R eprinted from: J.C .J. N ihoul (E ditor), Coupled O cea n -A tm o sp h ere Models, pp. 1 0 9 -1 1 9
© 1985 Elsevier Science Publishers B.V., Am sterdam - Printed in The N etherlands
c h a p te r 9
109
Instituut voor Z e m t e c h a p p e l i j k onderzoek
Instftuíe for Ma.;m e Scientific R esearch
P r in ses t lls a b e t h la a n 6 9
T R A N SIE N T E FF E C T S DUE TO O C E i^ ilß THERM AL JHfi%TiA) IN ¿|N 0 5 9 / 8 0 5 7 15
ATMOSPHERIC M ODEL COUPLED TO TWO OCEANS
A.H. TAYLOR, D. MUIR and N. MURDOCH
ABSTRACT
A m odel o f th e m ixed layers o f th e N orth Pacific and N orth A tlantic Oceans has been coupled to
a hemispherical, quasigeostrophic, beta-plane m odel o f the atm osphere. The tw o oceans are
represented by th e sectors 9 0 °W -9 0 °E and 0 °-4 5 °W , respectively, w ith the N orth Am erican and
Eurasian land masses by 4 5 °-9 0 °W and 0 ° -9 0 ° E . The mixed-layer m odel is a sim plification o f that
o f Kraus and T urner (1967). The m eridional heat flux in each ocean is prescribed during each run o f
the m odel and several experim ents were carried out betw een w hich these transports were varied. This
paper considers th e role o f oceanic therm al inertia in these experim ents. Each experim ent began with
a m ixed layer which was everywhere in dynam ic equilibrium with the unperturbed heat transport.
The results show how th e m ixed layer affects the dynamics o f the m odel. T here are teleconnections
betw een th e m ixed layers o f the tw o oceans w ith tim e scales o f m onths. The m odel shows an e a s twest oscillation rem iniscent of th e seesaw in n orthern hem isphere tem peratures described by Van
L oon and Rogers (1978), w hich involves th e n orthernm ost m ixed layer o f th e oceans.
INTRODUCTION
M anabe (1 9 8 3 ) h ig h lig h ted th re e w ay s in w h ich th e o c ea n s a ffe c t th e c lim a te , via:
(1 ) th e h y d ro lo g ic a l cy c le ; (2 ) th e ir th e rm a l in e rtia ; and (3 ) th e tr a n s p o rt o f h e a t. The
first o f these is n o t co n sid ered in th e p re se n t m o d el. M u rd o ch a n d T a y lo r (in p re p .) have
investigated th e in flu e n c e o n th e clim a te o f th e m erid io n al o cean ic h e a t flu x using a
h em isp h erical, q u a sig e o stro p h ic , b eta -p la n e m o d e l o f th e a tm o sp h e re w h ich is c o u p le d to
tw o land m asses an d tw o o ce a n s, e ac h o c ean having an in te ra c tiv e m ix ed lay er. The
tr a n s p o rt o f h e a t w ith in each o c e a n w as p re sc rib e d th ro u g h o u t a n y e x p e rim e n t so th a t
its im p a c t o n th e a tm o s p h e ric c irc u la tio n c o u ld b e d e te rm in e d . T h e e x p e rim e n ts show ed
th a t: changes in th e su rface te m p e ra tu re span n in g th e w h o le n o rth e rn h em isp h ere
a c co m p an ied p e rtu rb a tio n s o f th e o cean ic h e a t flu x es; z o n a l w in d stre n g th s w ere
inversely related to th e s tre n g th o f th e h e a t tra n s p o rt, th e w in d changes bein g g enerally
such as to o p p o se a n y ch an g e in th e h e a t flu x b u t w ith e ffe c ts in b o th o c ean s; and the
regions o f deep c o n v e c tio n in th e n o rth e rn A tla n tic w ere im p o rta n t d u rin g th e re a d ju st­
m e n t b e tw e e n c lim atic p h ases. T h ese re su lts w ere o b ta in e d b y analysing th e average
c o n d itio n s d u rin g th e la st 1 5 0 d a y s o f e a c h 4 5 0 -d a y ru n a n d assum ed th a t th e averages
p rovided a n in d ic a tio n o f th e e q u ilib riu m to w a rd s w h ic h th e m o d e l w as m oving. The
p resen t p a p e r ex am in es th e ro le o f th e th e rm a l in ertia o f th e o cean s in th e d y n a m ic s o f
th e clim atic sy stem b y s tu d y in g th e b e h a v io u r o f th e m ix ed la y e r d u rin g th e e v o lu tio n
w ith tim e o f th is m o d el.
