The influence of snow cover on northern hemisphere climate variability

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1 Atmosphere-Ocen ISSN: (Print) (Online) Journl homepge: The influence of snow cover on northern hemisphere climte vriility Judh Cohen & Dr Entekhi To cite this rticle: Judh Cohen & Dr Entekhi (2001) The influence of snow cover on northern hemisphere climte vriility, Atmosphere-Ocen, 39:1, 35-53, DOI: / To link to this rticle: Pulished online: 21 Nov Sumit your rticle to this journl Article views: 307 View relted rticles Citing rticles: 45 View citing rticles Full Terms & Conditions of ccess nd use cn e found t Downlod y: [ ] Dte: 03 Decemer 2017, At: 11:42

2 The Influence of Snow Cover on Northern Hemisphere Climte Vriility Judh Cohen* Atmospheric nd Environmentl Reserch, Inc. 131 Hrtwell Ave., Lexington, Msschusetts nd Dr Entekhi Rlph M. Prsons Lortory, Msschusetts Institute of Technology, Cmridge, Msschusetts [Originl mnuscript received 3 My 2000; in revised form 14 August 2000] ABSTRACT The importnce of snow cover nomlies on the locl energy lnce is well known, however, the potentil impct of snow cover nomlies on locl nd remote tmospheric dynmics is less understood. We present oservtionl evidence demonstrting sttisticlly significnt reltionship etween sesonl snow cover nd winter-time circultion nomlies over mid-high ltitudes. To explore snow forcing further, Generl Circultion Model is used to test whether the locl ditic chnges cused y snow cover cn induce lrge-scle dynmicl responses. A six-memer ensemle, three winter month (DJF) integrtion is performed for control cse nd cse where snow cover is incresed s oserved during the positive-nomlous winter of 1977/1978. Snow cover vriility results in ltered generl circultion ptterns resemling oserved nomly ptterns t mid-high ltitudes in the Northern Hemisphere winter. RÉSUMÉ [Trduit pr l rédction] L importnce des nomlies de l couverture de neige en rpport vec le iln énergétique locl est très ien connue, toutefois, l impct potentiel des nomlies de l couverture de neige sur l dynmique tmosphérique locle et éloignée est moins compris. Nous présentons une preuve pr oservtion démontrnt une reltion sttistiquement significtive entre l couverture de neige sisonnière et les nomlies de l circultion hivernle ux ltitudes polires et moyennes. Afin d étudier d vntge le forçge de l neige, un modèle de circultion générle est utilisé fin d exminer si les chngements ditiques locux, cusés pr l couverture de neige, peuvent produire des réctions dynmiques à grnde échelle. Un ensemle de prévisions de six memres, pour trois mois d hiver (DJF), est exécuté comme cs témoin et ussi dns le cs où on ugmenté l couverture de neige comme on l oservé pendnt l hiver de 1977/1978 vec des nomlies positives. L vriilité de l couverture de neige donne comme résultt des configurtions modifiées de l circultion générle ressemlnt ux configurtions des nomlies oservées à l hiver ux ltitudes polires et moyennes de l hémisphère septentrionl. 1Introduction During the short period it hs een extensively monitored, Northern Hemisphere (NH) snow cover hs gone through noticele trends, peking in the lte 1970s followed y generl decrese until reching record minimum vlues in the lte 1980s nd erly 1990s (Roinson, 1996; Wllnd nd Simmonds, 1997). This trend is consistent with trends oserved in the NH climte s oserved in the climtes of the North Pcific (Mntu et l., 1997), the North Atlntic (Rogers, 1990; Hurrell, 1995) nd the zonl-men circultion (Ting et l., 1996). Of prticulr interest hs een the North Atlntic Oscilltion (NAO) or the more recently nmed Arctic Oscilltion (Thompson nd Wllce, 1998) ecuse of its strong influence on the climte in estern North Americ nd Western Europe (Rogers, 1990; Pittlwl nd Hmeed, 1991; Hurrell, 1995; Serreze et l., 1997). In the NH, snow cover is the most vrile lnd surfce condition in oth time nd spce (Gutzler nd Rosen, 1992; Cohen, 1994); mking it vile cndidte for t lest mplifying climte nomlies. In this study we demonstrte the link etween snow cover nd the NH generl circultion on sesonl timescles. The most widely known nd studied impct of snow cover on climte is its suppression of locl surfce ir tempertures mostly due to its high ledo (Nmis, 1960, 1962, 1985; Wgner, 1973; Dewey, 1977; Klein, 1983, 1985; Klein nd Wlsh, 1983; Wlsh et l., 1982, 1985). There hve lso een studies, ut fewer in numer, on the impct of snow cover on tmospheric dynmics, most notly those significntly correlting Eursin snow cover with Asin sucontinent monsoon rinfll (Hhn nd Shukl, 1976; Chen nd *Corresponding uthor s e-mil: jcohen@er.com ATMOSPHERE-OCEAN 39 (1) 2001, Cndin Meteorologicl nd Ocenogrphic Society

