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T H E N 'O RTH A T L A N T IC C U R R E N T - S U B P O L A R F R O N T S Y S T E M :

A S T U D Y C O M B IN IN G F L O A T D A T A A N D

H IS T O R IC A L H Y D R O G R A P H Y

B Y

P A U L A P ER EZ B R U N IU S

A D IS S E R T A T IO N S U B M IT T E D IN P A R T IA L F U L F IL L M E N T O F T H E

R E Q U IR E M E N T S F O R T H E D E G R E E O F

D O C T O R O F P H IL O S O P H Y

IN

O C E A N O G R A P H Y

U N IV E R S IT Y O F R H O D E IS L A N D

2002


UMI Number: 3053116

UMIUMI Microform 3053116

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D O C T O R O F P H IL O S O P H Y D IS S E R T A T IO N

O F

P A U L A P E R E Z B R U N IU S

A P P R O V E D :

D isse rta tion C om m ittee :

M a jo r Professor.

D E A N O F T H E G R A D U A T E S C H O O L

U N IV E R S IT Y O F R H O D E IS L A N D

2002


A bs tra c t

T he How o f su b tro p ica l waters carried in to the no rthe rn N o rth A t la n t ic by

the N o rth A tla n tic C u rre n t-S ub p o la r F ron t (N AC '-SPF) system is an im p o rta n t

component, o f the m e rid io n a l ove rtu rn in g c ircu la tio n . M uch o f the w a rm -to -

co ld w ater p re con d ition in g th a t allows fo r deep convection in the Lab ra d o r and

N o rd ic Seas takes place in the subpo la r N o rth A tla n tic . T h is s tu d y addresses

tw o processes th a t co n trib u te to the w a rm -to -co ld w ater conversion: S ubpo la r

M ode W ater (S P M W ) fo rm a tion , and cross-fron ta l m ix ing . Using G ravest E m

p ir ic a l Mode* (G E M ) p ro jec tions o f h is to rica l hydrography, we fin d th a t S P M W s

are form ed on the flanks o f the N A C -S P F th rough w in te rtim e convection. The

mean characte ris tics and approx im ate loca tion o f fo rm a tio n fo r the d iffe ren t

S P M W classes found in the N A C -S P F region are ob ta ined . To q u a n tify the

heat lost by the N A C -S P F waters in th e ir tra n s it towards the Eastern Sub

p o la r N o rth A tla n tic (E S N A ). we develop a technique ca lled the flo a t-G E M

m ethod . I t combines G E M fields w ith R AFO S floa t da ta to o b ta in the abso

lu te transpo rts o f mass and tem pera tu re in the top lOOOdb fo r the tim e period

1993-2000. T he N A C -S P F appears as a "p ip e ", tra n s p o rtin g 15.0±3.1 Sv from

the subtrop ics in to the subpo la r region. The no rthw a rd flow ing N A C fo llow s a

we ll defined m eandering path . No evidence o f perm anent branches pee ling o ff

the cu rren t are found upstream o f the N orthw est Corner. T he cu rre n t seems to


s p lit in to two branches upon ente ring the N orthw est Corner, w hich d iverge as

they tu rn east, c o n s titu t in g the SPF. The tw o branches converge as they ap

proach the M id -A t la n t ic R idge, crossing i t above the C’harlie -G ibbs and Faraday

F racture Zones. The X A C -S P F loses 0 .27±0.06 P \Y on its tra n s it tow ards the

E S X A . w hich is much la rger than the correspond ing heat lost to the atm osphere

( ~ 0.07 P \Y ). N early a ll the heat lost by the X A C occurs between the m eander

crest inshore o f the M ann E ddy (~ 4 2 .5 °X ). and the fo llow ing tro ug h (located

at 44XX). due to e n tra inm en t o f co ld waters from the inshore side o f the stream ,

and a loss o f warm waters to the su b tro p ica l side. We conclude th a t cross-fron ta l

exchange', induct'd by the steep meanders o f the no rthw ard flow ing X A C . is the

m a in mechanism by w h ich heat is lost a long the curren t.


Acknow ledgm ents

I dedicate th is w ork to m y parents P etra and E duardo, and to m y g rand

parents U lla and Teddy, for always be liev ing in me.

T h is thesis is one o f m any end p roducts o f the process I went th rough in

G radua te School. The whole experience was more than pu re ly academ ic, and

it w ou ld have been much harder (m aybe even pointless?) to go th rou g h it i f it

w asn 't for a long lis t o f t ru ly nice people who co n trib u te d one way o r another

to make th is happen.

I ’d like to tha n k F u lb rig h t who provided me w ith a scholarsh ip th a t saved

me from the hassle o f dea ling w ith my visa fo r three and a h a lf years: special

thanks go to the In s t itu te for In te rn a tio n a l E duca tion in M exico C ity . The mex-

ican equ iva lent to the N a tio na l Science Foundation (C O N A C Y T ) covered my

l iv in g expenses and hea lth insurance for five years o f m y s tudent tim e : I thank

D ebra H a lte r Borsuk a t C O N A C Y T in M exico C ity fo r ta k in g care o f th a t so

e ffic ie n tly and goodhearted ly. R u th C u rry at W oods Hole O ceanographic In

s t itu t io n k in d ly provided recent W O C E hydrog raph ic data . C h ris M einen at

the U n ive rs ity o f H aw aii let me use his 42°N N A C section, and gave useful

h in ts for m y w ork. Peter Lundberg and the rest o f the oceanographers a t the

M eteoro logy In s t itu te a t S tockho lm 's U n ive rs ity were very nice hosts fo r the

sho rt bu t p ro du c tive period I spent there: I am p a r tic u la r ly in debt w ith A nna

iv


X iko lopou los . W a lte r Zenk was real nice to me d u rin g m y v is it to K ie l, spe

c ia l thanks go to Saskia Esselborn and K a tja Lorbacher fo r th e ir hosp ita lity .

C h ris tin e S o litro made m y move to Rhode Is land a very sm ooth one.

I am very g ra te fu l I came across Tom Rossby. He has been a great friend,

someone I fe lt com fo rtab le w ith even before a c tu a lly m eeting h im . 1 have no

doub ts th a t I made the r ig h t decision when I chose h im as adv isor fo r m y

graduate studies. A ll the l i t t le coincidences makes the whole th in g even more

special. Academ ica lly , he made me become an independent th in ke r, and gave

me a ll the too ls needed to do w ell on m y own. in c lu d ing a lo t o f freedom and

constant suppo rt. T h is w ork is the result o f long and live ly ta lks , from which a

lo t o f e xc iting questions and ideas came ou t. He exposed me early on w ith the

in te rn a tio n a l oceanographic com m un ity , and encouraged me* to p a rtic ip a te in

a ll sorts o f d iversions, w h ich m ay have kept me from g ra d u a tin g ea rlie r (he-he).

bu t ce rta in ly gave me a much broader and in te res ting overa ll tra in in g . A l l k inds

o f nice words go to h im .

Peter Lazarevich, the best officem ate ever. We went th rough th is together,

and I've been very lucky to have such a cheerfu l, down to E a rth , and la id back

team m ate a ll along. Very useful discussions and ideas, and loads o f help from

com pute r re lated questions, to academic, to p ra c tica l day-to -day s tu ff. Thanks

b ro the r, it 's been real nice and fun to have had you around.

I encountered a very open and relaxed atm osphere in the Physica l Oceanog

raphy departm ent o f the G radua te School o f Oceanography. I m ust say th a t I

v


fe lt at. home in W a tk ins a ll those years. In p a rtic u la r. I was q u ite happy w o rk in g

w ith our R A FO S group. O lga Sato helped me to get s ta rted . Sandy Fontana

provided me w ith nice and clean R A FO S floa t data , and I th a n k her fo r o rga

n iz ing the ski tr ip s ... George Schwartze was always k in d and w il lin g to share

a sm ile. M a rk P ra te r always lis tened, showed in terest, helped and encouraged

me. p ro v id in g useful com m ents and h in ts a ll along. I thank .Jim Fonta ine for

his patience: I m ust confess I fe lt p roud when I f in a lly gained a l i t t le b it o f his

tru s t when i t came to R A FO S m aking and ba llas ting . Those long crazy hour

days at the barn were a c tu a lly fun. H u a i-M in h a p p ily shared his ideas w ith me.

It was fun and he lp fu l having O la f Boebel a round. S cott S toerm er p rovided me

w ith the tem p la te th a t made the fo rm a tt in g o f th is thesis a piece o f cake: La tex

rules...

R andy W a tts was key fo r the H oa t-G E M concept to flourish . I tha n k h im

fo r hours o f discussion, w hich inc luded the n it ty g r i t ty de ta ils that, go a long

w ith G E M in g and O A ing . He also showed me the tr ic k for w r it in g : fo r th a t

I am t ru ly g ra te fu l. M a rk W im bush read ca re fu lly m y m anuscrip ts, and his

hawk eye and good Eng lish made th is thesis a much more readable one. I also

enjoyed very much being his teach ing assistant. B u t I am more g ra te fu l o f have

gotten to know h im and Reiko at a personal level, you bo th are b e a u tifu l people

indeed. .Jim M ille r was k ind to accept p a r tic ip a tin g in yet ano the r PO s tudent

com m ittee , and I tha n k S tephan G r i l l i fo r ju m p in g in last m inu te to serve as

C h a ir fo r m y d isse rta tion defense.

v i


V ery special thanks go to Joyce and M aggie a t the su p p o rt office, who made

it possible fo r me to get a paycheck regardless o f the som ewhat com p lica ted

visa and f in a n tia l status I had. Aside from th a t, they 've been ju s t real nice

people to have next door. K aren Tracey helped w ith neat M a tla b rou tines.

K a th y Donohue was always up to lis ten to a s tudent in distress. B ig thanks go

to a ll the PO students th a t passed th rough , o r s t i l l are a t GSO. Wo a ll were

very coopera tive , and it is always co m fo rtin g to have partne rs in crim e th a t you

can go to and com p la in w ith when th ings are not going well...

I have no words to express m y g ra titu d e to the people th a t helped me stay

on the r ig h t P ath , and made o f th is a w o rth w h ile .Journey. As I bum ped in to

them : A m y and the Lapollas: Dah-veed: L i V Doug: the Venus E nvy gals and

L’ lt im a te Fans: Meg V K ra ig : Lady C h ris tin e . Jay. K u r t. Russ. Sasha, and N ick:

La G ran F a m ilia o f bostonians: .Jaim ito: E lin <!L B runo . C a t. S un ita . Tocaya:

M arice la . M ike and A nn: the Basque. French. Swede, and Eston ian dudes: my

yoga teachers R ichard and Rose. A Very Special T h a n k You goes to C 'hanita in

M exico , to P ep ita . Rowie V A lfredo in Boston, and to P od rito . O i ge <Ss: Fa tih .

B i l ly J i l l in R I: I got th rough the hist year much thanks to you .......

N ils . B e a u tifu l Special G if t , yes!

To a ll the cuates th a t stayed in tune and connected w ith me a ll th is tim e ,

no m a tte r the distance. G R A C IA S !

v ii

Table o f Contents

A b s tra c t ii

Acknow ledgem ents iv

Tab le o f C ontents v iii

L is t o f Tables x ii

L is t o f F igures x iv

1 T ra n s fo rm a tio n o f the warm waters o f the N o rth A tla n tic from a stream

fun c tio n perspective 1

1. In t r o d u c t io n ...................................................................................................... 2

2. G ravest E m p irica l Mode p ro je c t io n s ....................................................... 6

2.1 D a ta and m e t h o d s .......................................................................... G

2.2 Lab rador C u rren t w a te r s ............................................................... 9

2.3 A nnua l mean and residual f ie ld s ................................................. 11

2.4 P o ten tia l v o r t ic i t y .............................................................................. 11

2.5 P ro je c ting onto 6 s u r fa c e s .......................................................... 12

v ii i


3. C onvection and S ubpo lar M ode W aters f o r m a t io n ............................ 13

4. D ow nstream e v o lu t io n .................................................................................. 18

5. D iscussion and s u m m a r y .............................................................................. 25

2 O b ta in in g the mean s tru c tu re o f the N A C -S P F system by com b in ing

R A F O S floa t d a ta w ith h is to rica l hyd rog raphy 40

1. In t r o d u c t io n ........................................................................................................ 47

2. F loa t-C IE M te c h n iq u e ................................................................................. 51

2.1 G E M d is c u s s io n ................................................................................. 51

2.2 F lo a t-G E M descrip tion ................................................................. 53

2.3 E rro rs associated w ith f lo a t-G E M te c h n iq u e ......................... 54

3. D a t a ...................................................................................................................... 50

3.1 G E M fields fo r the subpo la r N o rth A t l a n t i c ........................ 50

3.2 F loa t da ta for the region .............................................................. 59

3.3 F lo a t-G E M errors for the n o rth e rn N o rth A t la n t ic . . . . 01

4. Test o f m ethod : reconstruction o f hyd rog ra p h ic sections from

s im u la ted floa t d a ta ........................................................................................ 02

4.1 H yd rograph ic sections .................................................................... 02

4.2 S im u la ted float d a t a ....................................................................... 02

4.3 S im u la ted flo a t-G E M profiles ..................................................... 03

4.4 Specific volum e anom aly s e c t io n s .............................................. 04

4.5 Tem pera tu re s e c tio n s ........................................................................ 05

ix


4.6 B a ro d in ic t r a n s p o r ts ....................................................................... 67

5. C onsistency check: ho rizon ta l maps using real float da ta . . . . 69

6. C o n c lu s io n s ....................................................................................................... 74

.'3 A bso lu te tra nsp o rts o f mass and tem pera tu re for the X A C -S P F system 101

1. In t r o d u c t io n ....................................................................................................... 103

2. D a ta and m ethods ......................................................................................... 107

2.1 F lo a t-G E M p r o f i le s .......................................................................... 107

2.2 P IES section at 42°.\ ....................................................................... I l l

2.3 O b jec tive a n a ly s is .............................................................................. I l l

3. A bso lu te tra n sp o rt m a p s .............................................................................. 115

3.1 B a roc lin ic tra n sp o rt p o t e n t ia l ..................................................... 116

3.2 B a ro tro p ic tra nsp o rt p o te n t ia l ..................................................... 118

3.3 A bso lu te transpo rt p o te n t ia l ......................................................... 119

4. Transects ........................................................................................................... 121

4.1 X A C -S P F b ra n c h e s ........................................................................... 122

4.2 T ra n s p o r ts ............................................................................................. 123

5. D iscussion and S u m m a ry .............................................................................. 127

A p p e n d ix 1: G E M errors 148

A p p e n d ix 2: F lo a t-G E M errors 153

A p p e n d ix 3: T ranspo rt errors 155


B ib lio g ra p h y 157

xi


L is t o f Tables

C h a p te r 1

1 L is t o f specific volum e anom aly surfaces and th e ir p o te n tia l den

s ity a n a lo g u e s .................................................................................................. 7

2 Subregions o f the N o rth A tla n tic used fo r the cons tru c tio n o f the

G E M fields ...................................................................................................... S

3 S ubpo la r M ode W ater classes .................................................................. 17

4 E stim a tes o f heat and freshwater fluxes, and m ix in g rates . . . . 22

C h a p te r 2


s ity a n a lo g u e s 7G

2 B a lla s tin g results for upper X A C f lo a t s ................................................. 77

3 B a lla s tin g results fo r lower X A C f l o a t s ................................................. 7S

4 B a lla s tin g results fo r AC’CE f lo a t s ............................................................ 79

C h a p te r 3


s ity a n a lo g u e s 133

x ii


A p p e n d ix 3

1 E rro rs involved in the mass tra n s p o rt p o te n tia ls estim ates . . . 157

x ii i


L is t o f F igures

C hapte r I

1 C lirn a to lo g ica l map o f dynam ic height a t 200dl) (referenced to

lOOOdb) ............................................................................................................. 31

2 S tream fun c tio n m ap for the N o rth A t l a n t i c .............................. 32

3 Subregions selected for the co ns truc tion o f the G E M fields . . . 33

4 M o n th ly differences from the annual mean o f specific vo lum e

a n o m a ly ..................................................................................................... 34

5 Specific vo lum e anom aly versus <1> a t various pressure levels fo r

M arch, region 1 ............................................................................................... 35

G Tem pera tu re versus <[> a t various pressure levels for Septem ber.

region G ............................................................................................................. 3G

7 T em pera tu re versus T at various pressure levels for the N A C region 37

S H is tog ram o f tem pera ture on <) = —5 x 10“ Hm !/ k g ........................... 38

9 A nnua l mean p o te n tia l v o r t ic ity G E M f i e l d s ...................................... 39

10 Seasonal evo lu tion o f the G E M fields in the N A C ............................ 40

11 Seasonal evo lu tion o f the G E M fields in regions 4. 5. and 6 . . . 41

x iv

12 A p p ro x im a te loca tion where d iffe ren t classes o f S P M W s are fo rm ed 42

L3 T /S d iag ram for the seasonal the rm oc line layer ................................ 43

14 T /S d iag ram for the the 250-500db dep th r a n g e ................................ 44

15 A nn u a l mean air-sea f lu x e s .......................................................................... 45

C h a p te r 2

1 S tream fun c tio n map for the N o rth A t l a n t i c ........................... SO

2 D iag ram illu s tra t in g flo a t-G E M technique ................................. SI

3 D iag ram illu s tra t in g flo a t-G E M e rro r associated w ith e rro r in

floa t p r e s s u r e .................................................................................................. 82

4 D iag ram illu s tra tin g flo a t-G E M e rro r duo to u nce rta in ty in float

b a l la s t in g ......................................................................................................... S3

5 Subregions selected for the co ns truc tion o f the G E M fields . . . S4

G Tem pera tu re vs. dynam ic height a t various pressure levels. X A C

region ................................................................................................................. 85

7 D is tr ib u tio n o f s ta tis tic a lly independent R A FO S floa t s ta tions . SG

S F lo a t-G E M errors for specific vo lum e anom a ly in subregion 1 . . S7

9 F lo a t-G E M errors for tem pera tu re in subregion 4 .......................... 88

LO C’T D transects across the X A C and S P F .................................. SO

11 Specific vo lum e anom aly transect across the X A C ........................... 90

12 Specific vo lum e anom aly transect across the SPF ........................... 91

13 T em pera tu re transect across the X A C .......................................... 92

xv


14 T em pera tu re transect across the S P F .................................................... 93

15 Pressure o f the 6 = —12.7 x 10-8 m 3/k g surface from deep N A C

B o a ts ..................................................................................................................... 94

1C T em pera tu re o f the 6 = —12.7 x 10_8m 3/k g surface from deep

N A C f lo a ts .......................................................................................................... 95

17 C lim a to lo g ie a l tem pera tu re on the 6 = —12.7 x 10-8 m 3/k g surface 96

IS T ra n sp o rt p o te n tia l (rel. to lOOOdb) as derived from N A C floats 97

19 Pressure o f the 6 = —12.7 x 10~8m 3/k g surface obta ined by ap

p ly in g flo a t-G E M te c h n iq u e ..................................................................... 9S

20 T em pera tu re o f the <) = —12.7 x 10_8m 3/k g surface obta ined by

a p p ly in g flo a t-G E M te c h n iq u e .................................................................... 99

21 T ra n sp o rt p o te n tia l (re l. to lOOOdb) derived by a pp ly ing floa t-

G E M te c h n iq u e ............................................................................................... 100

C h a p te r 3

1 S tream fun c tio n map fo r the N o rth A t l a n t i c ..................................... 134

2 P os ition o f R A FO S floa t s ta tions ............................................................ 135

3 Subregions selected for the cons tru c tio n o f the G E M fields . . . 13G

4 L oca tio n o f the cu rren t m eter m oorings and P I E S ........................... 137

5 N um ber o f floa t da ta po in ts per 1° x 1° b in ...................................... 13S

G B a ro c lin ic tra n sp o rt p o te n tia l fo r the top lOOOdb ........................... 139

7 B a ro tro p ic tra n s p o rt p o te n tia l fo r the top lO O O d b ........................... 140

x v i

8 A bso lu te tra n sp o rt p o te n tia l for the top lO O O d b ..................... 141

9 Transects chosen across the N A C -S P F "p*Pe" .................................. Id 2

10 B a ro c lin ic tra n sp o rt po ten tia ls fo r transect 1 and transect M . . 143

11 A bso lu te tra n sp o rt po ten tia ls for transect 1 and transect M . . . 144

12 A bso lu te tem pera tu re transpo rts a long the N A C -S P F "p ip e " . . 145

13 M aps o f the stream functions on the 6 surface o f the floats . . . 140

14 M ap o f the stream functions on the 6 surface o f the floats . . . . 147

A p p e n d ix 1

1 M ean-square e rro r o f the specific vo lum e anom a ly G E M fie ld . . 150

2 Percentage o f the variance expla ined by the tem pe ra tu re G E M

f ie ld s .......................................................................................................... 151

3 G roups o f hyd rod a ta specific vo lum e anom aly p ro file com pared

to G E M p ro f i le s .................................................................................... 152

X V I 1


C hapter 1

Transform ation o f the warm w aters o f the N orth A tlantic from a stream function perspective

A bstract

H is to rica l hydrog raph ic da ta from the subpo la r N o rth A tla n tic arc p ro jec ted

in to a b a roc lin ic stream function space, resu lting in three d im ensiona l gravest

e m p irica l mode (G E M ) Helds for tem pera tu re and specific vo lum e anom aly, pa

ram eterized by pressure, dynam ic he ight, and day o f the year. From the specific

vo lum e anom a ly G E M . the corresponding p o te n tia l v o r t ie ity fie ld is ca lcu la ted .

These* fields are* constructed for 12 subregions, chosen to fo llow the mean pa th

o f the N o rth A t la n t ic C u rren t-S ubpo la r Front (N A C -S P F ) system. A na lys is o f

the seasonal p o te n tia l v o rt ie ity cycle o f the G E M fields shows th a t the m a in

mechanism for the fo rm a tion o f S ubpo lar M ode W a te r is w in te r convection.

T he G E M fields are also used to o b ta in the a pp rox im a te loca tion o f fo rm a tio n

sites for the d iffe ren t Subpolar M ode W ater classes. The evo lu tion o f the mean

fie lds fo r the waters is studied along ba roc lin ic stream lines o f the N A C -S P F

system. T h is shows th a t cross-fronta l m ix ing , between the co ld and fresh sub

p o la r waters, and the sa lty and w arm waters com ing n o rth from the sub trop ics

1


v ia the G u lf S tream , is the dom inan t mechanism fo r the lig lit- to -d e nse tra n s fo r

m a tio n process o f the N A C -S P F waters th a t enter the western subpo la r region.

On the o th e r hand, a com b ina tion o f a tm ospheric coo ling and m ix in g w ith the

sa ltie r waters found on the northeastern su b tro p ica l gyre, are the m a in factors

tra n s fo rm in g the N A C -S P F waters th a t enter the eastern subpo la r gyre. T h is

suggests th a t an in flu x along the eastern m arg in o f sa lty w ater fro m the E uro

pean Basin plays a s ign ifican t role in the tra n s fo rm a tio n o f the N A C -S P F waters

th a t continue th e ir way towards the N ord ic Seas.

1. In troduction

The flow o f sub trop ica l waters in to the subpo la r N o rth A tla n tic form s an im

p o r ta n t pa rt o f the m erid iona l ove rtu rn ing c irc u la tio n . The re su lting heat flu x

plays a c ruc ia l role in m odera ting the European c lim a te [e.g.. K rauss. 19SG:

Bow er et a l.. 2000]. A m a jo r source o f these' warm and sa lty waters is the G u lf

S tream v ia the N o rth A tla n tic C u rren t (N A C ). The N A C evolves fro m a narrow

and s w ift cu rren t a t the T a il o f the G rand Banks, to a b roader S ubpo la r Front

(S P F ) w ith im bedded je ts once it tu rns east past the N orthw est C orner [e.g..

A rh a n . 1990: Kearns. 1996: Krauss. 1996]. T h is fro n t diverges a fte r crossing

the M id -A t la n t ic R idge (M A R ), w ith its co lder waters en te ring the rec ircu la

tio n o f the subpo la r gyre v ia the Irtn ing e r C u rre n t, w h ile the w arm er waters

enter the Iceland Basin and continue th e ir way tow ards the N o rd ic Seas [e.g..

o


Hansen O sterhus. 2000: Bower et al.. 2000], F igu re 1 shows the c lim a to lo g ica l

geostroph ic s tream fu n c tio n (dynam ic he igh t a t 200db. referenced to lOOOdb).

as ob ta ined from h is to r ica l hydrography. The X A C is the sharp fro n t flow ing

n o rth a ligned w ith topography east o f the G rand Banks o f Canada. The SPF

appears as a broad fro n t between <& = -1 J /k g and <f> = 6.5 -I/kg . d ive rg ing

once i t passes the M A R . A no the r supp ly o f su b tro p ica l waters in to the subpo la r

regions comes a long the eastern A tla n tic , w h ich brings w arm and sa lty waters

a long the eastern boundary current (F igu re 2. see review in Hanawa <k: T a lley

[2001 ]).

M uch o f the ligh t-to -dense water conversion th a t f in a lly leads to deep con

vection in the Lab rado r Sea and N ord ic Seas takes place in the subpo la r N o rth

A tla n tic . O n th e ir jo u rn e y towards the sites o f dee]) convection, the su b tro p

ica l waters s ta r t coo ling and freshening th rough w in te r convection, as well as

by m ix in g w ith tin* adjacent subpo lar waters [M cC a rtn ey Talley. 1982], The

degree o f m ix in g is im p o rta n t since i t determ ines the sa lin ity , and hence the

m a x im u m dens ity th a t a flu id parcel even tua lly can ob ta in . The w in te r tim e

heat losses resu lt in h igh annual v a r ia b ility in the hydrog raph ic cond itions o f

the upper waters, w h ich progressively reach deeper as the waters are advected

th rou g h the subpo la r region. Since the N A C -S P F m arks the bounda ry between

the su b tro p ica l and subpo la r gyres, it is a long th is fro n t th a t o u tc ro p p ing o f the

isopycnals from the sub trop ica l N o rth A t la n tic 's m a in the rm oc line occurs. The

weak s tra t if ic a t io n above the deepening isopycnals o f the m a in pycnocline make

3

possible the hom ogeniza tion o f th ick layers o f w a te r (M ode W aters) d u r in g w in

te r tim e 011 the w arm side o f the fron t, w hich are la te r cu t o ff from exchange

w ith the atm osphere as the seasonal pyenocline develops again in the w arm er

m onths [Hanawa A Talley. 2001].

T h is paper studies the tra ns fo rm a tio n o f the w a rm waters in the no rth e rn

N o rth A tla n tic , using a ll the hyd roda ta availab le fro m Hydrobase [C u rry . 199G].

We are confron ted w ith a process o f large sp a tia l and tem po ra l v a r ia b ility : the

XAC ' p os ition may sh ift la te ra lly up to 150 km [Kearns A Rossby. 1998], w h ile

the n o rth e rn edge o f the SPF near the C ha rlie G ibbs F racture Zone experiences

sh ifts between 200 km and .'300 km [B e lk in A: Lev itus . 1996]. To reduce the va ri

a b i l i ty associated w ith the m eandering and s p lit t in g o f the ba roc lin ic s tru c tu re

o f the X A C -S P F system, we use a technique called G ravest E m p irica l M ode

p ro je c tio n , in w hich hydrograph ic da ta are p ro jec ted in to geostrophic stream

fu n c tio n space1. T h is p ro jec tion has the advantage o f m a in ta in in g the ba roc lin ic

s tru c tu re o f the cu rren t in question. T h is w ou ld not be the case i f the d a ta were

p ro jec ted in geographical space, the s tru c tu re o f the b a roc lin ic system w ould be

sm oothed and broadened as a consecquence o f the loca l v a r ia b ility in the hydro-

g raph ic fie ld due to m eandering and eddy shedding o f the cu rren t stud ied . The

G E M technique has been very successful in reducing the variance associated

w ith m eandering o f o the r ba roc lin ic systems, such as the A n ta rc tic C ircum po -

la r C u rre n t [Sun A W a tts . 2001]. and the K urosh io extension region [W ille fo rd .

2001]. The h is to rica l hydrograph ic database for the subpo la r N o rth A tla n tic

4


is su ffic ien tly large, and the sam pling fo r each m on th su ffic ien tly well covered,

though less so in w in te r, to be able to cons truc t m o n th ly G E M p ro jec tions for

sm a lle r subregions. T h is allows fo r the s tud y o f the loca l seasonal e vo lu tio n o f

the lu d ro g ra p h ic fields, as well as dow nstream changes a long stream lines.