T h e m o d el uses a n u n c h a n g in g annual-average h ea tin g fu n c tio n th r o u g h o u t th e calc u ­
la tio n s so th a t th e h e a t c o n te n t o f th e m ix ed la y e r is a p p ro x im a te ly c o n s ta n t. T he real
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m ix ed la y e r w ill a d ju st to seasonal changes a n d so th e resp o n se tim es o f th e th e rm al and
p o te n tia l energ y c o n te n ts o f th e la y e r to e x te rn a l fo rcin g m u s t b e less th a n six m o n th s
an d m ay be sim ilar to th e d e cay tim e o f sea-surface te m p e ra tu re an o m a lie s (a b o u t tw o
m o n th s, F ra n k ig n o u l, 1 9 7 9 ; W ells, 1 9 8 2 ). T h e a tm o sp h e ric in d e x cy cle has a p erio d o f
a b o u t 2 0 d ay s so th a t som e resp o n se o f th e m ix ed la y e r to th e s e a tm o sp h e ric flu c tu a tio n s
can b e a n tic ip a te d . T h e re fo re , th e m ix ed la y e r m ay be e x p e c te d to a ffe c t th e d y n am ics
o f th e a tm o sp h e re o v er m o n th ly p erio d s, and th is is reflec te d in th e large-scale tra n sie n ts
to be d escrib ed . T he tra n sie n ts th a t o c cu r e x h ib it z o n a l p a tte rn s w h ic h are sim ilar to
fe a tu re s observed in clim atic d a ta .
MODEL DESCRIPTION
T h e c o m p le te m o d el is d escrib ed in d e ta il b y M u rd o ch and T a y lo r (in p re p .). T h e
a tm o sp h e ric p a rt, w h ic h is th a t o f G o rd o n and D avies (1 9 7 7 ), is a tw o-level, q u a si­
g e o stro p h ic , b e ta -p la n e sy ste m , in c o rp o ra tin g a m o d e l-d e p e n d e n t su rface energy b alan c e
e q u a tio n a n d , a t th e 5 0 0 m b level, a tim e -d e p e n d e n t h e a tin g fu n c tio n w ith associated
fe e d b a c k re la tio n sh ip s d u e to rad iativ e ex ch an g es w ith th e su rfac e . T h e su rface c o n d itio n s
are in te ra c tiv e ; th e a lb e d o , w h ich re p re se n ts snow and ice co v er, b e in g a fu n c tio n o f
te m p e ra tu re . W hen th e te m p e ra tu re a t a n y p o in t is b elo w 2 7 2 K th e lo cal a lb ed o is
ch anged to th a t o f ice and if th e area is sea it is tre a te d as la n d . R a d ia tio n tran sm issio n
p a ra m e te rs, sensible h e a t loss, la te n t h e a t loss and c o n d e n sa tio n h e a tin g w ere fro m
S m ag o rin sk y (1 9 6 3 ); sensible and la te n t h e a t flu x es w ere allo w ed t o v ary linearly w ith
su rface te m p e ra tu re s a b o u t th ese m e a n values.
S u rface te m p e ra tu re s over la n d , 71* , w ere c a lc u la te d b y assum ing th e rm a l eq u ilib riu m .
O ver th e sea th is is n o t p erm issible becau se h e a t can be sto re d in , o r released fro m , th e
w a te r co lu m n . T h e te m p e ra tu re , 7 7 , an d d e p th , h , o f each o c e a n ’s su rface m ixed lay er
w ere calc u lated b y th e m e th o d o f H o rg a n , D avies an d G a d ia n (1 9 8 3 ) w h ich is a
sim p lific a tio n o f th a t o f K rau s and T u rn e r (1 9 6 7 ). W ater te m p e ra tu re b e n e a th th e m ixed
la y e r is assum ed to b e a c o n s ta n t fu n c tio n o f la titu d e ( T h). T,:. an d h w e re d e term in e d
b y e n su rin g th a t th e th e rm a l and p o te n tia l en erg ies o f th e la y e r w ere conserved. T he
a tm o sp h e ric th e rm a l an d p o te n tia l energy fo rc in g fu n c tio n s a re w ritte n as S + B — M
and G — D + S / y , resp e ctiv e ly , in w h ich : S rep re sen ts th e c o n tr ib u tio n fro m so lar
h e a tin g ; B th e sum o f all b la c k -b o d y , la te n t h e a t a n d sensible h e a t losses fro m th e sea
su rface; G th e ra te o f g e n e ra tio n o f m ix in g en erg y b y th e su rface w in d s (d e d u ce d fro m
th e a tm o sp h e ric m o d el fields); SI 7 th e g e n e ra tio n o f b u o y a n c y b y th e p e n e tra tiv e solar
ra d ia tio n ( 7 is th e c o e fficie n t o f d e cay o f S w ith d e p th ) an d D th e ra te o f d issip atio n o f
en erg y w ith in th e lay er. F o llo w in g S te v en so n (1 9 7 9 ), D w as ta k e n p ro p o rtio n a l to th e
d e p th o f th e lay e r, th e re b y en su rin g n o irrev ersib le a c c u m u la tio n o f p o te n tia l energy.
