THE NORTH

DIAGNOSING CHANGES IN THE NORTH ATLANTIC CIRCULATION USING A VERTICAL SECTION MODEL

BY

JIEXU

A Thesissubmitted to theSchoolofGraduate Stud iesin partial fulfillment of the

requirements forthe degree of MasterofScience

Department of Physics MemorialUniversity of Newfoundland

June,1992

St .. John's

Newfoundlan d

1+1

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Abstr act

A two-dimenslonalvcrtiralsectioumodelisc!.>:;rr;I,,'.1. '1'11<'modeltilk.>:;den- sity data alonga sectionas inpntamiralclllatl'Sth.. vl'lur il,ythroughtln-SI'd;O Il referenced1,0the bottom,We haw used it to aualys.' dmll,l!;I's inl.lu-,.j,Tulllliu ll of theNort hAtlanticbytakingasinp utthr-ohj l'cLi\'l' lyiUmlys l,.1 tlt·nsil.y.1,\1.,1 of L.wit us( 1982,1989)fortheclimatologicalannual1l11', UIandFurtlu-pl'1\lad,~

1955-59 and1970-71.

andestimates ofthepolewardhealtr a nsJlort throughM.rl"Nutul2:1.r,"Nhavl' beenmade. Ekma n transportsam ca lclllat l't iIlsingtill'IIdll'fl wulandIl11S"U- steill(198:1)windstressfleldandwindstn's:; mmlysl·.1hyIh\ SilvlliU llll...·v il lisfur theperiod 1945-1989. At M.ri°N,mlls s h,llaun' is ;u:hilwe,1 hynlllIhillill~wilh the absolutetransportralculatiollsof Grm lh a tehI·t'11.(1!1!11),givingval1ws fm the polewa rd heattransportof0.61'W , 0.7PWumlO.r,/' Wfurtl l.~dimatu lop;ind annua lmean and the pentudsIlI!')!)-ri!) aue]IU70-71,rt~sp.~div..ly.'l'III' l'slillmt"lJ erroris ±0.2PW.These ValllCNcomparewell wlthprovicual'st imnll'sol.lllirwd usingsurface heat flux calculationsanrlsuggl~tthutthop(JI,~wllf{ 1h"lLlI.I'iUlsJltlrt in 1970·74 may havebeen marginallyless thall ill Wr,.')-.'i!J.WP.)mVl~p' lrr"rllll'11 a similar calculation fer23.!jON, thislimehyrequitingIrl1~".'lImll1lll:t~tllffl1ll!;h the sectionassuminglhat the nort hwardtra nllportaue!flowtl~IJlJlt!ratllr"oftill'

FI'Ir;' !;lCUrrtmtWIL'lth.~!IIUllf'ill ,'.adllJl:'nl.ad andequaltotheclimatologicalan- 1111...1IIwa nvah/f~,allIL'l.'llllll pliolJWI' hclie velohe justified .The calculated heat lritJls],ur lliilr'~I.:!/'W,I.OI'Wanda.RI'Wfortile climatologicalannualmean all,1t1w "f~lIli...ls I!J!'"J!"..!I!)aile!1970-74,rf'Spccti vely,wit han erroror± O.3 P W.The dimat ulu,e:kalVilhll'ap;rc..~withpre vious est imate:.atthislat itude andthereis

;l~ailttill"su~''''li"nthllttlH~1!170·74valueisIN Sthanth..olh ers. part icula rly illf'lIlltparisollwilhllll' r.lilllatologiralannualmean.AlollgM.s oN, thereduced IWIILtranspurlill1!1711·14isAltrihutedloadeepe r North Allant icCur rentami a wurtuern-nnunowintht~Labrador Sl1<1.Along23.!l°N,all theo~herhand,the

SUIlU IW1Ir, [HowIIVt'rtill'interioroftht'North AtlanLicismoresurfaceconfined in1!170·711liiall intllC'dilllatologir.alcaSt'.

Olhf!1'""'1111.11 ronrernL1w vf'l1.icaldistribut ionoftheabsolutetransportchanges ,lia,e:llul'<'f1hyGro·athatd.dal.(1991).Along55.S"W,thetransport oftheGulf Stro'aalln·rc'T\·ll n ..1Lathe'hotLamWlUIsome:roSv!('SlIill1970-74 thanin1955-59,

itrhallgt"'rolllpa ralll('illma gniLudeto tha Lroundby(lreatb atc beL al.( I99I).

IlI1Wi'Vl'r, tIll'maximumcl..Ul!:<'roundbyGreat baLcher"I.isdisplacedt.othe l'<lulhoftha trdl·rt·nn ·t1tothebottom,indicatingtheim port a nce or chan gesin hultulll vr-kn-ity,Grt';llhatrh<'L,II.alsocousldereda ca seinwhichthedensit y IwluwIrlunIIIisiIllHll1llt·l!tohave remained unchangedbetweenthe pentads,and tlill,l1;lIu.."t·tl IIlranspo rlrh/\1lg<'IcrtheGnUStrea morover20S v,On theother hand,the'rh<1lJgl'inlransport refere ncedt.oan dabove1500misonly7S v,in-

iii

dic;lting that ovrnin this,'as",rhill1p;,'S in hllt.t um \,.,I,wily1'1 ,1~';111 illll'tlrlll ill role.Thereis a sUJ;g,'sLionin th,,'model fI'slllll't.hutilltIlt'1!1711-7,\1"'lil'\l1,lilt' northernrrdrculaliollIU'T"(Iftill'(lulfSt.n'amwusweakerthanill huthI!l!i;h'i!l and tIlt' clhnatolegirelrnse.

iv

Acknowledgemen t s

11'011111lIu1pos.~ilJlynann-allt111J);1~whoha\·'~rontrihutedtomy und l'rstall,liug of ur:"llllup;tapIIY,hutsl~v,~ralmontc rnd(':lI'rVl~special meuticn: Rich ardGreat-

I,atdl,IIn,,1,11~Yllll1l~,AI"xlIay andKevinLamb,fromwhomIlearnednotonly

U'·"illlllp;ta lll ly1,utll!:i,'nlifk llisr.iplilll'.

Ilkh,trolUn 'illha tl"llandHred '!INulIllg guided methrou gh grad ual!'5c11001, IJru vi>linp; 1I11pporlnml'~ll('l)lInlp;I'l11alltal crucialjuncture, Espe ciallyRicherd

<Jr"atlmkh ]lat i"lIl1yr,'vi,'w,!(lmyl'arlyrlll11!Jcrl101l1p.rnaullllcriptfurmanylimes whir-Itrl'sull.t'llinIImlll~l"IlUllimpu rtantrevisions.

I1l11l"lSi) grab, fultuSy" Levitusfor providingIdsdensity fields,to Arlindo MlIrw'l<

"a

^Silv,lfur provillingIIIlwiththe IlaSilvaandLevltus windstressfields, ilIlll1.11Amlro'wWI'i1Vi'rforIlilleneoueagc mem011firs t hraringof ourhea ttrans- I'urt r.'Sult,.;,YingH"IIpruvidr,1assislalH~,1withthegraphics,AllanGoulding lu'l ppcIilld.'alingwith I':Olll]lllt"r problems andGusFanninghelped in providing

ThiswurkIUL'i111'1' 11("arri,'!1outwithsupportfrom theNetworksof Centres

ufE",·,'111'11'·I'programorlh(~NaturalSdl' lll':c andEngineeringResearchCounci l IlfCall1l,lalllr1mgh

nil'

OceanProduction EnhancementNelwork(OPEN).Sup- portfW1l11,111'NSlmCColloharutiveRcsoarchInitiative Programm e in suppo rt of(~all'lili<l1luniversity 'lI'livjtit>SinthoWorldOce.111 Olrculation Experimen t

(\VOC E)is nlsoal'klllJwll'II~" 11.

Fiuully,Iwlllll,llik.'IIIthallk11l.\' p'Ir<'lLls'1I1l11l1,\·I ,rul,lwrfoetln-irSUI'I'"tI fllldt'uo.:ollr.lg t·1ll1·nl,

Contents

1 Int rod uct ion

2 TheModel

:/.1 TIll'(:uvl' rtling Equations 2.2 Thl"'MdhodorSoluuon

i,:I'l'ln-Cnkulaliollor VolumeTrunsport,IIrillTra nspo rtandSterk Sl';t J.I'vI·1

:I The ModelResults

:1.1 Sortion throughfi.';" W and fi5"W longitu de :l.:! S.'l,t ion thrlJllgh.'H" Nand24~Nlatitude

1 Summaryand Concl usions

vii

15 15 20

35

63

105

List of Figures

IlIe Nol'lhtlll rUl/if 'circulutiou,II/"'"n/ill!/III....','nll'll/'rt III(J.I14:!, 1(q. IHi).

\.2 Charf1<11O ",illllllir,qfllbrrl"'I/.rlr/l'l'IIfI"r1J1l:,."",/Ht/irll'";rr'lllllf;uJl eella".~lIrjalrdwith NAfH\'/lrflliudirlll.'flrrl'in'/nl 'lUIlll'''1m'mIl·

unu:/1,11'ill SI'f'IYlrlIIJII'IIil'/,an' I"r/I,T/ni[orIllli/",.m1I/J11~-Iljtl!/,,/

'hfNflOWwi,h(j/11'(111'11'1;1111 m/Inf!J(JSm',~h·"ll.Adu/JI"II /,mll (JrmlOIl,1.91'10',I<'ig_!Ja.

1.:1 TrmJH:rnhin(illdl'91"fT.~C'rl.~irl.~)al/d.~fllill ;l!J(/IITmil)dilfl'nlllT/<

for1970./ 974mjllll.~/!J.'j.'j- /% .?Iii fj(J(/-1II1/,'/1'",IInvmlillf/lo1,1"1"

illl$(J.fJH9tl,jig.7,H) .

