group, 1970],was a year of strongcon- Group, 1998]. vection, but 1971 was not [Gascard, 1978]. Vigorous Even when standardmeteorological observations are deepconvection (to 2200 m) returnedin 1987,causing a available, the derived fluxes are sensitiveto the choice of very homogeneouswater body of tro = 12.79øC,S = parameterization.Smith and Dobson[1984] applied co- 38.45 psu (practicalsalinity units) [Leamanand Schott, efficients tuned to conditions in the central Labrador 1991].Convection in 1991did not reachas deep (only to Sea and found that the annual mean heat loss at station 1700m), nor did it mix the water columnas thoroughly. Bravowas 70 W m-2, or about60% smallerthan that obtained by, for example, Bunker [1976] using global 2.3. MeteorologicalForcing bulk parameters.Such large differencesmay significantly Direct measurements of air-sea fluxes are difficult to contribute to uncertainties about the evaluation of obtain. One way to estimate them is by using climato- mixed-layer models in describingthe development of logical formulae applied to routine meteorologicalob- deep convection. servations. Latent and sensible heat fluxes are deter- Much profitable use can now be made of the vastly mined from bulk formulae that involvewind speedand improved fluxes derived from meteorological opera- air-sea moisture and temperature difference, respec- tional models. European Centre for Medium-Range tively.Long- and short-waveradiative fluxes can alsobe Weather Forecasts (ECMWF) analyzed fields have 12 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

Gulfof Lions 27-28 Nov 1991 section 5 E RV Suroit pre condition

29.051 29.081 29.07.1- 500 29.091-----

1000 - •29.096•• _

1500 I I I I i 41 ø30' 41045 ' 42 ø 42o15 ' 42o30 ' 42ø45'N

(b) 20-22 Feb 1992 section5 E RV Poseidon after convection

97 29051_•• ' •00,1•

500

lOOO

ci = 0.005 for•e > 29.071 = 0.040 1500 i • • ' I 41 ø30' 41 ø45' 42 ø 42o15 ' 42o30 ' 42ø45'N

Figure 10. Meridional sectionsalong 5øE throughthe Gulf of Lions convectionregime (see Figure 9 for location):(a) November27-28, 1991,preconditioning; (b) February20-22, 1992, after deep convectionto 1500 m.

proved to be very useful in the interpretationof obser- 2.3.1. LabradorSea. In winter months,cold, dry vations of Labrador Sea and Greenland Sea convection. air streamsout of the arctic over the relatively warm In the northwestern Mediterranean, fluxes of the French surface waters of the Labrador Sea. Large fluxes of model PrOvisionh Ech•ance Rapproch•e Integrant des sensibleand latent heat resultfrom the strongwinds and Donn•es Observ•eset T•l•d•tect•es (PERIDOT) have large air-seatemperature contrasts associated with these been evaluated and found to be of good quality when outbreaks.Over the region the magnitudeand distribu- comparedwith estimatesfrom researchvessel observation of the fluxes are modulatedby both synoptic-scale tions using bulk formulae [e.g., Mertens, 1994]. Some and mesoscaleweather systems[LabSea Group, 1998]. relevant observationsand model data are now briefly The strong northwesterly flow that occurs after the summarized;fluxes typical of individualdeep convection passageof an extratropical cyclone can result in heat casesdescribed elsewhere in this paper are presentedin fluxesas large as 700 W m-2. One alsooften observes Tables2a and 2b, where estimatesof correspondingbuoy- the de•,elopmentof short-livedpolar lows in the re- ancyfluxes are alsoincluded. gion. 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott:OPEN-OCEAN CONVECTION ß 13

TABLE 2a. Heat and BuoyancyFluxes During SpecificConvection Events in the LabradorSea, the GreenlandSea, and the Mediterranean

Heat Flux, W m -2 Incoming Back Solar • Radiation Latent Sensible Total

Labrador Sea March 1-8, 1995 (ECMWF) 89 -115 -167 -220 -412 GreenlandSea March 3-6, 1989 (ECMWF) 22 -130 -136 -252 -495 MediterraneanFeb. 14-18, 1992 (PERIDOT) 133 -112 -250 -38 -268 MediterraneanFeb. 18-22, 1992Poseidon* (all) 128 -98 -188 -46 -204 MediterraneanFeb. 18-22, 1992Poseidon* (nights) 0 -98 -196 -48 -342 MediterraneanFeb. 16-20, 1987 (PERIDOT) 180 -123 -297 -108 -348

BuoyancyFlux, 10 -8 m2 s-s Thermal Haline Total

Labrador Sea March 1-8, 1995 (ECMWF) -8.4 -1.7 -10.1 GreenlandSea March 3-6, 1989 (ECMWF) -4.3 -1.4 -5.7 MediterraneanFeb. 14-18, 1992 (PERIDOT) -13.5 -2.8 -16.4 MediterraneanFeb. 18-22, 1992Poseidon* (all) -10.3 -2.1 -12.4 MediterraneanFeb. 18-22, 1992Poseidon* (nights) - 17.3 - 2.2 - 19.5 MediterraneanFeb. 16-20, 1987 (PERIDOT) -17.6 -3.3 -20.9

* Poseidonwith coefficientsfrom Smith[1988, 1989] for latentand sensibleheat loss;and from Schianoet al. [1993]and Bignami et al. [1995] for longwaveradiation.

Little is known about the spatialdistribution and the The standard deviation of the monthly mean total temporalvariability of surfaceheat fluxesat high lati- heat flux (not shown)in the Labrador Sea region is of tudes.This is primarily becauseconventional heat flux the orderof 150W m-2. The variabilityof the monthly climatologies(such as thoseof Bunker[1976] and Cayan means is sensitiveto the location and intensity of the [1992])are baseddirectly on shipreports, of whichthere Icelandic Low. This in turn is associated with the North are very few at high latitudes,particularly in the Labra- Atlantic Oscillation[van Loon and Rogers,1978; Wallace dor Sea since the withdrawal of OWS Bravo. The hori- and Gutzler,1981] and concomitantchanges in the major zontal distribution of heat flux during February 1995 North Atlantic storm track [seeRogers, 1990]. A time from ECMWF analyzedfields is shownin Figure 11a, seriesof ECMWF fluxesat the Bravoposition, shown in suggestingthat the highestheat loss is located to the Figure lib, revealsseveral maxima over the winter and northwestof OWS Bravo,near the ice edge (markedby particularlyintense cooling in early March 1995. This the large gradientsin Figure 11a). triggereddeep convectionobserved by moored temper-

TABLE 2b. Typical Winter Meteorological Conditions and Fluxes at the Three Convection Sites

Labrador Greenland Parameter Sea Sea Mediterranean

Air temperature(dry), øC -9 -14 8 Air temperature(wet), øC -7 -13 5 Wind speedu •0, m s- • 13 13 15 Cloud cover, % 60 60 40 Precipitation,mm d- • 7 3 5 Evaporation,mm d- • 6 4 13 Heat fluxes Sensibleheat flux, W m -2 -370 -400 - 150 Latent heat flux, W m -2 - 140 - 140 -400 Shortwaveradiation, W m-2 80 40 120 Longwaveradiation, W m-2 -60 -30 -80 Net heat flux, W m-2 -490 -530 -500 Buoyancyfluxes Thermalbuoyancy flux, 10 -8 m2 s-3 10 5 25 Halinebuoyancy flux, 10 -8 m2 s-3 2 1 5 Totalbuoyancy flux, 10 -8 m2 S-3 12 5 30 14 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

flux and wind stressfields are presentedin Figures12a 66øN-•••[ and 12b during a period of in situ observationsof convectionin the central Greenland Sea during 1988-1989. The evolution of the stratificationin the underlying

62 o ocean, together with the periods of ice cover over the station as deduced from the ADCP surface backscatter [Schottet al., 1993],is presentedin Figure 12c.It is clear that convection does not occur when the area is covered 58 o by ice. Brine rejectionby ice into the mixedlayer during November-Januaryplays an important role in preconditioning[Roach et al., 1993; l/isbecket al., 1995] and in the convectiveprocess itself [seeRudels, 1990]. Under 54 o the ice the mixed layer deepensslowly as the density increases(Figure 12c). Southwardwinds are instrumen- tal in exportingthe ice and openingthe ice-freebay (the

50 ø Nord Bukta, evidentin Figure 8). In February,dramatic mixed-layer deepeningdue to strong wind bursts and coolingoccurs, and deep convectionis initiated by the large heat lossmaximum in early March [Schottet al., 65øW 55o 45o 1993;Morawitz et al., 1996]. The major coolingevent of Figure 11a. Spatial distributionof total heat flux in the La- March 3-6, 1989, that triggered deep convection brador Sea from the ECMWF model for February15 to March amountedto a total heat lossof about500 W m-2, of 1, 1995. which half was in sensibleform (Table 2a). The corre- spondingbuoyancy flux was 5.7 x 10-7 m-2 s-3. The haline fraction of the buoyancyflux is large in the low- ature sensors and an ADCP. The heat flux for March temperature conditions of the Greenland Sea and 1-7, 1995,averaged -400 W m-2, withmore than half of amountsto about one quarter of the total. it by sensiblefluxes. The buoyancy flux of 10-7 m-2 s-3 2.3.3. Northwestern Mediterranean. Meteoro- is dominatedby the thermal component(see Table 2). logical forcing over the Gulf of Lions is primarily a From this time series,one can seethe episodicand quasi- consequenceof the cold and dry mistralwinds that blow periodicnature of the fluxesthat givesrise to great vari- out of the Rhone valleyover the preconditionedcyclonic ability. Compared with the magnitude of the heat flux dome (Figure 9) and, to a lesserdegree, of the tramon- variationsover short periodsof time during the winter, tane from the northwest.Because the water temperature the buoyancycontribution of precipitationis rather small. is about 12øC and the air temperature only 5øC or so, 2.3.2. Greenland Sea. The central Greenland latent and sensibleheat fluxes are enormous.Cooling Sea, where convectionmay occur in late winter, is cov- rates in excess of 1000 W m -2 have been estimated ered by ice during November-January.ECMWF heat duringmistral events[Leaman and Schott,1991].

ECMWF 1994/95 at OWS Bravo

I I

200I0 • • • • •

-200

-400

-600

-800 I I I I I I I Dec 1 Dec 15 Jan I Jan 15 Feb I Feb 15 Mar I Mar 15 Apr I

Figure 11b. Time seriesof ECMWF total heat flux during winter 1994-1995 at positionBravo in the Labrador Sea. 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 15

, , 200 EC•MwFheat flux - o -200 -400 -600

-800 I I I

ECMWF wind stress

Figure 12. GreenlandSea: (a) Heat flux from the ECMWF modelnear 75øN,5øW, during November 1988 to April 1989, (b) 1988 1989 the wind vector time seriescorresponding to Figure 12a, and (c) temperaturedistribution recorded at moored station near 74.9øN,5øW, at 60-350 m, showinggrad- m -1.5 -1.25 Tpot ual mixed-layerdeepening during the period of ice cover and drastic deepening :'•':•:i•"::! ! ...... >o- after the opening of the Nord Bukta, The 200 bar graph on top indicatesthe presenceof ice. After Schottet al. [1993]. 1.0 400

øC 6O

•- 40 L[Lk

-2 J 'A S O F A 1988 1989

Figures 13a and 13b showthe evolution of heat flux correspondingto a buoyancyflux of 2.1 x 10-7 m2 S-3, componentsand windsfrom the PERIDOT model, dur- 85% of which was due to cooling. ing the 1991-1992 convectionevent [Schottet al., 1996]. Shortly after the onset of convection,the R/V Posei- The observedwinds at coastalstations Pomegues are a don was in the region and bulk fluxeswere derived from goodindicator of the mistraland thoseat CapeBear (for meteorologicalship observations.In contrast to other location,see Figure 9) monitor the tramontane.Typi- winter convection sites,the northwestern Mediterranean cally, the first coolingperiod occursduring late Decem- gains heat during the daytime at rates of up to 500 W ber. The mixed layer deepensand, at first, it warms m-2 (evenin February).Thus in Table2a the heat fluxes before coolingbecause of higher-salinity,warm water for theend of thatforcing Period, February 18-22, are being mixedupward (Figure 13c). Severalweaker cool- givenseparately for the nightperiods, when plumes were ing eventsfollowed, completingthe preconditioning,so more vigorouslygenerated, and for the total time period. that by mid-February the integratedbuoyancy loss was Thelaighttime heat loss was•342 W m-2 comparedwith sufficientlylarge that the Secondstrong cooling evei•t of only204 W m2 forthe total p•dOd February 18-23, 1992. the seasoninduced deep COnvection(Figure 13c). i n summarythen, typical buoyancy fluxes during deep The integrated heat fluxes during 1987, when a very convection in the western Mediterranean are !-2 x 10 -7 large patch was generated[Leaman and Schott,1991] m2 s-3, Extremelyhigh heat losses have been reported, (Figure10b) together with fluxes during 1992, are shown exceeding1000 W m-2, but not duringperiods that in Table 2a. In the period from February14 to February coincided with the in situ measurements reviewed here. 18, 1992(the largestcooling phase during the convection The flux estimatesare clearly incompletebecause they period (Figure 13)) the averageheat losswas 286 W do not includeprecipitation. The direct contributionof m-2. Duringthe 1987convection period, the mean heat precipitation to buoyancyflux, however, is generally losssuggested bythe PERIDOT model was 348 W m-2, consideredsmall on the timescale of a few days. It is 16 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 /REVIEWS OF GEOPHYSICS

400I, Q [W m 2] I I I I I 200 - :...... ,.,,.,,,.r,.... t'•i'":'"',.r.! ti,f'"'•"•i ...... '•"•"'"? ...... ;•,.'...•-',',•,. .t'...... "...... •.",Peridot?"):C ...... heatflu',.t"\,'"'"' .... ',, ..,• ...... W!i ,. , ,. ,½, ,• ,' .,•- , ,:?':"'-,?''•i,, "•...... ---,,f,.,,•:,r"

-200

-400

-600 , , I © I Dec '91 1Jan '92 1 Feb 1Mar 1 Apr 1May

...... incoming shortwave sensible total back radiation latent

!lPerido,t I .. ' Wind

......

I1 "ø , i , I , 1 Dec '91 1 Jan '92 1 Feb 1 Mar 1 Apr I May

0 ' 200 13.4 A1temperature

i:.i::ii:i.... 13.25 :!:!:!:13.1 400 .-..•: • 12.95 600 : .. ==12.8 --'•ii::ß'-':'-'•.ß ii.:.:•.....•.,..:..i ::::::i::iiiii::::ii•i::ii::i!•::::::!,.:.•...... ;{!. ":": :!{•"?! ;: 13.5 Om I ' ' ' I ' øc A1 temperature , 322 rn

13.o - 14•0 1800 © 1 Dec '91 1 Jan '92 1 Feb 1 Mar 1 Apr 1 May

Figure 13. Mediterranean:(a) heat flux (incomingshortwave, sensible, latent, and total) from the PERI- DOT model near 42øN,5øE, duringDecember 1991 to April 1992, (b) the correspondingwind vector time seriesfrom PERIDOT and coastalstations Pomegues and Cap Bear (for positions,see Figure 9), and (c) temperaturedistribution recorded at moored stationnear 42øN,5øE, showingmixed-layer deepening, deep convection,and restratification.After Schottet al. [1996].

certainly important, however, on the preconditioning 3. CONVECTIVE SCALE timescale(several months), and it is a factor in interannual variability [Mertensand Schott,1998]. We now review what is known about the underlying Meteorologicalconditions and fluxesat all three con- hydrodynamicsof the convectiveprocess in which a vection sitesare drawn together in Table 2b. columnof oceanis overturnedby convectioninduced by 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 17 widespreadbuoyancy loss at its surface(the "deep convection" phase in the schematicdiagram, Figure 3b). Be ½ thermal•/ layerboundary

The detailsof the processare inherentlycomplicated but free convection may not be crucial for understandingthe integral effect of convectionon the large scale.Thus here we empha- l' &.•.•'•i layer size the benefit of thinking about the ensembleproper- ties of convection rather than the individual elements. We argue that the gross transfer properties of the plumes are dictated by demandsplaced upon them by the large scale:that they draw buoyancyfrom depth at a rate sufficientto offset the lossimposed by the meteo- Figure 14. A schematic diagram showing the convective deepeningof a mixed layer. An initially restingstratified fluid rology at the surface. This leads to simple and very is subjectto widespreadand uniform buoyancyloss from the useful scalinglaws and the identificationof key nondi- surface;fluid in the "thermal boundarylayer" is directlyinflu- mensionalparameters that have been very successfulin enced by buoyancyloss at the surface,becomes dense, sinks, bringing order to observationsas well as and to labora- and drivesthe deepeninglayer of free convectionbelow. The tory and numerical experiments. "free convectivelayer" draws buoyancyfrom depth at a rate that offsets its loss from the sea surface. 3.1. GravitationalInstability; "Upright"Convection Considera restingocean of constantstratification Nth (subscript"th" for thermocline)subject to uniform and widespread buoyancy loss from its upper surface as important to realize that irrespectiveof thesedetails, the shownin Figure 14. On the large scalethe flow is under grosstransfer properties of the populationof convective geostrophiccontrol and is therefore almosthorizontally cells must be controlled by the large scale; the raison nondivergent,so the fluid cannot simultaneouslyover- d'•tre for the overturningis that it must flux buoyancy turn on these scales;rather, the qualitative description vertically to offset loss at the surface.A useful "law" of must be that the responseto widespreadcooling is one vertical buoyancytransport can be developedusing par- in which relativelysmall convectioncells (plumes) de- cel theory as follows. velop. Fluid parcelsin contactwith the surface(in the Supposethat the net effect of overturningis to ex- "thermal boundarylayer" sketchedin Figure 14) will changeparticles of fluid, of buoyancyb • and b2, over a becomedense and sink under gravity,driving the "free depth Az; the particlesare labeled 1 and 2 in Figure 14. convectivelayer" below. Buoyancy is drawn upward, Water made denseby buoyancyloss at the surfacesinks, acrossthe convectivelayer, offsetting its loss from the displacinglighter water below and releasingpotential surface. energy to power the convectivemotion and buoyancy The thermal boundary layer may be thought of as flux vertically. being analogousto Howard's[1964] conductivelayer in The changein potential energyAp consequenton the laboratory convection between parallel plates, which idealized rearrangementof particlesis given by communicatesthe boundaryconditions from the plates AP = poAbAz to the interior of the fluid. However, unlike the classical problem, the thermal layer in the open ocean is not the where Ab = b• - b2 is the buoyancydifference of the rate-controllingone. Jonesand Marshall [1993] argue exchangedparticles and Pois a representativevalue of that its depth 8, measuredagainst h, that of the free the density.Equating the releasedpotential energy to convectivelayer, is given by the acquired kinetic energy of the ensuingconvective •/h • 1/Pe •/2 motionK = 2(3•p0w2) (there are two particles and isotropyhas been assumedwith velocity scale w), we where Pe is a Peclet number measuringthe efficiencyof then find buoyancytransfer on the plume scalerelative to turbu- W2 1 lent processesin the thermal boundarylayer. In the ocean the thermal Peclet number is large (---100);that is, the plumesin the interior are muchmore The implied "law" of vertical heat flux on the plume efficient at transportingproperties vertically than the scaleis then, using(7), turbulent elementsthat make up the thermal boundary •]•p= wAb= (Az/3)•/2(Ab)3/2 (8) layer near the surface.Thus the boundarylayer is shallow (perhaps 100 or 200 m deep; see section 3.2.1) where w is the vertical velocityin the plume, Ab is the relative to the scaleof the convectivecells occupying the difference in buoyancyof the rising and sinking fluid, interior of the fluid. and Az is the vertical scale over which particles are 3.1.1. Transfer propertiesof "free convection." transportedby the convectivemotion. Many competingeffects collude togetherto control the Now if, actingin concert,the plumes achievea verti- detailed dynamicsof the convectivelayer. However, it is cal buoyancy flux sufficient to balance loss from the 18 ß Marshalland Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

(a) Temperature (-), streamfunction(--) and flow of the mixed layer can be neglected(see discussionby o Turner[1973]), then integrationof the buoyancyequa- tion 200 ' ,,' ', ','.. [',,' ,:, l":',, , ,:•" ,,':,•:,,,,,,•,•,.•'•,•,•,.,r•i.',t.,•,'/' ,UF',,• 400,,,,,,,:, :,,,,. ,, ,,,..,. ,. z i• i,t,',,/ ,'t •. f •,l,' '•;•l,I •'.'i',"';d•'t¾.,'•','•'., •1t , r xt ,• k"; Db/Dt = B (9) •'600 .... '•' 1 ' ,'• '1'•'•' • / ' '1't' • I• '•'1'•'• .... ' ' '"

8OO (whereb is the buoyancyand B - 003/Ozis the buoyancy %- .t i '-- ..-=i _ i •- lOOO forcing,the divergenceof the buoyancyflux 03) tells us lO 12 14 16 18 20 that its depth h must increaseaccording to Across channel distance (km) (b) (c) 0 o 2 O3odt •00 200 400 400 h = Nth (10) o o 600 o 600 •) 8OO o 800 assumingthat Nth is constant. o The erosionby convectionof a resting,stratified fluid lOOO 1000 11.5 11.6 11.7 11.8 0 5 10 consideredabove can be readily studiedin two dimen- Acrosschannel mean Time (days) temperature (C) sions using a nonhydrostatic(incompressible Navier- Stokes)numerical model (see Figure 15). The model Figure 15. Deepening by upright convectionin a numerical used here is describedby Marshall et al. [1997a, b]. simulation:(a) Vertical sectionshowing isotherms (solid), Convectionis inducedby a steadyand spatiallyuniform overturningstream function (dashed)and flow indicatedby buoyancyloss of 030= 2 x 10-7 m2 s -3 fromthe surface. small dashesgiving particle displacementsduring a 30-min There are no Coriolis effects.Energetic vertical over- period.The peak speedsare (0.069,0.024) m s-• in the turning can be seen in a convectinglayer severalhun- horizontal and vertical directions; the thick dashed line is the dred meters thick, with much weaker flow below. The predictionof the 1-D law for the depth of the mixed layer convectioncells are verticaland maintainthe layer close (equation(10)). (b) Mean verticaltemperature profile corre- to neutral,apart from an inversion(the "thermalbound- spondingto Figure 15a, showingthe stratifiedlayer below,the ary layer") close to the surface.The interior of this almost vertically homogeneouslayer of vigorousconvective activity,and the adversegradient at the surface.(c) Time series mixed layer has a temperaturecontrast of only a few of mixedlayer depth. The solidline is the 1-D predictionusing hundredthsof a degree over its depth, in accordwith (10), and circlesare model results. that impliedby the flux law (8). We estimatea depthfor the mixed layer from the mean temperatureprofile (Figure15b) andplot its time seriesin Figure15c along with the prediction(equation (10)). The agreementis surface,then •p = •0' Typically,in the LabradorSea very close. duringconvection, for example(see Table 2b), We will return to this examplein section3.6 whenwe zXz= 1000 m 030= 10-7 m2 s-3 considerthe influenceof angularmomentum and rotational constraints on convection and the "switch-over" (equivalentto a heat lossof---500 W m-2 inducing from convectionto baroclinicinstability. convectionover the top kilometer).Equation (8) then implies(solving for Ab) that the temperaturedifference betweenupward and downwardmoving particles (as- 3.2. The ConvectionLayer sumingfor simplicitythat all the buoyancyloss manifests itselfin temperaturechange) is onlyAT • 10-2øCand 3.2.1. Mixed patches. Observationsof deep, that the intensityof the convectivemotion is w • 10 cm mixed patchesare sparsebecause ship surveysare sel- s-1,not untypical ofthe observations (see section 3.4). It dom carried out under the very adverseconditions of is notable that such a tiny temperature differencebe- winter coolingperiods. More frequent are observations tweenrising and sinkingfluid parcelscan drivevigorous of homogeneouswater bodiesin the springor summer convectivemotion and achievesuch a large heat (and periods following convection,underneath the newly buoyancy)flux. With temperaturedifferences across it of stratifiedsurface layer. only a few hundredthsof a degree,the convectivelayer Severalexamples of open, deep mixed regimeshave is indeed well mixed and stratification within it vanish- been documented from winter observations in the Gulf ingly small,yet it can still easilyprovide the required of Lions,for example,in 1969,1987, and 1992 (Figure 9) buoyancyflux. when deep convectionoccurred in the secondhalf of 3.1.2. Rate of deepening. In the limit that the February of each year. The hydrographicobservations convectivelayer is vertically homogeneous,and to the within these convectionregimes reveal characteristic extent that entrainment of stratified fluid from the base features that we now discuss in turn. 37, 1 / REVIEWSOF GEOPHYSICS Marshalland Schott: OPEN-OCEAN CONVECTION ß 19

CT D - TOW-YO 22/23 Feb '92 o ' ti !i ' (a)

1000

2000 79øCl I I I , ' 'cf'4 0 (b) m s

lOOO

+38.44 6 '& i 2000

0 f r' m [ (c)

lOOO

+29.10 2000 i I I 0 5 10 15 20 25 km 30

Figure16. Closelyspaced profiles of (a) potentialtemperature (relative to 12.79øC),(b) salinity(relative to 38.44),(c) potential density (relative to 29.10) from a CTD-TowYo sectionalong 5øE through the deep mixed regimeof 1992.For position,see Figure 9. FromSchott et al. [1996].