T h e te rm M is th e o ce a n ic h e a t-flu x divergence w h ic h rep re se n ts th e m erid io n a l tr a n s p o rt
o f h e a t w ith in e a ch o cean . Z o n a lly averaged values o f M (fro m S m ago rin sk y , 19 6 3 )
w ere used and v ariatio n s in th e o ce a n ic h e a t flu x w ere im p le m en ted b y ch anging M.
EXPERIMENTS
T h e m o d el (F ig . la ) p a rtitio n s th e N o rth e rn H em isp h ere in to fo u r secto rs: Pacific
( 9 0 ° E —90°W ), N o rth A m erica ( 9 0 ° - 4 5 ° W ) , A tla n tic ( 4 5 ° W - 0 ° ) an d E urasia
Ill
a
N or th
Pole
90
Ice Ed ge
60r
t
h
Pacific
A
m
e
Eurasia
30-
Equator
90E
1----90E
90W
180W
r 90
Control
Increased
D ecreased
-60
-100
-80
-60
-40
-20
0
20
40
60
80
100
M (Langleys)
Fig. 1. a. The geom etry used in the m odel. The e x te n t o f sea- and land-ice for the control run are
show n, b. T he latitudinal distribution o f heat-flux divergence used in each ocean during the control
run and during the runs w ith increased M and decreased M. Each u n it o f M represents 1 Langley in
the Pacific or 4 Langleys in th e Atlantic.
( 0 ° —9 0 ° E ). T h e grid-spacing is 7 .5 ° o f lo n g itu d e and 2 .9 ° o f la titu d e . T h ere is n o to p o ­
g rap h y .
T h e e x p e rim e n ts w ere designed to in v estig ate th e sen sitiv ity o f th e sy stem to changes
in th e o cean ic h ea t-flu x d iv ergence (M ) o c c u rrin g in e ith e r o ce a n . In th is m o d e l, M is
p re sc rib e d in an y ru n . T h ere is c o n sid e ra b le u n c e rta in ty a b o u t th e relativ e stre n g th s o f
th e z o n a lly averaged ocean ic h e a t flu x d iv ergence in th e tw o ocean s. M erid io n al h e a t
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tra n sp o rts in th e N o rth P acific an d N o rth A tla n tic O ceans are sim ilar, d e sp ite th e g reater
area o f th e P acific (B ry a n , 1 9 8 2 ); p a rtly b ecau se th e re is a larg er re tu rn flow o f h e a t in
th e P acific and p a rtly b e ca u se o f th e w id e c o n n e c tio n b e tw e e n th e A tla n tic and A rctic
O ceans. T h e re fo re , in th e m o d e l, M w as se t u p to be fo u r tim e s as g re a t in th e A tla n tic
se c to r as in th e P acific se c to r so th a t th e tw o m o d e l ocean s tra n s p o rte d th e sam e a m o u n t
o f h e a t n o rth w a rd s. T h e d iv ergence w as d is trib u te d u n ifo rm ly w ith lo n g itu d e. T his
arran g em en t w as used fo r th e c o n tro l ru n .