G E M p ro jec tions o f specific vo lum e anom aly, tem pera tu re , and p o te n tia l

v o r t ic ity are constructed its functions o f dep th , geostroph ic stream fun c tio n , and

tim e o f year, for various subregions in the N o rth A tla n tic (Section 2). These

fie lds are then used to s tudy the seasonal evo lu tio n o f tin* hydrog raph ic con

d it io n s in the area, in p a rtic u la r the fo rm a tio n o f M ode W aters, as well as to

o b ta in the mean characteristics o f the various classes o f Mode W aters found

(Section .'3). The dow nstream evo lu tion o f these th ick layers o f w ater, as well

as the dow nstream changes o f the seasonal the rm oc line waters are explored,

lead ing to some statem ents o f the re la tive im po rtance o f heat loss to the a t

mosphere. freshw ater in p u t from the atm osphere, and m ix in g w ith the adjacent

waters in the tra ns fo rm a tio n o f the warm waters carried by the X A C -S u b p o la r

F ron t system (Section 4). We fin ish by com paring o u r residts w ith previous

S P M W studies, and w ith a discussion o f the ro le th a t the salt in f lu x from the

eastern A tla n t ic plays in p recond ition ing the waters for deep convection to occur

in the N o rd ic and Labrador Seas (Section 5).

We use specific volum e anom aly (<)) in our analysis, since these surfaces

are closer to neu tra l surfaces than the more com m on ly used p o te n tia l dens ity

((To) surfaces [M cD ouga ll. 1989]. especia lly i f a loca l s a lin ity and tem pe ra tu re

5

mean are used as reference values in ca lcu la tin g S. In the absence o f ex te rna l

fo rc ing , w a ter prefers to flow along n eu tra l surfaces. A lso, p o te n tia l vo rtic ity .

ca lcu la ted w ith the height between 6 surfaces, is conserved a long these surfaces

[M cD ouga ll. 1989].

2. G ravest E m pirical M ode projections

2.1 D ata and m ethods

We now describe the co ns truc tion o f the G E M pro jec tions fo r tem pera tu re ,

specific vo lum e anom aly, and p o te n tia l v o rt ic ity . which cap tu re the m o n th ly

average ve rtica l s tru c tu re o f these variables in stream fun c tio n space. We use

q u a lity con tro lle d C T D and b o tt le da ta from Hydrobase [C 'urry. 1996] taken

d u r in g 1910-1997. and 21 W O C E sections taken a fte r 1996. w ith in the region

4 0 'X -6 0 °X . 5 ()W 3-1 5 'W . O n ly s ta tions th a t reach deeper than lOOOdb are used.

For the case o f b o tt le da ta , on ly those w ith a t least 5 samples in the m ain

the rm oc iine are kept. Specific volum e anom aly (6) is ca lcu la ted from the tem

pera tu re and s a lin ity profiles, a t each sample dep th . We reference the specific

vo lum e anom alies to 34.6psu and 4.9°C. which are the mean values fo r the re

gion o f the X A C and SPF [Kearns. 1996]. To help the reader, a tab le o f S

values and th e ir correspond ing <7g values is p rov ided (Tab le 1). As a reference.

6

Ac) = 10 x 10 8m J/k g corresponds to a A a 0 ~ 0.1.

Specific Volum e A no m a ly (34.Gpsu. 4.9°C)

(10_8m :i/k g )

Specific Volum e A n o m a ly (35psu. 0°C) (1 0 -8m :i/k g )

P o te n tia l D ens ity

(a* ±0 .02 )70 s; 142 26.68 = 26.760 % 134 26.78 % 26.850 % 127 26.89 % 26.940 =s 119 26.98 % 27.030 % 109 27.08 % 27.120 = 93 27.18 % 27.210 % 85 27.28 ss 27.30 = 71 27.38 % 27.4

i -10 % 64 27.4S % 27.51 -20 ~ 57 | 27.59 ~ 27.6

-30 43 27.69 % 27.7

T ab le * 1: Lise o f specific vo lum e anom aly surfaces am i th e ir p o te n tia l dens ity analogues. S pecific volume* anom a ly value's in the firs t co lum n are referenced to an in te rm e d ia te te m p e ra tu re (4 .9 °C ) and s a lin ity (34.6 psu). The second co lum n has specific- vo lum e anom aly e-alculated using the* s tanda rd 0oC'and 35 psu values.

Tem pera tu re , sa lin ity , and <) are in te rpo la ted in to 20db bins. S ta tions w ith

i) inversions are* d iscarded. F ina lly , we check the in te rp o la te d hydro casts for

the rm od yn am ic consistency fo llow ing Kearns [199G], re jec ting s ta tions fo r w hich

the d ifference between the in te rpo la ted <), and the specific vo lum e anom a ly

ca lcu la ted from the in te rpo la ted tem pera ture and sa lin ity , d iffe red m ore than

3 x 10-8 n r '/k g (w h ich corresponds to ~ 0.03ct« u n its ). A fte r the* cp ia lity co n tro l

discussed above has been app lied to the hydroda ta , we are le ft w ith 2-1.244

h is to r ica l hyd rog raph ic stations.

Since the hydrog raph ic cond itions change m arked ly across the area o f study,

we d iv id e d the subpo la r N o rth A tla n tic in 12 overlapp ing regions (F igu re 3.

i

Table 1).

Region # Region name # o f hydrocasts

1 southern X A C (M ann eddy) 52672 northe rn N'AC (F lem ish Cap) 64503 N orthw est C orner S444 S ubpo la r Front (C ha rlie G ibbs Fracture Zone) 107815 western European Basin L1S1 |6 R ockall P la teau and Trough 2590

Icleand Basin and Reykjanes R idge 10699S Irm inge r Sea 12649 western N ew found land Basin 169310 eastern N ew found land Basin 73611 southern European Basin 103512 northe rn European Basin 1266

T a b le 1 2: Subregions o f the N o rth A tla n tic used fo r the co n s tru c tio n o f the G E M fields in the S u b p o la r N o rth A tla n tic .

For each region, dynam ic height anom aly ( ‘h-joo-tuuo) is ca lcu la ted from the

in te rp o la te d A profiles as:

2m,tb

‘FjOOUh-lomdb = ~ j <)dp. ( 1 )

t O W W f)

where [> is pressure.

<f> is a geostrophic stream function [M cD ouga ll. 1989j. and is here used as the

param ete r fo r the G E M pro jections o f the hydrog raph ic data . T h is param eter

is a pp rop ia te fo r reducing the spa tia l v a r ia b ility associated w ith the m eandering

o f the cu rren ts s tud ied , considering th a t the mean oceanic Hows are dom ina ted

by geostrophy. Since the stream func tion fie ld moves w ith the m eandering o f

the b a ro c lin ic fro n t, the tim e v a r ia b ility o f the unsteady flow is reduced by the

p ro je c tio n [Sun A: W a tts . 2001]. I t is useful to have no seasonal s ignatu re in

8

the param ete r used fo r the G E M pro jections, so th a t we t ru ly have a s tream

coord ina te system in w hich com parisons o f the G E M holds can be done b o th

in space (d iffe ren t subregions) and tim e (d iffe ren t m on ths). F igure 4 shows the

ve rtica l ex ten t o f the seasonal influences fo r a ll subregions. M ost o f the annual

v a r ia b ility takes place on the upper 200db (a lthough regions 1, 2 and G have

s ig n ifican t v a r ia b ility below 200db). Hence, the shallow l im it fo r is taken to

be 200db in o rder to reduce the effect o f seasonal v a r ia b ility in the in teg ra l.

We now exam ine the annual evo lu tion o f the tem pera tu re and specific vo lum e

anom a ly Helds, and the spa tia l changes o f those p ro p e rty variables a long the

X A C -S P F system : we seek to express tem pera tu re (T ) and <) as a func tion o f

pressure ( /^ v e rtic a l coo rd ina te ), stream func tion (^ -h o r iz o n ta l coo rd ina te ), and

tim e o f year (t ). The construc tion o f these fields fo llows a procedure s im ila r to

th a t em ployed by [W ille fo rd . 2001]. For each region, the da ta are separated in to

th ree -m on th bins, centered on each consecutive m onth . T h is ensures enough

d a ta coverage* for the less sampled w in te r period . C ub ic splines as functions o f

d> an* fit te d to the tem pera tu re and d data , a t each pressure level and for each

tim e b in . F igures 5 and G are examples o f the t ig h t re la tion (I> luis w ith <) and

T a t various pressure levels, for regions 1 and G. respectively.

2.2 Labrador Current waters

T h is p ro je c tio n works well for bo th tem pera tu re and 6 in most regions analyzed

(see A p p e n d ix 1). There is one exception, the tem pera tu re p ro jec tio n fo r tin*

9

upper oOOdb in the region o f the X A C (regions 1 and 2 in th is w ork). F igure

7 shows th a t there is a range in for w hich the re la tion sh ip between T and

 in the upper 160db is no longer single-valued. The reason for th is b im oda l

s tru c tu re is th a t the cold and fresh Labrador C u rre n t (L C ) meets the w arm and

sa lty X A C in th is region. The LC is a fresh and cold, la rge ly ba ro trop ic cu rren t

th a t flows inshore o f the X AC . A lth o u g h there is a s trong the rm oha line fro n t

between these tw o currents, the specific vo lum e anom a ly surfaces are themselves

nearly level between them : the specific volum e anom a ly o f the waters o f bo th

curren ts a t each level is the same due to s a lin ity com pensation . T h a t is w hy the

geostrophic stream func tion is insuffic ient by its e lf to d is tin gu ish between these

two currents, and a b im oda l s truc tu re appears in the pro jected tem pera tu re

fie ld. Since th is paper focuses on the tra n s fo rm a tio n o f the warm waters, we

decided to exclude s ta tions sam pling the LC. To d is tin g u ish these cold waters,

the b im oda l d is tr ib u tio n o f tem pera ture a long a su itab le 3 surface is analyzed,

to o b ta in the c u t-o ff value o f tem perature tha t separates the two d iffe rent modes

(F igu re 8). S ta tions for which T < 3.1" C’ on 6 = —o x 10_8m ‘5/k g are considered

LC waters (triang les in F igure 7). and are discarded for the sp line fit. Im p o rta n t

to note is th a t the LC' ce rta in ly helps to cool and freshen the X A C waters

th rough cross-fron ta l m ix ing , nevertheless, we choose to exclude the LC waters

from our analysis, and we cannot address th e ir c o n tr ib u tio n to the w arm w ater

tra n s fo rm a tio n w ith the m ethod u tilized .

10

2.3 A nnual m ean and residual fields

As a resu lt o f the p ro jec tio n onto stream func tion space accord ing to the sp line

f i t t in g discussed above, we ob ta in G E M fields for tem pera tu re : Tc e m (p • ‘I*, m o n th ) .

and specific vo lum e anom aly: <V;£.w(/J- m onth ) . By averaging over tim e and

s u b tra c tin g the mean from the m o n th ly fields, the residual G E M fields are ob

ta ined :

' o7-;.\/(/; - month ) = \ '(!E. \ i {p-(b- m o n th ) - \ '(;e m (P-1 I‘ ) •

when* 1' is e ith e r tem pera ture or (). \ c ; e m is the mean \ } ; e . \ i fie ld, and \

is the residual fie ld . Note th a t the annual mean so constructed reduces the

bias th a t w ou ld o therw ise result due to the d iffe ren t sam p ling frequencies for

d iffe ren t m onths. The reason for th is is th a t the tem po ra l mean is ob ta ined from

the m o n th ly G E M fields, and these in tu rn are fitte d splines to da ta ava ilab le

fo r the m on th in question.

2.4 P oten tia l vorticity

N ext we es tim a te the po te n tia l v o r t ic ity G E M from the <)(;e m fie ld , using the

layer thickness o f <) surfaces 10 x 10~'sm !/k g ( ~ O.lrTo) apa rt. T h is num ber is

chosen so th a t i t is sm all enough to captu re the P Y s tru c tu re in the ve rtica l:

P \ C E u i P o - m o n t h ) = 10- '1/ — 7 p ~rr • (3)A p ( p 0. (I>. m onth )

where / is the C o rio lis param eter fo r the center la titu d e o f the subregion.

A p(p„ . <f>. m o n th ) = p I <){p„. T . m o n th ) — ) — p (<>(/v ‘I>. m on th ) -f-

11

where A p is g iven in decibars ( ld b ^ lm ) , and Ad — 10 x 10 in /k g .

To be able to compare our results to the ones obta ined from previous studies,

we had to include the fac to r o f 10-* in equation 3- aince mOSt ill lth o rs ca lcu la te

P V as:

P V = f Acr» 1 ( 4 )p A p '

Hence, equa tion 3 d iffers from equation 4 by il Otctoi ~ 1()00 (sinc.c

A d = 10 x L()_'Hm '/k g corresponds to Aery ~ 0.1. S(,(> Table* 1).

2 .5 P r o je c t in g o n to d s u rfa c e s

G iven th a t in the absence o f m ix ing or d iss ipa tion w ater is stronglv constra ined

to flow along neu tra l surface's, we can q u a n tify th ° changes th a t a w a te i parcel

experiences as i t flows w ith in the ocean by ana lyz ing vvatet p roperties a long d

surface's. Since we are in terested in s tu d y in g the tra n s fo rm a tio n o f the vvate is

d u r in g t l ie ir tra n s it th rough the subpo la r N o rth A tla n tic , we proceed to map

the tem pe ra tu re and p o te n tia l v o r t ic ity G E M fields onto d suifaces. T he specific

vo lum e anom aly G E M fie ld serves as a ‘ look up tab le from which the inverse

m ay be* found. T h a t is. the pressure fie ld correspond ing to a g rid o f d surface s

can be ob ta ined from the m o n th ly specific vo lum 0 anom aly G E M fielel.

dr;£.\/(/>- ‘E m onth ) — > p<;E.\r((h ‘E rnonfh) ■

H aving the pre'ssure fie ld as a fun c tio n o f d a llo 'vs us to m aP Tc e m {P- ‘E m o n th )

on to To e \ i (6-$ - m on th ) . P V on d surfaces can b4-' ca lcu la ted qu ite s im p ly from

12

the p o e m ■

P VG E. \ i { t i - $ -m on th ) = ^ t t t (5)H(;E.\ i \b- (h. m o n t h )

where lI>. m on th ) = p c E \ t ( ~ "¥ • ch- m o n th ) — pc,E\t{& + ^ r - m onth )

is the layer thickness between d' surfaces ( in clecibars) separated by A d = 10 x

108m -,/k g un its .

F in a lly , a ll the m o n th ly fields are lin e a r ly in te rpo la ted in to yearday (from

day 1 to day 305). add ing the December fields to the beg inn ing o f t in ' rim e

record, and the .January fields to the end o f the record, to ensure c o n tin u ity

between day 365 and day 1. A discussion o f the e rrors associated w ith the fields

is g iven in A p p e n d ix 1.

3. C onvection and Subpolar M ode W aters form ation

M ode W ater is the te rm given to layers w ith v e rt ic a lly u n ifo rm properties. These

are usua lly found on the w arm side o f a cu rren t o r fro n t, between the surface

and the perm anent pycnocline. B y d e fin it io n , they are characterized by th e ir

low p o te n tia l v o rt ic ity . and th e ir fo rm a tio n is usua lly associated w ith w in te rtim e

convection [e.g.. Hanawa M T a lley. 2001]. In the n o rth e rn N o rth A tla n tic , such

low p o te n tia l v o r t ic ity waters are called S ubpo la r M ode W aters (S P M W ) a fte r

M cC a rtn e y .N T a lley [1982]. T hey stand o u t c le a rly in the mean p o te n tia l

v o r t ic ity G E M fields constructed fo r the subregions m entioned in Section 2.1

13


(F igu re 9). where ‘ poo ls ' o f P V less than 10 x 10_ u m _ ls_I are found on the

w arm side o f the X A C and SPF (regions 1-5 and 9-12). between the m a in and

seasonal the rinoc lines. The low P V w ater (P Y < 4 x 10- l m -1s-1 ) found on the

co ld side o f the fro n t, below the m ain pycnocline. is Lab rado r Sea W ater, and is

the densest M ode W ate r found in the N o rth A tla n tic . T he n o rthe rnm ost regions

(regions G-S) have very l i t t le s tra tif ic a tio n , most o f the density layers o f the m ain

pycnocline have outcropped, and we have in general very homogeneous waters

th ro u g h o u t the en tire dom ain , w ith P V less than 8 x 10_ u m - l s -1 . N oticeable ,

though , an* the very low PV waters (less than 4 x 10- n m - l s_ l ) present in the

R ocka ll P la teau and Trough region (region 6). Such low P V waters are also

present in the western European Basin fa rth e r south (regions 11 and 12).

The G E M pro jec tions constructed in the previous section p rov ide an effective

fram ew ork in w hich to analyze the mean characte ris tics o f the S P M W . since they

com prise a ll hydrog raph ic data availab le fo r the region. The m ethod a llows

us to look at the seasonal evo lu tion o f the hydrog raph ic Helds, w hich in tu rn

helps id e n tify the ven tila ted layers, and the pos ition w ith in the ba roc linc fro n t

associated w ith the X A C -S P F where they ou tcrop . A n exam ple o f th is is given

in F igu re 10. where tw o d iffe rent stream lines o f the X A C in region 1 are selected:

one on the co ld side o f the fron t ( = 4 J /k g ) . and the o the r on the w arm side

( ‘I» = 7.5 J /k g ) . The evo lu tion o f the seasonal the rm oc line stands ou t c learly,

show ing th a t on the cold side o f the fro n t, w in te r convection does not reach

deeper tha n lOOdb (F igu re 10(a). specific vo lum e anom a ly pane l), re su ltin g in

14

a h ig h ly seasonally s tra tif ie d layer th a t reaches down to 200db (F igu re 10(a).

p o te n tia l v o r it ic ity panel). On the o the r hand, w in te r convection reaches dow n

to 300dl) on the w arm side o f the fro n t (F igu re 10(b). specific vo lum e anom a ly

panel), w h ile the seasonal pycnocline is m a in ly trapped to the upper 150 — 200(11)

(F igu re 10(b). specific volum e anom aly and p o te n tia l v o r t ic ity panels). As a

resu lt, the layer th a t gets ven tila ted (S € [50. GO] x 10~'sm ’ /k g ) is q u ite th ick

(% 100 db. w h ich corresponds to £= 10 x 10-11 m - l s'~l ). In o the r words. F igure

10(b) shows the process o f mode w ater fo rm a tio n v ia w in te r convection, and

helps to id e n tify where w ith in the fro n t th is occurs (i.e on which s tream line ),

as well as the corresponding density class o f the M ode W ater in question.

To id e n tify the' density classes and correspond ing tem pera tures o f the M ode

W aters in the various subregions analyzed in th is w ork, i t is more useful to look

at the fields w ith specific volum e anom a ly as the ve rtica l coord ina te . Three

adjacent regions (regions 4. 5 and G) are shown in F igure 11. fo r a s tream line

(<[> = G .I/kg) at which Mode W aters are form ed (i.e.. the low P V layer w in te r

ou tcrops). For the SPF section (region 4). the layer o f low P Y has <) € [20. 40] x

10-Hm ! /k g and tem pera tures o f 9 —12CC. T he M ode W ater found in the n o rth e rn

European Basin (region 5) has <) 6 [10.30] x 10_Hm '/k g and tem pera tures o f

8 — 123C*. F in a lly , in the Rockall P la teau and T rough area (region G) the layer

w ith lowest P Y (less than 6 x 10_ u m _1s_l is found fo r 6 € [—10. 10] x 10_8m ,!/k g

and tem pera tures o f 7 — 10°C’ . Note th a t each o f these SPM W s are form ed along

the same stream line , suggesting th a t the densest mode w ater results b o th from

15

advection o f the lig h te r classes form ed upstream , as well as lo c a lly th ro u g h

w in te r convection. In o the r words, the mode w ater form ed in the SPF (reg ion

4. <) ~ 30 x 10_8m i /h g ) is being advectcd by the XAC’-SPF on to regions 5

and 6. where i t is lo ca lly cooled by the atm osphere th rou g h w in te r convection,

becom ing denser. Hence, d u rin g its tra n s it th rough the R ocka ll P la teau and

T rough area (region 6). its 6 has been raised by ~ 30 x l0 _8m -,/k g (i.e .. the

w ater has experienced a buoyancy loss o f abou t 0.3oq u n its ), re su lting in mode

w a ter o f <) = 0 x l( )_sm 1/kg . Note, however, th a t the discussion above' trea ts

the p rob lem in tw o dimensions: a long-stream and in the ve rtica l. We expect

th a t cross-fron ta l m ix ing also plays a ro le in the tra n s fo rm a tio n process, and we

w il l discuss th is in Section 4.

Wo have shown in th is section th a t we can use the G E M tields to id e n tify the

ve n tila te d layers, th e ir PY and tem pera tu re , and the loca tion w hen ' those layers

ou tc ro p in stream func tion space. We used th is to cons truc t an a lg o r ith m th a t

identifies the M ode W aters, finds th e ir mean characte ris tics, and the regions

where they are form ed. For regions south o f 53°N. P Y < 10 x 10-11m _ ls_l is

used as the id e n tifie r o f Mode W aters: w h ile P Y < S x 10-11m _ ls _ l is used fo r

regions to the n o rth . These waters are grouped in to specific vo lum e anom a ly

classes, correspond ing to layers A d = 10 x 10_8m '!/k g th ick . T he region o f

fo rm a tio n o f each M ode W ater class is defined as the range o f s tream lines where

the specific vo lum e anom aly bound ing the layer on the lig h t side ou tc ropped

in M arch . Table 3 presents a sum m ary o f th is analysis. In co n s tru c tin g the

1G

tab le , the c lirna to log ica l map o f (I> (F igu re 1) was used to id e n tify where in the

N o rth A t la n t ic the S P M W class in question is form ed and found. We used the

fo llow ing c rite ria : > 7 J /k g represents the re c ircu la tio n o f the N A C in the

N ew found land Basin: T € [4. 6.5] J /k g in regions 4 and 5 are the SPF branches:

R ocka ll P la teau and T rough correspond to <[> > G J /k g in region G: the Ice land

Basin corresponds to 6 [4.6] J /k g in regions G and 7: and the Irm in g e r Sea

is defined as < 4 J /k g in regions 7 and S.

<) lay er j T e m p e ra tu re

( = 5 ■- UJ- ' r « 1 A:;/) | ran g e I 3 f.')

L ayer th ic k n e ss

(til))

R eg ions

w h ere fo rm ed

A p p ro x . s t r e a m lin e s i

w here fo rm ed (.1 / kg) j

Ill) 1:1.7- ir,.:i < 200 N A C

! l . J . ,C- '.))

•l> > 0 .5.7 0 |

50 1 1 2 ..1- 11.11

< 250 N A C ‘t’ -E 55.0.7.5! '( i . j . . c - n | j

10 11.1- IT 1 < .100 so u th o f S P F an ti j •!> -3 7 ..i.S .0 i

N ew fo u iu ila in i B.'lsiu I

i 1.5.0.10. .C 11)

j :u)ii

1 0 . 1- U .5 •3 1 -10.250] h e tw eeu S P F b ra n c h e s

(1 .<2 5 i

•l> -3 ;.5.7.7.:H

1 'JO

s

s . o - u . n € [JOO.aOOj n o r th e rn E u ro p e a n Ib isin

(1 J)

•I- Z '5 .1.7 7' !i1

i o h .o - i o .j

i

]200.500i R ockall P la te a u \ > 0..5 |

am i Trough (0) j

I) j I', .0-0.0 ■E ]1 tO.llOO; Ice lan d R.esin

(0 . t 7)

•l> ~ ’ i.5 .0 .2 :

!-10 5.0-7 .5

j

•E ] 170.200] e a s te rn Irm in g e r Sea

(7. k S)

-I* -Z ii.9j

-JOit

1.0 -0 . .5 Z ] 170.200] I rm in g e r S ea

( « )

•V > :J r, |i

i - n o ! n . s - o . j

1 !

6 [200..500] L S U - fo rtne ti in 11 i

L a b ra d o r Sea ] j

[a b le 3 : S ubpo la r M ode W ate r classes: mean cha rac te ris tics , and regions and a p p ro x im a te stream lines where thev are form ed.

In conclusion. S PM W s w ith <) > 40 x l tC N n '/k g (<7o < 27.0) are form ed

on the w arm edge o f the N A C and south o f the SPF. and are p a rt o f the

re c ircu la tio n o f the sub trop ica l gyre. We call these Class I. Mode waters w ith

17

6 = 30 x 10-8 m 3/k g (er0 < 27.1) form between the SPF branches (Class I I ) .

The th ickest M ode W aters (Class I I I ) are form ed in the n o rth e rn E uropean

Basin (6 = 20 x 10~8m 3/k g . erg % 27.2). as well as in the R ocka ll P la teau

and T rough region (6 = 10 x 10~8m 3kg. erg % 27.3). S P M W s w ith d = 0 x

10-8 nvJ/k g (erg % 27.4) fo rm in the Iceland Basin (class IV ). M ode waters w ith

/) £ [—10. —20] x 10_8m !/k g (e rg £ [27.5.27.6]) are form ed in the Irm in g e r Sea

(Class V ). The densest M ode W ater (<!> < —20 x 10-8 m '5/k g . erg > 27.6) is

Labrador Sea W ater, found in a ll regions analyzed. The analysis presented here

provides the app rox im a te loca tion in stream function space where the d iffe ren t

Mode W a te r classes arc form ed. T h is , in tu rn , ind icates where, w ith in the

fronts. M ode W ater fo rm a tion takes place. From the G E M analysis alone, it is

not. possible to accura te ly determ ine the d is tr ib u tio n in geograph ica l space of

the sites where fo rm a tion o f S P M W takes place. Nevertheless, using the results

from Table .'3. we present a sum m ary in F igure 12 o f the a pp rox im a te loca tions

where d iffe ren t M ode classes m ay be formed.

4. D ow nstream evolution

A no th e r way to investiga te the trans fo rm a tion o f the waters ca rried by the

N A C -S P F system consists o f look ing at how properties change a long a s tream

line. Since w a te r parcels flow a long stream lines, th is approach w ou ld address the

Lagrangian changes in the p roperties o f the w ater parcel in question. Since the

18

G E M fields are p ro jec tions on to ba roc lin ic geostrophic stream fu n c tio n space,

the analysis is q u ite s tra ig h tfo rw a rd under the assum ption th a t the flow is

geostrophic. coherent in the ve rtica l, and th a t the b a ro tro p ic and ba roc lin ic

com ponents o f the flow have the same d irec tion .

U sing the annual mean G E M fields o f tem pe ra tu re and specific volum e

anom a ly (i.e. (h). Tc;e m (p - ( )) - dep th averages fo r va rious stream lines

are ca rried out fo r tw o d iffe re n t depth ranges: between 0-250db (w aters w ith in

the seasonal tho rm oc line ). and 2o0-550db (w h ich corresponds to the dep th range

o f the S P M W . in the regions and ranges where they are present). The firs t

dep th range is chosen to s tu d y the effects th a t bo th the a tm osphere and m ix in g

have in tra ns fo rm ing the waters near the surface, and to q u a n tify the re la tive

role th a t the tw o processes p lay in changing the w ater co lum n 's characte ris tics .

The second range is p u rpose fu lly chosen to focus m a in ly on m ix in g : where dot's

it take place, and which w ater masses are g e ttin g m ixed. For th is , the fo llow ing

averages are ca lcu la ted :

fo r each stream fun c tio n value, where (pb„t-PtoP) correspond to the dep th in

tervals m entioned above. Each (< T > . < 6 > ) p a ir was p lo tte d on a T /S

d iag ram , from w h ich the correspond ing s a lin ity < S > was in fe rred (F igures

13 and 14). Each p o in t represents the value o f < T > and < S > fo r each

( G )

19

region, and co n to u r lines fo r various values o f < S > are shown fo r reference.

N ote from F igu re 1 and F igure 2 th a t i f we fo llow a w ater co lum n a long the

X A C . by going from region 1 to region 8. depend ing on w h ich s tream line ()

th is h yp o th e tica l w a ter co lum n is. i t w il l e ithe r loop back tow ards the Irm in g e r

Sea, sk ip p ing regions 5 and 6 (co ld waters. < 4.5 .J /kg): enter the Iceland

Basin and continue northw ards, sk ipp ing region 8 (SPF waters. 6 [5. 6] J /k g ) :

o r rec ircu la te w ith in the su b tro p ica l gyre, sk ip p ing regions G-8 (w a rm waters.

 > G.5 J /k g ) .

The dep th averaged tem pera tu re and specific vo lum e anom a ly provide a

measure o f the hea t/buoyancy content o f the w a ter co lum n stud ied . For the

dep th range correspond ing to the seasonal the rm oc line (0-250db). we expect

th a t any dow nstream changes resu lt bo th from m ix in g w ith ad jacent waters,

and h ea t/fresh w a te r exchange w ith the atm osphere:

D < T > w . Q — ----- = M i x i r u j + • ( < )

D t pC p h„D < S > w „ 1 dh— 5 j— = Ui x < n a - < S > l r - . IS)

where t is tim e . Q is the ocean heat flu x to the atm osphere, p is density. C'p

the ocean heat capacity. h„ the dep th o f the w a ter co lum n in question. ^ is

the ra te o f p re c ip ita tio n m inus evapora tion . M i x i n g is the rate o f m ix in g (b o th

h o rizon ta l and ve rtica l, isopycnal and cross-isopycnal). T he second dep th range

is less affected by the atm osphere (except in the case where the s tream line cor

responds to th ic k layers o f S P M W ). so the changes in tem pe ra tu re and s a lin ity

20

are m a in ly due to m ix ing .

