A regional climate model coupled to ocean waves: Synoptic to multimonthly simulations

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. D16, PAGES 17,753-17,771, AUGUST 27, 2001 A reginal climate mdel cupled t cean waves: Synptic t multimnthly simulatins William Perrie Ocean Sciences Divisin, Maritimes Regin, Fisheries and Oceans Canada, Bedfrd Institute f Oceangraphy, Dartmuth, Nva Sctia, Canada Yacun Zhang Department f Atmspheric Sciences, Nanjing University, Nanjing, China Abstract. The NCAR reginal climate mdel RegCM is cupled t the WAM cean mdel, using the sea-state-dependent rughness parameterizatin derived in the HEXOS experiment. Cupled mdel simulatins are shwn t give reduced wind speeds U 0 cmpared t uncupled simulatins. This is in accrd with ther recent studies. Hwever, the wave-atmsphere cupling is effected thrugh the frictin velcity field u,, rather than thrugh the wind field U 0. Thus because the cupling gives enhanced resistive frictin, U 0 is weakened, whereas u, is enhanced. Wave heights, driven by u,, are als increased in ur cupled mdel simulatins cmpared t uncupled mdel simulatins. Cupled mdel utputs are shwn t cmpare favrably with air-sea bservatins cllected during the recent Labradr Sea Deep Cnvectin Experiment in 1997, bth fr synptic strm timescales and fr seasnal timescales. 1. Intrductin Exchanges f mmentum, heat, and water vapr at the airsea interface have lng been recgnized as imprtant physical prcesses fr the study f climate dynamics and climate change, ccurring n different timescales. Better representatins f these fluxes are essential fr climate mdeling n all timescales. This is particularly true with regard t cupled atmsphere-cean climate mdels, whether implemented reginally r glbally. In the case f cupled atmsphere-cean general circulatin mdels (GCMs) it is ften necessary t apply the flux crrectin methd t remve the climate drift effect [Sausen et al., 1988]. Mrever, in present cupled GCMs the cmplicated air-sea interactin prcesses at the cean-atmsphere interface are nrmally parameterized in terms f simple bulk frmulatins. The interactins f surface waves with the ceanic and atmspheric bundary layers, n either side f the interface, have received cnsiderably less attentin. Hwever, because the mmentum and heat fluxes thrugh the interface are mdified by the presence f cean surface waves, a better knwledge f the sea state might imprve estimates f air-sea mmentum and heat fluxes. A better knwledge f these fluxes may result in imprved simulatins f depressins, as well as lnger climate timescales, particularly fr mdeling the atmsphere-cean system. The cupling f an atmspheric mdel t a wave mdel invlves dynamic interactins, thrugh the air-sea mmentum flux, as well as thermal interactins, thrugh air-sea heat fluxes. Dynamic interactins remve mmentum frm the atmsphere and transfer it t cean waves and currents, tending t decelerate the atmspheric mtins. Thermal interactins pass latent and sensible heat frm the cean t the atmsphere, Cpyright 2001 by the American Gephysical Unin. Paper number 2001JD /01/2001JD $ ,753 which can intensify atmspheric mtins. The interplay f mmentum and heat fluxes, between atmsphere and cean wave mdels has been the subject f a number f recent studies [Weber et al., 1993; Dyle, 1995; Janssen and l/iterb, 1996; Linell et al., 1998; Desjardins et al., 2000; Lalbeharry et al., 2000]. Using a rather carse grid, Weber e! al. [1993] cupled a versin f the cean wave mdel (WAM) t a T21 versin f the ECHAM mdel, a state-f-the-art glbal climate mdel, at that time. They cncluded that while cean waves d nt have great imprtance t understand large-scale atmspheric circulatin, they can be imprtant during individual strms. Cupling is achieved thrugh the wave-induced stress mechanism f Janssen [1989, 1991]. Thus wind speed U was used t drive the WAM wave mdel. The Charnck parameter a c was mdified t include wave-induced stress in WAM and passed back t the atmspheric mdel. A finer 30 km reslutin was implemented by Dyle [1995]. He cnsidered idealized midlatitude cyclnes and cupled WAM t the U.S. Navy Cupled Ocean-Atmsphere Messcale Predictin System (COAMPS). Dyle [1995] fund increased sea surface rughness leads t decreased U and increased heat and misture fluxes during explsive deepening, cmpared t uncupled simulatins. The rughness effects f the cean waves appeared t give en- hanced filling f the lw-pressure depressins. Cmpared t Dyle [1995], Linell e! al. [1998] used carser grids f 60 and 120 km, which resulted in reduced sensitivity t cyclne intensity and surface fluxes. Mrever, while they fund that atmsphere-wave cupling gives small effects n strm develpment and atmspheric circulatin, the impact n surface variables was ntable. Relative t uncupled simulatins, they fund a slight weakening f the central pressure depressin, as well as reduced wave heights and surface wind speeds, with increased mmentum flux. Desjardins et al. [2000] and Lalbeharry et al. [2000] selected fur real strm cases and cnsidered the impact f atmsphere-wave cupling n varius factrs affecting the structure

