cloud parameterization for climate modeling

7/29/2019 Cloud Parameterization for Climate Modeling

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Atmospheric Research, 23 (1989) 345-361 345Elsevier Science Publishers B.V., Am sterdam -- Printed in The Netherlands

C l o ud P a r a m e t e r i z a t i o n f or C l i m a t e M o d e li n g :S t a t u s a n d P r o s p e c t sDAVID A. RANDAL LDe par tme nt o[ Atm osph eric Science, Colorado Sta te University, Fort Collins, CO 80523(U.S.A.)(Received August 23, 1988; acc epte d aft er revision M arc h 27, 1989)

ABSTRACTRandall, D.A., 1989. Cloud Param eteriz ation for climate modeling: sta tus a nd prospects. Atmos.Res., 23: 245-361.

The current status of cloud param eterization research is reviewed. It is emphasized that theupper tropospheric stratiform clouds associated with deep convection are both physically impor-tan t and poorly parameterized in current models. Em erging parameterizations are described ingeneral terms, w ith em phasis on prognostic cloud wate r and fractional cloudiness, a nd how theserelate to the problem just mentioned.RESUME

L'~ta t actuel de la recherche en param ~trisatio n des nuages est pass~ en revue. On souligne queles nuages stratifo rme s de la ha ute troposph ere associ~s avec la convection profonde so nt h la foisphysi quem ent impo rtan ts et mal paramdtris~s dans les modules actuels. Les param~t risations que~mergent sont d~crites en termes gdndraux, en insistant sur l'eau du nuage prognostiqude et lan~bulosit~ fractionnelle, et co m m en t ces quan titds son t reli~es au probl~me m entionn~.

I N T RO D U CT I O NA s w e a p p r o a c h t h e e n d o f t h e 1 98 0s , s e v e r a l i m p o r t a n t d e v e l o p m e n t s h a v e

p u s h e d c l o u d p a r a m e t e r i z a t i o n t o th e f o r e f r o n t o f c l i m a t e r e s e a r c h. R e c e n to b s e r v a t i o n a l a n d t h e o r e t i c a l s t u d i es h a v e p o i n t e d t o t h e r a d i a t i v e e f f e c t s o fc l o u ds a s a n i m p o r t a n t f o r c in g f u n c t i o n f o r b o t h l a r g e- s c a le a t m o s p h e r i c c i r -c u l a t i o n s a n d d e e p c u m u l u s c o n v e c t i o n ( e. g. , C o x , 19 69 ; A l b r e c h t a n d C o x ,1 97 5; C o x a n d G r i f f i t h , 19 79 ; S t e p h e n s a n d W e b s t e r 1 97 9; W e b s t e r a n d S t e -p h e n s , 19 80 ; A c k e r m a n e t a l. , 1 9 88 ) . I S C C P , E R B E , F I R E , a n d o t h e r o b se r -v a t i o n a l p r o g r a m s a r e s t r e n g t h e n i n g t h e e m p i r i c a l b a s is f or c l o u d - c l i m a t es t ud i e s. C l i m a t e s i m u l a t i o n s h a v e d e m o n s t r a t e d s o m e su c c e s s i n s i m u l a t i n gt h e e f fe c t s o f c l o u ds o n t h e e a r t h ' s r a d i a t i o n b u d g e t ( C h a r l o c k a n d R a m a n a -


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tha n, 1985; Ra nd all et al ., 1985; Slingo, 1985; R am an at ha n, 1987a,b; C har locket al ., 1988; H ars hv ard ha n et al ., 1989). Num eric al exp er im ents have revealeds t rong, di rect ef fects of the clouds on the large-scale atmo sphe r ic ci rcu lat ion(H erm an et al. , 1980; R am an at ha n et al. , 1983; Slingo and Sl ingo, 1988; Ran -dal l e t a l . , 1989) . At the same t ime, uncer taint ies concerning cloud feedbackhave emerged as the most ser ious obs tacle prevent ing rel iable predict ion ofc l imate change due to increas ing greenhouse gas concent ra t ions (Ha nsen e tal. , 1984; Cess and Pot te r , 1987; Schles ing er and Mitchel l , 1987; W ethe raldand M anabe , 1988).One approach to c loud parameter i za t ion , and to param eter i za t ion in genera l,i s to ident ify in tu i tive ly p lausib le r e l a t ionships be tw een the unkn own s , suchas c loud amount , and the know n var iab les of the problem, such as r e la t ivehumidi ty, s tat ic s tabi l i ty , and ver t ical veloci ty. This approach was pioneeredby Sma gor ins ky (1960), an d has rec ent ly been pu rsued by Sl ingo (1980, 1987 ) .The resul t ing parameter i za t ions are of t en ca l l ed "empi r i ca l " , but tha t t e rmseems inapprop r iate , s ince in ma ny cases no scat ter diagram s or other sys tem-at ic observat ional bas is are presented. A more accurate descr iptor might be"indu ct ive", s ince general rules are formu lated on the bas is of a f inite num be rof par t icular cases. An adv antage o f the induct ive approach is tha t i t can quicklyyie ld param eter i za t ions tha t a re un deniably useful , e .g ., for nume r ica l weatherpredic tion . A d i sadvantage i s tha t induct ive param eter i za t ions l ack theore t ica lun derp innin gs tha t could indicate thei r l imi ts of appl icabil i ty .

The a l t e rna t ive , "deduct ive" approach i s based on the phi losophica l v iewthat parameter izat ion development should proceed, as far as poss ible, f romgeneral phys ical pr inciples . A deduct ive parameter izat ion provides a con-densed repre senta t ion of the impo r tant phys ica l processes of in teres t , and socan g ive phys ica l ins ight in to the ph eno me non being parameter ized . T he l imi tsof appl icabi l i ty of such a parameter izat ion can be infer red, a pr ior i , f rom i t sphys ical bas is . I t s assumpt ions must , of course, be observat ional ly tes table.Thi s r ev iew ar ti c l e emphas izes deduct ive parameter i za t ions .We ca n pose the fol lowing ques t ions con cern ing the role of clouds in cl imate.