For the sha llow dep th range, we q u a n tify the re la tive ro le o f m ix in g versus

a tm ospheric fluxes in the tra ns fo rm a tio n process o f the w ater co lum n by ob

ta in in g estim ates o f the d iffe ren t term s in E quations 7 and S. T he air-sea fluxes

are estim a ted using two fu ll years (199S-1999) o f the gridded N’C E P /X C A R

reanalysis d a ta [K a lnay et ah. 1996]. The da ta inc lude net heat flux , la ten t

heat flux , and p re c ip ita tio n ra te on a 1.9° x 1.9° g rid . The evapo ra tion ra te is

derived from the la ten t heat flux. F igure 15 shows the annual mean heat flux

from the a tm osphere to the ocean (Q) and e va p o ra tio n -p re c ip ita tio n rates for

the region o f in terest ( — ^ ) . D < T >. D < S > in equations 7 and 8 are

rh(> change' in tem pera tu re and s a lin ity between adjacent regions (see Figure*

13). D t refers to the Lagrangian tim e scale (i.e.. the tim e it take's fo r the wa

te r parce'l to ine)ve» between the adjacent re'giems). w h ich we* e 'stim ato using the

ve'leje-ity o f isopyenal R A FO S floats from twe) experim ents carrieel out betwe'on

1996-2000 [Perez-B run ius. 2002bj. and the app rox im a te length o f the s tream line

in question, estim ated from F igure I. The m ix in g term s are then derived using

E quations 7 anei 8. T h is is a ra the r crude way o f g e ttin g such e'stimates. bu t

we are* in terested in orders o f m agn itude to com pare the m ix in g te rm w ith the

a tm ospheric exchange term s. The results are sum m arized in Table 4. where the

average over a ll regions fo r each te rm is presented.

We now proceed to analyze the changes in the w ater co lum n shown graph

ic a lly in F igures 13 and 14. R a the r d iffe ren t results are ob ta ined fo r the two

21

•I*

J / k g

D < T >Dt1 0 - - ° (_ '/d ay

H ea t

1 0 " 2 ° C /d a y

M ixing

10~2 ° C /d a y

D< S~>Dt10- 3 p su /d a y

F re sh w a te r

10- 3 p s u /d a y

M ix ing

10“ 3 p s u /d a y

4 - 0.0 -1. 1 0.8 0.1 -0.5 5.9 |

6 - t . : i -1 .9 -2.4 -2.7 -0.2 -2.4 j

Table 4: E stim a tes o f heat and freshw ater fluxes, and m ix in g ra tes (see E qua tions 7 and S). fo r the de p th range between 0-250db. on tw o d iffe ren t s tream lines. Heat refers to the te rm f)C lh in equ a tio n 7 (p o s itive fo r net heat gain in the ocean), w h ile F reshw ater refers to the

te rm — < S >■£-'■$■ in equa tion 8 (pos itive when evapo ra tion exceeds p re c ip ita tio n ).

dep th ranges selected. In the seasonal the n no c line layer (F igu re 13). we ob

serve th a t on the cold side o f the stream (T < 4 J /k g ) the waters got about

40-50x l( )_Hm i /k g ( ~ 0.4 — Q.ocro) denser as they move around the subpo la r

region, a ltho u gh not by cooling , but ra the r by m ix in g w ith progressively sa ltie r

waters. W hen they enter the Irm inge r Sea. they have a fina l s a lin ity 0.5 — 0.G

psu h igher than the one they had in the X A C . However, the tem pera tu re stays

nearly constant (w ith in L° C’ ). T h is suggests th a t, in the cold side o f the fro n t,

the buoyancy loss is m o s tly due to m ix in g w ith the sa ltie r waters Mowing n o rth

w ith the X A C . T h is is indeed w hat we ob ta in from the b u lk estim ates in Table

4: cross-fron ta l m ix in g w ith the warm , sa lty waters o f su b tro p ica l o rig in com

pensates the h igh heat loss to the atm osphere, resu lting in a re la tive ly sm all

change in the tem pe ra tu re o f the w ater co lum n. X ote also th a t p re c ip ita tio n

exceeds evapo ra tion in th is region (F igu re 15 (b )). even though the s a lin ity o f

the w a te r co lum n is increasing. T h is gives conclusive evidence o f the im portance

o f m ix in g w ith the sa ltie r sub trop ica l waters in the tra n s fo rm a tio n process o f

the co ld waters o f the XAC '-SPF system, on th e ir jo u rn e y tow ards the deep

convection region in the Labrador Sea.

B y con tras t, w aters on the warm side o f the stream (<& > 5.5 J /k g ) are

g e ttin g denser by coo ling ( A T 22 4° C ). as well as freshening (ss 0.1 — 0.4 psu).

In th is case, b o th heat loss to the atm osphere as well as the excess p re c ip ita tio n

m inus evapo ra tion have the same sign as the change in tem pera tu re and sa lin ity .

Table 4 suggests th a t cross-fron ta l m ix in g w ith the colder subpo la r waters, and

heat loss to the atm osphere, co n tribu te a p p ro x im a te ly the same to the coo ling

o f the w ater co lu m n on the warm side o f the fro n t. O n the o the r hand, m ix in g

con tribu tes an o rd e r o f m agn itude m ore than the air-sea freshw ater tlu x to

freshen the w a te r co lum n. In the m idd le o f the stream ( ‘h G (4 .5 .5 ) J /k g ) . wo

have an in te rm e d ia te s itu a tio n , where waters get denser bo th by increasing th e ir

s a lin ity and by coo ling (F igure ' 13).

In the dep th range below the seasonal the rm oc line (F igu re 14). the general

trend is th a t the w a te r co lum n gets sa ltie r past the N orthw est C orner (region

3) fo r a ll s tream lines. C onsidering th a t th is layer rem ains m ostly blocked from

the atm osphere, we a ttr ib u te the increase in s a lin ity to m ix in g w ith the sa lty

waters en te ring the subpo la r region b o th from the N A C and from the eastern

subtrop ics. N ote th a t regions where S P M W is present in the w ater co lum n are

m arked w ith a c irc le in F igure 14. On the cold side o f the stream ( < 5 J /k g ) .

the specific vo lum e anom a ly does not change s ign ifican tly , in d ic a tin g th a t most

o f the m ix in g takes place along isopycnals. W aters get sa ltie r as they m ix across

the fro n t w ith the sa ltie r waters tha t came along the G u lf S tream v ia the N A C .

B y con tras t, as w aters on the warm side o f the SPF (<!> > 5.5 J /k g ) enter the

23

Ice land B a s in /R o c k a ll P la teau and T rough area (region 6 ). they reduce the ir

buoyancy content by as much its S.6 = 10 x 10_8m 3/k g . N ote th a t largest

changes are observed between regions 5 and 6. hence suggesting th a t much o f

the tra n s fo rm a tio n o f the w ater co lum n occurs in the western European Basin

and the R ocka ll P la te a u /T ro u g h area. A lso noticeable is th a t the w in te r m ixed

layer reaches down to 500db in region G (R ocka ll P la teau and Trougharea).

lead ing to the fo rm a tio n o f the thickest S P M W s. It is in te res tin g to observe

the d ifference in how the buoyancy change is achieved at th is dep th range' and

a t the range1 w ith in the1 seasonal the rm ocline layer (F igure ' 13). be'twe'en the

N orthw est C o rner (re'gion 3) and the Rockall T rough and P la teau area (re'giem

G). In the' upper dep th range, cooling drive's m ost o f the' buoyancy loss o f the

w arm waters. A t dep th , however, the buoyancy loss resu lts fro m an increase*

in s a lin ity , w h ile any teunperature change's re'rnain co m p a ra tive ly sm all. We

a ttr ib u te ' the* increase* in s a lin ity tej m ix ing w ith the saltie'st su b tro p ica l wate*rs

o f th is dep th range, located in the northeastern subtrop ics. in the European

Basin (regions o and 12).

As eliscussed above, on bo th the warm and co ld side's o f the SPF. the water

co lum n below the seasemal the rm oc line gets denser by increasing its sa lin ity

as it emters the subpo la r region. The colei side is g e ttin g sa ltie r by m ix ing

across the cu rren t w ith the sa ltie r and w arm er waters em the r ig h t hand siele

o f the stream . T he la tte r are in tu rn g e ttin g sa ltie r as they continue towards

the eastern subpo la r gyre. T h is suggests th a t there is an a d d it io n a l source o f

24


sa lty w a te r to the system besides the supp ly com ing from the G u lf S tream v ia

the X A C . We conclude th a t the warm SPF waters th a t enter the Ice land Basin

(reg ion G). and presum ably continue tow ards the N o rd ic Seas, are g e ttin g denser

th ro u g h m ix in g w ith the very sa lty waters found in the European Basin, on the

northeaste rn b ounda ry o f the sub trop ica l gyre.

5. D iscussion and sum m ary

The p ro je c tio n o f h is to r ica l hydrograph ic da ta in to stream fu n c tio n space a l

lowed us to look closer at the process o f tra n s fo rm a tio n o f the waters carried

by the X A C -S P F system in to the subpo la r region. The analysis o f the seasonal

e vo lu tio n o f the p o te n tia l v o r t ic ity and tem pe ra tu re G E M fields as a function o f

specific vo lum e anom aly, perm its us to id e n tify w ith g reater c la r ity where and

when those th ick layers o f u n ifo rm w ater p roperties are form ed by w in te r con

vection . and then cu t o ff from the influence o f the a tm osphere as the seasonal

therm ocU ne develops.

The view o f how and where the d iffe ren t S P M W classes are form ed has

changed since they were firs t described by M cC a rtn e y A: T a lley [1982]. There

it was suggested th a t these M ode W aters are form ed in the X A C region and

then advected a long the cu rren t as they get cooler and denser. From there

some rec ircu la te back in the sub trop ica l gyre, and the rest enter the eastern

subp o la r region as pa rt o f the warm in flow in to the subpo la r gyre. In o the r

25


words, the S P M W s w ou ld be transfo rm ed g ra d u a lly in to denser classes as they

are advected a long the N A C -S P F system. In a la te r s tudy. T a lle y [1999] suggests

th a t there m ay no t be such a sm ooth connection between the d iffe ren t dens ity

classes o f S P M W . She suggests th a t the warm est modes are associated w ith

the re c ircu la tio n o f the sub trop ica l gyre, and hence do not enter the subpo la r

region. A lso , she finds no connection between the M ode W aters found on e ithe r

side o f the Reykjanes R idge (see review in Hanawa .k: T a lle y [2001]). O u r results

co rrobo ra te th is p o in t o f view: the lig h te r M ode W a te r classes fo rm and rem ain

on stream lines associated w ith the rec ircu la tio n o f the su b tro p ica l gyre. A lso,

the M ode W aters form ed on e ithe r side o f the Reykjanes R idge are form ed

on d iffe ren t geostroph ic stream lines. Hence, the denser classes found in the

eastern Irm in g e r Sea are form ed loca lly , and do not result, from the com bined

adveetion and buoyancy loss o f lig h te r M ode W aters form ed in the Iceland

B asin-R ocka ll P la teau and Trough region. On the o th e r hand. M ode W aters

form ed w ith in the SPF branches {6 = 30 x 10~'sm l /k g ) suffer a buoyancy loss

o f around A d = 20 x 10_sm !/k g un its its they enter tin* Iceland B asin-R ocka ll

P la teau and T rough region. T h is po in ts ou t th a t the largest tra n s fo rm a tio n

o f the su b tro p ica l waters as they flow tow ards the N o rd ic Seas, occurs on the

w arm side o f the S ubpo la r Front a fte r i t (‘lite rs the R ocka ll P la teau and Trough

area.

We o b ta ined the mean characteris tics fo r the d iffe re n t M ode W a te r classes,

as well as the regions and stream lines where they are form ed. The lo ca tio n o f

26


the d iffe re n t S P M W classes genera lly agrees w ith T a lle y [1999]. a lthough a m ore

d e ta iled com parison cannot be carried o u t since ou r m ethod does not p rov ide a

su ffic ie n tly fine descrip tion o f the geographical d is tr ib u t io n o f these th ick layers

o f u n ifo rm water.

We suggest the fo llow ing p a tte rn o f c irc u la tio n fo r the d iffe ren t S P M W

classes. Those w ith d > 30 x 10~8m 3/k g rec ircu la te in the su b tro p ica l gyre.

M ode W aters form ed w ith in the branches o f the SPF (6 = 30 x 10_8m 3/k g )

( 'lite r the eastern subpo la r N o rth A tla n tic , where they get transfo rm ed in to

denser classes (J € [10.20] x 10_8m 3/k g ) . In the Iceland B as in /R o cka ll P lateau

region. M ode W aters w ith d = 0 x l()~8m 3/k g are form ed. T in* rest (<) <

— 10 x l()~8m 3/k g ) are form ed w ith in the re c ircu la tio n o f the subpo la r gyre,

w ith () = —30 x I0 ~ 8m 3/k g being Lab rador Sea W ater, the densest M ode W ater

found in the area.

T h is s tud y shows th a t the ligh t-to -dense conversion o f the waters adverted

by the N A C -S P F is not o n ly due to fluxes o f heat and freshw ater between the

ocean and the atm osphere: there is s trong evidence fo r the im portance o f cross-

fro n ta l m ix in g in the tra n s fo rm a tio n process. In te res ting is the fact th a t, at

dep ths below the influence o f the atm osphere, waters get sa ltie r as they enter

the subpo la r N o rth A tla n tic , in d ic a tin g th a t the w arm and sa lty in flu x is not

o n ly com ing from the G u lf S tream via the N A C : the European Basin con tribu tes

w ith a s ign ifican t am oun t o f heat and sa lt a long the eastern m arg in . Evidence

fo r th is has been shown by Reid [1994]. who discusses the role o f the sa lty

27

M ed ite rranean O verflow in p recond ition ing the waters for deep convection in

the N o rd ic and Lab rador Seas. M cC artney M au ritzen [2001] suggest th a t the

M ed ite rranean O verflow W ater con tribu tes to the s a lin ity in flow in to the subpo

la r G yre not by d irec t advection (as suggested by Reid [1994]). b u t by m o d ify in g

the te rnp e ra tu re -sa lin ity characteris tics o f the eastern su b tro p ica l gyre waters.

In the same paper, they suggest a polew ard flow a long the co n tin e n ta l slope

o f S P M W o rig in a tin g from the Bay o f Biscay. O the r studies suggest th a t the

saline Eastern N o rth A tla n tic W ater found in the eastern European Basin, and

tra nsp o rted n o rth a long the con tinen ta l m arg in , is also a c o n tr ib u to r to the sa lt

in f lu x in to the subpo la r region (see review in Haaawa A: Ta lley [2001]).

O u r s tud y [jo in ts ou t the im p o rta n t role m ix in g plays in the tra n s fo rm a tio n

o f the N A C waters found on the cold side o f the fro n t, w hich are the ones th a t

en te r the re c ircu la tio n o f the subpo la r gyre. B o th at dep th as well as in the layer

in fluenced by the atm osphere, waters get denser by an increase in th e ir sa lin ity .

We a tt r ib u te th is to m ix ing w ith the sa ltie r waters found across the s tream , a

process th a t seems to be im p o rta n t in p re con d ition in g the N A C waters fo r deep

convection in the Labrador Sea.

The s itu a tio n for the N AC waters on the warm side o f the fro n t is ra th e r

d iffe ren t. These are the waters th a t enter the Iceland B asin -R ocka ll P la teau

region, presum ably con tinu ing tow ards the regions o f deep convection in the

N o rd ic Seas. For the top 250db. the waters get denser by coo ling , w h ile th e ir

s a lin ity tends to decrease. Hence, b o th a tm ospheric coo ling and cross-fron ta l

28


m ix in g p lay a ro le in tra ns fo rm ing the upper X A C waters. A t depths below the

in fluence o f the a tm osphere (> 250clb), however, the buoyancy loss is m ostly

due to an increase in sa lin ity . The s a lin ity increase at dep th seems to be due

to advection o f sa lty waters from the European Basin. T h is suggests the sa lty

in flu x a long the eastern m arg in plays an im p o rta n t role in the ligh t-to -dense

tra n s fo rm a tio n o f the X A C -S P F waters th a t continue to the N ord ic Setts. T h is

is in con tras t to M cC a rtn e y M a u ritzen [2001]. where they suggest th a t the

ligh t-to -dense tra n s fo rm a tio n o f the w arm X A C waters is m o s tly due to coo ling

o f the waters th rough a tm ospheric heat loss, and e n tra inm en t in to a deepening

m ixed layer by h o rizon ta l flow across the m ixed layer base, as the layer cont inues

its tra n s it th rough tIn* subpo la r region. In the same paper, they observe the

XAC' waters g e ttin g co lder and fresher as they enter the eastern subpo la r gyre.

O u r resu lts suggest th a t the transfo rm ed waters below 250db become denser by

g e ttin g sa ltie r, w h ile th e ir tem pera tu re rem ains re la tive ly unchanged.

In conclusion, the tra n s fo rm a tio n process fo r the top 500db o f the water

co lum n is d iffe ren t for the two pathways th a t the X A C -S P F waters fo llow in

the subpo la r region. C 'ross-frontal m ix in g seems to dom ina te in p recon d ition in g

the X A C -S P F waters fo r deep convection to occur in the Lab rado r Sea. The

process seems more com plex fo r the waters a long the southern m arg in o f the

SPF. w h ich get denser as they enter the Ice land B a s in /R o cka ll P la teau and

Trough area by a co m b ina tion o f three processes: cross-fron ta l m ix in g w ith the

sa lty in f lu x flow ing n o rth along the eastern m arg in : en tra inm en t by m ixed layer

29


deepening: and a tm ospheric cooling. In a re la ted s tudy. P erez-B run ius [2002a]

find th a t flow across ba roe lin ic stream lines, induced by the steep m eanders o f the

no rthw a rd flow ing XAC '. results in exchange o f waters across the cu rre n t. T hey

p o in t ou t th a t cross-fron ta l exchange is the m a in m echanism by w h ich the X A C

waters get cooled in th e ir tra n s it towards the n o rth e rn X o r th A tla n tic . T h a t

s tud y calls on cau tion in using baroe lin ic s tream lines to deduce the flow o f the

waters in the X A C . since they depart s ig n ifica n tly fro m the tru e w a te r pathways.

T h is fact, however, does not a lte r the conclusions ob ta ined in th is study. I f

the evo lu tion o f the hydrog raph ic field was stud ied along the mean absolute

geostrophic pathways, the m a jo r differences com pared to the analysis presented

here would occur in the no rthw ard flow ing X A C . and w ou ld resu lt in fu rth e r

c o n tr ib u tio n o f c ross-fron ta l exchange in the ligh t-to -dense tra n s fo rm a tio n o f

the X A C -S P F waters.

30


60 - '5.5'. - <

Z 5 3 '

>■ »

J

3 A

-3 5-4 0 -3 0 -2 5-4 5 20 15

Long itude (° E)

F igure 1: C 'lim a to log ica l map o f dynam ic h c ig iit a t 200db (referenced to lOGOdb) for the no rth e rn N o rth A tla n tic (constructed w ith da ta from Hydrobase [C u rry . 1996]. I t represents the app rox im a te mean geostrophic How fo r the region.

31

6 0 -

LSo

23 5o-

FC

40-50 -45 -4 0 -3 0 -25 -20 -1 5

Longitude ( 0 E)

F igure 2: S tream fu n c tio n m ap fo r the X o rth A t la n t ic ob ta ined from R AFO S floats on the 27.5<To surface by Bower et al. [2002j . using objective1 analysis to o b ta in the m ap on a g rid made up by 111x111 km squares. C ontours are d raw n every 2 .o x 10'!n r / s . D ynam ica l features: XAC’-X o r th A t la n t ic C u rren t: X W C -X o rtIn ve s t C orner: S P F -S ubpo la r F ront. Topograph ic features: M A R - M id -A t la n t ic R idge: F C -F lem ish Cap: C’G F Z : C ha rlie G ibbs F ractu re Zone: R P - R ocka ll P la teau: IB - Iceland Basin: R R - Reykjanes R idge: IS- Irm ing e r Sea: LS- L ab ra d o r Sea. The X A C sp lits from the G u lf S tream near the T a il o f the G rand Banks, and continues n o rth fo llow ing the topography o ff the coast o f Canada. A t the X o rthw es t C orner, i t tu rns east, and is here refered to as the SPF. Past the M id -A t la n t ic R idge, i t b ifurcates, w ith p a rt o f the w a ter cu rv ing back tow ards the Irm in g e r Sea. and the rest tu rn in g northeast in to the Iceland Basin.

32

2

-1H 5 0 -j

i S E fZ S t : .

<^»-x-*-»-- f. • \ |

1 - '^ - :

i*:

40 -j

50 -4 0 50 25 20 15 10

Longitude <° E)

F igu re 3: Subegions selected for t lie cons truc tion o f the G E M fields. Dots represent the hydrog raph ic s ta tions used, ob ta ined from Hydrobase [C u rry . 199G].

33

Region 1 Region 2 Region 3

200 200 200

400 400 400

600 600 600

aoo 800 800

1000 1000 1000-50 0

Region 4

50 -50 -5050 0 50

200

400

600

800

1000-50 0 50

0

200 200 -----

400 400

600 600

800 800

1000 1000-50 50 -50

Region ‘J

200

400

600

800 [

1000-50 500

200

400

600

800

500

0

200

400

600

800

1000-50 0 50

Region 10 Region 11 Region 12

200 200 200

400 400 400

600 600 600

800 800 800

J 100050

J 1000 50

1000-50 0 -50 -50 0 50

F igu re 4: M o n rh ly differences from the annual moan o f specific vo lum e anom aly fo r the regions o f F igure 3. Dashed line is the dep th fo r w h ich the difference is less than 8 x 1 0 _8 m 3 /k g . Note th a t the seasonal in fluence is in general cons tra ined fo r the upper 2 0 0 db.

34


Pressure level= 60db150

50 41O

-503 4 5 6

Pressure level= 100db7 8 9

150

2 100

50

-50


2 100

0 -

-503 54 6

Pressure level= 500db7 8 9

150

5 1 100 -

50

-50


2 100

0 h

-503 4 5 6 7 8 9

Dynamic Height (J/ltg)

Figure 5: Specific vo lum e anom aly versus <f> at various pressure levels for M arch, in region 1 (southern X A C ). The line is the sm oo th ing sp line f it te d to the h yd rod a ta (do ts), which results in the correspond ing G E M fie ld.

35

Pressure !evel= 60db

20

ISOo 10

5

0

20

15OO 10

5

0

20

15Uo 10

5

0

20

15O = 10

1 * I

a . > . .. / A ' *

... r -----------------------.------------ • i* / *. ‘ 1.

- *. v . : t * i l V ?*. > .*7 * y • r

_

6 6.5 7 7.5 8 Pressure level= 100db

8.5 9

. . . i * *.*•£* . * * V **»* - . x V i ; * * *

1

* y * **

6 6.5 7 7.5 8 Pressure level= 300db

8.5 9

l 1 1

* ^ ?.** | .-ajUL.. ?•*«» ■ > . 1 M‘ > V 1

I6 6.5 7

. --------------p_

7.5 8 Pressure levels 500db

. T ■ “

8.5 9

6.5 7 7.5 8Pressure level= 700db

8.5

7 7 5 8Dynamic Height (J/kg)

F igure G: T em pera tu re versus <f> at various pressure levels for Septem ber, in region G (R oekall P la teau and Trough region). T he line is the sm oo th ing sp line fitte d to the h yd ro d a ta (do ts ), which results in the correspond ing G E M field.

3G

Pressure level = 40dbar30

20

-1 02 3 5 76 a 104 9 11

Pressure level = SOdbar25

20

15

10

5

0

52 3 5 7 8 106 94 11

Pressure level = lOOdbar25

20

15

10

5

0 w5

2 5 7 103 6 8 94

Pressure level = lOOdbar

-52 3 5 7 8 106 9 114

Dynamic Hetght in J/kg

F igure 7: T em pera tu re versus at various pressure levels, fo r the region o f the sou thern X A C (region 1). Note the b im oda l s tru c tu re o f the Held for <f> < 4.o.J/kg. The dots represent hydrocasts in the Lab ra d o r C u rre n t, w h ile the triang les are s ta tions taken w ith in the X A C .

37

40 -L X

35-

30-

Temperature in 1 C

F igure 8 : H is tog ram o f tem pera tu re on d = —5 x 10- 8 m :i/k g . The bim oclal s tru c tu re is due to the presence o f cold Lab rador C u rre n t waters flow ing side1 Inside w ith the w arm X A C waters. The arrow represents the cu t o ff tem pera tu re ( T ~ : i . l° C ) used to d is tin gu ish the two currents.


Region I Region 2 Region 3 Region 4

Region 6 Region 7

5 6 7 -1 5 5 5,5 6 6.5 4 5 5 3.5 4Region 9 Region 10 Region 11 Region 12

Dynamic height (J/kg)

F igure 9: A nn u a l mean p o te n tia l v o r t ic ity G E M fields fo r the 12 regions o f F igure .‘3.

39


Specific volum e anom aly Potential vorticity T em perature( IO*s m '/kg ) t I0 ‘ “ m " 's '1) ( ” C)

Specific volum e anom aly ( lO '^m '/kg )

Potential vorticitv( l ( ) ' " m ' , s ' i )

T em perature( "C>

0 100 200 300 0 100 200 300 0 100 200 300Year day

Figure 10: Seasonal evo lu tion o f the G E M fields fo r two d iffe ren t s tream lines in the X A C region (reg ion 1 ): (a) cold side o f the cu rren t (<f> = 4 .J/kg). (b ) w arm side o f the cu rren t (<f> = 7.5.J/kg).

40

Potential vortidtv

°> -»0

-20

0 to o 300200

Temperature( l’ C)

S> 40

100 200 300

40

Y ear dav

Y ear dav

T ear dav

F igure 11: Seasonal evo lu tion o f the G E M fields, using specific vo lum e anom aly as the ve rtica l coo rd ina te , for three d iffe ren t regions, on = G.J/'kg. (a) SPF (reg ion 4). (b) n o rth e rn European Basin (region 5). (c) R ocka ll P la teau and T rough region (reg ion 6 ).

41

6 0 -

z

'CLASS I I I

LASSU

4 0 -

-4 0 35-4 . 30 -2 5 -20 5

Longitude (° E)

F igu re 12: A p p ro x im a te loca tion where d iffe rent classes o f S P M W s are form ed, from Table .'3.. Class I: <) > 30 x 10_8m 3 /k g . Class II : <5 = [30] x 10~Hm 3 /kg .C lass I I I : <> € [10.20] x 10- 8 rn3 /k g . Class I \ ' : <) = [0] x 10~8 m 3 /k g . Class V : 6 € [ — 2 0 .—10] x 10- 8 m 3 /'kg . On top are shown contours o f dyna m ic height at 200db (ref. to lOOOdb) w ith in terva ls every 0.5.J/kg.

42

0= 6 .5

0 = 6.0

14 -0 = 5 .5

34.2 34.4 34.6 3534.8 35.2 35.4 35.6 35.8Salinity (psu)

F igure 13: T /S d ia g ra m fo r the seasonal the rm oc line layer waters, constructed from the1 annual mean tem pe ra tu re and specific vo lum e anom a ly fie lds, averaged over the top 250db. I t shows the dow nstream e vo lu tio n o f the properties o f a w ater co lum n flo w in g a long the X A C -S P F system (fro m region 1 to region 8 ). Each group o f sym bo ls jo in e d by a line represent a s tre am lin e , and each sym bol on a given s tre am lin e is the mean value o f tem pe ra tu re , s a lin ity and 6 fo r each region (labeled by the sym bo l). C ircles draw n around a sym bo l ind icates the presence o f S P M W in the w a te r co lum n.

43


h'i.%pt(> Pl_

' ' " * ' n h u ; T / s ' /<Va

2 ^ 5 ^ 3 = = ----

/ _<*—

Hy,Psu) 3s-2

" 'JO' s ° O d h ,h.'n th r .ing0

Soo p;lmn>

l i t - , >r

4-1

0oPyri(m °wnerFurth,er reProdl

Potion

withoUt n Utpermis.lssion

65 r

60

-200 -150—' 3

45

40 L- -50 -4 0 -20-30 -1 0

(b)

60

H 55

20

45

40 L- -50 -3 0 -20-4 0 -1 0

Longitude ( ° E)

F igure 1 5: A n im a l mean air-sea fluxes obta ined from 2 years o f NC’EP d a ta .(a ) N et air-sea heat flu x in W /m 2 (a negative value indicates th a t heat is lost to the a tm osphere), (b) Net air-sea freshw ater flu x in 10- 2c m /y c a r (a negative value ind icates freshwater gained by the ocean).