2 17,754 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL and evlutin f these strms. As in earlier cupling studies, U is passed frm the atmspheric mdel t WAM. In WAM the Charnck parameter a c is mdified t include wave Cupled Mdel Descriptin Mdel induced stress and passed back t the atmspheric mdel. Mrever, t estimate ac, they implemented nt nly the Janssen [1989, 1991] wave-induced wind stress (WS) mecha- The versin f RegCM used in this study is that described in detail by Girgi et al. [1993a, 1993b]. RegCM is a limited-area mdel whse dynamical cmpnent is essentially the Penn nism but als the wave age (WA) parameterizatin fr rugh- State-NCAR messcale mdel versin 4.0 (MM4). The mdel ness Z derived by Smith et al. [1992] during the HEXOS is hydrstatic and cmpressible. It is based n primitive equacampaign in the Nrth Sea. Overall, the WA and WS results tins and emplys a terrain-fllwing a-vertical crdinate. were similar, fr surface variables such as U, r significant Sigma is defined tr = (p - Pt)/(Ps - Pt), where p is wave height H s. Relative t the uncupled simulatins, Despressure, Pt is pressure at the uppermst mdel level, andps is jardins et al. [2000] and Lalbeharry et al. [2000] fund that the the surface pressure. Fr ur simulatins, Pt is set t 100 hpa. We used 11 vertical sigma levels with tr = 1.0, 0.99, 0.97, 0.93, presence f yunger rugher seas in cupled simulatins can and 0.85 fr the lwest five levels. The ther six levels are give a -10% reductin in U, particularly near the strm equally spaced (0.75 -> tr _> 0) with A- = The mdel has peak. They als fund reductins in wave heights, as well as a surface physics package, BATS, the Bisphere-Atmsphere increases t sensible and latent heat fluxes and sea surface Transfer Scheme [Dickinsn et al., 1992], an explicit planetary rughness. Althugh these mdificatins may affect cnvective bundary layer [Hltslag et al., 1990; Hltslag and Bville, precipitatin and surface cnvergence, they tend nt t mdify 1993], a calculatin package fr atmspheric radiatin [Brfactrs cntrlling vertical strm structure r strm develpiegleb, 1992], and a Ku-type cumulus parameterizatin ment, fr example the presence f a lw-level jet. Thus while scheme [Anthes, 1977]. small beneficial effects f cupling were fund fr surface The bttm bundary layer is cmpsed f parameterizaparameters, they fund that synptic-scale aspects f the strm tins fr bth land and cean. Surface-atmspherexchange were nly weakly affected. They suggesthat atmsphere-wave fluxes are cmputed using BATS, with each grid pint specified cupling may have a strnger impact fr lnger timescales, with the characteristics crrespnding t a single vegetatin fllwing Janssen [1994]. Janssen [1994] and Janssen and Vit- and sil class. The sea ice distributin is btained frm arerb [1996] cupled WAM t a T63 versin f the ECMWF mdel. They shwed that sea-state-dependent mmentum transfer has definite impact n bth synptic timescales and seasnal frecasts. Imprvements were nted in the mean 500 hpa height field and high-frequency variability, as well as surface wind speeds, cmpared t uncupled runs. In this paper, a reginal climate mdel was cupled t an chived data at Bedfrd Institute f Oceangraphy. Air temperature, humidity, pressure, winds, radiatin, and precipitatin are prvided t BATS by the atmspheric mdel at each dmain grid pint. Fr grid pints designated as land, BATS cmputes surface radiative, sensible and latent heat, mmentum fluxes, and surface temperature based n the assigned vegetatin and sil parameters. Exchange between the atmcean wave mdel fr the Nrth Atlantic t cnsider the sphere and the cean is cmputed by BATS, using timeimpacts f waves n reginal climate simulatins. As described in sectin 2, the cupled mdel system cnsists f the NCAR reginal climate mdel (RegCM) and the WAM cean wave mdel. The atmsphere-wave cupling is effected by the wave-age (WA) dependent rughness HEXOS dependent sea surface temperatures interplated frm AVHRR (advanced very high reslutin radimeter) data, frm The effects f bundary layer turbulence and vertical transprt are cnsidered by a frmulatin develped by Hltslag et al. [1990] and Hltslag Z, frmulated by Smith et al. [1992], fllwing Desjardins et al. [2000] and Lalbeharry et al. [2000]. Simulatins with the resultant cupled RegCM-WAM mdel give reduced wind speeds U cmpared t uncupled simulatins. This is in accrd with recent studies, fr example Desjardins et al. [2000]. Cupled simulatins als give enhanced resistive frictin and u,, cmpared t uncupled simulatins. A nvel aspect f ur study is that the wave mdel is driven by u,, whereas previus studies used U. The decisin t fcus n u, rather than reference wind speed U is mtivated by the fact that a given U can be assciated with a large set f wind prfiles each with a different u,. In principle, each different u, gives a unique frcing field and crrespndingly unique wave spectra. Driving the wave mdel with u, leads t higher wave heights in cupled simulatins, cmpared t uncupled simulatins. Cupled mdel utputs are shwn t cmpare favrably with air-sea bservatins cllected during the recent Labradr Sea Deep Cnvectin Experiment (LSDCE), fr synptic strm timescales in sectin 3, as well as seasnal timescales, in sectin 4. Later studies will extend this wrk t cuple reginal climate and cean mdels, apprpriate t investigate the impacts f climate change scenaris n marine strm climatlgies. and Bville [1993]. This is a medium-reslutin scheme with five levels in the lwest 1.5 km abve the surface. Within planetary bundary layer (PBL) an eddy-diffusin term plus a "cuntergradient" term, fr nnlcal transprt due t deep cnvective plumes, represent the vertical eddy flux. The RegCM requires initializatin f mdel prgnstic variables (u, v, T, q, Ps, and Ts) at each hrizntal mdel grid pint and each mdel level, excluding surface pressure P s and surface temperature T s. Because this is a reginal mdel, the dmain is a limited area and the lateral bundaries require time-dependent frcing fr the prgnstic variables. This is achieved by applying external cnditins. The initial and lateral bundary cnditins are prescribed using the reanalysis data frm the Natinal Centers fr Envirnmental Predictin and the Natinal Center fr Atmspheric Research (NCEP/ NCAR). The reslutin f the reanalysis data is 2.5 ø, which is interplated linearly t the mdel grid at 6-hurly intervals. Vertical interplatin frm the NCEP/NCAR reanalysis data t the RegCM sigma levels is linear in pressure, fr wind and specific humidity, and linear in the lgarithm f pressure fr temperature. In hrizntal dimensins, a bilinear prcedure is used t achieve interplatin t the RegCM grid. Once the reanalysis fields are interplated nt the RegCM grid, the lateral bundary cnditins are prvided, using a relaxatin the

