Studies of the ocean-atmosphere system using a coupled climate model

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Studies of the Ocean-Atmosphere System Using a Coupled

Climate Model

by

A u g u stu s Francis F anning

B.Sc. (H onours). M em orial L’niversity of N ew fo u n d lan d . 1991 -M.Sc.. .Memorial U niversity of N ew fo u n d lan d . 1993 .A D issertation S u b m i t t e d in P a r tia l Fulfillment of th e

R e q u ire m e n ts for th e D egree of D O C T O R O F P H IL O S O P H Y

in th e School of E a r t h an d O cean Sciences We acc ep t this d is s e rta tio n as conform ing

to th e requ ire d s ta n d a r d

Dr. .A.J. W eaver. Supervisor (School of E a r th a n d O cean Sciences)

---Dr. 1. Fung. D e p a rtm e n ta l M e m b e r (School of E a r t h a n d O cean Sciences)

Dr. R. Lueck. D e p a r tm e n ta l M e m b e r (School of E a r t h a n d O cean Sciences)

Dr. C..J.R. G a r r e t t . O u t s i d e A W s b e r (Physics D e p a rtm e n tj

Dr. E. S ^ x a c h ^ E x t ë ^ a l E x a m in e r (U n iv ersity of W ash in g to n ) _______________________________

© .Augustus Francis F anning. 1997 U n iversity of V ictoria

.All rig h ts reserved. T h is d is s e rta tio n m ay n ot be re p ro d u c e d in w hole or in p a r t , by photo c o p y in g or o th e r m e a n s, w ith o u t th e perm issio n of t h e au th o r.

.ABSTR.ACT

.An idealized a tm o s p h e r ic m odel consisting of en erg y a n d m o is tu re c o n s e rv a tio n

eequations is dev elo p ed for studie s of th e o c e a n 's role in clim a te . T e s tin g u n d e r

fi.xed o c e a n ic c o n d itio n s yie lds a clim ato lo g y c o m p a r a b le w ith direct o b s e rv a tio n s,

as does th e case w hen th e in t e r p e n ta d a l ( 19.55-59: 1970-74) se a surface t e m p e r a t u r e

fields a r e ap p lie d .

T h e a t m o s p h e r ic m o d e l is th e n coupled to an o c ea n g e n e ra l c irc u la tio n m ode l

as well as a t h e r m o d y n a m i c ice m odel w ith o u t t h e use o f Hux a d j u s t m e n t s . W h e n

config u re d for a global realistic geom etry, th e m o d e l fa ith fu lly rep re s e n ts d e e p wa­

t e r f o r m a tio n in th e .Atlantic a n d S o u th e r n O ceans w ith upw elling th r o u g h o u t th e

Pacific a n d I n d ia n O ceans. T h e m odel is th e n utiliz ed to in v e stig a te t h e influence

of m e l t w a t e r disch arg e on t h e s ta b ility of N o r th .Atlantic D eep W a te r (N.ADW )

p r o d u c ti o n a n d th e Y ounger Dryas (Y D ~ 14ka). R e s u lts suggest p re -Y D m e ltw a ­

t e r is c a p a b le of d im in is h in g N.ADW to t h e point w here d iv e rsio n of m e l t w a t e r from t h e G u lf of M exico to t h e S t. Law rence c o m p le te ly in h i b its its p r o d u c tio n . T h e

c o u p le d m o d e l a p p e a rs to b e stab le in this s ta t e , e q u iv a le n t to th e " S o u th e r n S ink­ ing" e q u i lib r i u m identified in previous m odels. Inclusion of th e wind s t r e s s / s p e e d

feedback, however, has a d r a m a t i c effect c a u s in g a r e e s ta b lis h m e n t of N.ADW p ro­

d uction.

T h e m odel is th e n configured in a four basin -tw o h e m is p h e re s e c to r geom etry,

c rudely re p re s e n ta tiv e of t h e global oceans. T w o identically f o rm u la te d m odels

(one of which em ploys d ux a d ju s t m e n t s ) a r e th e n p e r tu r b e d to assess th e role

of dux a d j u s t m e n t s on th e o c e a n 's response to a "global w arm in g -lik e" scenario.

Signidcant global a n d b asin-scale differences e x ist betw een th e cases which is linked

to th e ind u e n ce of th e s a lt - d u x a d j u s t m e n t on th e o v e rtu r n in g cells w ithin th e

m odel .Atlantic a n d S o u th e rn O ceans. R esu lts f u r th e r suggest t h a t m in im izin g th e

coupling shock prior to a p p ly in g th e p e r t u r b a t i o n leads to re s u lts slightly closer

betw een th e m odels, a lth o u g h large differences still persist.

T h e m odel is th e n c o n d g u r e d for a highly idealized 60° s e c to r g e o m e try to

s tu d y th e in d u e n ce of h o riz o n ta l resolution a n d p a r a m e te riz e d e d d y processes on

polew ard h eat tr a n s p o r t. .As resolution increases, th e to tal o c ea n ic h e a t tr a n s p o r t

s tead ily increases. T his re s u lt is also ev id e n c e d in a parallel series of ocean-only

m odel studie s driv en by r e s to r in g b o u n d a ry co n d itio n s. In each case t h e increase in

h e a t tr a n s p o rt is associated w ith th e ste a d y c u rre n ts . In p a r ti c u la r t h e baroclinie

gyre tr a n s p o r t (our m ode l a n a lo g of th e t r a n s p o r t associated w ith th e "W a rm

Core" je t region of th e G u lf S tr e a m ) increases by a factor of -5 b e tw e e n coarsest

a n d dnest resolution.

is th e rm a ll y driven by a n advective-convective m e c h a n is m a n d linked to th e value

of th e h orizontal dilfusivity em ployed. Increasing th e difFusivity in th e high reso­

lution cases is enough to destro y t h e variability, while decre asin g t h e diffusivity in

th e m o d e ra te ly coarse resolution case is enough to in d u c e th e variability. T h e s e

results p o in t to th e im p o r ta n c e of highe r resolution in t h e oceanic c o m p o n e n t of

cu rre n t c lim a te m odels, yielding e n h a n c e d poleward h e a t tr a n s p o r ts a n d reveal­

ing th e ex isten ce of richer d ecadal-scale variability in m ode ls which re q u ire less

p a r a m e te r iz e d viscosity a n d diffusion.

E x am in ers:

Dr. .\..J. W eaver. S u p ervisor (School of E a r t h and O c e a n Sciences)

---Dr. I. F ung, D e p a r tm e n ta l M em b er (School of E a rth a n d O cean Sciences)

Dr. R. Lueck. D e p a rtm e n ta l M e m b e r (School of E a r t h a n d Ocean Sciences)

Dr. C..J.R. G a r r e ^ M e m b e r (P h y sics D e p a r tm e n t)

Dr. "«E T aarachikÆ xterind E x a m in e r (U n iv ersity of W a s h in g to n )