45


C hapter 2

O btaining the m ean structure o f the N A C -SP F system by com bining R A FO S float data w ith historical hydrography

A bstract

The N o rth A t la n t ic C u rre n t (N A C )-S u b p o la r F ront (S P F) cu rre n t system

serves as an im p o rta n t co nd u it o f w arm sa lty waters in to the n o rth e rn N o rth

A tla n tic . I t is the upper lim b o f the the rm oha line c irc u la tio n o f tin? A t la n t ic

Ocean, and plays a c ruc ia l role in the m odera tion o f European c lim a te . Its

tra n s p o rt and correspond ing heat fluxes rem ain uncerta in , m a in ly because the

s tru c tu re o f the system is not well known. T h is paper presents a m ethod to

o b ta in the mean s tru c tu re o f tem pera tu re , specific vo lum e anom aly, and ve loc ity

fo r the N A C -S P F region, using isopycnal floa t da ta com bined w ith G ravest

E m p ir ic a l M ode (G E M ) fields ca lcu la ted from h is to r ica l hydrography. A G E M

fie ld is a p ro je c tio n on geostrophic stream fun c tio n space o f h yd rog raph ic data ,

w h ich captures most o f the ve rtica l s tru c tu re associated w ith fro n ta l regions.

The perform ance o f the flo a t-G E M m ethod is tested in two ways. F irs t, two

syn op tic hydrog raph ic sections (one across the N A C and the o th e r across the

S PF) are reconstructed from s im u la ted isopycnal floa t pressure measurem ents.

46


The baroe lin ic tra nsp o rts o f vo lum e and tem pera tu re (re la tive to lOOOdb) across

the sections are reproduced accura te ly by the fio a t-G E M m ethod . In the second

test, ho rizon ta l maps o f pressure and tem pera tu re on the 6 = -12.7 x lO ~ sm ;!/k g

specific vo lum e anom a ly surface (ag =27 .5 ) are produced, using R A F O S floa t

da ta from two experim ents in the region between 1993 and 2000. These maps

com pare w ell w ith s im ila r maps constructed by C a rr e t al. [1997]. and estab lish

the consistency o f the m ethod.

The good perform ance o f the flo a t-G E M m ethod gives us confidence in th is

novel way o f using isopycnal floats to o b ta in in fo rm a tio n on the s tru c tu re o f the

ocean. C om bined w ith the ve loc ity measured by the floats, i t has the p o te n tia l

to estim ate absolute tra nsp o rts and heat fluxes along the N A C -S P F system .

1. Introduction

The N o rth A tla n tic C u rre n t (N A C ) - S ubpo lar Front (S P F) system form s part

o f the upper lim b o f the the rm oha line c ircu la tio n o f the N o rth A tla n tic . It

transpo rts s ign ifican t am ounts o f w arm and sa lty w ater in to the subpo la r region.

The resu lting heat flu x plays a c ruc ia l role in m odera ting European c lim a te

[Krauss. 19SG].

F igure 1 shows the c ircu la tio n o f the upper subpo la r N o rth A t la n t ic . The

N A C separates from the G u lf S tream a t the T a il o f the G rand Banks, and

continues a long the co n tinen ta l she lf u n til i t tu rns east a t the N orthw est C o rner

47


( ~ 50°NT). The N A C undergoes a m a jo r tra ns fo m a tion a t th is p o in t, fro m a sharp

baroe lin ic fro n t it tu rns in to a broader flow w ith embedded residual fron ts . We

denote th is eastward flow as the S ubpo la r F ron t (S P F). which has a c lear surface

expression at its no rthe rnm ost ex ten t [Rossby. 1999],

There is a lack o f accurate estim ates o f transpo rts ca rried by the N A C -

SPF system . Meinen W a tts [2000] ob ta ined the mean s tru c tu re and absolu te

tra n sp o rt o f the N A C at 42°N . using a m ethod th a t combines inverted-echo-

sounder da ta w ith h is to rica l hydrography. They report an average tra n s p o rt o f

146 Sv (w h ich includes a p o rtio n o f the M ann E ddy). Instantaneous snapshot

estim ates are availab le for the N A C (e.g.. absolute tra nsp o rt: 1 1 2 Sv ( in c lu d in g

a p o rtio n o f the M ann Eddy. [M einen et ah. 2 7 7 baroel i ni c tra nsp o rts : 78 Sv

re la tive to b o tto m [C larke et al.. 1980]: 74-97 Sv re la tive to b o tto m [W o rth in g

ton . 1976]). Dow nstream o f th is lo ca tion . Lazier [1994] ob ta ined an abso lu te

tra n sp o rt o f 50 Sv from a cu rren t m eter line across the N orthw est C orner, w h ile

B ubnov [1995] reports 108 Sv fo r the two no rthe rn branches o f the SPF near

the C 'harlie-G ibbs F racture Zone. B a roe lin ic transports for the tw o n o rth e rn

SPF branches have been reported by Sy et al. [1992] (17 Sv referenced to a

va riab le layer between 1500 and 2900m ). and Bubnov [1995] (29 Sv between

0 and 2000m ). Tem pera tu re tra n sp o rt estim ates are even scarcer [B ubnov.

1995] (ba roe lin ic referenced to 2000m: 8 8 8 x 101* W . absolute dow n to 2000m:

lO S S x lO 1-’ W ). In sum m ary, tra n sp o rt estim ates exist on ly for a few sections

across the N A C -S P F system . No a tte m p t to ob ta in the dow nstream changes

48


95

o f the vo lum e and tem pera tu re tra nsp o rts o f the curren t system has yet been

made. Such estim ates w ou ld be possible to o b ta in i f the mean tem pera tu re ,

density, and ve loc ity s tru c tu re o f the cu rren t system were b e tte r know n. We

present a m ethod by w h ich isopycnal floats can be used to o b ta in such estim ates.

Isopycnal R AFO S floats have been used to provide hydrog raph ic in fo rm a

tio n on the sam pled surfaces by C a rr et al. [1997] (henceforth C K R ). A R A FO S

floa t is an acoustica lly tracked, n e u tra lly buoyant d r ifte r . A lth o u g h it is com

m o n ly known as an isopycnal floa t, in re a lity it tends to fo llow a specific vo lum e

anom a ly surface. I ’sing h is to r ica l hydrography. C K R find a s trong co rre la tion

between the p o te n tia l energy anom a ly (referenced to 2 0 Q0 db) and the dep th o f

the ta rge t surface o f the floats. T h is a llows them to construc t a p o te n tia l energy

anom aly m ap for the N A C -S P F region, using the R A FO S floa t pressure records.

Kearns [L99G] uses the same d a ta and procedure as C K R to produce a m ap o f

the p o te n tia l energy anom aly referenced to lOOOdb. T h is means th a t in fo rm a

tio n on one surface (the target surface o f the floats) can provide in fo rm a tio n on

the in teg ra ted ve rtica l s tru c tu re o f the ocean (p o te n tia l energy anom a ly ).

T h is paper extends the idea presented in C K R . show ing a m e thod in w hich

R A FO S floats are used to provide the fu ll th ree-d im ensiona l s tru c tu re o f the hy

d rog raph ic fie ld o f the region sam pled. The m ethod combines the pressure da ta

measured by the floats w ith G ravest E m p irica l M ode (G E M ) fields con trac ted

from h is to rica l hydrography. A G E M fie ld is a p ro jec tio n o f hyd rog raph ic d a ta

on geostrophic stream fun c tio n space, c a p tu rin g m ost o f the ve rtica l s tru c tu re

49


associated w ith fro n ta l regions [Sun &: W atts . 2001]. I t takes advantage o f the

observa tiona l fact th a t the dens ity s tru c tu re is t ig h t ly locked in the v e rtica l,

and varies s low ly in the ho rizon ta l.

We ca ll th is technique the flo a t-G E M m ethod. To establish its u t i l i t y for

the N A C -S P F region, we make tw o tests. G E M Helds o f tem pe ra tu re and spe

c ific vo lum e anom a ly construc ted by Perez-Brunius [2 0 0 2 c] are used fo r th is

purpose. We Hrst reproduce know n C T D sections across the N A C -S P F . using

s im u la ted floa t data . Second, we app ly the m ethod to R AFO S floa t d a ta from

two experim ents, and cons truc t ho rizon ta l maps o f tem pera tu re and dep th o f

the <) = —12.7 x 10_8 m '/k g ( ~ 27.5(Jo) specific vo lum e anom a ly surface. We

com pare these maps w ith s im ila r maps constructed d ire c tly from the pressure

and tem pera tu re records from a subset o f the same floats in C a rr et al. [1997].

to prove th a t the m ethod is consistent.

N ote th a t when we refer to the floats being isopycnal. i t means th a t the

floats track very closely the neu tra l surfaces upon which w a te r parcels move

[C a rr et a l.. 1997]. We w il l use specific volume anom aly (<)) in th is paper,

since h-surfaces are b e tte r app ro x im a tio ns to neu tra l surfaces than the more

com m on ly used p o te n tia l dens ity (<jg) [M cD ouga ll. 1989]. To help the reader.

Table 1 shows various 5 surfaces and th e ir corresponding a 0 coun te rpa rts . The

J values are referenced to 34.6 psu. and 4.9 'C . w hich are the mean values for

the region o f the N A C and SPF [Kearns. 1996].

50

2. F loat-G E M technique

2.1 G EM discussion

T h e large-scale the rrnoha line fie ld o f the ocean is sub jec t to processes o f large

s p a tia l and tem po ra l v a ria b ility . In regions a round large currents, th is va ri

a b i l ity is m o s tly due to the m eandering and eddy shedding o f the ba roe lin ic

fro n t associated w ith the cu rren t. Near the surface, we have an added source o f

v a r ia b ility due to in te rac tio n w ith the atm osphere, w ith the largest s ignal found

011 seasonal tim e scales. For exam ple, the X A C p os ition m ay s h ift la te ra lly up

to 150km n o rth o f the T a il o f the G rand Banks [Kearns Jc Rossby. 1998], and

B e lk in Lev itus [1996] suggest th a t the SPF has excursions o f 200-300krn near

the C h a rlie G ibbs F racture Zone. The seasonal s igna l is confined to the upper

2()()<lb. w ith an a m p litu d e o f abou t 3 -5 'C (~ 0.4 — I. Oct#. Perez-Brun ius [2002c] ).

In recent years, several studies have shown how the v a r ia b ility o f the hy

d ro g rap h ic fie ld in regions where ba roe lin ic fronts are present can be accounted

fo r in te rm s o f a s im p le r unde rly ing dynam ica l concept: th a t ve rtica l m otions

are s tro n g ly coupled thoughou t the w ater co lum n [C a rr et al.. 1997: M einen t

W a tts . 2000: Book et al.. 2002: W ille fo rd . 2001]. Sun & W a tts [2001] developed

a techn ique th a t helps reduce the v a r ia b ility in the hydrog raph ic da ta associated

w ith the m eandering o f baroe lin ic s truc tu res . T h is technique derived from an

ea rlie r version firs t proposed by M einen cA W a tts [2000]. I t consists o f p ro je c t

ing the h yd rod a ta onto geostrophic stream fu n c tio n space. The resu lting fie ld is

51

ca lled a G ravest E m p irica l M ode (G E M ) p ro je c tio n . The G E M technique has

succesfu llv cap tu red abou t 90% o f the variance o f h yd rog raph ic da ta co llected in

the A n ta rc t ic C ircu m p o la r C u rre n t [Sun ic W a tts . 200L], K urosh io [W ille fo rd .

2001: B ook et a l.. 2002], and in the no rth e rn X o r th A t la n t ic [M einen A: W a tts .

2000: P erez-B run ius. 2002c],

G E M fie ld p ro jec tions resu lt in 7 g( p . xV. t ) fie lds, where 7 is the va riab le

we are in terested in (e.g. tem pera tu re , specific vo lum e anom aly, s a lin ity ) , p is

pressure. T is a geostrophic stream fu n c tio n (such as dynam ic height a t the

surface, fo r exam ple), and t is tim e (fo r the well sam pled regions o f the ocean,

enough d a ta are availab le to construc t m o n th ly means). Note th a t from a

G E M fie ld for specific volum e anom aly 6,j(p. v&. t ). o the r re la ted fields can be

construc ted , such as the dynam ic height a t every level (referenced to p r,-frrvnrr)'

I f the geograph ica l region o f in terest is large, and the the rm oha line p rope rties

change s ig n ific a n tly w ith in it . i t is advantageous to com pute in d iv id u a l G E M

fields in sm a lle r overlapp ing subregions. T h is w il l reduce discrepancies between

G E M values and the hydrograph ic da ta , and thus resu lt in a more accurate

m odel fo r the mean ve rtica l s tru c tu re . The reason to have the subregions overlap

is to prom ote' c o n tin u ity between G E M fie lds o f ad jacent subregions.

p

( 1 )

52


2.2 F loat-G E M description

W h ile the G E M fields give us a good account o f the mean ve rtica l s tru c tu re o f

the the rm oh a lin e fie ld in a p a r tic u la r region, the next step is to o b ta in h o rizon ta l

in fo rm a tio n by co ns tru c tin g the geostroph ic stream fun c tio n fie ld in geographic

coord ina tes . T h is fie ld m ust be ob ta ined independently . The idea o f the flo a t-

G E M techn ique is to use the pressure measured by isopycnal floats as the inde

pendent m easurem ent th a t is needed to o b ta in the geostrophic stream fun c tio n .

Once th is fie ld is know n, the three d im ensiona l s tru c tu re o f a ll variables w ith

co rrespond ing G E M fields can be reproduced.

The procedure is as follows. We use the isopycnal float da ta in an Eule-

rian way. The floats are ballasted to fo llow a given specific vo lum e anom a ly

surface <)fi,mt. Each float measurement o f pos ition (A ') and pressure ( ) at

tim e t.fioll, i-s trea ted as a "s ta tio n " measurem ent. A t a given s ta tio n (A '„) . the

co rrespond ing value o f the geostrophic stream fun c tio n '& /ff(A '„) is ob ta ined by

look ing up the {pfiant - ^fhmt) P*dr in the correspond ing specific vo lum e anom a ly

G E M fie ld {S,j{p. xi - t f i „ at))- T h is is illu s tra te d in F igure 2. Once the value o f

the s tream fu n c tio n is known, the ve rtica l p ro file o f the variab le *• is given by

~f<j{p. A n) = ^ f tJ{ X 0). t f i oat). [2]

where "• can be specific vo lum e anom aly, tem pera tu re , o r any o the r va riab le for

w hich a G E M fie ld is available.

N o te th a t i f the G E M fields used were constructed for several overlapp ing

53

subregions. there m ay be floa t s ta tions found in the in tersection o f two o r m ore

o f these subregions. W hen th is is the case, the fin a l f lo a t-G E M generated p ro file

o f the p ro p e rty variab le and the co rrespond ing value o f the stream fu n c tio n

on th a t s ta tio n , are given by the mean over a ll the subregions:

~!fa(p. .Y„) = Y1 T /9 (p. ( ;3>- i= i

'&/9(-Y0) = (4)-v : = i

where .Y is the num ber o f subregions co n ta in in g A '„.

2.3 Errors associated w ith float-G EM technique

There are three errors associated w ith the f lo a t-G E M technique. The G E M fie ld

m ean-square e rror, the e rro r in pressure m easurem ent o f the Hoat. and the e rro r

in floa t ba llas ting .

The G E M mean-square e rro r te lls us how well the G E M fie ld reproduces t in '

profiles o f the hydrocasts used in its co ns tru c tio n , and is given by

( A % ( p . 'F. t ) ) 2 = < (~rJ(p. 'I ', t) - ~h,j,trarnst.s{P- . t ))~ > . (5)

when* < ... > represents the average over a ll the hydrocasts.

Because o f e rro r in the pressure measured by the float { A p f loat). the value

o f the geostroph ic stream fun c tio n ob ta ined from the specific vo lum e anom a ly

G E M fie ld has an u nce rta in ty associated w ith it . w hich we ca ll A Pvl / / a (see F igu re

3). The e rro r in the geostrophic stream fu n c tio n value results in u n ce rta in ty

on the profiles o f ~ f tJ(p. A '). We q u a n tify th is e rro r by ta k in g the m a x im u m

•54

difference between the profiles in the G E M fie ld th a t correspond to the in te rva l

v&/a ± A ^ /a ;

± PV y (P ) =

M a x [ | ^ / 9, t f [oat) - flJ + ± PxVflJ. tJUmt)| .

i7y(p- v /«- ^/io.n) - ~'y(p- vP/a - A ^ 1? /y. t j lo,l t ) | ] . (G)

S im ila r ly , an u n ce rta in ty in floa t ba lla s tin g (S S f i0,l t ) results in an u n ce rta in ty

A ,)' l ' / , ; (/). A ') on the stream func tion value (see F igu re 4). T h is in tu rn trans la tes

in to an e rro r in the p ro file o f which we denote by A '* " /y(/;. A '). We estim a te

th is e rro r in the same way as A ,'" y y(/J. A ').

Hence, the to ta l e rro r on the H oat-G E M generated p ro file o f - on floa t s ta tio n

.V is g iven by

[A -./s,(p ..V )]- = [A»-./s ( , , . .V ) ] %

[A ''-./9 ( , , .A ) ] 2 + [ A ' S ^ . A ) ] 2 . (7)

assum ing th a t the three errors are independent.

In a case where the float s ta tio n is found in the in tersection o f tw o o r m ore

subregions fo r w h ich G E M fields have been constructed, then the co rrespond ing

f lo a t-G E M e rro r fo r the p ro file ~(p. X ) . and the corresponding stream fun c tio n

value1 '&/,,( A*). are given by

[a - .,,( „ . a-)]- = ■£ [a -.},(,,. .V)]- . (S)1 = 1

[a >P/!,(.V)]-! = X I [A 't^e -V )]- . (9)1 = 1

55


where the sum is carried o u t over the N subregions co n ta in in g s ta tio n X .

The fio a t-G E M errors described in th is section are the associated u n ce rta in

ties o f the estim ates o f (g iven the unce rta in ties o f the hydrog raph ic da ta

and floa t observations used), and should be taken as confidence in terva ls fo r the

estim a te .

3. D ata

We a p p ly the flo a t-G E M technique to hyd rog raph ic and R A FO S floa t da ta

co llected w ith in the la titu d e -lo n g itu d e box bounded by (50°W .-10°N) to the

southw est, and (1 5 'W .6 0 J. \ ) to the northeast.

3.1 G EM fields for the subpolar N orth A tlantic

M o n th ly G E M fields o f tem pera tu re , specific vo lum e anom aly, and d ynam ic

he igh t have been constructed by [Perez-B runius. 2002c] (referred to as P -B

from now on) fo r the region o f in terest. These fie lds are availab le fo r various

subregions in the X o rth A tla n tic , m ak ing use o f C T D and b o tt le da ta fro m H v-

droBase [C u rry . 1996] collected between 1910 and 1996. anti d u rin g 21 W O C E

cruises taken a fte r 1996. k in d ly p rovided by R u th C u rry a t W oods Hole Oceano

g raph ic In s t itu t io n (F igu re 5). The G E M fields were constructed using d yna m ic

he igh t a t 200db (referenced to lOOOdb) as the geostroph ic stream fu n c tio n th a t

56


param eterizes the G E M fields:

JOOtib

* = J 60(p. S. T ) d p . ( 10)1000(/i

where

So(p.S .T) =1 1

p ( p .S . T ) p(p. 35psu. 0°C )

anti p ( p . S . T ) is the in s itu density a t pressure p. s a lin ity S. and tem pera tu re

The G E M fields were constructed by f it t in g cubic sm o o th ing splines to tin*

d a ta a t each pressure level, for th ree -m ou th long bins centered a t the m on th o f

interest.. Day o f the year G E M fields are also ob ta ined by lin e a rly in te rp o la tin g

over tim e between consecutive m o n th ly fields.

T he fields so constructed exp la in about 90% o f the h o rizon ta l variance in

the regions o f s trong b a ro c lin ic ity and s tra tif ic a tio n , fo r depths between 1 0 0 and

lOOOdb (regions 1-4 in F igure 5). However, in the subpo la r region, the b a ro c lin

ic ity and s tra tif ic a tio n decrease, and so does the variance' o f the tem pera tu re

and specific vo lum e anom aly o f the hydrocasts. S t ill, the G E M mean-square

e rro r rem ains abou t 1 0 % o f the ve rtica l range o f specific vo lum e anom aly and

tem pe ra tu re variances (P -B ). T h is allows confidence in using the G E M p ro jec

tions as m odels o f the mean ve rtica l s tru c tu re for the region we are in terested

in.

P -B found th a t tem pera ture is not a single valued fu n c tio n o f d/ in the N A C

region (subregions 1 and 2). T h is is because the L a b ra d o r C u rre n t, th a t flows

r .


a long the inshore side o f the X A C . has very co ld and fresh waters. The Lab rado r

C u rre n t waters have the same density as the w arm er and sa ltie r X A C waters

by s a lin ity com pensation. There is no dyna m ica l fro n t separa ting these two

curren ts between 200 and lOOOdb. hence cannot d is tin g u ish them . F igure

6 shows the b im o da l dependence o f tem pe ra tu re w ith fo r subregion 1 . P -B

construc ted the m o n th ly tem pera ture G E M fie ld o f subregions 1 and 2 fo r the

warm waters o f the X A C . For th is , the d is tr ib u t io n o f tem pe ra tu re a long the

specific vo lum e anom aly surface <) = - 5 x I0 _8 m 1/k g (~ =27.-13) was used to

o b ta in the cu t o ff value (3.1°C) tha t d iv ides the tw o modes. Hence, o n ly s ta tions

w ith tem pera tu res h igher than th a t cu t o ff value were used fo r the co ns truc tion

o f the m o n th ly tem pera tu re G E M for the w arm X A C waters (T,,{p. 'k .m o n th )) .

The rest o f the s ta tions are assumed to be sam p ling Lab rador C urren t waters,

w hich specify th e ir own annual mean G E M fie ld for tem pe ra tu re T j A (p. 'F) for

subregions 1 and 2. There is not enough coverage for a ll seasons to construct

m o n th ly moans. Since the sam pling o f those waters is m o s tly taken by the Ice

P a tro l, the d a ta lim ite d to the w in te r-sp rin g m onths. So the T ^ c {p. VF) fields

may be biased tow ards cold values, especia lly near the surface, where seasonal

effects are im p o rta n t. The m atch between the tem pe ra tu re G E M s and the da ta

at various levels fo r subregion 1 is shown in F igu re G.

So far. the flo a t-G E M m ethod presented in Section 2 does not a llow one

to choose w hich o f the two values o f the b im o d a l tem pe ra tu re G E M fie ld is

to be used fo r floa t s ta tions w ith in the X A C -L a b ra d o r C u rre n t region. T h is

58

is where the tem pe ra tu re measured by the floa ts becomes handy: i t provides

the a d d it io n a l in fo rm a tio n needed to d is tin gu ish between the tw o G E M s. For a

floa t s ta tio n A ' 0 w h ich has VI, / 3 (A '0) w ith in the range a t w h ich the tem pera tu re

G E M is b im o d a l. the correspond ing p ro file o f tem pe ra tu re Tf,t (p. X „ ) is given

by

r ;!,(/,.,v„) = { , ; [ ; Tj " ° ” a n1. ^ < J \ P ' ‘ f y t f l o a t ) “ 1 f l o a t ^ I r u t a f f •

where TrlUl)f j is the tem pera tu re w h ich d iv ides the two modes on the floa t's

ta rge t surface 6f[oat. and t corresponds to the day o f the year a t which the

floa t m easurem ent took place. We ob ta in the cu t o ff tem pe ra tu re by m ak ing a

h is tog ram o f tem pe ra tu re on from the hyd rod a ta , in the same way as the

cu t o ff tem pe ra tu re was chosen fo r the co ns tru c tio n o f the tem pe ra tu re G E M

in P -B .

3.2 F loat data for the region

We use d a ta from R A FG S floats deployed d u r in g tw o experim ents: the X A C

expe rim en t (1993-1995). and the A tla n tic C lim a te Change E xpe rim en t (ACC’E).

w h ich too k place between 1997 and 2000.

From the X A C experim en t, we use 50 floats ta rge ted fo r <io =27 .3 (3 ~

10 x 10_8 m ! /k g ) and 37 floats targeted fo r h# = 27 .5 (3 % - 1 0 x 10_Hm ! /k g )-

T h ey were deployed d u r in g three d iffe ren t cruises th a t too k place in .Ju ly-August

1993. X ovem ber-D ecem ber 1993. and O ctobe r-X ovem ber 1994. P rogram m ed to

sam ple fo r 300 days, the floats collected p os ition , tem pe ra tu re , and pressure

59

da ta tw ice a day [A nderson-Fontana et a l.. 1996].

F rom t lie A C C E experim en t, we use the da ta fro m 50 floats ballasted fo r 27.5

<j0 (6 js: — 1 0 x 10_8 m '! /k g ) . These floats were deployed across the SPF d u rin g

tw o cruises. T h e f irs t cruise took place in Novem ber 1997. and the second one

in J u ly 199S. T he floats sam pled pos ition once a day. and tem pe ra tu re and

pressure 6 tim es a day. T h e ir m issions were p rogram m ed to be 540 days long.

T he accuracy o f the R.AFOS floa t pressure m easurem ent is lOdb and th a t

o f tem pe ra tu re is 0 . 1°C [C a rr et a l.. 1997].

These two d a ta sets resu lt in over 64.000 floa t "s ta tio n s " . To ensure a degree

o f s ta tis t ic a l independence, we subsam pled the da ta so th a t o n ly "s ta tions"

w inch were more' than A t = 2.5 days and A x = .'30 km away from each o the r

rem ained. These are the in teg ra l tim e and leng th scales, respective ly, fo r th is

region [Zhang et a l.. 2001]. T h is results in 13.457 independent floa t s ta tions,

w ith a sp a tia l d is tr ib u t io n shown in F igure 7.

Float ballasting

K n o w in g w ith accuracy the specific vo lum e anom a ly o f the floa t is c ruc ia l for

the f lo a t-G E M technique. To estim ate the ac tua l value oi<)f loat fo r each floa t, we

made use o f the specific volum e anom a ly p ro file ob ta ined by the C’T D cast taken

a t the floa ts dep loym ent site. A set o f <) values was ob ta ined by m a tch ing the

C T D specific vo lum e anom aly p ro file w ith the f irs t 1 0 pressure measurements

taken by the floats. T h is corresponds to the f irs t 5(2) days o f da ta fo r the

60

X A C (A C ’C E) expe rim en t. The Sfloat is then given by the mean o f those values,

using the s tandard d ev ia tio n as the u nce rta in ty in floa t b a lla s tin g A S f ioat. We

choose the 1 0 firs t measurements to ensure su ffic ien t s ta b il ity and precision in

the average and s tandard d e v ia tio n o f the es tim ated floa t's <). For the 1 0 % o f the

floats w hich had no s im u ltaneous C T D cast, the mean and s tandard d e v ia tio n o f

the 6 fo r each flo a t expe rim en t were used. The results o f the floa t ba llas tin g

are shown in Tables 2. 3. and 4.

3.3 F loat-G E M errors for the northern N orth A tlantic

Figure S shows the annual mean flo a t-G E M errors fo r specific vo lum e anom aly

in subregion 1 . The results fo r the o the r subregions are very s im ila r. The

errors were ca lcu la ted using = - 1 0 x 1 0 _Mm '!/k g as the ta rge t surface for

the floats (close to the mean value for the AC’C E and deep X A C floa ts), and

= 10db and A 6f iotU = 3 x 10~8 m ,!/k g as the floa t errors. The float

b a lla s tin g e rro r represents the mean e rro r fo r the floats w hich had a C T D cast

associated w ith them when deployed.

Xear the surface, the largest e rro r is the G E M erro r. In the pycnocline . the

e rro r due to u n ce rta in ty in floa t ba llas ting is the largest. X o tice th a t the e rro r

due to u nce rta in ty in the floa t pressure is much sm a lle r than e ith e r o f the o the r

two. The to ta l e rro r is genera lly less than 10% o f the ve rtica l range in <).

E rro rs for tem pe ra tu re in subregion 4 are shown in F igure 9. The o the r

subregions have s im ila r pa tte rns. In the tem pe ra tu re case, the largest uncer-

G1

ta in ty a t a ll depths is the G E M mean-square e rror. T he second in im po rtance

the floa t ba llas tin g e rro r, and lastly , the e rro r due to flo a t pressure unce rta in ty .

Nevertheless, the to ta l flo a t-G E M e rro r is less than 15% o f the ve rtica l range in

tem pera tu re , w ith la rger uncerta in ties near the surface.

N ote th a t the flo a t-G E M errors for bo th tem pe ra tu re and specific vo lum e

anom a ly appear to fo llow the slop ing specific vo lum e anom a ly surfaces.

4. Test o f m ethod: reconstruction o f hydrographic section s from sim ulated float data

4.1 H ydrographic sections

To test the perfom ance o f the flo a t-G E M technique, we reconstruc t tw o transects

o f C T D profiles using s im u la ted floa t da ta (F igu re 1 0 ). T he firs t one is a transect

across the N A G . near the T a il o f the G rand Banks, taken on board R /Y Oceanus

d u r in g August 1-7. 1993. T h is section has been discussed by M einen et al.

[2000]. The second one is a section across the SPF. a long 37°\V . taken d u rin g

J u ly 22-24. 199S. on board R /Y K no rr.