3.2.1.1. Homogeneityof the "mixed" regime: In the Labrador Sea, extensiveand deep mixed re- The degreeof horizontalhomogeneity of the convection gimes,but cappedby newlystratified surface waters, patchcan be veryvariable. While in the 1987observa- have been observedin summersmany months after tionsof Leamanand Schott[1991] the homogeneitywas convectionperiods (e.g., Lazier [1980, 1995] and Figure nearlycomplete, significant vertical and horizontal tem- 7), with horizontalhomogeneities to betterthan 0.02øC peratureand salinityinhomogeneities remained in the and 0.002psu in the core.However it is not possibleto deepconvection patch of 1992[Schott et al., 1996],as can know the degreeof homogeneityat the time of, or ho coonœrc•rn elc•qoly qnaeocl cnnchlctivitv-tomnorat•re- qhc•rtl.y after, convecticmIn the,•reenland Sea, exten- depth(CTD) profilesin Figure16. Horizontal standard sivedeep mixed layers have not beenreported, perhaps deviationsin the patch were 0.015øCand 0.002 psu, because of the shutdown of Greenland Sea convection broadlyconsistent with the scalingarguments intro- over the past decade.In 1989, deep convectionwas duced in section3.1.1. The mean profileswere warmer triggeredin the preconditionedregion of the Nord by 0.06øCand saltier by 0.004psu at 1500rn thanin the Bukta and was mappedby towedundulating fish CTD upperfew hundredmeters. In density,however, these measurements[Sandyen et al., 1991](Figure 8). Individ- water massinhomogeneities were nearlycompensated ual deepmixed profiles were observedwithin the strat- (Figure16c), both for the individualanomalies and for ified environmentby conventionalshipboard hydro- the profile-meangradients. It seemsthat in 1987a very graphicprofiling [Rhein, 1991; Schottet al., 1993]. intensemistral in early Januarymixed the regimethor- Similarly,a CTD surveyin the precedingwinter, 1987- oughlyand then a secondconvection event in February 1988,yielded only one homogeneous (to middepth)pro- mixedit again.By contrast,the 1992convection event file [Rudelset al., 1989]. On the other hand, inverse was briefer and weaker, and plumes.did not have the analysisof integralmeasurements by acoustictomogra- time to homogenizethe water to the samedegree. One phy acrossthe centralGreenland Sea in winter 1988- mightcall that latter case incompletely mixed, compared 1989revealed a coolinganomaly that reachedto deeper with the completelymixed caseof 1987. than 1000m [Morawitzet al., 1996].The coarsehorizon- 20 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

tal resolutionof the acousticarray yielded a lateral scale observationsof mixed-layerdeepening over a convection estimate of 50 km or so. Hence the winter 1988-1989 seasonwith the evolutionof the layer aspredicted by this convectionevent must have been an incompletelymixed simple1-D model (due to Rahmstorf[1991] but concep- casewith significanthorizontal inhomogeneities. tuallysimilar to that of Krausand Turner[1967]). Should 3.2.1.2. Deep convection,penetrative or nonpen- the column become statically unstable as a result of etrative.•: At the bottomof deepmixed patches, steps buoyancyloss at the surface,convective adjustment is are often found in the temperatureand salinityprofiles performed until the layer is vertically mixed with no (Figures 16a and 16b) but they are compensatedin density gradient at the base. In addition, mixed-layer density(Figure 16c), at least as suggestedby observa- deepeningdue to wind stirringis alsotaken in to account tions available in the Mediterranean. Similarly, steps througha turbulentkinetic energyequation. The model seemto be absentin deep mixed profilesof the Green- was initialized with CTD casts obtained in mid-Decem- land Sea. Profilestaken duringthe springin the Labra- ber 1991 and stepped forward using fluxes from the dor Sea and summer after wintertime convection do not French PERIDOT weather-forecastingmodel. Broadly show densitysteps at the bottom of the deep mixed similar fluxes were obtained when calibrating coastal regime.The evidencethen suggeststhat deep mixingby meteorologicalstation data againstship measurements convectiveplumes is, to zero order, nonpenetrative.Pos- [Mettens,1994]. sibledynamical explanations are discussedin section3.5. The densitychanges are calculatedfrom temperature 3.2.1.3. lherrnal boundarylayer: During active and salinity using a linearized equation of state of the convection,density inversions have been observedat the form of (3). A seriesof temperatureand salinityprofiles top of the mixed layer, the thermal boundary layer from near 42øN, 5øE in the center of the deep mixed sketchedschematically in Figure 14 and discussedtheo- patch is shownin Figure 17a, alongwith model predic- reticallyin section3.1. Leaman and Schott[1991] found tions. The developmentof mixed-layer salinity in the that the existenceof inversionsin the CTD surveysof model for the upper 150 m and for the LevantineInter- 1987was associatedwith periodsof strongsurface cool- mediateWater layer of 150-500 m alsocompares favor- ing. Density differencesbetween the surface and the ablywith the CTD observations(Figure 17a). When the homogeneouspart of the profile ranged up to about mixed layer reachesinto the salinity maximum of the 10-2 kgm -3 withsome indication that the magnitude of LIW layer (see Figure 2c), the surfacesalinity (and the inversionwas inverselyrelated to the layer thickness temperature)increases. (as seenin Figure 16c). Unlike in the classicalproblem Model runshave been comparedwith observationsof where convectionoccurs between two perfectlysmooth the depth of the mixed layer assumingstatic erosion of plates,we do not believe that the physicsof this layer is the stratificationdue to surfacebuoyancy loss alone (i.e., a centralfactor in controllingthe transferproperties of when all entrainmentterms are set to zero). Departures the convectivelayer as a whole. occurwhen the mixed layer is shallow,and wind mixing 3.2.2. Observedand modeledmixed-layer evolu- is important,but the ultimate depth reachedby convection. Time sequencesof mixed-layerdevelopment are tion dependssolely on the surfacebuoyancy flux and is sparsebecause observations from ships are infrequent independentof entrainment.As was discussedabove, and seldom occur during the winter. Moored instru- observationsshow that deep convectionbelow the wind- ments can yield time seriesrecords throughout a con- affectedlayers is typicallynonpenetrative. vectionseason but are not alwaysin an optimumposi- Visbecket al. [1995] used the same model to study tion and often do not have sufficient vertical resolution mixed-layerdevelopment during the GreenlandSea Ex- to accuratelychart the developmentof the mixed layer. periment of 1988-1989, when intermediate-depthcon- However, the developmentof the depth of the mixed vectionwas observed [Schott et al., 1993].The modelwas layer in the Gulf of Lions was successfullyobserved driven by ECMWF fluxes (Figure 12) and initialized during winter 1991-1992, usingCTD castsand moored with the November 1988 stratification from observa- stations.During this period air-seaflux and stratification tions. Only a fraction of the surfacecooling is now felt, measurementswere also available(see Figure 13), en- throughice-free areasand conductionthrough the ice, abling one to drive a 1-D mixed-layermodel and com- by the underlyingocean. Moreover, an additionalbuoy- pare the results. ancyflux mustbe includedthat representsthe effect of We have argued in section3.1.1 that free convection brine rejection on ice formation and subsequentice is a very efficienttransferring agent and doesnot require export. Comparison with the observationswere most large verticalbuoyancy gradients to supportit. A simple favorable(Figure 18) whenan ice exportof 8 mm d-1 model that assumesthat the convectivelayer is vertically over the winter period was taken into accountand the homogeneous,such as that of Krausand Turner[1967] cooling rate below the ice was reduced by 40%. The (see also Niiler and Kraus [1977] and, briefly, section observedinterannual variability in the depth of convec- 5.1.2 for a review), might then be expectedto capture tion, in particular that no convectionbelow 400 m oc- many of the grosseffects of the convectionon the large curred in 1990-1991, could then be reproducedby the scale(see, for example,Lascaratos et al. [1993]), at least simplemodel. Such modeling work suggeststhat ice, and in the initial phase of the process.Here we compare then ice export,is a key playerin the convectiveprocess 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 21

92/119 92/2/22 Potential92/2/23Temperature •_.•2•26 92/2/29 92/3/2 ' I * ==-=" I ,' ' 11' i • 1 I •' I• II :,

500 ,,• ,• ,,

// I: 1000

1500

I • I I I I I I I I I 1__. I 12.7 12.9 12.7 12.9 12.7 12.9

Salinity

I! l

• lOOO I I • • I ,

15oo

i i i I I I I I I i I I I 38.4 38.S 38.4 38.5 38.4 38.5 38.4 38.5 38.4 38.5 38.4 38.5

Upper Layer (0 - 150 m) Intermediate Layer (150 - 500 m) 13.6

13.4

13.2

'"x i 12.8

12.6 ' ' ' Dec15 Jan1 Jan 15 Feb1 Feb15 Marl Dec i15 Jan1i Jan15i Feb1i Feb ,15 Marli (• 38.55 38.5[

38.5 38.[ e• tie 38.45 ,,,•--•.---.•-; 38.4[

._ ß=- 38.4 [ 38.• 38.35 // 38.3[

38.25 ...... 38.2! Dec15 Jan1 Jan15 Feb1 Feb15 Marl Dec 15 Jan1 Jan 15 Feb1 Feb 15 Marl

Figure 17. Mixed-layerdepth development in the northwesternMediterranean convection regime during winter1991-1992: (a) individualCTD castsnear 42øN, 5øE (dashed) and from mixed-layermodel, driven by PERIDOT modelfluxes; (b) averaged(top) temperature and (bottom) salinity for the (left) upper(0-150 m) and (right)Levantine Intermediate Water (150-500m) layersin the Gulf of Lionsduring winter 1991-1992 frommodel run (PERIDOT fluxes,solid) and from moored thermistor string records (dashed) and CTD casts (dots).(After Mertens[1994]). 22 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

Model Sta. 319 observations II I øI JaljJl•--•_..\_.-- x \ , • • I, • %• %l -lOO _100J••-,.• • • • • ,.. lVJlL,•'•??"'"•I•..• , ,,, ', ' '•' ,.,,,...•NI¾'JV ,V'%,• Ill I II •-200 E Ill ^, IN •', ',',', 'o -300

-400

350 40O 450 350 400 450 time time

0 ' '200m' ' ' ' ' o_0.5.:;,_ ,..... ';".•,-;'•--•-'---,-: .... :,..•;.,-', -• ' ',;v ;, ', ', ,,, . .,,½,>, ;•- : /I, ,I I," ,I H I, ^ 35I

34.8

34.6! I, ,I I, . ,I I, . / 320 340 360 380 400 420 •0 460 480 time [days of year 1988]

Figure 18. (a) Mixed-layerdeepening in the GreenlandSea duringthe winter of 1988-1989 (from Visbeck et al. [1995]):for a stationat the southernmargin (position 319, Figure 8), (left) as predictedby the model driven by ECMWF model fluxesthat are reducedby 40% during times of ice cover and include a brine rejectionterm that is dueto an iceexport of 8 mmd -• and(right) as observed by moored thermistor string temperatures.(b) Observed(top) temperaturesand (bottom) salinitiesat depthsof 60 m and 200 m at the southern(light dashed)and central(light solid)compared to thoseobtained from the mixed-layermodel for 60-m (heavydashed) and 200-m depth (heavysolid).

in the central Greenland Seaby facilitatingthe necessary then the "stiffening"of the fluid by the Earth's rotation reduction of mixed-layer stability. could be felt by the convectiveelements, the plumes, In summary,simple mixed-layermodels can be suc- themselves.Second, the convectiveprocess is spatially cessfullyused to representthe evolvingmixed layer and localized in the ocean, and lateral as well as vertical interior mixed patch properties on short timescales. exchangeof buoyancyand fluid is important:convection However, lateral advectionplays an increasinglyimpor- can give way to baroclinicinstability. This latter theme, tant role as time progressesand can dominate over that of the role of baroclinic instability, will be intro- seasonal and interannual timescales. duced toward the end of this chapter but will be the central focus of attention in section 4. 3.3. PlumeDynamics 3.3.1. Scalingideas. Imagine that lossof buoy- Once a mixed layer is established,subsequent convec- ancy associatedwith a sustainedsurface flux of magni- tionoccurs into fluid in whichN 2 • 0. Accordingly,we tude •0 drivesconvection in to a homogeneousfluid of now considerconvection into a neutral fluid of depth h, depthh as illustratedschematically in Figure 19. A layer and review physicallymotivated scalingideas that have of 3-D, buoyancy-driventurbulence will deepen as the been very influential in the developmentof our under- plumesthat make it up evolvein time, penetratinginto standingof ocean convectionand have provided orga- the fluid below. Ultimately, the convectionwill extend nizing principles. We draw out two particular aspects down to the depth h. Let us supposethat in the initial that are of considerable theoretical interest. First, the stages,plumes extending into the convectivelayer are so Earth's rotation may have an influenceon the convective small in scalethat they cannot feel the finite depth h. processitself in the ocean. If convectionreaches very Furthermore,for timest << f-•, rotationis unimpor- deep and the associatedtimescales are sufficientlylong, tant; only •0 remainsas the controllingparameter. It is 37, 1 /REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 23

b •-. bnorot = (•;• •/h) (12c) layer The subscript"norot" indicatesthat theseare the scales adopted in the absenceof rotation; these are the scales implicitin the flux law equation(8). 3.3.1.2. Scaleconstrained by the Earth'srotation: If h is sufficientlylarge then the evolvingconvection will come under geostrophiccontrol before it arrives at the h ..-...• .'•- . depth h. The transition from 3-D buoyancy-driven • ' "• 1 plumes to quasi-2-D, rotationally dominated motions ,• ' • .•.- , e' • '.•'•Rotationallycontrolled (represented schematically in Figure 19) will occuras t approachesf- • at whichpoint, replacing t byf- • in • '... equation(11), the followingscales pertain [see Fernando et al., 1991]: Figure 19. A schematicrepresentation of the evolution of a populationof plumesunder rotationalcontrol sinking in to a grot-(•0/f3) 1/2 (13a) homogeneousfluid of depthh, at a latitudewhere the Coriolis parameteris f, triggeredby buoyancyloss •o. If the fluid is U •-' Urot = (•o/f) 1/2 (13b) sufficientlydeep (as drawnhere) the plumesthat makeup the convectivelayer will comeunder rotationalcontrol on the scale b • brot = (•;•0)•)1/2 (13c) grot' wherethe subscript"rot" (for "rotation")has been used to denote the scalesat which rotation beginsto be then not possibleto constructscales for the depth, important.Golytsin [1980] appears to havebeen the first buoyancy,or velocity of the plumes. The convective to writedown the scales(13). Relations(12) and(13) are processmust evolve in time, and we supposethat it enumeratedin Table 3 for a range of buoyancyfluxes typical of deep convection. proceedsin a self-similarway. The followingscales can be formed from •0 and t (a more detailed accountis At thesescales the plume Rossbynumber is unity: givenby Jonesand Marshall [1993] and Maxworthyand U Urot Narimousa[1994]): Ro= = 1 fl f/rot l- (•0t3)•/2 (11a) It shouldbe noted that the foregoingscales are inde- u - w - (•0t) •/2 (lib) pendentof assumptionsconcerning eddy viscosity and diffusivity,provided that theyare sufficientlysmall; they b (Oao/t) are the velocity,space, and buoyancyscales that can be where l is a measure of the scale of the convective constructedfrom the "external"parameters •0, f, and elements. h. However,the constantsof proportionalityin (12) and (13) will be dependenton viscous/diffusiveprocesses 3.3.1.1. Scale constrainedby the depth: If it is and can be determinedexperimentally from laboratory the depth h that ultimately limits the scaleof the cells and numericalexperiments (see section 3.5.1 and equa- then putting l = h in (11a), the following scalingis tion (18)). suggested[Deardorff, 1985], independent of rotation: Helfrich [1994] has vividly illustratedpossible rota- l-/norot- h (12a) tional constraintson convectiveplumes in the laboratory. Figure 20 showsa sequenceof photographsfrom U •-' Unorot = (•;•0h)1/3 (12b) an experimentin which a salt solution,dyed for flow

TABLE 3. Velocity,Buoyancy, and SpaceScaling in the Open-OceanDeep ConvectionRegime

Heat Flux Heat Flux Heat Flux Heat Flux = 100W m-2; = 500W m-2; = 1000W m-2; = 1500W m-2; BuoyancyFlux BuoyancyFlux BuoyancyFlux BuoyancyFlux Scaling = 5.00 X 10-8 m2 s-3 = 2.25 x 10-7 m2 s-3 = 5.00 X 10-7 m2 $-3 = 7.25 X 10-7 m2

/rot,km (•o/f3) •/2 0.22 0.47 0.71 0.85 Urot,m s-• (•o/f) •/2 0.02 0.05 0.07 0.09 bt.... t, m s-• (•oh) •/3 0.04 0.08 0.09 0.12 Ro* •/21f3/2h 0.11 0.24 0.35 0.43 /p,km hX/•* 0.67 0.97 1.19 1.31 Here h = 2 km andf = 10-4 s-1 24 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

(d) (e) (f)

Figure 20. A sequenceof photographsfrom a laboratoryexperiment carried out by Helftich [1994]. The effectsof rotation are evident in Figures20d through 20f. The radiusremains nearly constant,and the front falls to form a columnarstructure, which ultimately undergoes geostrophic adjustment to form an anticyclonic conicaleddy of densefluid on the tank bottom. 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott:OPEN-OCEAN CONVECTION ß 25 visualization,was introduced into a rotating volume of exponent (1/3 rather than 1/2). Julien et al. [1996b] freshwater. As the plume sinksit will fold in (entrain) include a short history of convectiveRossby numbers. fluid from the surroundings,leading to expansionin the Marshallet al. [1994]discuss the physicalcontent of (14) lateral scaleof the plume as it reachesfarther down. at length. However, if the neutral layer is sufficientlydeep, the How large is Re* in the ocean, and how do typical entrainingplume will attain a lateral scale at which it oceanicand atmosphericvalues compare?Typical ver- becomes "aware" of rotation before it strikes the bot- tical heat fluxesachieved by a populationof convective tom. This inhibitionof lateral growthin the presenceof elements are comparablein atmosphericand oceanic rotation is a consequenceof the existenceof "Taylor" convection;indeed, they have to be becauseheat lossto columnsthat impart rigidityto the fluid columnand that the atmosphere drives convection in the ocean. The resist lateral displacement.In view of the foregoing buoyancyfluxes are very different, however, with the discussion,one might expect this lateral scale to be a verticalbuoyancy flux in the atmosphereexceeding that function of/rot' In the experimentshown in Figure 20, in the ocean by many orders of magnitude. If the two the buoyancyflux and rotation rate were suchthat/rot fluids achievethe sameheat flux, the ratio of the buoy- was much lessthan the water depth. Figures 20a to 20c ancy flux is show the early evolution before rotation becomesim- portant. The effectsof rotation are evident in Figures • atmos DwCw =--• 105 20d through 20f. The radius remains nearly constant, •ocean paOtCaT•a and the front forms a columnar structure, which ultimately undergoesgeostrophic adjustment to form an where p is the density,c is the specificheat, and o•is the anticyclonic,conical eddy of convectedfluid on the tank coefficientof thermalexpansion of water,with O• -• the bottom. The radius of the column is found to scalevery analogousquantity for air (where Oa is a typical air closelywith an appropriatelydefined/rot' temperature). Subscriptsw and a representwater and A considerationof angular momentum constraints air, respectively. readily suggeststhat if rotation is indeed felt on the Insertingtypical meteorological values (see Table 2b), convectivescale, radial inflow at upperlevels will spinup we findthat atmospheric buoyancy fluxes are some 10 s cyclonicvorticity and radial outflow below anticyclonic timesgreater than oceanicbuoyancy fluxes, giving an/rot vorticity (see Chandrasekhar[1953, 1961]; Verenis of 100 km or more in the atmosphere,compared with [1959],who addressedthe problemfrom the perspective only 100 m or so in the ocean.Typical vertical scalesof of linear theory;and alsoDavey and Whitehead[1981]). convectionin the atmosphereare setby the depth of the Thus, superimposedon the overturning circulation, troposphere,h = 10 km, givingRe* • 10; the convec- there will be lateral circulation,cyclonic above, anticy- tion "hitsthe ceiling"before it feelsthe effect of rotation. clonicbelow. The degreeof lateral circulationdepends Contrast this with the ocean. At the site of deep on the degreeto which the fluid is stiflenedby rotation convection in the western Mediterranean Sea, for exam- (i.e., the smallnessof the natural Rossbynumber intro- ple,where h • 2000m, f • 10-4 s-•, andheat fluxes duced now in section 3.3.2). The horizontal swirling in excessof 800W m-2 havebeen observed, •0 • 4 x motionsmay be important agentsof horizontal mixing 10-7 m2 s-3 [Leamanand Schett, 1991] then Re* = 0.3. (seeJulien et al. [1996b]and section3.5.2). Deep convectionencompasses regimes from the Labra- 3.3.2. Nondimensional numbers. We now con- dor Sea to the Weddell Sea, and so relevantranges for h sider the important nondimensionalparameters that are1000 m to 4000m, •0 from10 -7 m2 s-3 to perhaps govern ocean convection. 5 x 10-7 m2 s-3 (seeTables 2 and3) andf fromits 3.3.2.1. Natural Rossbynumber: The consider- Mediterraneanvalue up to 1.5 x 10-4 s-1 in polar ations discussedabove suggest that if lrot/h is small, one oceans.Consequently values of Re* from---0.01 to 1 are might expectto see an upper convectivelayer beneath mostrelevant to oceanicdeep convectionsuggesting that which plumes,under rotationalcontrol, extend down to rotation cannotbe ignoredeven on the plume scale(see the bottom, as shownschematically in Figure 19. Table 3). In summary,then, Re* is large in the atmo- The natural Rossby number [Maxworthyand Nari- spherebut small in the ocean. meusa, 1994;Jones and Marshall, 1993] Finally, in view of the importance of Re* in the developmentof ideasabout the plume-scaleand mixedpatch dynamics,it is useful to have a number of inter- Re*: h - (14) pretationsof it. Using the rotational scalingoutlined above, Re* is a measure of the fraction of the total is a measureof this ratio, comparingthe scale/rot, at depth that a particlereaches in a rotation period. Alter- which convection comes under the influence of the natively, one can think of Re* as a measure of the Earth's rotation, with the total depth of the convective number of vertical excursionsa particle makes in a layer h. Some authors [e.g., Raaschand Etling, 1991; rotation period; strong forcing makes the particle un- Julien et al., 1996b] use the term "convective"Rossby dergo many circuits in a day and rotation is felt little. number,which differs from (14) only in the value of the The squareof Re* is a nondimensionalmeasure of the 26 * Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