[A S/'I';rHenIr:lwI,liff""f1lr1J<illurlib

( JI

liYllami,'l·r'lllimdf:/".~(I,[.IIIWIII

=

lOOnCl/l~.~-2)forl.fJ7(J·W7.jmilill.~If/,'j!j· I !!.';.'!Jfll'Iii,.11-til15(J()·m depthill/cI'lJaf,RI'('amillf!tnIJf'~ihl.'(/.9.90, }if/·

n..

viii

Ih".~ilylIt/III(b)1970-19711l1illdand dCI..~ilydata, accordil/gto f;,.,'lIlIlII/flt rlal.(J.?9/.J(q.:J).7'1lcr:I1lllourilllcrvali»10Sv alld Ill/':::1'I"tl f"tJIlIOlIl'i.~,widrawn. DalllicdeOlllollrllilldicalenegative IUlI'II"",..~I}lirlrIJllltJllr.~,IJlmi/;"rIIIdur.s. ,.,,,.. .,,.,, ,,

:1.1 '/1/1"Iltlsi/;tm

Ilf

'he[our"~er/i(JII.~beingslullird

:I.<! II'n.,ITIIIlIYl llrltwilyfirld""~ill!1dilllalofogicalennuelmrllli(lala(a) I","rll'l,el' 11/1I1f:/,rrfel'cflud10 1.';00 III (b)fhelouwrpalld, ref-

l'I1"'UTI/10litebnl/mt/, 1'111','(m llllll'iJllrrlJa{ill0.01m.~-I,witlt

12

25

:16

"lIillml"'l/Ilt!lIl~~i"rli,·alill.lJIIJc,~/l/Iardvdorilyand.~o/ideOllfours mstwnrd,The/IIi";7II 1I111alldmeeimnmvaluesal't:given illmJl-1 . :18 :1.:1 ,I11'111'",ll/di'lIIIIf Figlll1'fibfl1J111flic1lardlloll,/985. COlltoured

;;1I11111m"/rwif.II.~,.r/ioll(nil.~-I)allll/gf.iI'iGWlindl1Iml/g1l llieGlIlf Sln"amfl'O /IIdrif!fTS,Jloa/.~,aun currelltfIIr1er.~,ll,jllitheoind r1l'ifll,,.{nfi/IIIY'/llrJ lJerl. Ba,.'wanllJrlorityis sllfldrd.Dotsilldienle

1.,.1111"1....fJfbnrr.~Illlfi/illl·alell/llli".1] velocityexceptal,JOOOIn,where 11/1".'1"~Iwrt,I'llr/'{",,1mclcr lm·afimill. 40 :1,"1 1,,(1/111,"/rllll"l'nl'/llll;lI,qRllIluall/lrrllldala

ix

., ...••• 41

;J.ri Etllltll'aI-d lwlol'illljiddIllIi","1,97tJ·1.97$dcte,(a) fhl' llf!lllT flllllrl, l'Cfcl'CIlCcd10150011/(b) IIII'lower /HI/uf,Iljfll'l/cnlto fhl'{lfIfflOlll, Thel'OllfOll l'ill / r l'/!tl /j.~0.01m,~-',wilhIlr1,~"(d"0 1110 111'"illdim lill,q we.~lupaI'IlIlrlocilyalld,~olid rOIlI(lIU',~/'t1"lwfllll.'11'1'mil/iII/limfrltll maximumIJa/lIcsaregillf'11illIII.~-I ,

:).6 Ea.dulfIrdpriorityficldtlsill,"1,95,5-J.f)Mlilllfl,(a)1I1f~IIJlfI"l'/lIIl1d,

!'rfel'C!lrrd10{:iOtJIn(b) /helowerIllIlIrl,I'r11'1'I'lIcI'lll(/1111''illi/filII.

TheCOli t O/II'in/crudill0.01111...-1,IO;/IiI{a,~hfd1'111I1"111','i/l(lim/ifl,q we.slwltl'd IIrlocityIllId solidf'1I11101l1'SI'ffillwal',{,'1'111.minimlwlllltri maximumvaluesmrgilJrllillm.~-I,,.

a.7

Ea,~lw(lI'd/leloeilyjield oj1970.J,97~millll,.1.9,'J.';- I,% 9 1'1".'1/1, (n) Iheuppel'/mlld,rrf f.l'f'II ITll l o W(J(JIII(b) Ihc Imllt'I'11111I1'1,l~if~I'­

elll'Cd10thebottom, The rontovri,llel'vltli«

o.un,'j

m.~-l ,wil"

dashedeOllloul'.~indicaling'fIlwll/!tlNIIJclocil1lflit/I",,{idrnnlnnrs ea,~t!llllrd.Theminimumalldma;ri lllllmlJfllllf~.•nn!Jim:IliiilIl,~-I. -Ir, 3.8 Val l/in Ctransportusin,"(a)tlU'tl]lPI:I'lltwel,/lnO-I.97.{fwd (b)till'

lomer,Jand,1.9/;5-1 959 dalll 17

3.9 Volum eIlYm.~poI,tllsillg1," 10· 19 7$minu: 19,';,';·1.9.';,fJIlfdtJ• , , . -1,11 :1.10StericsealeveldiJJr.re1Icr.~jor1970- 191.{minus 19.';5- 1,9,';,911~HlIlI.. fil

:1.1IHtI.~l lrltml","I",. it,fir.Mq .•inglu m 'l al mlallJala. (a)th~v.pJH'r IHuul,rrfr lTlltTdttl/fiOnm(6)the10lllcrplllltl,rrfertJlCf.dto the OOtin",.111t:rOIlI ni ri,d"'Ml"11i.0.01111.. - 1,If'ilhd41lJu:JCOlltOl1"ll j"Jintlil/g1IIf"1d-m orlocilytl.adMlidconf"ul"Ilra..dlOflrd.Themin-

illlllllla"d lflIU"il/llHlIvaJutJllllrrgiveninm••-I.. :1.12 VI'!III1lr.Im llJ<]mrltI"~i" !J1I1/II 11 al meandafll ••

:U :IIJYUfllllir',/'i!lhif(lr 1111'hoI/mil

re..

tlrflletdf;l'l h i,der valusing all-

lIlud//Inlllr/',III , .

:t1,1811.~lllll1nll!rfrwilyfirld'-r/tI'rllcrd 10Iilf;boltom llsitlg(a)thf;up- I"Tpl/lld ,UnO. /914tllIIl{b}lilt loverpallt t,/955-/9 59data.

nitrmllo /u·;,d t r l1lJIi,.O.OI111••-1,u/ill,da...JiedtOni oUNind i u l ing

1iIf'"lltlflnl,"'/Of"ilyand Ifolidronlou r••eashrord. TheminimumlInJ

55

flllU";mllll IHI1llrlf1Ir'f'g;ocll in 111,1;- 1.•. ..• •••.•.•.•.•• 56 :!.I ."if.'".~l lIIfl nl"rlD('ityjidd rrfrrrQl"fdtothe6011om,tUing19 10-1914

millllif19:jfj. 1959 rrJlvll.Thrrent ourin/rrvtJ!i..0.005m~-1Jwith nfL.Jm/n"'/OlmljnJin dillglIlf.dul4nlvelocityalld 1I0fid<:ordOl1'll

:I, lIi1'lIll1 mr11"a 1l.~II11 I"ulIi".q(11)1I1f;upper1'11'1(:1,1970.19 1~and (b)the

Irlllll'l·/111111"1,l.9/i5·19/i,9dala•• .. • • • • • • • • •.•• 59

:\.17 Slrl'il'~fI/{n,ddilJrrf"lIrr.~1I"~hlg/970. 191~lIIill ll..1955·1959results 60

3. 18 AI/II I/a!mUIIIIl/lOlI/aly ,"rn11'1'1'1(illccutimctcrs}/m'(II)11,,'/IN''''

pUlld,IlR/i/ Rxalld(b)rill' mi fidll'ptllld,I/""II/lldll,(I')11",If'll'" '' pand,HuH/ aTandfir /'m llda, u"i/I,qIIII'flJ,,~rr.'t"d...nl"'1'..1d"' ,,1m",

lidrgaugrl',af'f"0l'flil/910 I,r"if ".... I,q.r}() (it :1.11)NOl'IIi",ul'fl.IJrlori/!IfirM1I,<iI,.'!aununt mconliI,II' .(I')thr"I""'''

bottom."iiI'I"olliourinlr "Dn/i.•0.0111I,.. -1,lI'i/1l,1".../,...1I·(II//ml '·...

in diealin,q,.onillwal'dTwforil,ll allliH(lfill l'Oulllll/'"1/(1I"11I1I'II,.,l, 'f 'I,,' mi/limll1llandmll;rimlUIl Im/lIr" 111'(',Ii i I..." ill ",,,_1••

(a)theUllllfl'IIIIIIrl ,100IIIdeplhIIl1/f(I,)I","1",,,,,,·1",,,,1,H}fJ/J III deplh ,uuo,'dill.qtoOlbcr.• d. al,{J9Hli) , jilJ.Ii

3.21Volllm elm1U1/wl'l1I,.ingamnlllt meand'lt'l 3.22Volum e trans port.1I••in!!flIl1l1ud1""1111,frda

3.2:3Bol/ om velocityill all1lllRIml;fJI' rstsr: :1.24llrfll l m ll,. /ltI r / I/.•ill,qII1W UII/IIU'fllIrillla . 3,2.')flcallmllsporlll.•in.qIIImualm canrlaln .

3.26Dyna m ic lici!lhIhI'tilt,bfJl/om1l!'"Utilltl:rnal1I"ill ,f/nllfnut/""'1m dala

xil

uu

li7 IlK fi!J 711 711

:t.27VdtJdly jil:/fi_,/.~iIl9/.970./.97./daln. (a) the upper panel, refer-

/;w;flll.IJIfiOOm(b)llietowor pand, referencedto thebottom. The

nmlfJlll'i'ltr.7'l'alill0.005f/lS-I,withdashed contours illdiealiug .~(JIdhllla"llldor.ilyand solid cOlltours northward.Theminimum IIJlfIJlIII:r:iul1lmvlI(lle,~Ilrc ,qillcnillfnS-I•

;I.:~H Vd m·jtyjir.lrlll.~ill!1/.955-1.95.9data. (a)theupperpallel, rcler-

I'1lf' r:I[llJ/fiOOIII(b)tiletomor/Jallel,rcfcrcuccdto the bottom. The

("(If/1m/I'intervali.i0.005m,5- 1,with dashedcontoursi11dicatillg .~()Id"fllmv1IIclf}/:itg fwd fiolid colltours IIOrthward,The minimum

IIII1[l/If!:l:il/llllfllllllIICfiIlI'CgivCII inms-1,

:I.:!!lI/d flr:ily jief,/ difference1.970- 1.97.(minus1955-/ 959.(a)the upper IJ(llIrl,I'cJcl'Cllrrdto/500In(b) thelowerpallel, nJenli cedto the bat/filii.'/'firl:fIIl t Ot/l·inlcI'11f11is0.005m.~-l.withdn.~hedcontours