T h e in itial values o f th e stre a m fu n c tio n s w ere o b ta in e d b y ru n n in g th e m o d e l w ith o u t
a m ix ed lay er u n til th e a tm o sp h e re cam e in to e q u ilib riu m w ith th e sp ecifie d clim ato lo g ical
h e a tin g (th e z o n a lly averaged h e a tin g fu n c tio n s o f S m ag o rin sk y , 1 9 6 3 ). S u b se q u e n t
in itialisatio n o f th e m ix ed lay e r w as carried o u t using th e su rface te m p e ra tu re and su rface
w ind fields, averaged over several energy in d e x cycles. B y re q u irin g t h a t th e rm al and
p o te n tia l-e n e rg y fo rcin g fu n c tio n s be sim u lta n e o u sly z e ro , th a t is:
S + B - M
= 0
(1 )
and:
G + D - S /7 = 0
(2 )
th ese average field s co u ld b e used to p ro v id e in itia l ocean ic-su rface te m p e ra tu re s and
m ix ed -lay er d e p th s. T he first c o n tro l ru n w as o b ta in e d fro m th e su cceed in g 4 5 0 d ay s
a fte r th e m ixed lay er b e c a m e activ e. T h e c a lc u la tio n w ith o u t a m ix e d lay e r w as c o n tin u e d
as a second c o n tro l ru n .
F o u r e x p e rim e n ts w ith d iffe rin g M -values w ere carried o u t (F ig . lb ) : ( A l ) M w as in ­
creased b y 50% in th e A tla n tic se c to r; (A 2 ) M w as d ecreased b y 50% in th e A tla n tic
se c to r; ( P I ) M w as in creased b y 50% in th e P acific se c to r; and (P 2 ) M w as decreased b y
50% in th e P acific se c to r.
E ach o f th ese e x p e rim e n ts sta rte d w ith th e sam e in itial m ix e d lay e r a n d a tm o sp h e re as
did th e first c o n tro l ru n a n d ra n fo r a t least 4 5 0 d a y s. C o m p a rin g th e p a ir o f o p p o site
ru n s A Í and A 2 (o r P I a n d P 2 ) to see w h ic h resp o n ses reverse sign p ro v id es an in d ic a tio n
o f signal to noise ratio .
RESULTS
F igure 2 show s th e te m p o ra l v a ria tio n o f th e a tm o sp h e ric e d d y k in e tic en erg y fo r th e
c o n tro l ru n w ith and w ith o u t a m ix e d lay er. W hen th e o cean s have a m ix ed lay er th e
k in e tic energ y varies m o re s m o o th ly w ith tim e , an d th is is c o n siste n t w ith analyses o f
m odels u n d e r sto c h a stic fo rc in g (e .g ., F ra n k ig n o u l, 1979) in w h ich th e th e rm a l in ertia o f
th e o cean tra n sfo rm s a w h ite no ise sp e c tru m o f sea-surface te m p e ra tu re v aria tio n s in to a
sp ectru m w ith g rea te r en erg y in th e lo w -freq u e n cy regim e. Flow ever, F ig. 2 show s this
red d en in g to b e m o re c o m p le x , fo r p eak s a t 3 0 d ay s and 75 —100 d ay s are sm eared in to a
b ro ad b an d c e n tre d o n a p e rio d o f 5 0 days.
T he presence o f o c e a n ic m ix e d lay ers in th e m o d el leads to a g en e ra lly w a rm e r clim ate
(M u rd o ch and T a y lo r, in p re p .). F o r in sta n c e , a lth o u g h ice co v er o n land d o e s n o t change
ap p reciab ly , th e e x te n t o f sea-ice is re d u c e d b y a b o u t six degrees o f la titu d e . T his
w arm ing can b e u n d e rs to o d i f th e d e v e lo p m e n t in tim e o f th e m o d el is e x am in ed in th e
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o
0
50
100
1
150
200
250
300
400
0.00
450
0 .0 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5
Period
(cycles
day)
Control without a mixed layer
0 .1 5
« 0,10
n
In
c
>
0 .0 5
0 .0 0
Day
I
■
r - - ^ i V
0 .0 0 0 .0 1 0 .0 2 0 .0 3 0 .0 4 0 .0 5
Period (cycles
day)
Fig. 2. T im e series o f m ean eddy kinetic energy for th e c ontro l run w ith and w ithout a m ixed layer.