C o n te n ts

A b stract

ü

List o f Tables

viii

List o f Figures

ix

A ckn ow led gem ents

xii

1 In trod uction

1

2 M odeling the C lim ate S y stem

9

2.1 T h e A tm o s p h e ric E n erg y M oisture B a la n c e M o d e l ... 9

2.1.1 M odel P a r a m e te r s ... 13

2.1.2 L 'nce rtain ty in M odel P a r a m e t e r s ... 19

2.2 T h e Ice M o d e l ... 20

2.3 T h e O cean G eneral C irc u la tio n M odel ... 22

3 T esting U nder F ixed O ceanic C on ditions

26

3.1 P resent D ay C l i m a t o l o g y ... 26

3.2 S ensitivity to Model P a r a m e t e r s ... 37

3.3 In te ra n n u a l V a r i a b i l i t y ... 40

4 C oupling to an O cean G eneral C irculation M od el

51

5 S e n sitiv ity to N orth A tlantic Freshw ater P ertu rb ation s

61

Ô.1 S e n s itiv ity to M e ltw a te r D i s c h a r g e s ... 65

5.2 C o m p a r is o n of M odeled C li m a t ic Signal to t h e Y o unger D ryas . . . 70

5.3 R e e s t a b lis h m e n t of th e N o rth .Atlantic C o n v e y o r ... 77

5.4 D i s c u s s i o n ... 80

6 On th e R ole o f F lu x A d ju stm en ts in C oupled M od el P ertu rb ation

E xp erim en ts

84

6.1 M o d e ls ’ D e s c rip tio n an d E q u i l i b r i u m ... 85

6.2 C li m a t e P e r t u r b a t i o n E x p e r i m e n t s ... 99

6.3 D i s c u s s i o n ...108

7 A H orizontal R esolu tion and P a ra m eter S e n sitiv ity Study o f P o le ­

ward H eat Transport in the C ou p led M odel

112

7.1 M odel D escrip tio n a n d E x p e r i m e n t a l D escription ... 116

7.2 P o lew ard H eat T r a n s p o r t ... 121

7.2.1 Basic D e f i n i t i o n s ...121

7.2.2 T h e C o u p le d Model R e s p o n s e ... 122

7.2.3 C o m p a ris o n to C o x - B r y a n ...133

7.3 D i s c u s s i o n ... 137

8 T h erm ohalin e Variability: T h e E ffects of H orizontal R eso lu tio n

and D iffusion

141

8.1 D e c ad al-S cale V a r i a b i l i t y ... 143

8.2 D i s c u s s i o n ... 150

9 C onclusions

R eferences

2.1 S u m m a r y of .-Xtmospheric M odel P a r a m e t e r s ... 14

2.2 S u m m a r y of Ice M odel P a r a m e t e r s ... 21

3.1 S u m m a r y of M odel S e n s itiv ity E x p e rim e n ts ... 38

3.2 B asin M ean I n te r p e n ta d a l M odel F i e l d s ... 43

•5.1 Im posed R unoff by B a s i n ... 65

5.2 Inferred Cooling D uring th e Y ounger D ryas... 75

6.1 S u m m a r y of F lu x .Adjustm e n t M odel E x p e r i m e n t s ... 89

7.1 Resolution S tu d y E x p e r i m e n t s ... 120

7.2 R esolution E x p e r i m e n t s ' \ iscosity a n d D i f f u s i v i t y ... 120

L ist o f F ig u res

1.1 .Atlantic C o n v e y o r ... 2 1.2 M u ltip le E q u i l i b r i a ... 5 2.1 .A tm ospheric Diffusion ... 16 2.2 .A tm ospheric P a r a m e t e r s ... 16 2.3 D alton N u m b e r ... IS 3.1 L ev itu s' C lim a to lo g ic a l S S T ... 27

3.2 C lim a to lo g ic a l S urface .Air T e m p e r a t u r e ... 2S 3.3 C lim a to lo g ic a l Surface Specific H u m i d i t y ... 30

3.4 C lim a to lo g ic a l E v a p o ra tio n R a t e ... 32

3.5 C lim a to lo g ic a l P r e c ip ita tio n R a t e ... 33

3.6 C lim a to lo g ic a l F re s h w a te r F l u x ... 35

3.7 C lim a to lo g ic a l S urface H eat F l u x ... 36

3.S S u m m a r y of P a r a m e t e r S e n s itiv ity S t u d y ... 39

3.9 I n te r p e n t a d a l C lim ato lo g ic al C h a n g e ... 41

3.10 L e v itu s ’ I n te r p e n t a d a l SST C h a n g e ... 44

3.11 I n te r p e n t a d a l C lim ato lo g ic al C h a n g e (M arginal C a s e ) ... 46

3.12 I n te r p e n t a d a l C lim ato lo g ic al C h a n g e (U n a c c e p ta b le Case) ... 47

4.1 R ealistic G e o m e t r v M odel D o m a in ... 52

4.4 E M B M - O G C M Zonal T e m p e r a t u r e P r o f i l e s ... 57 4.5 E M B M - O G C M Zonal A t l a n t i c S a l i n i t y ... 58 4.6 E M B M - O G C M P o lew ard H e a t T r a n s p o r t ... 59 5.1 In ferred G r e e n la n d C li m a t e R e c o r d ... 62 5.2 M e lt w a t e r In tr o d u c tio n R e g i o n s ... 67 5.3 D eglacial M e ltw a te r E x p e r i m e n t s ... 68

5.4 T i m e E v o lu tio n of A tla n tic C o n v e y o r ... 69

5.5 Y D -like C l i m a t e S t a t e ... 72 5.6 M odeled Y D -like T e m p e r a t u r e C h a n g e ... 73 5.7 E s t i m a t e d W i n d Stress A n o m a l y ... 79 6.1 Idealized S e c to r G e o m e t r y ... 88 6.2 Non-flu.x A d ju s te d S S T ... 91 6.3 Non-flux A d ju s te d S S S ... 92 6.4 N on-flux A d ju s te d Zonal T e m p e r a t u r e ... 93 6.5 .Non-flu.x A d ju s te d Zonal S a l i n i t y ... 94

6.6 Non-flux .Adjusted .A.tlantic O v e r tu r n in g ... 96

6.7 .Non-flux A d ju s te d Pacific O v e r t u r n i n g ... 97 6.8 N on-flux A d ju s te d H eat T r a n s p o r t ... 98 6.9 F lux A d j u s t m e n t Fields ...100 6.10 A p p lie d R a d i a ti v e F orcing P e r t u r b a t i o n ... 101 6.11 T i m e D e p e n d a n t M odels’ R e s p o n s e ...103 6.12 N on-flux A d ju s te d A n o m a l y ... 105 6.13 F lu x V ersus Non-flux A d j u s t e d A n o m a l y ... 106 6.14 C o u p lin g S h o c k ...107 X

6.1-5 F lu x Versus N on-flux .\d ju s te d . A n o m a l i e s ...109

7.1 S olar Insolation a n d W ind Stress ... 117

:1 T o ta l H eat T r a n s p o r t Coupled Versus H a n e y ... 123

.2 C o n t i n u e d ... 124

.3 D ecom p o sitio n of H eat T r a n s p o r t s ... 126

.3 C o n t i n u e d ... 127

.3 C o n t i n u e d ... 128

.3 C o n t i n u e d ... 129

.4 T i m e M ean a n d V arying Heat T r a n s p o r t s ... 131

.4 C o n t i n u e d ... 132

.5 R e s to rin g P r o f i l e s ...134

.6 T o ta l H eat T r a n s p o r t ( R e s t o r i n g ) ...135

.7 B aroclinie G yre T r a n s p o r t ( R estoring) ... 136

.8 P ow er S p e c t ru m of K inetic Energy D e n s i t y ... 138

.9 T i m e V ariant H eat T ran sp o rt ( R e s t o r i n g ) ... 140

8.1 H igh a n d Low P h a s e of Decadal O s c i l l a t i o n ... 145

8.2 T i m e Series of K in e tic Energy D e n s i t y ...146

8.2 C o n t i n u e d ...147

8.3 S en s itiv ity to N o n lin e a r .-Vdvection T e r m s ...148

8.4 S en s itiv ity to D i f f u s i v i t y ... 148

This w ork has been carried o u t w ith su p p o rt from th e A tla n tic A c c o rd C a re e r D e­ v e lo p m e n t A w a rd 's p ro g ra m m e , an d o p e ra tin g g ra n ts a w a rd e d to .Andrew W eaver from X S E R C . .AES. CTCS. a n d th e XO.A.A S c rip p s -L a m o n t C o n s o r t i u m on t h e O cean 's R o le in C lim ate.

C h ap ter 1

In tr o d u c tio n

O n e of t h e fu n d a m e n ta l roles of t h e ocean in c l i m a t e is its a b ility t o s to r e and effectively t r a n s p o r t h e a t polew ard. T h e th e r m o h a l i n e c irc u la tio n ( T H C ) . driven by th e c o m p e tin g effects of h eat a n d fresh w a ter fluxes, is a n i m p o r t a n t c o m p o n e n t in h eat t r a n s p o r t from low to high la titu d e s . I n te n s e h ig h l a t i t u d e co o lin g and low la t i t u d e h e a tin g ac c e le ra te s a polew ard surface flow w ith high l a t i t u d e sinking in th e n o r th e r n N o r th .Atlantic, b ala n c e d by a d e e p r e t u r n flow o f cold dense w a te r at d e p t h - th e N o rth .Atlantic deep w a te r (N .A D W . see F ig u re 1.1). T h e n o r th w a r d surface flow t r a n s p o r ts w a rm w a te r to h ig h n o r t h e r n l a t i t u d e s , w arm in g t h e E u ro p e a n c o n tin e n t along its route.

Interestingly, since w a rm w aters a re less dense, s u c h a t r a n s p o r t s h o u ld act to d estro y th e o v e r tu r n i n g circ u latio n . F u r th e r m o re , for w aters n e a r 0 ° C . it is t h e salin ity which p r im a r ily d e te rm in e s its density. T h i s p re s e n ts a n o t h e r caveat, s u b p o la r la titu d e s a re regions of m o is tu r e converg e n ce in t h e a t m o s p h e r e (see Fig­ u re 1.1). w ith p r e c i p ita tio n exceeding e v a p o ra tio n , y e t t h e w aters o f t h e n o r th e r n N o rth .Atlantic are q u i t e saline (cf. 32.S psu (p r a c t ic a l s a li n ity u n its) in t h e Pacific versus 34.9 psu in t h e .Atlantic). T h is high l a t i t u d e A t l a n t i c s a li n ity is in part d u e to th e o v e rtu r n in g circ u la tio n t h e r e (a n d conv ersely its a b sen ce in t h e Pacific).