;,ulil'ating .ioulhlllardl!d flCily alld.~olidcOldo ll r snorthward. The 74

minimum^IlIldmazimllm valtle'" nrcgiv(:IIj'lms-^{I• • •} 15

:t:lll1/0 11llllctl'fllli</JOl'tIIsifl.q/970-/974dflla. 11

:l.:11I'ulumrtrnll.qportIMillg1955-1,959data 18

:I,a'.'.VlI/IIl11CIm ll$IICJr'/rliff cl'Cllf C1970-1974millu.q1955-1959 19 :I.:t lIIr altmll " lml'!l/'iill!/1970./9 7./dut_a., ... . . . • . •. . 83 :1.a'l/11'111.ll'flll,"jIOrllmill91955-/95.9dala , , 83 :\.:15/1t'lll / m llsjlol'ldiffclY'll(Y'1910.197./milllM1955-1959•,•. 84

xlil

3,:36Stevie,~calevelclral/ g r ll/,970.197./m;'I1I.~I!J,'j5-/!I.'j,9. ••• ••• :\li 3.:17No/'thwa/'d velorily fieldullillgmll/ual meandll/ ll.(a)till'11/1111'1'

pand,I'Cje/'ellerd10/fjn OIII(6)the lowrl'1//IlId,nfnnm:dIIItill' bol/om,The contouril/lr/'MIill0,0051Il.~-I ,wilhI!w,h rt{('r",lll llI',~

iudical.iugsoulhwardlJelod l11and solid:r'O/lIO I(/',~IWI',hll'llnJ.Tlu:

minimumalld maximlwiImllte.~^{alY!lillenill}1II.~-1

3.38 Volllllletmllil]IOl'tusingall/walmmn dala :1.39Vertically avelYl.qcrlpo/rmlialtemllefY/llll."along"H"N

:1,40 Heal trallspol'l.lI,~illgallll1lalIIImll r/aln ,•'., , 3.41Velocityfield!lSillg/970-f.974Il al n. (It)ttcelIJ1f1r:/'/l1l1ld,I~fl"/'·

elleed to 1500In(b)tiltIflll1el'IJflllrl,l~fen:llf'CllloIhebol/ mll.Tlu'

COIltOIlT illtervali,~0.0057/111-1,wi/hIla,~hrrl I'rmlmll·.~ill/lim/i " fl so"l/lllla,'JIIC/orilyImd.~olid{'OlllvllrllIlOl"I/llj)fun.'1111'miuilllllf/i alldmazimulltlm/IICSal'CgilJCl1ill1II.~-1,

a.42 Velocity fieldIISillg1955· /959Il ata.(a)II/(:1lpflr:1'1J1llld,nft: I·.

eflced to1500til(b)theIOIlICf'lJfmrl,nfcl'f,/I('I,din

'''1'

/wlll/Ill.'I'I1f' cOlltourintervalill0.005m.~-I,Ijlilli fl(/"~JiI'III:(mtr!1l" 1IilUli r'ljli'lf!

,'loulltwanlvelocity and.~oliJcOfllollr,~lIortl nmml. 'nil:minimlim alldmaximumvalues aT'f,,q i lll:11i'lm,~- I.

xiv

:\1\

HI

!Jl

!J!i

!lff

:!A:IVdm:iLyjidddifftl'wtt1,?70-/97,fminus/95.5-19.59. (a)theupper ptUtd, njr"'f.,wt dI"1.500m (6) litelowcrpand,referencedtoLite {mit/Jm.'/'lll:r:mtLOll rin ferv al isO.OOSnll:/-l,withdashed caniours ililliralilt,q.~olllhUlardvelocilyand~olidCOIL/ours Ilorthward.The IItilli/llltllland1/1I1ZimumlIaluf;saloegivclIinm.~-l 97 :1.'11 VIIIIIIIlI:lrn.flllJ!(Jrllllliug1.970.1974daln. 100 :I.'1.'JVfJIll lllr:h'all'~ll/Jrl,IIsillg 1.9/j5·/9,rj9dala . 100 :J.'1fiVO/lllltrlrfw'~l)(JrldijfrlTllf'('.1970·/974mill'l.~1955-1959 101 :1.'1 7'It:allmllf<prll'lllsillg1970-/97./ dala. 102 :I.'1X fJra l. l m 71l?{Jot'l ll$jllg19.'ifj-/959dala. 103 :IA!'IfClIl l ro7lspOl"diffcI"Cllec/9 70- 197-1minus1955·1959• 103

I i

I

1:

\

\

I

List of Tables

ward.Itltli~climatologyCI'I.~r.,ji,qlll'ri/illbmckdl/fi n'(',d"II/f1/nt usillglift"U'I11alldl,CVi!.IIS'lrlilHl.~Lm"" X~

tllI'Ough24° N .Posit i'l!"1'(:111"(\'1',,,11<lLol'lIl1unnllltlllUI',flflfilJ1",'«Illlh·

ward, IIIthe climalology,'Il.' C,jir/lll,(,.~illIII·adw/.~1m"I'flin/iit/fli

xvi

Chapter 1

Int r o d u ction

TIlt' Nurth AlillulichM1l("~11subject edto intensivestudy and most ofits 1l;1'IIt'Tlllr-in-ulntioupaUI'TIlShav~hC'C1idiscovered. The salientfea t ureisthetwo

K,Yrt'S,uuu istill'subt ropicalgyre, which is anticyclonic(clockwisein the northern

IU'llIisp lll'!'('),nuutheristhesubpolar gyre,which is cyclonic[eut iclockwlsein the northern hemisphere}.

A sdlt' 1l11ltiedmr!(Ifthe surface currentis shown in Fig.1.1,followingthat 1l1"l'SI'IlI,('d hySverdrupdat (1912) antidiscussedbyStonnnel(1965).Aclockwise gyn' runIM\1'a.~i1yldeutlfiedandisconventionallycalledthe subtropicalgyre,It

st.utl!with lilt'NorthEquatorialCurrent.Asthiscurrentflows to thewesv,;~

isjllint'llfromtltu~l1IthbytheSouth EquatorialCurrent,part of whichcrosses tl1l'('CJUOItU!' in tothe NorthAllantic.TIll'com binedflow splihiutotwo parts wlwnitrt'a(~ht~theCariblwallIslands.One,whichflowsOilthe northsideis

Figure1.1:Chari$hOll'i!19tlsel'Ml'{{mllirrsof/l,e Mlr{ar r:-lllfil rl' r;n'lllfll;ollo{

theNorth Atlalltir cil'culation, a« ord;1I9to S,lf,'drul'rlal(In!!!,

fi!J,

lto'7),

called Anti llesCurrent,whereas anotherflows on thl'southsi.lointtl1.ltf~GuUof Mexicoand,from there, escapes betweenFlorida andCuba toIWCUll Wtill' Flurirla Current,The FloridaCurrentmeets the Antilles CurrenL

orr

tIll!wast of Ploeldn tobecom etheGulfStrcilllland LIt('combined currentcontinuesto flowllorth'l'i~~L alongshoreuntil itreachesabout Cape Hatteras,where till'currentIIn'iLksuway from the North Americancoast.TIll'GulfStream thenflowsllor th'I'as ttowards thetailofGrand Banks ofNewfoundla ndataholitilOQN,riOQW.Fromtlu!r", part of theflow turnssouthwardtoclosetlw gyre system ,wlll'n'IL~tlwutllN part continuesto gonortheast, whichiscalledtheNort hAtliUltirCUrtl'llt. Thls currentalsodividesasitflowsnortlU'a.\ t,withpartof theNorthAtlantic.<:urrr!llt flowing betweenScotla ndandIcelandtojoint1lf'circulation oftile Nurwf'giall,

(:Il~·II II.II,11111,1ArdkS'MS,part1.1lfllill~southpastSpain lunlNorth Afrin. to ':.lI1lpldl~t1wslll.tropirlLlRYWandtofec.1into theNorthEquatorialCurrent,and wit htimr" lI1a illd.,r ftowingwestward011 the southernxlde ofIceland ,in whatis l:alll'(ltl)(~Irlllillgl' r (;Ilm'u t.Orfthesout herncoastof Greenland,thiscu rre ntis juirwlil.y tIl(' EiI.<;l(Jrt'I~lIlan ,1Cum~lll.ThedrclIit ofthegyre iscompletedto till'WI'SI. by;1ImUldloftill'LahrmlorCUrrf'llt[probablyoffshore from theshe lf IIrt'ak).

TIJis sllilll" w drc:ullOtiulIlnthc Nort hAtlantir.isprimarilywind-driven in most rl'giollSami111L'!111'('11sl lll!iel! and int er pret ed by IlUmerOU5authors.Sverdrup ([IIH) shllw" dhowthe mainfeatures oftheequ a t orialsu rfacecur re nts could Ill" IOLLril lllll'lltutllt~windaslLdrivingagent. In 1948, Stormnelexplained the westwardilltt'llsiliratilillofthewlnd-driveu circulation.Combi ningmostprevious work,Muuk (11)!'jO)olJlain('l!analytic expressionswhichquali tativelydescribed t.lll'main ft';ltllTl'Softhl'wind-drivencirculat ion ill terms ofthe observedwind

Alt huughwindIlriving probably dominates theshallow circulation,to about SOUIIIIIrSII. till'l,lr('('tsor l!1'llsiLychanges,in drivingwhatiscalledthe'ther.

llIulllllitlt" rire-ulntion,ill alsowry important,playing the dominant role in the .11'I'pdrt'lliatillll.Forthl' NorthAtlantic,when warm saltywaterspreads into

\.111'uortlu-mNorthAtlantir.itiscooledbybothsensibleand la ten t heatloss.

Th;lI1'1l1l11'11 snlty watersinkstotht'deep ocean, formingthe NorthAtlantic

0::=:>.... .."... ..

- -

~:::~:.~.:~.I:

--. -

-.

...

Figure1.2 : Chartshowing the gloklMltchcrt ol thc tJtt:rmohaUlie cirr:ulaliu nrodl GS&ociatedtDithNADWprod. di on.ThecirdedtHJlllt.sart vol.mefluinSwrJrvp lIIhichareupectedlorni/orm.plDdling oltheNA DWUtith1&productionndeof fO SlJenlnap.AJaplt Jfro m. Gonlon,1986,Fig.!!a.

1l1,('PWate'r (NAIJW).TIll' :-JAUWfromthetwo northern sites (LabradorSea au, lllll'C:tl'e'lIlarlllSl'a -NorWI~~itillSe~aoVI'rnUW)movessouthwardwithintile ,le....1'lnyer ,ill whatisl:tillHI IIhnUI'(1PwestemHouudary Und ercur rent,while tlll'warmsaltyupper layurwaterisdrawnintothe northern NorthAtlant ic, fllrl1lill~L111'gcm-mlpeuorn ofllwthermohaline<:ire••lat ion . As NADWmoves S<lIll.hw.ml.it p;ralillallyris(~sovermost ofllwmidd leandlowlatitu deareasof Nurl.llAUlllltk.(;ot!lo li(J!JXfi)poilltt"fl outthatNADWmeyspread andupwell l,h ruup;J.UlIltill'At.1allticOn' lll(andis exported to tlte Ind ian and Pacific Oceans

"ylIl1'AnlnrdkCirr.ulIJpCllar {lurrent,tl'tlltllillgwatertotbeupper layer withi n tilt' AlIl.ardkrt'p;iullandint o1I11' thermocline [Ilg.1.2 ) .Tileuppe rlayer wa t e r then rl'lutllstilthl'Alla lllir Oceanfrom two possibleroutes-DrakePass agefrom LIlt' P,ldl korthnsout hofAfrk aIrorutheIndianOcea n,closingan extraordinary lullpaflt·titjtJll tlll~ythro\lghtilt' worldocean. Because ofthedifficultyofmak- illp;1l1l'1~"llrl'm('ntllill tilt'dl'l'Pwater,thether mohalinecirculationis muchless wellknown andlesswelldescribed dynamically thantheupper-layer circulation.