( 1 ) Wh at is the distribu tion o[cloudiness?. Th e In terna t ion al Sa te l li t e CloudCl imatology Proje ct ( ISCCP ; Schif fer and Rossow, 1983) i s inten ded to pro-vide an observa t ional answ er to this ques t ion. Al ternat ive cloud cl imatologiesare also being produced, us ing a var iety o f satel l ite ret r ieval algor i thm s (e.g. ,Su sski nd et al ., 1987; Stow e et al . , 1988) a nd su rface dat a (W arre n et al ., 1986 ) .S imula ted c loudiness d i s t r ibut ions produced by genera l c i r cu la t ion model s(GCM s) mu s t be cr it i ca lly comp ared wi th such observat ions .

(2) Wh at d etermine s the dis tribution of cloudiness? This i s one of the twokey problem s of cloud para me ter izat ion . L arge-scale mot ions , surface f luxes ,mois t conv ent ion, and radiat ive cool ing can al l inf luence the d is t r ibut ion ofcloudiness over the globe. Observat iona l s tudies des igned to address this ques-t ion include FIR E (Cox et al. , 1987).


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347(3) What are the direct effects of the clouds on the atmosphere? This i s the

s e c ond ke y p r ob l e m o f c l oud pa r a m e t e r i za t i on . C l ouds a s s er t t he i r i n f l ue nc et h r ough t h r e e d i s t i nc t bu t i n t e r r e l a t e d a nd m or e o r l e s s e qua l l y i m por t a n t"c l oud f o r ci ng" m e c ha n i s m s , none o f w h i c h a r e a de qua t e l y i nc l ude d i n a nyexis t ing c l ima te mode ls :( a) C l ouds m odu l a t e t he s o l a r a nd t e r re s t r ia l r a d i a t i on f ie ld s. R a m a n a t h a n(1987a ,b) has t e rm ed these ef fect s the "c lo ud rad ia t ive forc ing" (CR F) . Th eCR F can be de f ined a s the d i f fe rence be twee n the rad ia t ive f lux (a t the top o fthe a t mo sphe re , s ay) w hich ac tua l ly occurs in the pre sence of c louds , and t ha tw h i c h w ou l d oc c u r if t he c l ouds w e r e r e m ove d bu t t he a t m os ph e r i c s t a te w e r eo t he r w i se unc ha n ge d . T h e t e r m C R F c a n a l so be u s e d to de no t e w a r m i ng o rc oo li ng t e nde nc i e s due t o c l o ud - r a d i a t i on i n t e r ac t i ons . M e a s u r e m e n t s o f t heC R F a t t he t op o f t he a t m os phe r e a r e be ing p r ov i de d t h r ou gh t he E a r t h R a -d i a t i on B udge t E xp e r i m e n t ( E R B E ; R a m a na t ha n e t al ., 1989), a s w e ll a s se v-e ral o the r sa te l l i t e -based obse rva t ion a l s tud ie s . Pa rame te r iza t io ns of the CRFr e qu ir e i n f o r m a t i on a bou t t he a m ou n t a n d t ype o f c l oud pa r ti c le s i n a G C Mgr id volum e , as we ll as the d i s t r ibu t ion of the pa r t i c le s ins ide the volume . Th ef o r m e r p r ob l e m is u s ual l y d i s cus s e d in t e r m s o f t he "c l oud w a t er c on t e n t " , a n dt he l a t t e r i n t e r m s o f t he " f r a c t iona l c l oud i ne s s" . A s po i n t e d ou t by H a r s hva r -dha n a nd R a nda l l ( 1985), bo t h t h e c l oud w a t e r c on t e n t a nd t he f r a c ti ona lc l oud ine s s m u s t be know n i n o r de r t o de t e r m i ne t he C R F. A pa r a m e t e r i z a t i onof rad ia t ive t r an s fe r in a pa r t ly c loudy gr id vo lu me should t ake in to acco untf i n it e c l oud e ff ec ts , w h i c h r e s u l t f rom ph o t on s t ha t e n t e r o r e s c ape t h r oug h t h es ides of c louds .

(b) C louds a re a s soc ia ted wi th l a ten t hea t r e lease and prec ip i t a t ion . Thisc a n be t e r m e d t he c l oud l a t e n t f o r c i ng ( C L F) . I t ha s be e n a dd r e ss e d t h r ougha num be r o f m a j o r obs e r vat i ona l s tud i es , no t a b l y i nc l ud i ng G A T E ( H ouz e a ndBe t t s , 1981 ). C l ima te m ode ls typ ica l ly d iv ide the CL F in to two som ewh a t ar -b i t r a r i ly d i s t inguished components , name ly cumulus e f fec t s and la rge - sca les a t u r a t i on e ff ec ts . C ons i der a b l e e ff o r t ha s be e n e xpe nd e d on t he de ve l op m e n to f C L F pa r a m e t e r i z a t i ons .

(c ) C louds a re a s soc ia ted wi th s t rong sma l l - sca le convec t ive c i rcu la t ionst ha t c a r ry o u t i m p or t a n t ve r ti c al t r a ns f e rs o f ene r gy , m o i s tu r e , m om e n t um ,and va r ious chemica l spec ie s . These mot ions a re c lose ly a s soc ia ted wi th there lease of l a ten t hea t , bu t they a re log ica l ly d i s t inc t f rom i t . Th is th i rd typ e ofc loud forc ing can be ca l l ed the c loud convec t ive forc ing (CCF ) .

(4) W ha t role does the cloud forcing play in regulating or main taining thepresent climate? Th e c l ima te sy s tem ' s r e spon se to c loud forc ing i s r ea li zed inpa r t t h r ou gh h i gh l y non l i ne a r i n t e r a c t i ons a m ong r a d i a t ion , c onve c t i on , a ndthe l a rge - sca le a tm osph er ic c i rcu la tion . GCM s a re idea l too l s for inves t iga t ingt he s e i n t e r a c t ions , t h r ou gh c on t r o l l e d num e r i c a l e xpe r im e n t s .(5) How do the clouds feed back to influence climate change? T h i s p r o b l e m


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can only be addressed wi th conf idence a f te r sa t i s fac tory answers to the pre -ceding four ques t ion s have been e s tab l i shed .