strengthof theforcing, comparing G0 with f3h2; a ve- expressionfor the Nusseltnumber. Then, identifying locityscale fh timesa measureof acceleration,f2h. Ra = Abh3/•2 as a Rayleighnumber, the flux law Finally, as we shall see in section4, its squareroot is a derivedin section3.1 (equation(8)) implies measure of the radius of deformation relative to the Nu --- Ra •/2 depthof the ocean,pertaining after the convectiveover- turningof an initially unstratifiedocean has ceased. TheRa •/2 dependenceis the onlyone that gives a flux 3.3.2.2. Rayleigh,laylor, and Nusseltnumbers: law (that in (8)) that is independentof the diffusivity. In addition to Ro* there are a variety of other nondi- This should be contrasted with the 1/3 or 2/7 debate of mensionalparameters that help us to interpret labora- the "hard turbulence" community,who are attempting tory and numericalstudies in termsof the observations. to understandlaboratory plume convection(see the The influence of diffusion of momentum and buoyancy discussionof Werne [1995]). In hard turbulencethe may be characterizedby the flux Rayleigh number nature of the thermal boundarylayer (i.e., how the heat (whichis independentof f), getsfrom the plate in to the bodyof the fluid) is the •h 4 rate-controllingprocess and is crucial in setting the Raf-- K2v characterof the free convectivelayer between the plate. One is then led to scalinglaws that are sensitiveto where v and K are the ("eddy") viscosityand thermal boundaryconditions (no-slip 2/7 or slip 1/3) anddepend diffusivityrespectively, or by the Taylor number, on the moleculardiffusivity •. This makesthe relevance of theselaws to geophysicalfluids problematical (for a further discussionof theseissues, see Emanuel [1994]). Ta=Ek 2= (16) Given that ocean convectionis not in a regime con- and Ek is the vertical Ekman number. Boubnov and trolled by molecularprocesses, with momentumand Golitsyn[1990] employed a regimediagram that divides heat being carried by turbulent processesthat are not the (Raf- Ta) plane into the followingregions, for distinctfrom the convectionitself, it is appropriateto set increasingflux Rayleigh number and Taylor number: (1) v = K and assumethat the Prandtl number is unity: the conductionregime, in which diffusion suppresses Pr = v/• (17) convectiveinstability, (2) a regimeof regularstructure, in whichconvection takes the form of uniform cells,(3) where v and • are an eddy viscosityand diffusivity, a geostrophicturbulence regime, and (4) a fully turbu- respectively. lent regime. Appropriatevalues of Raf and Ta for oceanicdeep 3.4. Observations of Plumes in the Ocean convectionare not knownwith any certaintybecause the turbulentprocesses must be representedby eddyviscos- 3.4.1. Space and velocity scales of plumes. ities and diffusivities, which are not distinct from the Given the technicallimitations of observing3-D, small- convectiveprocess itself. For this reason,Klinger and scale phenomenain the ocean, it is not possibleto Marshall[1995] attempt to characterizethe flowin terms rigorouslytest the scalingarguments presented in the of (Raf, Ro*), rather than the more commonchoice last sectionwith field observations;that is more sensibly (Raf, Ta). The formerpairing leads to a tidy divisionof done by controlledlaboratory and numericalexperi- the externalparameters between a viscous/diffusivepa- ments as describedin section 3.5. However, one can look rameter independentof rotation (Raf) and a rotational for broad consistencybetween observationsand the parameterindependent of diffusion(Ro*). This is es- scales set out in Table 3. pecially useful for applicationto the ocean because In MEDOC 1970, the first field experimentwith di- althoughRo* is rather readilycalculated for convection rect measurements,downward velocities of 12 cm s-• in the ocean,Raf dependson poorly known valuesof were observedby a rotating float [Voorhisand Webb, eddy diffusivity. 1970]. The floats residedat constantdepth and were A Nusselt number can be defined that comparesthe equippedwith fins that made them rotate in a field of convectiveto the diffusivebuoyancy transport: vertical motion. The character and scale of the convective elements could not be determined. In the Labrador •p Nu = Sea,however, Gascard and Clarke[1983] found from two •Ab/h closelyseparated floats that one showeda downward Here Ab is the buoyancydifference between two flat motionof 9 cm s-• andthe otherunderwent oscillatory platesand • is a diffusivity(for buoyancy).This problem motion,suggesting a decorrelationscale of the order of differsconsiderably from our (and indeedmost other) lkm. geophysicalproblems because in naturea buoyancyflux With the advent of self-recordingacoustic Doppler is demandedfrom the fluid, rather than a Ab imposed, current profilers, detailed observationsin convection and there is no lower boundary.Nevertheless, suppose regimeswere made possible.Time seriesof ADCP ver- that using(15), we substitutefor •p in to the above tical velocityrecords from the differentconvection sites 37, 1 /REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 27

Moored ADCP, Bin 2 • M229537m, Gulfof Lions, 1987

-5

A1 280m, Gulf of Lions, 1992

5 I _

• 5

GSM05480m,Greenland Sea,1995- 5

o -5 "1' _ 5

o I , , ,,5

-5

I I I I I , Feb I Feb 15 Mar I Mar 15 Apr I

Figure21. ADCP time seriesof verticalvelocities measured during deep convection events: (a) Gulf of Lions,1987; (b) Gulfof Lions,1992; (c) GreenlandSea, 1989; (d) GreenlandSea, 1995; and (e) LabradorSea, 1995.All showshort-period, strong downward motions resulting from the plumes with weaker upward motion in between. are shownin Figure 21 for the periodsof late winter A plume experimentwith moored ADCPs both near cooling.The first experimentusing moored ADCPs was the surface(200- to 550-m depth) and at middepth carriedout in the Gulf of Lionsin early1987, after deep (1100-1400m) wascarried out by Schottet al. [1993]in convectionhad occurred [Leaman and Schott, 1991; the central Greenland Sea (the positionof GSM is Schottand Leaman, 1991]. A mistral with heat fluxes markedin Figure 8). Convectionthere wasfound to be reaching500 W m-2 causedvertical motions of upto 13 weaker than in the Mediterraneanexperiment of 1987 cms -• withduration of only1-2 hoursat the moored with muchmore sporadic occurrence of plumes(Figure sites(Figure 21a). Vertically coherentdownward flow 21c). One eventwas found (Figure 22) wherevertically over the 300-m observationalrange of the ADCPs was shearedadvection from the east carried a plumepast the observed.From the advectionspeeds recorded and the site; the plume was slantedwestward because of the passagetime of the plume past the Eulerian measure- strongercurrents at upper levels.When the upper part ment, its horizontalscale was estimatedto be of O(1 of the plume arrived, currentsat the 400-m level were km). Determinationof the senseof horizontalrotation deflectedto the south, suggestingcyclonic rotation, of an advected feature from Eulerian measurements is while currentsat -1200 m were deflectedto the north, rather difficult because one has to determine how the suggestinganticyclonic rotation and in agreementwith mooredstation cuts the plume.Plumes were found to be angularmomentum considerations (see section3.3.1). associatedwith horizontalcirculation but withouta pre- Much more intense vertical velocities were observed at ferred senseof rotation[Schott and Leaman,1991]. that sitein winter 1994-1995(Figure 21d). 28 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

16 March event stat. T6

11oo

•1200 Figure 22. (a) Time-depthplots of verti- 1300 cal velocitiesduring a plume passagein the central Greenland Sea. (b) Horizontal ADCP currentsat depthsof 403-437 m and 1180-1214 m.

1180-1214 m

I I Oh GMT 6 12 18 0 6 12 18 16 March '89 17 March

In an experimentwith a triangular,2-km-side array in velocityof 2 cms -•, plumesshould begin to bedetected the Gulf of Lions duringwinter 1991-1992 (see Figure at the 300-m level ---4 hours after the coolingbegins to 9), three ADCPs simultaneouslycovered the range200- be effective (i.e., after the buoyancygain causedby 500 m at the stations, and a fourth one extended the daytimewarming has first been erased,here typically3 range at one stationdown to 600 m. A time seriesof the hours).Vertical velocityvariance picked up drasticallyat verticalvelocities from the preconditioningperiod (mid- about2200 (Figure 24c), in reasonableagreement. After December1991 into spring1992) is shownin Figure 2lb coolingstopped, the vertical velocityvariance decayed for one of the ADCPs at a depth of 280 m. In the early froma levelof 6-9 cm2 s-2 duringthe night and morn- part of winter the ADCP wasstill locatedin the stratified inghours to only1-3 cm2 s-2 in theafternoon and early intermediate layer, and the mistral of late December evening(Figure 24c);this yields a plumedecay timescale causeda burst of internal wave energy.Deep convection of a mere 6 hours. occurredduring February 18-23 (Figure2lb) within the Vertical velocitiesmeasured by ADCPs might not be confinesof the regionmarked in Figure 9, but the mixed due solelyto plumes,because active migration of zoo- patch was much lesshomogeneous than during 1987. plankton scattererscan amount, on occasions,to several Another way to estimatehorizontal plume scalesis to centimetersper second.However, the comparisonof the use the beam spreadingof the four beam ADCPs (see describedvariances during the mistral with those from Figure 23). With a 20ø beam angle, the beamsare sep- the quiet period before (February5-15) showsthat this arated horizontally by 200 m at a vertical distance of effectwas minor comparedwith the plumeactivity (Fig- 300 m from the transducer. Hence the increase of deco- ure 24c). rrelation with increasingtransducer distance allows es- In the Labrador Sea, where convectiveactivity had timatesof the horizontal scale.Comparing the resultsof been large in the early 1990s, an ADCP was deployed artificialplume modelswith the measureddecorrelation over the winter 1994-1995, covering the depth range scales,M. Visbeck (private communication,1994) con- 150-440 m. In early March, vertical velocityevents with cluded that the plumesindeed had horizontal scalesof temporal and verticalvelocity scales typical of other sites 500-800 m. were observed(Figure 21e). Maximumspeeds were 7 cm The strong diurnal cycle of the heat flux, changing s-•, andthe vertical velocity variance during the forcing from200 W m-2 duringthe day to 400W m-2 coolingat phasewas 1.5 cm 2 s -2. Despitewidespread convection in night(Figure 24a), allowedan estimateof the lifetime of the Labrador Sea during the observingperiods, these plumesthat were generatedat night.With an rms plume verticalmotions appear to be somewhatless intense than 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 29

I ! -lOO

-200

-300 -12 -6 0 6

-400

-500

Figure 23. Time-depth plots of vertical ve- stat. A1 -600 locitiesfrom the four ADCPs in the triangular moored array, February 22, 1992, showingdu- ration and depthsof plumes (for location see -300 Figure 9): (a) positionA1, 100- to 280-m and 360- to 630-m depth; (b) positionA2, 320- to -400 580-m depth; and (c) position T6, 320- to 580-m depth.

-500 stat. A2

-600 i I

-300 ,

-400

-500 stat. T6 !

-600 I, , I Oh 3h 6h 9h 12h 15h 18h 21h 24h 21. Feb 1992

those associatedwith the strong mistral case of the 3.4.2. Net vertical mass-fluxof a populationof Mediterranean. convectiveplumes. A law of verticalheat transport Do plumes entrain on their way down? One would for a collectionof plumeswas developedin section3.1. then expect to find cells that widen with depth. An We considerhere the role of plumes in the net vertical increase of horizontal scale with depth could not be masstransport and deep water formation rate. establishedby analysisof the ADCP beam spreading, On the large scale,stretching/compression of Taylor and neither was there a significantincrease of passage columnson the rotating Earth generateshorizontal cir- timescalewith depth [Visbeck,1995]. This issueremains culation, thus enabling one to relate the net vertical unresolvedon the basisof the presentlyavailable in situ velocity over an area to the time rate of changeof the measurements. circulation around the patch of ocean: In summary,convection cells of scalesbetween a few hundredmeters and 1 km have been observedby direct measurementsat all three major convectionsites. Plume Ot0• u . dl = f 0WOz'area scalesare in reasonableagreement with the scalingar- gumentspresented above based on the observedbuoy- where 1•2area is the vertical velocity averagedover the ancyfluxes (see Table 4). The evidencefrom the obser- patch and f is the Coriolis parameter. Observationsin vationssuggests that the plumesappear to decaybefore the Gulf of Lions [Schottet al., 1996] suggestthat the they become subjectto the effects of the Earth's rota- changein circulationaround the peripheryof a convection. So far there is insufficient evidence to observe tionpatch over a fewdays does not exceed 20-30 cm s -•. lateral entrainmentby plumes,but plumesdo not seem The above formula then yields a net w of less than 0.1 to entrain significantlyat the bottom of the convective mms -• overa patch50 km in diameterand 1 km deep. column. This is a very smallvertical velocity,tiny comparedwith 30 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

vertical velocities ( bins 2 ) Figure 24. (a) Mean diurnal heat flux cycle duringGulf of Lions convection.February 18- ß ':1' ' .'! • ' i 23, 1992; (b) vertical velocity,hourly means, :! ::, :; I ';,... ß I. :. ,s li, -•- .!' Ii-'." and standarddeviations; and (c) verticalveloc- ,..•:.:•.• .....,'-*::..: ..' :..'. ,.!,::•,"--:-.-:.....' '-.t'.*'.' -' . .. -. :.....' : :,..•.-;• '.;..'•'-.i,.. ity variance at 280- to 340-m depth during (February18-23) andprior to (February5-15) ß .. deepconvection showing generation and decay .lOt' ß i i i ''. lO timescales of plumes. (From Schott et al. ß vertical velocity variance (bins 2) [1996].) 8 ß ß ß 280- 340 rn * •18- 23 Feb ß E4 ß ß

2 5-15 Feb ß ß ß ß ff o o o 8 * o o 0 0 0 0 0 0 0 0 8 o 0 0 0 OiO 0 0 0 Q Oh •h 1Oh 15h 20h t i me of day

those associatedwith individualplumes and so small as deepwater formation(for example,the numberof sver- to be insignificantin the context of deep-waterforma- drupsof Labrador Sea Water formed) cannotbe com- tion. We conclude (the argumentsare developed in puted directly from measurements(or deductions)of moredetail by Sendand Marshall [1995]) that the plume vertical velocity w; these are vanishinglysmall when scale does not play a significantrole in vertical mass integrated over the mixed patch. Instead, it is best to transport: downwellingin a plume is almost entirely relate rates directlyto the volumesof homogenizedfluid compensatedby upwellinglocal to that plume. However, created in the mixing phase. the plumesare very efficient mixersof properties(see For example, supposethat convectionhas created discussionin section3.1). This has important implica- dense water over an area .4 down to a depth h. The tions for the way in which plumesare parameterizedin volume createdis .4h. Taking, for example,.4 = ,r(60 numericalmodels (see section 5). Evidently,the ultimate km)2 andh = 1 km,values typical of theMediterranean sinkingof the homogenizedcolumn to its neutrallybuoy- [seeSend et al., 1995],we obtaina deepwater formation ant level occurs on much longer timescalesand, we rateof 1.1x 1013m 3 peryear. This is -0.3 Sv,from just believe, is associatedwith geostrophiceddy dynamics one event and in approximateagreement with the ob- (Figure 3c). A further implicationis that the rates of served outflow of deep water through the Strait of

TABLE 4. Comparison of Observed Length and Velocity Scales of Convective Elements, Deduced From ADCP Field Observations, With Scaling Laws Developed in Section 3.3

Parameter Labrador Sea (1995) GreenlandSea (1989) Mediterranean(1992)

Depth of convection,m 1800-2200 800-1500 1100-1500 Buoyancyflux, m 2 s-3 l0 X 10-8 6 X 10-8 20 X 10-8 Coriolisparameter, s-• 1.2X 10-4 1.4X 10--4 0.98X 10--4 Ro* = •/2/(fa/2h ) 0.1 0.1 0.4 Nonrotating w = (•oh) i/a, cms -1 6.4 4.5 7.7 l = h, m 2000 1500 1800 Rotating Wrot= (•o/f)l/2, cms- 1 3.2 2.1 5.5 /rot= (•o/fa) •/2, m 260 150 560 Observations Wobs,cm s-• 8 6 10 Plume diameter, m 1000-1500 600-1000 800-1000 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 31

Gibraltar [Brydenand Stommel,1984; Bryden and Kinder, nandoand Ching [1994],where suchdependence is evi- 1991].Observed volumes and water masstransformation dent in the case of the single plume. Boubnov and rates in the Labrador, Greenland, and Mediterranean Golitsyn[1990] presentan empiricallaw for the lateral Seas are reviewed in section 4.1. plume scale,which is dependenton the Rayleigh and Taylor numbers,and has nothingto do with (18). 3.5. Numericaland LaboratoryStudies of Oceanic 3.5.2. Numerical experiments. Numerical stud- Convection ies of rotating convectionclearly demonstratethe features schematizedin Figure 19 and observed in the 3.5.1. Laboratoryexperiments. Laboratorystud- laboratory(see, for example,Figure 20). Figure 25 ies of rotatingconvection have a long history(see, for showscurrents and temperatures in a veryhigh (---50 m) example,Nakagawa and Frenzen[1955], Rossby [1965], resolution non-hydrostaticnumerical experiment 24 and, more recently,Boubnov and Golitsyn[1986, 1990], hoursafter vigorous cooling (800 W m-2) wasapplied at Fernandoet al. [ 1991],Maxworthy and Narimousa [ 1994], the surfaceof an initially restingunstratified, rotating and the book by Boubnovand Golitsyn[1995] and ref- oceanwhere Ro* = 0.1 andRaf = 109[see Jones and erencestherein). They can be classifiedinto two broad Marshall,1993; Klinger and Marshall,1995]. As the cool- categories:convection from horizontallyhomogeneous ing persists,plumes penetrate progressively deeper into sources[Fernando et al., 1991] and convectionfrom the interior, lowering the mean base of the convective isolatedpatches (see the review of Maxworthy[1997]). layer, and, in time, distribute the influence of intense We will postponea discussionof the latter until section4. surfaceheat lossover the whole depth of the ocean.A Fernandoet al.'s [1991] rotating experimentsfrom a linear equationof state (equation (3)) was used, and homogeneoussource are in the geostrophicturbulence there wasno salt. In Figure 26a the horizontalvelocity regime,having an Raf in the rangeof 2 x 10•2 to 9 x variance(u '2 + V'2)1/2 at day2 isplotted as a function 10•2 anda Ta of 109to 2 x 10TM. The naturalRossby of depth for this seriesof experiments,normalized with numberwas not employedby Fernandoet al. [1991],but respectto the nonrotatingscaling/gnorot (equation (12)). we can deduce from their published parameters that Velocities in the (essentially)nonrotating experiment Ro* rangedfrom 0.0006to 0.033 in their studyand from withf = 10-6 S-1 doindeed scale as/gnorot: the curve is '--10-4 to unityin thatof Boubnovand Golitsyn [1986, centeredon unity in Figure 26a. However,we seethat in 1990]. the "high-rotation"regime, typical eddy velocitiesde- Fernandoet al. [1991] showedthat the scalingequa- creaseas the rotation rate increases,as is suggestedby tions (12) and (13) are appropriatefor the nonrotating the scaling(13). Figure26b again plots (u '2 + v'2)1/2 and rotating(low Ro*) cases.For the caseof horizon- againstdepth but now normalizedwith respectto /grot tally uniform convection,they estimated that the rms (equation(13)). The normalizedvelocities from all the velocity and integral length scalesof rotationally af- high-rotationexperiments collapse on to the same line fected convectionis in accordwith (13) with scaling centered on unity; /grotis indeed the velocity scale factors thus: adoptedby the plumes.Note that it is only the velocities in thef = 10-6 S-• case(essentially f = 0) thatappear l = 3-2/rot (18a) anomalouswhen scaledwith respectto the rotational velocity/grot' u = 2.4Urot (18b) Laboratory experimentsreported by, for example, b = ].75brot (18c) Maxworthyand Narimousa [1994] and Coates et al. [1995] suggestthat the numericalexperiments presented above The values inferred from numerous other studies are and thoseby Jones and Marshall [1993] may overempha- alsobroadly consistent with (18). size the role playedby rotation in oceanicplume-scale In the rotating case,Fernando and collaboratorsalso dynamics.The consensusof the laboratoryexperimen- found that the convectiveu and b were independentof talistsis that rotationaleffects are felt onlywhen Ro* < depth and time, at leastat distancesgreater than '•5/rot 0.1, rather than Ro* < 0.7 or so in the (rather more from the boundary where a heat flux was imposed. diffusive)numerical experiments of Jonesand Marshall Similar experimentswere carried out at small Ro* by [1993]. Maxworthyand Narimousa[1991, 1994] and Brickman Sanderet al. [1995] investigatethe dependenceof and Kelley[1993]. Focusing on the first stageof the flow, plume scalingon numericaldiffusivities. As long as the Maxworthyand Narimousa[1994] alsofound that veloc- numericalfluid is inviscidenough, the scaling(13) re- ities scaledwith /grot'The experimentsof Boubnovand mainspertinent, but the constantof proportionalitybe- Golitsyn[1990] also showedthat the velocityscale was tween, say, the modeledu and the scaledu, /grot,de- relativelyinsensitive to f in the fully turbulentregime. pends on diffusion, as does the transition between There remain a number of unresolved issues,how- rotational and nonrotational regimes. This has some ever.There is no clearconfirmation of the role of/rot in practicalrelevance because typical values of Ro* in the setting the lateral scale of convection; however, see oceanare just in this transitionalrange: 0.1 -• 1. It seems Helfrich [1994],Ayotte and Fernando[1994], and Fer- that deep convectiveplumes in the oceanare not dom- 32 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

(a) w (m/s) day I (z =-lkm) (b) u,v dayI (z =-lkm) ..... •..:....•...... ,,..•. ;. ....;. .•. • . .,.,•;--...... •-%•:.•½,.. : ..:•..(,..,-•,•,.. •...•, ;•.,...-.,:.•.. ;%...... ,:.½;•:.•½•:..,•,,½. ,:.:•...•....' ,•. .. .•... •...,•.::•..• .•,.:,..:,.•...... •q½•.. -.•...... :. • '•'•j.:.•:• ß•*' ..: '-.",':½?..• ." '.:, '"'•:5•.: ...... '•;• .... •. '; ß ß '• 8'--,..';.. -.ß Y•.•..•?,:.•'..'•*..',::•' ... , -•...: '.;;..: ...... ;•,• :"'..•%• 5•.-• .....' "•.••,.,:•. "."":4;';,•'.. .•- .- ...-...'..,.•'.';.%,..:-..• ;•'-....:;...... •;•;•'•:.:.•:,-.•."•,.•-.•.. •-•.. '..,:::,• •...•. -•.:.-. •..;.:.•".%....•, .-...., -....,"'. .• • 6::. ,•..•-::•-.,-.-....:•";•.•,'.• -...... -.•.; .*"**...... '.'..,'•-• ...... :..-...... •:':...-; ' .,• - ..•.q...•:.,•.•. ....;•.• •,::....•-:•.;.. q• •: 0.20 0.15 ' 0.10-.• ". .... :c,,:•.-,,,• ;' ;-•'."t..•;½.•:%•.½ 0.05-;•.•.• •; 5-, ß ½-.-•s-. '• --:::h.•>•,..•½•,.. ;;•,..½•. ,.. -o.o5 • E 2 ;'.:'7%.-:', ,"'*';;•.:,.-•,:? .-.- '•..':-;**•½•;.7;•;(•' . -o. lo -o. 15 :.... .½.,•-.-.½•-..,...½.•..,•...:•.• .-. •. **., .... ; • ... .'. ß.'" &'.' .. "":*'• '2:•' '-"'.' % •; .'•'•- 0 2 4 6 8 0 2 4 6 8

(m/s)day I EW(y = 5km) (d) in-situtemp. day 1 (z =-lkm) ,../,•.•...... ½:i...... ,•,-•...?::.•.t.•.....•-..•- .•'•:•½....•½..:-,••••' E •..• ...., -•::?.•;•.••:;-•:,:..½•..(. :•.-...½•.. •½: .:•-• •oBl•t• -••'••'•••'•••-••••••;••:'••••"••"•'""•"'•'"' .....