I1UIVl'vN,lilt'1111'r ll1 ol 111' i n ~circulationis nowbeinggivenwidespreadattention bytlI't'll1w~mpht'rsdueto its possibleimportantroleingeneratingvariabilityon tinu-srait'll"fdeeades tothousandsof years(e.g.Gordon,Zebiakand Bryan, l!l!I:!)uml illlransfl'rill~\wal innorth-southdirection.

II.hilS11l1i1tIWI'lIknownthatincomingsolar energy exceeds outgoing infrared l'lll'r~yatlowlalitm h'l'whilethereverseis trueathighlatitudes.However, the

broll,;htint ohll)IIIU'", thlluk" tutill'pul,'wllr,1IH'II1trRII"f.'rill11...,ll m..""I...", antieo-an.Ah holl,;htlw1ll1....!Jllni"lIl"furtili"It,'atIran"IH.,tha\'I'10" '11,,11l,li,..1 for~'fIIcen t ury,thl't., Iath"1"illll)(.rl mlf"I' "f""1\an,1aira"Ill"I'tl ,l" mi llan lll,'a t

glohalenergy halallf", Lall"rinIll:I:I,Bj,'rk1lt~,SulI",t~111101n,'r';" tll1l(1!1:l:I) regl lt d edrhocont ri hntiun"uf I«'l'lUltllllm!.ul<l'lll' tI,all11,'p;IiV;iloh'all.1m;lIill;lIt,,1til<' 1"ILdill'; roleill lrnnsf('rri llg111',11todn-trullu"lllu'r,', In tI,,·t'llty"ilr",

uu-

work ofVondc-llanr/tllll Ourt,\!.I7:I,....ullOurtandVundt'rllM r,W71i,irlC liml",l lIl1It theoreaura r rit"Slll11rl"Iwal lhanW1\." pN'violislySUSI",'l..,I.alllllllllll S.till111 I'lt.,1 milchrceeutinte restintill'lIlIhjl"rl.IIfIIlI"fi.licmlllhe'iLl!II1XI.ytl1O'.,n'IUI,Itis , thereforeofinlA ,n~ttoM1tilll/tW t1H'1)(.lc'Wanl111'111trlUl:<I)(.rl llln,m,!!;11W1riulls sect ionsinNort h Atllllltk.

The traditional method,i.e, tl1l"lIurfan'Iu,athl,III/U'I'IIwtlt" ,I,ist".'xllmil'"

air-seaexchangesoralltYII("!L"fIwat.'I1f"C,Qtuc:akula tc'till"l.,ralllu. lr.'1'l'1awl sinks,and thenintegratt' everen c,ut in-pillarI:apI~xt"ll. l i lJ gfromtill" pul.' I.u lL fixedlatitudetoobtaiu thepolewardheatIluxm~,:(~"aryttlutalntuin('ljll ilil, rilllll,

knowledgeof heatcontent allli11I1\....stra nspor t by lIll'f.I:.oall{",j("Uryall,J!lli'l

;lIul Hall111111 Hryduu, l!IH2).IIIthepas t,thedirect method hasbeen the least IIs",1ydI.a.~:tis..lx-en Rivf'r1lIlUrt' end more attention .Itis this meth od weha ve IIsf,,1til f'St.illlOltf·hf'i~ ltralls po rtthrough varioussectionsin theNort hAtla ntic.

TIll',I"tail.~willIII'dalll)riltl~dlatl'r .

OurkllllWbl~I'

fir

till' intereuuualvaria hility in the large-scalecirculation of Uu'NorthAt lalltkismndl 11l1lT('limited than thegeneralpict ureof the circu- latif/II .e;iVi'1I,'arl if'r.OnlyillT('n, "1YI'aTShasthemagnit ude andim portanceof r,',is v;'l'i" llilily"' 1lI 1l!t" I",.1./,pr"datN](Gordo n,Zebia kandBryall.1992). For f'Xlllltpll',inn""'lIt~(('rjf!,"flf pa pf!rS,Lc vnus(1!J89a,b,c,1990) has showntl)atthe 1Ill'rlllllha Jilll',..trllrt llrt'of the NorthAtlantkunde rwentsomerema rkablecha nges

!wtwl..'utill'tWfI pf'nl a.flsImi!i- 1!lli!Jand 1970-1974, Hefoun dthat,Oilconsta nt- .h'pt hsllrfnf"('s,tllf'subtroplc algyrt,(500.1:100m ) of theNort h Atl anti c was colder lUI.1frl'Slwrdurin,!!;m711-1!l7,1compared to1955-1959.withcharacteristic magni- tlllll'Stlf ll'll1lwfiltUrt'eud sali nity decreases oforde rofseveraltent hs

or

^{a deg ree}

l'l'l1ti,e: rmll'alltl lJ.025-0.10u

1 00.

respeetlvely.Atinterm edi atedep th s theeast- ernIllJrlilln

or

1.\11'subpolargyre was also colderandfresher duringthe 1970-1974 pt'lIl,lIllwhen-astilt'IVI'Stl'f11portlou ofthe subpola rgyreexhibited higher tem per- alurt's andsllliuit il'l!during1!J70-1971 com pa red to1955-1959, with cha racteristic lWll:uil,llll.,s

ur

tf'1l1 1wrntur l'and salinitychang essim ilarto thoseobservedinthe lIuht,rtlJlk a l~'rl'(fi~.1.:1),In th(' tropics,there were increases intem peratu re and salinity, yl'twit h magn it udes lIl11alll'rthanthoseinthesubt ropi caland subpolar

Figure 1.4: ,5'frr'ic sca[Cl,el dijJcloenusinunits ofdynamicCC1ilimtters (I tlywm=:>1000cm1.~-~)for1970- 197/ mi nus1955-1959fo rth e0-to 1500-m tlrplhilll rrva l, accordillg toLcvitu s (1990, fig.,f).

gyrus.Com paring1970-74with1955-59,potentialdensity surfaces werefound tohaverisenillthe subt ropicalgyre, which isconsistentwitbtherelativelylarge changes ill temperat ure and salinityon constant-depth surfacesin thesubt ropical gy re. Upward displacement s ofapproximately25moccu rredfor sur facesbelow the' 26.9kg1/1_ 3potentialden sity surface. Maximumdis placemen tsofanysur- fac('$wereapproximately175m, whichoccurredforthe 26.5kgm-³potential Il"nsily sur fa ce,Incontrastto tlle shoaling which occurr edinthesub tropics.

b"IlYt'nalsilllIlt'western porti on of thesubpolar gyre,im mediatelytothenorth ofthe GulfStreamandsouth ofAtl ant ic Canada,increasedin depthbyasmuch MI100m. 1'1\('$<'C1l1\11g.'\I. S\lggestasubstant ialweakeningoftheGulfStream during1970·197·1comparedto1955-1959.

A ca lc.-ulillionofintl'tl)('ntlula lvatia hility oftlu-"h'rir""aIC'\'I'I an.1~I'I'I'''­

tentialthleknessofthl'NorthAtlanticCk\'an alj;t)n'\'l'al"Ii\r~'dlllllgt'll,Thl' gecpotent lalthickllC"lllIill cll'Rnrd;\''1thl'vI' rti"1l1 cli"tllllC1.'1....1\\1.'1'111WIIi",.l'ilril·

surfaces and dependsontht"c1t"ll"ityofti,l'walc'tinIwtWt'l'u.H.rtWII i!'ullOtrit- surfaces1>-J (uPPI'f)alltl,JI(lowl'r ), tin'J!;1't)pull'lllialt!lic-knlos."ill:

(1.1)

wheren isthespt·cifie volum e(0 =:

1 /pl.

Iftlu-lIpp"tsurfan'i.~Lilt'fr,,'!'mfal'I', thenthe departu reinthisthirknt'ssFrom aSL1l111I,trdl"l'f" rI'lIfC! 1.hi c:klll 'HSism]].,,1 thesterlosealevel.Levltus!lholV.~ 1tllaL,rOlllllar111 p;1!170·1!l7,1111I!Jr,.'i-]!I!i!lfur the0-1.015(1).01(Ieplhink 'rval,slt·ticst'lLIl'Vl,IllllIlNWt'liLsnllsllU1 1ialdmllll;l'lI (fi~. 1.4).The storic S<'aleveldocreasedbyuplA.,11..'iIIYIIC~IIIilllllC' C'iL'Il o-ntralportlonofthr. sllb t mpiralRYn~.wllt'n~ltllintill'wl '!;lC'tIlp'lI"ttlflhiliI!,.vn ', differences areofth~onlerof10.0 dyn nil.TIl\' c'ash'rllIJtJllIu lary"ftlu-i\llantir Oceanexhibitedsea level(1('('.tt,a,'i('lI011theorderof!"'Vi"...1n·lItil1l('l.'tS(!J.Iyll em)betweenthe1911).1974and1!l!')!"rl9!i!}l)('Ilt Nls. lIuwC'wr ,illtill'WI'lItc'rn subpolargyre{northofthe Gulf!ittl'iUIIalllisOlll lJ(IfAtliluli.·Cauad a )sll'rk sc'a le velincreasedbyanamountup to7.!idYIiWI.

Further workhasbce~ncarriedcut11Y[:n~1I1bOlLdll'l1l1.(I!J!JJ).TIII!SI~;.I ILhul"~

attemptedaninfere nceofthedlal1Kt~illvoillmelrllll~IJUrLl...tween11m/wul,;..11l usingdiagnosticclLlculaliollsofthe:cirr.III/l1iu!Iillt111~Nnrthi\lIalltic:,fllll"wjll~

the dlagnosucmodel

o r

MellorI:tal.(19H:.!). TllI~lIIuddt:;Jklllillf~lt1l.IISl'fJtl III

frwl!Sl)l~r.ilie,ld,msityand windstress fields by integratingwestwardsalong

JI

H contoursfrom1I1l~east.I'r11houndary,where a conditionofnotransport normalto th,~hClUlIllnryisnllpl il~d.Here

f

lstheCoriolis parameter andHisthedepth of

lli,~CWI'IlI).TilelIIUfldi.~arranged alla1° x1°grid for the North Atl anticOcean

Ilsi n~rc'alislkbcuomtopogra p hy, windforcingand dens itydata.The density (lataIlsc~1intll(~ndeulaliclllsweretbut of Lcvitus(1982,1989a,b,c:1990)andthe wludst n'ss was derivedfrom theComprehensiveOceanAtmosphere Data Set (CO AUS)by,ll~Silvn( HI9J).Theyst udiedthreebasicCllSC!I:theclimatological tlll'allllt./Itc·andthe pentads10))5-1059and1971).1974,Fromtheir results, they

sl]()w{~dlhat tIll' transpor tof tim diagnosedGulfStream is some30Sv less for

llu'l!J7Il-I!J74pentudthan for the19))5·1959pentad, 20Sv of whichbeingdue tuIldratl1'll.ir.decreasein the sLrl'ngthof thediagnosedsubtropicalgyre(fig, I.))).This:lO Sv cha nge isroughlyone-third ofthetotalclimatologicalmean Iruusport.through55°WestimatedbyRichardson(1985). Althoughroughlyhalf Utili lrUllRlltll't ch1l.1Ip;11 wasatt ributedto density changes in waterbelow 15001ll Ilc'ptll UIIII.lUisuch, may netbereliable,even a cha ngeof15-20 Svis significant . Wi1J(III1.r\·s~wasfound to play verylitt le role inthe calculationof thetransport ('haugc'bdw('t~1Ithe pentads. Almost allthe informatio nwas contained inthe ch'll:-lilylh-ld.