3 36 / Judh Cohen nd Dr Entekhi Yn, 1978; Dey nd Kumr, 1982; Brnett et l., 1988, 1989; Vernekr et l., 1995). Less studied hs een the potentil impct of snow cover on the extrtropicl tmospheric circultion nd storm trcks. Proly the first to propose possile connection etween snow cover nd sesonl storm trcks ws Nmis (1962). This ws sed on oserving the lte, severe winter of in estern North Americ. He concluded from the study tht the initil positive snow cover nomlies oserved during tht winter, through positive feedck, resulted in further positive snow cover nomlies nd negtive temperture nomlies oserved during tht winter. The positive feedck occurred ecuse greter thn norml snow cover ltered locl storm development which fvoured incresed snowfll nd colder tempertures. Nmis (1962) limited his study to, wht is currently referred to s, the entrnce region of the North Atlntic storm trck Other studies of the impct of snow cover on storm development nd storm trcks hve een primrily sed on generl circultion models (GCMs). Possily the first GCM study on snow forcings of climte ws y Wlsh nd Ross (1988). They found tht incresed North Americn snow cover resulted in deeper Icelndic low while incresed Eursin snow cover produced deeper Aleutin low. Ysunri et l. (1991) found tht positive nomlous Eursin snow cover in GCM experiment during Mrch, excites the propgtion of Rossy wve trin which results in positive Pcific/North Americn teleconnection pttern cross the North Pcific nd North Americ in the spring. Wllnd nd Simmonds (1997) found tht with incresed NH snow cover cme wekened storm trck in the North Atlntic nd strengthened storm trck in the North Pcific. In ddition to the GCM study, Wllnd nd Simmonds (1997c) performed n oservtionl study compring empiricl orthogonl functions (EOFs) of snow cover nd 700-hP heights for Jnury over North Americ nd Eursi seprtely. They concluded tht there is reltionship etween the snow cover nd the locl tmospheric circultion. However, they elieve tht the oservtionl evidence etter supports the hypothesis tht the tmosphere is forcing the snow cover rther thn vice vers. Similrly, Clrk et l. (1999) compred snow cover nomlies with three EOF ptterns derived from the 700-hP geopotentil heights over Eursi for Decemer, Jnury nd Ferury (DJF). They concluded tht the tmospheric circultion forces snow cover mostly through the resultnt temperture nomlies dvected y chnges in the dominnt circultion ptterns. Frei nd Roinson (1998) lso performed EOF nlysis on snow extent nd 500-hP geopotentil heights to identify dominnt modes of vriility in oth snow cover nd the tmospheric circultion. They found tht over 60% of the vrince in continentl snow cover ws ssocited with smll, regionl chnges in tmospheric circultion rther thn hemispheric scle circultion ptterns. Wtne nd Nitt (1998, herefter referred to s WN98) performed GCM study where they decresed Eursin snow cover s oserved during the negtive-nomlous fll of In ddition to ltering snow cover they prescried oserved nomlous se surfce tempertures (SST) for the cool seson of 1988/89, during which strong L Niñ conditions occurred. WN98 found decresing Eursin snow cover wrmed surfce tempertures over Eursi nd produced the oserved nomlous dipole in 500-hP heights during the winter of 1988/89. The dipole consisted of lower heights over the pole nd higher heights over the mid-ltitudes. This is consistent with the results of Cohen nd Entekhi (1999, herefter referred to s CE99) sed on oservtions (stellite for snow cover nd renlysis for the tmosphere) over the longer period of 25 yers. In second pper Wtne nd Nitt (1999) found tht nomlies in Eursin snow cover during utumn were importnt in mplifying chnges in the generl circultion. Wht is common to ll of the ove mentioned studies (with the exception of CE99) is tht they focus on the Eursin snow cover impct on the downstrem generl circultion over the Pcific. In CE99, nd in this study, the focus is on Eursin snow cover during utumn nd winter nd the forcing of the dominnt mode of vriility in the NH mid-troposphere nd the North Atlntic sector. Correltions etween oserved snow cover with se level pressure (SLP), 500-hP heights nd stndrd climte indices ll show significnt snow-climte sttisticl