0.15 0.t0 11.995 o.• 11•990• -0.05 -0.10 11.985 -0.15 2 4 6 8 0 2 4 6 8 Domain Distance (km) Domain Distance (km)

Figure25. Numericalsimulation of convectioninduced by surface cooling in aninitially neutral, unstratified rotatingfluid in a 10 x 10 x 2 km doublyperiodic box. Fields are plottedafter 1 dayof integration.The horizontal resolution of the model is 50 m. The vertical resolution varies from 6 m at the surface to 100 m at middepths:(a) horizontalsection of verticalvelocity at middepths(z = 1 km); (b) patternof horizontal currentsat z = -1 km; (c) an east-westsection, chosen to passthrough the downwellingcenter apparent at x = 4.5 km; (d) a horizontalsection of in situtemperature at middepths(z = -1 kin).

inatedby rotation,but they may be influencedby rota- An alternativeapproach is that of direct numerical tion in importantways (see below). simulation(DNS), in which all the dynamicallyactive The approachof Jonesand Marshall[1993] is that of scalesof motion, down to the Kolmogorov scale, are a largeeddy simulation (LES) anduses highly simplified resolved.It is being pursuedby Kerr et al. [1995] and closureassumptions (Laplacian diffusion of heat and Julienet al. [1996a]but, becauseof the enormouscom- momentum with constantdiffusivities). Even the most putationalcosts, is limited in the range of Ra it can sophisticatedLES assumethat the turbulenceis isotro- study.However, anisotropies in mixingproperties and pic and homogeneous,so making grossassumptions boundary layer processes can be examinedby DNS with- about the nature of the small-scaleturbulence. (Mason out anypreimposed bias. Because realistic Ra cannotbe [1994]gives a criticalreview of the methodin the atmo- examined,the DNS approachinstead searches for scal- sphericcontext; 'see Garwood et al. [1994],Denbo and ing behaviorin the solutionsand then extrapolatesto Skyllingstad[1996], and ?aluszkiewiczet al. [1994] for realisticvalues, assumingthat the flow remains in the examplesof LES appliedto oceanconvection.) How- same dynamicalregime. Studiesof Rayleigh-Benard ever, rotating convectionis stronglyanisotropic, both convectionusing DNS byJulien et al. [1996b]push up to becauseof the natureof the plumes,which are stiffened Ra = 108and Ta = 109. Althoughnot in a parameter by rotation,and because of the organizationof the flow regimedirectly applicable to the ocean,they nonetheless by rotation.The advantageof LES is that simulations revealan importantinfluence of rotationon the dynam- with Rayleighnumbers approaching realistic values can ics of convectiveplumes, making them lesspenetrative be made; its disadvantageis that resultsobtained using than they might otherwisebe. this methodmay dependon assumptionsimplicit in the At sufficientlylarge diffusivetimescale compared to assumedclosure hypotheses. advective timescale, convectiveplumes impinging on 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 33

o! ', ! ! ! i I"1'i ! i .... ! i i I i i ..0.1•...... i...... i,...... •...... ,..... iM'•'"•"•"'" ...... '• ...... 4,...... i...... i..... {.... i...i.- ! i i i.:..:•'..• { • .• : : : ' ' ' ' -0.2...... !...... :,...... •i:.•:.,8j..i..4...l..i/...... •.i ...... :...... -':...... ':..... l ..... i.... i...i.-

-0.3 ...... !..... ;e:• ...... •..-•,.-.• j,..i....j•..."r ...... •"": ...... -i...... :? ...... +..... i..... !...4...i.- ..0.4 ...... •;...+..... i.• ....i./,...,.'. ....i!.i•.. ,•.i ...... • ..... -.':...... !...... !...... •..... i..... i.... i...i.- 'l : : ' i *'* :i : : ; ; : : '1 i i : : ...... •i ..... •....L& .... iJ•,,L..• LL.,i,.,L.• ...... 4•...... • ...... i ...... Ji...... •..... i..... i.... L.i., "i •. '..• : .: :t'..' :' i i ;" i i -1 -0.6 ...... i.:•....V....:•i....•,}..•.i•....{...kl ...... ½...... •...... ; -io.o,',o-' i.-

-0.7 ...... :J ...... :g.::•...•....•i,.•,...i•.}-,,-,...--,, . : { . :.... '-•, ...... !: ...... i,i -I o.•ox,o-, l'-i

-0.8 • !-,..:"L-•i,•i L•....Li•."%. i • ß I zoox lo-', • ...... t',, I,.ooxlo-. -0.9 i i :.."•-..?•,•,•'?Li• %_ i i . 13.00x ,o-, {/ ...... •...... f...... +....• i -..•i...i.ut ...... -:...... + 4'•'1 -I lO 4 10o I0'

Figure 26. Horizontalvelocity variance (a) nor- (•oU)t' (a) malized with respect to the nonrotating scaling Unorot and plotted as a function of depth over the convectivedisk, and (b) normalizedwith respect 0 i i i i i i I I1 i I t ' i I l '!"li" .... "iL i ! i ! ! t ! to Urotand plotted as a function of depth. From -0a ...... i...L.i..LLi...... •; ...... i...... : .... •'"':"i"•:",•..•16•::""'• .....i .... Jonesand Marshall [1993]...... ,...... '...... •4l ...... i...... ;...... • .... •...;...i..i..•.• ...... i...... i...... i.... •.::•.hi.• ...... • ...... •..... • .... •...•..•..L• z •sL ...... •...... i...... • .... ;...•;..•..•i ...... i...... •...... • .... •..•i.i$ ...... •...... •..... •.... •......

•.• -. o.ozx •o .t..•..:• ...... •...... •...... •.... f"'!•"T ...... f ...... • ..... •.... •-"f-'•-•'• 0 o.2ox•o--4 •h•: : : : •= •: :• ••: • :: •: •: •: •: ; : : : •.7 .. u o.•o x •o-4 ....• ,..i.•j_•i• ...... j• ...... • • • {•../• ..• ...... • • • i • •i•'

i i::i • : : : : . . : : : • : •...* •.oo•o-, .:...:..L•: ; : t: ...... • ß...... :•: ...... : .... •...•.••: : ., ß ...... :: ...... •.:; ..... : .... :...:..:..•.:: . , . :

---" ' 4 "wr'r':':...... :..... •...... •.... U'{'. ....•"T ...... T..... •.... •'"T"::"T'T

-1 10-• 104 10o 10•

stable stratificationmay overshoottheir neutral buoy- associatedwith plumes of low Rossbynumber lead to a ancylevel and penetrate into the stablystratified region. quasi-2-Dvortex dynamics,stirring the fluid in horizon- This may result in entrainment of fluid from below and tal planes(see Figure 27). This enhancedlateral mixing a reverse buoyancyflux at the base of the convective inhibits the vertical transportsof densityanomalies and zone [Deardorffet al., 1980].This reverseflux can lead to leads to the establishmentof a finite negativetempera- a sharpeningof the pycnoclineat the base of the mixed ture gradient(rather than the homogeneousmixed layer layer, a faster rate of deepeningof the convectivelayer, seenin nonrotatingconvection). The magnitudeof the and a transferof propertiesbetween the stablelayer and adverse temperature gradient, although enhanced convectivelayer. Observations,however (see section over that seen in the nonrotating case,is rather small, 3.2.1), suggestthat entrainmentis not commonlyseen at however, for typical oceanographic parameters and the base of deep mixed layers. The direct numerical conditions [see Klinger and Marshall, 1995]. In the simulationsof rotatingconvection by Julien et al. [1996a] field it would be very difficult to isolate from other suggestone possibleexplanation: they show that rota- effects. tion significantlydecreases entrainment and reducesre- We discusshow theseresults are modified by nonlin- verse buoyancyfluxes. The localized cyclonicvortices earities in the equation of state in section3.7. 34 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

(a) tryingto returnthe b surfaceto the horizontal(-by). What are the consequencesof the presence of this thermal wind on the convectiveprocess? 3.6.1. Slantwise convection. Let us again consider overturningin the (y, z) plane, as sketchedin Figure 14, but now in the presenceof more generalized rotationaland angularmomentum constraints (see Fig- ure 28). If there are no downstream(x) variations,then (b) stripsof fluid conservetheir absolutemomentum: m - u -fy (20) where u is the zonal velocity. If u were zero or a constant then lines of constant m would be vertical: the fluid is stiffened parallel to the rotation vector, and m varies only horizontally. This is the 2.5-D analogue of the rotational stiffnessdiscussed in section3.3. If m is conservedfollowing fluid elements (here the elementsare imagined to be strips of fluid extendingin x to _+oc), then theywill acquirea speedu = -fay on moving a distance By, or /,trot On moving a distance/rot, where /rot is the rotational scale given by (13). If fluid sinks in convectionthe m surfacesare squeezedtogether at the top inducingcyclonic vorticity, pushedout below generatinganticyclonic vorticity there. Now supposethat the combination of rotation and lateral densitygradients leads to a zonal flow in thermal 0 + wind balance and so u is not constant.Equation (20) again places important constraints on the convective process.Moreover, the m surfacesare now tilted over if Figure 27. The vertical componentof vorticity from direct du/dz -• O, and they will induce fluid particlesto move numerical simulationwhere the convectiveRossby number = along slanting, rather than vertical, paths; the upright 0.21. (a) A vertical sectionthrough the convectivelayer and convection of Figure 15 will become slantwise, as is into the penetrationzone. (b) The horizontalsection at the top of the convectivelayer. Cooling correspondingto a flux Ray- leighnumber of Raf = 1.4 x 10• is appliedat the upper (a) surface,into an initially stablystratified volume. The maximum value on the vorticityscale corresponds to 26f, wheref is the Coriolis parameter. Vertical vorticity is concentratedin surface-intensified,localized cyclonicvortices as a result of fluid convergenceinto convectionplumes. Adapted from Julienet al. [1996a]with permissionfrom Elsevier Science.

3.6. Role of LateralInhomogeneities Thus far we have discussedthe convectivedeepening (b) of a mixed layer in the absenceof lateral inhomogene- /.•therrnalwind ities. In the ocean, however, there are many sourcesof , •, •'©•' , lateral inhomogeneity,such as lateral shears,fronts, and preexistingeddies. Indeed, the "normal" state of affairs in mixedlayers (drawn schematically in Figure 28) is one in which the densityvaries in the horizontal acrossthe ', ',Xo',.'x ',.X ',. mixed layer (becauseof more vigorousconvection on one sideof it than the other, for example).On the large Figure 28. (a) Lateral gradientsin mixed-layerdepth and scale,in geostrophicand hydrostaticbalance, a "thermal density induced by spatial inhomogenitiesin the buoyancy forcingand/or the preexistingstratification. The mode of buoy- wind" currentu(y, z) will developgiven by ancy transfer through the mixed layer can change to one in fu z -- -by (19) which fluid parcels are exchangedlaterally in, for example, baroclinicinstability. (b) Schematicdiagram showingangular representingthe balancebetween differences in (Corio- momentum(m) and buoyancy(b) surfacesin the presenceof lis) "overturningforces" (fuz) and the actionof gravity a thermal wind shear. 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 35

sketchedin Figure 28b. (In practice,particles may take a fairly constantdensification in the northern third equiv- "zigzag"route, particularlyif the sinkingbranch is tra- alentto a heatloss of 800W m-2, anda sharptransition versed very quickly. Ultimately, however, the particle in between. A linear equation of state is specifiedde- "realizes"that it is in the "wrong" position and moves pendent on temperature alone and the resolution is acrossto where its m matchesthe surroundings.)The sufficient to represent gross aspectsof the convective stability of the layer will depend on the sign of Vb process.Figure 29a showsthe numerical solutionafter 9 measuredin the m surface,or the sign of the absolute days of cooling of an initially resting stratified fluid in vorticity normal to the b surface (correspondingto a which N/f = 10. It is clear from the isotherms and centrifugalinstability). Both viewpointsare complemen- streamfunction that the overturningmotions cause fluid tary and entirely equivalent.Emanuel [1994] calls this to move systematicallyin slanting paths and therefore more general mixed instability "slantwiseconvection." maintain a nonvanishingstratification in the region that The stability dependson the sign of the potential vor- is being actively mixed. Here the contours of absolute ticity (PV), momentum m are closely aligned with the isotherms, indicatingthat the potential vorticity (PV) is close to 1 zero. The temperaturefield alone is ambiguousat high- Q= • xl'Vb (21) lightingthe regionsof activeoverturning. Rather, potential vorticity is the key dynamicalvariable as shown by a measureof the stratificationVb in the direction of xl = Figure 29b. There are distinctplumes, of negativePV, 211 + curl v, the absolutevorticity vector, or, equiva- draining the surface source of negative PV into the lently, a measure of xl normal to b surfaces. interior. The present discussionmakes it clear that the pres- The integrationwas carried on for another 24 hours, ence of 211 cos (lat) Coriolis terms will also have the but nowwith the surfacecooling switched off. Figure 29c effect of tilting over the m surfaceseven in the absence shows that after cessationof cooling the convection of a backgroundzonal flow, becausethen m = -fy + rapidly dies away leaving a layer with very small poten- az, wherea = 211cos (lat) is the horizontalcomponent tial vorticity(around 1% of the undisturbedvalue) but, of the Coriolisforce [seeDenbo and Skyllingstad,1996]. significantly,nonvanishing vertical stratification. The Parcel theory can be readily (and rigorously)em- plumes of negative PV have been mixed away by the ployedto analyzethe stabilityof a zonal flow in thermal symmetric instability, erasing density gradients along wind balance to overturning in a vertical plane while absolute momentum surfaces, over a timescale consis- conservingangular momentum. It yields exact results tent with the predictionof the parcel theory,but leaving (see,for example,Emanuel [1994] or Haine andMarshall the end state vertically stratified. [1998]). It can be shownthat, and as is in accordwith These ideas help in clarifying,and form a contextin one'sphysical intuition, if Q is negative,then the flow is which to think about, the effect of convection on the convectivelyunstable to so-called "symmetric instabili- large scale and the parameterization of convectionin ties"; slantwiseconvection might then be expectedto large-scalemodels (see section5). ensueand return the Q of the layer to zero, the state of 3.6.2. Switchover from convection to baroclinic marginal stability: instability. We have arguedthat spatialinhomogeni- Q < 0 • convection (22) ties in the buoyancyforcing and/or the preexistingstratification induce lateral gradientsin mixed-layerdepth Theoretically,then, one has compellingarguments that and density.Now, if the angular momentum constraint stronglysuggest that (1) if Q < 0, then convectionwill of section3.6.1 is relaxed,the mode of buoyancytransfer occur,and (2) the end stateof the convectiveprocess will throughthe mixedlayer can changeto one in which fluid be one in which Q •- 0. Note, however,that in general, parcelsare exchangedlaterally in baroclinicinstability. thiswill correspondto the vanishingof N 2 measuredSuppose that we perform an experimentidentical to that along the m surfacesrather than in the direction of shownin Figure 29 but now in a 3-D domain allowing gravity.These ideas are readily borne out in numerical zonal variationsto break the angular momentum con- experiments. straint. It is found that baroclinicinstability ultimately Consider again the numerical experiment presented takes over as the primary agencyof buoyancytransfer in Figure 15 and discussedin section 3.1.1. We now through the convectionlayer. A typical example of the repeat it but m•ko. tW..C•changes' (1) we introduce the flow developmentis shownin the "bird's eye" view of possibilityof rotational control by includingf and mak- Figure 30. The near-surfacefields of temperaturereveal ing the model 2.5-D (y, z) with no x variations,so that a progressionfrom plume-scaleconvection at day 3 to zonalstrips of fluid conserveangular momentum and (2) finite amplitude baroclinic instability at day 6, with a introducea meridional gradient in the coolingto induce mature field of geostrophic turbulence by day 9. A lateral buoyancygradients and so supporta zonal wind. surface-intensifiedjet evolvesin balancewith the across- The coolingrate increasesacross the channelfollow- channeltemperature gradient, with the eddyingpart of ing a hyperbolictangent variation. Thus there is weak the flow dominating.Because there is no stressapplied surface forcing in the southern third of the channel, at the oceansurface, the globalzonal momentumcannot 36 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

(a) Temperatureand flow 0 ..• .

• I t . . . , •

looo 10 12 14 16 18 20

(b) PV and flow Figure 29. Vertical sectionsof (a) temperature 1.0 and (b) Ertel potentialvorticity (PV) normalizedby the PV of the initial condition,both at day 9, from the 2.5-D integration for the central part of the channel,and (c) the solutionat day 10, after the surfacecooling has ceased for 24 hours,showing the close alignment of m and b surfaces,indicative of vanishinglysmall PV. In each figure the flow and

lOOO 1-D mixed-layerdepth are shownas in'Figure 14. lO Peakspeeds (v, w) are(0.11, 0.050) m s-• in the(y, z) directions.From Haine and Marshall [1998]. (c) Temperature(-), absolutemomentum (:) and flow

10 12 14 16 18 20 Acrosschannel distance (km)

change,and eastwardflow at the surfaceis compensated plified equation of state of the form (3) can be used. by a westwardcurrent below. The length scale for the Then, irrespectiveof whether fresh water or heat fluxes baroclinicinstability at day 6 is -5 km, somewhatlarger are imposed,the densityequation behaves in a symmet- than the predictionof Stone's[1970] nonhydrostaticlin- rical way. However, this is not alwaysthe case,particu- ear instabilityanalysis of -3 km [see Haine and Mar- larly when the water is cold. Then nonlinearitiesin the shall, 1998]. For typical mixed-layer depths of 200 m, equationof statemanifest themselves more strongly,and stabilityanalysis predicts, and explicit calculationscon- in extreme conditionsthe water may change phase to firm, that baroclinicwaves with lengthscales of 0(5 km) form ice (the interactionof convectionwith ice is outside developwith timescalesof a day or so. the scope of the present review, but see Kaempf and A fascinatingand central aspect of the convective Backhaus [1998, and referencestherein] and Gawark- processin the ocean, then, is the interactionbetween iewiczet al. [1997]). In addition,the moleculardiffusivity convectionand baroclinicinstability, which we see being of salt and heat differ by a factor of 100, leading to played out in Figure 30. As time progressesthe fluid "double diffusion."We considernow, briefly, how some finds it more efficient to transfer buoyancyby the latter of these effects may influence and change the "pure" processrather than the former. Moreover, in the ocean hydrodynamicsconsidered thus far. (and unlike the atmosphere)there is no significantscale 3.7.1. lhermobaric effects. The thermobaric ef- separationbetween the convectiveand the baroclinic eddy scale.Before returning to this theme in section4, fect is the name associatedwith the pressure depen- we briefly mention complicationsthat arise from the dence of the thermal expansioncoefficient o•. It is neg- nonlinearityin the equationof state of seawater. ligible in the Mediterranean Sea, small in the Labrador Sea, but important in the Greenland Sea (see Table 1). 3.7. ComplicationsArising From the Equation For example,evaluation of the equation of state in the of State of Seawater roughly3øC water of the top kilometer of the Labrador The densityof seawateris a rather complicatedfunc- Sea showsthat 0p/00can be approximatedto within 12% tion of temperature,salinity, and pressure.Often a sim- by a constantvalue. In colder water, however,such as in 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 37

(a)

(b)

25 Figure 30. The evolution of the tempera- 20 ture at a depthof 65 m at (a) 3, (b) 6, and (c) 9 days,in which the zonal angularmomentum constraintoperating in Figure 29 is relaxed. •o We see the convectionevident in Figure 30a give way to baroclinic instability in Figure ['7 11.6 Surface 30c. The color versionof this figure appears on the cover of this issue. • 0 '"':":.:x:'.:..;•.....'...':.:.'.'.:7 •..:'.:':'(".'...'.'.'.!.: :':-'.":•::: Temperature