T h e e a r l i es t G C M s i nc l ude d t he C L F , s inc e t h i s w a s a l re a dy know n t o be akey ene rgy source for the l a rge - sca le c i rcu la t ion of the a tmo sphe re , and theya ls o i nc l ude d s im p l e pa r a m e t e r i z a t i ons o f t he C C F. I n c on t r a s t, m a n y o f t he s esame mod e ls used presc r ibed zona l ly ave raged c loudiness d i s t r ibu t ions a s in -put s to the i r so la r and te r re s t r ia l r ad ia t ion pa ram e te r iza t ions . In those days i twas not un ive rsa l ly recognized th a t th e C RF has s t ron g d i rec t e f fec ts on thea tm osp her ic gene ra l ci r cu la tion .

B e g i nn i ng i n t he m i d -1960s, s e ver a l G C M s i nc o r po r a t e d s i m p l e pa r a m e t e r -i za t ions o f r ad ia tive ly in te rac t ive c loudiness , typ ica l ly pa rame te r ize d in t e rm sof wa te r vapor mix ing ra t io , t empe ra ture , and ve r t ica l mot ion . Th e C RF as-s oc ia t e d w i t h t he s e i n t e ra c t ive c l ouds f ed ba c k t h r ou gh t h e r a d i a t ion p a r a m e -t e r i za t i on t o m od i f y t he t e m pe r a t u r e , a nd s o i n f lue nc e d t he de ve l op m e n t o f t helarge-sca le c i rcula t ion. Up unt i l the la te 1970s , however , very few publ isheds tudie s addressed the s imula ted c loudiness or i ts e f fec t s on th e m ode ls ' c lima te .Thi s m ay have been pa r t i a l ly due to a l ack of obse rva t ion s su i t ab le for com-pa r i son w i th mod e l re su l ts .

Th e next s t ep , insp i red by the w ork of L il ly (1968), was to a l low the rad ia -t ive ef fect s of the c louds to in f luence the tu rbule nce pa ra me te r iza t ion of theG C M. S i nce a ll G C Ms c on t a i n a pa r a m e t e r i z a t i on o f boun da r y l a ye r t u r bu -lence , the mo s t na tu ra l p lace to in t rodu ce a coupl ing be tween c loudiness andturbu lence i s in the pa ra me te r iza t io n of bou ndary - laye r c louds. L i lly 's idea wasi m p l e m e n t e d i n t he U C L A G C M dur i ng t he m i d - s e ve n ti e s , unde r t he d i r e c ti onof A . Arakawa , and the re su l t s o f th i s e f for t were publ i shed by Sua rez e t a l .( 1983 ) and Ra nd al l e t a l . ( 1985 ) . In this app roach , th e coup l ing be twee n th eturbu lence an d the c louds i s a d irec t, " fa s t " , pa ra me t r ic coupl ing , a s opposedto an ind i rec t coupl ing throu gh the p rognos t ic f i elds; the l a t t e r occurs on ly onthe t ime an d space sca les tha t a re expl ici t ly r e so lved by the GCM. In th i s c la ssof mode ls , however , the c loud- turbulence coupl ing i s "one -way" ; the c loudsdi rec t ly in f luence the turbulence , bu t the turbulence does not d i rec t ly in f lu-ence the c louds . This a l lows a s t r a igh t forward computa t iona l a lgor i thm: thec loud prope r t i e s a re d e te rm ine d fi rs t; they a re provid ed as inp ut to the rad ia -t ion pa ram e te r iza t ion ; and f ina lly the rad ia t ive f luxes are used ( toge the r wi tho t he r pa r a m e t e r s ) t o de t e r m i n e t he t u r bu l e nc e s ta t is t ic s .

T h e e m e r g i ng pa r a m e t e r i z a t i ons de s c ri be d l a te r i n t h i s p a pe r f e a tu r e ne wprog nos t ic var iables for c loud par t ic le spec ies such as c lou d water or ice, fol -lowing the p ion ee r ing work of Sund qvis t (1978, 1981 ) . In addi t ion , th e va r ia -b i li ty o f c loud op t ic a l p r ope r ti e s w i t h t e m pe r a t u r e a nd o t he r a t m os ph e r i c s t a teva r iab le s i s now be ing recognized a s a po ten t ia l ly im po r tan t a spec t o f c loud -c l ima te feedback (e.g ., Somervi l l e and Remer , 1984; P la t t a nd Har shv a rdh an ,1988) . New, physica l ly based f rac t ional c loudiness schemes (e .g. , Randal l ,1987) a re l ink ing c loud am ou nt wi th turb ulenc e va r iab les . I t appea rs l ike ly


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t ha t i n t he ne x t ge ne r a t i on o f pa r a m e t e r i z a t i ons , t he c l oudi ne ss , t he r a d ia t ivetendenc ie s , and the tu rbulen ce s ta t i s t i c s wi ll have to be so lved for s imul tane -ous ly , g rea tly inc reas ing the a lgor i thm ic comp lexi ty of the mode ls .

T h e p u r pos e o f th i s pa p e r i s t o r e v ie w t he c l oud pa r a m e t e r i z a t i on p r ob l e m ,w i t h e m ph a s i s on w ha t c u r r e n t p a r a m e t e r i z a t i ons t e l l u s a bou t t he r o le o f c l oudr a d ia t ive f o r ci ng i n m a i n t a i n i n g t he p r e s e n t c l i m a t e, a nd a ls o on t he s t a t u s a n dpr os pe c t s f o r f u r t he r i m pr ov e m e n t s o f c l oud ge ne r at i on pa r a m e t e r i z a t ions .KEY DEFICIENCIES OF CURREN T CLOUD PARAMETERIZATIONS