T he low -frequency spectrum is shown for each series.
lig h t o f th e a tm o sp h e ric d y n am ics and th e rm o d y n a m ic s. T h e in itial stages o f Fig. 2
illu s tra te th e w ay th is d iffe re n c e in clim a te arises. B o th tim e series show a tro u g h a t a b o u t
d a y 10, a fte r w h ic h e ach g ra p h clim bs to a p eak . T h e series fro m th e e x p e rim e n t w ith a
m ix ed la y e r h as a m u c h hig h er first p ea k . T his o c c u rs b ecau se th e p resen ce o f a heata b so rb in g m ix ed lay er re q u ire s th a t m o re h e a t be tra n s p o rte d n o rth w a rd s b y th e
a tm o sp h e ric ed d ies to p ro d u c e a given te m p e ra tu re ch an g e. S o , m o re vigorous ed d ies
can b u ild u p b e fo re th e te m p e ra tu re g ra d ie n t a t th e 5 0 0 m b level is fo rced b a c k to w ard s
b a ro c lin ie s ta b ility . D u rin g th is p e rio d , h e a t th a t w o u ld o th e rw ise be lo s t b y ra d ia tio n to
space is sto re d in th e m ixed lay er. S u c h a sto ra g e o f h e a t o c c u rs d u rin g each o f th e
a tm o s p h e re ’s e n erg etic phases a n d th is h e a t can be released a t less e n e rg e tic tim e s to
im p e d e th e fo rm a tio n o f ice. T h u s, th e m ix ed lay e r a ffe c ts th e clim ate o f th e m o d el
b y in flu e n c in g th e a tm o sp h e ric th e rm o d y n a m ic s via th e 5 0 0 -m b te m p e ra tu re s and h en ce
th e d y n a m ic s o f th e a tm o sp h e re th ro u g h th e m erid io n al te m p e ra tu re g ra d ie n t. T h e m ixed
lay er is th e re fo re seen to have a sig n ifican t e ffe c t o n th e sy stem even in th e ab sen ce o f
seaso n al fo rcing.
T h e flu c tu a tio n s sh o w n in Fig. 2 are d o m in a te d b y th e a tm o sp h e ric en erg y cycle.
H o w ev er, th e e x p e rim e n ts A Í , A 2 , P I and P2 h aving m o d ifie d o c e an ic h e a t flu x es each
beg an w ith m ixed lay ers w h ich w ere n o t in “ e q u ilib riu m ” since, d u e to th e altered h e a t
tr a n s p o rts , th e ir th e rm a l and p o te n tia l-e n e rg y fo rcin g fu n c tio n s w ere n o t zero . A s a
re su lt th e sy stem g rad u a lly ad ju sts d u rin g each ru n to w a rd s c o n d itio n s w h ich satisfy
eq n s. (1 ) a n d (2 ) an d flu c tu a tio n s w ith lo n g er tim e scales are also o b serv ed . T hese flu c tu ­
a tio n s c an b e seen in Fig. 3 w h ich d isp lay s fo r tw o ty p ic a l cases, A Í and A 2, successive
5 0 -d ay averages o f th e h e a t sto re d in th e m ix ed lay er (a fte r s u b tra c tin g th a t o f th e c o n tro l
114
ru n ) a t a s o u th e rn la titu d e and a t a la titu d e n e a r th e n o rth e rn m o s t ex p o se d reg io n o f each
o cean. F o r th e w h o le o f th e P acific and th e s o u th e rn p a rt o f th e A tla n tic th e changes are
slightly o scillato ry and it is possible th a t a n e q u ilib riu m is bein g ap p ro a c h e d . In th e
n o rth e rn A tla n tic , h o w ev er, a clear tre n d is a p p a re n t. M ixed-layer d e p th s in th e tw o
ocean s (F ig. 3) also show less tre n d a t low la titu d e s b u t, a t h ig h la titu d e s, th e d e p th s
show a tr e n d w h ich has th e sam e sign in b o th ocean s. A ll o f th ese tre n d s change sign
w h e n th e p e rtu rb a tio n in o cean ic h e a t flu x is rev ersed . T he m ix ed lay ers a t h igh la titu d e s
w ill ta k e lo n g er to achieve a d y n am ic e q u ilib riu m th a n th e lay ers a t lo w la titu d e s becau se
th e y are m u c h deep er a n d so re q u ire th e tra n sfe r o f a c o n sid erab ly larger q u a n tity o f h e a t
to cause a given te m p e ra tu re change.
A t low la titu d e s, th e tre n d in th e h e a t c o n te n t o f th e m ix ed la y e r is th e sam e in b o th
oceans an d co rre sp o n d s to th e u n d e rly in g tre n d in th e m ix ed -la y e r d e p th (F igs. 3 an d 4 ).