4.2 Sim ulated float data

We sim u la te float measurements by o b ta in in g the pressure and tem pe ra tu re

on i)fi„at = — 1 0 x 10"Hrn'5/k g (~ 27.otto) from the C T D casts. The cruise

s ta tions are ou r s im u la ted float s ta tions. We choose to be w ith in the m ain

the rm oc line . I t also corresponds to the ta rge t surface fo r the A C C E and deeper

62


X A C floats described in Section 3.2. To ob ta in rea lis tic f lo a t-G E M errors, we use

a ba llas tin g e rro r o f A6f i ,mt = ± 3 x 10- s n i-1/kg - T h is value is the mean b a llas tin g

e rro r o f the X A C and A C C E floats fo r w hich a C T D cast was ava ilab le a t flo a t

dep loym ent. The u nce rta in ty in pressure used is the one associated w ith the

R A FO S float pressure sensor A p f toat = 1 0 db (see Section 3.2).

4.3 Sim ulated float-G EM profiles

We now have the d a ta needed to a p p ly the flo a t-G E M technique in an a tte m p t

to recreate the specific vo lum e anom aly, tem pera ture , and d yna m ic height tra n

sects from the G E M fields presented in Section 2.

For the X A C section, we use the August G E M fields on subregion 1. To

d is tin gu ish between the two modes o f the tem pera tu re G E M . we use the s im u

la ted float, tem pera tu re . The correspond ing cu t o ff value fo r tem pe ra tu re in the

^}i,mi = — 1 0 x I0 ~ 8 m !/k g surface was found to be TrtU„ f f = 3.o 'C '.

In reproducing the SPF section, the Ju ly G E M fields from subregions J and

7 are used. In th is case, the tem pe ra tu re G E M fields are s ing le-va lued, so we

have no need o f the s im u la ted floa t tem pera tu re data . X ote th a t there are four

s ta tions found in the in tersection o f the two subregions (F igu re 10).

We ob ta in the profiles o f specific vo lum e anom aly, tem pe ra tu re , and dynam ic

he ight (referenced to lOOOdb) fo r each floa t s ta tio n , using the f lo a t-G E M m ethod

described in Section 2.

G3


4.4 Specific volum e anom aly sections

N A C transect

F igure 11 shows the results fo r the specific vo lum e anom a ly section across the

X A C . We w il l refer to the C T D section as the 'rea l' section. N o te th a t the

section crosses the M ann Eddy, the core o f w h ich is found a t a pos ition between

400 and 600km from the western end o f the transect. The b a roc lin ic s igna l o f

the X A C is found at a pos ition between 220 and 470km. centered a round 320km

[M einen et al.. 2000].

The s im u la ted flo a t-G E M generated section reproduces the C T D line m od

e ra te ly well. We find the largest differences from the real section w ith in the

M ann Eddy. The two eddies found in the real section in the upper 230db (at

50-90km and 280-400km ). an? not reproduced in the H oa t-G E M section. T h is

is expected, since the G E M p ro jec tions f ilte r ou t any sm a ll scale v a r ia b ility .

O therw ise, the differences are genera lly less than 10'X o f the to ta l ve rtica l range

in specific volum e anom aly.

The s im u la ted flo a t-G E M errors also are genera lly less than 10(/c o f the

ve rtica l range in S. as [jo in ted ou t in Section 3.3. We find the largest s im u la ted

f lo a t-G E M errors near the edges o f the M ann Eddy, a round the p o s itio n o f

400km and 600km .

64


SP F transect

F igu re 12 shows the results fo r the SPF transect. There are three regions o f

re la tive ly high b a ro c lin ic ity . w hich we here refer to as N o rth e rn SPF (X S P F .

centered at ~ 125km ). M id d le SPF (M S P F . centered at ~ 3G0kni). and southern

SPF (SSPF. centered at ~ 500km ). A sm all eddy is present on the top lOOdb at

~ -ISOkm. Note th a t th is region is less s tra tified than the N A C section. T h is is

because the SPF is the bounda ry between the sub trop ica l and su bp o la r gyros,

so m any o f the sha llow isopycnals o f the m ain pycnolino o f the su b tro p ica l gyre

o u tc ro p along the fron t.

The most p rom inen t difference between the real and f lo a t-G E M sections is

in the s tra tif ic a tio n found between the XSPF and M S P F. in the to p 300db.

A lso, the sm all eddy on the southern pa rt o f the section is no t reproduced by

the floa t-G E M .

The flo a t-G E M errors an* a ll sm a lle r than 1 0 ‘a o f the ve rtica l range in <).

w ith the largest ones found beneath the XSPF.

4.5 Tem perature sections

N A C transect

T he real X A C tem pe ra tu re section (F igu re 13) shows sm a ll scale v a r ia b ility

w h ich is filte red ou t in the flo a t-G E M section. Note the cold Lab ra d o r C u rren t

w ater found on the western edge o f the section [M einen et a l.. 2000]. T w o

s ta tions sampled th is water, and the flo a t-G E M reproduces a sm ooth version o f

65

the cu rre n t's tem pera tu re .

The d ifference between the real and the flo a t-G E M sections is in general

less than 1°C. The exceptions are in the sm all scale eddies (a t ~ 70km and

300km ). and in the regions where the real section has large sm all-scale va ria

tions. found m a in ly where the X A C and Labrador C u rren t waters meet (between

SO - 120km).

F lo a t-G E M errors are less than 15'T o f the ve rtica l range o f tem pe ra tu re

below 2 0 0 dl).

SPF transect

Note th a t the* real SPF tem pera tu re section (F igure 14) does not have as much

sm all scale v a r ia b ility as the X A C section (F igu re 13). In th is region, the w arm

X A C waters have* m ixed w ith the co lder subpo lar and Lab rador C u rre n t waters,

and the SPF is no longer as s trong a p rope rty fron t as is the X A C near the T a il

o f the G rand Banks.

As was the case fo r the specific vo lum e anom aly transect, the la rgest d if

ference between the real and flo a t-G E M sections is in the s tra t if ic a t io n found

between the X S P F and the M SPF. The flo a t-G E M does not reproduce the sm a ll

eddy in the top lOOdb th a t shows up in the real tem pera tu re section, centered

at ~ 480km.

F lo a t-G E M errors ra re ly exceed 15(T o f the ve rtica l range in tem pe ra tu re

(see Section 3.3). w ith the largest ones located on the X SP F and M S P F .

GO


4.6 B aroclin ic transports

A n o th e r way o f checking how well the flo a t-G E M reproduces the d is tr ib u t io n

o f specific vo lum e anom aly o f the real sections, is to com pare the b a ro c lin ic

tra n sp o rts associated w ith them . We estim ate the vo lum e tra n s p o rt re la tive to

a lOOOdb (Qiooo) follows:

L is the length o f the transect, x is d istance along the transect. is the baro

c lin ic ve loc ity across the section (referenced to LOOOdb). / is the C o rio lis pa

ram eter. and <1* is dynam ic height (referenced to LOOOdb).

For the flo a t-G E M generated sections, we o b ta in the p ro files o f dynam ic

he igh t at each s ta tio n from E qua tion 1.

T he real sections have tra nsp o rts o f 24 Sv to the n o rth (N A C ). and LL Sv

to the east (S P F ). fo r the top LOOOdb. The correspond ing tra n sp o rts fo r the

flo a t-G E M sections are 23 ± 2 Sv fo r the N A C . and 13 ± lS v fo r the SPF. N ote

that, the N A C tra n s p o rt is w ell represented V>y the f lo a t-G E M ca lcu la tio n w h ile

the SPF tra n sp o rt is overestim ated by 20%. The errors rem ain less than L0%

o f the to ta l transpo rts . For a discussion on how we ca lcu la te the errors, refer to

I. Qtlb

Q 1000 = J0 UlOlMii

where

(13)

lOOOr/h

G7

A p p e n d ix 2.

H av ing the tem pe ra tu re (T ) and b a roc lin ic ve locities (V ) . the tem pe ra tu re

tra n s p o rt fo r the top lOOOdb ( H 1000) can be estim ated:

where p is the in si tu density, and C p is the specific heat capac ity o f seawater.

T he p roduc t pC'p is assumed constant (4000 x 10-,J / m !oC ).

The real XAC' section transpo rts 1.23 P \V . w h ile the SPF tra nsp o rts 0.39 P \Y

( fo r tin* top lOOOdb). The correspond ing transpo rts fo r the f lo a t-G E M sections

a rt1 1.03 ± 0 .1 5 P \Y and 0.42 ± 0 .0 3 P \V . respectively. A lth o u g h the accuracy for

tem pe ra tu re is less than fo r volum e tra n s p o rt, the flo a t-G E M is s t i l l w ith in S5‘X

o f the 're a l' value, and the errors are w ith in 15% o f the to ta l tra nsp o rts . The

ca lcu la tio n o f the errors in the tem pe ra tu re transpo rts is described in A p p e n d ix

S um m ariz ing the tests perform ed in th is Section, we find th a t the m ethod

reproduces q u ite well the hydrog raph ic transects used fo r tin* test, especia lly

when considering th a t the flo a t-G E M is based on the mean ve rtica l s tru c tu re o f

tem pe ra tu re and specific vo lum e anom a ly fo r the region, and hence has in t r in

s ica lly filte red o u t any sm all-scale v a r ia b ility found on the 're a l' h yd rog raph ic

transects.

T in 1 fact th a t the b a roc lin ic tra nsp o rts are so well reproduced gives us con

fidence in using th is m e thod to make such estim ates, especia lly i f good floa t

I I pCpV ( p . X ) T ( p . X ) d p J 0 JlQOOdb (15)

•)

68


coverage for the region is availab le.

The m ethod works best in the N A C . because the s tra t if ic a t io n and baro-

c lin ic itv for th a t region is strong. A t the SPF. the ba roc lin ic fron ts are weak,

and the s tra tif ic a tio n gets weaker as we go fa rth e r n o rth , since i t is a long the

SPF th a t m any o f the isopycnals in the m ain pycnocline o f the su b tro p ica l gyre

ou tcrop .

5. C onsistency check: horizontal maps using real float data

C 'K R use R AFO S float d a ta from the N A C experim ent (Section 3.2) to cons truc t

the pressure o f the <)tnr>irt = —12.7 x I 0 _sm !/k g surface (ta rge t isopycna l for

the deep N A C floats). To p ro jec t a ll the float da ta on the same surface, they

correct each floa t fo r the e rro r in pressure due to u n ce rta in ty in floa t b a lla s tin g .

T hey then take the m edian o f the da ta on each b in o f a 0 .5 ’ x 0.5° g rid , and

fit a b icub ic sm oo th ing sp line surface to ob ta in the maps shown in F igu re 15.

S im ila r ly , using the float tem pera tu re data , and co rrec ting th a t fo r the e rro r in

floa t ba llas ting , they o b ta in the floa t-derived tem pera tu re o f the same ta rge t

specific volum e anom aly surface (F igu re IG).

In the same paper. C 'K R show the c lirna to log ica l tem pera tu re on (F ig

ure 17). ca lcu la ted from h is to rica l b o tt le da ta fo llow ing the same g r id d in g and

in te rp o la tin g procedure as fo r the floa t-derived map.

U sing h is to rica l hydrography. C K R find a s trong co rre la tion between the

G9

dep th o f the ( W y,., = —12.7 x 10 8 m 3/k g and p o te n tia l energy anom a ly ( \ )

re la tive to 2 0 0 0 db:C)db

X. = - J p t idp . (16)JOOO db

T h e b a ro c lin ic tra n s p o rt between two geographical po in ts is given by the d if

ference in p o te n tia l energy anom aly between the po in ts , d iv id ed by the C o rio lis

param ete r. Kearns [1996] also finds a s trong co rre la tion w ith the tra n s p o rt po

te n tia l ( ^ ) re la tive to lOOOdb. Using the pressure record from 6 S X A C floats

and the a forem entioned h is to r ica l re la tionsh ip . Kearns [1996] o b ta ins the fioa t-

derived tra n sp o rt p o te n tia l, a p p ly in g the same in te rp o la tin g and m app ing p ro

cedure as C 'KR T he resu lting m ap is shown in F igure IS.

To check the consistency o f the flo a t-G E M m ethod, we use a ll the floa t d a ta

from the X A C and AC'CE experim ents, and ca lcu la te w ith the technique the

pressure and tem pe ra tu re on the ta rge t specific vo lum e anom a ly surface used

in C 'KR . as w ell as the tra n sp o rt p o te n tia l re la tive to lOOOdb.

Since each floa t is associated w ith a s lig h tly d iffe ren t specific vo lum e anom aly,

the cu t o ff tem pe ra tu re needed in the X A C region w ou ld , in p rin c ip le , lie d iffe r

ent for each floa t. By look ing a t h is togram s o f tem pe ra tu re fo r a w ide range o f

f) surfaces (s im ila r to F igure 6 ). and the d is tr ib u tio n o f tem pe ra tu re versus '['.

we conclude th a t 3 .5 'C e ffective ly d e lim its the two modes o f the tem pe ra tu re

G E M fie ld.

For each floa t s ta tio n , the fu ll pro files o f specific vo lum e anom a ly and tem -

70


pe ra tu re are obta ined , using the day o f the year G E M fields constructed in

P erez-B run ius [2002c], as described in Section 2 . We then ca lcu la te the dep th

o f 6 tar get a t eacli s ta tio n , by lin e a rly in te rp o la tin g the specific vo lum e anom a ly

profile'. H av ing the dep th o f the ta rge t surface at a given s ta tio n , the correspond

ing tem pe ra tu re is ob ta ined from the s ta tio n 's tem pe ra tu re G E M pro file . The

p o te n tia l energy anom aly is derived from the specific vo lum e anom a ly pro files

using E qua tion LG.

We create ho rizon ta l maps fo r each season, separa ting the floa t s ta tions in

b ins three m onths long, centered in M arch (S p ring ). June (S um m er). Septem ber

(F a ll) , and December (W in te r) . T in* da ta are m apped onto a 0 .5 ' x0 .5 * g rid w ith

o p tim a l in te rp o la tio n , using a Gaussian co rre la tion fu n c tio n . To save com pute r

tim e , on ly d a ta po in ts w ith in a 5° w indow around the g rid po in t are used in the

in te rp o la tio n . Since o p tim a l in te rp o la tio n applies o n ly to variables w ith zero

mean, we have to remove a mean held from the data , and app ly the m ethod to

the residuals. The fina l held is the mean held plus the o p tim a lly in te rp o la te d

res idua l Held. To o b ta in the mean Held, a hrst pass o f the o p tim a l in te rp o la tio n

is app lied to the raw data , using a co rre la tion length scale o f 150km. fo llo w in g

W a tts et al. [2001]. We substraet the mean held from the data , and app ly the

o p tim a l in te rp o la tio n procedure to the residuals, using a co rre la tion leng th scale

o f 90km . The seasonal maps resu lt from add ing the residual held to the mean

held. The fina l maps are the mean over the fou r seasons, shown in F igures 19.

20. and 21. T h is ensures th a t a ll seasons have a pp ro x im a te ly equal weights for

71


the annual mean. O n ly g rid po in ts for w hich the e rro r in the o b je c tive m app ing

is less than 50% are shown. Note th a t we chose 90km as the a pp ro x im a te

co rre la tio n length scale for the o p tim a l in te rp o la tio n o f the residua l fie lds, since

i t corresponds to the zero crossing o f the co rre la tion fu n c tio n fo r th is region,

as ob ta ined from a ltim e te r d a ta [S tam m er. 1997]. In S tam m er [1997], the zero

crossing o f the co rre la tion fu n c tio n is given as a func tion o f the b a ro c lin ic rad ius

o f de fo rm a tion . The rad ius o f d e fo rm a tion for our region o f s tu d y is 10-20km

[C he ltou et al.. 1998). which corresponds to a zero crossing o f ~ 90km accord ing

to S tam m er [1997].

T he dep th o f ob ta ined w ith the flo a t-G E M technique com pares well

w ith the corresponding m ap produced by C 'KR (F igures 15.19). T in* largest

d ifferences occur in the region where the SPF crosses the M id -A t la n t ic R idge.

T h is region is where bo th the N A C and AC'CE float da ta overlap, w h ile i t is the

l im it o f the extent o f the N A C da ta used by C'KR. B o th factors m ay account

fo r the difference. A lso, the in te rp o la tin g techniques are ra th e r d iffe re n t, hence

sm a ll differences are to be expected. Note how b o th maps show a d is tin c tiv e

tro u g h (or eastward m eander) o f the N A C at 44°N.

The flo a t-G E M produced m ap o f tem pera tu re on Star,j,,t (F igu re 20) is harder

to com pan* to the correspond ing maps generated by C 'KR. The reason is th a t tin*

f lo a t-G E M tem pera tu re profiles are ob ta ined from the G E M p ro jec tio n s o f the

h is to r ica l hydrograph ic data , w h ile the spa tia l d is tr ib u t io n o f the tem pe ra tu re

fie ld is given by the floa t s ta tions. On the o the r hand, the c lim a to lo g ic a l m ap

72


o f F igu re 17 corresponds to an E u le rian average o f the h is to r ica l hydrography,

w h ile the floa t-de rived m ap o f F igu re 16 is derived from the a c tua l tem pe ra tu re

measured by the floats. We w ou ld expect the flo a t-G E M m ap to b e tte r com pare

to the c lim a to lo g ica l one. since the sm a ll scale features cap tu red by the a c tua l

measurem ent o f tem pera tu re o f the floats w ou ld be filte red o u t w ith the Hoat-

G E M technique. T h is is recognized from Figures 17 and 20. show ing pa tte rns

and ac tua l values th a t bas ica lly are the same. The m a jo r d ifference is found on

the trough o f the X A C a t 44CX . w hich is not present in the c lim a to lo g ica l m ap.

N ote th a t the m ap constructed w ith the ac tua l tem pera tu re o f the floats shows

th is trough , hav ing the same extension ;is the one in the flo a t-G E M map.

F in a lly , the tra n sp o rt p o te n tia l m ap constructed w ith the H oa t-G E M tech

nique (F igu re 21) shows the same basic p a tte rn and tra nsp o rts as the m ap

produced by Kearns [1996] (F igu re 18). The m a jo r difference is found in the

Northwest. C orner, where the flo a t-G E M map shows a more pronounced loop

than the m ap derived in Kearns [1996].

In conclusion, the H oa t-G E M maps agree well w ith s im ila r maps found in

the lite ra tu re , even though they are constructed in very d iffe ren t ways. The

differences found between e ithe r the C’K R or Kearns [1996] maps and the flo a t-

G E M maps are sm all considering th a t the in te rp o la tin g and averaging rou tines

used by us are d iffe ren t than those employed by the o the r au thors . A n o th e r

reason th a t m ay account for the differences, especially in the SPF region, is th a t

we use tw o datasets covering a much longer tim e period (1993-2000). instead o f

73


on ly the deep X A C floats (1993-1995) as in C’K R and Kearns [1996].

6. C onclusions

The flo a t-G E M technique presented in th is paper serves as a good to o l to ob

ta in in fo rm a tio n on the ve rtica l s tru c tu re o f the mean th ree -d im ensiona l hy

d rog raph ic fie ld, fo r the region and tim e period covered by the isopycna l floa t

experim en t in question.

\Ve tested the technique by reconstruc ting two C T D transects w ith s im u la ted

floa t data: one across the X A C near 4 2 'X. the o th e r across the SPF along

37"'\V. The flo a t-G E M reproduces sm oothed versions o f these transects. M ore

in te res ting ly , the b a roc lin ic transpo rts o f volume and tem pe ra tu re com puted

from the C T D transects are reproduced accurate ly by the technique. Hence,

the flo a t-G E M m ethod looks p rom is ing in m aking such estim ates in regions

where there is good Hoar da ta coverage.

We also checked the consistency o f the m ethod , by using real flo a t d a ta

to construc t h o rizon ta l maps o f tem pera ture and dep th o f the <) = —12.7 x

1 0 -Hm !/k g ( ~ 2 7 .5 (7 0 ) surface, as well as the tra n sp o rt p o te n tia l ( \ / f . re la tive

to lOOOdb). for the no rthe rn X o rth A tla n tic . S im ila r maps were construc ted

by C a rr et al. [1997] and Kearns [1996]. using a d iffe ren t m ethod w ith a subset

o f the float da ta used fo r the flo a t-G E M maps. The flo a t-G E M maps com pare

well w ith the maps in the lite ra tu re , the differences being sm a ll cons idering th a t

74

bo th the hydrograph ic and floa t da ta used are for d iffe ren t tim e periods and ex

perim ents. and the m ethodo logy and in te rp o la tin g rou tines d iffe r su bs tan tia lly .

The positive resu lts from b o th tests suggest th a t the f lo a t-G E M technique

can be succesfully used w ith the X A C and A C C E floa t data , to o b ta in estim ates

o f the ba roc lin ic tra nsp o rts fo r the X A C -S P F system.

In p rinc ip le , absolute transpo rts can be estim ated w ith th is technique, by

m aking use o f the ve loc ity d a ta measured by the floats. P erez-B run ius [2002a]

uses th is a p p lica tio n to es tim ate the absolute transpo rts o f mass and tem per

a tu re for the top lOOOdb in the X A C -S P F system. Moreover, they are able to

q u a n tify the heat lost by the cu rren t on its tra n s it towards the subpo la r X o rth

A tla n tic . Hence, the flo a t-G E M technique proves to be a pow erfu l too l to es

t im a te absolute tra nsp o rts fo r large regions, a llow ing float d a ta to be used ;is

rov ing hydrographers and cu rren t meters a t the same tim e.

I o


Specific Volum e A no m a ly (34.Gpsu. 4.9°C)

( 1 0 _'sm :!/k g )

Specific Volum e A nom a ly (35psu. 0 °C) t l 0 - Hm :,/k g )

P o te n tia l D ensity

(<t0 ± 0 .0 2 )

" ~ 70 = 142 26.G8 % 2G.7GO % 134 26.78 % 2G.S50 = 127 26.89 % 2G.940 ~ 119 2G.98 = 27.030 % 109 2 7. OS = 27.12 0 % 93 27. IS % 27.210 ~ S5 27.28 =s 27.30 ~ 1 1 27.38 « 27.4 |

- 1 0 ~ G4 27.48 % 27.5- 2 0 ~ 57 27.59 % 27.G |-30 % 43 27.G9 =2 27.7 [

Table 1 : L is t o f specific vo lum e anom a ly surfaces and th e ir p o te n tia l density analogues. Specific vo lum e anom aly values in the firs t co lum n are referenced to an in te rm ed ia te tem pe ra tu re (4.9°C ) and s a lin ity (.‘34.G psu). The second co lum n has specific vo lum e anom aly ca lcu la ted using the s tanda rd 0°Cand 35 psu values.

F lo a t # <>'(10- * m A/ k g ) F lo a t # <5(10 ani ‘i / k g ) A<>( l 0 ~ Hr n i / kg)

252 10.7 1.0 301 33.2 3.1259 15.9 21.7 303 10.3 4.72G0 11.0 1.1 304 50.0 0.92G1 8.5 2.3 305 4G.4 1.32G2 2.1 2.2 30S 49.1 1.2 j2G3 17.0 l.G 310 3G.0 2.G j2G4 1G.I 3.2 312 10.4 5.02GG 1.4 5.4 313 32.4 2.4 j2G7 8.2 2.0 31G 23.0 1.9 I275 18.0 1.9 3 IS 41.7 3.2 |27G | 13.G 0.7 322 1G.G G.3 j2SU | 5/J 2.G 324 21.7 2.9 I283 7.9 1.8 328 23.1 2.5 12S4 23.3 2.4 329 20.2 0.9 |2SG 28.G 1.5 330 31.9 2.1 i2SS 25.8 G.8 335 2G.G 1.4289 38.0 1.8 340 20.1 | 4.0 |

I 291 5.5 | G.7 344 21.7 j 1.3 || 292 3G.1 2.7 345 28.0 | 2.0i 293 ! 32.3 3.3 349 24.7 j 1.9| 294 | 14.7 2.9 351 24.8 j 2.7

I 1[i i 22.2 | 12.3 1 . . . 1 . . ........... 1

Table 2: B a llas tin g results fo r upper X A C floats. F loa ts 270. 273. 274. 279. 2S7. 323. 33G. 348 had no C T D cast taken at dep loym ent, hence th e ir specific vo lum e anom aly and ba llast e rro r correspond to the mean ( d / w ) find s tandard d e v ia tio n (n(<)/iollt )) . respectively.

F lo a t # 4(10 Hrn3/ k i j ) A r f ( io - 'sm-7C<;) F lo a t # A 4 ( lO -*m -7 A :y )

253 -28.9 1.5 309 -2.7 2.0 !255 -30.4 0.5 311 S.G 2.0 |25G -24.1 5.5 314 -19.5 2.2257 -13.0 1.4 315 -7.G 3.225S -18.0 0.4 320 -10.3 G .l2GS -23.2 2.3 321 G.3 4.0272 -17.7 1.4 323 0.2 0.7277 -22.S 0.5 32G 2.G * ) “J* j

2S2 -10.2 1.4 331 -7.0 1.4 |2S5 1.4 0.8 332 2.2 2.2 1295 -15.1 | 2.3 333 -3.0 3.G |29G 2.3 0.3 334 0.2 1.3 1298 -15.1 7.0 337 0.4 1.3 |300 i -8.8 3.5 339 -0.5 4.5 j30G -1.9 1.7 341 -8.2 2.S |307 j 12.4 4.8 342 55.5 2.3 |

[]_ 1 ^floot 17 ( f loot ) 1

ii i *0.2 15.5 | | 11

Table 3: B a llas tin g resu lts fo r lower X A C floats. F loats 254. 2G5. 269. 297. .'347 had no C T D east taken a t deployment., hence th e ir specific vo lum e anom a ly and ba llast e rro r correspond to the mean (<)//,„1() and standard d e v ia tio n {(r(SfimU)). respectively.

Float. # 6 { l Q - * m s/ k g ) A<5(10- *171*/ k g ) F lo a t # <5( / kg) A D 'flO - 'W /A .v y ) j

| 438 -15.2 0.7 544 -3.3 1.5 |440 -17.1 0.6 546 -5.1 2.G j448 -10.5 1.3 547 -3.6 0.5 |453 -3.8 3.6 54S -2.4 0.7459 -2.8 0.5 549 -G .l 1.44GG -8.G 0.3 550 0.1 2.7 |4G9 -S.7 1.3 552 -0.7 1.2 |475 -9.5 0.4 553 -3.1 1.8 j47G -13.4 1.3 554 1.7 0.4479 -1G.5 0.5 557 4.5 2.5480 -12.5 0.5 55S 3.5 0.5

j 497 -4.9 0.7 559 G .l 0.3502 -G.S 0.5 560 -0.6 1.3

j 510 1.9 0.4 5G1 -11.8 0.5i 530 -5.7 0.7 563 -G.l 1.4 !i 531 -5.G 0.7 564 -G.7 1.0 i

534 -9.0 0.6 5G6 4.0 4.7 |535 -3.0 0.3 569 -0.4 0.9 |530 l.G 2.3 570 -1.5 2.2

1 537 3.1 1.0 571 l.G o.7 ;j 538 0.3 0.6 572 -7.5 1.4 |; 539 -7.5 3.1 573 -0.1 1.5 ii 540 ! 5.G | 0.9 I 574 -9.3 1.5 ;! 541 | 1.5 | 0.4 1 575 -1.4 0.5 i! 542 1 - l - l I 1.3 j 57G -9.8 2.4 j

flotl t ) I 1-4.1 5.8 1

T ab ic 4: B a llas ting results fo r AC'CE floats. A ll floats had a C T D c;ist taken at dep loym ent. <)finat i*s the mean, and cr(S/i,mt) the s tandard d ev ia tio n .

60-

LS

TD

50-

FC

45-

-50 -45 -40 -35 -30 -25 -2 0 -15

Longitude ( 0 E)

F i l l in ' L: S tream fu n c tio n m ap for the N o rth A t la n t ic ob ta ined from R A F O S floats on the 27.5a 0 surface by Bower et al. [2002]. using o b jec tive analysis to o b ta in the m ap on a g rid made up by 111x111 km squares. C on tou rs are d raw n every 2 .5x 1 0 '!n r / s . D ynam ica l features: N A C -X o rth A t la n t ic C u rre n t: X W C -X o rth w e s t C orner: S P F -S ubpo la r Front. T opog raph ic features: M A R - M id -A t la n t ic R idge: F C -F lem ish Cap: C G F Z : C ha rlie G ibbs F ractu re Zone: R P - R ockall P la teau: IB - Ice land Basin: RR- Reykjanes R idge: IS- Irm in g e r Sea: LS- Lab rador Sea.

SO


'Y 4VI?

F igure 2 : D iag ram illu s tra t in g flo a t-G E M technique. (a) T he s tream fu iu 'tio u value vP/r,Vi.\r- correspond ing to the floa t s ta tion taken at t im e t f i „ al . is found by lo o k ing up the (pft,,,it- ^float) P<dr on the 6g fie ld, (b) Once x\! f g is know n. * y fie ld is used to o b ta in the corresponding p ro file o f p ro p e rty 7 f , j (p). p lo tte d in (c).