Altho ugh wa te r vap or i s no t a c loud va riab le pe r se, the re a re or sho uld bes t rong phys ica l l inks be tween a mo de l ' s s imula t ions of wa te r vap or an d c lou-d iness . Obviously , h igh absolu te hum idi t i e s a re f avorable for c loud forma t ion .Less obvious ly , the d i s t r ibu t ion of wa te r vapo r s imu la ted by a GCM is s t ronglyinf luenced by i t s c loud pa ram e te r iza t ions . Th is can be seen f rom the fo l lowingequa t ion :0(t + V' (V (t V' q' ) + I~,-C=O (1)8tHere q is the w a te r vapor mix in g rat io , E i s evapora t ion , C is condens a t ion ,and V is the three -d im ens io na l veloc i ty vec tor . An o ve rba r deno tes a gr id-boxave rage , and a pr im e deno tes a f luc tua t ion f rom the average. Th e co nde nsa t io nte rm of eq. I is obvious ly a s soc ia ted wi th c loud forma t ion , and the evap ora t ionte rm can rep resen t the e f fec ts of evap ora t ing prec ip i t a t ion fa l ling from c louds ,o r o f e va por a t i ng c l oud d rop l e ts . T h e s m a ll - sc a le t r a ns po r t t e r m is dom i na t e d ,above the b ou nda ry l aye r, by convec t ive t r ans por t s due to c louds . For exam ple ,b y f a r t h e m o s t i m p o r t a n t m e c h a n i s m f o r t r a n s p o r t i n g m o i s t u r e f r o m t h eboun da r y l a yer t o t he uppe r t r op os phe r e i s dee p pe ne t r a t i ve c um ul us c onvec -t ion . E v e n w i t h i n t he boun da r y l ayer , s t r a t oc um ul us c l ouds a nd s ha ll ow cu -m ul us c l ouds c a n s t r ong l y a f fe c t the t u r bu l e n t m o i s t u r e f lux . T he p o i n t is t ha tpa r a m e t e r i z e d c l oud pr oc e ss e s dom i na t e t h r e e o f t he f ou r t e r m s c on t r i bu t i ngt o t he t i m e - r a t e o f c ha nge o f t he m e a n w a t e r va por m i x i ng ra ti o . Fo r t he s ereasons, p red ic t ion of the w a te r vapor d i s t r ibu t ion i t s e lf i s an im po r tan t a spec to f t he c l oud pa r a m e t e r i z a t i on p r ob l e m . C ur r e n t G C M s c a n s i m u l a t e s om e i m -por t a n t f e a tu r e s o f t he obs e r ve d d i s t r ibu t i on o f a t m os ph e r i c w a t e r va por, bu tthe re a re s t il l m an y prob lem s wit h the resu l ts (e.g ., Ra nd al l e t a l. , 1989) .

A s m e n t i one d above, de e p c um ul us c onve c t i on is t he p r i m a r y m e c ha n i s mf o r t r a ns p o r t o f m o i s t u r e f r om t he p l a ne t a r y b ound a r y l a ye r t o t he up pe r t rop -osphe re , e spec ia lly in the t rop ic s and s um me r midla t i tudes . Each day , t ens oft hou s a nds o f c um ul on i m bu s c l ouds i n j ec t e no r m o us qua n t i t i e s o f bounda r y -laye r a i r in to the uppe r t roposphe re and lower s t r a tosphe re (e .g . , R ieh l andMalkus , 1958). Th e d e t ra in ed a ir forms hor izonta l ly ex tens ive and deep "an-v i l" c louds tha t cont r ibu te a s mu ch a s 40% of the to ta l p r ec ip i t a t io n tha t f a ll s


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f rom the convect ive sys tems . T he anvi l clouds conta in mesoscale c i r cu la t ions(e.g. , Houze, 1982) and probably also smal l -scale mois t convec t ive ci rcula-t ions , wh ich inf luence the evolu t ion of the convect ive sys tems and the l arge-scale ci rculat ions in w hich the y develop. The y also exe r t very powerful effectson both so lar and t e r res t r ia l r ad ia tion . Some of the c umu lus - in jec ted i ce crys -tals form ci r rus clouds , wh ich can rem ain in the up per t roposp here for severaldays, dur ing which the upper - t roposphere winds can car ry them thousand s ofk i lometer s f rom th e convect ive event s tha t genera ted them . A long the i r t r a jec-tory, they block inf rare d emiss ion f rom lower levels , and scat ter su nl ight bac kto space.Unfor tun ate ly , ex i s t ing genera l c ir cu la t ion model s do no t inc lude adequateparam eter i za t ions of upper - t ropospher ic s t r a t i form c louds or the convect iveprocesses that of ten give r i se to them. St rat i form clouds are incorporatedthrough " l arge- sca le sa tura t ion" parameter i za t ions , which are not d i r ec t lycoupled wi th the convect ive parameter i za t ion . S t ra t i form prec ip i t a t ion is typ-ically assum ed to fall out in s tantan eou sly, despi te observat ional eviden ce tha tice crys tals, in par t icular , can have long l i fetimes . No exis t ing GC M includesa d i rec t, phys ica l ly cons i s t en t coupl ing be tween the convect ion parameter i za-t ion an d the l a rge- sca le sa tura t ion parameter i za t ion , despi t e the overwhelm-ing observat ional evidence that such coupl ing exis ts . This may be the mostserious deficiency of the cloud param eterizati ons in current GCM s. Researchdes igned to rem edy this def iciency mu st address the fol lowing key ques t ions.

( 1 ) W ha t a re the phys ica l coupl ings be tween u pper - t roposphere s t r a ti formanvi l and c i r rus c louds and deep cumulus convect ion , and how do the c loudsand convect ion in terac t wi th the l a rge- sca le c ir cu la tion?(2) How can we parameter i ze the r ad ia tive ef fec t s of these con vect ive c loudsys tems wh en the cloudiness f luctuates s igni f icant ly on u nresolved scales?(3) How do convect ive c loudiness, and the r esu l ting radiat ive and l a t en theat ing, inf luen ce the large-scale ci rculat ion?Resul t s obta ined f rom cur ren t GCMs c learly dem ons t ra te tha t cu r rent par -ameter izat ions of the upper- t ropospher ic s t rat i form clouds associated wi th deep

convect ion are both def i c ien t and potent . Thi s is a dangerous combinat ion .Al though cur re nt GCM s do produce upper - t ropospher ic t ropica l c loudinessmax ima (e.g. , Ha nsen e t a l. , 1983; Char lock and Ra m ana than , 1985; Randal let al. , 1989; Ha rsh va rdh an et al. , 1989) , they are of ten wea ker tha n observed,in sp it e of the abu nda nt t ropica l prec ip i t a t ion produ ced by the models . In ad-di t ion, the s imulated t ropical clouds tend to f luctuate unreal i s t ical ly on sub-synoptic t ime scales (Charlock et al . , 1988; L.D. Smith, 1989).These def ic i encies s t em f rom the m odel ' s inadequate parame ter i za t ions ofboth cum ulus cloudiness and the c i r rus debr is associated wi th cum ulus act iv-i ty. In the models , the rad iat ive ef fects of convec t ive cloud sys tems " shu t of f"as soon as the convect ion s tops . In real i ty, of course, the upper- level cloudsheet s produced by cumulus de t ra inm ent p er s is t for hours or even days aft e r


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351

SEAWORLD20 I1 8 - -1614

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30N 0 30S 60S 90S

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L a t i t u d eF i g. 1 . M e a n m e r i d i o n a l c i r c u l a t i o n s f o r a c lo u d y r u n { a ) a n d a c l o u d - f r ee r u n ( b ) , i n s i m u l a t i o n so f a n o c e a n - c o v e r e d p l a n e t , a s r e p o r t e d b y R a n d a l l e t a l. ( 1 9 8 9 ) .