(:iWlltl1l'largl~changesinlhl~thcnuolndinestructureatthe NorthAtlant ic lH'I'\\"~'nm!'15-1!159peutedanti1970- 1974penta d,it is dearlyofinterestto ex-

11

Figure1.5:1hmsportstredml unction cd/curd edusing (d) 1955·1959winddnd densityJa~Q(II)1910·/97-/wind and density data,dccordingto Creathl elld al.{1991,fig.S).TAtcon!ourintervalis10$vand the zerocontourisnot draum.DtUhdCClntour,indicatenegatit;valuu ; lolidcontours,pO/itivc lH!lue••

iL1l1inc, thovI!rtk alstruc t ure

or

tlll~transportchange diagnosedbyGreatbatch d Id.{I!J!JI). Furexample, IIOWlllllf ,bof thetranspo rt cha nge takesplace ref- l,n,rwl'd 10thl' bottom or referencedtosomeassumedlevelof no motion,as illtill'"akllilltiullsufWorthillgtoll(1976,1977)? How much did the poleward IWilllriurslllIrl e1l/Ln,!!;l: ix-t wecuthl~penl ad s?The questionarises asto wheth er or n"ttlll!:!l'c:lrllllg(~are Innrlamentellywind-drivenor whether they ariseas iLn'.~llltuf dw.ngl·sinthethermohaline circulation oftheNorthAtlantic.Re- mrrlly,W<'l~Vl~randSarllcllik( 1991)!tav(, shownthatthe Brya n-Coxoceangeneral dn:lIllltiu u1II00ld (Bryan,HJ69jCox,1984)exhibit sdeeadal timescale oscille- tiullsillil.~tlll'rmohiLlint'clrculatlcnwhen rUIIinan idealis edoceanbasin using 'milwll'boundar yconditions, correspondingto having a fixedat mosphericstale.

Alll'c'ad alVll,l'iatinrrinthepolewardheattransport isafeatureof their resul ts.

If511('hvariat.;olllloccurin reality,they cou ld beexpected tohavealleffect.on Ull'ovr-rlyluguuncspherc and thls could,intum,feed back to the ocean. Indeed, III'''1Lcll~1tl5dll al ;Olls in bothgloballyavera gedand Northern Hemisphereaver- ap;I'c!surface airtemperaturehavebeeu noted(C hi! andVautard,1991). Viewed Lop;dlwr,lIrl'SI'r('~~llllssuggestthat decadaloscillationsmay be afeatureof the l't)1lllll'll,ul'I'anatmosplrerellylilem,alloriginally suggested by Bjerknes(1964) , and uri' tlwrl'fofl'ofrollshlc~rabll~interestfromthe point ofview of climate variability.

IIIthiHtlwsis,wedevelop a two dimcueicnal,density-stratified model to study thc'cll'\'c·ltlII1lWnt of currents,volumetransport, healtranspor t and sealevel across

13

II.!WCtiol1ofeither IlI.titu,l,.orlongililllf'illtlr,lrrlotry i!.1Il1:msw,'rsoun-Olftill' questions posedabo ve.The 1110.1..1isitF;" lIr ralizatiulluf till'd.1.III!OITlIF;...."'tn'l'lli.·

vf'locit ycomputat ion.Ittak('ll.wusi ty .IataI'lli!.\'4'rti ,'I\!Sl..·t i"ua"illl' t1tallli ealcnlatesth e veloci tyfidel throughtIll'liC'Ctionreft'O'lIn..1tiltill'hut tu m.S.,·tiunll along55.5"\V,Zl,r."NalltIS-IJi"Nhl\v(' be-nnm"i.kn,,1ami,'"knlaLiuIlIIuftil"

polewa rdheat.t.raIl5port.through2:1.5"NalulM.n"Nhav.. ht"'lIlllatl,',n"illF;.Ial a for theclimatological"'1IIU"! meanamiforthelwnt lld"I9rlr.. rl!1"'11111!1711-7,1Irorn Levitus(1982; 19891\,b,r.). I\trJ4.1i"N ,the'uou-zer oh"U tJlIlvdtlt,il.il'llrt'llull'O'll to achievemassbalance areobtaitwdIlsi ngtIl('II.h"ullll." trnn"llor t"llk nintiolill ofGrf"atbatrhet al.(199 1)andat.2:tS "N UllinI'( Ilntafrom tIll'Ploridu StrniLll (Niiler andRichardsoll, 197:1;Larsen,1992).Inadditiu n tiltilt'Hellerman;111.1 Rosensteill(19S:J)windstrt'Sllrid d (w'I'(1inthedilllatlllo~ir.Aloulllllallll.'/\l1r~UlI' to estimatetheEkman transpo rt),windslr,'SSri.,I.llllUlalY"'''t1hy .IaSilvaall.1 Levitus(perso nal commuulratjcu]are used.

Thepiau orthiRthes is isII.~rollows_IIIchllllLt'r:1.WI',1,~niI H'til<'1111,.1,,1 anditsformulation,In chapterJwepresentdi~lIo!ltir.n",ullltUJ.ta.iltl~1lI"il l"

theobj ectivelyanalysed dellsity da.taor1..I~vitll11(I9H1,1!IH!Ja,htr.,I!)!ICJ). Filially, chapter4providesa summaryamidiscusslou.

J<

Chapter 2

The Model

III thisdlap1.l~rW(~derivetheba.~icequationsof the model anddiscusstheir validity,TIll'methodsrot Cll.lculll.lil1gvolumetransport,heat transportann sea

It'Vc,llll1'alsuprescllit>n.

2.1 The Gover ni ng Equations

ThomuddisIItwo-dimensionalverticalsect ion model.Itassumes an infinite c'x1.c'111III'rflPllIlknla ttothesectionwit huc variabilityalongth a t direction.We include vurtirnlmixlngof mcmenuun and bottom friction in themodelformula- tiunillunh-rtoshowthat;\1a two-dimensionalsetting,itisnaturalto calculate tlu-vr-lm-ity throughthl' section referencedtothebottom .This is aslmplegener- nlisutlcnuf lilt' sterlcsea level method describedby Csanady(1979).Itshould be lluh '(l,htJIVC' Wf, that thereis lIO significantdifferencebetween model-calculated

15

the bottom,

'WeshallcOllsitlt"l'twot'll....,;: 011t'in whirhllir lIt-rliu!1illaJulIJ!;aIillt·t1f Iengliudeandtheo~h("rinwhichitill "Iuur;alilli' ul' lllti l ml.,.III lilt'!"it."'" ..I'a lineor longitu de,lilt,('(IIIIllio llsgt,,'t'fui nr;tIll'I1ltltld an'

(i.l)

III =

_....!...~

+

iJTlI~

apoiJq, ilz

O=-~- !JP

1 8{ } 8..

- -- t1WS' + - =0

a~,a; iJ::

whereas along a line01'latitude, limequal iolls an'

III =

j)TlI~

r)z

O=--:-

ai'

-gp ,h

16

(i.i)

(i.:l1

(i'<)

(i.li)

(i.7)

(2.8 1

1I1,rr'..\ illIU II ~i L ll<lc,'" illlatltude, ;; illthe verticalcoordinatemeasured I/l'witrrl:lwithz

=

0al LIIl':lUllsurface andz

=

-IIatthe ocean bottom;

/J

=

11(..\,

'M

^illtlll~ df~plhofthe ocean;Il,v,andwarethe velocitiesintheA,rP lUI.1;;llirl,diull:l,n~pl~divdy;aisthl~radius ofthe earth;Poisa representative valli!'rurt111 ~deuslty or :leawal'~r;II isthe pressure;p is thespecifieddensity;

(T^r:,TV')111'1~tl1rl JUII~llt111~Yl1 01d 'sstresses and!Jistheaccelerationdue to gravity.

Amougtill'twoseLs ofequations, (2.1),(2.2 ),(2.li) and(2.6 )arethehorizonl al 1l1111l11'lllIl1l1 1'111lnliUIlS, (2.a ) and (2.7)arethe hydrostaticequation,and(2.4)and (:l,H)arl~thoftlillillllityequations.It,l.I,..horizontalmomentumequations «2.1), (2.2)and(::!"'j),(2.6)),the baienois \,,·I.,\','enthe Coriolisforce, the horizonta l [In,,~slln'Sfil,diclltforce and the verticalmixing ofmomentum,

u

1I11lJ1l1,1benoted Llmtthelocaltime-derivative,non-linear advectionand herizontnlHeynoldllstressgradienttermshave beeuomittedfrom the momentum t't[u1Llinuli (2.1],(2,2), (2.5)and(2.6),Thismeans thatwe areworking withthe minimumsd ofequations consistentwith theassumptionthatthedominant Imlill\l'l~is geostrophy,111l ~whichalsoincludeverticalmixing.

Theproblemorparameterizationofbottomstressinterms of theproper- tit'li or111" 1111nowhasoften been discussed.Usually,the bottom stresscan be [airlynrcurately determined from aquadrat ic draglawinvolving theactualnear-

17

bottom velocity- thevelocity ahowathinwall llly,'r.Fur as1t"I,I~"S\ 'lt. -ur lcug-tluu-scnlcmodel, wher emuny high fr" f1Ut' IWYt1o\\'s h.\\','1.''' '11il\"'·ril~^...l,llU' pammcteriaatlonofbottom stressmayb.'showntort'llw"('to n linear furmul.\, i.e.theshea r stress equals a l'Ollstilnt(oftIlt'dhuenslonof\'(-]ur H.y)tiltU'l\tlu- near-bottomvelocity (s"'t' Usanady,1!)Il~ ) ,IIIthistlll'sis,IIPiltillllt'twi1.ilthm uf bottomst ressinterms of bot to mvelocity,IISillP;IIlim-arstresslaw,is IIst',I,i.r-.

-Hand risthe (linear)bottomfrictionrOl·md(~nt.

Whenassumin gzerosurfacewindstress, forbuths.~tsof('(Pl"liuns ,the-Imuml- arycondit ionsattheseaslirflU'.(~(z

=

0) andO(~(1.mholtullI(z

=

-II)um

('.111)

and

respec tive ly. Her e(T::,T:" )is thesurfacestress.