81

5 ( p . 'P . ts 1 ' (b)(u)

p ± A n* I * lit Ml

float

Figure 3: D iag ram illu s tra t in g the H oat-G E M erro r associated w ith e rro r in the floa t pressure measurement A p / ; („J(. (a) A set o f profiles o f 6 correspond to the in te rva l Pfi „ llt nr A Pfioat ')» the ta rge t isopycnal o f the floa t These profilesare associated to the stream func tion range 'FflJ ± A pVFf y. (h) S im ila r ly , a set o f profiles fo r ' are associated w ith th a t stream fun c tio n in te rva l, (c) Hence, the pro file ~.f,j has an u nce rta in ty bounded by the profiles " y(p. vF/,; 4 - A PvF /y ) and - y(p . 'F /(/ - A " 'F /y ).

82


(a) 5 (p.4M„ )g float' (b) y i p . f . t , iI! luut (ci y ip . 'f ' .t i£ Ij: le i l i u i

in ?\ \ \\K\ 'V'

i

VI1. N! i i\ i; i ii .\ i \ i \ .\ i

'v y ^\: 'N r1 \: ^

T tS 'Vtc t« V ±s^v

F i l l i n ’ 4: F lo a t-G E M e rro r due to unce rta in ty in fioa t ba llas tin g . See F igure 3 fo r descrip tion .

S3


Longitude (° E)

F igu re 5: Subregions selected fo r the cons truc tion o f the G E M fields. Dots represent h yd rog raph ic s ta tions from Hydrobase used [C u rry . 1996].

84


Pressure = 100db

20

15

10

5

0

53 5 6 7 84 9

Pressure = 200db

20 -

o

<D

CDQ.ECDI-

Pressure = 300db

20

Dynamic height (ref. to 1000db) in J/kg

Figure G: T em pera tu re versus dynam ic height a t various pressure levels, for the region o f the southern X A C (subregion 1 ). Note the b im o da l s tru c tu re o f the held for «E> < 5.1/kg. The triang les represent hydroeasts in the Lab rador C u rre n t, w h ile the dots are s ta tions taken w ith in the XAC '. The bo ld lines are the sp line fits fo r the G E M fields. For the case o f the w arm X A C waters, the line corresponds to the annual mean TtJ held, w h ile the h t fo r the co ld waters corresponds to the T ‘x Held.

85

Independen t RAFO S float data. 13457 stations

Spring 3560 stations Summer 2665 stations

60-

-

40 -j

-50 -40 -20-30 -10

65

60

55

r 50

45

1- 40

• V " .. " v .

V. 1 - \ pA , . - ...

)tr>O ' - V

-50 -40 -30 -20

1

-1 0

65

60

55

50

Fall 3170 stations

W . ’

W inter 4062 stations

A V •'

■v

45 - J 'lsJS t’ i:: v-

40

-50 -40 -30 -20 -1 0

65

60

55

50

45

40

-50 -30 -20-40

Longitude ( " E)

F igure 7: D is tr ib u t io n o f s ta tis t ic a lly independent R A FO S floa t s ta tio n s from the X A C (1993-1995) and A C C E (1997-2000) experim ents, fo r sp rin g (F cb rua ry - A p r i l) . sum m er (M ay-.Ju ly ). fa ll (A ugus t-O ctobe r). and w in te r (Xovem ber- .lanua ry ).

8 G


(a) Ag5 (10 ,SnvVkg)

0 C(b) Apn.u,5 (10 8rrd/kg)

500

1000

1500

500

1000

1500

<c> A^ii.jiS (10 ,sm'Vki:) (d) A lg5 (10 \n 7 k u )

500

1000

: -

1500

500

1000

1500

Dynamic height (ref. to lOOdb) in J/kg

F igure 8 : F lo a t-G E M errors fo r specific volum e anom aly in subregion G E M m ean-square e rror, (b) e rro r due to u n ce rta in ty in floa t pressure, (c) associated w ith floa t b a lla s tin g uncerta in ty , (d) is the to ta l f lo a t-G E M ( The bo ld line is the dep th o f the 6fioat = 3 x 10- 8 n rJ/k g .

87

H a )e rro r•rror.

1‘k'sm

iic Ui

ht

F iguredeta ils.

(a) AgT (°C ) g

(b) APii.miT ( °C)g

0.8

500

1000

15004 5 6 7

500

1000

15004 5 76

(c) A n.uiT ( C) g

!0) A,gT ( "C)

o

500

1000

1500 4 5 76

5000 6

1000

15005 6 74

Dynamic height (ref to lOOdh) in i/kg

9: F lo a t-G E M errors fo r tem pera tu re in subregion 4. See F igu re 8 for

88


65

RN Knorr section : .. Summer 1998

0 ... £ ■ < * ’

c *'R/VOceanus section A- "Summer.1993

60

55

Zo

•a 50 3

as_i

45

40

35- 5 5 -5 0 - 4 5 -4 0 -3 5 -3 0 - 2 5 - 2 0 - 1 5 - 1 0 - 5

Longitude (° E)

F igure 1 0 : C T D transects across the X A C ( R /V Oceanus). and SPF ( R /V K n o rr). used to test the flo a t-G E M technique. The G E M fie lds used correspond to subregions 1 . 4. and 7 co n ta in ing the C T D transects.

89

R/V Oceanus sectionOGaOOOCO o o ooo o o o ^■»tao—wSn /C ====^2£c~.

100

200

300

400

500

600

700

800

900

- 1 0 0 0200 400 600

Float-GEM section-gsBpppe e- o o ooo o o o

70-=== »sn 13Q-;100

r\\0 - &P200

300

400

500o 70

600

70040

800

900

1000200 400 600

3

Error associated with Difference between the real:) float-GEM section0 1—QGDODOgO O O 9 0 -0- 0 0 - Or-

7 5 e - aL 4' ''----

and float-GEM sections

Distance (km )

F igure 1 1 : Specific vo lum e anom aly transect across the X A C . The bo ld conto u r represents the dep th o f the ta rge t specific vo lum e anom aly Sfi<mt = — 1 0 x 1 0 ~ *u r5/k g . and the dots are the s im u la ted floa t pressure measurements. D istance is measured from the westernm ost s ta tio n , (a) C T D section, (b) S im u la ted f lo a t-G E M section, (c) flo a t-G E M errors fo r (b ). (d ) d ifference between (a) and (b ).

90

(a> R/V Knorr sectionO P O O g tg :

100

200

300

400

500

600

700

800

900

200 400

float—GEM section^ e o 0 0*0,0

•jn . . ' u err100

30

200

300

400

500 .-1

600

700

800

900

10000 200 400

Error associated withfloat-GEM section

G 0 0 3 0 0 —_ O O /O O O O 12- -4-., 5 ' 6 5

100

200

300-

400

,-3-500

600i f - 2 -

700

800

900

1000200 400

Difference between the real and float-GEM sections

■O O O O O ' O O Q<0 QJ? Q-6 -

1000400

Distance (km )

Figure 12: Specific vo lum e anom aly transect across the SPF. See F igure 11 for descrip tion . D istance measured fron t the n o rthe rnm ost s ta tio n .

91

(a) R/V Oceanus section (b) float-GEM sectionOGSODOOO O O O O O O O O

s 6100

200

300

400

500

600

700

800

900

1000200 400 600

100

200

300

400

500

600

700

800

900

1000200 400 6000

Error associated withfloat-GEM section

-0 - - Q o o o o

® T3*100

200

300

400

500 r

600

700

800

9000.8

1000200 400 600

Difference between the real and float-GEM sections

600Distance (km )

F igu re l-‘i : Tem pera tu re transect across the X A C . T he ho ld con tou r represents the dep th o f the target specific volum e anom a ly df[oat = - 1 0 x 1 0 _8 m i /k g . and the chits are the s im ula ted floa t pressure measurem ents. D istance is measured from the westernm ost s ta tion , (a) C T D section, (b ) S im u la ted flo a t-G E M section, (c) flo a t-G E M errors for (b ). (d) d ifference between (a) and (b).

92


R/V Knorr sectionOOO O' 0 - 0

100

200

300

400

500

600

700

800

900

1000200 4000

b) float-GEM sectionob o 9 -0 . 0 O'

1000400

(C)

Error associated with float-GEM section

OO O O O O O O O O O O O <y

300 -

Difference between the real and float—GEM sections

iq>o e-§>-o o .p o— o; o o o o

Distance (km )

F igu re 14: T em pera tu re transect across the SPF. See F igu re 13 for detia ls . D istance measured from the northe rnm ost s ta tion .

93

Median Depth on -12.7 for 1993-1995 (m)

-55' -50* -45* -40 ' -35' -30'

F igure 15: Pressure (db) o f the <) = —12.7 x 10~8 rn i /k g surface ob ta ined from the deep floats o f the X A C experim ent [C a rr et ah. L997j. C on tou r in te rva l 50(11).

94

Median Temperature on -12.7 for 1993-1995, all depl (C)

-50" -45' -}()• -35' -30'

F igu re 1G: T em pera tu re (CC) u f 6 = —12.7 x 1 0 _8 m !/k g surface ob ta ined from tem pe ra tu re d a ta measured by the deep floats o f the X A C experim ent [C a rr et ah. 1997], C o n to u r in te rva l 0.25’ C.

95


Temperature on -12.7 for all seasons (C)

50'

40'

*30’-40*

F igu re 17: C lim a to lo g ica l tem pera tu re C O on the ri = -1 2 .7 x 10_Mm J/k g surface ob ta ined from -10 years o f h is to r ica l b o tt le da ta [C a rr et a l.. 1997], C o n to u r in te rva l O .VC .

96


Float-derived PEA ref to 1000 m

60 60

-40’

F igu re IS: T ra n spo rt p o te n tia l (rc l. to lOOOdb) its derived from GS X A C floa ts ' pressure records [Kearns. 1996]. The d ifference between con tou r values is a measure o f tin* mass tra n sp o rt between those contours (in 10<Jkg /s Sv). C o n to u r in te rva l 2 Sv.

97

50

40

50 •45 •40 35 30

Longitude ( °E)

F igure L9: Pressure (dh) o f the <) = —12.7 x L0-Hnv{/k g surface ob ta ined by appdving the flo a t-G E M technique to the X A C and A C C E floa t da ta . C on tou r in te rva l 50db.

98

5 0 -

Z

u•a

J

Ao

40

50 ■45 •40 35 30

Longitude ( °E)

F igure 20: T em pera tu re o f <) = —12.7 x 10_8 m '/k g ob ta ined by a p p ly in g the f lo a t-G E M technique to the X A C and AC'CE float da ta , contours are shown every 0 .2 T C .

99

50 -

4 0 -

-5 0 -4 5 -3 5 -3 0-4 0

Longitude ( °E)

F igu re 21: T ra n spo rt p o te n tia l (re l. to lOOOdb) as derived by a p p ly in g the f lo a t-G E M technique to the X A C and AC'CE floa t da ta . The difference between co n to u r values is a measure o f the mass tra n sp o rt between those contours (in 1 0 °k g /s ~ -l Sv). C on tou r in te rva l 2 Sv.

100


C hapter 3

A b so lu te transports of mass and tem perature for the N A C -S P F system

A bstract

Tlu> flow o f sub trop ica l waters carried in to n o rthe rn N o rth A t la n t ic by the

N o rth A tla n tic C u rren t-S ubpo la r Front (N A C -S P F ) system is an im p o rta n t

com ponent o f the m erid iona l o ve rtu rn in g c ircu la tio n . These w aters become

co lder and denser as they flow th rough the subpo la r region, bo th by m ix in g w ith

th(> co lder subpo la r waters and by a tm ospheric coo ling . The re la tive roles o f

these tw o processes rem ain to be quan tified , and the mechanisms d r iv in g la te ra l

m ix in g need to be b e tte r understood. To address those questions, know ledge

o f the absolu te transpo rts o f mass and heat carried by the N A C -S P F cu rren t

is needed. In th is s tudy we estim ate the mean absolu te tra nsp o rts o f mass and

heat fo r the top lOOOdb in the region o f the N A C -S P F system for the tim e period

1993-2000. The transpo rts are obta ined by com b in ing h is to r ica l hyd rog raphy

w ith isopycnal R A FO S floa t da ta deployed in the area. The mean absolu te

tra n s p o rt p o te n tia l fie ld shows a N A C -S P F "p ip e ", defined by tw o bound ing

tra n s p o rt p o te n tia l contours. T h is p ipe transpo rts 15.0±3.1 Sv (to p lOOOdb)

101


fro m the subtrop ics in to the eastern subpo la r N o rth A tla n tic . The n o rth w a rd

flow ing X A C follows a d is tin c t m eandering pa th , w ith no evidence o f perm a

nent branches peeling o ff the cu rren t before reaching the N orthw est C orner. As

the cu rre n t enters the N orthw est Corner, i t appears to s p lit in to two branches,

w h ich toge ther co ns titu te the eastward flow ing SPF. The flow bewtween the

N orthw est C orner and the M id -A t la n t ic R idge is no t as well defined: the b road

ening o f the N A C -S P F p ipe in th a t transect suggests a divergence o f the tw o

branches. F in a lly , the two branches converge to cross the M id -A t la n t ic R idge

above the C ha rlie -G ibbs and Faraday Fracture Zones. We ca lcu la te the abso lu te

tra n s p o rt o f tem pera tu re (top lOOOdb) across seven transects crossing the N A C -

SPF "p ip e ". Since mass is conserved in the pipe, changes in the tem pe ra tu re

tra n sp o rts are due to la te ra l exchange and m ix in g across the p ipe's side walls,

and to air-sea fluxes across the surface o f the pipe. The N A C -S P F cu rre n t loses

0 .27±0 .00 P \V on its tra n s it th rough the region. T h is loss is much la rger than

the correspond ing heat lost to the atm osphere. We conclude th a t cross-fron ta l

exchange induced by the steep meanders o f the no rthw a rd flow ing X A C is the

m a in mechanism by which heat is lost a long the cu rren t. N early a ll the heat

lost by the X A C occurs between the crest inshore o f the M ann E ddy (~ 4 2 .5 CX ).

and the 4-T X trough , due to a d e tra inm en t o f w arm w ater in to the su b tro p ica l

side and an en tra inm en t o f cold w ater from the subpo la r side o f cu rren t. P art

o f th is w arm w ater feeds the re c ircu la tion o f the M ann Eddy, and the rest is

lost in to the basin in te r io r, p robab ly d iffus ing back in to the su b tro p ica l gyre.

102


1. Introduction.

The N o rth A tla n tic C u rren t-S ubpo la r F ron t system (N A C -S P F ) serves as the

m ain co nd u it o f w arm and sa lty w a te r in to the subpo la r N o rth A t la n t ic . No

o the r ocean cu rren t in the w orld brings w ater from the subtrop ics to such h igh

la titudes . I t constitu tes the upper lim b o f the the rm oha line c irc u la tio n o f the

N o rth A tla n tic Ocean, p lay ing a c ru c ia l ro le in m odera ting the c lim a te o f n o r th

ern Europe*, and most like ly has im p o rta n t im p lica tio n s fo r the general c ircu

la tio n o f the atm osphere over a la rger region o f the no rthe rn hem isphere [e.g..

Krauss. L9S6: Bower et al.. 2000: Rossbv. 199G]. M uch o f the w a rm -to -co ld wa

ter p re con d ition in g th a t a llows for deep convection in the Lab rador and N ord ic

Seas takes place in the subpo la r N o rth A tla n tic . On th e ir tra n s it th rou g h the

subpo la r region, the sub trop ica l waters transpo rted by tin* N A C -S P F cool and

freshen by m ix in g w ith the adjacent subpo la r waters and th rough w in te r con

vection [M cC artney A Talley. 1982]. There is s t i l l much to be understood on

the processes th a t transfo rm the su b tro p ica l waters in to in te rm ed ia te and deep

waters a t h igher la titudes , and the re la tive role o f la te ra l m ix in g versus a tm o

spheric coo ling needs to be quan tified .

The N A C -S P F is an extension o f the G u lf S tream , tu rn in g no rthw ards at

the T a il o f the G rand Banks. S ta rtin g as a narrow and sw ift n o rth w a rd cu rren t,

the N A C -S P F evolves in to a broad and weak flow once it tu rns east past the

N orthw est C orner (F igu re 1 ). M uch o f our knowledge o f the mean c irc u la tio n in

103


the su bp o la r N o rth A tla n tic comes from hydrograph ic studies, suggesting th a t

the b road eastward flow consists o f sm a lle r ba roc lin ic fronts, h ig h ly va riab le

in space and tim e [e.g.. D ie triech et ah. 1980: Sy. 19S8: A rhan . 1990: B e lk in

Hz Lev itus . 1996]. I t is believed th a t these fron ts result from s p lit t in g o f the

n o rth w a rd flow ing N A C -S P F (a t locations and frequencies yet unce rta in ). Some

au tho rs suggest th a t the fron ts o rig in a te upstream o f F lem ish Cap [D ie triech

et ah. 1980: K rauss et a l.. 1987]. w h ile others propose the s p lit t in g occurs a t or

past the N orthw est C orner [Sy. 1988: A rhan . 1990: Lazier. 1994].

Lag rang ian d rifte rs have also been used to s tud y th is system. The isopycnal

floa t stud ies reveal a h ig h ly s tru c tu re d and localised eddy k in e tic energy fie ld.

T he h ighest levels o f eddy k in e tic energy are found around the no rth w a rd flow ing

N A C -S P F . decreasing sha rp ly to the east, even a t the la titu d e o f the b a ro c lin ic

eastward flow [C a rr N' Rossbv. 2001: Bower et ah. 2002]. The no rth w a rd flow

shows a p a tte rn o f top o g rap h ica lly fixed meanders [Rossbv. 19961. whose am

p litu d e shows flu c tu a tion s o f ~ 150km [Kearns Rossbv. 190S]. Bower et al.

[2002] cons truc ted the absolute stream fun c tio n on the 27.5 rr0 surface, using

the ve lo c ity measured by a large num ber o f isopycnal R AFO S floats deployed

in the region as p a rt o f the A tla n tic C lim a te Change E xperim en t (F igu re 1).

T h is m ap shows a ra the r d iffe ren t c ircu la tio n p a tte rn than the one suggested by

the mean hydrog raph ic fie ld. O n th is density surface, i t suggests no s p lit t in g o f

the N A C -S P F upstream o f the N orthw est C orner, and a subsequent d iffiuence

and re-confiuence enroute to where the eastward flow crosses the M id -A t la n t ic

104


Ridge (M A R ) th rou g h the region o f the Faraday and C ha rlie -G ibbs F racture

Zones.

The d iscrepancy between the mean pa tte rns o f the b a roc lin ic flow (i.e .. de

rived pu re ly from hydrog raphy) and the absolu te flow suggests th a t, in o rde r to

get an accurate view o f the mean c irc u la tio n and tra nsp o rts fo r the region, d irec t

m easurem ents o f the How are needed. Few estim ates o f the absolu te tra n s p o rt o f

the cu rre n t are availab le. M einen & W a tts [2000) ob ta ined the absolute trans

p o r t ca rried by the n o rthw a rd Howing N A C -S P F a long a transect o f moored

cu rre n t m eters and Inverted Echo Sounders (near 42.5°N ). using a m ethod th a t

com bines the acoustic trave l tim e measured by the Inverted Echo Sounders w ith

h is to r ica l hyd rog raphy (called G ravest E m p irica l M ode, or G E M ). T h a t s tudy

is the firs t th a t provides a long te rm mean o f the absolu te volum e tra n sp o rt o f

the N A C -S P F (14G Sv. in c lu d in g a p o rtio n o f the M ann E ddy). There are few

estimate's o f the absolute' transpo rts o f the cu rren t dow nstream e ) f th is loca tion ,

w ith the exception e ) f the tra n sp o rt estim ate from cu rren t meters across the

N orthw est C orner reported by Lazier [1994] (50 Sv). and the eastward trans

p o rt fo r the twe> n o rth e rn branches o f the S ubpo la r F ron t near the C ha rlie -G ibbs

F racture Zone obta ined by B ubno \ [1995] (10S Sv). Tem pera tu re tra n s p o rt es

tim a tes are even scarcer. No a tte m p t to ob ta in dow nstream changes o f the

tra n s p o rt and heat fluxes o f the cu rren t has yet been made.

P erez-B run ius [2002b] developed a technique (ca lled f lo a t-G E M ) w h ich com

bines the pressure measured by isopvcnal floats w ith h is to r ica l hydrography, in

105


a s im ila r fashion to the G E M m ethod firs t app lied by M einen & W a tts [2000].

T he f lo a t-G E M technique can be used to o b ta in the mean three d im ensiona l

tem pe ra tu re and density fields (hence the b a roc lin ic ve loc ity fie ld ) fo r the tim e

pe riod o f the floa t experim ent. B y m ak ing use o f the ve loc ity measured by the

floats, the absolu te ve loc ity fie ld , and hence the absolute tra nsp o rts o f vo lum e

and tem pe ra tu re , can be estim ated.

T h is paper applies the flo a t-G E M technique to two isopycnal R A TO S floa t

experim en ts , carried ou t between 1993 and 2000. to o b ta in the mean absolu te

tra n s p o rt p o te n tia l fie ld in the N A C -S P F region fo r th a t tim e period . T h is m ap

is used to select the tra n sp o rt p o te n tia l isolines defin ing the cu rre n t, th a t is.

the boundaries o f the "p ipe " o f w arm w ater flow tha t brings waters from the

G u lf S tream in to the Eastern S ubpo la r N o rth A tla n tic . We then select seven

transects across the N A C -S P F . and o b ta in the transpo rts o f tem pe ra tu re co r

respond ing to the NAC '-SPF "p ip e ". Note th a t by selecting isolines o f absolu te

tra n s p o rt p o te n tia l as boundaries fo r the cu rren t, we ensure th a t imiss is con

served a long the pipe. T h is a llows us to estim a te the heat gained o r lost by the

cu rre n t on its tra n s it tow ards the subpo la r N o rth A tla n tic . The heat fluxes are

o f great in te rest from a c lim a tic p o in t o f view .

We w il l use specific vo lum e anom a ly (d) in th is paper, since h-surfaces are

b e tte r a pp rox im a tions to neu tra l surfaces tha n the more com m on ly used po ten

t ia l dens ity (<70) (M cD ouga ll [1989]). A lso, w o rk in g on specific vo lum e anom a ly

surfaces a llows fo r the a p p lica tio n o f the flo a t-G E M technique, since isopycnal

106

R A F O S floats fo llow specific vo lum e anom a ly surfaces m ore closely tha n they

fo llo w p o te n tia l density surfaces [C a rr et a l.. 1997], To help the reader. Tab le 1

shows various 6 surfaces and th e ir correspond ing a 0 coun te rpa rts . T he 6 values

are referenced to 34.6psu. and 4.9°C . w hich are mean values fo r the reg ion o f

the X A C -S P F [Kearns. 1996].

2. D ata and m ethods

2.1 F loat-G E M profiles

We describe next, how the H oa t-G E M technique [Porez-B runius. 2 0 0 2 b] is ap

p lied to isopycnal R AFO S floa t d a ta and G ravest E m p irica l M ode (G E M ) p ro

je c tio n s o f h is to rica l hydrog raphy availab le for the region. A R A F O S floa t is

an acous tica lly tracked, n e u tra lly buoyant d r if te r . A lth o u g h it is com m on ly

ca lled an isopycnal floa t, in re a lity it tends to fo llow a specific vo lum e anom a ly

surface [C a rr et ah. 1997]. A G E M fie ld is a p ro jec tio n on geostroph ic s tream

fu n c tio n space o f hydrograph ic d a ta [Sun lX W a tts . 2001]. I t captu res m ost o f

the v a r ia b ility in the hydrog raph ic fie ld , since ho rizon ta l m o tions o f large scale

s tru c tu re s are s t if f in the ve rtica l.

The float da ta come from tw o isopycnal R A FO S float experim ents: the

X A C experim ent (1993-1995). and the A tla n tic C lim a te Change E xpe rim en t

(A C C E . 1997-1999). b o th w ith the floats targeted fo r rr0 =27 .5 (m ean <)f —

107

— 5 x 1 0 _8 m i /k g ) . We use 33 floats from the X A C experim ent, deployed d u r in g

three d iffe re n t cruises th a t took place in Ju ly -A u g u s t 1993. Xovem ber-D ecem ber

1993. and O ctober-X ovem ber 1994. P rogram m ed to sample for 300 days, the

floats co llected pos ition (and hence ve lo c ity ), tem pera tu re , and pressure d a ta

tw ice a day [Anderson-Fontana et ah. 199G].

F rom tlit* AC’C E experim ent, we use d a ta from 50 floats, deployed across

the SPF d u r in g tw o cruises th a t took place in Xovem ber 1997. and J u ly 1998.

These floats sam pled pos ition (and hence ve lo c ity ), tem pera ture , and pressure

once a day. and th e ir m issions were 540 days long [Anderson-Fontana et ah.

2001: Porez-B run ius. 2002b],

T he ve loc ity , tem pera tu re , and pressure records o f bo th datasets wore f i l

tered by using a ru n n in g mean average w ith a w indow o f 7/. = 2.5 days. 77.

corresponds to the Lagrangian co rre la tion tim e scale derived for the region by

Zhang et ah [2001]. The da ta were then subsam pled every 2.5 days, to ensure

s ta tis t ic a l independence o f the float d a ta [jo in ts . The com bined ACC’E and

X A C d a ta resu lt in 27.GIG floa t "s ta t io n s ', shown in F igure 2 .

We use m o n th ly specific vo lum e anom a ly Sg(p. <F.>on) and tem pe ra tu re Tg(p. <F_>on)

G E M fields constructed by P erez-B run ius [2002c]. using more than 70 years o f

h yd rog ra p h ic d a ta from Hydrobase [C u rry . 199G]. The variab le p is pressure,

and Tjoo is the dynam ic height a t 200db (referenced to a lOOOdb) defined as

10S

'.>00 <lb

d’ joo = ~ j 6dp. ( 1 )1 ()00</6

chosen as the geostrophic stream func tion on which to p ro jec t the h yd rog raph ic

da ta . The in teg ra l lim its are chosen so as to m axim ize the num ber o f b o tt le and

C T D d a ta used (lOOOdb deep casts), and to reduce the seasonal effect on the

ca lcu la tio n o f dynam ic height, since the largest seasonal signal reaches dow n to

200-250db [Porez-B run ius. 2002c]. The G E M pro jec tions wore construc ted for

several regions in the subpo la r N o rth A tla n tic , shown in F igu re 3.

The flo a t-G E M technique uses the specific vo lum e anom aly G E M fie ld as a

lo o k -up tab le to estim ate the value o f ‘hjoo at each floa t da ta point.. The value

o f ‘1*200 ts chosen so tha t it agrees w ith the known specific vo lum e anom a ly

o f the float and its measured pressure p / ( = p(<)/)) [Perez-B runius. 2002b], In

o th e r words, we look up the value o f the geostrophic stream fun c tio n ‘I*200 / for

w h ich (i,,(/</. T 200 / ) = d/- Once T 200/ is know n, the correspond ing tem pe ra tu re

p ro file a t the floa t da ta p o in t may bo estim ated by the tem pera tu re G E M fie ld :

(p ) = T,j{p. ‘1*200/)•

A p p ly in g the flo a t-G E M technique, profiles o f tem pera tu re T ( x . t j . p ) and

specific vo lum e anom aly <)( . i : . i j .p ) are ob ta ined a t each float s ta tio n (a'./y).

The floats independently measure the ve loc ity a t the <)/ surface o f the floats

\ '[{.v. p. p (6 ( ) ) . From the specific vo lum e anom aly profiles, the M on tgom ery

109

stream fun c tio n F I/, referenced to lOOOdb. is ca lcu la ted on the 6f surface:

PfJ Mp- (2)lO O O .ft

where p j is the pressure o f the floa ts ’ surface Sj. D iv ided by the C o rio lis pa ram

e te r / . the M on tgom ery stream fun c tio n gives the baroe lin ic geostroph ic s tream

fu n c tio n on the surface o f the floats [M cD ouga ll. 1989]

The baroe lin ic stream func tion a t a given pressure level /; (re la tive to lOOOdb)

is given by

lUOOrfb

We also ob ta in the p o te n tia l energy anom aly \ (referenced to lOOOdb):

ihlb

\ = - / pddp. (5)lOOO./fc

w hich d iv ided by r,h<* C o rio lis param eter / gives the baroe lin ic tra n sp o rt po ten

t ia l for the top lOOOdb (in kg /s )

As a residt. we have the fo llow ing flo a t-G E M d a ta se t ~= { A(/ j ). T (p ) . \ / ( ( ) /) .

where p ranges th rough the ve rtica l p ro file , a t each o f

the 27.616 floa t s ta tions o f F igu re 2.