E V A P O R A T I O N

_ - 3 0N

cc

60S

Figure' L I. .Schematic of th e o v e r tu r n i n g c irc u la tio n in th e .\U a n tic . a n d of th e su rfa c e freshw ater flux, (from Held. 1993).

T h e h ig h e r sea surface te m p e r a t u r e s of th e A tla n tic favor s tro n g er e v a p o ra tio n at low la titu d e s , a n d t h e s h o rte r residence ti m e in regions of net p re c ip ita tio n are both consequences of th e T H C (W a rre n . 196:3). T h is p ic tu r e of a self-sustaining c irc u la tio n raises th e q u e s tio n as to w h e th e r a c l im a t e w ith o u t X.ADW fo rm a tio n (or in w hich it is i n t e r m i t t e n t ) m ight also be possible.

In a pioneering s tu d y . S to m m e l (1961) d e m o n s t r a t e d th e existence of a th e r ­ m o h a lin e circ u la tio n (in a two box m o d e l) w ith tw o s ta b le regimes of flow. T h e flow regim es ( n o r th e r n sinking, or s o u th e r n sinking) d e p e n d e d on w h e th e r heat loss or s a lin ity d o m i n a te d th e d ensity g ra d ie n t d riv in g th e circulation. B roecker ( I960) s p e c u la te d t h a t ra p id tra n s itio n s b etw ee n glacial m odes (observed in the c lim a te record) could be linked to th e r a t e of fo rm a tio n (or absence) of N.ADW. In effect, changes in N.A.DW p ro d u ctio n cou ld p ush t h e c lim a te s y ste m fro m one q u a s i-s ta b le m o d e of o p e r a tio n to a n o th e r. B ry an (1966) d e m o n s tr a te d t h a t m u l­ tiple ecpiilibria of th e th e rm o h a lin e c irc u la tio n could e x is t in a 2 h e m is p h e re , th re e d im en sio n al ocean general circulation m odel. He found t h a t a m odel w ith s y m m e t ­ ric forcing a b o u t th e e q u a t o r could easily s u s ta in a circ u la tio n with pole to pole o v e rtu rn in g , a n d deep w a te r form ation confined to o n ly one hem isphere. M a ro tz k e a n d W ille b ra n d (1991) fu rth e re d this s tu d y by c o n sid erin g a two basin, tw o h e m i­ sphere m o d e l (w ith in te rc h a n g e a b le . \ t l a n t i c a n d Pacific basins) linked by a cyclic, c irc u m p o la r circ u latio n in th e so u th e rn h e m is p h e re . T h e s e a u th o rs identified four sta b le e q u ilib ria (see F ig u re 1.2):

• C o n v e y o r Circulation (w ith deep sin k in g in t h e N o r th .Atlantic a n d upw elling in th e N o rth Pacific)

• Inverse C o n v e y o r ( th e opposite of th e presen t d a y conveyor.)

• N o r t h e r n S i n k in g (w ith deep sinking in th e n o r t h e r n h em is p h e re for b o th b asins)

etry, a n d o th e r m ode l p a r a m e te r s (e.g.. w ind s tre s s , im plied hydrological cycle ...) a n d were able to narrow M a ro tz k e an d W i lle b r a n d 's four e q u ilib ria to only two: e lim in a tin g th e N o rth e rn S inking an d th e Inv erse C onveyor sta te s .

E ach of the se th r e e d im e n s io n a l ocean m o d e l s tu d ie s have in c o rp o r a te d a m ix e d b o u n d a r y cond itio n for sp ecifying th e su rfa c e h e a t a n d salt fluxes. T h a t is. th e m o d e ls ' are initia lly s p u n up to eq u ilib riu m by r e s to rin g to specified surface t e m ­ p e r a t u r e s and salinities. T h e surface salt flux is t h e n diagnosed fro m th e e q u ilib ­ riu m s t a t e an d held fixed, w hile th e resto rin g b o u n d a r y cond itio n o n t e m p e r a t u r e is m a in ta in e d . U n d e r such b o u n d a r y co n d itio n s , t h e th e rm o h a lin e circ u la tio n is g en era lly near t h e s ta b ility tr a n s i tio n p o in t, allo w in g th e m odel to pass b etw een s ta b le a n d u n s ta b le regim es t h r o u g h only m o d e r a t e changes in t h e p rescrib e d fresh­ w a te r flux (B ry a n . 1986: W eaver a n d S ara c h ik . 1991b). Recent e x p e r im e n ts have s u g g ested th a t allowing for long wave r a d ia tiv e d a m p in g to space (Z hang et al. 1993). or th e inclusion of a tm o s p h e r ic heat t r a n s p o r t ( R a h m s t o r f a n d W illeb ra n d . 1995) g re a tly e n h a n c e s th e s ta b ility of th e th e r m o h a l i n e circ u la tio n This is also t h e case when t h e resto rin g tim e s c a le used in t h e sp in -u p p ro c e d u re , an d in th e m ix e d b o u n d a ry c o n d itio n is incre ased (P o w e r a n d K leem an . 1994: T z i p e r m a n et al. 1994: M ikolajew icz a n d M aier-R e im e r. 1994). T h is sta b iliz a tio n h as d raw n into q u e s tio n w h e th e r m u ltip le e q u ilib ria a n d h en c e tra n s itio n s b etw een these e q u ilib ­ ria (deca dal to m illenial tim e s c a le v ariability - see W eaver a n d H ughes. 1992) can exist in ocean m odels w hen d riv e n u n d e r m o r e realistic b o u n d a ry conditio n s. It h as also been sugg ested t h a t d e c a d a l scale v a ria b ility is in tim a te ly tie d to m o d e l resolu tio n , w ith th e possibility t h a t no v a r ia b ility w ould exist a t h ig h e r resolution ( W in t o n . 1996).

P A C IFIC A T L A N T IC

Kx

-. ■TTT rr r

F igure 1.2. SclicMiialic of tlic four tlicriuolialiue cq u ilih riiu u '.tates identified bv M arotzke a n d W i lle b r a n d (1991). Dashed arrows in d ic a te How a t d e p t h (re p r o ­ d u c e d frotn Held. 1993).

s im ilar to th e p resen t c lim a te (e q u ilib ria 1. F igure 1.2). w hile th e second s ta te has upw elling in b o th th e .Atlantic a n d Pacific (e q u ilib ria 4. F ig u re 1.2). T h e surface freshw a ter fiux differences b e tw e e n th e cases in d ic a te s a roughly 0.1 r n /y r freshening of th e n o r th e r n N o rth . \ t l a n t i c between th e tw o s ta te s (see F igure 21. M a n a b e a n d StoufFer. 1988). S tock e r a n d W right (1991) hav e also identified these s ta te s in a zonally av e ra g e d coupled o c e a n -a t m osphere m o d e l. T h e y in d ic a te th a t red u cin g t h e net salt fiux in th e N o rth .Atlantic by 0.03 Sv is enough to induce a t r a n s i tio n to th e S o u th e r n Sinking eq u ilib ria , an d t h a t on ce in duced it requires an increase of 0.36 Sv to re-establish t h e C o n v e y o r Circulation. Recently. R a h m s to r f ( 1995) h a s shown a s im ila r s en sitiv ity (0.06 Sv) in an idealized a t m o s p h e r ic model coupled t o a realistic geom etry , global o cean general circ u la tio n m o d e l (O G C M ).

Del w o rth et. al (1993) have also in d ic a te d th a t i n t e r m i t t e n t tra n s itio n s be­ tween t h e s tr e n g th of N.ADW p ro d u c tio n (decadal varia b ility ) can also exist in the model o f M a n a b e a n d StoufFer (1998). It is not clear, however, to w h a t extent th e v a ria b ility in th e s e studies is p re c o n d itio n e d by t h e h e a t a n d salt fiux fields em p lo y ed . In th e realistic g e o m etry cases, heat and salt a d j u s t m e n t fields (which are g e n e ra lly larger t h a n t h e prognostic fields) are recjuired to p revent c l im a t e drift (see F ig..A l. M a n a b e a n d StoufFer. 1988; W eaver and H ughes. 1996). T h e precip­ ita tio n s ch em e em p lo y e d by Stocker a n d W right (1991) is also e s s en tially a fiux a d j u s t m e n t . It is re a s o n a b le to ex p e c t t h a t these specified h e a t a n d sa lt fluxes (to­ g e th e r w ith th e a n n u a l m e a n fields) d e t e r m in e th e oceanic s ta t e . High frequency air-sea fluxes are th e n c a p a b le of p ro v id in g a stochastic c o m p o n e n t w hich can ex­ cite tr a n s i tio n s b e tw e e n e q u ilib riu m s ta t e s , leading to d e c a d a l scale v aria b ility (as in ea rlie r ocean only s tu d ie s - W eaver et al. 1991. 1993). S uch a n effect has also been d e m o n s t r a t e d in o c e a n only m o d e ls w hen driven u n d e r c o n s ta n t fiux forcing

( G r e a tb a tc h a n d Z hang, 1993: W in to n . 1996).