3 , PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,755 technique that invlves the use f Newtnian and diffusin terms t gradually drive the mdel fields tward the bundary cnditins ver a buffer zne f several grid pints width [Anthes et al., 1987]. As implemented in this study, the mdel area cvers the Canadian east cast, the Labradr Sea, and the Nrth Atlantic Ocean. It is centered at 55øW, 55øN, with a 4500 x 4000 km 2 size and a hrizntal grid pint spacing f 50 km. The simulatin perid is 58 days frm February 1 t March 30. During this time, strm systems crssed the Labradr Sea regin, typically passing ver the Canadian east cast tward Greenland. The cean wave mdel (WAM) used in this paper is the standard third-generatin wave mdel [Hasselmann et al., 1988; Kmen et al., 1994]. Wave spectra E (f, 0 ) are specified by the energy balance equatin, as a functin f space and time, accrding t the relatin _O_E(f, 0 )+ g. VE(f, 0): ½,n + ½a + ½n,, (1) Ot were shwn t give the WA frmulatin aw^ = 0.48(C,/ where ½in is the spectral energy input by the wind, ½as is the u,) v, with N = -1. The HEXOS Z is a generalizatin f dissipatin due t wave-breaking and white-cap frmatin, and the Charnck Z, because it incrprates wave age, C,/u,,,, is the nnlinear transfer f spectral energy due t wave- where Cp is the phase velcity at the spectral wave peak. When wave interactins. Parameterizatins fr i,, ½a,-, and, are waves are yung, fr example in a develping synptic system, thse f the WAM frmulatin given by Hasselmann et al. Cp/u, < 26 and HEXOS Z is larger than Charnck Z - [1988]. In this frmulatin, dissipatin ½as is tuned s that When waves mature and Cp/u, >- 26, the HEXOS Z is dimensinless wave grwth cmpares favrably with field meareplaced by the Charnck Z in this study. surements, such as JONSWAP [Hasselmann et al., 1973]. A Althugh Janssen [1992] fund very gd agreement bestandard implementatin f the mdel was emplyed, repretween WA and WS frmulatins, nt all field results have senting the spectrum by 30 frequencies, ranging frm supprted the HEXOS Z. Fr example, Yelland and 7 ylr t Hz, and 12 directinal bands, each having [1996] sugges that N = 0 and reservatins have been exa width f 30 ø. The frequency bands are n a lgarithmic scale pressed by Smith et al. [1996] and Janssen [1997] and Ost with zx]7f = 0.1, spanning the range fm x/fmin = 1'129' The [1998]. Hwever, the HEXOS Z was used by Gulev and ttasse WAM mdel area is 75øW-30øW and 37øN-65øN, which is [1998] t estimate wind stress frm ship-f-pprtunity wind mst f the Nrth Atlantic. The spatial grid is 0.5 ø and the time measurements. It was used by Burassa et al. [1999] t estimate step is 1200 s, s the CFL cnditin criterin fr stability is air-sea fluxes as a functin f sea state. Using a cmbinatin f mre than adequately satisfied. RASEX experimental data and data frm Dnelan et al. [1993],Jhnsn et al. [1998] cnfirmed its functinal frm, with 2.2. Cupling Scheme cefficientsimilar t thse f Mnbaliu [1994]. Mre recently, using the HEXOS Z t effect WA atmsphere-wave cupling In an uncupled atmsphere-cean mdel system, the rughness length Z ver the pen cean is typically given by the Charnck [1955] relatin, in studies using real strm data, Desjardins et al. [2000] and Lalbeharry et al. [2000] btained similar results t thse using the WS frmulatin f Janssen [1989, 1991], fr winds U and significant wave height Hs. Mrever, they fund that the 2 Z0 = ac--, (2) HEXOS Z gives a better agreement between the wind fields and surface rughness than the WS frmulatin, because the HEXOS Z is based n the wind-wave spectrum, whereas the where 17 the acceleratin due t gravity. The Charnck param- WS frmulatin includes swell. eter a c is usually set t , fllwing Wu [1980]. Thus ac T implement the HEXOS Z, we used the WAM frmuin the Charnck frmulatin makes n reference t sea state latin f Hasselmann et al. [1988], rather than later frmulaand cannt give a gd descriptin f yunger rugher windtins, such as the WAM-4 frmulatin f Kmen et al. [1994] generated waves. r the NCEP versin f Tlman and Chalikv [1996]. This was In the cupled mdel system, a c becmes a functin f sea necessary because the Janssen [1989, 1991] WS frmulatin has state. Sea state dependence can be expressed in terms f wavebeen implemented in the WAM-4 frmulatin, and ½d, has induced stress (WS) f Janssen [1989, 1991] r the wave age been tuned t ½,. The cupling scheme allws peridic data (WA) frmulatin f Smith et al. [1992], as derived in the cmmunicatin between the tw mdels, RegCM and WAM. HEXOS experiment. In this case (2) is In ur case, because RegCM and WAM have time steps f 150 H 2 Z0: a--, (3) and 1200 s, the data cmmunicatin time step is 1200 s. Therefre at eight RegCM mdel time steps, wind directin 0 and frictin velcity u, are passed frm RegCM t WAM. In turn, where a = aws = 0.01/V - rw/r in the WS frmulatin, WAM passes the peak phase velcity Cp t RcgCM, where it where rw is the wave-induced kinematic stress, btained by integrating the wind input ½, ver all frequencies and direcis used t cmpute a new sea surface rughness Z. This cmputatin f Z ccurs in the RegCM atmspheric bundtins. In the HEXOS parameterizatin, field measurements ary layer using the HEXOS Z. RegCM then prceeds t the 60N 50N 40N / Buys: ,, 2, R/V KNORR crume trck 7sw ½w s6w 46w' 30w Figure 1. Buy psitins (44141 and 44138) and R/V Knrr cruise track during the Labradr Sea Deep Cnvectin Exper- iment f 1997.