Therigid -lidnpproxlmatl on atz=0alll]l\ It~killfmH,ti!:f:l>1Ir1itjulIl,l.z=-11 give,

1J1

=

{J at z=0

18

1/1=-(1If1"

+

Ilfl~) ,It z=-1/ (2.12)

Wl'shnll!lOWworkwith lIwl'(luntions(:'!.!:i)-(2.8 ),l.e.a sect ionalonga line uflal,i llJ(l(~.Sim ila rN~~ll ltsan'validfor11111syste m (2.1)-(2.4 ).Letusbeginby verth'allyinll'J!:ra l ill,lt(V~)llsiTl~(2.12)to give

Wh ( ~ rl'

(iI,V)

= _(L~l

urlz,

L, ^urI::)

i.~l\lt~vl·ttically illtl1,l!;ratctlvolumetransport.Itfollowstha tifeithe rtheeastern ur west umhUlll11laryisitcoastline, aswillalwaysbethecasein th isthesis,then

u =o

(2.13)

Wernunlso vcr f irnlly Integr a t e(2.6) using(2. 10),(2.1I)and (2.13) toobtain

,,~ =0 (2.14)

IVht'rt'..~istht, vd od tythrong hthesectionat thebot tom.

Similarly, intheraM'of the sect ionalongitline of longitude(eolls.( 2. 1)-(2.4)),

V=o

(pmvillc'l!tlll'J'('isacoastllueat one endofthesection)and hence

1l~=

a

19

(2.15)

(2.16)

Equations(:U,l)nud(:Uli)showthatlilt';ISSll1Ilplilln"f1111\'m'i:llil\ll~pe-r- pendiculartotlu-section1,,;\(lsnat urallytillll1'nlllrlllsillnI,hill""lud l.i.·ssh..uld bel'<'ferl'IlI'l'(1 to tilt'bottom.OfrourSt'inrt'"l il,y,Imltolllwluci1.i" /Ilift' 1I111ik,·ly tobezero.Toallowfornon-zem bouom \,,'IU1·jt,iI'S.variutlcnsin llll',Iin",tiull perpendicula rto lilt'1I",'1.illumusthe'1'1l1lsilh'I'I'd;",~, liyIIl1ill~IInUIlI.,1fonnu.

latedilll,hrt't>-dillll'l1siOIlS, suchastha tufM,'l1l1rl'l.nl.(I!lS1).[IIl'hllpl,'r:1, rt'lIlIltll from ourtwo-dimensional,vl'r t ir al-Sl'l·tionIIlUlII'!willI","umliilll'liwith llll' di- ap;lIootic ealcuhwiousof Grt'l\thatchdal,(I!l!ll )illurdl'rt" "/ltiI11111,'l.nulllllorl associatedwith non-zerohottom\'d ud ti,'lI,It«houldII"lIul,''l1 t1ll1tuurlIuull,lis verysimilarto thatofCSl'lnady( Hl7!l)whichwnsmll'llhyhimI...,',,It-Illlt!.'' sk rlt- sealevel intill'Mitl·Allantk.Bight.SrutianSlwlfand(lrall,1B1LUklirl'~illnllur theeasternseaboardof NorthAl1wr1m.'i'heunly cliffe'n 'un'illlntil('Ila ra llu'tl'ri.

satlon ofthe bottomfrictionwhichintlH~ril./il 'ufCSlulmlyw;~~illkrltL~,ll,iUII'r bot tom gecsrrcphicvelocity (t lwc.~~c~mos tllimilllrtu onrx]urvr-rtlrullyIlvr'rn~" ,t velocity.

ThesetofequationshavebeendCISl~dand,III~X t ,we,1II0 V,"1111 l.ulll"111~ur il.l ll11 ofsolution.

2.2 The Method of Solution

Thesolutio n procedure is similar tothat Ulil"l lIyLynchd111.(1!)!12)'111f1 Greatbatc.hand Gouldillg(1992)andrequiresth«USI~of11simpl l~ lJ1Lrl1l1'dl~ris ll'

20

ti<>11 furI.Iwvl'rlkal mlxlug ofmome nt u m. To do th is,weshal l use a uniform VI~rlkld1~1 , lyvbr:osiLyl:{mlFi r:i'~ lI l .hshou ldhenot ed , howeve r,tha tthisis 110t ilJllltJrt anL furtill'rl~S ll lll'iwe presentslncethr:calculated ve locit ies do 110t differ siRuilinmLly frumgl~os t ro Jlhicvelocltles refe rencedto the bot t om . Wefirst sepa- mtc~till'pres su re term 11intotwoparts, oneduetosurfacepressureandanot her ,1111'tutIll'ncn-uulformcll'nsi tyof theflu idcolumn,usi ng(2.3)/(2.7)by writing

(2.17) wln-ru

(2.18) uml II,is LIlI!pressureatz

=

O.Wethe nwritethe moment umcquatio ns( 2.1), (2.2),(2.!i),(2.6)) inthe(a rm

ifq-.!!...{/I~) oz oz ;;

^R+G

when-i;;

A

amI q;;11

+

i»,Inthe case of(2.1) and (2.2),

1\1111

IIItIlt'l'l'S ('

or

(2.5)and(2.6) 21

(2.19)

(2.20)

(2.21)

(2.?.!)

{2.2:ll withsurfaceandbott om boundary{lllJtlilioll~

wherebothRamIG'ILf('complex.

a

isthILtpart(Iftlit~IIuriWlltlllW('s~lIn' gradientdueto thegrlllli"nlof ))rt'SSll",;Llz

=

^o.Ilisthat llilrtwhichlltilll'N from thedensity stratifiCAtion.

Wenowfollowit.proceduresim ilar to thalII~"(Iby1." ...11dal.(I!)!rl}anll

(2.2.'i)

and

22

/1(/1,=0 at z=O /'1/1,="'11 fit z=-f-1

(2.26)

ILsllou l,1 Ill'lIo tl ~t1thllt, giVl111thodensity field,Iicanbe calculate d using (:,!.JK)aud('itlll~r(2.2U)or(2.22),fromwhich itfollows thatbothq1andq2are knownqllil nl,i t il~lilImlC1U1e'L~i lylw calculated.

SillCP(,'isill rll~I"~l1dt~lItoftheverticalec ordiuate,and since(2.19) is alinear 1,<[lIalio ll,'/.:;r,nII<'written illtermsof1/1and{/1 as

(2.27) when-'II istIll' solutionto (2.19) wit h forcing RandGq2is thesolut ionwith

rIJrl~ ill~U.TIll'prchlem is nnwtodeterminetheunknown G.

Tod"this,weIl('gil1hyverticallyaveragingequat ion(2.27) togive (2.28)

WIU'rt'IUlovcrhurindicate s vertical average. Using (2.13)or(2.15),whichever Ilpl'r " l,ri;lh',it1I0Wfollows tha tG'can be expressed in terms of ql>qland the vcrtlrnllyil\'('rn~('dflow throughthe section.For example,if thesectionis along illilli'\IfI;ltitlllh~(1'<] l1atiulis (2.5)-(2.8)),

(2.29)

\\'111'1'('

(ii.il)

= * (lO'lud=,["vd=)

2:1

isthe vc rtlr-allya\"t>ragl'llvelor-lty.Sllhslj1ll~i l1p;lntu(:!.:fijUWIl p;iwlI

(:!.:lU)

Evaluat ing(2.:10)atz

=

-IInowp;i\'C'salloxpn-sslou ful'tIlt'hu~ltlll1""1,,l'ity, qb

=

^{(lib,Vb),amihence}the hottom sLn'lIs, (r(,Ttl/Pn

=

"(/lb."I,),illl.c'rllls Ill't.lu- knownquanti tiesfll,fllandUn'unknownii,III111(~"llSl'ofa lilll'til'li,t.itl1c1I ' ,

(2,:11)

(2,:I:!)

andthesu bsc ript"6"denotesevaluation;ll :;

=- // ,

We!lOWusc (2.14) to sdUb

=

O.

v

ca ll1I0 WIJl~f:akllla1.1~11from(2.:11),

Subsequen tly,GcallIwoluuincdbyeqn(2.2:1) lIlulthensllllSlilllt.l~intu(2.27)til obtainthevelocityfield [u, v).

Simil arly for asectio nalongalineoflungitll dl~,V

=

IIawl,asaill/llll,WI' obtain

24

• f

(AZ}l

(6Z)1

z=o

u;v

H

H H

Grid Arrangement

Figur e 2.1:arid Arr anqemcnt and,puuingtil,

=

^{0from(2.16),we obtain,}

11=-~

u,

^(2.35)

'I'oHolvl'flluudfh(nnd hence [n,tI)),a finitediffere ncesche me emp loying c'l'lllrt'ti-dilfctl"ud ngisused. The gridarrangement of thedepend ent variables II,t',II!IImlflisshowninFig.2.1.Inthehorlzo nt nl,theWtp,andHarestored illtill'»anu-grid point,withthe11,u pointstore d in between.In tbe verti cal, only wis ston-d at tilt'edge ofmd!::level, whereasu , u,Bndp arestored at the middle puint, ofc';\chzlevel. WlwllV,\!Ut'Sof Hat (u, v)is needed forthe calculationof

25

velocity field, two point averag ingisemployed. Inall tilt' calculat ions,uniform gridspacingisusedinboththehorizont al amiwrtin\1directlous,

Thetotalvelocityfieldhasnowbreusolve d. WI'can.tht'l"\,rllft,.fnrtlu-r tlc'd\'!' the volumetransport , heattrau s pcrtfprovlded tl1l1pou-ntlnllI.'lll p c·ml,lll'C'Ia-hliN known)andetericsea level,which willbe elabcratodinnext sr-et.iou,

2.3 The Calculation of Volume Tra ns p o r t , Heat Transport and Ster ic Sea Level

Itisst raightfo rwardtocalc ula tethevolumetralllllllwllllwuAht.1wNl't"tiu lI,In case or a line orlati t ude ,thevolume transportM(..\)isgivt~nhy

M(..\)

=fE:/tlrlz

f1c:usr/>rl..\

where..\~is thelongitu dea11llceastern bouurlary.Theinl "p;ral iclllur ::isfrulli -Hto0,Le.fromthehaltomto thesllTfar1~. 'I'lwinlt' ll;ratitmIIf>.isfrll Hl easternboundary.Integratingthe volume transllCltlIrumtht~c'lUll.l~rnhUIl\lflaty to western bounda rygivesthotot al volumetransportlhrou~ht.1wst~d iull.

Sim ilarly,volumetransportthrough<~Imctirlllor lougit lldnM(1J)i~ /l;jVI~1ll,y,

where cPn is the latitudeat thencrthctnbouudaey.Tileilllt~~ril.li\llluf'bi~frum

nhrt lwrn [muudxry.JlJtl'~ratingthe volume transportfromnort hern bounda ry tl,sulltlll'rlJhcundarygivesthelot alvolumetransportthroughthe section.