Given th e s e n s itiv ity o f t h e m o d e led th e rm o h a lin e circ u la tio n to t h e surface b o u n d a ry forcing e m p lo y e d , th e q u e s tio n n a tu ra lly arises w h e th e r m u l tip l e e q u i­ libria. or even d e c a d a l-m ille n ia l tim e s c a le variability can exist w hen full coupling of b oth th e heat an d fre s h w a te r duxes a r e em plo y ed in a m o d e l w ith o u t t h e use of flux a d ju s tm e n ts .

In th e present work we u tilize th e fact t h a t since th e tim e s c a le of a t m o s p h e r ic variability is generally s h o rt c o m p a re d to t h e oceanic tim escales of in te re s t (decadal- millenial) we a p p e a l to a s im p le e n e rg y -m o is tu re balance m odel for o u r a t m o s p h e r ic processes. We e x te n d t h e w ork of Z h a n g e t al (1993) a n d R a h m s t o r f a n d W ille­ b rand (1995) by in c lu d in g not only long wave radiative d a m p in g to s p a c e and diffusive a tm o s p h e ric h e a t tr a n s p o r t, b u t also surface long wave, sen sib le a n d la­ te n t heat fluxes: as well as a sim ple a p p r o x im a ti o n to th e hydrological cycle. Since th e tim escale of v a ria b ility of th e c r y o s p h e re lies between t h a t for t h e a t m o s p h e r e a n d ocean, a sim p le th e r m o d y n a m i c ice m odel (S em tner. 1976) (w hich includes heat in su lation a n d b rin e rejection) is also in c o rporated.

In C h a p t e r 2. th e c o u p le d e n e r g y - m o is tu re balance m odel ( E M B M ) is d ev el­ oped. a n d m odel p a r a m e t e r e s tim a tio n a n d u n c e rta in ty is discussed. T h e sim ple th e rm o d y n a m ic ice m o d e l w hich is e m p lo y e d is th e n detailed, along w ith a review of th e e q u a tio n s a n d a s s u m p ti o n s g o v e rn in g th e ocean general c irc u la tio n m odel. T h e a tm o s p h e ric m o d e l is t h e n te sted by specifying th e oceanic s t a t e (as c lim a ­ tological or in t e r p e n ta d a l (1955-59: 1970-74) sea surface t e m p e r a t u r e fields) a n d a discussion of th e c lim a to lo g y (or in fe rre d c lim a te change) is p re s e n te d a n d con­ tra s te d against d irect o b serv atio n s. T h e e n erg y -m o istu re b ala n c e m o d e l is th e n coupled to an ocean g e n e ra l circ u latio n m o d e l - th e G eophysical F lu id D y n a m ic s L ab o ra to ry (G F D L ) M o d u la r O cean M o d el ( M O M l . l . see Pacanovvski e t al.. 1993) as well as th e t h e r m o d y n a m i c ice m odel ( C h a p t e r 4). .A.s a s trin g e n t t e s t of th e

tic a l eq u ilib riu m s t a t e is th e n c o m p a r e d against o b serv atio n al e s t i m a t e s of t r a c e r q u a n titie s , as well as m e rid io n a l tr a n s p o r t rate s a n d polew ard h e a t t r a n s p o r ts . B eginning from th is c lim a te s t a t e ( C h a p t e r ô) a series of fre sh w a ter p e r t u r b a t i o n e x p e r im e n ts are carried out to in v e s tig a te th e possible influence of th e d e m is e of t h e L a u re n tid e ice sheet on tr ig g e rin g t h e Y ounger D ryas (Y D ) cold ev en t. T h e m o d e led Y D -like c lim a te s t a t e is th e n c o m p a re d to e x istin g p a le o re c o n s tru c tio n s of t h e ^ D clim a te , a n d m e c h a n is m s re g a rd in g th e tr a n s i tio n to th e p re s e n t H olocene a r e discussed. T h e m odel is t h e n configured in a highly idealized s e c to r g e o m e tr y ( cru d ely r e p re s e n ta tiv e of th e g lobal o c ea n s) to s t u d y t h e role of flux a d j u s t m e n t s in co u p led m odel p e r tu r b a tio n e x p e r i m e n t s ( C h a p t e r 6). .A c o m p a ris o n b etw ee n flux a d j u s t e d a n d non-flux a d j u s t e d m o d e ls driven by th e s a m e forcing p e r t u r b a t i o n is c a rr ie d out a n d c o n tra s ts a re linked to th e flux a d j u s t m e n t s e m p lo y e d . T h e m o d e l is th e n f u rth e r simplified ( C h a p t e r 7) to a single b asin in o rd er to in v e stig a te th e role of horizontal resolution a n d p a ra m e te riz e d d is s ip a tio n on t h e m o d e led p o le­ w a rd heat t r a n s p o r t. T h e p o le w a rd h e a t tr a n s p o r t is s u b s e q u e n tly d e c o m p o se d in to its various c o m p o n e n ts a n d c o n t r a s t e d against a series of o cea n -o n ly m o d e l s im u la tio n s. Finally, this s a m e m o d e l configuration is used to in v e s tig a te w h e th e r th e rm o h a lin e variability can still exist in a fully co u p le d m odel (w h ich does not e m p lo y fiux a d ju s t m e n t s ) a n d d o c u m e n t th e im p o r ta n c e of reso lu tio n a n d diffusion in allowing a n d m odifying th is variability.

C h ap ter 2

M o d e lin g th e C lim a te S y s te m

2.1

T h e A t m o s p h e r ic E n e r g y M o is t u r e B a la n c e

M o d e l

T h e e n e r g y - m o is tu re b a la n c e c l im a t e model we em p lo y is b a s e d u p o n th e v e r t i ­ cally in te g r a te d e n e r g y - m o is tu r e b a la n c e equations, in which a d v e c tio n te rm s a r e replaced by a n ed d y -diffusive a p p ro x im a tio n . O v e r t h e o cea ns, t h e energ y b a l a n c e (in ice-free a n d ice co v ere d regions), is expressed by.

d T

P a H a C p a - ^ = Qt + QsSW ~ QL\V + QRR + Q sH + QLH ( 2 . 1 . 1 a )

over land we a s s u m e no h e a t o r m o is tu re storage, a n d hen ce we w r ite

d T

P a H a C p a - ^ = Qt + QSSW ~ QLW + QLH ( 2. 1. 16)

w here pa is a c o n s ta n t s u rface a ir density. Cpa t h e specific h e a t c a p a c i t y of air. Ha a c o n s ta n t scale h eig h t d e p t h r e p r e s e n ta tiv e of t h e a tm o s p h e r e , a n d Tp th e s u rfa c e a ir t e m p e r a t u r e . T h e te r m s on t h e right h a n d side of (2.1.1) a re th e various

so u rc e s /s in k s o f h e a t i n t o / o u t of th e s y ste m . Here

is th e ed d y -diffusive h o rizo n tal heat tr a n s p o r t p a r a m e te r iz a tio n , in w hich A is th e lo ngitude, o is t h e l a tit u d e , a is th e ra d iu s of th e e a r t h , a n d u is a la tit u d in a ll y d e p e n d e n t h e a t t r a n s p o r t coefficient.

In general, t h e a t m o s p h e r e may a b s o rb upw ards of 30 % of th e to t a l incom ing short wave r a d ia tio n t h r o u g h the co m b in e d effects of w a te r vapour, d u s t, ozone an d clouds ( R a m a n a t h a n . 1967). To m im ic these effect, we a p p ly a so u rc e te rm in th e a tm o s p h e re :

Q ssw

= 1 — o ) ( l — Co) (2.1.3)

w here is t h e s o la r c o n s ta n t. 5 is t h e annual average d is tr i b u tio n of h eat flux e n te r in g th e to p of t h e a tm o s p h e re ( N o rth . 1975). q is th e alb e d o , a n d Co is a re d u c tio n p a r a m e t e r representing th e s c a tt e r in g / a b s o r p tio n processes d escribed above. O ver la n d , all s h o rt wave r a d ia tio n in te rc e p te d is a s s u m e d r e t u r n e d (via black b o d y ra d ia tio n ) to t h e a tm o s p h e re so th a t

Co

assu m es a value of zero th e re .

T h e net long w ave re la x a tio n to sp a c e is m odeled by co nsidering t h e planet as a grey b o d y w ith e m is s iv ity cp. T he in frared em ission is th e n given by

Ql w = cpcrT^ (2.1.4a) w here a is th e S te f a n - B o l tz m a n n c o n s ta n t. .Alternatively th e m o is tu r e long wave feedback effect c a n b e ta k e n into acc o u n t by em p lo y in g t h e p la n e ta r y long wave p a r a m e te r i z a ti o n of T h o m p s o n and W a rre n (1982).