reltionship concentrted in the North Atlntic. The reltionship is stronger thn tht over the North Pcific. CE99 hypothesize tht possile dynmicl mechnism linking Eursin snow nomlies nd North Atlntic climte vriility is through the strength nd position of the Sierin high. In this pper we continue the oservtionl study of CE99 with some dded oservtionl support for snow-climte reltionships nd numericl experiments complementing the oservtionl nlysis. In the rest of the pper we will present oth oservtionl nlysis nd numericl experiment tht demonstrtes n importnt climte response to snow cover nomlies. Snow cover nd SSTs re the importnt surfce oundry conditions during this seson. We will lso riefly present SSTinduced climte response for comprison. We feel it is importnt to use oth oservtionl nd numericl results in demonstrting climte forcing mechnisms. If significnt sttisticl reltionship etween snow cover nd the tmospheric circultion is identified from oservtionl nlysis, it does not yield definitive conclusions concerning cuse nd effect. Rther, sensitivity experiments using generl circultion model re etter suited to resolve pthwys of climte forcings. However, GCM experiment is not sufficient ecuse results my e limited to tht prticulr GCM. In Section 2 we discuss the dt used nd present oservtionl nlysis; in Section 3 we discuss the model used nd the numericl experiment; in Section 4 we discuss the results; nd in Section 5 we present our conclusions. 2 Oservtionl nlysis Dt We compute sesonl snow cover re y verging from weekly snow cover re dtsets compiled t Rutgers

4 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 37 University (Roinson et l., 1993). Snow cover dt t Rutgers University re derived from Ntionl Ocenic nd Atmospheric Administrtion (NOAA) visile stellite sensors (yers ). Snow cover dt re computed for 89x89 eqully spced grid oxes on polr stereogrphic grid for the NH. From sesonl snow cover, mens nd nomlies re clculted to form regionl nd hemispheric snow cover indices. A snow cover index is computed from the stndrdized nomly for sesonl totl. For oserved tmospheric vriles we used the Ntionl Centers for Environmentl Prediction/Ntionl Center for Atmospheric Reserch (NCEP/NCAR) renlysis dt yers (Klny et l., 1996; Bsist nd Chellih, 1997). All oservtionl dt results re tested using the student-t test for significnce for the rejection of the null hypothesis. Wintertime (DJF) Snow Cover nd NH Generl Circultion Indices We egin y correlting NH, Eursin nd North Americn snow cover nd vrious climte indices, shown in Tle 1. Tle 1 compres correltions of time series of DJF snow cover with the DJF zonl-men wind index (defined s the difference in the nomlous geostrophic component of the zonl wind t 500 hp etween 55 N nd 35 N), NAO index, Scndinvi or Eursin One (SCA) index, West Pcific Pttern (WPP) index nd Pcific/North Americn (PNA) index (Brnston nd Livezey, 1987). NH snow cover exhiits the strongest reltionships with the climtes of the North Atlntic nd the zonl men climte nd less with the climte of the North Pcific. The one exception is the significnt negtive correltion of North Americn snow cover nd the PNA pttern. From Tle 1, it is cler tht Eursin snow cover, mong the three groupings of snow cover presented, is the one most significntly correlted with the climte indices of the zonlmen NH climte nd the climte of the North Atlntic. This is somewht surprising given tht Wllnd nd Simmonds (1997) found strong co-vriility etween Eursin nd North Americn snow cover especilly in winter. They postulte tht the linked vriility in snow cover is result of the lrge-scle orgniztion of the tmosphere during winter. More work needs to e done to resolve this possile conflict in our results with those of Wllnd nd Simmonds (1997). Despite this, given the results of Tle 1 nd the work of WN98, we will focus on Eursin snow cover in the rest of the pper. In order to isolte the dominnt mode of NH climte vriility EOF nlysis is performed on oserved 500-hP heights from 1972/ /96 for the NH only. The dominnt mode of vriility during the three winter months (DJF), shown in Fig. 1, resemles wht is commonly referred to s the NAO mode, ccounting for 30% of the totl vrince. Recently Thompson nd Wllce (1998) identified the dominnt mode of vriility s the Arctic Oscilltion (AO, see their Fig. 1) which ers n even closer resemlnce to the dominnt mode presented here. The second mode of vriility, commonly referred to s the PNA mode, ccounts for 