4 0 17,756 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL Simulated sea level pressure by cupled mdel 10'10 O : N 102, , 75W 65W 55W 45W Difference f SLP between cupled and uncupled mdels ' 35W 35N 75W 65W 55W 45W 35W Figure 2. Sea level pressure (SLP) field estimated frm the cupled mdel at 0800 UTC n March 8 at the peak f the strm. The cntur intervals are 5 hpa fr SLP. Simulatins cnsist f a single run fr the entire 40 day perid. next time step, t generate a new wind field t frce WAM at the next cupling time step. An iterative relaxatin is included t prduce an equilibrium state amng the bundary layer winds, waves and Z 0 at each grid pint [Petrie and Wang, 1995]. The advantage f this iterative scheme is that it keeps u, and Z0 cnsistent in bth RegCM and in WAM. The values fr u, and Z 0 are the same in bth RegCM and WAM. This is achieved by mdifying the bundary layer wind prfile t accunt fr the strng interactins between the wind field and wind-generated waves. By cmparisn, earlier studies such as Weber et al. [1993], Dyle [1995], Janssen and Viterb [1996], and Desjardins et al. [2000] have been cncerned t pass U 0 frm the atmspheric mdel t the wave mdel. In this case, atmspheric mdel values fr u, and Z0 can differ frm thse f WAM. Our extensin n past wrk is t fcus n the cnsistency f u, and Z0 ver the atmsphere-cean interface, using u, t drive WAM Guidelines n Wave/Wind Intensificatin Schade and Emanuel [1999] suggested several factrs imprtant fr strm intensificatin, including fr example (a) thickness f the cean mixed layer, (b) strm prpagatin speed, (c) hrizntal strm scale, (d) thermal stratificatin belw the ceanic mixed layer, and (e) the relative humidity in the atmspheric bundary layer. These factrs influence air-sea fluxes f heat and mmentum and are impacted n by these fluxes. Fr example, Janssen and Viterb [1996] suggest that the timescale f the impact f cean waves n the atmsphere is abut 5 days, based n estimates fr the rate f decay f vrticity by surface frictin, using the quasi-gestrphic ap-

5 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,757 e. Z Z Z Z CO ud - 0 Z Z Z Z CO ud - D Z Z Z Z ud ud ud ud CO ud - 0

6 ß,, ß,,. 17,758 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL hpa loo (a) T and q bias vertical prfiles T bias q bias ' 900' 1000!! ' (b) Difference f cnvective precipitatin rate (mm/6hr) ß 35N 75W 65W 55W 45W 35W Figure 4. (a) Vertical temperature and specific humidity bias prfiles and (b) differences fr cnvective precipitatin rate fr the cupled minus the uncupled mdel simulatins. These results are at 0800 UTC n March 8 at the peak f the strm. Prfiles are averaged ver a few grid pints at the respective lcatins f the strm center, which are s clse that they are essentially the same psitin. The units fr temperature bias in Figure 4a are øc and, fr specific humidity bias, gm kg -. The cntur interval Figure 4b is 2 mm h -. prximatin [Pedlsky, 1987]. This estimate culd be mdified n a statinary strm is small. On the ther hand, a fastby a number f factrs. Fr example, because f the lng mving strm wuld experience greater impact frm cean timescale, nnlinear wave-wave interactins, r wave-current waves, because the yung rugh sea state wuld last lnger. interactins are als likely t be imprtant. Mrever, an en- Desjardins et al. [2000] present a simplified scale analysis t hancement in surface rughness may be assciated with increased sensible and latent heat fluxes, which culd intensify the depressin. Finally, they suggested that strm prpagatin Figure 5. (ppsite) (a) Difference fields fr wind speed speed has impact n variatins in sea surface rughness Z as AUt, fr the cupled and uncupled mdels, (b) the frictin well as wind speed U and wave height H s. Since the lifetime velcity u, estimated by the cupled mdel, and (c) the diff yung rugh waves is rather shrt (abut 6-12 hurs de- ference field Au, between the cupled and the uncupled pending n wind speed), it fllws that a statinary depressin mdels. The cntur interval is 1 m s- in Figure 5a, 0.3 m s- culd nly experience the yung rugh waves fr a relatively in Figure 5b, and 0.1 m s - in Figure 5c. These results are at shrt time. Therefre we expecthat the impact f cean waves 0800 UTC n March 8 at the peak f the strm.

7 (a) Difference f surface wind between cupled and uncupled mdels 35N 75W 65W 55W 45W 35W (b) Frictin velcity simulated by cupled RegCM-WAM at strm situatin... :'-*.6, 0.6, 0 4,, 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W (c) Difference f frictin velcity between cupled and uncupled RegCM-WAM

8 . 17,760 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL (a) Simulated sensible heat flux by cupled mdel O j5 loo 35N 75W 65W 55W 45W 35W (b) Difference f sensible heat flux between cupled and uncupled mdels ß.. i i ',' 35N,) ' 5. ø 75W 65W 55W 45W 35W Figure 6. (a) Sensible heat flux distributin F in the cupled mdel and (b) difference field AF between the cupled and the uncupled mdels, at the peak f the strm. The cnturs fr Fc are 50, 100, 175, 250 W m -2 and, fr AFt, 10 Wm -2. estimate the impact f cupled simulatins n surface variables. Of curse, the RegCM-WAM mdel invlves a full representatin f the bundary layer physics and ges beynd these simple guidelines. Using the HEXOS rughness Z t express the variatin in surface heat fluxes AFc/Fc in terms f the variatins in wind speed A U /U and drag cefficient ACD/CD, Desjardins et al. [2000] suggesthe relatin AFt ACD AUt Fc Z= 2CD + U ' (4) assuming that the rughness length assciated with heat fluxes Zr is cnstant [DeCsm et al., 1996; Janssen and Viterb, 1996]. Here the rati AX/X is cmputed as (cupled X - uncupled X)/uncupled X. In accrd with (4) the surface layer physics in RegCM is diagnstic in the sense that heat fluxes are determined frm the mmentum flux, which in turn is determined frm U. The relatin u, = X/-- r U reduces (4) t AF /F = Au,/u,, (5) which suggests that increased air-sea fluxes AF /F are determined by increased frictin velcity Au,/u,, assuming the air-sea temperature and humidity differences are unchanged. Wind fields u, and related stability parameters als determine the waves. The JONSWAP experiment f Hasselmann et al. [1973] and its reanalyses by Batties et al. [1987] and Kahma and Calken [1992] imply that fr grwing waves, dimensinless ttal wav energy with dimensinless peak frequencyf, vary as