11

where a,v = 6o.v + b i \ r + bo.xr’ , .V — 0, 1 . 2 .3 . and b \ f \ a r e e m p irica lly d e riv e d c o n stan ts (see T h o m p s o n a n d Warren. 1982. T able 3).

T h e long wave r a d ia tio n e m itte d by t h e o c e a n is s tr o n g ly ab sorbed by g r e e n ­ house gases p re s e n t in t h e atm osphere. T h e a t m o s p h e r e t h e n re-em its this a b ­ sorbed en ergy b o t h u p w a r d a n d dow nw ard resu ltin g in a long wave Hux a t th e base of th e a t m o s p h e r e , which we model as a grey b o d y em ission. T h e ra d ia tiv e flux is w r itte n as

f So(tTj — if ice-free:

Qr r = { (2.1.5a)

[ S{crT^ — z o th e rw ise

where To.T, is t h e sea. a n d ice surface t e m p e r a t u r e , re s p e c tiv e ly : and £q . c / . £a

are th e oceanic, ice. a n d a tm o s p h e ric em issivities. .A lternatively th e m o is tu r e long wave feedback effect c an b e ta k e n into a c c o u n t by e m p lo y in g th e p la n e ta r y long wave p a r a m e te r i z a ti o n of B erliand and B e rlia n d (1952)

f £ocrT^(0.'-i9 — O.Oo\/t)Fc + Ai£oO'T^{To — T J . if ice-free:

Ç/Î/Î = s (2.1.56)

[ c/crT^(0.39 — 0 .0 5 v /e)F c + À£ [ aT ^{ T, — Ta). otherw ise

where e is th e w a te r v a p o u r pressure (in m b . - e = 1.61 x ICPg). q is th e specific hum idity, an d F c is r e la te d to th e cloud cover fraction a n d various o th e r e m p ir ic a l co nstants (see E s b e n s e n a n d K ushnir. 1981 for a discussion).

F c = l l . 5 - 2 2.gr 4- ll.T r^

where r is th e r e la tiv e h u m id ity .

. \ tr a d itio n a l b u lk p a r a m e te r iz a tio n is u tiliz e d for t h e s e n s ib le heat flux:

f PaCRCpaF(To - Ta), if ice-free:

= I . ( - 1 6 )

[ PaCnCpai {T, — Ta), o th c rw is e

la te n t h e a t flux in to t h e a tm o s p h e r e ta k e s the form

Qlh — —— LuP ( 2. 1. 7)

.iijr

w h e re is th e l a t e n t h e a t of ev a p o ra tio n , s y r is th e n u m b e r of seconds in a year, a n d P is the p r e c i p ita tio n (in m e ters p e r year - a s s u m e d to o c c u r w h e n s a t u r a t i o n ex ce ed s So %).

.A m o istu re b a l a n c e e q u a tio n has also been a d d e d so t h a t t h e a t m o s p h e r ic h y ­ drological cycle c a n b e included. VVe o b ta in a p a r a m e te r i z a ti o n of t h e h ydrological cycle by considering a n a p p ro x im a tio n to th e b a la n c e e q u a tio n for w a te r vapor in t h e a tm o s p h e re . In th i s a p p r o x im a tio n we replace t h e h o rizo n tal a d v e c tio n t e r m s by a n ed d y diffusive t e r m . \'e rtic a lly in te g ra tin g over t h e d e p t h of t h e a t m o s p h e r e we o b ta in

^ I + a ( . . c o s o ^ ) I + (■> , . s )

a t a-COSO [ cos o c/A- a o \ o o y j s y r

w h e re is a c o n s ta n t scale height d e p t h for th e specific h u m id ity , k is an e d d y diffusive horizontal r e d is t ri b u ti o n t e r m . P is th e p r e c ip ita tio n , a n d E is t h e e v a p ­ o r a ti o n (abla tion o v e r ice is neglected in th e m o is tu re source te rm s , b u t r e ta in e d in t h e ice heat b u d g e t ) . T h e e v a p o ra tio n is c a lc u la te d from its tr a d i ti o n a l bulk fo rm u la

P .C 'E r s w r f ( g X r j - g j . if ice-free;

£ = (2. 1. 9)

Po [ ( ç ^ ( r .) — 7 u ) . o th e rw is e

w h e re Ce is th e D a lt o n n u m b e r. q s { T ' ) is th e s a t u r a t i o n specific h u m i d ity a t

13

e m p iric a l fo rm u la of B olton. 1980):

f ific e -fre e :

9. = 3.802 X 1 0-^ezp { (2.1.10)

I i f , +271%) • O t h e r w i s e

T ra d itio n a lly , a co n s ta n t h u m i d i t y is used in th e bulk p a r a m e t e r i z a t i o n for t h e e v a p o ra tio n (e.g. Haney. 1971). however, sin ce we also m o d e l t h e c o n s e rv a tio n of w a te r vap o r, th is is not n ec e ss a ry in th e p re s e n t fo rm u latio n .

To o b t a i n closure of (2.1.8) we p a r a m e te r i z e th e p r e c i p ita tio n as

p _ P a H r j y i (2.1.1 1)

P o ^ t

w here A / is t h e model ti m e s te p . qs[T^) is t h e s a tu ra tio n specific h u m i d ity a t 7),.

r is th e r e la tiv e hum id ity , a n d

r 1. if r > 85%:

/ / ( r ) = <^ (2.1.12)

1 0. o th e rw is e

2.1.1

M o d e l P a ra m eters

.A. n u m b e r o f p a r a m e te r s m u s t be specified in an effort to s i m u l a t e th e p re s e n t clim ato lo g y ( t h e reader is r e fe rre d to T ab le 2.1 for a c o m p le te listin g o f values). In th e p resen t s t u d y we have d r a w n upon p re v io u s works for m a n y o f o u r p a r a m e t e r s w ith a n eye to w a r d both s im p lic ity an d p h y s ic a l ju stific a tio n . To th is e n d we h a v e re ta in e d o n ly t h e la titu d in a l v a ria tio n of p a r a m e te r s , our o n ly ju s ti f ic a t io n for th is being m o d e l simplicity. .Although a n u m b e r of physical a n d d y n a m i c a l processes which are n o t included in th is m o d e l (e.g.. la n d surface processes) could in d e ed b e sy n th e s iz e d by d e ta ile d s p a ti a l p a r a m e te r i z a ti o n s . we take t h e view t h a t such "fine tu n in g " of t h e m ode l u lt i m a t e l y p ro h ib its its use over a w ide r a n g e of a p p lic a tio n s .

P a r a m e t e r Description Value

a radius of t h e E a r t h 6371 km

(I - q ) coalbedo see Figure 2 .2d

Pair surface air d e n s ity 1.2.3 k g /m ^

P sea sea surface d e n s ity 1024 k g /m ^

C'e D alton n u m b e r see Figure 2.3

c„

S tan to n n u m b e r 0.94Ce

Co solar s c a tte r in g coefficient see Figure 2.2c heat cap a city of dry air 10T j/(kgK ) = .4 atm o sp h eric em issiv ity see F igure 2.2a

-■p p lanetary em issivity see Figure 2.2b

oceanic em issivity 0.96

Ha atm osp h eric scale d e p t h 8400 m

specific h u m id ity scale d e p t h 1800 m

K eddy diffusivity for m o i s t u r e see Figure 2.1

L. latent heat of e v a p o r a tio n 2.5 X lO M /k g

u eddy diffusivity for h eat see Figure 2 . 1

s

solar insolation d is tr i b u tio n * * •

S'; solar co n stan t 1 3 6 0 \V /m ‘

model tim e s te p 0.5 (0.25) d ay s

a S te fa n -B o ltz m a n n c o n s ta n t 5.67 X l O - n V / ( r n - K ‘ ) T a b l e 2.1. S u m m a r y of . \ t m o s p h e r i c M odel P a r a m e te r s

15

in th e a t m o s p h e r ic tra n s p o rt te rm s . .As has b e e n p o in t e d o u t. th e l a t i t u d i n a l pro ­ file of 1/ is ju s ti f ie d by Lindzen a n d Farrell (1977. 1980) a n d is t h a t utilized by

N o rth et al. ( 1983). alth o u g h h ere we utilize a lower value (roughly 60%) since th e specified L e v itu s (1982) S S T im plicitly im p lie s a n o cea n ic heat t r a n s p o r t once air-sea fluxes a r e d e te rm in e d . To define th e l a t i t u d i n a l profile for m o i s t u r e diffu­ sion {k). we u tiliz e d observational e s tim a te s o f £" — P a n d in te g r a te d t h e s te a d y s ta t e , zonally a v e r a g e d form of (2.1.8). W hile s u c h a n in te g ra l c o n s tra in s t h e g e n ­ era l s h a p e a n d m a g n i t u d e of k. slight errors ( a c c u m u l a t e d d u rin g in te g r a tio n ) can

radically m o d ify t h e profile. H ence we s y m m e tr iz e d t h e profile a b o u t t h e e q u a t o r a n d tu n e d t h e final profile to m a tc h o b serv atio n al e v id e n c e t h a t E d o m i n a t e s over