T h e w in d s in th e m o d el re s p o n d ra p id ly (i.e. w ith in 50 d ay s) to th e c h an g ing oceanic h e a t
flu x and th e tren d in th e lay e r d e p th re p re se n ts a slow er a d ju s tm e n t to th ese w inds. A t
h ig h la titu d e s th is is also tr u e o f th e P acific in ru n s A l , A 2 (F ig . 3) and th e A tla n tic in
P I , P2 (e .g ., Fig. 4 ). T h u s, th e re is a te le c o n n e c tio n b e tw e e n th e tw o oceans a ffec tin g
m o s t la titu d e s. T he n o rth e rn m ix ed lay e r in th e o c ean w h o se h e a t flu x is p e rtu rb e d show s
a tre n d in its h e a t c o n te n t w h ic h is th e d ire c t re su lt o f th e ch anged h e a t tra n s p o rt an d is
in th e o p p o site d ire c tio n to th a t o f th e o th e r o cean .
S u p erim p o sed on th is overall tr e n d , th e m ix e d -la y er d e p th s in th e n o rth e rn reg io n o f
th e o c e a n show an o sc illa tio n o f p erio d a b o u t 4 0 0 d ay s w h ic h is o u t o f phase b e tw e e n
th e tw o o cean s, th e re b y h av in g th e a p p e aran c e o f an e a s t—w e st seesaw . T h e seesaw has
its g re a te st a m p litu d e in th e h ig h -la titu d e area o f e a c h o ce a n . A s a re su lt, th e resp o n se in
th e A tla n tic decreases to w a rd s m id d le la titu d e s and a t 5 7 °N in th is o cean th e o scillatio n
is less clear. T h is tra n sie n t resp o n se o f th e m o d e l is e x am in ed fu r th e r in Fig. 4 w h ic h
c o n ta in s th e sam e g rap h s fo r e x p e rim e n t P I to g e th e r w ith th e c o rre sp o n d in g tim e series
o f su rface te m p e ra tu re s and zo n al-w in d c o m p o n e n ts. T h e y are ty p ic a l o f th e fo u r ru n s.
A t low la titu d e s w h ere th e m ix ed la y ers are shallow th e flu c tu a tio n s in su rface
te m p e ra tu re are relativ ely large. T he te m p e ra tu re s a n d z o n a l w in d s a p p e a r inversely
re la te d to th e lay er d e p th s in d ica tin g th e im p o rta n c e o f v aria tio n s in w in d m ixing. In th is
“ tra d e -w in d ” region, th e w in d s are p re d o m in a n tly zo n al easterlies, th u s a positive zo n al
w in d d iffe re n c e m ean s a re d u c e d w in d stre n g th . T h e re is a sim ilar set o f re latio n sh ip s in
h ig h la titu d e s b u t, b ecau se o f th e tr e n d s in th e la y e r d e p th an d sto rag e, th e te m p e ra tu re s,
an d esp ecially th e w in d s, are less clea rly re la te d to th e lay e r d e p th s . T h e in te rp re ta tio n is
also co m p lic a te d because 5 7 ° N is in a b a n d o f w esterlie s, w h ile 7 5 ° N is in a b a n d o f
easterlies.
T h e m ix ed layers o f th e tw o oceans are co u p le d b y m ean s o f th e zo n al w in d s w h ic h
tra n s m it changes over o n e o c ean d o w n stre a m to th e o th e r. E q u a tio n s d escrib in g th is
o c e a n - o c e a n in te ra c tio n c a n be o b ta in e d fro m th o s e d escrib in g th e th e rm a l and p o te n tia len erg y b alan ces o f th e m ix e d la y e r, viz:
~
dr
l ( T , - T h)h] = S + B - M
w h e re T h is th e te m p e ra tu re b elo w th e su rface la y e r, and:
(2 )
115
A1
10
A2
30-,
-
20
Atlantic
7 5°N
-
Pacific
57°N
¡Ü - l o ­
oi
E
oi - 2 0
~
Pacific
57°N
Atlantic
7 5°N
-30-
« -4 0 -
-
•c
10-
-2 0 J
5
Atlantic
15 N
--Pacific
15 N
Atlantic
15 N
'Pacific
15 N
-1 0 J
-10
Atlantic
75°N
1 .0 -1
0 .8
-
0 .6
-
—
.Pacific
5 7°N
- 0 .2 -
-0.4
0 .2
-
0 .6
-
0 .8
-
o -1 .0
-
Atlantic
7 5°N
--Pacific
57°N
0 .2
0 .6 -,
ca
o
Atlantic
1 5° N
0.4-
0 .2
-
Pacific
1 5°N
0 .2
Pacific
1 5° N
-
-0.4T
Atlantic
1 5° N
-0 .6 J
1 1 1 1 1 1 1-100
200
Days
300
400
—
i—
100
i—
i—
200
i—
i—
300
i—
i—
400
Days
Fig. 3. T im e series o f 50-day averages from experim ents A Í and A2 for m ixed-layer depth and heat
co n te n t o f the m ixed layer a t latitudes in the northern and southern regions o f each ocean. T he series
are averaged zonally across each ocean and expressed as deviations from th e corresponding series o f
the c ontrol run.