Takillg.taud11 ill(2.:16)and(2.37)tobe thevelocitycaleuletcdby our /lllllld ,MwillbeLII(~(p;l'Ostropllic)transportreferenced tothebott om thatis lL<;Stwiat(~dwithUl t~111~llsityfield.Weshallcallthis transportAh. Whenwe lIis':lIsstll(~1lI11SSbaiauce for as(~l.ionoflatil.ude, weshallalsoestimate the EkuliLliLtillIsport(Meldthroughthesectiondue to thesurfacewind stressand ,.lIelrllllsp(JrllL'iS(Jdl~lt!'dwillIlion-zero bottomvelocity(MlJ ) . There fore the ItlJ.'i{,l llle~volu metrallsportMissplit intothree parts,

M=MT

+

MB

+

MEK (2.38)

wit h

Meli=

-1 :"

f;lacos¢>dzd>. (2.39) and

MB

= 1:" 1161°1/

acosq,dzd>' (2.40) whereIIIis thenou-zumbottomvelocityandTAis the eastward (in the case of a Iilit'oflnrlt udo] component of the surfacewindstress.

TheEkmuntransport(Mel( )is estimated using theHellermanand Rosen- sl,d ll(J!I~:llwind stressfield(used in the climato logicalannualmean cases) aswell

"Ii

tlu-wind stn'liSlidtlsallalyst~lbyda Silvaand Levit us(usedin the twopentad

t'aSt'1ialltlill theclimatological annual mean cases).The volumetransportasso- 27

elated with uou-eernbottomveior-ity(MR )is calculntcdbysulJstrnd illp;11ll'Mr andMEJ."fro mthe absolute volumetransport .At 54.5⁰N.thisahsulul.t' volun«- transportisobtained usingthrtra ns portrnlculntlonsof Grt'athalrht'l.itl.{I!Hl1) an d at2.1.l)°Nusing datafromtheFlorida Strait s[Niik-randHkli ar tlsu n,n 17:I;

Larsen ,1992).

IIIordertocalcula te the Iwaltrans port throughaSt~di{/ll.WI'm'l'tlt.1Iknow thepotenti altc mpcratllf\1as wellastht~velocity Ikhl.l'otl'n t.iil!lt'11l1Wraln rt, /Jis definedto bethetem peratur eo f!It.'a wet crrlli St,t1 l\(lii~halk i\lIy1llltlist'nt.rnpil'hlly to theocean surface,i.e.toa referencepressureofI'ltm. Clivl'ut.1lt~in.~itll te m peratu reandsalinityfieldfromLevlt us dat.a,the putl'uti'lltl1l1l!'t'ra tllrt'nm beca lculat e daccordin gtoBrytlt~1I's( 1 97;j)empiricalpo lynomial.

O(P,T ,S ) T- P(3.6!.i04x1O-~+8.:I\ !)HxIO-"'J'-!L4(Jfirjx1Il-⁷'1'1 +4.0'l74xIO-uT~)- P(S -35)(l.i4a!)xIU- r.

-2.9778x10-⁷1')- P~(H.!J309x10-⁷-a.Ifj~HxIII-It,/, +2.1987x 10-¹⁰1'1.)

+

4.1057x JO-tlfH - ;'!i) /'1 -P:l(-1.6056x10-¹⁰

+

5.041HxW-¹¹.l') (2.'11)

whe reO(P,T,S)isin °0_a.~a functionorsalinit yS (:10<8<40).telllpt ~rIItllrc~

l'(in°cwith2<T<sc,andpressureP(ill barsalld(J<l'<IOWI ).

Striclly speaking ,he attransport canonly1)(: calcul a t ed fur11.!md iol1lllrtllJ~li whic hthereis zero net mass tra nsp ort.(Muntgollwry. 1974;Bryan . I!JIi'l) ,fur,

28

(Jtlll'rwisl~,th(~n~slllt~willdependonthe unitschosenfor temperature.Howe ver, it isronveniont ttl dl'lilll)the heattranspor tfunctionHT{J.. )as

(2.42)

WIU 'I~ 'Pisth"density,Cpis theHped ficheat at constantpres sure,vis theabsolut e vd lld tythrough thesl'ct ioll, and0istilepote nt ialtemperaturein degreeCelsius.

pr,.eanIJI~1~~.~Ulllcdto have uuniformvalueofO.00409PwoC-^IS V-¹withinthe limits IIftheIm 'Be lit calcu lat ion.Integratingfromtheeasternboundaryto the Wl','lI.l\TlIlwutnlury p;ivl's thepolewardheatfluxthroughthe east-west secti o n.

Sil1cI~ourmodel calcu latesthe velocity fieldreferencedto the bottom, itis mllvl'nil~lItto split111'intothree parts,as wedid for tilevolume transport .

liT=llTT

+

HT s

+

HTEK 1/'1'1'istlll\thermoclinepartofthe heal transportgivenby

(2.43)

(2.44)

when-liTisthl~vdodLYfidel referencedto thebottom andcalculated by our 1Il1ll1l'1. 11T His that partof the heat transportassociatedwith the bottom

\'c'ludtyI!~,1\\11is~ivl1l1by

(2.45) aurl1I'1'F./\is till' Iwattransportassociated withthe wind-driv enEkmantra ns-

29

port and is givenby

(2Ati)

where.Osistheseasurfac.•~temperatureandT.\j"th"1" I.~t\Vanl(illtil<'l~il.~I'of alineof latitude]componentof the!lurfart'windsln's.'(, It ,,\111\11.1I...l\utl'll thatthisdecom position isdiffl'n~n~fromLhatf()ll(Jw~1hymustIlrt'villuSimt,hlll's (e.g.Bryan,1962, 1982;Hall and Bryden,1982;Molinurldnl,l!mll), hutislIw most naturaltolisewithour model.However , ithil.~till!t1isad vant,~gl~t.ha llilt' individualpart s,i.e.H1T,IITRandll1t.;/\[butnutthelrsu m,wht'llintl'/l;mt('l!

allthewayacros sthebasin),depend011til t!uuil:.lIs,>,1forpULt'lI ti iLlll'llIp " I'at 1l1"!, Sinceinthis caseWe useDC,this bcquivelont tolL~Slll1litlga return flowfo r{,ltdl componentatODe(difficultiesilldefining thetem perat ureofth,!n-tumllowaml hen ceindefiningexactl ywhatisllleant byeachcomponentof tIll' Ilt'attm nslllJrl, arediscussedillBryden ,Rocnnulch andChurch, 1!I!H).

Thestericsealevelcan alsobecalc ulat ed. Usually,l1U!tt'I:llIIiqul'(If t:UllI- putingdynamic height suireI'llfromSOIll/!lirnilati l)lIS,IIMLklll nrlyilln!~illllsor variablebottomtopogra phy,Oftc»,a.lf1vd ofno motionislL~Slllllt!dIUlIltill' velocities arecalculated rcrewnr.cdtothisdl~plh.GII~arly, prubll~IllSMist,if 111l' oceanis shallower thatthedepth

o r

^theassu med levelIJfnu mutlun. lldlIU1 /I- Hansen(1934)suggestedamethodwhich I!xterliisisupYnl alsImrho:ulltallyIlll,)l'r tile bottom

o r

the ocean fromtheirpoint,

or

int ersectionwithth{~sll/ pl!."'Idsr'ur- responds toassumi ngthatthegeostrcp hicvdfJ cityatt11(~ll11UfJlIIis alwllYs~I'r/j

30

utnlisl~llllivltbitto till'mdhollof CS1Lnady( 1979).Since our modelcalculates L1wvdud tyrdcTl'llCf:dtuthehaltom,we canuse themodel to calculatesteele senlevelillrC~Ri(Jllsof<Illitegeneralbottomtopography.We shallusuallytake the I,~vduf110motion to bo at tilegreatestdepth on thesect ion. Calculations refer- '~IIi:I~.1to l.'iO{Jmwill alsohepresentedfor comparisonwithLevitu s(1990).With this inmind,w«cnlculato th"dynamicheightbyint eg ratingG'(secc<}I1.(2.21)

(2.47)

whereIIisL1w upwardsdisplacementofsealevel fromsomereference level.As .IiSI:USlll '( !earlier,theintegrat ion startsatthepointofgreatestdepth, Thesea Il'vda~tillSpohl~is obtaincllbyverticallyintegrating thehydrostaticequatio n.

Assuming11=0at::=-fl,we have

I/a=-

r

(P- Po)dz

L H

Po (2AS)

Hen-thereference density(10is chosensothatthe sealevel is not far fromzero.

MlI~rncquirlugI/O,we usel,qll.(2.21) and (2.23)tointegrate towards thecoast ntnl henre,tlw wholeSl,alevelfieldcallbe constructed.Ofspecial interestisthe rcmpnrlsou

o r

sealevel changesbetweenthe19505and19705.

31

2.4 D ata

Thehydr ogr aphic data~etused inthisllwsis is thedOlt" ...,ml,i!,>,1nul!

analysedbyLevit us(1082). His resultswere based on til!'dat.awhichIVt'fl' obtained from the NationalOceaaogr aphlcData Veni N(NODe).Willlhill~lun, D. C., and represent allthedata available in 011'oC('lumgmphk stnliulldid,il.

file(SDF)as of the firstquarterof 1978.TheSOl<'fill!cout aiuedaboutfiOlI,nou hydrographic casts consisting mainlyofNanscnC~Nltsalongwithsl'wralLh tl llS lI ll tl

conductivityand saliu ity-tempcrature-dcpthcasts.

The obj ectiv ely analysed data arc available at]QresolutioninIouthlatiLlult ·

and longitude andat thestanda rdlevelsfromsurfacetollt'il. /lUOT,i.r-attlu- depths of 0,10, 20, 30, 50, 75,100, 12ri,150,200,250,:IOU,<1UII,."ilI(J,(iIlII, 700,800, DOO,1000, 1100,1200,1:100,1<100,1500,1750,

zeon,

~riOIl,:1O(J(J,

a!illll,

4000,4500,5000, 5500metres. Allc1ailllClIbyLevitus,thllohjedivl'mllLl y~ill procedur e su bst antia llysmoot hsoutfeatureswithwuvelengthscfIl'sli UHlllllI'vl'ral hundr edkilometer s.A det aileddeserlprlonofdatasoureI',;,qualityl~lJlI lml,1L1II1 theobject ive analysisprocedure forrAllllltrU(~ti llgthl~datafa-ldis Kivl'lIIJyI.e vitull (1982).