9 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,761 E0 f$, (6) wherea and 7 are cnstants and : = E172/u, 4. FrmKahma and Calken [1992] r the CASP (Canadian Atlantic Strm Prgram) data f Petrie and Tulany [1990], we infer The differentiated frm crrespnding t (6) is AE Afv Au, E- - = (7) In terms f significant wave height H x = 4 V and wave age WA, this becmes AHs 7 A WA Au, Hs : ' (8) Fr asympttic lng-time averages such as mnths r seasns, ne expects equilibrium cnditins between waves and wind. In place f (6) we assume wave energy E is related t u, by the Piersn-Mskwitz relatin E = I ß I x 103u '! as presented by Kamen et al. [1994, equatin (6.69)] which implies the lng-time relatin I (a) Sensible heat flux ver the Labradr Sea "' ' _L a,,- -.' *+' +' Measured ' 100 ß (b) Latent heat flux ver the Labradr Sea 'r,' ' ;1--_., _ : -4.i1 + AHs 3. Synptic Timescales Au, H-- : 2 (9) The Labradr Sea and the Nrthwest Atlantic Ocean are regins f extremes f wind and cld, incursins f sea ice, and great cntrasts in buyancy f air and seawater. Intense air-sea interactins ccur with strng upward heat flux at the sea surface. The regin's prximity t principal Nrth Atlantic strm tracks results in strng mdulatins f the air-sea interactins by passing extratrpical cyclnes. Heat lss frm the cean is enhanced by cyclnic atmspheri circulatin ver the Nrth Atlantic in winter, which advects cld, dry Arctic air ver relatively warm waters f the Labradr Sea. These heat fluxes int the atmsphere bring abut increased cnvective activity. During the winter f 1997, the Labradr Sea Deep Cnvectin Experiment [LSDCE, 1998] was cnducted t identify atmsphere-wave cupling effects n synptic/ seasnal timescales. The LSDCE campaign cllected air-sea flux measurements and related atmspheric/ceanic data. The ship track f the RV Knrr during LSDCE is given in Figure 1, alng with the psitins f buys and ff eastern Canada. $ Figure 7. Sensible and latent heat flux estimates, cmparing the cupled and uncupled mdel simulatins with the R/V Knrr bservatins during the March 6-8 strm. Cupled simulatin is slid line, uncupled is dashed, and measured is -2 pluses. Units are W m nrtheast f the strm, cmpared t the uncupled mdel. Far frm the strm center, the differences are negligible. The diple structure shwn in Figures 3a and 3b implies a slight suthward variatin in strm trajectry in the cupled simulatin, cmpared t the uncupled simulatin. Janssen and l/iterb [1996] als suggested that atmsphere-wave cupling culd result in a higher level f activity in the strm track area f the Nrth Atlantic, as well as a shift in the maximum f activity in the strm track area tward the suth, in the cupled mdel simulatins. Crrespnding temperature differences are 3.1. Impact n the Atmsphere The mst intense strm f the LSDCE campaign ccurred during March 6-8. This is a rather typical strm fr the Nrthwest Atlantic. It was generated arund Lake Erie at 0000 UTC n March 6 and deepened as it prpagated tward the Nrtheast. By the time it crssed Prince Edward Island a day later its central lw pressure was 980 hpa. This decreased t 965 hpa as it crssed the suthern Labradr Sea at 1800 UTC n March 7. By the time it had mved between Greenland and Iceland, 18 hurs later, it had reached a minimum f 960 hpa. Thereafter, it mved ut f the dmain f ur study. The sea level pressure (SLP) field and crrespndin geptential height difference fields at 500 and 1000 hpa, between cupled and uncupled simulatins, are given in Figures 2 and 3a and 3b. The cupled mdel generates a slight intensificatin tward the rear f the strm and a slight weakening t the 60N 50N 40N 75W 70W 65W 60W 55W 50W 45W 40W 35W 3( Figure 8. Wave age field WA frm the cupled mdel at 0800 UTC n March 8.

10 17,762 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL (a) Rughness length ZO simulated by cupled RegCM-WAM at strm situatin 60N 50N 40N 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W (b) Difference f ruhness length ZO between cupled and uncupled RegCM-WAM, - 60N ' ' 0 5ON - -., ø'! 40N 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W Figure 9. (a) Rughness Z and (b) difference in rughness AZ between cupled and uncupled mdels at 0800 UTC n March 8. given in Figures 3c and 3d. These shw that cupled mdel temperatures are slightly warmer t the rear f the strm center and cler just t the nrtheast, cmpared t the uncupled mdel. The difference lessens frm 1.0øC t 0.4øC as height increases frm 1000 t 500 hpa. Finally, the vertical temperature and specific humidity bias prfiles, giving the cupled minus the uncupled mdel simulatins at the center f the lw pressure, are given in Figure 4a. This shws that the biases f temperature and specific humidity are psitive, particularly fr the lwer levels f the atmsphere. Maximum temperature and specific humidity biases are achieved within the bundary layer, at abut 900 hpa. Impacts f atmsphere-wave cupling are reduced at higher levels. Differences in cnvective precipitatin rates between the cupled and the uncupled mdels are shwn in Figure 4b. This shws that the cupled mdel gives mre precipitatin t the rear f the strm center and less precipitatin just t the nrtheast f the strm center, cmpared t the uncupled mdel. In magnitude the difference is abut 20%. Differences fr ttal precipitatin results are als -20%, which is similar t cnvective precipitatin differences in Figure 4b. Althugh this result smewhat reflects different lcatins f strm centers in cupled and uncupled simulatins, the principal cause f the differences is atmsphere-wave cupling. This implies that cupling has an impact n atmsphericnvectin Sea Surface Variables Variatins in sea level pressure imply variatins in surface winds and surface stress. The difference field fr surface winds AUt between the cupled and the uncupled mdels is given