116
20-,
Pacific
5 7°N
0.30 .2
-
10-
-
20
-
0.1-
Pacific
57°N
O
x
- 0 .1 -
At l ant i c
7 5°N
-
,Atl ant i c
7 5°N
-30
A t la n ti c
: 1 5°N
•P a c i f i c
1 5°N
Mixed
layer depth
difference
( metr es )
10 -
«
-10 -
-
0.1
-
-
0 .2
-
-0.3At l a n t i c
1 5° N
-0.4 -
-2 0 J
Pacific
1 5°N
-0.5 -
-
0.6
Atlantic
l 7 6. 5°N
Pacific
- 57°N
• Atlantic
- 75°N
diff erence
(°C)
/Pacific
55.5°N
t e mp e r a t u r e
-
2
-
-3-4 -
Surface
a
o
, Pacific
' 1 5°N
/Atl anti c
1 5° N
-3-
'Pacific
16 . 5 ° N
-2-J
-4
r
0
100
200
Days
T
300
I
T
400
0
1------ 1------ 1------ 1------ P------ 1------ 1
100
200
Days
300
i------
400
117
— [ ( T , - T h) h 2] = G - D + S l 7
ot
(3)
F igures 3 an d 4 in d ic a te th a t th e to ta l h e a t c o n te n t o f th e m ix ed lay e r d o es n o t
o scillate b u t show s m e re ly a n a lm o st lin ear v a ria tio n w ith tim e . T his im plies th a t on
A1
A2
P1
P2
1
o4
-1
57 N
0 --
p
48°N
r
!
1-
-1
Days
Fig. 5. Tim e series o f 150-day averages from experim ents A l, A2, P I and P2 for surface tem peratures
at 15°, 36°, 48°, 57° and 7 5 ° N. T he series are averaged zonally across each continent and expressed as
deviations from the corresponding series for the control run. T he variation o f 50-day m eans about
these values is ± 0.75° at m id-latitudes, lower at th e highest latitudes and ± 0.25° at low latitudes.
Fig. 4. Tim e series o f 50-day averages from experim ent P I for mixed-layer depth, h e a t content o f the
m ixed layer, surface tem perature and com ponent o f zonal wind a t latitudes in th e n o rth ern and
southern regions o f each ocean. T he series are averaged zonally across each ocean and expressed as
deviations from the corresponding scries for the c ontrol run.
118
occasions th e m ix ed lay e r can shallow w ith o u t changing its h e a t c o n te n t, w h ic h is an
u n realistic fe a tu re o f th e m o d e l. H o w ev er, even w ith a m o re a c c u ra te tr e a tm e n t o f
p o te n tia l-e n e rg y losses, it is lik ely th a t flu c tu a tio n s analagous to th o se sh o w n h ere w ill
occur. T h u s, th e th e rm a l fo rcin g is ap p ro x im a te d as c o n s ta n t in tim e . In th e m o d e l D
w as w ritte n as D' h w h e re D' w as a d ecreasin g fu n c tio n o f la titu d e . A p p ly in g eqns. (2 )
and (3) to each o cea n , a p a ir o f eq u a tio n s d escrib in g th e tra n s ie n t b e h av io u r o f th e
oceanic m ix ed lay ers in th e m o d e l can be deriv ed :
dhA
dhA
( S + B A - M A)hA + ( S + BA - M A) t —
+H a
= GA —D h A + Sly
(4 )
(S + Bp — M p ) h p + ( S + B p — M p ) t — — + H p
at
út
Gp — D ' h p + S / y
(5 )
=
w here su ffix “ A ” refers to th e A tla n tic a n d “ P ” to th e P acific, and H A a n d H p are th e
in itial h e a t c o n te n ts o f th e tw o o c e a n s’ m ix ed layers. E q u a tio n s (4 ) and (5 ) are cou p led
by th e ra te s o f w in d m ix in g , G A and GP ; each o f th ese w ill b e a c o m p lic a te d fu n c tio n o f
th e te m p e ra tu re and m ix e d -la y e r d e p th d is trib u tio n s in th e tw o ocean s. It is th ese
fu n c tio n s w h ic h w ill d e te rm in e th e p e rio d s o f a n y o scillatio n s. T h e d issip a tio n term s
D ' h A and D ' h p w ill te n d to d a m p e n an y tra n sie n ts, a n d th is e ffec t w ill d eclin e n o r th ­
w ard s w ith D ' . As a re su lt b o th th e tre n d and th e o scilla tio n are m o s t p ro n o u n c e d a t h ig h
la titu d e s (F igs. 3 and 4 ).