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352the conv ec t ion has d ied out . In orde r to impro ve the m ode ls , we need to g iveup t he un r e a l is t i c a s s um pt i on t h a t a ll o f t he de t r a i ne d c l oud pa r ti c le s i m m e -dia te ly prec ip i t a te ou t or r eve r t to the v apor phase . A poss ib le so lu t ion is theuse of progn os t ic c loud var iab le s , a s d i scussed in th e nex t sec t ion .S l ingo a nd S l ingo ( 1988) pe r f o r m e d a n e xpe r i m e n t w i t h t he C om m u ni t yC l i m a t e Mode l ( C C M ) m a i n t a i n e d by t he N a t i ona l C e n t e r fo r A t m os p he r i cResea rch , in which the longwave a tmospher ic c loud rad ia t ive forc ing (he re -af te r , ACR F) was ar t i f ic ia l ly supp ressed. Clear-sky cool ing ra tes were used topredic t the a tmo sph er ic t emp era tur e , whi le the usua l ( c lea r and c loudy) long-wave f lux was used to pred ic t the l and-sur face t empera ture . J anua ry condi -t ions were chosen on the g roun ds tha t th e l and-sur face i s min ima l ly sens i tivet o l ongw a ve A C R F i n t he n o r t h e r n w i n t er . A pa rt i a l s um m a r y o f t he i r r e s u lt si s a s fo llows : the A CR F warm s the t rop ica l uppe r t ro pos phe re by 4 K an d coolsthe t rop ica l lower s t r a tosph e re by 6 K , caus ing an acce le ra t ion of the subt rop-ica l j e t s in bo th hem isphe res . I t p roduces a m ois ten ing of the t rop ica l m iddlet r opos ph e r e by i nv i go r a t i ng m o i s t c onve c t i on , w h i c h t r a ns p o r t s m o i s t u r e up -wards . I t causes inc reased prec ip i t a t io n and la rge - sca le r i s ing mo t ion ove r In-dones ia , and tend s to inc rease the ra te of prec ip i t a t ion in reg ions where pre -c ipi t a t ion is l ike ly to occu r anyway.

Rand a l l e t a l. (1989) p e r form ed an ana logous expe r ime nt wi th the ColoradoS t a t e U n i ve r s i t y ( C SU ) G C M ( f o rm e r l y t he U C L A / G L A G C M ) t o de t e r m i net o w ha t e x t e n t t he C C M - ba s e d r e s u l ts o f S li ngo a nd S l i ngo a re m ode l - de pe n -dent . A desc r ip t ion of the CSU mod e l i s om i t t ed he re for brev i ty , bu t can bef ound i n t he r e fe r enc e j u s t m e n t i one d . Su f f ic e it t o s a y t ha t t he C C M a nd t heCSU GCM are ve ry d i f feren t . Neve r the le s s , the C SU GCM gives re su l t s qual -i t a t ive ly s imi la r to those produced by the CCM. In pa r t i cu la r , bo th mode lssugges t tha t th e AC RF ac t s to inc rease the prec ip i t a t io n ra te ove r the t rop ica loceans .

To explore the reasons for th i s , Ran da l l e t al . (1989) p e r form ed num er ica ls imu la t ions of the a tmo sphe r ic gene ra l c i rcu la t ion of an o cean-cove red p lane t ,wi th an d wi th out the rad ia t ive e f fec ts of c louds . Th ey fo und tha t by rad ia t ive lyw a r m i ng c onve c t ive l y a c ti ve c o l um ns , t he A C R F s t r e ng t he ns t he l ar ge- sc a ler i s ing mo t ion , the low-leve l conve rgence , and the sur face evap ora t ion , l ead ingt o m or e c onve c t ive c l oud ine s s a nd a f u r t he r w a r m i ng o f t he c o l um n . T h i s pos -i t ive feedback m ech anis m o pe ra te s ve ry e f fect ively over the oceans, where th es imu la ted sea surface t emp era tu re i s e i the r s lowly va ry ing ( in the rea l wor lda nd i n c oup l ed oc e a n - a t m o s phe r e m ode l s ) o r fi xed ( in m ode l s o f t he a t m o-sphe re a lone ) . As show n in F ig . 1, they fo und tha t th e A CRF can ac tua l lydoub l e t he s t r e ng t h o f t he H a d l e y c i r c u l at i on on a n oc e a n -c ove r ed p l a ne t w i t hf ixed sea sur face t empe ra tures .


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353EMERGING CLOUD PARAMETERIZATIONSPrognostic cloud variables

Fol lowing the l ead of Sun dqv i s t (1978 , 1981 ) , s eve ra l mode l in g groups (e.g. ,R . N . B . S m i t h , 1989 ) a r e c u r r e n t l y de ve l op ing pa r a m e t e r i z a t i ons t h a t e m p l oyprogn os t i c va r i ab l e s fo r c loud spec ie s such a s c loud l i qu id wa te r , c l oud i ce , andc l oud r a in w a t e r . T he u t i li t y o f c onde n s e d w a t e r va r i a b le s is obvi ous ; c onde n -s a te s a r e t he phy s i c a l li nk be t w e e n t he l a t e n t he a t e f f e c t s a nd t he r a d i a t i vee f fec t s o f c louds, so t he con s i s t en t use of con den sa t e va r i ab l e s h e lps t o ensurephys i c a l c ons i s t e nc y a m ong t he l a t e n t he a t i ng , r a d i a t i on , a nd p r e c i p i t a t i ngpa r a m e t e r i z a t i ons . A l t hough i t is no t s o obv i ous t ha t t he c o nde n s a t e va ri a b le sm us t be prognostic (on e could envi s ion neg l ec t i ng t he t ime- ra t e -o f -chan ge t e rm,a nd s o lv i ng a d i agnos t i c o r ba l a nc e e qu a t i on f o r t he c ond e ns a t e s ) , t h e r e a r e a tl e as t tw o pos s ib l e m o t i va t i ons f o r de t e r m i n i ng t he c ond e ns a t e d i s t r i bu t i onprognos t i ca l l y .