P at m i d la t itu d e s , while p r e c ip ita tio n d o m i n a te s a t high la titu d e s . B y c o m p a r ­

ison w ith o b s e rv e d n o rth w a rd a n d eastw ard w a t e r v apor t r a n s p o r t (see P eixoto a n d O ort. 1992. F igures 12.9. 1 2.1 2) this is a g o o d a p p r o x im a ti o n for large-scale

a tm o s p h e ric a n d s ta tio n a r y - e d d y m otions, w ith t h e e x c e p tio n of th e In te rtro p ic a l C onvergence Z o n e (IT C Z ). C o m p a rin g with t h e z o n a l- m e a n tr a n s p o r t o f w a te r va­ p o r (see P e ix o to a n d O o rt. 1992. F ig u re 12.18). diffusive t r a n s p o r t is valid polew ard of roughly 20°. w ith in th e IT C Z . however, t h e t r a n s p o r t is u p -g ra d ie n t. T h e use of a negative diffusion coefficient w ith in this reg io n could m im ic this p h e n o m e n o n : however, t h e s o lu tio n te ch n iq u e we em ploy (w h ic h allows th e m o d e l's efficient im p le m e n ta tio n a n d solution) b reak s down w h e n a n e g a tiv e diffusion coefficient is em ployed. We th e re fo re tra d e resolution of th e I T C Z for n u m e ric a l efficiency. This also explains t h e p eak in k at th e e q u ato r; we s till re q u ire th e s tr o n g s m o o th in g of th e specific h u m i d i t y field th e IT C Z would p ro v id e .

T h e a t m o s p h e r ic em issivity (see Figure 2 .2 a) is d e t e r m in e d by fittin g (2.1.5) to th e da Silva e t al. (1994b) zonally a v e ra g e d n e t longw ave flux ( a n oceanic em issivity of 0.96 (Isem er et al.. 1989). and t h e L e v itu s (1982) z o n a lly averaged S S T d a t a a re also em ployed). T h e p la n e ta ry e m is s iv ity (see Figure 2 .2 b ) has been

Eddy Diffusive Coefficients 4 3 2 1 0^-- 8 0 - 6 0 - 4 0 -20 0 20 40 60 8 0 Latitude (N)

F igure 2.1. L a titu d in a l profile of t h e h e a t diffusion coefficient, u (solid lin e), a n d th e m o i s t u r e diffusion coefficient, k ( d a s h e d line). U nits a r e 10** m ’/s .

Atmospfieric Emissivity Planetary Emissivity 0.9 0.88 0.86 0.84 0.82 0.8 -5 0 50 Latitude (N) Scattering Coefficient 0.7 0.65 0.6 0.55 0.5 - 5 0 50 Latitude (N) 0.5 0.4 0.3 0.2 - 5 0 50 Latitude (N) C lear Sky Coalbedo

0.8 0.7 0.6 0.5 0.4 0.3 - 5 0 50 Latitude (N)

Figure 2.2. (a) L a titu d in a l profile of t h e a t m o s p h e r ic e m is s iv ity . £.4. (b) . \ s in (a)

b u t show ing th e p la n e ta r y em issivity. S p . (c) .A.s in (a) b u t sh o w in g th e s c a t t e r i n g coefficient. Cq- (d) .As in (a) b u t show ing t h e a p p lie d c o a l b e d o ( 1 — o ) ( th e d a s h e d

17

inferred by fittin g (2.1.9a) t o t h e C am p b ell a n d V e n d e r H a a r ( 1980) p la n e ta r y longwave Hux using th e z o n a lly averaged c lim a to lo g ic a l surface a ir t e m p e r a t u r e based on th e C o m p r e h e n s iv e O cean-.A tm osphere D a t a Set (CO.ADS) analysis of d a Silva et al. (1994a). T h e o b je c tiv e ly d e t e r m i n e d p la n e ta r y e m is siv ity ( z p ) is consistent w ith values u tiliz e d by Stocker et al. (1992). a lth o u g h it is s o m e w h a t lower tow ard t h e poles. N o tic e t h a t th e p l a n e t a r y e m is siv ity varies a g reat deal w ith la titu d e a n d is lower t h a n t h e a tm o s p h e ric e m is s iv ity a t all la titu d e s . T h is is re la te d to th e s im p lis tic p l a n e t a r y infrared Hux we em ploy. Top of t h e a t m o s p h e r e longwave Hux is m a d e up o f a co m b in a tio n of e m i t t a n c e from t h e surface of th e p la n e t and infrare d a b s o rb in g m a te ria ls in t h e a t m o s p h e r ic c o lu m n (e.g.. w a te r vapor, liquid, ice). In th is r e s p e c t, the p l a n e t a r y e m issiv ity is lower th a n th e a tm o s p h e ric e m is siv ity to a c c o u n t for the fact t h e e m i t t a n c e com es from highe r in th e a tm o sp h ere.

T h e s c a tte rin g coefficient we e m p lo y is also d e r iv e d from t h e CO.ADS analysis of d a Silva et al. (1994b). T h e i r incoming s h o r tw a v e r a d ia tio n is used (along w ith (2.1.3)) to infer C q . (see F ig u re 2.2c). T h e s c a tt e r in g a c ts to filter roughly 30% of the in c o m in g s h o rtw a v e ra d ia tio n , c o n s is te n t w ith th e 20 — 30% e s ti m a t e d from the r a d ia tio n b a lan ce for t h e E a rth . ( R a m a n a t h a n . 1987). Finally. F ig u re 2.2d indicates t h e la tit u d in a l profile of the a n n u a l coalb ed o (1 — q) as derived by G raves et al. (1993) from t h e E a r t h R ad iatio n B u d g e t E x p e r i m e n t d a ta .

In practice, t h e bulk t r a n s f e r coefficients Ce a n d C p (th e D a lto n a n d S ta n to n num b e rs) are o fte n ta k e n as c o n s t a n t s of th e s a m e m a g n itu d e ( ~ 1.3 x 10“ ^). T h e b u lk transfer coefficients are in a c t u a li ty d e p e n d e n t on th e wind s p e e d , air t e m p e r ­ a t u re . SST. a n d re la tiv e h u m id ity . Indeed, th r o u g h fine tu n in g of t h e bulk tra n s f e r coefficients, h e a t Hux e s t i m a t e s c a n be c o n s tra in e d for use in o c e a n m od e lin g (e.g. Isem er et al.. 1989). In a n effort to c o n s is te n tly a p p l y th e b u lk tra n s fe r coeffi­ cients. we con sid ere d th e b e s t lin e a r fit (in a le a st sq u ares sense) to w ind sp eed .

Zonally Averaged Dalton Number

1.4

1.2

- 8 0 - 6 0 - 4 0 -2 0 0 20 40 60 80

Latitude (N)

F ig u re 2.3. Zonally a v era g ed m o d e l-d eriv e d D a lto n n u m b e r. C'e. T h e S ta n t o n

n u m b e r can be o b ta in e d by C'h = 0.94Cg.

a n d air-sea t e m p e r a t u r e difference (see Isem er et al.. 1989. Table 2). T h e re s u ltin g e q u a tio n s for th e D alto n a n d S ta n t o n n u m b e rs a re th e n given by

6.0 X 1Q-’ < C'e = 1.0 X 10-^(1.0022 - .0 8 2 2 (A T )

+ . 0 2 6 6 D < 2.19 X 10"^

w here A T is th e air-sea or air-ice t e m p e r a t u r e c o n tra s t.

(2.1.13)

C'h = 0.94Cf: (2.1.14) In this m a n n e r th e e x ch a n g e coefficients a re c a p a b le of a d ju stin g ( d u r in g th e m o d e l in te g ratio n ) to changes in t h e m o d e le d air-sea t e m p e r a t u r e difference. T h e zonally averaged clim atological D a lto n n u m b e r o b ta in e d from our m o d e l in te g ra tio n is show n in F igure 2.3. T h e glo b a l m ean value of 1.26 x 10“ ^ c o m p a r e s well w ith o b serv atio n ally derived e s t i m a t e s (e.g.. Large a n d P o n d . 1982: S m it h . 1988). a n d t h e profile is also co n s is te n t w ith th e e s tim a te s of H siung (1986) a n d O b e r h u b e r (1988).