11 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,763 in Figure 5a. This shws a diple-type structure, with the cu- (a) Hs simulated by WAM and measured at pled mdel experiencing slightly higher winds t the rear f the 12 strm center, whereas the uncupled mdel has strnger winds near the strm center and t the nrtheast. The crrespnding 11t fields fr the cupled mdel frictin velcity u, and differ _... Uncupled ences Au, are presented in Figures 5b-5c. Largest values fr u, and Au, are lcated near the strm center, as fund in a!t similar analysis by Desjardins et al. [2000]. Figures 6a and 6b give the sensible heat flux F g frm the cupled mdel and the differences AFg. Latent heat fluxes are similar. In the cupled mdel simulatins these fluxes are enhanced, particularly ver the cean regin near the frnt f ;/+ /.:.: -+, the strm, where intensive cupling ccurs. The maximum enhancement is abut 20 Wm -2, r AFc/Fg 20%, cm- IvlAR 61 71V{AR BI 91 10MAR 1997 pared t the uncupled mdel. These enhancements imply (:b) hs simulated by WaM and measured strm intensificatin and cntribute t the changes in temperature and geeptential fields. The time series f sensible and latent heat fluxes, crrespnding t the March 6-8 strm, are given in Figures 7a and 7b, in cmparisn with measured fluxes 11 1{}.' ß ß frm the RV Knrr. The mdel flux estimates are btained by linear interplatin frm the nearest fur neighbr pints, 7 relative t the ship trajectry. As shwn in Figures 1 and 6, the 6 trajectry f the ship during this strm is in the regin f the Labradr Sea where AF c is quite small. Thus Figures 7a and 7b shw that cupled and uncupled mdel simulatins are very 3 ++ clse and in qualitative agreement with the measured fluxes. 2 _. '+ The heat flux fields f Figures 6 and 7 result frm ur 1 4-.' HEXOS Z cupling frmulatin, which is large fr yung rugh waves relative t the Charneck Z results. T cmpare 1997 regins f differing wave ages, C e/u, is given in Figure 8, Figure 10. Observed significant wave height H s at buys (a) shwing that yunger waves ccur t the nrtheast f the strm and (b) in cmparisn with estimates frm the center, in the strm trajectry directin, with lder, mre ma- cupled and uncupled mdels at 0800 UTC n March 8. ture waves t the suthwest. The yung C e/u, areas crrespnd t regins f high u, and zxu,, given in Figures 5b and Cupled simulatin is slid line, uncupled is dashed, and measured is pluses. Units are in meters. 5c. These are regins f strng wave-atmsphere interactins and large atmspheric mmentum transfers int the cean. Large mmentum transfers generate and build cean waves, simulatins are systematically higher than uncupled Hx simwith mmentum fluxes int the waves (½,,,) exceeding lsses ulatins. This differs frm the results f ther researchers due t wave breaking and dissipatin (½,/. ). Old wave ages ccur t the west and suthwest f the strm center. There, mmentum flux int the waves ½i,is in apprximate balance with dissipatin %/,, and waves are n lnger grwing vigrusly. Figures 9a and 9b shw the rughness Z and difference in rughness zxz between cupled and uncupled mdels. The main areas f high Z ccur near the strm center and in frnt f the strm. Additinal high Z areas, fr example the [Dyle, 1995; Janssen and l/iterb, 1996; Liehell et al., 1998; Desjardins et al., 2000; Lalbeharry et al., 2000], which suggest that cupled simulatins f tf s are lwer than uncupled simulatins. Hwever, in these studies, U l is the driving field fr the waves. Cupled simulatins f U 0 are typically lwer than uncupled simulatins, as we als fund in Figure 5a. In using u, t drive the waves in the RegCM-WAM system, ur resultant cupled simulatins have weakened winds zxu /U < 0 Labradr Sea, the eastern Grand Banks, and the regin near and enhanced drag ACD/C > 0 such that Au,/u, > 0, as Iceland, crrespnd t areas f enhanced and highly variable resistive drag C. As shwn in Figures 5a-5c, resultant values fr zxu, are enhanced and highly variable in these areas, cmpared t A U values, which shw relatively little variability. In ther regins, where waves are ld and smth and wave age shwn in Figure 5c. It fllws that wave heights frm cupled simulatins are als enhanced zxhs/h s > 0, cmpared t uncupled simulatins. Results frm cupled and uncupled simulatins at the buys in Figures 5c and llb imply zxu,/u, 1/6, AHs/If s 2/6, and small differences fr wave age, is greater than 26, the HEXOS Z is replaced by the Charneck AW /W << O(l). This is cnsistent with (8). Wave age Z in this study, and resultant zxu, values crrelate well with zx U values. Measured significant wave heights Hs at buys and ff eastern Canada are shwn in Figures 10a and 10b, differences are small at the buys because mre mature waves ccur t the suthwest f the strm center, as shwn in Figure 8. When wave age _>26, the HEXOS Z is replaced by the Charneck Z in this study. fr the March 8 strm. Cmparisn with estimated wave heights frm the cupled and uncupled simulatins are als 4. presented, which shw that cupled simulatin systematically Seasnal Timescales imprve estimates f H s, cmpared t uncupled simulatins. Cnturs fr H s and AH s at the peak f the strm are presented in Figures 11a and 11b. These shw that cupled H s In previus sectins we have seen that atmsphere-wave cupling has an impact n bundary layer parameters such as U and sea level pressure SLP, as well as upper level atm- i ": Cupled -,!-"l"+"l-

12 17,764 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL (a) Significant wave height simulated by cupled RegCM-WAM at strm situatin 60N - 50N 40N 7 iw 76W 6 W 66W 55W 50W 45W 40W 35W 30W (b) Difference f =ignificent were height between cupled end uncupled RegCM-W 60N - 5ON- - 40N 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W Figure 11. Cntur plts f (a) the significant wave height H s estimated by the cupled mdel and (b) the difference field AHs, in units f meters at 0800 UTC n March 8. spheric variables, such as geptential height and temperature reanalysis, althugh the strength and extent f the simulated n synptic timescales. In this sectin we cnsider the impact lw is smewhat underestimated, especially at the 500 hpa f changing the cean surface parameterizatin n seasnal level where the cntur lines are slightly smther than thse timescales. f the NCEP reanalysis data. Similar cmparisns between 4.1. Reginal Mean Climate RegCM and NCEP reanalysis can be prduced fr the basic patterns f temperatures. Therefre by itself RegCM is capa- As a baseline, we cmpare results frm nly the RegCM system with averaged NCEP/NCAR reanalysis data, fr the 2 mnth LSDCE campaign. Figures 12a-12d give the 500 and 1000 hpa geptential heights ver the Nrth Atlantic and eastern Canada. Tw planetary-scale circulatins are evident in the 500 and 1000 hpa height fields. One is the subarctic lw ver nrthwestern Labradr Sea in the 500 hpa height field. The ther is the Icelandic lw in the 1000 hpa height field. Overall, the height patterns frm RegCM agree with NCEP ble f simulating the Nrth Atlantic climate. T identify the impact f WA cupling dynamics n seasnal timescales, we cmputed the mean geptential height and temperature difference fields fr the LSDCE perid. The differences between cupled and uncupled mdels are presented at 500 and 1000 hpa levels in Figure 13. The geptential results indicate slight negative biases at the 500 hpa level ver the pen cean, where WA cupling is effective. At the 1000 hpa level, slight psitive biases appear near Iceland and