A n o sc illa to ry te le c o n n e c tio n is also p re s e n t in th e c o n tin e n ta l-su rfa c e te m p e ra tu re s.
T h ese te m p e ra tu re s are m u c h m o re v ariable in tim e th a n o cean ic te m p e ra tu re s, so th a t
th e e ffe c t is m o s t clearly illu s tra te d b y using 1 5 0 -d ay averages (F ig . 5 ). W hile te m p e ra tu re
flu c tu a tio n s at th e h ig h est a n d lo w e st la titu d e s are sim ilar over th e tw o c o n tin e n ts , in
m id d le la titu d e s ( 4 5 ° —6 0 ° N ) A m erica a n d E u rasia show v aria tio n s th a t are o u t o f ph ase.
In general, th e te m p e ra tu re o ver e a c h c o n tin e n t te n d s to be sim ilar to th a t o f th e o cean
u p stream o f it (i.e. to th e w e st in th e w esterly w in d b e lt).
DISCUSSION
C hanging th e o cean ic h e a t flu x in th e m o d el leads to a tra n s ie n t resp o n se w ith a
d is tin c t s tru c tu re w h ich sh o w s co u p lin g b e tw e e n th e oceans. A lth o u g h a t low la titu d e s
little or n o lo n g itu d in a l v a ria tio n is sho w n , in m id d le a n d h igh la titu d e s th e re is a
p ro n o u n c e d zo n al a sy m m e try , w ith an e a s t—w est seesaw o f p e rio d a b o u t 4 0 0 d ay s
o cc u rrin g in each o f th e fo u r ru n s. T h e m ix ed layers o f th e n o rth e rn regions o f th e ocean
and th e ir resp o n se to v ary in g w in d -m ix in g and v arying h e a t sto rag e fo rm an im p o rta n t
elem en t o f th is o scillatio n . T h e o scilla tio n is also re fle c te d in c o n tin e n ta l-su rfa c e
te m p e ra tu re s. H aving o n ly o n e cy cle p e r e x p e rim e n t, w e c a n n o t c o n c lu d e th a t th is m o d e
is tru ly p e rio d ic ; it m a y b e a te m p o ra ry fe a tu re o f th e a d ju s tm e n t p ro cess. V an L o o n and
R ogers (1 9 7 8 ) have d e sc rib e d a seesaw b e tw e e n w in te r te m p e ra tu re s at G reen lan d and
th o se in n o rth e rn E u ro p e . T h is p a tte r n is re la te d (R o g ers a n d V an L o o n , 1 9 7 9 ) to th e
stre n g th o f th e z o n a l w in d s a n d is acco m p an ied b y large an o m alies in th e a tm o sp h e re —
o c e a n - ic e sy ste m , som e o f w h ic h p ersist th ro u g h th e su b se q u e n t sp rin g and su m m e r. T he
idealised calc u la tio n s p re se n te d h e re suggest th a t su c h a seesaw e ffe c t c o u ld be a tra n sie n t
119
m o d e o f th e clim atic sy stem , p e rh a p s trig g ered b y a n a lte ra tio n o f th e o cean ic h e a t
tra n s p o rt.
ACKNOWLEDGEMENTS
T h is w o rk fo rm s p a rt o f th e P hysical P rocesses p ro g ra m m e o f th e In s titu te fo r M arine
E n v iro n m e n ta l R esearc h , a c o m p o n e n t o f th e N a tu ra l E n v iro n m e n t R esearch C ouncil,
and is fu n d e d in p a rt b y th e M inistry o f A g ricu ltu re , F ish eries and F o o d . N . M u rd o ch was
s u p p o rte d b y a g ran t fro m th e E .E .C . C lim ate R e se a rc h P rogam . P relim in ary calc u latio n s
fo r th is s tu d y w ere carried o u t b y C. R eeve. We are g rate fu l to J.A . S te p h e n s a n d T.
W oodrow w h o p rep ared th e figures and ty p e d th e te x t.
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