18% of the totl vrince (see Fig. 2). In Fig. 3 we present the two dimensionl correltion plot of the time series of Eursin DJF snow cover with the gridpoint time series of winter 500-hP heights; lso included is the regression of snow cover (vlue tken from winter 1977/78) with 500-hP geopotentil heights. Wht is immeditely pprent is tht the pttern of the correltion coefficients resemles the pttern of vriility for the dominnt mode. Positive snow cover nomlies re ssocited with higher mid-tropospheric heights over the Arctic (centred north of Icelnd) nd rod region of lower heights cross the entire mid-ltitude North Atlntic with two low centre nomlies, one centred over the estern United Sttes nd the other centred over western Europe. Snow cover is significntly correlted (95% nd 99% confidence levels re shded) with estern North Americ, North Afric, western Europe, northern Europe, the North Pole nd Sieri. Snow cover does not correlte significntly with either the tropicl regions or the North Pcific. From Figs 1 nd 3, it ppers tht snow cover exhiits strong reltionship with the dominnt mode of vriility in the NH winter-time extrtropics. Shown in Fig. 4 is the dominnt mode derived from n EOF nlysis of DJF SLP fields (which compres well to other EOF nlyses in Hurrell (1995) nd Thompson nd Wllce (1998)). The importnt gross fetures show higher pressures over the Arctic nd lower pressures over the North Pcific nd the North Atlntic, prticulrly in the region ner western Europe. These fetures re very similr to those shown for 500-hP heights nd the dominnt mode of DJF SLP is highly correlted with the dominnt mode of 500-hP heights (correltion coefficient = 0.95, Thompson nd Wllce, 1998). Also presented in Fig. 4 re the correltions of Eursin DJF snow cover nd DJF SLP. The pttern is similr to the dominnt EOF of SLP. Positive nomlous snow cover is ssocited with higher SLPs cross most of the Arctic (centred northest of Icelnd) nd lower pressures cross the mid-ltitude North Atlntic. However significnt correltions re confined to the Arctic, northern Cnd, the estern North Atlntic nd western Europe. c Reltive Role of Ocens in Mid-High Ltitude Internnnul Climte Vriility As comprison to the correltions found etween snow cover nd the climte indices presented in the pper, we hve lso crried out similr correltions etween SST time series (the remining importnt oundry condition for this seson) nd the zonl-men wind index nd regionl climte indices. To extrct n SST time series we performed n EOF nlysis on oserved NH SSTs following Wllce et l. (1990) nd others. For oserved SSTs we used the Reynolds SST dtset (Decemer 1968 to Novemer 1992, Reynolds nd Smith, 1994, 1995). The first EOF which explins 40% of the vrince is esily recognizle s the El-Niño SST pttern. The second is referred to s mid-ltitude SST response (Wllce et l., 1990; Deser nd Blckmon, 1995), with nding of

5 TABLE / Judh Cohen nd Dr Entekhi Correltion coefficients of snow cover nd SSTs with hemispheric nd regionl climte indices. Snow cover, SSTs nd climte indices re ll for DJF. Climte indices re, zonl-men wind (ZMW) index, NAO, SCA, WPP, PNA. NAO nd SCA re dominnt modes of vriility in the North Atlntic nd PNA nd WPP re dominnt modes of vriility in the North Pcific in winter (Brnston nd Livezey, 1987). Sttisticl significnces greter thn the 95% confidence level re in itlics nd greter thn the 99% confidence level re in old. The correltion coefficient included in prentheses corresponds to the sttistic excluding the El-Niño yers 1972, 1982, 1986, Climte Index NH NA EU c SST1 d SST2 e ZMW index 0.36 (0.36) (0.44) NAO index 0.50 ( 0.57) ( 0.61) SCA f index (0.45) WPP g PNA h index ( 0.32) NH snow cover North Americn snow cover c Eursin snow cover d First EOF of SSTs e Second EOF of SSTs f Scndnvi pttern or Eursin One pttern g West Pcific Pttern or West Pcific Oscilltion h Pcific North Americn Pttern, SCA, WPP, nd PNA ptterns re defined y leding modes of vriility produced y rotted principl component nlysis of 700 hp Brnston nd Livezey (1987) Fig. 1 () First Empiricl Orthogonl Function (EOF) of NH 500-hP heights sed on dt of 24 winters (DJF) 1972/ /96. Also shown is frction of vrince ttriuted to the first EOF. () Time series or Principl Component (PC) of first EOF (solid line). Included is time series of Eursin snow cover stndrdized nomlies for DJF (dshed line) nd correltion coefficient etween the two time series (.40 is significnt t the greter thn 95% confidence level).