13 . ß ß PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,765., E Z Z Z Z z z z CO ud ' 0 Z Z Z Z Z Z Z Z CO ud ' D CO ud ' 0

14 17,766 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL -O.. - Z Z Z Z Z Z Z I..O I..O I..O I..O I..O I..O r4:) I..0 r'o r4:) I..0 0" Ix Z Z Z Z Z Z Z Z LO LO LO U") LO LO LO LO r4:) I..0 r'o r4:) I..0 r'o

15 0 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL 17,767 Table 1. RMS Errrs fr the Cupled and Uncupled Mdels in the Standard Pressure Levels Relative t the NCEP/NCAR Reanalysis Over the Ocean Area and Land Area Ocean Area Land Area Temperature Geptential Height Temperature Geptential Height Cupled Uncupled Cupled Uncupled Cupled Uncupled Cupled Uncupled 850 hpa hpa hpa hpa hpa hpa hpa slight negative biases in the Labradr Sea, with values f nly 2-3 gpm magnitude. Over the pen cean, temperature differences are negative at bth 500 and 1000 hpa levels, with very small biases. This implies that the WA cupling frmulatin slightly weakens the strm climate n mnthly-t-seasnal timescales, in the regin that is apprximately dminated by Nrth Atlantic strm track trajectries. These results are similar t the analysis f Janssen and Viterb [1996] fr the Nrth Atlantic. Table 1 presents rt-mean-square (RMS) errrs fr the temperature and geptential height fields fr the cupled and uncupled simulatins at standard pressure levels f this study, relative t the NCEP/NCAR reanalysis data. This shws that the cupled simulatins are a slight systematic imprvement ver uncupled simulatins, at almst all levels, ver cean and land. Crrespnding fields fr ttal precipitatin and cnvective precipitatin are als reduced due t weakening f the pressure system, in cupled mdel simulatins cmpared t thse f the uncupled mdel. In magnitude, the reductins are f the rder f -- 10% fr bth fields, reflecting small negative biases. This result ccurs in the regin f the Nrth Atlantic dminated by strm tracks and large sea-statedependent mmentum fluxes. Figure 14 gives the difference between the cupled and the uncupled mdel estimates fr mean A U 1 fields, averaged fr the LSDCE perid. The distributin f A U1 is quite cmplicated ver the cean. There is a negative bias arund 45ø-55øN and a psitive bias near the Icelandic lw. These features are qualitatively similar t the Nrth Atlantic climate results b- tained in the glbal study by Janssen and Viterb [1996]. The WA cupling slightly decreases U ver much f the Nrth Atlantic strm track regin, with a slight increase in U l, near the atmspheric active center suth f Iceland. The maximum wind speed variatin is small, AUl/Ul 10%, cmparing cupled and uncupled mdels. The tw-mnth mean vertical temperature and specific humidity bias prfiles, between the cupled and the uncupled systems, ver the cean, are presented in Figure 15. We see that in lw atmspheric levels, the biases f temperature and specific humidity are negative, but the values are very small n seasnal timescales. Thus the dminant impact f the WA cupling n seasnal climate mdeling ccurs in lw atm- spheric layers. Crrespnding difference fields fr sensible and latent heat fluxes imply that the cupled mdel simulatins result in slight decreases t the sensible and latent fluxes int the atmsphere frm the cean surface, cmpared t the uncupled mdel. The differences are very small, AFc/Fc 5 %. ", 0.2.".z, 'v.;,, "'70'2... 2:> _ '. '-' 0.2 ß i: -. C? ' '-'.,. 35N 75W 65W 55W 45W 35W Figure 14. Difference field averaged fr the LSDCE perid, fr wind speed A U1 fr the cupled and uncupled mdels. The cntur interval is 0.2 m s-1.