15 ; .• • •...•..*..• ...... •..••••••••••

?.r.x....:...... ' :...... ,.,•.•..•:•,..•... •:•::•:.,.,,:.•:.•..•.....,.....•....,.:.,.....•..•.•..?...:.•.•.•,,•. .•.:•..•.•..:•.:.:..•....•,.:•.,..•...?,,.,:..•.•..•..•,,?,..•,.,..?.,.•:•,.?•..•, ...... •j 0 ]0 20 30 40 50 Alongchannel distance (km)

the Greenland and Weddell Seas, Op/O0displays a to depth changeof 1 km), 0 is in degreesCelsius, and S greater sensitivityto pressure. is in practical salinityunits. Gill [1973] and Killworth [1979] first recognizedthe Thermobariceffects make it possibleto generatecon- role of thermobaricenhancement of thermal expansion ditional instabilitiesif salinity stratificationis partially in their calculations/modelsof hydrostaticstability in the balancedby thermal stratification(as is typical in the water column in the Weddell Sea. They showedthat a Greenland Sea,where a cold, fresh layer overliesa warm plume of saline water could experiencean additional salty layer). These classesof instabilityare mathemati- decreasein stabilityas it flowsdownward because of the cally analogousto conditionalinstabilities of a moisture- thermobaric effect. laden atmosphere(reviewed by Emanuel [1994]; see Consider,for example,the GreenlandSea. For water Garwood et al. [1994] for a review of thermobaric con- with 0 •-- -IøC, and 34.8 < S < 35 psu, typical of the vection). It appears,though, that such effects are not Greenland Sea, a good approximationto the densityis often driving factors in the water mass transformation (B. Klinger,unpublished manuscript, 1993) processbut can act as important modifiers. Consider, for example, a two-layer fluid in which 0 p = -•'0 + •'S- •Op (23) and S jump by an amount A0, AS, acrossthe interface where o•' and [3' and e are constantsand constantterms at pressurePh. From (23) the densityjump acrossthe and thosethat dependon p alone have been subtracted interface is given by out. The term -eOp in (23) is the thermobariceffect. Ap- •'AS- (o•' + eph)AO (24) For water in this range of 0 and S, the constantshave the valueo•' = 0.0329kg m -3 øC-•, [3' = 0.8kg m-3 psu-•, Supposewe displacea particle on one side of the inter- andœ = 0.0306kg m -3 øC-• (107 Pa) -•, ifp ismeasured face by an amount(in pressure)dp, then the difference in thousandsof decibars(so that a$p of 1 is equivalent between the densityof the particle and its surroundings 38 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 /.REVIEWS OF GEOPHYSICS

is (again using(23)) dp= -Ap + œAOdp.The condi- double-diffusivelydriven lateral intrusions,which can be tion for thermobaric instabilityis that dp> 0 and will traced for distancesgreater than 2000 km acrossthe occur when basin.The water masstransformations caused by double diffusionwithin the Arctic Basin may play an important dp >/•p/œ/•0 role in preconditioning the waters exported through Fram Straitto the convectionregion of the GreenlandSea. which, using(24), can be expressedas (see B. Klinger, Another role for the diffusive-convectiveinstability unpublishedmanuscript, 1993) ariseswhen a layer of cool, fresh water "caps off" the upper ocean. This is a common situation in the high- dpc= -• X• 1 + •-7Ph • (25) latitude ocean, where coastal runoff and ice melt can have a major impact on near-surfacestratification. As a where dpc is the criticalpressure change. For conditions fresh water cap is progressivelycooled by winter heat typical of the Greenland Sea, h = 200 m, A0 = 1.5øC, flux, the potential for diffusiveconvection at the baseof and AS = 0.118 psu, we find that dpc = 78 bars or the mixed layer increases.Because the double-diffusive 780 m. Thus particles must be displaceda substantial process transports heat but not much salt, it has a distanceto trigger instability in this manner. stabilizingeffect on the stratification.This may prevent Thermobaric effects can readily be detected in nu- or delay the convectivelydriven deepeningof the mixed merical simulationsof deep-reachingplumes, however. layer that would be expectedin the absenceof diffusive Sanderet al. [1995] repeat the nonhydrostaticcalcula- convection.An implementation of this effect in a 1-D tions of Jones and Marshall [1993] but with a more model improvedagreement between it and the observed realistic equation of state and show that thermobaric evolutionof mixedlayer temperature,salinity, and depth effects lead to enhanced vertical accelerations in the in a winter-cooledwarm-core ring [Schmittand Olson, water column. Gatwood et al. [1994] and Denbo and 1985]. Only a few preliminaryefforts to incorporatesuch Skyllingstad[1996], using LES models,also find impor- processesin larger-scalecirculation models have been tant modificationsto the verticalprofile of buoyancyflux made [Zhanget al., 1998], thoughKelley [1990] provides in deep polar sea thermal convection. a suitableparameterization. 3.7.2. Double-diffusive convection. The molecular diffusivityof dissolvedsalt in water is about 100 times lessthan its thermal conductivity.This can trigger static 4. DYNAMICS OF MIXED PATCHES instabilitywhen the vertical heat and salt gradientsop- poseeach other in their effectson density.Because such The plumes reviewed in section3 act in concert to warm-saltyand cold-freshcorrelations are so commonin homogenizean extensivepatch of ocean.We now review the ocean and turbulence is generally weak away from what is understoodof the dynamicsof the mixedpatch as topography,double-diffusive effects are thought to be a whole. The definingfeature of homogeneouspatches is nearly ubiquitous[Schmitt, 1994] and may play a role in that properties(such as T and S) are mixed by convec- water mass transformation.At high latitudes the cold, tion, leading to a local diminution of property gradients fresh over warm, salty stratificationoften observedfa- interior to the patch but an enhancementof gradients vors the diffusive-convectiveinstability. In this case a around the periphery (see the schematicdiagram in series of thin interfaces alternates with convectively Figure 3). This localizationin spacemakes the problem stirred layersto provide an enhancedupward heat flux distinct from the myriad classicalstudies of convection with only a small salt transport.Numerous observations rooted in the Rayleigh problem (convectionbetween of such "staircases"have been reported in both Arctic two platesextending to _+•); as one might anticipate,in and Antarctic seas. Padman and Dillon [1987, 1988] the ocean edge effectsultimately come to dominate the found extensivediffusive layering in the Beaufort Sea evolvingflow fields.Large horizontalbuoyancy gradients and Canadian Basin in the Arctic. Muench et al. [1990] on the edge of the convection patch support strong report diffusivelayering to be a common feature over horizontal currents in thermal-wind balance with them: much of the Weddell Sea. They estimatean upward heat the "rim current." If the patch has a lateral scalegreater fluxof 15W m-2 thathelps maintain ice-free conditions than the radius of deformation, then baroclinic instabil- in the summer. The effect of such heat loss with little salt ity theory(see section 4.3.2) tellsus that it mustbreak up exchangeis to provide a subsurfacecooling of the af- into Rossby-radius-scalefragments. We shall see that fected water mass without air-sea exchange.Carmack baroclinicinstability plays a dominantrole in the dynam- and Aagaard [1973] and McDougall [1983] have pro- ics and thermodynamicsof the mixed patch, orchestrat- posed that this is an important effect for the transfor- ing the exchangeof fluid and buoyancyto and from it. mation of Atlantic Water into Greenland Sea Bottom Indeed one can consider the process of water mass Water. Within the Arctic itself, Carmack et al. [1997] transformationin deep convectionas an extreme exam- have reported on a major recent change in middepth ple of the "switchover"from convectionto baroclinic water massproperties becauseof a strong incursionof instabilityintroduced in section3.6.2. warmer, saltier Atlantic Water. This is likely a result of After reviewingsome of the relevant observations,we 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 39

considerthe overturningof a neutral,rotating fluid to an of 2 km, then a water massof volume3.8 x 10TM m 3 is extendedbut localizedloss of buoyancy.We then go on to transformed,and if this is taken as annually released considerthe sameproblem but in a stratifiedrotating fluid. LSW, the flux would amountto 12.7 Sv.This is an upper limit, appropriateto the period of extremelyactive LSW 4.1. Observed Volumes and Water Mass thicknessand production of the early 1990s. Further- Transformation Rates more, as shownby the summer AR-7 sections,LSW is Here we review what is known of the scales,volumes, not "flushedout" eachyear; subsequentwinter convec- and water mass transformation rates that are associated tion actson previouslyformed LSW, reducingthe aver- with mixed patches.As was emphasizedin section3.4.2, age annual transformation rate. a deep mixed patch is not akin to a chimney,in which a 4.1.2. Greenland Sea. In the Greenland Sea, downdraft carrieswater to deep layers. Rather, it is a deep convectionwas not active during the 1980s,when volume of water mixed by the action of convection.The intense surveyswere made. Indirect evidencefrom the rate at which a water mass is formed in a transformation activeconvection period of the 1970s,for examplefrom event is thus related to the volume of the mixed patch tracer concentrations, has allowed estimates of renewal that is subsequentlyabsorbed into the surroundingwa- times to be made [e.g., Schlosseret al., 1991] and these ters via geostrophiceddy exchangeand deep boundary have been comparedwith those of the subsequentqui- currents. In a typical winter, perhaps only one deep- escentperiod [Rhein,1991]. However, direct evidenceof mixing event occursper region and regime, but occa- the extent of convectionregimes is sparse.The 1989 sionallya previouslymixed site that has alreadypartially preconditionedpatch within which individual plumes exchangedits propertiesis stirred up again. subsequentlydeveloped is sketched in Figure 8. In 4.1.1. labrador Sea. In the Labrador Sea, moni- 1996 a small patch of about 30-km scalewas observed toring of convectionover many years occurredat Bravo near 75øN,3øW (J. Backhaus,personal communication, (Figure 5, site B), but that did not yield informationon 1997). As was discussedin section2.2.2, the existence the lateral extent of the deep-mixedregime. However, and extent of Greenland Sea deep-mixedregimes are during February and March 1997, R/V Knorr conducted confined to the limits of the Nord Bukta. Transforma- an extensivehydrographic survey of the Labrador Sea tion ratesfrom the GreenlandSea Project (GSP) surveys during a period of active convectionas part of the of 1989 are still being deduced (J. Meinke, personal Labrador Sea Convection Experiment [see LabSea communication,1997). Group, 1998]. The spatial variability in the CTD casts 4.1.3. Mediterranean Sea. The logisticaladvan- was remarkable. Intrusions were prevalent, and often tage of the closenessof the Gulf of Lions convection the downcasttrace would differ significantlyfrom that of regime to the southern coast of France has permitted the upcast.Some of this rich structuremay be due to the severalobservations of the scalesand winter develop- proximity of the convectionto the boundary, where ment of the deep-mixedregime in different years. Ex- strong contrasts exist between resident water masses tents of the deep-mixedpatches observed in 1969, 1987, (R. Pickart,personal communication, 1997). and 1992 are sketchedin Figure 9. The mixed patch In recent years, several repeats of the WOCE AR-7 created in 1987 must have been a record one because it hydrographicsections have been carried out, which runs occurredin the year of greatestwinter heat lossduring through Bravo acrossthe Labrador Sea to Greenland. the past three decades[Mettens and Schott,1998]. How- They reveal large mixed patches, of about 500 km in ever, the observationwas taken during February 17-23, lateral extent (J. R. Lazier, The Labrador Sea after when a secondmistral had reopened the stratification, winter convection: 1990-96, submitted to Journal of which had been evolvingfrom a mixing event associated PhysicalOceanography, 1997), but thesesurveys all took with the mistral of January 10-12, 1987. In early Febru- place in the summer, many months after mixing oc- ary, between the two mistrals,the surfaceexpression of curred (see Figure 7). In 1976, Clarke and Gascard the homogeneouswater masshad shrunk to about half [1983]observed a smallerpatch of about200 km in scale of the size sketchedin Figure 9 [Leaman and Schott, when productionwas low. Combiningwith observations 1991]. From hydrographytaken in 1992, the volume of from 1978,they estimatedthat the extent of the patch in transformed water masseswas estimated to be 1.5 x l0 •3 the alongshoredirection was -450 km (marked in Fig- m3 [Schottet al., 1994].Inferences from acoustic tomog- ure 5). With a depth of 1750 m this givesa volume of raphysuggested a lower value of 0.95x 10•3 m3, how- 1.2x 10TM m 3, corresponding to a transformationrate of ever [Se_ndet al., 1995]. These valuescorrespond to 0.5 3.9 Sv over the year. This estimateis similar to Wright's Sv and 0.3 Sv of annual renewal, respectively. [1972] deduction of the transformationrate based on Recently,Krahmann [1997] estimatedthe water mass heat budgetconsiderations, who obtained3.5 Sv. Worth- transformationrates by calculatinga water masscensus ington [1976] estimatedthat a volume of water of 6 x from a newlycomposed hydrographic climatology of the 1013m 3 iscooled every year to below4øC, which yields a westernMediterranean. He estimateda deepwater pro- somewhat smaller transformation rate of 2 Sv. duction rate in the northwestern Mediterranean of 1.8 _+ If the deep mixed patch of the early 1990s was of 0.6 x 10•3 m3 yr-1, correspondingto 0.6 _+0.2 Sv.The cylindricalshape with a diameterof 500 km and a depth newlyformed deep water comprises 1.3 x 10•3 m3 of 40 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

(b)

Figure 31. (a) Sideview of plumesdescending from the discat the surfaceunder rotationalcontrol. This is the most rapidly rotating melting-iceexperiment, with Ro* = 0.03 and a 15-s rotation period. (b) Cones marked by dye showingthe geostrophicallyadjusted end state of the convectiveprocess after ice has melted and hence coolinghas ended.

Levantine Intermediate Water and 0.5 x 10•3 m 3 of man and Kelley[1993], Maxworthy and Narimousa[1994], Modified Atlantic Water. Earlier, Bethoux [1980] esti- Whiteheadet al. [1996], Coates and Ivey [1997], and mated 1.35 x 1013 m 3 from the evaluation of the then Narimousa [1997], all being motivated, in part, by the sparserhydrographic database. oceanographiccontext. Becauseof its simplicity(it can be carried out at home using a record player as a 4.2. Mixed Patchesin Numericaland Laboratory turntable and a dyed melting ice disk as a source of Experiments buoyancyloss), we now briefly describea seriesof ex- In section3 we describedexperiments in which con- perimentsperformed by J. Whitehead and B. Racine in vection was induced by uniform buoyancyloss at the Woods Hole in 1991. They are describedin more detail surfaceof the fluid. Here we considerthe problem in by Marshall et al. [ 1994]. which convectionis induced by an extended but finite A discof colored ice was gentlyfloated on the surface patch of cooling. of a rotating tank of water 10 cm or so deep. Convection 4.2.1. Mixed patchesin unstratifiedfluids. Stud- cells were observed to form and extend to the bottom ies of the convectiveoverturning of neutral fluids are of beneath the ice (see Figure 31a). As the ice melted, importancebecause they enableone to focuson the role small eddiesformed and migrated awayfrom the edgeof of rotation in isolation from stratificationeffects. They the ice. The meltingof the ice induceda buoyancyloss of also have some practical oceanographicrelevance be- •0 • 6 x 10-6 m2 s-3 andwith rotation rates of 15s or causedeep convectionsites are (almost by definition) so, a rather small Ro* = 0.03. Other rates of rotation rather weakly stratified and well mixed (see section were used rangingRo* up to a value of unity, the range 3.2.1). We shall see that Ro* emergesagain as a key of interestin the ocean(see Table 3). nondimensionalparameter of the "patch," along with By the time the ice was completelymelted, the cooled r/H, a measure of the aspect ratio of the convection fluid had broken up in to about half a dozen eddiesthat patch of lateral scaler and depth H. continuedto spreadapart with time. A sideview of the 4.2.1.1. laboratory analogues: Convection in- dyed water is shown in Figure 3lb. The eddies are ducedby disk-shapedsources has been studiedby Brick- conical in shape, with cold water (tagged with dye) 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 41 spreadingout over the bottom but "contained"by rota- predictionsof baroclinic instability theory and the nu- tion. Above each conical eddy, pronounced counter- merical experimentsof Jonesand Marshall [1993] (see clockwise(cyclonic) circulation was observed,with little below). The experimentalso provided constants of pro- circulationin the convectedfluid itself. This picture is portionalitythat dependon the nature of the (rotation- consistentwith the upper cycloniccirculation being as- ally influenced)entrainment process. sociatedwith a low pressurethat "holdsup" the placid These laboratoryexperiments have been followed up lens of densefluid. On the large scale,cyclonic circula- and extendedby Brickman[1995], who studiesthe tem- tion built up aroundthe peripheryof the ice, and simul- perature of the mixed patch at equilibrium and its de- taneously,anticyclonic circulation started to develop at pendence on external parameters; we return to this the bottom. This is readily understoodfrom a consider- important aspectin section4.3.3. ation of angular momentum and its conservationbe- Note that these studiesadopt aspectsof the scaling causefluid flowsinward near the top and outwardbelow. reviewedin section3 for an infinite coolingpatch, even One of the important messagesto be taken from this though the convectionpatch is of finite size. However, experiment is again that "chimney" is a misleading recent experimentsby Coatesand Ivey [1997] and B. M. name: the convectionsite does not function as a pipe Boubnovand H. J. S. Fernando(private communication, down which fluid flows and thence spreadslaterally 1997), suggestthat the Ufot and /rot scaling(equation away.Rather, the plumesact as mixingagents, churning (13)) may not be entirely appropriate in the case of the column vertically. On scalessomewhat (but not cooling over an extended but finite patch. Moreover, much) larger than the plume scale, however, rotation both groupsfind that backgroundrotation indeed affects has a controllinginfluence, and the lateral spreadof the convectiveturbulence even when the Rossbynumber dense body of convectedfluid is constrained almost definedin termsof turbulentvelocity and length-scalesis immediately by the Earth's rotation. The "spreading of O(1). phase"is a geostrophicprocess in which baroclinicin- The reason that the /rot and Ufot scalesmight be stabilityis one of the key mechanisms. modified in the case of convection from isolated sources In another important study, Maxworthy and Nari- is the strong horizontal exchangeof fluid between the mousa[1994] combined laboratory experimentation with convectiveregion and the ambient fluid, thus imposing scalingarguments to determine the size and velocity the size of the patch r as an additional variable. The scalesof newly formed baroclinicvortices (the cones experimentsof Boubnovand Fernando(private commu- seenin Figure 3lb) generatedby surfacebuoyancy loss nication, 1997) showthat even in the absenceof rota- over an extendedbut finite patch.Salty water was intro- tion, the scalingunder convectingpatches is different ducedover a central circularregion using a showerhead from that of the horizontallyhomogeneous case because so that the convectivelyprocessed water could escape of strong entrainment flow from the edges of the the forcing and geostrophicallyadjust under rotation patches.They suggest that the velocity scale is (030r)•/3, and gravity,mimicking the fate of convectedfluid. rather than typicalfree convectivescaling (•0h) •/3 Maxworthyand Narimousa [1994] argued that after (equation (12)). Similar scalingneeds to be developed convectionhas ceased, convectivelymodified fluid is for the rotating case,where there is strong lateral ex- found in geostrophicallyadjusted cones, the remnantsof changebecause of baroclinicinstabilities shed from the the mixed patch broken up by baroclinicinstability into convectiveregion [Jonesand Marshall, 1993;Maxworthy radius-of-deformation-scalefragments. The aspectratio and Narimousa, 1994; Whiteheadet al., 1996]. To this of the cones of dense fluid, lcone/h,scales with the end, the experimentaldata of Coatesand Ivey [1997]will (squareroot of the) natural Rossbynumber of the sys- be of utility. tem thus: 4.2.1.2. Numerical analogues: Numerical simulationsof the creation and evolutionof patchesof mixed /conelp 1 (#'h)•/2 •/4 fluid in neutral ambient conditions have been carried out -• • • =• f =f3/4 h1/2: Ro* 1/2 (26) using nonhydrostaticocean models (see, for example, Jonesand Marshall[1993], Send and Marshall[1995], and where #', the reducedgravity, has been assumedgiven Marshallet al. [1997a]).The implied flux Rayleighnum- by bro t from (13c) and Ro*, dependingonly on "exter- ber Raf is 109,and the Taylornumber Ta rangesbe- nal" parameters,is the natural Rossbynumber discussed tween102 and 108, placing these experiments in the fully in section3.3.2). developed turbulence-geostrophicturbulence regime The experimentsof Maxworthyand Narimousa[1994] (regions3 and 4 of Fernandoet al. [1991, Figure 1]). As ranged Ro* from 0.08 to 1.0, spanning the oceano- in the simulationsof convectiondriven by spatiallyuni- graphicallyrelevant range. The slopeof the experimen- form coolingpresented in section3.5.2, the grid spacing tal data could be rationalized in terms of the scaling of the model is small enough that gross aspectsof argumentsreviewed in section3.3. In particular, it was convectiveplumes themselvescan be resolved.In con- found that the velocityand spacescale of eddiesshed by trast to thosesimulations, however, cooling occurs over the baroclinicallyunstable, convectivelydriven vortex a patch, and the domain of integration is sufficiently couldbe expressedas a functionof Ro*, consistentwith large to permit a study of both the influence of the 42 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

Figure 32. The temperature field rendered in three dimensionsat (a) 1 day, (b) 2 days,(c) (b) 4 days,and (d) 6 days,showing the evolutionof an initially homogeneouspatch of ocean cooled over a 16-km disc at its surface. Cold water is dark, warmer water lighter. As an aid to perspective,a box 16 km on the side and 2 km deep has been outlined.

(d)

plumeson the large scaleand the geostrophicadjust- cone ment/baroclinicinstability of the convectedwater as it -- • 5Ro* 1/2 (27) movesout of the formation region. An exampleis presented in Figure 32 simulating the overturning and in accordwith the study of Maxworthyand Narimousa break-upof a mixedpatch. A buoyancyloss of 0g0 = 4 x [1994].This formula can be usedto successfullypredict, 10-7 m2 s -3 (correspondingto a heat loss of 800W m-2) for example, the scale of the conesproduced by the wasapplied over a 16-kmdisc centered at the surfaceOf meltingice experimentdescribed in section4.2.1.1. The a 32-km,doubly periodic, 2-km-deep ocean. The implied scalelp = hRo*1/2, is tabulated inTable 3 asa function Ro* is 0.1. The water was initially homogeneouswith a of the buoyancyflux 0g0 for an oceanof depthh - 2 km linear equation of state dependent on temperature andf = 10-4 s-1. alone. 4.2.2. Mixed patchesin stratified,rotating fluids. The sequenceof events(sinking in plumesand the We now considerthe evolution of mixed patchesform- subsequentspreading of the convectedwater in ba- ing in initially stratifiedfluid. Now, in addition to Ro* roclinic structures)can be readily seen in Figure 32, and r/H, another nondimensionalnumber, N/f, playsan where the temperatureis renderedin three dimensions importantrole. Here N, the Brunt-Vfiisfilfifrequency of at variousstages in the developingmixed patch, resulting the ambient fluid, is measuredagainst f. If N/f is large in imagesreminiscent of those obtained in the labora- enough,deepening of the mixedpatch can "bottomout" tory usingdye (see,for example,Figure 31). As in the before it feels the bottom, as is often the case in nature. laboratory,the combinedeffect of the plume-scalecon- Here we describesome relevant idealized experiments; vectionis to drive an increasinglystrong, large-scale rim theory to explain and quantify them is presented in current around the disk of cooling, cyclonicat the sur- section 4.3. face and anticyclonicbeneath. This rim current servesto 4.2.2.1. Mixed patchesin laboratoryexperiments: confinethe convectedfluid to the volume definedby the Whiteheadet al. [1996](see also Narimousa [1996, 1997]) diskof cooling.Fluid outsidethe mixedpatch is unmod- report on a setof laboratoryexperiments in whichbuoy- ified, and there is little lateral transfer of fluid between ancyloss is prescribedover a patch at the surfaceof a the overturningand the non-overturningregions. By day rotating,stratified fluid (see Figure 33). The convective 2, however,there is evidenceof the growthof meanders layer penetratedrapidly downwardin the early part of in the rim current as it becomesbaroclinically unstable, the experiment.The dye would typicallycollect under an instabilitythat eventuallyleads to the breakupof the the sourceas a rapidly deepeningmixed region. After patchof convectedwater and lateral exchangeof fluid some time, however, the rate of advance of the layer with the surroundings.By day 4 the patch of homoge- slowedmarkedly but generallynever entirely ceasedfor nized coldwater hasbroken up into a numberof distinct the duration of an experiment. Usually, when the ad- conical structuresextending through the depth of the vance slowed, the side view revealed considerablelateral model ocean. These cones have a definite space and slumpingof the sidesof the dyed region.As time pro- velocity scale. gressed,the patch of dense dyed fluid broke in to a From studiesof a number of laboratory and numer- number of eddies, thus arrestingthe deepeningof the ical experimentssupport for the parameterdependence mixed patch (see the side view in Figure 33). Much suggestedby (26) is found and the constantof propor- quantitativeinformation was obtained from dozensof tionality found to be: suchexperiments and interpreted in terms of the theo- 37, 1 / REVIEWSOF GEOPHYSICS Marshalland Schott:OPEN-OCEAN CONVECTION ß 43 retical ideas set out in section 4.3. First, however, we day 2 day 2 mention parallel numerical studiesthat have helped :.: !':•:!:iiii:i:;i:!:!!!:::.:. :::. shed light on the problem. ======4.2.2.2. Mixed patches in numerical models: Killworth[1976] realizedthat mixedpatches ought to be ...... , [ •..... • ...... 1,•...... susceptibleto baroclinicinstability and carried out sta- .::!::::.•;[•I• ;,:•-,]•:- • ,]•:::::: ......