19

2 .1 .2

U n cer ta in ty in M o d el P a ram eters

T h e p a r a m e t e r s d escribed in t h e p revious se c tio n have been e m p iric a lly d e t e r m i n e d from a p a r t i c u l a r set of o b s e rv a tio n s. T h e i r values would be slightly d iffere n t if a different s a m p le of o b s e r v a tio n s (or b u lk form ulae) were p rescrib e d . H e re we a t t e m p t to place lim its u p o n th e u n c e r t a in t y a sso ciated w ith o u r m odel p a r a m e t e r s . W h ile th e larg e n u m b e r of o b s e rv a tio n s u tiliz e d in defining a c lim ato lo g ic al a n n u a l m e a n held w ould te n d to m i n im i z e th e u n c e r t a i n t y (as would th e zonal a v e r a g in g we e m p lo y ), o b je c tiv e analysis p ro c e d u re s e m p lo y e d (as in th e works of L e v itu s ( 1962) a n d d a Silva e t al. (1 9 9 4 a.b.c. a n d d)) as well as the "fair w e a th e r bias" in d a t a collection in tro d u c e an u n q u a n t i h a b l e u n c e rta in ty . To this end. th e u n c e r t a i n t y we d e h n e below is s o m e w h a t s p e c u la tiv e a n d s h o u ld be viewed m erely as a h r s t - o r d e r e s ti m a t e .

B lanc (1987) in d icate s t h e r m s u n c e r t a in t y in surface air t e m p e r a t u r e is 0.6 K. while P e ix o to and O o rt (1992) in d ic a te t h a t th e C a m p b e ll a n d V o n d e r H a a r ( 1980) p l a n e t a r y longwave h u x h as an u n c e r t a in t y of 1 0 W / m " . in d ic a tin g a n r m s

u n c e r t a in t y of 5% in o u r p l a n e t a r y e m issiv ity Sp (see (2.1.4a)). Fung et al. (1984) c o m p a re d eight different b u lk fo rm u lae for t h e net oceanic longwave h u x . T h e i r results suggest a 10-15 W / m * u n c e r t a in t y a s s o c ia te d w ith th e use of vario u s b u lk form ulae. T h is , to g e th e r w ith t h e roughly 0.6 K u n c e r ta in ty in th e a i r / s e a s u rfa c e t e m p e r a t u r e s , results in a n rm s u n c e r t a in t y in t h e a tm o sp h eric e m is siv ity 0 . 4 (see

(2.1.5)) of r o u g h ly 4.4%.

C o m p a r in g th re e different p a r a m e te r i z a ti o n s of the sh ortw ave ra d ia tio n r e a c h ­ ing th e o c e a n surface su g g e s ts a n u n c e r t a in t y of a p p ro x im a te ly 15 W / m " (or roughly 8 .6% ). If we a s s u m e th e G raves e t al. (1993) coalbedo has an a s s o c i­

a te d u n c e r t a i n t y of 5% (c o n s is te n t w ith th e u n c e r t a in t y in C a m p b e ll a n d V o n d e r H a a r's s a te llite -d e riv e d o u tg o in g longwave r a d ia tio n e s tim a te ), we o b t a i n a n r m s

u n c e r t a i n t y of 10% in t h e s c a t t e r i n g coefficient Co utilized in (2.1.3).

F inally. B la n c (I9S 7) in d ic a te s a 10% rm s u n c e rta in ty in s h ip -d e riv e d su rface w in d s p eed s d u e to sensor e r r o r a n d ship bias. T h e p resen t analy sis utilizes th e C O .\ D S - b a s e d w ind s p eed e s ti m a t e s of d a Silva et al. (1994b). T h e s e e s ti m a t e s a r e c o n v e rte d from B e au fo rt w inds a n d o b je ctiv e ly an a ly z e d to a 1° x 1° grid. .\s we h av e m e n tio n e d , th e g rid d in g analysis introduces som e a m o u n t of u n c e r ta in ty : h ow ever, t h e B e a u fo rt conversion also in tro d u c e s some d eg ree of u n c e rta in ty . S ince we a re in c a p a b le of e s t i m a t i n g t h e u n c e r t a in t y in these processes, we a s s u m e a 10% u n c e r t a i n t y as in t h e w ork of B lanc (1987).

2 .2

T h e I c e M o d e l

T h e ice m o d e l we e m p lo y is b ased on th a t d escribed by S e m t n e r (1976). T h e m o d e l p re d ic ts ice s u rfa c e t e m p e r a t u r e ( T , ) a n d ice thickness ( / / , ) . T h e ice th ick n ess is c a l c u la te d u tiliz in g th e net en e rg y b ala n c e of th e ice slab.

•-), ~ 7 { Qtop Qhot) (2.2.1 )

a t p, L j

w here p, is a r e p r e s e n t a tiv e value for th e ice den sity (see T able 2.2). L f is th e la te n t h e a t of fusion of ice. Qt op is t h e h e a t flux from th e ice su rface to th e a t m o s p h e r e , a n d Qbot is t h e b asal h e a t flux to t h e ice (h ere we assum e a positiv e flux o u t of th e ice). .At t h e i c e / a i r interface, t h e energy b ala n c e is specified as

Qt op = Q r r + Qs h + L ^ E — ( 1.0 — ) (2 .2 .2 )

sijr

w h ere E is t h e a b la tio n . L , is th e la te n t h eat of su b lim a tio n for ice. /c, is a b u lk e x t i n c t i o n coefficient for ice. Qr r is given by (2.1.5). a n d is t h e in c o m in g

21

P a r a m e te r D e s c rip tio n Value

ice e m is s iv itv 0.96

Cond ice c o n d u c t iv it y 2.52 VV/mK

bulk e x t i n c t i o n coefficient 1.5 m “ ‘

h la te n t h e a t of fusion of ice 2.93 x IO T J/k g Ls la te n t h e a t of a b la tio n of ice 2.835 xlO'^.J/kg p. r e p r e s e n t a tiv e ice d e n s ity 913 k g /m ^ 5. r e p r e s e n t a tiv e ice salinity 4 psu

T able 2.2. S u m m a r y of Ice .Model P a r a m e te r s

s h o rtw av e ra d ia tio n reaching t h e o c e a n / i c e surface

Q s w = 1 — a )C o (2.2.3) .At t h e ic e /o c e a n interface, t h e en erg y b ala n c e is th a t re q u ire d to m a in ta i n th e ocean s u rfa c e t e m p e r a t u r e a t t h e freezing po in t. Tj.

g f a . = { T , - (2.2.4)

where T / is given by (U N E S C O . 1983)

T f = - .0 5 7 5 5 o + 1.710523 x 1 0 " ^ - 2.154996 x IQ -»5;^ (2.2.5) A c is t h e d e p t h of t h e first o c e a n m odel grid box. Cpo is t h e heat c a p a c it y of seaw ater. A f is th e m odel ti m e s te p , a n d So is th e sea surface salinity.

T h e ice surface t e m p e r a t u r e is c a lc u la te d by e q u a tin g t h e c o n d u c tiv e flux th ro u g h t h e ice with t h e s u rfa c e e n e rg y flux from th e ice

r . = T o - (2.2.6)

w here /<-ond is a co n s ta n t ice conductiv ity . If. how ever, th e en erg y d u x is in to t h e ice. m elt is a s s u m e d to occur, a n d T, = T/ . T h e resu ltin g e q u a t io n for t h e ice surface t e m p e r a t u r e (when g ro w th is o ccurring) is

T. = r , - _Qrr + Qsh h

•s/yr

(2.2.7)

2.3

T h e O cea n G e n e r a l C ir c u la tio n M o d e l

In th e c l im a te m o d e l we em p lo y th e G e o p h y sical F lu id D y n a m ic s L a b o r a to r y (G F D L ) M o d u la r O cean .Model (P acanow ski e t al. 1993). w hich is based u p o n th e p rim itiv e ecjuations for a Boussinesq. h y d r o s ta t ic fluid u n d e r t h e rigid lid a p ­ p ro x im a tio n . T u rb u le n t closure is p a ra m e te riz e d as a Laplacian m ix in g process. T h e h orizontal m o m e n tu m ec[uations (inclu d in g nonlinearities) in sp h e ric a l g e o m ­ et rv are th e n —1 d p „ . —

du

I t

w here

dv

I t

d

di

p.^a cos o aX a : -Pod d o d z -(2.3.1)

(2.3.2)

d dt a d V d a cos o dX ^ a d o d z = 1 — t a n ’ o ' I — tan" o ' d_ ')z 2 sin o d v

u —

V 4-cos^ o dX 2 sin o dll a- cos^ o dX

[J-^ T' ^) a re t h e horizontal L aplacian te rm s r e p r e s e n tin g th e h o riz o n ta l m ix in g of

m o m e n tu m : is th e horizontal Laplacian o p e r a to r : A is longitude: o is l a tit u d e : a n d c is t h e vertical co ordinate. Here, th e v elo city c o m p o n e n ts a r e u. v. a n d

23

p a r a m e te r , a is t h e rad iu s of t h e e a r t h , p is p re s s u re , po is a r e p r e s e n t a t i v e density for s e aw ate r, t is tim e , a n d Ah- -dv are th e la te r a l a n d v e r tic a l e d d y viscosities.