(3)

(0)

1 1 0

2.2 PIE S section at 42°N

We w il l use the results from an earlie r a p p lica tio n o f the G E M technique, im p le

m ented on a line o f moored ins trum en ts across the X A C at ~ 42.5°X . w h ich co l

lected d a ta from A ugust 1993 to A p r il 1995 [C la rke et ah. 199G]. I t consisted o f

e ight ta l l cu rren t m eter m oorings, as w ell as s ix PIESs (Inve rted Echo Sounders

equ ipped w ith b o tto m pressure sensors). M einen &: W a tts [2000] ob ta ined fu ll

w ater co lum n profiles o f tem pera tu re and specific vo lum e anom aly, by com b in

ing G E M pro jec tions w ith acoustic trave l tim e measured by the PIESs. T hey

also ob ta ined absolute geostrophic ve loc ity profiles, using da ta from the b o tto m

pressure sensors and deep cu rren t meters to reference the ba roe lin ic ve locities

derived from the 6 profiles. As a resu lt, they produced d a ily snapshots o f abso

lu te ve loc ity , specific volum e anom aly, and tem pe ra tu re fields across the X A C .

These fields were then averaged in tim e , in stream -w ise coord inates [M einen.

2 0 0 1 j . th a t is. by centering each snapshot on the ve loc ity core o f the cu rren t

[H a lk in Ross by. 1985]. We w il l use th is section as a "co n tro l" to check the

results o f the flo a t-G E M technique, fo r a s im ila r tim e in te rva l.

2.3 O bjective analysis

We seek to o b ta in the mean fields o f the f lo a t-G E M derived da ta { r~(.r. //. p ) }

on a selected geographical g rid { x , . / / , }. The general procedure is as follows.

F irs t, we b in the flo a t-G E M data on a n ° x n ° g r id covering the region o f in

terest (.Cfj.i/i,). resu lting in ^ ( . c The s tandard dev ia tio n o f the da ta in

111


each b in is com puted ~pMu(xb, yb, p): i t provides a measure o f the v a r ia b ility not

resolved by the b inn ing . To in te rp o la te the results in to e m p ty bins, as well as

to get a sm oo ther fie ld, we use m u lt iv a r ia te ob jec tive analysis (O A ) fo llo w in g

the procedure suggested in W a tts et al. [2001]. The covariance fu n c tio n fo r the

O A is assumed to be a Gaussian w ith an e -fo ld ing length scale o f R. We app ly

a firs t pass o f the O A . using R b as the co rre la tion length scale, to o b ta in a

sm oo th "background" fie ld ^ blJ{x b. i/b, p). T h is mean fie ld is sub trac ted from the

observations, and the residuals are ob ta ined

r - r r . s ' r ' r b i j •

and a p p ly in g a second pass o f the O A to ^ r, w i t h RT < Rb to resolve the sm alle r

scales, the residual fie ld is m apped on the desired g rid { . r , . / ; , } . S tam m er [1997]

ca lcu la ted the reg ional covariance func tions for the A tla n tic from a lt im e te r data,

and found th a t the zero crossing o f the covariance functions is a fu n c tio n o f the

rad ius o f de fo rm a tion . The rad ius o f de fo rm a tion for our region o f s tudy is

a round 20-‘30km [C helton et ah. 1998]. which corresponds to a zero crossing o f

~ 9 0 km . We use th is value as the app rox im a te co rre la tion leng th scale R fo r the

region.

The fina l fields are then given by:

r ( r . • Hi -P) = Ph., ( • U, ■ P) + Prr, !h ■ P) ■

N ote th a t the O A technique is a linea r es tim a to r, hence we can o b ta in the

es tim a te o f a linea r ope ra to r app lied to ^ from the same in p u t da ta [B re th e rton

112

f t i l l . . L97G]. T h is a llows us to o b ta in the absolu te stream func tion fie ld a t the

6/ surface o f the floats V1/ a(p (d f) ) . using the floa t ve lo c ity da ta \ } . assum ing

th a t the flo a t's ve loc ity is the absolu te geostrophic ve lo c ity on its ta rge t surface

Since b o th the ba roe lin ic and absolu te geostrophic stream functions ( fybc{p(d j ) .

KVa{p(d f ) ) on the 6 j surface o f are sam pled a t the same tim e and p os ition , and

in te rp o la te d in the same m anner, i t is reasonable to o b ta in the absolu te stream

fu n c tio n a t the' reference level by using 'l>b,:(p (d f) and '&“ (/.)(<>/)

^ bt = ^ , l ( Sf ) - ^ hr{i)f ) . (7 )

where 'I/1'' is the "b a ro tro p ic " stream fun c tio n . B y "b a ro tro p ic " we mean the

stream fu n c tio n representing the absolu te ve loc ity fie ld at the LOOOdb reference

level. T h is b a ro tro p ic stream fun c tio n needs to be added to the b a roe lin ic

s tream fu n c tio n to o b ta in the absolu te stream fun c tio n fie ld at a ll pressure

levels sam pled. Hence1, the absolute stream func tion at any pressure p is

T " ( p ) = ^>hr( p ) + T ' ;t . (S )

and ou r focus is upon p < lOOOdb.

F u rthe rm ore , the absolute tra n sp o rt p o te n tia l fo r the top LOOOdb can

be ca lcu la ted :

Qumo = Qioon _r Qiooo- (9)

where

Qi<m = p D * bt (LO)

113

is the "b a ro tro p ic " tra n sp o rt p o te n tia l. D = 1000m the height o f the w a ter

co lum n, and p the mean density o f the w a te r co lum n {p = 10'27kg/m3). B y

"b a ro tro p ic " we mean the tra n sp o rt fo r the top lOOOdb obta ined fro m the

b a ro tro p ic ve locity. Note th a t we are using the fact th a t ld b corresponds to 1m

w ith in V X . T he tra n sp o rt po ten tia ls have un its o f kg /s in the SI system . We

w il l use mass-Sverdrups (109 kg /s correspond ing to 1 0 f,m 3 / s = lS v w ith in abo u t

3%) as the u n it to represent these transpo rts .

T he abso lu te and baroe lin ic ve locities ( I \ 'h,' (p)) are derived from the

co rrespond ing stream functions:

= ( r ; \ \ ; / ) . v * = t r f . v f ) . ( i i )

w tiere

d T " d ' V Lr ° = . r ° = . ( I T

Oy w Ox 1

and

, d'Vhr , O' vhr\ >r = -----------. I = . (13)Op " Ox

F in a lly , the tem pera tu re transpo rts ( H 100o) across a section is g iven by:

l O O O r f i

= / ;C p j f \ \ T d l d z . (14)

l O O O r f i

^lUOOOm .si.Tfrari

where / is the d istance along the section, c is dep th . \ ] the ve loc ity p e rpend icu la r

to the section, and C’p the specific heat o f seawater. We use C p = 4 x lO hJ/kg^C .

and p = 1027kg /m 3. The baroe lin ic and absolu te tem pe ra tu re transpo rts are

es tim a ted from E qua tion 14 using the co rrespond ing ve locities.

114


3. A b solu te transport m aps

O u r purpose is to dete rm ine the heat gained o r lost by the X A C -S P F cu rre n t

in its tra n s it from the subtrop ics in to the subpo la r region on the top lOOOdb o f

the w a te r co lum n. T h is necessitates de fin in g the edges o f the cu rren t, th a t is.

spec ify ing boundaries to the flow o f w arm w a te r th a t enters the region a t the T a il

o f the G rand Banks and leaves i t crossing the M id -A t la n t ic Ridge, south o f the

Rev k j a nos Ridge. Hence, we proceed to ca lcu la te the baroe lin ic . b a ro tro p ic . and

abso lu te tra n s p o rt po ten tia ls fo r the region whose bounds are (50 °\V .25°\V ) and

(-10aX .55 °X ) by a p p ly in g the in te rp o la tin g m ethod described in Section 2.3 to

the flo a t-G E M da ta described in Section 2.1. The fields are binned on a l c x 1°

g rid {./'/,.///,} covering the region, and m apped on to the same g rid , a p p ly in g the

O A technique w ith Ri, = 300km for the background fields, and R r = 150km for

the residual fields. S tam m er [1997] ca lcu la ted the reg ional covariance func tions

for the A t la n t ic from a ltim e te r da ta , and found th a t the co rre la tion length scale

is a fu n c tio n o f the rad ius o f de fo rm a tion . The rad ius o f de fo rm a tion fo r ou r

region o f s tudy is around 20-30kin [C he lton et a l.. 1998]. which corresponds to

a co rre la tio n length scale R o f ~ 90krn . T he leng th scales are purpose ly chosen

la rger than the co rre la tion scale correspond ing to th is region, since we w ant a

sm oo th m ap on w hich the largest features are enhanced. F igure 3 shows the

num ber o f floa t d a ta observations per b in . N ote th a t a ll transpo rts reported

here on correspond to the top lOOOdb o f the w ater co lum n.

115


3.1 Baxoclinic transport p oten tia l

T he re su lting ba roe lin ic tra n sp o rt p o te n tia l fie ld Q^ooo(x 6- fib) for the top lOOOdb

is shown in F igure 6 . The dark tra n sp o rt lines, correspond ing to Q ^ )00 = 22.5 Sv

and 37.5 Sv. are shown as boundaries o f the flow ente ring the region a t the T a il

o f the G rand Banks, and co n tin u in g eastwards tow ards the MAR.. The e rro r o f

Q umo *s 1-3 Sv (see A pp e nd ix 3).

F igu re G suggests a broadening o f the no rthw ard flow ing X A C th a t s ta rts to

occur upstream o f F lem ish Cap. and continues as the cu rren t approaches the

N orthw est Corner. The ba roe lin ic fie ld has been estim ated in previous studies,

most o f them derived from c lim ato log ies constructed from h is to r ica l hyd rog ra

phy [e.g.. Iselin. 1036: Kearns. L99G: Lozier et ah. 1995]. T h is com ponent has

also been ca lcu la ted com b in ing the floa t da ta from the X A C expe rim en t w ith

h is to r ica l hydrography, using the s trong co rre la tion between the pressure o f

the target, isopycnal o f the floats and the p o te n tia l energy anom aly fields [C a rr

et ah. 1997: Porez-Brunius. 2002b], In a ll c;uses. the resu lting pa tte rns show an

eastward flow about 700krn w ide, from 45°X to 52°X . S ynop tic hyd rog raph ic

surveys have observed the eastward flow to the n o rth o f 45 ‘ X composed o f tw o

or more sm a lle r ba roe lin ic fronts, h ig h ly variab le in space and tim e [Sv. 19SS:

Sy et ah. 1992: A rhan . 1990: Bubnov. 1995: B e lk in X' Lev itus . 199G]. Hence,

one w ou ld expect th a t long te rm E u le rian averages o f these m eandering and

h ig h ly variab le baroe lin ic s truc tu res w il l smear ou t the fronts, resu lting in w ha t

116


appears as a b road and slow eastward d r if t .

I t is s t i l l no t clear where the branches o f the eastward flow ing N A C -S P F

o rig in a te . I t has been hypothesised th a t they resu lt from s p lit t in g o f the n o r th

w ard flow ing X A C . occurring upstream o f F lem ish Cap [D io trieeh et ah. 1980:

K rauss et a l.. 1987] and upstream of. a t. o r past the N orthw est C orner [Sy. 1988:

A rh a n . 1990: Lazier. 1994], and there is no clear evidence on how perm anent o r

sporad ic those branches are.

The w ide eastward flow transpo rts ~ IS Sv (referenced to lOOOdb) from

the T a il o f the G rand Banks in to the eastern subpo la r region, crossing the

M A R between 4 G°X and 53°X. A b o u t 12.5 Sv o f the' n o rth w a rd flow en te ring

the region a t 40 X recircu lates w ith in the M ann Eddy, centered a t (4 4 '\V .4 1 : X ).

We believe the re c ircu la tin g cell shown east, o f the M ann E ddy may be spurious.

Found in a region o f low da ta density (< 25 observations per b in . w ith a to ta l

o f G58 d a ta po in ts ), and sampled by 1G floats, i t m ay no t be representative

o f the tru e mean fie ld for tha t region, and m ay be biased by the few float

observations present there. W h ile the region o f the M ann E ddy also has low d a ta

dens ity per b in ( ~ 50). it was sampled by 5G floats, p ro v id in g 1.971 independent

observations over 3 years, and therefore is lik e ly to be representative o f the mean

fie ld.

117

3.2 B arotropic transport potential

F igure 7 shows the ba ro trop ic tra n sp o rt p o te n tia l Q*ooo(j ; 6 - Ub) fo r the top

lOOOdb. T h e e rro r o f Qiooo *s -•& Sv (soe A p p e n d ix 3). N o tew o rth y are the

three re c irc u la tin g cells su rround ing the N A C -S P F : two a n ticyc lon ic cells, the

M ann Eddy, and the F lem ish C ap-N orthw est C orner rec ircu la tions : and one

cyc lon ic cell found inshore o f the N A C . south o f F lem ish Cap. w hich includes a

trough centered at 44°N.

T in ' M ann Eddy, centered at abou t (44°\V .42°N ). has a b a ro tro p ic tra n sp o rt

o f ~ 7.5 Sv. The cyc lon ic re c ircu la tion reflects the Lab rado r C u rren t flow ing

south th rou g h the open ing between the G rand Banks and F lem ish Cap. tu rn in g

it no rthw ards as i t encounters the N A C -S P F at the T a il o f the G rand Banks.

The trough at 44°N has been reported before [e.g.. L a V io le tte . 19S3: Krauss.

198G], bu t i t is p a r tic u la r ly extended to the oast for the period sam pled by

the N A C floats (1993-199G) [C arr et. al.. 1997: Kearns cN Rossbv. 1998: Ross by.

199Gj. T h is cyc lon ic cell recircu lates abou t 5 Sv in the top lOOOdb.

The largest re c ircu la tio n extends from the N orthw est C o rner dow n to

45 \N . south o f F lem ish Cap. I t recircu la tes abou t 7.5 Sv in the top lOOOdb.

ju s t as much as the M ann E ddy b a ro tro p ic tra n sp o rt. T he map gives a sm a ll

in d ica tio n th a t th is ce ll consists o f two sm a lle r ones: one w ith its center just,

east o f F lem ish Cap. extend ing from 45°N to 51°N: the o th e r centered a round

(44C\V .52°N ) in the N orthw est C orner. P revious studies have also found a

118


detached eddy iu the N orthw est C orner [Lazier. 1994: Kearns. 1996]. The reso

lu t io n o f the m ap ( 1°) m ay be too coarse to d is tin gu ish between these two cells,

m erg ing them in to a single, extended rec ircu la tion .

The b a ro tro p ic tra n s p o rt east o f 40°\Y is noisy, b u t suggests an eastward

How past the N orthw est C orner rec ircu la tion , found between 49°N and 51°N at

35C\Y . w h ich then tu rns northeastwards to cross the M A R th rough the Faraday

and C h a rlie -G ib b s F racture Zones. T h is How tra nsp o rts abou t 5 Sv in the top

lOOOdb.

3.3 A b so lu te transport potential

The abso lu te tra n s p o rt po te n tia l for the top lOOOdb w hich results

from the sum o f the baroe lin ic and ba ro trop ic maps o f F igures 6 and 7. is

shown in F igu re S. T he corresponding e rro r is 3.1 Sv (see A p p e n d ix 3). One

feature th a t stands out is a continuous no rthw ard How th a t tu rns east, past the

N orthw est C orner, and crosses the M A R between 47CN and 5 1 'N . The th ick

tra n sp o rt lines = —35 and —20 Sv are shown as the boundaries o f the

above m entioned How. and represent the edges o f the N A C -S P F . N ote th a t there

is no evidence o f branches s p lit t in g o ff the cu rren t upstream o f the N orthw est

C orner. R a the r, the N A C -S P F appears as a narrow cu rren t, abou t 1 0 0 - 150km

w ide, a ll the way from the T a il o f the G rand Banks to F lem ish Cap. It. is

not u n t il en te ring the N orthw est C orner th a t the cu rren t broadens, o r p robab ly

sp lits , before tu rn in g eastwards. .Just past the N orthw est C o rner (a round 40°\Y .

119


51°X ). the eastward flow ing X A C -S P F is abou t 230km wide. I t seems to broaden

even more, to abou t 400-500km . a t 37°W . b u t the tra n s p o rt lines converge as

the How approaches the M A R . crossing i t in the region o f the Faraday and

C h a rlie -G ib b s F racture Zones, where the eastward flow is a bou t 300km wide.

T h is resu lt is ra d ic a lly d iffe ren t from the ba roe lin ic tra n s p o rt m ap o f F igu re G.

where the X A C -S P F seemed to s p lit and broaden far upstream o f F lem ish Cap.

w ith an envelope between 300 and 700km wide.

The fact th a t the flow across the M A R is constra ined to the Faraday and

C h a rlie G ibbs F racture Zones has been noted before [Sy et ah. 1992: A rh an .

1990: Bower et ah. 2002]. suggesting th a t topography has an im p o rta n t effect,

on "s tee ring" the cu rren t in to the subpo la r region, despite the fact th a t the

crest o f the M A R is more than L700db Inflow the sea surface.

The b a ro tro p ic rec ircu la tions shape the absolute tra n sp o rt contours, by fo rc

ing flow across the ba roe lin ic transpo rt lines, bo th up- and dow nstream o f the

X orthw est C orner. The cells appear in the absolute tra n sp o rt m ap. and rec ir

cu la te 25 Sv in the M ann Eddy. 5 Sv in the cyc lon ic cell inshore o f the X A C .

and 5 Sv in the F lem ish C ap -X orthw est C orner re c ircu la tio n (a ll tra nsp o rts are

fo r the top lOOOdb).

Based on the above results, we w il l refer to the X A C -S P F as a "p ip e " o f w arm

w a ter flow. lOOOdb deep, bounded by the tra n sp o rt lines C?“ 000 = —35 Sv on the

co ld side. C?“0()() = —20 Sv on the w arm side o f the cu rren t. T he w arm w ater

flow m ay extend much deeper than th is , o f course, b u t th is s tu d y on ly focus on

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the to p lOOOdb. Hence, a to ta l o f ~ 15 Sv are ca rried from the sub trop ics in to

the subpo la r region by the top lOOOdb o f th is cu rren t.

4. Transects

Since we are in terested in ca lcu la tin g the am oun t o f heat th a t is lost by the X A C -

SPF cu rren t as i t flows th rough the region o f s tudy, we use the absolute tra n s p o rt

m ap construc ted in the previous section (F igu re 8 ) to select 7 transects crossing

the X A C -S P F "p ip e ", shown in F igure 9. T ransect num ber 1 corresponds to

M einen 's transect. (Section 2.2). and w ill be used to com pare the residts o f

a p p ly in g the flo a t-G E M technique to the R A FO S floa t da ta set used in th is

study. The absolute ve loc ity fie ld and the tem pe ra tu re fields are ob ta ined on

each transect, a pp ly in g the O A technique described in Section 2.3. For th is case1,

we o b ta in the background fields su rround ing the transects on a O ' R x 0 .5 cg rid .

using Rf, = 130km. The geographical region !/>>} used for the background

fie ld has a 2 .5 : m arg in around the transect in question, given by { x , . / / , } . The

residuals arc1 ob ta ined fo r the background region, and O A onto { x , . / ; , } w ith

the co rre la tion length scale associated to the region R r = 90km . The spa tia l

reso lu tion o f the transect g rid is 25km . A d d in g the value o f the background

fields, the fin a l transect is ob ta ined . X ote th a t we have used a h igher reso lu tion

g rid , and sm a lle r length scales fo r the O A m app ing than the ones used for the

co ns tru c tio n o f the maps o f the previous section. The reason fo r th is is th a t

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wo w ant to cap tu re m ost o f the cu rren t's s tru c tu re , to o b ta in b e tte r estim ates

o f tem pe ra tu re tra n sp o rt across the narrow p ipe th a t cons titu tes the X A C -S P F

cu rren t. T h is is possible given the h igher d a ta dens ity in the area o f these

transects (F igu re 5). The transports o f tem pe ra tu re are ca lcu la ted between the

boundaries o f the X A C -S P F “ p ip e ", defined by the tra n s p o rt p o te n tia l isolines

found in the previous section (Q '^ qq € [ —35 Sv. —20 Sv]).

4.1 N A C -S P F branches

The p ro jec ted floa t ve locities perpend icu la r to the transects suggest th a t the

X A C -S P F sp lits when (Uttering the X orthw est C orner, w ith tw o branches flow ing

east ju s t past it (F igu re 9). There is evidence o f o n ly one branch crossing

transect G. located between -19.5 and 5 0 .5 'X . and a region o f weak mean flow

south o f it . From the absolute transpo rt lines p lo tte d in F igure 9. th is branch

seems to be the sm all one found in the n o rth e rn end o f transect 5. ju s t p;ist

the X orthw est Corner. The tra nsp o rt carried by the southern branch appears

to be f in ite diffuse, and on ly a h in t o f it can be seen near 45.5 ’ X in transect

G. Xevertheless. a t transect 7. the How eastwards is c lea rly composed o f two

branches, each crossing the M A R at the Faraday and C ha rlie -G ibbs F racture

Zone regions respectively, co rro b o ra tin g the idea p u t fo rw ard by Bower et al.

[2002] o f the F racture Zones ac ting as funnels th rou g h w hich the X A C -S P F is

restra ined to flow.

122


4.2 Transports

M einen transect versus float-G EM transect 1

In Section 1 we noted th a t M einen W a tts [2000] used a transect o f m oored

in s tru m e n ts to ca lcu la te the mean abso lu te ve lo c ity and tem pe ra tu re s tru c tu re

o f the n o rth w a rd flow ing N A C -S P F along transect 1 . T he mean section is an

average on "s tream -w ise" coordinates, th a t is. each snapshot was centered at

the h igh ve loc ity core o f the stream , and then averaged over tim e . We w il l refer

to th is as transect M . o r M einen's transect. F igure 10 shows the com parison o f

the ba roe lin ic tra n s p o rt po ten tia ls o f vo lum e and tem pe ra tu re across M einen's

transect M and the flo a t-G E M transect 1 . N ote th a t the flo a t-G E M transect

captures the southw ard flow o f the M ann Eddy, w hich is centered a t ~500km

(h ighest p o in t o f the absolute tra n sp o rt p o te n tia l dom e th a t represents the

re c ircu la tio n o f the M ann E ddy). The n o rth w a rd flow in transect 1 is 250km

w ide r than in transect M . re flecting the g ro w th /d eca y and la te ra l m o tio n o f the

N A C -S P F crest inshore o f the M ann Eddy, d u r in g the 3 year period (1993-1990)

sam pled by the floats in th a t region. T h is la te ra l m ovem ent o f the cu rren t and

M ann E ddy leads to a broader E u le rian average fo r the f lo a t-G E M transect, and

is m ore e ffective ly filte red o u t from the stream -w ise average ob ta ined by Meinen

[2001]. Nevertheless, the baroe lin ic tra nsp o rts across the transect are the same

for b o th sections w h ich , in c lu d ing the M ann Eddy, ca rry 40 Sv and 2 P W

tow ards the n o rth . The absolute tra nsp o rts o f transect 1 (60 Sv and 3 P W

123


to the n o rth ) on the o th e r hand, are 15-20% sm a lle r tha n M einen 's (F igu re

1 1 ). T h is d iscrepancy is caused by the E u le rian average used in ca lcu la tin g the

f lo a t-G E M transect tra nsp o rts : i f the center o f the M ann E ddy moves la te ra lly

a round its mean pos ition (500km in transect 1 ) d u r in g the sam p ling period o f

the floats, the E u le rian average o f the abso lu te ve locities a t the reference level

resu lts in an u nde res tim a tion o f the mean abso lu te ve loc ities a t th a t level. Due

to the s trong g rad ien t in ve loc ity ( it changes sign a t the center o f the Eddy)

th is eu lerian average is very sensitive to la te ra l s h if t in g o f the M ann Eddy.

T h is in tu rn results in an unde restim a tion o f the b a ro tro p ic tra n s p o rt across

the transect (see E qua tion 10). Averag ing in s tream -coord ina tes (as was done

for transect M ) reduces th is effect s ign ifican tly . In te res ting ly , the effect o f the

E u le rian average on the ba roe lin ic com ponent o f the tra n s p o rt is much sm aller.

T h is is because the ba roe lin ic tra n sp o rt is given by the p o te n tia l energy anom aly

(see E qua tion G). w hich is a function th a t reaches its m a x im u m at. the center

o f the M ann E ddy (and thus is nearly constan t there). Hence, the E u lerian

average o f the b a roe lin ic com ponent o f the tra n s p o rt is less sensitive to la te ra l

m o tio n o f the center o f the M ann Eddy.

Transports along the N A C -SPF

We now proceed to observe the changes in the tem pe ra tu re tra nsp o rts a long

the X A C -S P F '"p ipe". N ote th a t mass is conserved a long the p ipe, since it

is chosen w ith in absolute tra n sp o rt p o te n tia l isolines. Nevertheless, mass ex-

124


change across the p ipe side w alls is a llowed, as long as the net mass tra n sp o rt

th ro u g h the p ipe is conserved. Hence, changes in the tem pe ra tu re transpo rts

between the transects crossing the p ipe (F igu re 9) resu lt from heat lost th rough

la te ra l exchange across the side walls o f the pipe, and heat exchange w ith the

a tm osphere. We assume th a t heat fluxes th rough the b o tto m o f the pipe are

neg lig ib le . F igure 12 shows the transpo rts o f tem pe ra tu re co rrespond ing to the

15 Sv o f w ater flow ing w ith in the X A C -S P F "p ip e ". T he tra n sp o rts were ca l

cu la ted fo r 4 d iffe ren t pairs o f absolute tra n sp o rt lines (each p a ir separated by

15 Sv). to evaluate the s e n s itiv ity o f the estim ates to the som ew hat a rb itra ry

se lection o f the cu rren t's boundaries. The e rro r bars are given by

where E ' //= ().0 (3 P W is the e rro r in the tem pera tu re tra n sp o rts (see A pp e nd ix

3). and E 17H is the s tandard e rro r for the mean tem pe ra tu re tra n s p o rt obta ined

fo r the fo llow ing absolute tra nsp o rt p o te n tia l pairs: Q “ 000 = { ( G4 S v . -19 Sv).

( -35 S v.-20 Sv). (-33 Sv. -18 Sv). (-3 7 S v.-22 S v )}:

w ith o being the s tandard d e v ia tio n o f the tem pe ra tu re tra n sp o rts ca lcu la ted

fo r each the fou r tra n sp o rt p o te n tia l pairs ( / /fo o ^ )- M ost o f the c o n tr ib u tio n

to E H comes from E 1 H . except in transects 2 and 3. where E " H has values

n/ 4(1G)

~0 .04 P W .

125


The tra nsp o rts o f tem pera tu re are s ig n ifican tly h igher fo r transect 1 (~

42°N ) com pared to the rest o f the transects th a t cross the N A C -S P F dow n

stream . T h is im p lies th a t m ost o f the heat losses o f the cu rren t occur between

the m eander crest inshore the M ann E ddy (transect 1 ), and the trough at 44°N

(transect 2). A to ta l o f —0.27 ± 0.06 P W are lost between the two transects.

Past th is trough , the changes on the tem pera ture tra nsp o rts are sm a ll (a round

—0.0 L ± 0.06 P W are lost between transect 2 and transect 7) a lthough a p a t

te rn o f heat gain and loss emerges. Heat is gained when en te ring the crest at

46°X (tra nse c t 3). and lost again a t the 47°N trough (transect 4). O u r estim ates

show no heat loss in the Northwest. Corner. A w a rm ing takes place in the region

whore the eastern flow is w idest (transect 6 ). and fin a lly , coo ling occurs upon

reaching the M A R (transect 7).

A tm o s p h e r ic h e a t losses

We can es tim ate the heat lost to the atm osphere H nlm a long the N A C -S P F

"p ip e " by:

H 'u,n = 11' x L x Hff™. (17)

where IF and L are. respectively, the w id th and leng th o f the N A C -S P F "p ipe "

between transects, and is the a tm ospheric heat flu x in W / n r . To estim ate

th is flux , we consider the no rthw ard N A C flow ( IF ~~ 100km. L ~ 1000km ).

and the eastward SPF flow ( IF 500km . L ~ 1000km) separa te ly (see F ig

ure 1 ). The mean a tm ospheric heat flux , estim ated from the average o f two

126


fu l l yours (1998-1999) o f X C E P /X C A R reanalysis da ta [K a ln a v et a l., 1996:

Perez-Brun ius. 2002c], is H f^ ]. ~ ( — 200, —100) W /m 2 in the X A C and SPF.

respectively. T h is results in a to ta l o f H atm ~ (0.02 P W . 0.05 P W ) lost to the

atm osphere by the X A C and SPF segments, respectively. A d d in g the tw o. ap

p ro x im a te ly 0.07 P W are lost to the atm osphere by the X A C -S P F in its tra n s it

th rou g h th is region. O f course, th is is a ra the r crude es tim ate considering the

h igh seasonal and in te rannua l v a r ia b ility in the atm ospheric heat fluxes, as well

as the unce rta in ty o f the estim ates o f the a tm ospheric heat fluxes themselves.