...... ;;:;:an't-•"•' :•.t;- ß bility analysesof mixedpatches to predict the expected ...... ; ...... scaleand growthrate (seesection 4.3.2). He reportedon ......

...... attemptsto numericallystudy the breakupof the patch - - - 5kin -.:.:.: but, for reasonsthat are not clear, was unable to obtain numerical solutionsthat exhibitedbreakup. day 4 day 4

The deepeningof a mixed layer into an initially strat- ======.... ::::::::::::::::::::::::::::. : ... ified, restingfluid was studiednumerically by Jonesand ======Marshall[1993], as illustratedin Figure 34. Using a fully nonhydrostaticmodel, they attempt to resolveboth the ...... ::...... ,• ,,'",,•.U"... __'.".L' _..".1• .,,: convectiveand geostrophicscales. As in the laboratory, •:...T:,;:.,,]...... ß buoyancyis extractedfrom the surfaceover a disc of radiusr at a rate G 0. In this calculation,cooling at a rate : i: i L'-::::.-:.-:.•:==__-:------.•;;;:;:::::: i i! i•ii: of 500W m-2 wasimposed over a discof 30-kmradius. ß:::::: :;: ::::::::::::::::::::::::::,'::::: :::- Initially, the mixedlayer deepensby the actionof plumes •2 ' at a rate closeto that givenby a nonpenetrativeconvec- day 6 day 6 tion model (equation (10)). However, just as in the ) laboratoryexperiments, as rotation takes over and baroclinic instabilitysets in, the deepeningof the mixed layer is arrested as baroclinic eddies sweep the convectedfluid awaysideways and draw stratifiedwaters in from the side.The developingeddies can be readilyseen in Figure 34. This line of investigationhas been carried further by Alversonand Owens[1996], who model the evolutionof _)

Figure 34. A numericalsimulation of a mixed patch induced by a localized but extendedpatch of cooling applied to the surfaceof a resting,stratified ocean at days2, 4, and 6. Plan views at the surfaceare shownon the left, with hydrographic sectionsthrough the evolvingmixed patch on the right.

a mixedpatch trappedover a topographicfeature in the presence of a large-scalecurrent (see also Alverson [1997]). These may be importantfactors in the convection sitesof the westernMediterranean (preconditioning by the Rh6ne Fan [Hogg,1973]) and in the WeddellGyre. Creponet al. [1989] and collaboratorshave usedhy- drostaticmodels togetherwith a convectiveadjustment scheme(see section5.1.1) to model the formation of deepwater in the Gulf of Lions(see Figure 35). Starting from an idealized preconditionedstate, Madec et al. [1991] were able to obtain deep water with realisticT and S characteristics.Moreover, they demonstratedthe impactof meandersgenerated by baroclinicinstability of the mixed patch and its role in advectinglighter waters from the peripheryinto the convectionzone, restratifying the mixed patch at the surface,and inhibitingdeep convection.Madec et al. [1991]also studied the impactof Figure 33. Side and top photographsof the dispersalof the variabilityof the forcingand resolutioneffects. convectedfluid from awayan evolvingmixed patch in a linearly Finally, we discussmixed patches in a numerical stratifiedlaboratory fluid. From Whiteheadet al. [1996]. model that attempts to remain faithful to some of the 44 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

POTENTIAL DENSITY

250. MONTH3 •

•29.10• 29.10 -

i I i I i i i i I O. 250. 500. X (kin)

C.i. = 0.02 kg m-3 !. I I 250. X ( km ) NORTH

Figure 35. (left) North-southvertical section of potentialdensity induced by a cylindricalpatch of cooling after 3 monthsof integration.(right) Horizontalsection of potentialdensity at a depthof 225 rn (just above the LIW layer) at the sametime. From Madec et al. [1991].

geographicaldetail of one of the important formation undergoingvigorous baroclinic instability, which, we will regions.Figure 36 showsthe pattern of surfacecurrents, argue, are important in orchestratingthe exchangeof mixed-layerdepth and a hydrographicsection through a fluid to and from the patch. mixed patch in the Labrador Sea during March, as capturedin a limited area numericalmodel [seeLabSea 4.3. Theoretical Considerations Group, 1998]. The model [Marshallet al., 1997b] was configuredwith realisticgeometry and topographywith 4.3.1. Local circulation induced by convection. sufficienthorizontal resolution (0.1 ø) to capturethe ba- Mixed patchesobserved at each of the convectionsites roclinic instabilityof the mixed patch, as is evident in of the world ocean have certain common features de- Figure 36b. The mixingby convectioncannot be resolved spite many differencesof regional detail: they are sur- on sucha coarsegrid and so must be parameterized.A rounded by rim currents,are more cyclonicat the sur- convectiveadjustment scheme of the kind discussedby face than below, and are characterizedby doming Klingeret al. [1996] was used;we discussthe rationale isopycnalsand vigorouseddy activitywithin and on the behind it in section 5. The model was initialized from a edge of the mixed patch. Here we attempt to discuss climatologicalhydrographic data set and drivenby twice- thesegeneral features in the contextof, and as a conse- daily fluxes of heat, fresh water, and momentum taken quenceof, the modificationof the large-scalepotential from National MeteorologicalCenter (NMC) analyzed vorticity field by the convectiveprocess. fieldsduring a period August 1991 to August 1992. The We have seen how convectionin the ocean, as well as lateral boundary conditions on the depth-integrated convectionstudied in laboratory and numerical fluids, transportwere suppliedby a 1ø global integrationof the overturnsa previouslystratified fluid, mixingaway prop- samemodel (see section5 and Figure 47) which itself erty gradientsto create a volume of "convectivelypro- was driven by twice-daily fluxes over a much longer cessed"water that is very homogeneousin its properties. period from 1979 to 1996. The stratificationis resetto very smallvalues over large Figure 36 indicatesthat many of the featureswe have areas.It is highly instructiveto considerthe convective been discussingfrom an observationaland, in idealized processand the subsequentevolution of the mixedpatch abstractions,a theoretical point of view, are not ob- from the perspectiveof the potential vorticity Q, the scuredby geographicaldetail. We seean extensivepatch fundamentalproperty of a rotating, stratifiedfluid. The of ocean within which properties are remarkably uni- potential vorticity has a direct influenceon, and is inti- form, surroundedby a regionof enhancedgradients and matelyconnected to, the hydrodynamics.Insights gained strongcurrents. The rim currentand the mixedpatch are from this PV perspectiveilluminate the observations 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 45

(and models) and motivate simple theoretical abstrac- (a) tions,which point to parametricrepresentations of both 500 the convective(mixing) scale and the eddy (stirring) scale.They thus provide an important theoreticalback- Depth (m) drop to the more pragmaticissues of parameterization 1500 of section 5. If on the smallscale the convectiveprocess sets (in a violentmixing process) the potentialvorticity to zero (as 25OO discussedin section3.6.1) and, in the aftermath of convection, fluid now "tagged"with zero Q evolvesquasi- adiabatically,what are the consequencesfor the large 3500 scale?To answerthat questionwe invoke the "invert- 56øN 58ø Latitude 60ø 62øN ibility principle" [Hoskinset al., 1985]. If the large-scale Currents at 70 rn flow is in geostrophicand hydrostaticbalance, then on (b) entering the geostrophicand hydrostaticrelation in to (21), Q can be expressedin terms of the pressurefield through an elliptic operator. This Q field can then be inverted, subject to boundary conditions,to yield the influenceof convectionon the large scale. The top panel of Figure 37a showsthe expectedQ distributionof a mixed patch schematically,just after convectionhas ceased.The mixed patch, made up of convectedfluid is imaginedto have Q = 0, and the sea surfaceis dense;outside of the mixed patch the ambient fluid has Q = Qref and the sea surfaceis at its ambient density.The inverted b andv a impliedby the PV distribution are shown in the middle and bottom panels, respectively. Mixed Layer Depth (m) 65øN We seethat the highlyidealized Q distributionshown (c) in Figure 37a doesindeed induce a large-scaleflow that has many of the characteristicfeatures of observedand 62øN numerically simulated mixed patches. There is a rim current, strong and cyclonictoward the surface, somewhat weaker and anticyclonicbelow, circumscribinga 59øN large, mixed pool of fluid. On the edge of the homoge- nized pool, isopycnalsarch upwardto the surfaceover a 56øN lateral scale of the deformation radius Nh/f. Thus by invokingthe "invertibilityprinciple," we see that if the 53øN convectiveprocess mixes Q away to 0, it must induce large-scaleflow much as is observed(see, for example, 50øN Figure 7 or Figure 10) and much as is seenin numerical 64øW 56øW 48øW 40øW models(see Figures34 and 36). We can take "PV thinking" further to considerthe Figure 36. Simulation of water-mass transformation in a hydrodynamicalstability of the mixed patch by making high-resolutionmodel of the Labrador Sea: (a) hydrographic use of a "mathematical trick" that is due to Bretherton sectionof potentialtemperature across the LabradorSea, (b) [1966]. In the inversionthat resultedin Figure 37a, an currentsat depth of 100 m, and (c) mixed-layerdepth during inhomogeneousNeumann boundarycondition that de- March 1992. pendson the surfacedensity distribution was employed at the surface.However, it is well knownfrom "potential theory" that any suchinhomogeneous boundary condi- strength of the PV sheet, g_, is just that required to tion can be replacedby a homogeneousone, provided ensurethat the verticalintegral of (Q + •_) over each that the sourcefunction is appropriatelymodified. Thus column of ocean vanishes.The Q has been "evacuated" in the (numericallyobtained) solution shown in Figure by convectionfrom the interior (Q -• 0 there) and 37b, homogeneousNeumann boundary conditionson concentratedin to a sheetof Q just beneaththe surface. pressureare applied in conjunctionwith an appropri- However, now, in Figure 37b, boundary conditionsand ately modified source function: a g function sheet of interior sourcesare given an equal footing; moreover, positivepotential vorticity anomalyis addedjust under- they are the potential vorticity distributionsthat can be neath the surface to represent the cold surface. The inverted subjectto homogeneousboundary conditions. 46 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

(a) (b)

o I mim. I :.: I 0.002 0.16 '; 0.16 ,

I -1 , Z (km)- •",2 ...... v::"(-," -2 -2

Q• max. -3 -3 1.6 -500 ' -4(•0 ' -300 -2•)0 -100 0 -500 ' -480..... -300 -200 -100 0 0 :.;:,'.;::•7,•:• i • \ ?.•:...... •--,z,..;/7'?-'-:::-'- ...... '...... ::'--:-?•"\:..-"Z. .... C,." .:'• :' :-',\ .....'"• "..'"/•," / ••"-." .....' mim. - -•'•7.2.:..." •7.3 27.g ...... 27.2- -1

-2 •.•2•;.•..•.::.•2•:f•Z•::•..•..•;g•"•....Z.•.-.•...•:5•:•:.•.:•.•....2"2' 7:'"';,...... ;...... 7'77..... •;õ"":,',"•.777; ...... 7...... 1:"'-:' •-:"::":."':"::'::'::':":':: •½;•'::"::"'"'::'"":: '• - -- -3 "'2"2"::"-'"Z"::."Z'""2"Z"2"Z'•;•'-"ZZ'Z'Z'-"Z'---'max. -3 -- 28 -50:0 400 -300 -200 -1 O0 0 -5i io '-460 ' -360 -200 --00 0 ;•0.••2.•.__.._.4.,:,.,4:4:f4./v,.t:•;;•.!::•h:•:•;•.:•:;,:: ,: ,••:..•,..•0.24•. o ::':i::::::::::::::::::::::::::::::::::::::::::•0oo'8•••'.J/I'-••' -0.24mim, --1 -1

-2

-3

-500 ß-400 -300 -200 -1 O0 0 -500 4.-400 -300 -200 -1 O0 0 Y (km) Y (km)

Figure 37. PV inversionfor a mixed patch with (a) inhomogeneousand (b) homogenousboundary conditionsat the surface.PV distribution,isopycnals, and currentsare plotted. In Figure 37a the potential densityat the sea surfaceis specifiedand an idealizedinterior PV anomalyinverted to give the hydrography and azimuthalvelocity of a baroclinicvortex. In Figure37b an interior PV field identicalto that of Figure37a is used,but now the coldsurface is representedby a sheetof highPV just beneaththe upperboundary, which is prescribedto be an isopycnalsurface. Note that in Figure 37b, unlike Figure 37a, the isopycnalscannot cut the upper surface,which itself is an isopycnal.

For example, we can now easily see why a dense stabilityof suchstructures using the "method of pertur- (cold/andor salty) surfaceinduces cyclonic circulation. bations"can readily be carried out within the confinesof It is equivalentto a positivesheet of PV. The low PV of quasi-geostrophictheory [e.g.,Killworth, 1976; Pedlosky, the interior of the mixed patch induces anticyclonic 1985;Helfrich and Send,1988]. If the radiusof the mixed circulation(PV isvery small there). Moreover,"Brether- patch is large in relation to the Rossbyradius of defor- ton PV sheet" conceptsalso clearly indicate that the mation, then the analysisasymptotes to that of Eady mixed patch will be subjectto baroclinicinstability and [1949]. The growth rate of the fastestgrowing mode is suggesthighly instructiveidealized modelsof the lateral exchangeof fluid with its surroundingsbased on point vortices. These are now discussed in the next section. 4.3.2. Hydrodynamicalinstability of mixedpatches. We have argued that the convectiveprocess resets and redistributesthe PV of the ambient fluid, resulting in mixedpatches that are highlysusceptible to, and strongly modified by, baroclinic instability. The homogeneous column of water is cold and dense at the surface relative to its surroundings,and so V Q points inward to the g functiondisc of high PV at the surface(see Figure 38). The interior of the mixedpatch has very low (essentially Figure 38. A schematicdiagram showing the large-scalepo- zero) PV, and so below, VQ points outward from the tential vorticity(Q) distributioninduced by convectivemixing patch. Thus the necessaryconditions for baroclinic in- of a patch of ocean. The patch is readily susceptibleto ba- stability(reversal in sign of VQ somewherewithin the roclinic instability;V Q points inward at the surfaceand out- fluid) are manifestlysatisfied. Analytical study of the ward in the interior beneath. 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 47

10-

-5- Figure 39. Four pictures charting the developmentof a mixedpatch comprising -10- an evolvingcluster of hetons.Each picture showsthe trajectoriesof the hetonsover a

-15 ' ' ! I I i i I period of 0.6 days:(a) 0.6-1.2 days,(b) 1.2-1.8 days,(c) 1.8-2.4 days,(d) 2.4-3.0 days.The trajectoriesof the upper layer vorticesare marked by solid circles,while thoseof the lower layervortices are shown

10- with open circles.The horizontal scale is presentedin units of the deformation radius and the hetons are introduced over a 5- disc of diameter of 5 Rossbyradii. From

0- Leggand Marshall [ 1993].

-5-

-10 -

-15 I ! ' I I 'l .... -15 -10 -5 0 5 10 15 -15 -10 -5 0 5 10 15 foundto be proportionalto f/Ri •/2 on a scaleclose to During the first 2 days, most of the hetons remain NH/f, whereH is the depth of the mixed patch and Ri is within the patchof cooling(see Figures 39a and 39b).As the large-scaleRichardson number of the ambientfluid. the number of hetons within the patch increases,a Becausethe ambientN is relativelysmall in deep con- shearedcurrent develops around the rim, cyclonicabove vection sites,N/f--- 5-10, typical Ri values are also and anticyclonicbelow, reaching a magnitudeof ---20cm small(--•10), the growthrates are rapid (a few days),and s-•. Thisrim currenteffectively constrains the vortices the scalesare small (a few kilometers). within the disc.Initially, they are preventedfrom form- Laboratory and numerical experimentssuggest that ing self-propellingpairs by this strongshear current: any linear theory is a useful guide in the early growth of pairs are torn apart before they can "escape."However, instabilitiesbut nonlinearprocesses soon take hold; ed- over time the rim current developswaves of mode num- dies mature and merge as the patch disintegrates.Legg ber 4-5 (see Figures39b and 39c) throughthe mecha- and Marshall [1993] exploit Brethertonsheets to model nismof baroclinicinstability. After ---2 dayswe seetilted the mixed patch as a collectionof paired point vortices clusterscontaining several hetons that burst out of the (called"hetons" by Hogg and Stommel[1985]) and soare main cloud, breaking through the shearedrim current able to addressnonlinearity. In numericalexperiments (Figure 39c). The convectionsite therefore breaksup usingGreen's function techniques in a two-layermodel, into severalsmaller tilted clusters,which propagate out- they pepper the convectionsite with paired point vorti- ward. The heton clusters continue to travel outward ces,one (of strengthq + ) in the upperlayer to represent (Figure 39d), carryingcold water far from the area of the cold surfaceand one (strengthq-) in the lower cooling.These extendedhetons, clumpingtogether on layer to representlow PV. The rate of introductionof the radius of deformation scale, are very efficient at vortices can be directly related to the rate at which fluxingheat laterally into the coolingarea (as described buoyancyis lost from the sea surface.In the experiment in section 4.4.2). Linear theory is very successfulin shownin Figure39 a constantcooling of 800 W m-2 predictingthe scaleof the clumping.As time progresses over a disk of diameter 16 km (about 10 times the and the hetonsdisperse, the magnitudeof the rim cur- Rossbyradius of deformation) is assumed,consistent rent diminishes,and so it is easierfor subsequentgroup- with the explicit calculationsof Jones and Marshall ings to move outward. Ultimately, a steady state is [1993]. Cooling at this rate createshetons of strength reached in which the flux of hetons out of the area of 0.6f at a rate of 33 per day. They are introducedwith cooling, in the form of tilted clusters,approximately random initial coordinates. balancesthe rate at which hetonsare generatedand so 48 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

250 supposedthat the eddy velocity v' would scalelike a Days length f multiplied by a growth rate proportionalto 200 f/Ri 1/2,as given by Eady theory, and b' wouldscale like M2•, yielding

150. f v'b'= otRil/2 M2• 2 (29) 100' whereo• is a constantof proportionality;M 2 -- Ob/Oyis a measure of the stratification in the horizontal, analo- 5O gousto N2; the large-scaleRichardson number is:

O0 '1•0 200 3•)0'4(•0'500 Ri = v27M4 (30) Q Watts/m 2

Figure40. The curveof t•_i•= (N2/h2/2•) (equation(10), and • is the lateral scale of the eddy transfer process. with • assumedconstant) and tequi1 (equation (33)) as a Usingthe eddyclosure equation (29) they solve(28) for functionof the coolingrate if h = 100 m, r = 50 km, andN = hequi 1and deduce that 10 -2 S-•. (•r) 1/3 hequil:'Y N (31) the number of hetons in the area of cooling remains where•/ = 1/(2o01/3. approximatelyconstant. In an evaluation of many numerical and laboratory Hetons are used by Brickman [1995] to model the experimentsof baroclinicallyunstable mixed patches, lateral transportsof heat in baroclinicinstability and so Visbecket al. [1996] confirmthe parameterdependence reconcilethe mean temperature attained over a warm discin his laboratorymodels of convectionheated over of hequil on •, F, andN suggestedby (31) andfind that (a fit from experimentaldata) a patchfrom below.The equilibriumlimit in whichheat input (or output) is entirelybalanced by lateral flux, the -y - 3.9 _+0.9 one discussedin section4.3.3 below, is alsostudied using heton modelsby Legget al. [1996] and preconditioning implyingan o•in (29) that has the value effectsassociated with barotropicflow by Leggand Mar- o• - 0.008 +- 0.005 (32) shall [1998]. Hetons are also useful analoguesof the eddiesseen in the environsof observedmixed patches. This is remarkablyclose to the value obtainedby Green [1970]in his studyof heat transportby barocliniceddies. 4.3.3. Equilibriumdepth and timescales. The ed- These resultswill be used later, in section 5.2, where we dies observedin the laboratory and numerical experi- discussthe parameterizationof barocliniceddies. ments reviewed above carry buoyancylaterally inward Visbecket al. [1996]also show that the timetequi 1to and upwardto arrestthe deepeningof the mixedpatch reachthe depthhequil is givenby (see,for example,Figure 33). Visbecket al. [1996]study and quantifythe equilibriumproperties of a mixedpatch tequi1: [•(r2/•)1/3 (33) embeddedin a linearly stratifiedocean, if buoyancyloss [3=12+_3 through the sea surface,0go, were entirely balancedby lateral buoyancyflux accomplishedby eddiesaround the where [3 has been determinedempirically from labora- peripheryof the mixedpatch, across the rim currentv'b': tory and numericaldata. What are the implicationsof theseresults for the dynamicsof mixed patches? 03 dA = v'b' dl dz (28) In Figure40 we plot tequi 1(equation (33)) andtl_r• = N2h2/20g,the time it takesfor a 1-D nonpenetrative hequd modelto get to the depthh, as a functionof the cooling Here the overbardenotes a time averagethat is long in rate for h = 100 m, N = 10-2 s-1 (typicalof the comparisonwith a typicaleddy lifetime. Of course,such stronglystratified surface waters; see Figure 2), and r - an equilibrium state may not always be achieved in 50 km. We seethat for persistentcooling rates in excess nature (seebelow), but it is an interestinglimit stateand of 350 W m-2, the mixedlayer will reacha depthof one that is amenableto analysis. 100 m in less than 30 days, before it is arrested by Visbecket al. [1996] solve (28) for the equilibrium baroclinic instability. If the cooling rates are smaller depthh equi 1 using the eddytransfer theory of Green than this critical value, however,the deepeningwill be [1970] (developedto describethe lateral heat flux by arrested by baroclinic instability. Choosingsomewhat barocliniceddies in the atmosphere),which relatesthe different,but not untypicalvalues (see Figure 2, section eddy buoyancyflux to the large-scalegradient. Green 1) Nsurface • 5 X 10-3 s-1, •o -' 7.5 x 10-8m 2 s-3 37, 1 /REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 49