T h e m odel is a s s u m e d h y d ro s ta tic , so th a t

d p

-qZ ~ ~ ^ P (2.3.3) w here p is d e n s ity a n d g is th e ac c e le ra tio n d u e to gravity. T h e c o n t i n u i t y e q u a tio n is given by

dll' 1 ( d u d ^ \

-I--- ^ + — ( c c o s o = 0 (2.3.4)

d z a cos o \ d \ d o )

T h e co n serv atio n laws for heat a n d salt m a y b e w r i t t e n as

f . V . (.T D = ^ C2.3.Ô)

f ^ . i , S ) = A . V ' g + g g + % g (2.3.6)

w here T is t e m p e r a t u r e . 5 is salin ity . K u . a n d K y are th e l a t e r a l a n d vertical diffusivities. a n d 6{p). 6[k) a re K ro n eck er d e l ta fu n ctio n s d efin e d as

f 1. if k = 1 ;

= ] .

,

.

L 0. o th e rw is e w here k is th e vertical d e p t h level, a n d

<)(/)) =

(

\ 0. o th e rw is e

th e case 8(p] = 0 re p resen ts in s ta n ta n e o u s c o n v e c tiv e a d j u s t m e n t t h a t restores a n e u tra l s tr a tific a tio n w henever u n s t a b l e s tr a t if ic a tio n occurs ( h e r e p a r a m e te r i z e d im p lic itly by s e tt in g K y = lOOm's"^ when t h e local d e n s ity p rofile was found to

be s ta tic a lly u n s ta b le ). T h e e q u a tio n of s t a t e for seaw ate r can be w ritte n as

p = p { S . T , p ) (2.3.7) w ith th e density a nonlin ear e q u a tio n of t e m p e r a t u r e , salinity a n d p ressure ( L'.N- E S C O . 1981).

. \ t th e surface, t h e m odel is driv en by b o t h w in d stress (a p p lie d as a bod y force over t h e d e p th of th e first grid box) a n d s u rfa c e buoyancy forcing. T h e s u rfa c e b o u n d a r v conditions a re therefore

d T

ds

d z d z

d u

' 5 •

w here are th e zonal a n d m erid io n al s u rfa c e wind stresses. T h e s u rface b u o y an cy forcing is app lied d ire c tly to th e t r a c e r conservation e q u a tio n s (2.3.5. 2.3.6). T h e net h e a t flu.x into th e ocean is d efined as

f Q s w — Q s h — Q r r — Q l h - if ice-tree:

Qh = \ (2.3.8)

iQbot + Q s w e - otherw ise

T h e definitions of Qs h- Qr r- Qsu - a n d Qbot a re th e sam e as th o s e in (2 .1.6 ).

(2.1.7). (2.2.3). a n d (2.2.4): while th e la te n t h e a t flux out of t h e o cean takes th e form

Ql h = ~ — LtyE (2.3.9)

s y r

a n d th e freshw ater flu.x over th e ocean tak es t h e form

( ^ ( E - P - R ) if ice-free: "

I

+ R) - o th e rw ise

'O

w here 5 " . 5, a re r e p r e s e n ta tiv e salinities for th e o cean a n d ice respectively. R is th e runoff from th e la n d m a s s . a n d B is th e freshw ater flux from ice fo rm a tio n or

O*

B =

me lt given by

p . s y r A H , Po A f

At th e lower b o u n d a ry o f t h e ocean m odel we specify a no Hux c o n d itio n on trac ers ( h e a t / s a l t ) , and no n o r m a l flow

n . A/

u- = —— = —— = 0 at z = —H

d z d z

We fu rth e r ap p ly a q u a d r a t ic b o t t o m friction (in cases w ith to p o g ra p h y ) as

. 4 v ' 4 ^ = C'oK |(« cosQ — u s i n a )

d z d v

. 4 i ' — = C o | f ' | ( u s i n a + u cos a )

d z

w here C p is t h e drag coefficient, a n d a is th e tu r n i n g angle. . \ t lateral walls, no flux of trac ers is p e r m i tt e d , a n d a no slip condition is applied to th e h orizontal flow:

ti = V = —— = — = 0

d n On

C h a p ter 3

T estin g U n d e r F ix e d O cean ic

C o n d itio n s

3.1

P r e s e n t D a y C lim a to lo g y

In a s im p le a p p l ic a t io n of t h e e n e rg y - m o is tu r e balance m odel, we begin by c o n ­ sidering t h e in ferred a t m o s p h e r i c clim a to lo g y when th e S S T is fixed to t h e a n n u a l L evitus ( 1982) s u rface c lim a to lo g y a n d t h e surface wind speed a n d so lar in s o la tio n are fixed to t h e a n n u a l clim ato lo g ie s of d a Silva et al. (1994b). a n d G rav es e t al. (1993). respectively. F ig u r e 3.1 in d icate s th e SST held we p re s c rib e as t h e lower b o u n d a r y c o n d itio n for t h e a t m o s p h e r ic m o d e l, th e la n d m a s s is s h a d e d .

F ig u re 3.2a in d ic a te s o u r m o d e l- p r e d ic te d surface air te m p e r a t u r e s . S p a tia lly , th e se p a t t e r n s a re q u i t e realistic. T h e b asin m e a n m odeled surface a ir t e m p e r a t u r e over t h e o cean regions is 17.91°C for t h e clim atological case, c o m p a r a b le to th e basin m e a n value of 17.9S°C b ased on t h e G O A D S an alyzed d a t a of d a Silva e t al. (1994a). F ig u re 3.2b d e p i c ts a c o m p a ris o n of th e zonally averaged d a t a of d a Silva e t al. w ith o u r m o d e le d helds ( n o te t h a t as CO.A.DS d a t a exist only over t h e o c e a n

27 0 0 ° N 6 0 ° N 4 0 ° N 2 0 ° X 2 0 ° S 4 0 ° S 6 0 ° S 6 0 “ S 3 4 0 ° W 3 0 0 ° W 2 6 0 ° * 2 2 0 ° * 1 8 0 ° * 1 4 0 ° * 1 0 0° * 6 0 ° * 2 0° *

F ig u re -'M. C lim a to lo g ic a l sea s u rfa c e t e m p e r a t u r e (S S T ) specified as th e m o d e l's lower b o u n d a r y c o n d itio n , from L e v itu s (1982). S h a d e d regions in d i c a t e land. T h e c o n to u r interval is 2 °C . w ith d a s h e d contours in d ic a tin g negative values.

regions, o u r fields a r e zonally a v e ra g e d only over t h e ocean for c o m p a r is o n p u r ­ poses). Clearly, t h e m o d e le d fields a r e q u ite close to o b serv atio n s, w i t h differences ge n e ra lly less t h a n 0.5°C . It is in te r e s tin g to n o te t h a t the s o u t h e r n h e m is p h e re t e m p e r a t u r e s ( p o le w a r d of 65° — 70°) a re actu ally w a r m e r th a n c lim ato lo g y , w hile th e s a m e region in t h e n o r th e rn h e m is p h e re is cooler. We a t t r i b u t e th is effect to (1) th e lower p l a n e t a r y em issivity in t h e s o u th ern regions as c o m p a r e d to n o r t h ­ ern p o la r regions a n d (2) th e lower ap p lied coalb ed o in the n o r t h e r n h e m is p h e re

(F ig u re 2.2d).

B lanc ( 1987) in d i c a te s th a t b e c a u se of ship a n d s e n s o r error, rm s e r r o r s of 0.6°C a re not u n c o m m o n in ship-b ased e s ti m a t e s : hence t h e note d differences of roughly 0.5°C are not u n r e a s o n a b le . T h e g e n e ra lly lower s u rfa c e air t e m p e r a t u r e s in th e n o r th e r n region o f o u r m ode l d o m a in m a y sim ply b e a consequence t h e buffering effects of ice p ro cesses which are m issin g in th e p re s e n t model d u e to th e "fair

8 0 ° N 60"N 4 0 ° N 2 0 ° N 6 0 ° S 3 4 0 ° W 3 0 0 ° W 2 6 0 ° W 2 2 0 ° W 1 8 0 ° * 1 4 0 ° * 1 0 0 ° * 6 0 ° * 2 0° *

Comparison of Surface Air Temperature 30

20

0

--60 -4 0 -20 20 40 80

Latitude (N)

Figure 3.2. (a) E n e rg y -m o ist u re balance m odel ( E M B M ) c a l c u la te d clim atological surface air t e m p e r a t u r e . T h e co n to u r interval is 2°C . w ith d a s h e d contours i n d i c a t ­ ing negative values, (b) C o m p a ris o n of zonally avera g ed m o d e le d surface air t e m ­ p e ra tu re s (solid) w ith th e C o m p re h en siv e O cean -.A tm o sp h ere D a t a Set (C O A D S ) based o b s e rv a tio n s (d a s h e d -d o tte d ) from d a Silva e t al. (1994a).