A s im ila r ca lcu la tion leads to a mean heat loss to the atm osphere between tra n

sects I and 2 on the o rder o f ~ 1 0 _ !PW . Since losses to the a tm osphere are

so sm all, th is suggests th a t the flu x lost by tin* X A C -S P F across the side walls

o f the p ipe between those tw o transects m ust p lay the d om ina n t ro le. Hence*,

subs tan tia l coo ling by la te ra l exchange across the X A C -S P F waters occurs ju s t

past the M ann Eddy. To the level o f accuracy o f ou r estim ates, no s ign ifican t

coo ling occurs past the tro ug h a t 44CX. suggesting th a t m ost o f the co o ling o f

the waters carried by the X A C -S P F pipe takes place between the M ann E ddy

and tin* trough at 44CX.

5. D iscussion and Sum m ary

The flo a t-G E M technique [Perez-B run ius. 2 0 0 2 b] is app lied to isopycnal R A F O S

floa t da ta to o b ta in the mean three d im ensiona l tem pera tu re , specific vo lum e

127


anom aly, and absolute ve lo c ity fie ld fo r the top lOOOdb o f the N A C -S P F region.

T h e technique combines the ve lo c ity and pressure records o f the flo a t da ta w ith

p ro jec tions on geostrophic stream func tion space o f h is to r ica l hydrography.

The mean baroe lin ic and absolute tra n sp o rt p o te n tia l fields were constructed

fo r the top lOOOdb o f the N A C -S P F region, representing the mean c irc u la tio n

o f the w arm waters fo r the 1993-2000 tim e period. These tw o fields d iffe r sig

n ific a n tly : w h ile the ba roe lin ic tra nsp o rts suggest a broad and weak eastward

flow , pea ling o ff the no rthw a rd flow ing N A C -S P F upstream o f F lem ish Cap. the

absolu te tra nsp o rts show a well defined and narrow n o rth w a rd -flo w in g cu rren t,

a long a well defined m eandering pa th , w ith no evidence o f s p lit t in g before reach

ing the N orthw est C orner. As the N A C -S P F enters the N orthw est C orner, it

appears to s p lit in to tw o branches. These tu rn eastwards and make up the SPF

system . The mean flow between the N orthw est C orner and the M id -A t la n t ic

R idge is less organised, as can be seen from the w ide envelope o f the tra n s p o rt

lines defin ing the N A C -S P F "p ip ° hi th a t segment, p ro ba b ly re flec ting the

m eande ring /eddy shedding o f the eastward flow ing branches o f the SPF. N ev

ertheless. the flow converges dow nstream to cross the M A R above the Faraday

and C ha rlie -G ibbs F racture Zones.

W hy art* the baroe lin ic tra n sp o rt pathways so d iffe ren t to the absolute ones?

We th in k th is is because the baroe lin ic stream lines are co n tro lled by d iffe ren t

processes tha n the b a ro tro p ic stream lines. The ba roe lin ic fie ld depends on the

dens ity fie ld , w hich is its e lf dom ina ted by: 1 ) shoa ling tow ards the n o rth o f

128


isopycnals, due to o u tc ro p p ing o f the m a in the rm oc line o f the sub trop ics a long

the bounda ry between the su b tro p ica l and subpo la r gyres (w h ich corresponds

to the S ubpo la r F ron t, [e.g.. Rossby. 1996; D u tk iew icz et al.. 2 0 0 1 ]): 2) o u tc ro p

p ing o f the lig h t isopycnals due to a tm ospheric coo ling th rough the process o f

S ubpo la r M ode W ate r fo rm a tio n on the w arm side o f the X A C -S P F : w ith in the

a n ticyc lon ic re c ircu la tin g cells: between the branches o f the eastward flow ing

X A C -S P F : and in the N ew found land Basin [M cC a rtney A: Ta lley. 1982: Perez-

B run ius . 2002c]: 3) eddy m ix in g across the curren t in the fo rm o f w a te r parcels

m oving in to and o u t o f the X A C -S P F . w hich results in a net flu x o f subpo la r

waters in to the sub tro p ica l side [D u tk iew icz et al.. 2001].

The b a ro tro p ic fie ld , on the o the r hand, is s tro n g ly influenced by the to

pography o f the region. The loca tion o f the meanders o f the n o rth w a rd flow ing

X A C -S P F . the p os ition o f the X orthw est C orner re c ircu la tion , and the cross

ing o f the cu rren t th rough the M A R appear to be top o g rap h ica lly co n tro lle d

[Rossby. 1996: Bower et al.. 2002], The meanders set up re c ircu la tin g cells: the

M ann E ddy: a cyc lon ic c irc u la tio n inshore o f the X A C -S P F . in c lu d in g a p ro

nounced tro u g h a t 44°X : an extended re c ircu la tio n o ff F lem ish Cap: and the

X orthw est C orner. The cyc lon ic and F lem ish Cap - X orthw est C o rner rec ircu

la tions are m ostly b a ro tro p ic . and they shape the absolute tra n sp o rt p o te n tia l

fie ld. T h is results in flow across ba roe lin ic contours, suggesting s tro ng cross-

fro n ta l flow. T h is is in agreement w ith p a rtic le exchange across a m eandering

fro n t [Bower. 1991]. W ater parcels en te ring a crest tend to flow up a long th e ir

129


isopycna l surface, crossing the cu rren t fro m the w arm to the cold side, w h ile the

oppos ite is true when the How aproaches a m eander trough . I f the m eanders

are steep, there is greater f lu id exchange between the cu rren t and su rro u n d

ing waters. XAC '-SPF waters leaving a steep crest have large negative shear

and cu rva tu re v o rt ic ity . and may not be able to ad jus t th e ir v o r t ic itv to the

pos itive cu rva tu re o f the fo llo w in g tro ug h , hence g e ttin g expelled o u t o f the

cu rre n t [Rossby. 199G]. T h is is the m echanism th a t causes the h igh heat loss

between the crest o f the M ann E ddy and the trough a t 44° X (see F igu re 13).

T he fact th a t the trough is so pronounced leads to a re la tive ly large loss o f

w arm XAC ’-SPF waters in to the M ann Eddy, com pensated by e n tra in m e n t o f

co ld waters inshore o f the cu rren t, lead ing to a net heat loss th rou g h the side

walls o f the XAC’-SPF pipe. We es tim a te th a t 0.27 ± 0 .0 9 P W are lost th rou g h

th is m echanism , w h ich is 1 0 0 tim es la rger than the heat lost to the a tm osphere

between the two transects (o rder ~ 1 0 - ! P W ). T h is suggests th a t m ost o f the

w a rm -to -co ld tra n s fo rm a tio n o f the su b tro p ica l waters en te ring the region oc

curs a long the n o rthw a rd flow ing XAC '-S P F. th rou g h exchange o f w a te r parcels

between the cu rren t and its surround ings. M oreover, our results suggest th a t it

is between the M ann E ddy and the 4 4 °X trough where nearly a ll the net heat

loss o f the XAC '-SPF pipe takes place. W here does th a t heat go? P art o f the

w arm waters lost by the cu rren t feed the re c ircu la tio n o f the M ann Eddy, and

some o f the heat is lost w ith in the M ann E ddy by w in te r-tim e convection, w h ich

leads to the fo rm a tio n o f the warm est S ubpo la r M ode W aters [P erez-B run ius.

130


2002c]. Heat pum ped in to the M ann E ddy may also be lost to the in te r io r o f

the basin th rou g h eddy d iffus ion . The rest o f the waters lost by the cu rre n t to

the su b tro p ica l side m ay diffuse back in to the su b tro p ica l gyre, possib ly feeding

the Azores C u rre n t fu rth e r south, as suggested by K rauss et al. [1990].

M eander induced exchange results in heat lost and gained by the cu rren t in

the crest and tro u g h n o rth o f 44° X. E n tra in m e n t o f waters from the su b tro p ica l

side occurs as the cu rren t approaches the crest a t 4G°.\. leading to the sm a ll

w a rm ing observed between transects 2 and 3. A b o u t the same heat is lost when

subpo la r waters enter the X A C -S P F as i t approaches the trough a t transect 4

(F igu re 14). However, our estimate's are not accurate enough to es tim a te the

heat lo s t/g a in e d by the current past the 44°X trough , since the noise* h've'l is

abou t as h igh as the fluxes.

Pe'rez-Brunius [2 0 0 2 c] s tud ied changes in the mean T /S p roperties o f the

wate'ts fo llo w in g b am c lin ic stream lines. The resu lts pointe'd emt th a t cress-

fro n ta l m ix in g was a t least as im p o rta n t as a tm ospheric coo ling in tra n s fo rm in g

the* waters fo r the upper 500db. T h is s tu d y suggests th a t i f the analysis were* to

be* done? a long absolu te stream lines, the c o n tr ib u tio n due to cross-fron ta l m ix in g

in the reg ion o f the no rthw ard flow ing X A C w ou ld tu rn ou t to be even large'r.

The residts o f th is s tudy p o in t o u t the im po rtance o f having d ire c t measure

ments o f the flow in the X A C -S P F region, since the streandines in fe rred from

hydrog raphy alone do not reflect the pathways o f flow in th is area. Hence, ana l

ysis a long b a roc lin ic stream lines does no t show as c lea rly the im p o rta nce o f the

131


X A C -S P F in changing the properties o f the w arm waters th a t tu rn northeast

past the M A R . as p a rt o f the upper lim b o f the the rm oha line c irc u la tio n o f the

N o rth A tla n tic .

132


Specific Volum e A no m a ly (34.6psu. 4.9°C)

( lU _'snt:i/k g )

Specific Volum e A no m a ly (35psu. 0 °C ) ( 1 0 - 8 m :,/k g )

P o te n tia l D ensity

(a 0 ± 0 .0 2 )

70 2= 142 26.68 ss 26.760 2= 134 26.78 2= 26.S50 = 127 26.89 2= 26.940 2= 119 26.9S ~ 27.030 2= 109 27.08 2 ; 27.12 0 = 93 27.18 % 27.2

| L0 2r S5 27.2S 2= 27.30 ^ 71 27.38 2= 27.4

- 1 0 2= 64 27.48 % 27.5 j- 2 0 ~ 57 27.59 % 27.6-30 % 43 27.69 % 27.7 1'

Table L: L is t o f specific vo lum e anom aly surfaces and th e ir p o te n tia l dens ity analogues. Specific vo lum e anom aly values in the firs t co lum n art* referenced to an in te rm ed ia te tem pera tu re (4.9°C ) and s a lin ity (34.G psu). The second co lum n has specific vo lum e anom aly ca lcu la ted using the s tandard 0oC'and 35 psu values.

133


60-

LS

50-

FC

45-

40-50 -45 -40 -35 -30 -25 -20

Longitude ( 0 E)

Figure 1 : S tream fu n c tio n m ap for the N o rth A t la n t ic o b ta ined from R A FO S floats on the 27.5<ry surface by Bower et al. [2 0 0 *2 j . using ob jec tive analysis to o b ta in the m ap on a g rid made up by 1 1 1 x 1 1 1 km squares. C on tours are d raw n every 2.o x I 0 !n r / s . D yn a m ica l features: NAC’-N o rth A t la n t ic C u rre n t: X W C - Xorthwest. C orner: S P F -S ubpo la r Front. Topograph ic features: M A R - M id - A tla n tic R idge: FC '-F le in ish Cap: C G F Z : C ha rlie -G ibbs F ractu re Zone: F F Z - Faraday F racture Zone: R P- R ockall P la teau: IB - Iceland Basin: R R - Reykjanes Ridge: IS- Irm in g e r Sea: LS- Lab rador Sea.

134

-50 -40 -30 -2 0 -10Longitude ( ° E)

F igure 2: P os ition o f the R A FO S floa t s ta tions used in th is study. T he black dots represent the floa t da ta from the N A C expe rim en t (1993-1996). the w h ite dots show the floa t da ta po in ts fo r the A C C E expe rim en t (1996-2000).

135


60

Z

o2

r<“ . ’ V} " 10

40 -j

-40 ■3550 -4 5 2530 10

Longitude (° E)

F igure 3: Subregions selected for the cons truc tion o f the G E M fields. Dots represent hyd rog raph ic s ta tions from Hydrobase used [C u rry . 1996].

136

Longitude ( ° E)

F igaro 4: Loca tion o f the ta ll cu rren t m eter m oorings (triang les) and PIES (squares) used in M einen W a tts [2000]: M einen [2001].

137


50

45

40■35-4 5 2550 -4 0 30

Longitude ( ° E)

F igure 5: N um ber o f float da ta po in ts per 1° x 1° b in.

138


■ S '

40-55 -5 0 -45 -4 0 -3 0 -25

Longitude ( l) E)

F igaro G: B a roe lin ic tra n sp o rt p o te n tia l for the top lOOOdb. re la tive to lOOOdb (^u ioo)- shown in 109 k g /s % l Sv. The difference between con tou r values is a measure o f the tra n s p o rt in mass-Sv between those contours. T he two bo ld lines show the boundaries o f the w arm w ater flow en te ring the region a t the T a il o f the G rand Banks, and con tin u in g eastwards tow ards the M A R . The flow is abou t 2 0 0 km w ide as it enters the region, and broadens as i t continues eastwards, having an envelope o f abou t TOOkin.

139


|.\C7»-

-55 -5 0 -45 -3 5-4 0 -3 0 -25

Longitude ( l) E)

F igure 7: B a ro tro p ic tra n s p o rt p o te n tia l for tlie top lOOOdb (Q f000). in u n its o f 1 0 9 k g /s % l Sv. N o tew o rth y are the rec ircu la tions found su rro u nd in g the n o rth w ard flow ing X A C . The M ann Eddy, centered at 44°\Y . 42°N: the cyc lon ic cell inshore o f the XAC ’ . in c lu d in g the trough at 44°X: and the N orthw est C orner- F lc in ish Cap. ex tend ing from 4o°X to 52°X.

140


40-55 -5 0 -45 -4 0 -35 -3 0 -25

Longitude ( ° E)

F igure S: A bso lu te tra n sp o rt p o te n tia l fo r the top lOOOdb (Q'fuoo). in u n its o f K C k g /'s ^ l Sv. The X A C -S P F appears as a well defined cu rre n t, flow ing n o rth along a m eandering pa th , and then tu rn in g east past the N orthw est C orner. Note th a t there is no evidence o f s p lit t in g in to perm anent branches upstream o f the N orthw est C orner. A lso n o te w o rthy is the convergence o f the tra n sp o rt contours as the flow approaches the M A R . crossing above the region o f the C ha rlie -G ibbs and Faraday Fracture Zones. The bo ld isolines represent the boundaries o f the NAC’-S P F "p ip e " th a t transpo rts 15 Sv from the sub trop ics in to the eastern subpo la r N o rth A tla n tic .

141


-5 5 -5 0 -4 5 -4 0 -3 5 -3 0 -2 5

Longitude ( ° E)

F igure 9: Transects chosen across the X A C -S P F “ p ip e ". T he arrow s show the absolute ve lo c ity pe rpend icu la r to the transect, a t the specific vo lum e anom a ly o f the floats <)/ = —5 x 10-s m '5/k g .

142

(a)

7 0 -

6 0 -

4 0 -

:o-

1 0 -

:oo 400 5(H) 7001(H)-MX) 0 6(H)

ih i

X

-2(H) -MX) 0 100 200 300 4(H) ‘'00 600 700Distance in km

F igure 1 0 : B a roc lin ic tra n sp o rt p o ten tia ls for fio a t-G E M transect 1 (c irc les) and M einen 's transect M (triang les), referenced to lOOOdb.(a) Mass tra n s p o rt po ten t ia l C? 0)00 in Sv. (b) C um u la tive tem pera tu re tra n sp o rt / / fo 00 in P W . Transect M is centered at the core o f the no rthw a rd flow (Okm). w h ile transect 1 has the zero a t the westernm ost s ta tion .

143


(a)SO

7 0 -

6 0 -

5 0 -

4 0 -

10-

-2(H ) 200-H X) 400 600 7000 l(X)

ihl

- 0 5200 500 700-100 4<X) 6000 HX)

Distance in km

F igure 1 1 : A bso lu te tra n s p o rt p o te n tia ls fo r tlo a t-G E M transect 1 (c ircles) and M einen 's transect M (trian g les ), fo r the top lOOOdb. (a) Mass tra n sp o rt poten- t ia l Q'iqoo in Sv. (b ) C u m u la tive tem pe ra tu re tra n sp o rt / / “ 000 in P W . Transect M is centered a t the core o f the n o rth w a rd flow (Okm). w h ile transect 1 has the zero at the w esternm ost s ta tio n .

144

0.9 -

0.S

0.6 -

0 .4 -i

Section number

F igure 1 2 : A bso lu te tem pe ra tu re tra nsp o rts / / “uoo a long the N A C -S P F "p ip e ", in P W ( 1 P W = K )1 ’W ). Sym bols represent the tem pera tu re tra n s p o rt ca lcu la ted for each mass tra n sp o rt p o te n tia l pa ir: squa res= (-34 .-l9 )S v . tr ia n g Ie s= (-3 3 .- 18)Sv. s ta rs= (-35 .-20 )S v . and c irc les= (-37 .-22 )S v. The bo ld line is the mean tem pe ra tu re tra n sp o rt (taken over a ll pa irs). Note th a t the X A C -S P F transports s ig n ifica n tly more w arm w ater across transect 1 than across any o the r transect found dow nstream .

145


47

46 -

45 -

z

43 -

40-5 0 -4 2 -4 0-4 8 -4 6 -4 4

Longitude ( E)

(b)

ZC 44 -

' / / / / / / / ,

AL40-5 0 -4 8 -4 6 -4 . -4 0-4 4

Longitude ( 1 E)

F igu re 13: M ;ips o f the stream functions on the 6 surface o f the Hoats. show ing the m echanism o f la te ra l exhange induced by the meander crest near 42.5°X and the fo llo w in g trough (~ 4 4 °X ). (a) Dashed contours show the b a ro c lin ic s tream fu n c tio n 'I>6r (ref. to lOOOdb). bo ld contours are the ba ro trop ic stream fu n c tio n

(b) B a roc lin ic stream lines (4>6c) are shown its dashed contours, abso lu te s tream lines ( '[ '" ) in bo ld contours. For b o th (a) and (b). transects 1 and 2 are shown as the bo ld lines at ~ 42.5°X’ and ~ 44°X . The arrows show the d ire c tio n o f the la te ra l exchange across the stream .

14G


5 0 -

Z

4 5 -

»\U40

-5 5 -5 0 -4 5 -3 5-4 0

Longitude ( ° E )

Figure1 14: M ap o f the s tream functions on the 6 surface o f the floats, show ing the m echanism o f la te ra l exhange induced by the m eandering M AC. The dashed contours show the ba roc lin ic stream fun c tio n '&6c (ref. to lOOOdb). bo ld contours are the b a ro tro p ic stream fun c tio n v&6t. The arrows show the d ire c tio n o f the la te ra l exchange across the stream .

147


A p p en d ix 1: G EM errors

T he errors associated w ith the G E M technique have been th o ro u g h ly ana

lyzed by M einen <!c W a tts [2000], B ook et al. [2002], and Sun & W a tts [2001].

T he mean-square e rro r (<7 r ) is used to q u a n tify how w ell the G E M fie lds rep ro

duce the profiles o f the hydrocasts used in th e ir cons truc tion :

= < 1,-a.i<*)" > • Below lOOdb. the mean-square erro rs correspond

to less than 1 0 % o f the ve rtica l range in specific vo lum e anom a ly (o r tem pe ra

tu re ). w ith the largest dev ia tions present in the m a in and seasonal the rinoc lines .

T he exception is region G. where the correspond ing percentage fo r the m a in the r-

m oeline is abou t 15% (F igu re 1). The G E M fields exp la in above 90% o f the'

variance o f the hydrocasts in regions w ith s trong b a ro c lin ic ity (la rge range in

) and s tra tif ic a tio n , such as the X A C (region 2) and SPF (reg ion 4). As the

s tra t if ic a t io n and b a ro c lin ic ity are reduced, so does the variance in the hydro-

easts. and the G E M fields w ork less w ell a t rep roduc ing the v a r ia b il ity (F igu re

2). T h is is because in those regions, the v a r ia b ility in the hyd rog ra p h ic co nd i

tions is less associated w ith the mesoscale eddies and m eandering fron ts , and

m ore to changes in the properties o f the w ater masses present. T h is becomes

c learer in F igu re 3. where we see enhanced v a r ia b ility a t dep th in the v e rtica l

p ro files o f specific volum e anom a ly o f region 6 . where the variance exp la ined by

the G E M is poor. For the o th e r regions, however, the G E M s reproduce w ell the

148

hydrog raph ic profiles.

149


CT compared to the vertical ranee in 5(9f )(a) r (b) - (c)

Rockall Plateau andSouthern NAC (Mann eddy) Subpolar Front (CGFZ) Trough

• /5

O'\ l f

-500 -500 -500

1o

'Ul-1000 -1000 -1000

A*,-1 5 0 0 l-1500 -1500

8 4 5Dynamic Height (J/kg)

F igu re 1 : Mean-square e rro r o f the specific vo lum e anom aly G E M fie ld , contou red as the percentage o f the ve rtica l range o f 6. for three d iffe re n t regions: (a) region 1 (Southern X A C ). (b) region 4 (S P F). and (c) reg ion G (R ocka ll P la teau and T rough).

150


-500

-1000 -

- 1 5 0 0 L

R egion 2

Percentage o f the variance explained by the temperature G EM fields

R e g io n 4 R e g io n X

•500

iI v1000|-

50■^-i-1500L

100 0

0

-500

\ '

! :1 i .i 1I 1

/ i

/ :,/ :

/

-1000

-1500

f1 !

-500

1000

Region 10

50 100 0 50 100

F igure 2 : Percentage o f the variance expla ined by the tem pe ra tu re G E M fields, fo r fou r different, regions. Region 2- N o rthe rn X A C . region 4- SPF. region 8 - Irm in g e r and Lab rador Seas, and region 1 0 - eastern N ew found land Basin.

151


(a) (b)

-500

-1000

-1500-200 0 200 400 600

Region I

-500=4 9

-1000

-1500-200 0 200 400 600

-500

-1000

-1500-200 0 200 400 600

(d )

-500

-1 0 0 0

-1S00L-200

Rcuion 4

r

> -3 3<t>=3 5

<t>=3

Region 60 200 400 600

Rcuion S

Figure’ 3: G roups o fh y d ro d a ta specific volum e anom aly profiles ( th in lines) com pared to the correspond ing G E M specific vo lum e anom a ly profiles ( th ic k lines) for various values o f <F. in fou r regions. The profiles are sh ifted 100 x 10_sm :1/k g u n its : (a) region 1 (h yd ro da ta profiles w ith w ith in 2 J /k g - southern N A G ). ( I)) region G (h yd ro da ta profiles w ith <f> w ith in O.G J /k g - Rockall P la teau and T ro u gh ), (c) region 8 (h yd ro da ta profiles w ith (f> w ith in 0.4 J /k g - Irm in g e r and Lab rado r Seas), and (d) region 11 (hyd roda ta profiles w ith w ith in 0.2 J /k g - southern European Basin).

152

A p p en d ix 2: F loat-G E M errors

F loat-G E M volum e transport errors

Since the variables we use are discrete, we estim a te the in teg ra ls and deriva tives

o f E qua tions 12 and 15 in C h a p te r 1 as follows

Gtouu is the vo lum e tra n s p o rt, the indexes ( i . j ) correspond to ve rtica l and

h o rizo n ta l b ins, respectively. is the b a roc lin ic ve loc ity (referenced to lOOOdb).

 is dyna m ic height (referenced to lOOOdb). and x is d istance along the transect.

T he sums are ca rried out the ve rtica l bins between 0 and lOOOdb. and h o rizo n ta l

b ins covering the entire section.

T he e rro r associated to the transpo rts ca lcu la ted front the fio a t-G E M

art' ca lcu la ted as follows

Q 1000 = H X I ■ ( 1)‘ J

where

ooo )* = ^ 2 ( E QA l ) ^ x ( j ) f (3)

where

{ E Q l ( i ) f = Y . ( E v ( i J ) ± P ( i ) ) 2 • (4)j

153

E v i i . j ) = • O)/ AxO)

^ ( i . j ) ) 2 = (•£’•!>(^ j + \ ) ) ~ + - i ) ) ' . (G)

and E.p is the flo a t-G E M e rro r associated w ith dynam ic height.

Float-G E M heat transport errors

In a re la ted m anner, the tem pe ra tu re tra n s p o rt H iUOo ca lcu la ted using E qua tion

15 in C h a p te r 1 is estim ated as follows

tftooo = \ ’ ( i J ) T { i . j ) ± p { i ) ± x ( j ) . (7)< j

where () is the mean density o f seawater. C p the specific heat o f seawater, and

T is tem pera tu re . The correspond ing e rro r E h is given by

[E h i , ]

. ( F.rU.J) V \ n * . j ) ) ~ \ T h . j ) J

( 8 )

where E r is the flo a t-G E M e rro r o f tem pera tu re . E quations 3 and S resu lt from

the p ropagation o f errors fo r sums and p roduc ts [Em ery Thom son. 2001],

154

A p p en d ix 3: Transport errors

The estim ate o f va riab le ^ ob ta ined by b in n in g the flo a t-G E M d a ta ^ {J lias

an e rro r E V given by

2 . Section 3.3). and

is the s tandard e rro r o f the mean value ^ in the b in in question. is the

standard dev ia tion o f the H oat-G E M da ta in the b in . and .V is the num ber o f

observations in the b in .

For most o f t in ' variables invo lved in the ca lcu la tion o f the absolu te trans

po rts o f mass and tem pera tu re , the b in n in g e rro r E b is la rger than tin* floa t-

G E M e rro r E^'J. Please refer to C hap te r 3. Section 2 for the d e fin it io n o f tin*

sym bols used in th is A ppend ix .

M ass transport errors

The errors in the mass tra n sp o rt po te n tia ls ca lcu la ted in C hap te r 3. Section 3

are given by

( 1)

w hen' E f '- 'r is the e rro r associated w ith the flo a t-G E M technique (see C h a p te r

(3)

155


E ‘ Q%00 = pDEt}J/ b t . (4)

E l Q i a1000

where

E ‘ * bt = >/[ ^ ( /; ( (v ) ) ] '- + [E ‘ ^ ( / ; ( ()/ ) ) ] - .

E t ^ a(p{Sf )) = E V f A x .

(G)

p = lO 'iT kg /m * is the mean density. D = 1000m the height o f the w a te r co lum n.

E \ i s the (>rror in the ve loc ity measured by the R.AFOS floats, and A x is the

size o f the bins. E quations 5 and 6 assume th a t the errors in the ba roe lin ic

and baro trop ie com ponents are uncorre la ted . The bins are l ° x 1°. w h ich results

in A x srlOOkm in the no rth -so u th d ire c tion . and A x ssTOkm in the east-west

d ire c tio n . For s im p lic ity , we use A x = 100km in the e rro r ca lcu la tio n . Table 1

shows the mean values o f tin ; errors m entioned above for the XAC ’-S P F region.

A b solu te tem perature transport error

T he errors in the absolute tem pe ra tu re transpo rts fo r the X A C -S P F "p ip e ”

ca lcu la ted in C hap te r 3. Section 4 are given by

where C'p - 4000.J/kg=C is the specific heat o f sea w ater. T = S.G°C’ is the mean

tem pe ra tu re and l ‘ = 1 0 c m /s the mean speed o f the waters w ith in the X AC ’-SPF

i ooo ( 8 )

156


V ariab le E rro r o f the E rro r due to T o ta l e rro rflo a t-G E M technique

E f< J

b inn ingE b E l

V * 3 .0cm /s 2 .6 e m /s 3 .9cm /s{[>(,)/)) 3 . 0 x 1 0 :tm J/s 2 .6 x 1 0 3 m -/s 3 .9 x l0 ;!m - /s

^ c(p (S f )) 5 .1 x l0 '- n r /s 7.4 x 10~rn"/s 9 . 0 x 1 0 '-m 2/sij>bt l.O x 1 0 ;$m '-/s 2 . 6 x 1 0 'n r / s 2 . 8 x 1 0 :!n i" /s

Qwoo 0.45 Sv 1.2 Sv 1.3 Sv

Q \m i 1.0 Sv 2.6 Sv 2.S Sv

Qumo 1.6 Sv 2.7 Sv 3.1 Sv

T a b le L: E rro rs invo lved in the mass tra n s p o rt p o te n tia ls estim ates. N o te th a t the e rro r cine to b in n in g E h is in general la rge r than the e rro r o f the flo a t-G E M E^'J.

"p ip e " . A .r = 2 5 km is the s ta tio n spacing used for the transects, and

E 'T = y J { E f 'J T f + { E hT ) ~ . (9)

E l Y = \ j {E S '->Y f + ( E H ' ) 2 (10)

are the co rres i)o iu ling mean errors fo r tem pera tu re and ve locity , respectively.

T he errors have the fo llo w in g values: E^'JT =0 .37°C . E bT = 0 .4 5 'C \

=* E ' T =0.5:8 °C: and E I,JV = 5 . lc m /s . E h\ ' = 5 . Ic in /s . => E 'V = 7 .2 cm /s . T h is

resu lts in an e rro r E ' = 0.0G P \V for the absolute tem pera ture ' tra n sp o rt.

157

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