T h e f i rs t pos s ib l e m o t i va t i on i s t ha t a P C V is de m a nd e d by the phys i c s , int he s e ns e t ha t t he c u r r e n t d i s t r i bu t i on o f t he c onde ns a t e i s i n f l ue nc e d by i tspas t h i s t o ry ov e r t he space a nd t ime sca l es o f i n t e re s t . I f t h i s i s t he ca se, ac -c u r a t e d e t e r m i na t i o n o f t he d i s t r i bu t i on o f t he c ond e ns a t e ne c e s s a r i l y i nvo lve sthe u se of a p rognos t i c e qua t ion . I t is no t a t a ll c lea r , howev er , t h a t t he p hys i c sac tua l l y does dem an d a PCV for al l t ypes o f c louds. Con s ide r a sub t rop i ca lbou nda r y - l a ye r s t r a t oc um u l us c loud , c ons i st i ng e n t i r e l y o f l iqu i d w a t e r d r op -l et s. T he s e d r op l e t s a r e f o r m e d by c on de ns a t i o n t ha t oc c u r s p r i m a r i l y i n m i -c r o s ca l e ( i.e . t u r bu l e nc e - s c a l e ) c onve c t i ve upd r a f t s a f ew hun d r e d m e t e r sa c ros s , w i t h l if e t i m e s o f a f ew m i nu t e s . M a n y o f t he s e d r op l e t s a r e s ub j e c t e dt o e va po r a t i on i n ne a r by m i c r os c a l e dow nd r a f t s . T he l i fe t im e o f a n a ve r a gec l oud d r op l e t in t he s t r a t oc um ul us l a ye r is, t he r e f o r e , ve r y b ri ef . T h i s m e a nst ha t t he c ons e r va t i on e qua t i on f o r t he large-scale average l i qu id wa te r con cen-t r a t i on i s dom i na t e d by s t r ong c onde ns a t i on a nd e va po r a t i on t e r m s , w h i c hve r y ne a r l y ba l a nc e e a c h o t he r . F o r t he s pa c e a nd t i m e s c a l e s r e s o l ve d by ac l i m a t e m ode l, t he l oc al ti m e r a t e o f c ha nge a nd a dve c t i on t e r m s a r e qu i t eneg lig ib l e, com par ed t o t hese so urce and s ink t e rms . A s imi l a r l ine of rea son inga pp li e s f o r s om e o t he r c l oud type s , s uc h a s f a i r - w e a t he r c um u l us c l ouds o rf r on t a l s t r a t u s c l ouds . I t s hou l d be no t e d , how e ve r , t ha t t he s e a r gum e n t s dono t a pp l y t o t he m e s os c a l e a nd m i c r os c a l e m ode l s t ha t a r e u s e d t o s i m u l a t eind iv idua l c loud e l eme nt s . T hi s is wh y such sm a l l - sca le mode l s have bee n us -i ng P C V s f o r m a ny ye a r s .

T he l oc al t i m e r a t e o f c ha ng e a nd a d ve c t i on t e r m s a r e i m por t a n t f o r c i r ru sc louds, even on t h e re l a t i ve ly la rge space and t im e sca le s re so lved by a c l im a tem ode l . T yp i c a l c ir r u s c l ouds c on t a i n m a n y s m a l l c r y s t a l s w i t h t e r m i na l ve l oc-i ti e s l e ss t ha n or on t he ord e r o f 0 .1 m s - 1, and a l so l a rge r c rys t a l s wi th t e r m ina lve loc i t i es on th e o rde r of 0 .5 m s -1 (e .g . , He ym sfie l d , 1975; S tar r an d C ox,


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354

1985a), and so take several hours to fall through the depth of the troposphere.Of course, the smaller crystals, which are radiatively important , fall even moreslowly. The effective fall speed can be fur ther reduced by mesoscale rising mo-tion and/or convective lofting associated with the cirrus clouds themselves.Crystals are capable of surviving for extended periods as they fall through sub-saturated air (e.g., Hall and Pruppacher, 1976).Observat ions (e.g., Webster and Stephens, 1980) show that cirrus outflowsfrom tropical convection can extend for many hundreds or even thousands ofkilometers downstream from the convective disturbance that generates them.In such cases, the local time rate of change and advections terms of the con-servation equation for the large-scale average cirrus ice water concent rationmust be comparable to the source and sink terms, so that a prognostic approachincluding advective effects is necessary for accurate predictions of the cloudi-ness. In short, PVCs are necessary for accurate simulations of the effects ofcirrus clouds on climate.

A second, very practical reason for the use of a PVC is that a prognosticscheme can actually simplify the computationa l algorithms of the cloudinessparameterization. This should not come as a surprise. There are many prob-lems for which quasi-equilibrium assumptions complicate the mathematics,even though they can be justified by scaling arguments. Examples include qua-sigeostrophic models, in which the vertical velocity is determined through thenotorious w-equation; turbulence models based on higher-order closure, inwhich balance assumptions can lead to poorly behaved algebraic systems, andanelastic models, in which filtering of sound waves is achieved at the expenseof a troublesome elliptic equation for the pressure. A PCV potential ly providesa relatively convenient algorithm to determine the cloud water content of GCMgrid volumes.