(correspondingto a heatflux of 150W m-2),h = 200m, stratified environment has not yet been quantified by we find that t•_r) = 60 days.This is long in comparison direct observations. with typical baroclinic instabilitytimescales, and so for One way of determining the associatedexchange lower coolingrates, perhapsmore typical of the clima- rates would be through use of moored stations with tology, baroclinic instabilitymay indeed control the ul- temperature-salinityrecorders and current meters,from timate depth to which the mixed layer reaches.But if which covariances could be determined. Moored sta- buoyancy is extracted rapidly, in one or two violent tions were maintained in the Greenland Sea and the events,baroclinic instability will not have sufficienttime Mediterraneanduring and after convectiveepisodes, but to limit the depth: 1-D ideas ought to be adequateto the occurrenceof eddiesfollowing individual convection determine the depth to which the rapid deepening eventshas been observedonly infrequently.The eddies reaches.The patch of homogeneousfluid will neverthe- appearedto be few in number, and the moored stations lesssubsequently break up by baroclinicinstability, and did not alwayshappen to be in an optimum positionto the eddieswill disperseand play a role in restratifying make such covariancesmeaningful [e.g., Schottet al., the convectionsite (see section4.4). 1996].Ensemble statistics could perhaps be derivedfrom In the winters of 1969 [MEDOC Group, 1970] and Lagrangian floats, but until the Labrador Sea Experi- 1992 [Schottet al., 1994] convectiondid not reach the ment [LabSeaGroup, 1998], coverageof activeconvec- bottom but stoppedat intermediatelevels. Perhaps the tion regimes has not been sufficient for statistically deepeningof the mixed patch was arrested by lateral, meaningful results to be obtained. Moreover, in the eddy-inducedbuoyancy flux, which offset the surface northwesternMediterranean, and probably elsewhere, cooling.For a Mediterraneanmixed patch with width of there exists intense geostrophiceddy activity that is ---60km anda typicalmistral heat loss (600 W m-2) independentof the convectiveprocess, possibly associ- equation(33) givestequi 1• 30 days.Therefore it seems ated with topographicwaves along the boundary [e.g., unlikely that baroclinic eddies played a central role in Millot, 1991], addingfurther to the difficultyof identify- arrestingthe deepeningchimney because the period of ing the eddyflux contributionassociated with convection. strongheat loss lasted only 10 days.However, close to An effectiveway to monitor the 3-D developmentof the rim current, significantlateral heat and tracer fluxes water masstransformation in a convectionregime and must have occurredassociated with geostrophiceddies. thus indirectly quantify the lateral eddy exchangeis Barocliniceddy fluxesare likely to be of great impor- through acoustictomography from sound sourcesthat tance,however, on the seasonal(preconditioning) time- are distributedwithin and around the regime. In the scale becausethe geostrophiceddy instability time is 1992 experimentin the Gulf of Lions, good comparisons then considerablyshorter than that of the forcing.If the with hydrographicdata were obtained [THETIS Group, heat loss is ---200 W m -2 and the diameter of the 1994;Send et al., 1995] that demonstratedthe usefulness convectingregion is ---200km, parametersperhaps more of the tomographicinversions as a meansof measuring typical of the Labrador Sea gyre, then (33) yields a the integral developmentof the mixed patch. However, breakuptimescale of ---60days. This suggeststhat by the for the 1988-1989 experiment in the Greenland Sea, end of winter baroclinic eddies can influence the mixed- discrepanciesexist between, on the one hand, the con- layer budgetsignificantly even at the center of the gyre. clusionsfrom the few collected hydrographicprofiles and sparselydistributed moored stations and, on the 4.4. Restratificationand GeostrophicEddy Effects other, the tomographicinversions. The former led to the conclusionthat an extendeddeep mixed patch did not 4.4.1. Observations. We now briefly review the exist during that winter with only a few convective fragmentaryobservations of lateral exchangeprocesses plumes occurringwithin the mostly stratified environ- between the convection site and its environs. ment [Schottet al., 1993]. Tomographicinversions, how- 4.4.1.1. Eddy exchange: While plume develop- ever, suggestedthat a mixed patch scale of 0(50 km) ment and the creation of mixed patches have been was present [see Worcesteret al., 1993; Morawitz et al., reasonablywell observed,the observationsthat pertain 1996]. to the integral effectsof convectionon the large-scale The development of the convectionregime during environment are still sparse. The development of early 1992 in the Gulf of Lions, following a period of geostrophiceddies, their associatedtimescales, and their intenseconvection during February 18-23, is shownin exchangewith the environmentalwater masseshas not Figure 41. Surroundingthe deep mixed patch there is a been well documented.Gascard [1978] first investigated zone where the homogeneousproperties of the patch the role of eddies at the margin of the deep mixed are covered by upper layer stratification.This is the regime and their generationby baroclinicinstability, as region characterizedby marked geostrophiceddy ex- did Gascardand Clarke [1983] for the Labrador Sea change.Here vertical profilesrevealed homogeneity be- convectionregime. The scale of the cyclonic eddies neath the stratified top, and freon concentrationswere traced in these casescorresponded to the local Rossby found to correspondto those in the deep mixed patch, radius.However, the role of geostrophiceddies in the identifyingthe water asrecently ventilated [Rhein, 1995]. lateral exchangesbetween the convectivepatch and the Sendet al. [1995] measuredthe developmentof restrati- 50 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

43*

42'

41'

3' E 4 5 ø 6' 3' E 4' 5' 6'

43*

42*

41' Figure 41. Horizontal extent of the deep convectionregime, togetherwith eddyzone aroundit, in February-March 1992 in 3 ø E 4 o 5 o •ø the Gulf of Lions. From Schottet al. [1996].

ficationin the Gulf of Lionsby monitoringthe presence stratified near-surfacelayer developedon top of the of the LIW temperature maximum at 150- to 500-m mixed patch (see Figure 42). In 1992 the warm, near- depthusing acoustic tomography. They deducedthat the surface water appeared to migrate in from the side, deep mixed patch was reoccupiedby LIW in about 40 althoughattempts to measurethe near-surfaceflows by days,not inconsistentwith the theorypresented by Jones upwardlooking ADCPs were unsuccessful[Schott et al., and Marshall[1997] (see section 4.4.2). Of course,these 1996].Because acoustic rays are surfacetrapped in strat- integral measurementsdid not allow the distinctionbe- ificationtypical of winter, tomographyhas its bestverti- tween the effectsof horizontaladvection and eddy ex- cal resolutionnear the surfaceand socan readily be used change. to measuresurface capping. The inversionfor the aver- 4.4.1.2. Surfacecapping: One result of the exper- agetemperature of the upper 150 m by Sendet al. [1995] imentalwork wasthe findingof "surfacecapping" [Lea- showedthat to the southof the mixed patch, capping man and Schott,1991; Send et al., 1995]. From hydro- occurredwithin a few days,while to the north, where the graphic casts and tomography inversions it was patch abutsthe shelf edge,the surfacelayer restratified discoveredthat after cessationof intensecooling, a thin within --• 1 week. 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 51

Pose[don 189, CTD Profiles 60,61,63,64,75

500

•-1000

1500

I 12.8 13 13.2 13.4 13.6 13.8 Potential Temperature (øC), offset = 0.2 øC

Figure 42. CTD profilesshowing "capping" during the restratificationphase of convectionin the Mediter- raneau.

We now go on to describelikely physicalmechanisms was placed in an initially resting stratified fluid and that might be responsiblefor the rapid restratification. allowedto freely evolvein the absenceof external forc- 4.4.2. Restratificationand dispersalmechanisms. ing. They were inspiredby the early "cylindercollapse" There are a number of possiblerestratification and dis- experimentsof Saunders[1973] (see also Herman and persal mechanisms.A mixed body of fluid that abuts a Owens [1993]). The radius of the cylinder is 50 km, boundarywill excitetopographic waves that are forerun- greatlyexceeding the deformationradius L p (here 4 ners of the "bleeding"of the convectedfluid awayfrom km). Initially, the edgesof the columnmerely slump as the reservoirin boundarycurrent. Indeed, the observa- the densefluid sinksand spreadsunder the influenceof tions presentedby Sendet al. [1996] hint at a boundary gravity.The spreadingis limited (initially) to a deforma- "event,"the passageof (cold) fluid that, it is surmised, tion radiusby rotation as azimuthal(rim) currents,cy- was convectivelymodified a few weeks before by the clonic on top and anticyclonicbelow, are set up in mistral. Boundary signalshave also been studiedin nu- thermal wind balancewith the lateral densitygradients merical simulations(for example,Madec et al. [1991] at the edge of the column.Subsequently, however, ba- show such a signal of convectedfluid in the boundary rocliniceddies grow (here a mode 14 instability),reach current north of the convection site in the Gulf of finite amplitudeby day 20, and lead, over a period of a Lions). While Kelvinwaves are possible,indeed inevita- further week or so, to the breakupof the mixed patch. ble, and do carry awaysome of the convectedfluid, their The densefluid that definedthe cylinderat t = 0 has,by transport seems quite limited. Hallberg and Rhines t = 50 days,broken up and been dispersedby geostro- [1996] emphasizethe role of topographicRossby waves phic eddies over the whole of the (doubly periodic) in whichthe attendantvorticity pattern is transmittedby domain at its neutrally buoyantlevel. topographicwave dynamicswith considerablerecircula- Jonesand Marshall [1997] concludethat lateral eddy- tion and counterflowsadjacent to the main current. By transport of fluid from the buoyant boundary current contrast, with a vertical sidewall the "Kelvin wave that typicallysurround convection sites is a likely re- plume" has a simpler structure.Hermann et al. [1989] stratificationmechanism. Moreover, by quantifyingthe use contour dynamicsand explicit simulationto show efficiencyof the lateral eddy transportprocess, in a how the Kelvin plume developsthrough nonlinear vor- manner that parallelsthe developmentin section4.3.3, ticity dynamics. they are able to deduceand supportby numericalex- Wind-drivenEkman layerprocesses are likely to play periment, the followingrestratification timescale. If the a role in the advectivesupply of stratifiedfluid to the mixed layer has a depth h and lateral scale r and is convection site. However, it is not yet clear whether characterizedby a densityjump at its edgeof magnitude ageostrophicadvection is of the appropriate sign or Ab, then they find magnitudeto accountfor the very efficient restratification processthat is observedto occurover a rather deep surfacelayer. Trestrat•' 56(hAb)•/2 (34) Jonesand Marshall[1997] attempt to quantifythe role of geostrophiceddies in the breakup and dispersalof Choosingh = 500 m; Ab = 2 x 10-3 m s-2, andr = mixed patches.We have seen that if the radius of the 200 km, broadly consistentwith Labrador Sea condi- mixed patch is greater than the Rossbyradius of defor- tions,for example,then we find that Trestrat m 100 days, mationL p = Nh/f, thenit is proneto baroclinicinsta- a plausibletimescale and not inconsistentwith the frag- bility. Figure 43 presentsresults from a numericalcal- mentary observationalevidence that is currently avail- culationin which a cylinderof densehomogeneous fluid ablein the LabradorSea. Parameters more typicalof the 52 ß Marshalland Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

h1500r50N05f1 after 5, 20, 35 and 50 days

ß 150

• 100 -lOOO

as 50 - 1500 E o

-2000 50 100 150 50 lOO 15o Domain Distance (km) Domain Distance(km)

t ...... c -1000 Figure 43. Numerical illustration of the 0.• '

ß O.IB baroclinicinstability of a cylinderof dense 0.4•'::I:I•"• fluid, of depth 1500m and radius50 km in an ambient fluid in which N/f -- 5. The -2000 "plan view" panelson the left chart the 50 100 150 50 100 150 developmentof a passivetracer at the base Domain Distance(km) Domain Distance (kin) of the cylinderat a depthof 1400m at (from ß . top to bottom)5, 10,35, and50 days.On the

• • :?½•'•½-,,•""•,;'• •'•:. ;C , -•.'•'•.,',' ." ,.• right we showa "hydrographicsection" of ..- •. ,,-,.•, ,-• •:•, •: •. ,. ,:. m . ,?,.' ¾•.... :.+•.- ...... :,. :•,•,..•,,'..':...... -. -500 0 .•,- ,;•.•,•,::..• .- .• -•, .:.,.• densitythrough the center of the patch. • • :•f•'<.....:.: . ..•...: (SeeJones and Marshall[ 1997].) - 27 .-?. I :::.;..;.'•::;::•.:.':•½•:•"x .. ",. •: '-' ' ,'•.'-'

. ß ;? ::, .... 4)4 :" o

a ...... '•':•,,;;,:.:::'•' .':•!'•'...... •o 1• 15o 50 100 150 Domain Disl,n• (•) Domain Distance (kin)

. • •- ..u..:.• •-• ,•;:.... • ':'•---.'"?:.,, •'x'""'..':: ...... %•;•x ...... • .<..:.4.... • '•. :•:-•R•"';;'.'. x. •:•. ., .-. -500 • •] -.• • ,. ß•.• ,•r..•..,...,::...:,•:,...,Ls:• .:x::.::•' :. .. • - t•.:.:....•:::,' • •.Z•?•:• '•;•',-.: •.,.'" 'r'•:• ' :': "' -1000 100...... ,,.,:,,,:•,,•%;•q?Z ...... ':•:x•,;•, ....,,, •- )...:..•...•.•:...... ,•/,...... :..... •.•x•L:...... :,•.•, • ...... '..•;•.::.t.•½•:;• ...... •::•...,.:L•c•:.:,r: ',•"• ..... "•;•f;•:'•';:?:""•?7J?• ß:•' ...... 'R• ....." 08 ' o$ -1500; • •3'::•:.•:-:•71-::-'::•:•:.•.:.•q:•.:.:::,:•.:•:' .x•...... •;..':":.; o.(i71!:,.: '

-200O GO 1• 150 50 100 150 DomainDistance (km)

Mediterranean(h = 100m; Ab = 2 x 10-3 rn$-2, and research,typically have horizontal resolutions of several r = 100 km) give'rrestra t •' 20 days,again not untypical hundreds of kilometers. Then both the convective scale of what is observed. and barocliniceddy scale are "subgridscale." Both pro- The unravelingof the relative importanceof these cessesand their interaction must be parameterized. competingprocesses during each stage of the convective However, water masstransformation in oceanmodels is, processdemands further observationsin the light of more often than not, discussedsolely in terms of the theoretical and numerical study. verticalaxis and "recipes"of verticalmixing and adjustment. However, we have seen that the processinvolves lateral exchangebetween the convectionsite and its 5. PARAMETERIZATION OF WATER MASS environmentby baroclinicinstability as well as vertical TRANSFORMATION IN MODELS mixingin localizedregions by convection.On the basis of the observations,theory and modelsdescribed in the Ocean modelsused to studythe general circulation previouschapters, and the discussionbelow, we believe and,when coupledwith atmosphericmodels, in climate that the ability of low-resolutionocean models to ade- 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 53

quatelyrepresent water masstransformation is compro- before water propertiesat the bottom of a mixed layer mised primarily by the rudimentary nature in which are significantlychanged by buoyancyforcing at the top. lateral rather than vertical processesare parameterized This timescaleis related to the transittime of a particle in models. as it descends,in a convective plume, from the sea One way forward is to increase the horizontal reso- surfaceto the bottom of the mixed layer. For convective lution of suchmodels down to 5 km or so enablingthe plumescharacterized byvertical speed Wplume, it takes a small baroclinicscales typical of convectionsites to be time of the order of resolved.Then only the convectivescale need be parameterized.Even if rather simple"mixing" or (equivalent- tmix • h/Wplume (35) ly) "adjustment"schemes were employedto represent the convectivescale in suchhigh-resolution models (as to bring dense surfacefluid to the bottom. For vertical in Figure 36, for example),the water masstransforma- velocitiestypical of deep convection(see Table 4), tmix tion processwould be much improved over that of can be 12 hours or longer, perhaps long enough that coarse-resolutionmodels. With presentlyavailable com- settingtmi x to zero compromisesthe scheme. puters,however, this direct approachis possibleonly in Klingeret al. [1996] discusssimple parameterizations regional models. In ocean climate models the geostro- of convectionthat attempt to representthis finite tmix. phic scaleand its interactionwith convectionmust also For example,one could employan appropriatelychosen be parameterized,and therein lies the intellectual chal- vertical diffusivityof temperature and salinity in stati- lenge. The parameterizationof the convectivescale is callyunstable regions. It would seemdesirable to deduce discussedin section5.1, followed by in section5.2, dis- the magnitudeof the diffusivityfrom physicalknowledge cussionof the concomitantgeostrophic scales. of tmix. Because a diffusive systemtakes a time of the orderof h2/k to senda signala distanceh, thediffusivity 5.1. One-DimensionalRepresentation of Plumes ought to be [seeSend and Marshall, 1995]

5.1.1. Convectiveadjustment and vertical mixing. kv• h2/tmix= hWplume (36) The observationssuggest, and it has been argued on physicalgrounds, that convectiveplumes efficiently mix If weassume Wp•lume: 0.05 m S- • andh = 1000m, then propertiessuch as temperature, salinity, and density(see k v • 50 m2 s- •, significantlylarger than, for example, sections3.1.1 and 4.2) rather than actingas an agencyof thevalue of 1 m2 s-• usedby Marotzke [1991]. vertical massexchange. "Convective adjustment" algo- The appropriatescaling for Wplume and hence tmi x are rithms are often used to remove static instabilities discussedby Klingeret al. [1996],who comparedparam- (heavy fluid over light) in general circulationmodels. eterized numerical simulationsof mixed patchesdeep- While there are severalnumerical renditions, all adjust- eningin to stratifiedfluid (of the type shownin Figures ment algorithmsshare the sameprinciple: the potential 31 and 33) with explicitsimulations in whichthe convec- densityof fluid at one model level is comparedwith the tive plumes themselvesare resolved. Results are not level below, and if it is found to be denser, a vertical sensitiveto tmix,provided that it is sufficientlyshort, mixing of parcels occurs. The first implementations suggestingthat althoughsimple, convective adjustment [Bryan,1969; Cox, 1984] comparedadjacent levels only, has many merits. in an iterativeprocess, but more recent ones [Marotzke, Before we go on, it is worth noting the common 1991; Yin and Sarachik, 1994] mix the whole unstable misconceptionthat convectiveadjustment (or enhanced part of the water column to give a vertically homoge- vertical diffusion) must be used in hydrostaticocean neous state. However, the column is adjustedinstanta- modelsto representconvection because such models, of neously.Enhanced vertical diffusion, with a somewhat themselves, cannot overturn. It is the coarsenessof the arbitrarily chosenvalue of vertical diffusivity, is also horizontal resolution, rather then the limitation of the commonlyused to parameterize convection[see Cox, dynamical description,that suppressesthe convective 1984; Marotzke, 1991]. As was shown by Klinger et al. instability.In fact, the hydrostaticmodels exhibit more [1996, appendix],vertical diffusionis formally the same vigorous static instability than nonhydrostaticmodels as "adjustment"with a finite, rather than an instanta- when convectivescale is resolved [see Marshall et al., neous,adjustment timescale. 1997a]. The following questionscome to mind in regard to 5.1.2. Mixed-layerschemes. More oftenthan not the efficacyof adjustmentand verticaldiffusion schemes deep convectionis representedin ocean models in the to represent plume-scale mixing. If an adjustment framework of "mixed-layermodels," which are used to schemeis employed,is it reasonableto supposethat representthe surfacemixed layer in the ocean,without adjustmentoccurs instantaneously? If the mixing pro- specialtreatment of deep mixed layers.There are a large cessis represented by an enhancedvertical diffusion, number of mixed layer modelsthat have been compre- how large shouldthe diffusivitiesbe? hensivelyreviewed by Nurser [1998]. Here we only very Sendand Marshall [1995]characterize convective mix- briefly outline the nature of some of them and their ing by a timescale,tmix, that determineshow long it takes relevanceto the deep convectionregime. 54 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

The first mixed-layermodel (due to Krausand Turner local transport can result, with a property transported [1967]) is a "slab" model and assumesthat the mixed directly from the surfaceto the interior. layer is fully mixed. It includes,as part of its represen- While plume schemesattempt to mimic the actual tation, a convectiveadjustment scheme of the kind de- convectiveelements, many assumptionsare made that scribed in section 5.1.1 above. However, the entrainment are difficult to motivate from observationsor theory. For rate at the base of the layer and the rate of warming of example,the Arakawa and Schubert[1974] schemeas- the layer are related to the changeof column-integrated sumes a quasi-equilibriumbetween convection and potential energy and thence to sourcesand sinks of large-scale convergenceto determine the convective turbulent kinetic energy(TKE) and radiative and sur- massfluxes. Another commonlyused closure minimizes face buoyancyfluxes. This model was assumedin the the availablebuoyant energy [e.g.,Fritsch and Chappell, mixed layer calculationspresented in Figures 17 and 18 1980]. Mesoscaleatmospheric models more commonly and doesremarkably well in the deepeningphase of the assumelocal closures,for example, an empirical rela- mixed layer becausethe assumptionthat the mixed layer tionshipbetween the convectiveinstability of the lowest can be treated as a slabwhen it is coolingis a good one. model level and the initial plume massflux [Gregoryand In the originalmodel of Krausand Turner[1967] the only Rowntree,1990]. sourceof TKE was wind stirring,but Niiler [1975] and Two plume-based schemes have recently been Niiler and Kraus [1977] extendedthis classof model to adapted for use in ocean models. The first, due to include a sourcethat was due to shear instability at the Paluszkiewiszand Romea [1997] is basedon the scheme base of the mixed layer. of Fritschand Chappell[1980] with modificationsfor the The family of "Richardsonnumber models" (see, for ocean. The second, due to Alves [1995], modifies the atmosphericscheme of Gregoryand Rowntree[1990]. example,Pollard et al. [1973] or Price et al. [1986]) are Both of these schemesappear to generate plausible conceptuallysimilar to adjustmentschemes but mix only profilesof densityin responseto surfacebuoyancy loss when the Richardson number within the layer falls be- but need to be tested further against observationsor low a critical value, although when they mix, they mix explicit numerical simulationsto demonstratethat sig- perfectly.Instead, in the "K profile" model of Largeet al. nificant added fidelity resultsfrom the considerablein- [1994] (perhapsthe modelwith greatestfidelity), turbu- crease in complexity. Nevertheless,these models at- lence partially mixes properties in the vertical rather tempt to build up a schemethat is rootedin assumptions than mixing them perfectly as in a "slab" mixed layer. about the dynamicsor kinematicsof the plume scale. However, all of the aforementioned schemeshave been 5.1.4. Grid-scale instability of vertical mixing developedfor shallow mixed layers and not regions of schemes. Cessi[1996] showsthat instantaneouscon- deep convection,where convectiveplumes may be more vectiveadjustment schemes applied at a horizontalma- intermittent, where the Earth's rotation may be impor- trix of pointslead to the spontaneousemergence of the tant, and where there is significantlocalization of the smallest resolved horizontal scale. Because convective deep mixing region. For this reason, "plume models" adjustmentvertically mixes properties at eachgrid point, have been developed that attempt to address the irrespectiveof the horizontal distributionof suchprop- "plumey"nature of the mixingprocess in deepconvection. erties,horizontal spatialgradients are amplified as long 5.1.3. Plume models. Plume-based schemes have as adjustmentis faster than the horizontaldiffusion (or recently been developed to parameterize deep ocean advection)time betweenneighboring grid points.This is convection.Also known as mass-fluxschemes, they have a very stringentcondition. For example,if the horizontal a long history of use in the atmosphere,beginning with currents associatedwith the large-scaleflow are 30 cm Arakawaand Schubert[1974]. Convection within the grid s-• andthe timescale for the adjustmentassumed to be cell is modeled as an ensembleof convectingplumes. 12 hours,then the horizontalgrid must be finer than 15 The fraction of fluid contained within the plume is km if the amplification is not to occur. transportedfrom one level to the next,with entrainment of ambient fluid. If the pressureis assumedto be in 5.2. GeostrophicEddies and the SpreadingPhase hydrostaticbalance with the mean temperature,the evo- How does one parameterize the geostrophiceddy lution of the plume quantitieswith height can be pre- scalethat, as we have seen, plays a central role in the dicted usingconservation of mass,heat, and momentum transformationof water masses?One way forward, con- following a parcel, modified by entrainment and buoy- ceptually at least, is to view the spreadingphase of ancy acceleration. Ultimately, the parcel reaches a water-mass transformation as one of redistribution of height at which it is no longer buoyant in relation to the potential vorticity on isopycnal surfaces.The PV of surroundings,and detrainmentis assumedto occur.The water particles, set to very low values in convection,is net effect of the plume-basedscheme is a redistribution subsequentlyadvected away, conserving PV, at least on of densityand tracers,which is basedon the dynamicsof synoptictimescales. In manyways the "hetonic"descrip- an entrainingplume. If a tracer is injectedinto a plume tion of Legg and Marshall [1993] is much more than a near the boundary,it will not be mixed into the ambient representationaltool: it gets to the heart of the spread- fluid until detrainmentoccurs. Hence a significantlynon- ing mechanism.Convection modifies the preexistingPV 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 55