16 17,768 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL hp ' 500' 600' T bias looo Figure 15. Vertical temperature and specific humidity bias prfiles between the cupled and the uncupled mdels averaged ver the cean fr the LSDCE perid. Slid line indicates temperature bias and dtted line specific humidity. The units fr temperature bias are øc and, fr specific humidity bias, gm kg Ocean Wave Climate Having discussed changes in seasnal reginal climate, we nw fcus n the cean wave climate. Significant wave heights H s frm the cupled mdel, as well as the difference fields between the cupled and the uncupled mdel simulatin AHs, averaged fr the LSDCE perid, are given in Figures 16a and 16b. As ne may expect, the highest H s and differences AHs ccur clse t the dminant atmspheri center, i.e., the Icelandic lw, at lng fetches frm the Nrth American cast, in assciatin with the dminant Nrth Atlantic strm track regin. This is cnsistent with results fr wind field U and geptential height. As shwn in Figures 16a and 16b, cupled mdel simulatins f wave climate H s are higher than results frm the uncupled mdel simulatins, by as much as 30%. Hwever, as in the strm case f Figures 11a and 1lb, this results frm the fact that we use u, t drive ur waves, rather than U. In related studies [Janssen and Viterb, 1996], U, rather than u,, was used t drive the waves. In that case, lwer estimates fr U, as given in Figure 14, necessarily lead t lwer wave heights. Mrever, H s frm the cupled mdel is in qualitative agreement with TOPEX-Pseidn altimeter data fr this perid, as given in Figure 16c. The latter was averaged n 1.5 ø x 1.5 ø bins fr February-March The maximum H s values are -5.0 m fr the cupled mdel and -5.6 m fr the TOPEX-Pseidn data. Cmparisn f Figures 16a and 16c als indicates that the cupled mdel wave climate is fields given in Figure 14, due t enhanced changes in air-sea frictin. Enhanced AC areas are particularly evident in several large areas such as the Labradr Sea, the eastern Grand Banks, and near Iceland. This is cnsistent with glbal studies by Janssen and Viterb [1996] fr the Nrth Atlantic. They accunted fr the Au, magnitudes in relatin t the AUt fields in terms f dminant Nrth Atlantic strm tracks, which cnsist f prevailing nrtheasterlies during much f the winter. It fllws that because assciated cean waves are fetch- limited and waves are relatively yung, increased rughness results in this regin. T cmplete ur discussin f the differences between cupled and uncupled simulatins, we nte that lng-time averages f frictin velcity u, and wave heights H s are related. Fr seasnal timescales the details f wave generatin and grwth are nt imprtant. In Figures 16a and 16b and 17a and 17b the largest u, values ccur in regins where H s is als maximal, near the Icelandic lw. The maximum lng-fetch AHs/Hs value is abut 0.4 at (35øW, 57øN), which is in gd agreement with 2Au,/u, fr that regin, which is suggested by the asympttic Piersn-Mskwitz relatin given in (9). 5. Cnclusins Our bjective was t assess whether the cupling f cean waves t the atmsphere can imprve simulatins f synptic marine strms as well as reginal climate n timescales f mnths/seasns. A cupled reginal atmsphere-cean wave mdel system fr the Nrth Atlantic was cnstructed, cnsisting f the NCAR reginal climate mdel (RegCM) and the WAM cean wave mdel. The cupled system was effected using the HEXOS wave-age-dependent rughness parameterizatin f Smith et al. [1992]. Frictin velcity u, rather than wind U was used t drive the WAM mdel. Cupled and uncupled simulatins were cmpared with bservatins cllected during the Labradr Sea Deep Cnvectin Experiment (LSDCE) f Our results indicate that fr synptic-scale fields as well as fr seasnal climate timescales, the atmsphere-wave cupling has significant impact n bth meterlgy and waves. Our cupled simulatins give enhanced rughness frm yung seas, which affects synptic lws, as well as mean strm cnditins in strm track areas. Further results include reductins in the sea level pressure (SLP) near the strm center, increases in 1000 hpa temperatures, and enhanced cnvective precipitatin, cmpared t the uncupled mdel. Cupled simulatins result in systematic imprvements in almst all geptential height levels and als in wave heights, fr synptic strms as well as fr LSDCE 2-mnth averages. These results are cnsistent with recent studies, fr example Janssen and Viterb [1996] and Desjardins et al. [2000]. The bundary layer parameterizatin f the atmspheric mdel has sufficient generality t allw the pssibility f all kinds f temperature stratificatin cnditins. Hwever, the standard WAM mdel f Hasselmann et al. [1988] emplys biased lw by abut 1 m fr much f the lwer half f the cean empirical frmulas t prduce frictin velcity u, fields that prtin f these figures, which is the typical distance necessary can differ frm u, fields generated by the atmspheric mdel. fr waves t becme fully develped. This bias is due t wave In ur cupling frmulatin u, and rughness Z are cnsisenergy that prpagates tward the nrtheast, after being generated suth f ur dmain f study. Crrespnding fields fr u, and differences Au, are given Figure 16. (ppsite) LSDCE perid averages fr (a) H s in Figures 17a and 17b. The Au,/u, fields exhibit relatively frm the cupled mdel simulatins, (b) differences zxhs, and greater magnitudes and variability, cmpared t the A U /U (c) the TOPEX/Pseidn altimeter data, in units f meters.

17 (a) Mean significant wave height simulated by cupled RegCM-WAM i : : \: 60N... ß 50N N - 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W (b) Difference f significant wave height between cupled and uncupled RegCM-WAM 6ON- - 5ON- - 4ON- 75W 76W 6 W 66W 5 W 56W 4 W 40W 35W 30W (c) Tw-mnth mean f significant wave height frm TOPEX/Pseidn 50N 40N ' 75W 70W 65W 60W 55W 50W 45W 40W 35W 30W

18 17,770 PERRIE AND ZHANG: COUPLED REGIONAL CLIMATE MODEL (a) Mean frictin velcity simulated by cupled RegCM-WAM - 5ON- ' )> W 70W 65W 60W 55W 50W 45W 40W 35W 3()W (b) Difference f frictin velcity between cupled and uncupled RegCM-WAM, 'D. ' _ 50N i. 40N..04,, ; ',; 71iW 70W 65W 60W 55W 50W 45W 40W 35W 3I)W Figure 17. As in Figure 16 fr (a) u, frm the cupled mdel and (b) differences Au,, in units f m s --1 tent in bth the atmspheric bundary layer mdel and the wave mdel, acrss the air-sea interface. By cmparisn, studies that have used U frm the atmspheric mdel t drive the wave mdel have typically maintained the cnsistency f u, within the atmspheric mdel, which differs frm u, as estimated within the wave mdel. In the cupling prcesses between atmsphere and cean waves, there are tw kinds f interactin prcesses. One is dynamic cupling, in which yunger cean waves prduce rugher cean surfaces, with larger rughness lengths and drag cefficients. These rughness enhancements lead t mdificatins f the wind prfile, as well as the frictin velcity in the bundary layer, resulting in enhanced atmspheric mmentum flux transfers t the cean frm the atmsphere and enhanced ceanic frictin acting n the atmsphere. Dynamic cupling is a fcus f this paper. The ther interactin prcess is thermal cupling, cncerning the relatins between rughness lengths and thermal drag cefficients, and the cnditins under which enhanced heat fluxes (sensible and latent heat) are transprted int the atmsphere frm the cean. In the real atmsphere, whether dynamic cupling r thermal cupling dminates depends n the atmspheric and ceanic cnditins. Further study f these interactins is the tpic f a related study, which is presently under way. Acknwledgments. This study was funded by the Panel n Energy Research and Develpment (PERD) f Canada under prject We are very grateful fr the use f the NCAR reginal climate mdel, RegCM, the NCEP/NCAR reanalysis data, and AVHRR sea surface temperature data. We want t thank Serge Desjardins fr stimulating discussins and Peter Guest fr access t the heat flux data cllected during the Labradr Sea Cnvectin experiment frm the RV Knrr. We als want t thank three reviewers fr very helpful and detailed reviews f ur manuscript. References Anthes, R. A., A cumulus parameterizatin scheme utilizing a nedimensinal clud mdel, Mn. Weather Rev., 117, , 1977.

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Bx 1006, 1 Challenger Drive, Dartmuth, Nva Sctia, Canada B2Y 4A2. Y. Zhang, Department f Atmspheric Sciences, Nanjing University, Nanjing , China. (Received August 24, 2000; revised January 25, 2001; accepted March 30, 2001.)