The difficulties of implementing a PCV should not be underes timated, how-ever. In particular , advection of a lumpy, non-negative scalar is a difficult nu-merical problem (e.g., Rood, 1987). A GCM may need vertical resolution onthe order of 500 m to adequately resolve the precipitation physics. The smallequilibration times and high terminal velocities of some precipitating particleswill require careful design of unconditionally stable time-dif ferencingschemes,in view of the relatively long time steps used in GCMs (not less than severalminutes ). On these multi -minute time scales, the microphysical processes willnever stray significantly from equilibrium, but under some conditions the large-scale advective processes ment ioned above can produce significant nonequili-brium behavior.For climate modeling, precipitation processes and the radiative effects of theclouds are of roughly equal importance. This suggests tha t it may be useful todistinguish between precipitating and nonprecip itating drops. The same lineof reasoning is more compelling for ice particles. Small ice particles are radia-tively very important (Prabhakjara et al., 1988), but in many cases representonly a tiny fraction of the ice mass in a grid volume. The total ice mass is,


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355therefore, not necessarily a good measure of the radiative properties of thecloud. On the other hand, the larger ice particles are important because theyprecipitate and are involved in latent heat exchanges. These considerationssuggest tha t is may be useful to separately prognose precipitating and nonpre-cipitating liquid water drops and ice particles.The use of PCVs to determine the large-scale average distribution of precip-itating and nonprecipitat ing cloud particles obviously amounts to an alterna-tive parameterization of "large-scale saturation", which can directly replacethe large-scale saturation parameterizations that are typically used in cu rrentGCMs to determine the ra te of precipitation from strat iform clouds. For con-sistency, the same PCVs should also be incorporated into the cumulus para-meterization. The parameterized convective clouds can then act as generatorsof cloud particles for the parameterized strat iform clouds. In this way, a truecoupling of the convective and stratiform cloud parameterizations can beachieved.Fractional cloudiness

Methods exist to det ermine the optical properties of a grid volume contain-ing a known concentration of cloud water (e.g., Stephens, 1978). This does notimply, however, that a PCV solves the problem of determining the cloud radia-tive forcing. As discussed by Ha rshvardhan and Randall ( 1985 ), the distr ibu-tion of cloud water inside a grid volume strongly determines its optical prop-erties. For example, if all of the liquid water is in one lump, its optical effectswill be negligible. On the other hand, if the same mass of water is distributedover the grid volume as a uniform aerosol, its optical effects will be formidable.There is as yet no proven method, based on physical principles, to de terminethe subgrid-scale distribution of cloud water in a GCM grid volume. Thissubgrid-scale cloud water distribution is related to but more complex than whatis usually called the "fractional cloudiness".

It is useful to distinguish between two types of fractional cloudiness. Thefirst, which was discussed by Sundqvist (1978, 1981 ) occurs because a cloudsheet of arbitrary shape must be imperfectly resolved on a finite grid (Fig. 2left). Such extrinsic fractional cloudiness depends in an essential way on thegrid used. The cloud fraction can change dramatically as the grid spacing isaltered by a factor of two (say), so tha t a moderate increase in the resolutionof the grid can lead to a significant improvement in the representation of thecloud field. For this reason, extr insic fractional cloudiness is essentially a prob-lem of resolution, comparable to the man y other problems of resolution facedby numerical modelers.

In contrast, intrinsic fractional cloudiness is associated with the mesoscaleand microscale dynamics of a cloud field. Examples are the cloudiness associ-ated with cumulus convection, and with thin stratocumulus and cumulus hu-


12/17

356milis layers (Fig . 2 r ight ) . Ex pl ic i t reso lu t ion of in t r in s ic f rac t ional c lou dinessrequ i res a g r id - spac ing a t l ea s t two to th ree o rde rs o f ma gn i tu de f ine r tha n tha to f ex i s t ing GCM s. W i th i n t he range o f typ ica l cu r re n t r e so lu tions , the in t r in s icf rac t ional c loudine ss is no t sens i t ive to the gr id size .Th rou gh the use o f a PCV, we can p red ic t the large-scale average c o n d e n s a t emix ing ra tio fo r each GCM gr id vo lume . Th e cloud-scale average c o n d e n s a t emix ing ra t io wi th in ind iv idua l c loud e lem en ts has been shown , in bo th obse r -va t iona l and th eore t ic a l s tud ies (e.g. , Fe ige lson , 1978; Som ervi l le and Re mer ,1984; Be t t s and H arsh va rd han , 1987; P la t t an d Ha rshv a rdh an , 1988) , to va rysys tema t ica l ly wi th t em pera tu re ; these c loud-sca le ave rage m ix ing ra t io s a recon t ro l led by mic rophys ica l and sma l l - sca le c loud-dynam ica l p rocesses , andso shou ld be amena b le to sem i-empi r ica l pa ram e te r iza t ion .

T he ra t io of the la rge-sca le average mixing ra t io to the c loud-sca le averagemix ing ra t io i s a measu re o f the f rac t ion o f the g r id vo lume tha t i s occup ied bycloud. Le t th is ra t io be d eno ted by w, i .e .

la rge-sca le average con den sa te mi xing ra t ioW-- c loud-sca le ave rage cond ensa te mix ing ra t io (2)A poss ib le app roach i s to de te r min e the nu me ra to r o f eq. 2 f rom the PCV, andth e d e n o m in a to r b y a n e m p i r ic a l a s s u m p t io n i n t h e s p i r i t o f t h o s e m e n t io n e dabove . In case the c loud-sca le me an mix ing ra t io i s un i fo rm wi th in the c loudelements , w is exac t ly equal to the f rac t ional c loudiness ( in a volume sense) .Even whe n the c loud-sca le me an m ix ing ra t io va r ie s wi th in the c loud e lemen ts ,w shou ld be usefu l measu re of the smal l -sca le var iab i l i ty of the c loud f ie ld.Ev idence fo r th i s was p rese n ted by Step hen s (1988) , who found tha t the sa t-e l li te obse rva t ions o f the mer id iona l d i s t r ibu t ion o f large-scale average c loudwate r r epo r ted by Praba kha ra e t al . (1986) do no t show the sys tema t ic pole -ward dec rease to be expec ted f rom the obse rved dependence o f the local average

TWO TYPES OF FRACTIONAL CLOUDINESS

o ~ o

o o "

- D ~a o~:

- ~ ~ ~o~ ~,~EXTRINSIC INTRINSIC

Fig. 2. Diagrams illust rating extrinsic and int rins ic fractional cloudiness. See text for details.