distribution, creating one that is prone to baroclinic If the eddy-inducedvelocities (v*, w*) are con- instability (see Figures 37 and 38). The mixed patch structedso as to satisfya nondivergentcondition breaksup into fragments,and the fragments,clusters of paired point vorticesin the heton model, disperse,car- ß - 0 (39) rying away the convectivelymodified water taggedwith V v*+ •z its anomalously low PV that then influences its sur- then the large-scaleflow can evolve in a manner that, roundingsthrough the "invertibilityprinciple." Indeed, unlike (37), conservesthe quantity of tracer between PV has been used to vividly map the dispersalof con- isentropicsheets. vectivefluid awayfrom its sourceregion [see Talleyand As is shown by the formalism of the TEM, the McCartney,1982]. Although simpleto describe,the rep- (v*, w*) are givenby resentationof this processin ocean models (in which primitive variables,rather than potential vorticity, are 0M the prognosticvariables) is not straightforward.One v* = --' w* = --Vh- M (40a) must attempt to representthe spreadingprocess as an adiabatic,advective one, in which the propertiesof fluid where particlesare conserved.If one likens the spreadingof 1 convectedwater by geostrophiceddies to an "eddy- M - • (u'b',v'b', 0) (40b) diffusive"process, in whichproperties are diffusedaway in to the background,one might adopt a "Fickian diffu- is a vector stream function that depends on the eddy sion" description buoyancyflux (u'b', v'b'). It shouldbe noted that (40) and TEM theory assume,and are only formally valid in, Dx/Dt = KV2-r (37) the zonal average and the quasi-geostrophiclimit, a where K is an "eddy diffusioncoefficient" for the tracer point that shouldbe borne in mind when applyingit in the contextof the convectiveprocess in the ocean. quantity -r. If, following Gent and McWilliams [1990], it is as- However,unless very specialforms are chosenfor the sumed that K, equation (37) is not faithful to important conserva- tion propertiesbecause it likens the redistributionpro- v'b' = -KV• (41) cess to a diffusive, rather than an advective one. For example, in the limit that small-scalemixing is vanish- where K is an eddy transfer coefficientwhose variation ingly small,the quantityof tracer betweentwo isopycnal hasto be prescribed(see section 5.2.2), then (40) implies surfacesought to be conserved. that Instead, it makes more physicalsense to frame the Vhb dispersalprocess as an advective,rather than a diffusive one, by associatingan "eddy-induced"velocity to it. The M =-K N2 (42) appropriate theoretical framework is provided by the If K is set to zero on all boundaries, then M is zero there, transformedEulerian mean (TEM), first introducedin ensuringthat the componentof v* normal to the bound- the study of tracer transport in the stratosphere[e.g., ary vanishes.The impositionof K - 0 at the surfaceis Andrewset al., 1987] and used to great effect by Gent intimatelyrelated to, and can be rationalizedin terms of, and McWilliams [1990] in large-scalemodels of ocean the use of an isothermalupper boundaryin association circulation. with [Bretherton,1966] PV sheetsat the surfaceof the Representingthe eddy transfer processin the tracer model; see section 4.3.1. equationusing TEM, we obtain [seeAndrewset al., 1987] We now go on to considerthe dispersalof a mixed

0•r patch of ocean in terms of the pattern of eddy-induced velocity. at + V. V, + W •zz = ISO (38) 5.2.1. Eddy-inducedvelocity in a mixed patch. where Let us return to the statisticallysteady mixed patch overlying an adiabatic thermocline in which surface V:Vh+V* buoyancyloss over the patchis compensatedby a lateral influx of buoyancyby transient geostrophiceddies (as W=w+w * discussedin section4.3.3). The cylindricallysymmetrical patch is sketched in Figure 44, taken from Marshall are the advectingvelocities comprising(Vh, W), the [1997]. There is no mechanicalforcing due to the wind. Eulerian velocitiesof the non-eddy-resolvinglarge-scale Buoyancyloss results in a deep mixed layer within the model, togetherwith (v*, w*), the eddy-inducedveloc- patch, and upward doming of isopycnalstowards its ities.Note that in (38) andfollowing Gent and McWilliams center. The Eulerian mean circulationis identicallyzero [1990],an along-isopycnalstirring term ISO is employed because the net vertical and radial Eulerian motion in on the rhs to representthe isopycnalstirring of tracer. the patch is vanishinglysmall as a result of vorticity 56 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWS OF GEOPHYSICS

the convectionsites contract dramatically in horizontal extent and have a more realistic distribution. The mixed layers are kept shallow in the Antarctic Circumpolar Current by the "eddy-inducedvelocity" that is directed 2500__.?fi, g¾i *'½**'•i;:;•,• •.2 Sv southwardacross the current, carryingbuoyant fluid and stabilizingthe column. The same eddy-inducedcircula- • 0.2Sv tion in part cancelsout the Deacon Cell, reducingthe ...... strengthof the (transformed)circulation. ,,, 2Z90 I I The TEM clearly provides a fruitful framework for discussing"adiabatic" aspectsof the spreadingphase of Figure 44. The solutionobtained by Marshall [1997] for the deep convection.There are a number of outstanding eddy-inducedvelocity associated with the instabilityof a mixed theoretical questions,however. The TEM has yet to be patch. The eddy-inducedcirculation carries fluid from below placed on a firm theoretical basis in three dimensions up to the surface,where it is exposedand changedby convec- even in quasi-geostrophictheory. Moreover, the quasi- tion. The convectivelymodified water slides down into the geostrophicassumption clearly breaks down in mixed interior, out, and away. The buoyancycarried laterally by the patches,where even the hydrostaticapproximation must eddy-inducedcirculation is just that required to offset buoy- be questioned.Furthermore, geostrophic eddies are also ancyloss from the surface.The contourinterval for the isopy- important diabatic transferring agents in the mixed cnalsis 0.0125kg m-3. patchesand not just responsiblefor adiabaticrearrange- ments. The interaction of an adiabatic interior with a mixed layer has been touchedon in the recent studyby constraintsthat preclude any significantstretching of Treguieret al. [1997]. vortextubes (see Sendand Marshall [1995] and section 5.2.2. How strongare the eddy-inducedvelocitiesf 3.4.2). All of the circulationis eddy induced.The con- What sets the strength of the eddy-inducedvelocity vectivelymodified water is carried awaybelow by eddies shown in Figure 44? In section 4.3.3 we discussedthe and replacedwith ambientfluid from the sideby eddies. depth a mixed patch reachesbefore the deepeningis The pattern of eddy-inducedvelocity can be deduced arrested by eddies. At this depth, lateral transfer of using(40) and (42), noting that K -= 0 at the surface. buoyancyby eddies exactly balancesloss from the sur- The eddybuoyancy flux is directedradially inward and is face. The depth reached leads directly to information a maximum at the radius of the rim current. The v* computedby Marshall[1997] makinguse of (40)-(42) is sketched in Figure 44. The eddy-inducedcirculation carries fluid up from below to the surface,where it is 90øN exposedand its properties are changedby convection. The convectivelymodified water slides down into the 45øN interior, out, and away.

After the buoyancyloss has ceased,the eddy transfer 0 ø processcontinues until the conditionsfor baroclinicin-

stabilityare no longersatisfied. It is clear from the sense 45øS of the eddy-inducedvelocity sketched in Figure 44 that

buoyant,ambient fluid will be drawn in from the periph- 'o 90os ery sealingover the mixed-patch,and the convectedfluid ß'- B ß• 90ON will be drawn away in to the interior below--just as it is sketchedschematically in Figure 3c. The sealingover of the surfaceanomaly on cessationof the surfacecooling removesthe conditionsfor instability(i.e., removesthe surface PV anomaly sketched in Figure 38) and "quenches"it. Figure 45 shows the distribution of convection as 0ø' 45øS' !ß modeledin the world oceanusing the GeophysicalFluid DynamicsLaboratory (GFDL) oceanmodel by Danaba- 90os : 0 ø 90 ø 180 ø 270 ø 360 ø soglu and McWilliams [1995] and two different eddy Longitude parameterizationsbut the samevertical mixing scheme. When horizontal diffusion is used to represent eddy Figure 45. The % of all times and level when convection transferone observes(see Figure 45a) extensiveregions occurswhen geostrophiceddy transfer is representedin the of convection,particularly in the Southern Ocean, and GFDL model using (a) horizontal diffusion and (b) a trans- much more extensive than is observed to occur in nature. formed Eulerian mean. From Danabasogluand McWilliams When a transformed Eulerian mean is used, however, [1995]. 37, 1 / REVIEWS OF GEOPHYSICS Marshall and Schott: OPEN-OCEAN CONVECTION ß 57

about the efficiencyof eddy transfer (essentiallythe eddy/plumes MIX NEW a=1.5% strengthof the eddy-inducedcirculation in Figure 44) 0 and its dependenceon large-scalestratification parameters. In particular, the closure for the buoyancyflux, 500 ;00 :,...... -.-...... :. equation(29), led Visbecket al. [1996]to a predictionof the dependenceof the equilibriumdepth h equi ! on the 1000 •---•..•...... :• •.:'-3.....'•.!• )oo externalparameters, •, r, andN, and a quantificationof

,, the constant of proportionality, or, a measure of the 1500 1500 efficiencyof buoyancytransfer by barocliniceddies (see

equation(32)). These predictionshave now found sup- 2000 ' 2000 )oo port in numerouslaboratory and numericalexperiments 0 10 20 0 lO 20 o lO 20 reportedby Visbecket al. [1996], Whiteheadet al. [1996], ttaine and Marshall [1998], Jonesand Marshall [1997], Narimousa [1997], Chapmanand Gawarkiewicz[1997], 500 500 and Chapman[1998]. The latter two papersapply these • 1000 ...... •.-.•..••••• 1000 ideas to coastalregions. 1500...... 1000 Turning the argumentaround, one may interpret the abovestudies as providingsolid "experimental" support 1500___._.___•__' 1500 for an eddy-transferclosure of the form of (29). The 2000 2000 2000 eddy fluxesin (41) may be characterizedby a transfer 0 lO 20 0 lO 20 0 10 2O coefficientK, which dependson large-scaleparameters 0 •:..-g :...'.:•!.::..• thus:

500 5OO ...... •••:...:• K- otRiU2 f 12 (43) ooo no data lOOO 1000 wheref is the Coriolis parameter,1 is a measureof the 500 1500 1500 lateral scale over which parcels of fluid are transferred by barocliniceddies, ot is the constantof proportionality 2000 2000 2000 0 10 20 0 10 20 in (29) whosevalue was determinedby laboratoryand 0 10 20 numericalexperiment, and Ri is the (large-scale)Rich- ardsonnumber given by (30). Figure 46. Azimuthally averaged density as a function of depth and radius at day 6 in a nonhydrostaticeddy-resolving Spall and Chapman[1998] presenta different deriva- model (left column), in a parameterizedmodel using NEW tion of the eddy flux relationshipproposed by Green (right), and horizontaldiffusion (middle). The contourinterval [1970] and employedby l,qsbeck et al. [1997] by consid- is 0.005 and two isopycnallayers are shaded.The black bar at ering how barocliniceddies are formed in frontal zones the surfaceindicates the cooling region. From Visbecket al. and how they interact after they are formed. They obtain [1997]. the same functional relationship proposed by Green [1970]and alsofind that the scalingcoefficient ot in (43) is indeed a nondimensionalnumber. They deduce ot to In the right columnof Figure 46 we showresults from be 0.046. This is to be comparedwith the empiricalvalue the parameterizedmodel; a 2-D model was configured of 0.015 deducedby Visbecket al. [1996] making use of for an azimuthally averageddomain in which convective Figure 45. mixing in the vertical is representedby a convective Visbecket al. [1997] attempt to parameterize the adjustmentscheme and eddy transfer is parameterized. eddy-inducedvelocity associated with the restratification A number of eddy parameterizationschemes were com- and dispersal of a mixed patch. They compare their pared,but the one that employed(38)-(43) wasfound to parameterizedmodel with an eddy resolvingnonhydro- be the most satisfactory.This scheme,called "NEW" by staticsimulation of a mixed patch in which both plumes Visbecket al. [1997], combinesthe best elementsof Gent and baroclinicinstability are resolved.A linearly strati- and McWilliams[1990] (hereinafterreferred to as GM) fied volume of water is cooled at the surface over a disc with Green [1970] and Stone[1972] (referred to collec- as describedin section4 (see Figure 34). Azimuthally tivelyas GS): transfercoefficients that vary in spaceand averaged sectionsacross the baroclinic zone in the re- time accordingto (43) (GS), togetherwith the adoption solvedmodel showthe generationof a mixed patch due of a transformedEulerian mean formalism (GM). It to convectivemixing and its breakupby lateral fluxesdue predicts a large lateral buoyancyflux near the surface to baroclinic eddies. As time progresses,the lateral associatedwith the strong baroclinic zone of the rim buoyancytransfer growsin magnitudeuntil it is of suf- current. At depth the convectedfluid is advected out- ficient magnitudeto offsetthe surfacebuoyancy loss and wards and appears as a layer of reduced stratification establisha quasi-steadystate (see section4.3.3). (see Figures44 and 46). 58 ß Marshall and Schott: OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

In these mixed-patchsimulations the-eddy transfer the MassachusettsInstitute of Technologyocean circu- scalel is set equal to the radiusof the patch, and so the lation model (the model is describedby Marshall et al. schemehas essentiallyonly one tunableparameter, c•. It [1997a,b]). The ideas set out abovehave been imple- was tuned to obtain the "best" resultsjudged by com- mented in that height coordinate model: a convective parison with the resolved experiment. The optimum adjustmentscheme of the kind describedby Klingeret al. value of c• is 0.015 for the NEW scheme;the K implied [1996] is used to representconvective mixing, and the by (43) is then300 m 2 s-• for theexperiment shown in NEW parameterizationof geostrophiceddies described Figure 46 and is within a factor of 2 of that determined by Visbecket al. [1997] is implemented(equations (38)- from laboratory experiments of mixed patches (see (43) above).The model,extending from 80øSto 80øNat equation(32)). 1ø horizontal resolution, is configuredwith 20 levels in Finally, note how poor is the "diffusive"parameter- the vertical,ranging from 20 m at the surfaceto 500 m at ization(middle panel in Figure46). Justas is observedin the deepestlevel, typical of the oceaniccomponent of the globalmodel of Danabasogluand McWilliams[1995] coupledglobal models. Full sphericalgeometry and to- (see Figure 45), the mixed patch is too deep, much pographywas employed. deeper than in the resolvedmodel. Figure 47a shows the mixed-layer depth in March 1997, and Figure 47b showsthe spatial variation in K 5.3. PuttingIt All Together givenby the NEW parameterization,evaluated using the Our comparisonof resolvedand parameterizedmod- depthaverage of the stratificationparameters over the top els in sections5.1 and 5.2 leads us to the following kilometerof the ocean,together with (43) and (30), as conclusionsconcerning the representationof the water masstransformation in large-scalemodels. We believe that grossaspects of the mixing processassociated with Kh= od2• •- dz (44) H convection can be captured by vertical adjustment schemes(or throughthe useof enhancedvertical mixing where H = 1 km and l was set to 400 km. coefficients).The adjustmentis never instantaneous,of The general pattern of mixed-layerdepth is not un- course, and as was described in section 5.1.1, arrested realistic:we see deep convectingregions (in excessof 2 adjustmentschemes can be implementedand have sat- km) in the Greenlandand LabradorSeas with a tongue isfyingproperties. However, from the perspectiveof the of shallowermixed layers (-200 m thick) extending large-scaleflow, the mixingtimescale (at most 12 hours) southwestwardacross the basinto the south.The pattern is essentiallyinstantaneous; we find that the arrestedand of K shown in Figure 47b picks out regions that are instantaneousschemes show no significantdifferences in knownto be high in eddy activity(the Gulf Stream and parameter ranges of interest. Rather, it seemsthat the North Atlantic Current,for example)falling to lowback- fidelityof water masstransformation in large-scalemod- groundvalues of -300 m2 s-• in thequiescent interiors els is compromisedlargely by the representationof the of the subtropicalgyres. The winter of 1991-1992 was exchangeof the fluid and fluid propertiesto and from indeed characterizedby huge buoyancyloss over the the convectionsite. Comparisonof explicitand param- Labrador Sea, and deep water was observedto a depth eterizedmodels clearly shows that (1) the "transformed of 2500 m. However, there was no evidence that the Eulerian mean" representationadvocated by Gent and mixed layer in the Greenland Sea during 1992 was as McWilliams [1990] is an appropriateframework for de- deep as is seen in Figure 47a. Thus although the model scribingthe adiabaticdispersal of convectivelymodified seemsto be able to capture the preferred sitesof deep fluid and (2) the transfertheory of Green and Stoneis a convection(compare Figure 47 with Figure 1, for exam- useful closureto get at the magnitude and spatial vari- ple), the depth of the mixing and the volume of fluid ation of the eddy-inducedvelocity. "processed"by it are sensitiveto factors such as the There are many outstandingquestions, however, the prevailingmeteorological fluxes, the underlyingstratifi- most urgent of which is to understandwhat controlsthe cation, and the parameterizationof lateral exchange. eddy-transferscale l. The importanceof equation(43), however,is that it ascribesphysical attributes to K and therefore a contextfor inquiry and further refinementof 6. CONCLUSIONS AND OUTLOOK a transfer scale l, a timescale associatedwith baroclinic eddiesM2/N, and a proportionalityconstant c• that In this review we have attempted to draw together measuresthe efficiencyof the transferprocess. A deeper resultsof observationsand of laboratory and numerical understandingof those processesthat determine these experimentsand, in the contextof relevant theory, sum- key factors [see Larichev and Held, 1995] is required marize our current understandingof the underlyinghy- before a more complete representationof K can be drodynamicprocesses at work at ocean convectionsites deduced. and the interplay between the convectiveand geostro- To concludeour discussionof the parameterization phic scales.We have seenthat there is a complexinter- of the water masstransformation process in models,we play of scales,ranging from plumes at scalesof <1 km, present resultsfrom a global 1ø x 1ø calculationusing through eddies on and above the Rossbyradius of de- 37, 1 / REVIEWSOF GEOPHYSICS Marshall and Schott:OPEN-OCEAN CONVECTION ß 59

mixed layers all the time, everywhere in the ocean. However,the localizedand deep-reachingnature of the

70øN convectionregime exposes,in an exaggeratedform, the role of lateral inhomogeneitiesand baroclinicinstability. In the oceanthere is little scaleseparation between the mixing (up-down) and geostrophic(lateral) processes: /rot,H, andL p are not verydisparate, and the fluid is "stiflened" by rotation even on the convectivescale 50øN itself. Herein lies the reasonwhy water masstransfor- 200200 mation is sucha fascinatingphenomenon from a theoretical point of view and why it is sucha challengingand demandingprocess to observeand model. It is worth remarking on the central role that new 30øN technologiesand diversemethodologies have played in improving our descriptionand understandingof the processesat work. Artful use of the ADCP and tech- niquesof acoustictomography have given us novel information about the dynamicalprocesses at work as a 10øN function of scale.In the ongoingLabrador Sea experiment these techniquesare being supplementedby profiling floats,Lagrangian floats that track fluid parcelsin 80• 60• 40øW 20• 0ø three dimensions,surface drifters, profiling CTDs, au- tonomousunderwater vehicles, as well as hydrography and moorings,the stalwartsof observationaloceanogra- phy [seeLabSea Group, 1998]. It is interestingto note the central role played by laboratoryexperiments, such as thoseby Maxworthyand Narimousa [1994], in the developmentof the ideas reviewed here. These not only illuminated and exposed key theoreticalquestions in beautifulways, but havealso been a central thrust of the recent resurgenceof interest in the general problem of rotating convection.Ocean convection has also been the context in which, for the first time, nonhydrostaticocean models were developed and applied to the ocean [Bruggeet al., .1991;Jones and Marshall, 1993;Marshall et al., 1997a, b]. The challenge for the future is to transform these insightsin to parametric representationsthat address the complex3-D nature of the processesat work. Rep- resentationswidely used in large-scalemodels today remain stubbornlyone dimensionaland bear little relation to what we know of the process.Curiously, the more detailed our descriptionbecomes, from observations, laboratory,and numericalstudies, the more it seemsthat the mixingprocess plays "secondfiddle" to preexisting 80øW 60øW 40øW 20øW quasi-horizontalprocesses that are rapidly and vigor- LONG ITU DE ouslyenergized as the convectionproceeds. As is often the case,the fidelity of our descriptionof Figure 47. (a) Mixed layer depth in March in the Atlantic sectorof a globalintegration of the MIT model at 1ø horizontal processesin modelsis severelycompromised by inade- resolution.(b) Spatial variation of the K valuespredicted by quate resolution.Although in principle one could re- the NEW parameterizationin the samecalculation. solvedown to the plume scale,this is neitherpossible (in the foreseeablefuture) nor desirable.In limited-area models, such as the one of the Labrador Sea shown in formation, right up to the scale of the general circula- Figure 36, horizontalresolutions of a few kilometerscan tion. These key elementsappear to be commonto all be achieved.We believe that the fidelity of the repre- open-oceanconvection sites that have been studied. sentationof the water masstransformation process will Moreover,the phenomenologythat we havedescribed in then dependlargely on the quality of the forcingfluxes the contextof deep convectiongoes on, we believe, in (of heat, freshwater and momentum)and knowledgeof 60 ß Marshall and Schott:OPEN-OCEAN CONVECTION 37, 1 / REVIEWSOF GEOPHYSICS

the preexistingstratification, rather than the details of Arakawa, A., and W. Schubert, Interaction of cumulus cloud assumedvertical mixingscheme. However, in the global ensemblewith the large-scaleenvironment, I, J. Atmos.Sci., modelsused for climateresearch it is the representation 31,674-701, 1974. Astraldi, M., and G. P. Gasparini,The seasonalcharacteristics of the geostrophicscales that remain the key. Use of the of the north Mediterranean Basin and their relationship transformedEulerian mean as advocatedby Gent and with atmospheric-climaticconditions, J. Geophys.Res., 97, McWilliams [1990] providesa solid basis on which to 9531-9540, 1992. contemplatethe adiabaticpart of the process.Use of an Ayotte, B., and H. Fernando, The motion of a turbulent eddy-inducedvelocity, which dependson the large-scale thermal in the presenceof backgroundrotation, J. Atmos. Richardsonnumber followingGreen [1970], providesa Sci., 51(13), 1989-1994, 1994. 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