In this model,theinpu tdensityda tuof Levltus] 19M2,I!JK!JIL,IJ,e) ill trans fllf"('11 tothemodel gridbymeansoflinear inte rpolation,Itisworthill/l inKtlJat1ll/IllB- times theinp ut density andbathy met rydatado 110talwaysmatch.In lJartkulllr, it some times happensthatthe bathynwtrydata indleate thattllll wdllrdllplllis

k~sthanilml indicatedbythedensitydata, inwhichcase, density data below lhll {Iepl lljlltl i l~llt{~dbythe bat hymetrydataarediscarded. The otherpossibil- ity istltj~ltill'hath YJIIHl ry data indicateadepthgreaterthan doesthedensity llal.a.IIIsuch(:as{~~ ,,Il~n sitydata are create dby extending isopycuals horizon- l"lly,~L'Iillthemethod

o r

Jlelland·ll ansen( 1934).This procedureis alsocarried {jillwll(m{~ vl ' rflensity datais requiredhelow thebottom in order the calculate

1I1C~vdodtyfield.Gridpoints atwhichextrapolateddensitydata meet (rom

lwuside·s art't11~altwithfly calculat ingthevelocity using densitydatafrom one lIil te~finly. This apprOIlc/1 ensures thatthe impactof the extr apo lationprecedure

011th«vdm:ityneldillkep t til amluimum(itshouldbenotedthat extending i.'IflllynJil.1.'1horizontal lyensuresthat thevelocityat theoceanbottom is always lwm).

As1I1111't!earlier,whencalculat ingthe Ekmanpartofvolumetransportand

IIt'll~tmllsport,we shalluse the Hellerman and Rosensteill(1983)wind stressfield

(lIsl·d in tlwelhuatologlcalauuual mean case to estimatetheEkmantransport), andlilt'windslrt'llSfieldsanalysed by111'0Silva.and Levitu s (pe rsonalccnununioa- tlon].'l'heciaSilvaand Levitus windstress fieldsare derivedfromCOADSdata hy enalyeiugonch individu a l shipobservation, making a correct ion for the Beau- fur~limll'(}\auft'ld ,Hl81;da Silva,YoungandLevitus ,1992)andanadjustme nt furam-mcnu-ter heightto 10m(Cardone et11.1.,1990; daSilva,Young and Levi- tus,1!I!12). Details can be found elsewhere,althoughapreliminar y comparison,

using dillcrentwindstressclimatologicstodrivea nutucrh-almodcl,ranln-fount!

illFan ninget a1.(1992).Itisthesewindstn-ssfieldsWI'u~efurthetwopt'lltntls, Weshall also show thedft'l~tofIIsingllafiilvaandLt,.,.i lnl<'~dimatnl"ro',r;~Ull'r than thatofHellerman and Rosenstein,inl1wdilllatnllJgin,l l~Cll<e.

In allthemodel runs10bedl'scriht'(lWI' llSl'auniform Vl'rtki d"lillyvisroslty coefficientof/I

=

O"OO lm:l.~-landa haltomlrictionI',wllkil'lltof,"

=

ll.lJOI111,0;-1, {Both valuesarcquotedaa being reasonablebyCSIIll1uly(I!IH~).) Itrollmvs thatexcept very near theequator,theEkman layer depth

F1i

^{isIt'SS lImn}

10m and is only3m at 45°N.Since thetliaglltl.'\t·(1wludlYllmmp;htill!St'd ilill isgeostrophiceverywhere exceptwlthluallEkmanlayl!rdepth of 1I1l' lop and bottom, itfollowsthatthese velocities,11.'\raku lall'dhy tile1I111111'11U'(~/l;1·osl.l'IJI,hk almosteverywhere[departures from geostrophy willalso occur inw/I;iulIS wlll'T!' thegeostrcphicvelocityvari(~sinthevl~rticnltillasl~ul(!

or

orderlIl(!gkm,ul layl!r depth; there arenosuchregionsinournnalySl';l;).The muddwill 1mUSI,I!tu diagnose thevelocityfieldfromt1wknown densityfield, withthort!SlIltslwill/l;

shownin the following ehupter,

Chapter 3

The Model Results

Wl~nlll'1i(~tlthe modeltofoursuctlcua.two sectionsthrough55°Wand65°W l11IlAiLul[f'andtwos(~lionsthrough24^aNand 54°N latitude(fig.3.1).

3.1 Se ction through 55' W and 65'W longitude

WI~IIst~Llll'S1~twosedi ol1~tostudy the veloc ityst r uct ureend transport,par-

tloularlyt1mt uftheGulfStream ,The GulfStreamisof central importance to tlwgl'tll'ra l circulationof NorthAtla nticand a great dealof attentionbaslong ht'l'u ,l;iVt111toth('nudcrsteudingofthe Stream'smean velocit yst ructure and lrilllslM.rl(n.g.Stommol,1965). But becauseof the swift ness and variabilityof tln-rurn-ut, itisdinkultto obtain dlrect long- term measurements.According to 11H'n-viewoftill'NorthAtlantic circulationbyWorthington(1976 ),theaverage transpurtofFioridn Currl'nt{offFlorida )is30Sv(withvariationsfrorn15to 38

degreeW

Figure 3.1 :The positionoj flir.JOIn'sl'dilJn.~b(·iJl.q.,tudil'tI Svaccordingto otherstudiesusin g thedcdru magncticmotho.l}.'1'I11~tr<lllsllUrl inc reasesno\·t!J·castto85SvorrC.tPI~HaLl...rIl.'l llmlto150Svhyfi5°Wan(Il\Il~1l decreaseseastward to37 Sv at ,1OuW (Knauss,IHlIfI).

Twomethodshavebeenused to estimalllth(~absolut eGulfSl rl\lLllll.r'l llHllort for theregion50 - 70oW.IIIthefirst,velocityscd iullsW(i[limadel~Cr(~'\!;tilt' Stream usingtransport floats- instr umentsthatfallfred y through theWltlt,r anddirectlymeasuretran sportper unitwidth. TheStl.~orll.lmethodl;u lIIlJilU'H

geostrophic(ba roelinic)velocitysecr'cnswithabsolutevdodtyI1wll.~umdflyIJI't'1J floatsorcurrentmeters. Both method shavetheproblemthatit is verytlil[jt;ult to determinethelimits oredges ofth"Stream. Velocity sectleus usually slJuwIi

36

"'I1I1I,lk al."dpllLtl,rnof meander s,multiple cj-ossiugsofthe Strea m ,edd ies,ccun- l.', r' :' lrrl:llt:>illlfl»mall-sculeembcddedjds.These fea tu re sfrequentl ychange from lIt'd i"n1.11seetlon, awlit isnot obvious which ofthe mto include asGulfStre am lra usl' urL.MtIlJl"l:dI:llrrl'ulmetermeasur emen tsunderandnearthe Streamre- v,'al larw' iUlIplitll!lctim,..,lup,:lItlentfluctu ations(e.g. Schmitz ,1980). Howto lIUitillJly1:UlIIl,iul' thes«stl"OllglyOlldllalillgvel ocities withthe more stable hydro- II;rllpl,i"and gC11Str<ll'hkft'alliresis et .llfunsolved. Itisnoticed that using the deep floa ttll·t:lIr rl' Jlt11l1'1l:rvelucity tendstoincreasethetranspo rtove r tilegeos trophic I.r'Ulspur trt'fl:Il~IlC(':dto theseafloo rbylarg e amounts.Fugli5te r(1963)report s lUIincrcusr-From?iSSvrelativ e tozeroveloci ty attheseafloort«1478'1with float Vt'lod1.i,~~wln-reasRobilll;oll etal,(1974)repo rt transport of778vreferencedto

theSl' i!tloor amlI1nahsolnte transportof 226Sv.

WI'new«howresultsobtainedusing ourmodel along.'jfi~W.We begin with thissl ~~li<) l1NOlhilt WI"cancompareourresult s withthose of Richardson (1985).

Wt~tookasocuou along55"W andbetween8-45"N andappliedthediagnostic modelIustudylilt· lr<lllsportandvelocity.Threeset s ofdensi t y da ta-namely, I!H'ilIs, 1!170sanddimatologicalannualmean data ,allfrom Levitue,havebeen llM'11lolirsl. dia gliONt'thevelocityandsubseq uently, calcula tethe volumetrans-

Fip;urt·:t :la,b showsthe maud-calcu latedvelocityfieldthroughthe section (l' ullil,il"l' Iwing I';lstwa.nl)referencedto 1500 111,and to the bottom,respecti vely .

:17

Minimumvalue -O,0702R

",..dm u m vlllun0.1545 1\

Inlerval 0,010 0 0

Mi nim umvalue -O,OOHi4 Ma x lmumval ue0.103 88

Inlerval 0.010 00

dcgr ces NlIIonI( 55.5""

Figure3.2:Eastwardvelocityjidtllt.~illgc1imat/J( flgicfLlfl lWlI.fLl m fCU lldfllfl(II)lIlI upper panel,rrferrllcedto1500In(b)tile (miter"antl,n!t,r't:rlt:cfl l fJUu,11fJ1l 1l/l t ,

Tile cOlltour intervalis0.01m,~-l,Wil/Ida,'<lwlCnll/OUNIilldil'lllill!11II1'llt'Jltll'fJ velocityandsolid COlltOUl'1!cas/ward. 1'hrminimumandmnrimumImilll'llIWf' givellill m.,-l ,

TIll'.lc~lIsityfieldisthl~annualmeanfromLe vit us (1982), andso shouldbe rep- resoututlveoftlwclimatologicalmean state.Infigure 3.2a, the calculat ionis per- {orlllc'd using :lOIJ(jllallyspacI1dzlevelsat a. horizonta lresolutionofI".Inllgure :U!IJ,tIlt·ndell latio llisperformedusiug80equall y spacedz levels at ahorizon tal ll'sulut ilJllofI".IIIalllIwrnlcuhulons, thereisnobottomvelocity tecccrding 1.0t~llll(:l. Ifi) ).Thl~rdore,lhc~velocityfieldshownis actually velocityreferenced toI!jlJOm lUlIlLIlt'ecoanbottomrespectively, Fromthe figures,we can clearly illc'lItifytIlt'GnJr StnJumtohe the eastward flowcenterednear40"N, extend ing Inun:l£i"Nto44"N, Rpproximately 900 killwide.It has amaximumsurfaceveloc- ity uf 17nll.~-lreferenced to the bottom ,center ednear -lO"N.The GulfStr eam ishtlllll<ledhythesouthern countercurrentbetween3J"Nami36"N whichflows Wt'stwarcl,

()urllparinp;tlJl'.~nfiglltl'Swith the cont ouredzonal velociryeectio nalongfj5"W in/lidwl'Clsou 'spall11 r(h is figure6b)revealgood agreemen t inthe mainfeatures.

Jli~flguro[reproduced hemas rig.3.3) is the velocity from drifte rs,floats, and t"l1fl"t'1I1rtll'h'rswith lIlt'wimldrift velocityremoved. Note thathisvelocityis 1,lll'ahsul lltt~wltll'ityandnottht~velocityreferenced tothe bottom. Thereare sunil'~i llliIO\ritit'Sbetweenthedirect lymeasuredvclocity (Fig,3.3)andthemodel- c'nlr-ul1l1t'tlv(·lot'iLy(Fig.:1.2a,b),Theupper levelGulfStream is sim ilar - both

;ltl'n'lltl'l'l'llllt'llr ·lOoNami have approximat elythesam ewidth. In fig.3.3,the mnxlmnru~lIrfO\t·t'w!ud ly referenced tothebott omis about20cms-^I,whichis