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c l oud w a t e r m i x i ng r a ti o on t e m pe r a t u r e . T h i s s ugges t s t ha t t he obs e r ved va ri -a t ions in the l a rge - sca le ave rage c loud wa te r a re do mi na ted by va r ia t ions in"c l oud a m o un t " r a t he r t h a n l oc al cl oud w a t e r c onc e n t r a t i on . I t m a y be pos si b leto deve lop a pa rame te r iza t io n of the rad ia tive , dynam ica l and c loud-phys ica leffec ts of the smal l -sca le var iabi l i ty of c loudiness , based, in par t , on thi sa pp r oa c h .

I t ma y a l so be necessa ry , however , to t ake in to a ccoun t the ro le of sma l l -scale convec t ive mot ion s in de te rm inin g the f rac t iona l c loudiness . Th ese m o-t i ons a re k now n t o p la y a n i m p or t a n t r o le e ve n in s t r a t i f o r m c l oud sys t e m s(e.g. , Li l ly , 1968, 1988; Star r a nd Cox, 19 85a ,b) . Ran dal l (1987) has pro po sede lem ents of a pa ram e te r iza t i on for convec t ive ly dr iven sma l l - sca le c loudinessf l uc tua t i ons. Pe r ha p s t he m os t na t u r a l c l oud t ype s to pa r a m e t e r i z e i n t h i s w a ya r e s t r a t oc um ul us a nd s ha l l ow c um ul us c l ouds t ha t r e s i de i n t he p l a ne t a r yboundary l aye r (PBL) , s ince ex i s t ing c l ima te mode ls a l ready inc lude bound-a r y -l a yer t u r bu l e nc e pa r a m e t e r i z a t ions . A l t houg h s t r a t oc um ul us c l oud s he e tsa re s om e t i m e s c om pl e t e l y unb r oke n ove r t e ns o f t hou s a nds o f s qua re k i l om e -t e rs , bo t h c om m o n e xpe ri e nce a nd s a te l li te pho t o s s how t ha t t he y a r e o f t e nr idd led wi th sm a l l ho les th a t appea r to be a s soc ia ted wi th th e turb ulen t cha r -ac te r of the c loud . Eve n wh en the c loud shee t is unbro ken , the re a re s ign i f i can tund ula t io ns of c loud top and c loud base, so tha t a t a g iven leve l the f rac t iona lc l oud ine s s c a n be be t w e e n z e ro a n d one . T he c om m onl y obs e rve d b r e a k - up o fa s t r a tocum ulus shee t in to sha l low cum ul i (R anda l l , 1980) necessa r i ly en ta i l sa r educ t ion in the f rac t iona l c loudiness ; a sa t i s fac tory theo ry of the b reak-upmu s t a l low a rb i t r a ry c loudiness .

Be t t s (1973, 1983), Hans on (1981), Penc and Albrech t (1986) , and W anga nd A l b r e c h t ( 1986) ha ve d i s c uss e d m ode l s o f pa r t l y c l oudy PB L s c on t a i n i nga s ing le fami ly of convec t ive c i rcu lat ions . Th e c i rcu la t ions have both a scendingand desce nding branches , an d c loudiness can occur (or no t ) in e i the r branch .S imi la r ideas have been used in obse rva t iona l s tud ie s (based on condi t iona ls a m p l in g a n d / o r j o i n t d i s t r i b u ti o n f u n c t i o n s ) b y L e n s c h o w a n d S t e p h e n s( 1980, 1982 ) , G ree nh ut a nd Kh alsa (1982) , an d W ilczak an d B usin ger ( 1983 ) ,M a hr t a nd Pa um i e r ( 1984), G r os s m a n ( 1984), K ha l s a a nd G r e e n hu t ( 1985),a nd Pe nc a nd A l b r e c h t ( 1986).

These mode ls show tha t the f rac t iona l c loudiness i s c lose ly re la ted to thef rac t iona l a rea cove red by r i s ing mo t ion , and a l so to the convec t ive fluc tua -t i ons o f t e m p e r a t u r e a nd m i x i ng ra ti o . T o da t e , no m e t hod t o de t e r m i ne t he s equa nt i t i e s has been dem ons t ra ted . Even i f one can be found, the re su l t ing frac -t iona l c loud iness pa ram e te r iza t ion wi ll be ra th e r compl ica ted , s ince the f rac-t iona l c loudiness wil l be de te rm ined , in pa r t , by the turbulen ce , bu t a t the samet i m e t he i n t e ns i t y a nd c ha r a c t e r o f t he t u r bu l e nc e w il l be de t e r m i ne d i n pa r tby the pre sen ce of the c louds and the i r e f fec t s on th e rad ia t ion f ie ld . Th e c loud ,turbulen ce , an d ra d ia t ion pa ram e te r iza t io ns wi ll give r ise , the re fore , to a cou-p led sys tem o f equa t io ns th a t mu s t be so lved s imul taneous ly . I t w il l be a cha l-


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358lenge to devise an algorithm that is accurate yet computat ionally fast enoughfor use in a GCM.

CONCLUSIONSInteractiv e cloud param eteri zati ons are now accepted as necessary compo-

nen ts of any climate model, but th eir d evelop ment is still at a n early stage. Welack adequate un der sta ndi ng of what the distribut ion of global cloudiness ac-tually is, what determ ines it, what effects the clouds have on t he large-scalecirculation of the atmosphere and on the climate system generally, and howthe clouds feed back to influence climate change. The clouds most urgent ly inneed of bette r para meteriz ation, in view of their importan ce for climate andthe inadequacies of current parameterizations, are the upper-troposphericstrat iform clouds associated with deep convention. Two key modeling issuescurren tly facing us are how to use prognostic cloud water variables, a nd howto paramete rize fractiona l cloudiness. These are critical problems, since reli-able cloud paramet erizat ions are a necessary prerequisite for reliable predic-tions of anthrop ogenic climate change.ACKNOWLEDGEMENTS

Graeme Stephens instigated this paper. Ha rshv ardh an and an anony mousreviewer contr ibut ed useful comments .This work has been supported by NASA's Climate Program, under Grants

NAG 5-1058 and NAG-I-893 to Colorado State University. Computing re-sources were provided by the Nu merical Aer odynami c Simulatio n Program atNASA/Ames.

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