6 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 39 Fig. 2 Second Empiricl Orthogonl Function (EOF) of NH 500-hP heights. Also shown is frction of vrince ttriuted to the second EOF. temperture nomlies cross the mid-ltitudes. The SST EOF time series re used to determine the correltion etween nomlous tmospheric circultion ptterns ssocited with NH extrtropicl vriility nd ocenic forcing. As cn e seen from Tle 1, the NH zonl-men nd North Atlntic climte indices hve significntly higher correltion with snow cover thn with SSTs. In contrst, the Pcific sector is strongly linked to SST vriility s evident in the sttisticlly-significnt correltion of the WPP nd PNA indices with the time series from the SST EOFs (nd the lck of correltion with snow cover, with the possile exception of North Americn snow cover). The two-dimensionl correltion plot of the time series of the dominnt SST EOF or the El Niño Southern Oscilltion (ENSO) SST pttern with the gridpoint time series of 500-hP heights, s discussed y Wllce et l. (1990) nd Deser nd Blckmon (1995), is ssocited with 500-hP height pttern resemling the PNA mode. However, significnt correltions etween El Niño nd 500-hP heights re mostly confined to the tropics. We performed the sme sttisticl nlysis with the second EOF of SST ptterns, nd sttisticl significnce ws confined mostly to smll region north of Jpn. Correltions of SLPs nd the first nd second EOF of SSTs lso show different pttern from tht of snow cover. The first EOF of SSTs or the El Niño pttern significntly correltes with lrge regions of the tropics nd su-tropics. Significnt correltions outside the lower ltitudes resemle PNA pttern with negtive correltions in the estern Pcific; positive correltions over the Rockies nd Plins; nd negtive correltions in the southestern United Sttes nd the djcent costl wters. The second EOF of SSTs lso significntly correltes with SLPs mostly in the Pcific sector with lrge region of negtive correltions in the mid-high ltitude North Pcific, centred southest of the Aleutins; the pttern most closely resemles the WPP. In conclusion, significnt correltions etween snow cover nd 500-hP heights or SLP re predominntly found in the North Atlntic nd djcent lnd msses. In contrst significnt correltions etween SSTs nd 500-hP heights or SLP outside of the tropics re predominntly found in the North Pcific, nd djcent lnd msses. d Forcing Mechnisms A strong reltionship etween snow cover nd the tmospheric circultion during winter rises the importnt question of which wy the forcing is going. CE99 nd Wtne nd Nitt (1999) present significnt correltions when snow cover leds the winter tmospheric circultion. However, even lg correltions do not demonstrte cuse nd effect conclusively. In ddition, it is difficult to identify from oservtionl nlysis the physicl forcing mechnisms. Therefore, to gin insight into the pthwys through which snow cn force the tmospheric circultion, consistent with the oservtionl nlysis presented, we performed GCM sensitivity experiment to positive-nomlous snow cover. 3 GCM experiment Numericl Model To test the strength nd sptil ptterns of the forcing of tmospheric regionl nd hemispheric circultions y winter snow cover, the Goddrd Institute for Spce Studies (GISS) GCM is employed. Since such tmospheric circultion fetures re lrge scle nd resolved in numericl glol climte models, the influence of nomlous surfce forcing of wintertime mid-ltitude climte vriility my e studied using

7 40 / Judh Cohen nd Dr Entekhi Fig. 3 () Percent correltion etween oserved Eursin DJF snow cover nd oserved NH DJF 500-hP heights. Light shding indictes correltion vlues with 95% sttisticl significnce nd drk shding indictes correltion vlues with 99% sttisticl significnce. () Regression of snow cover from DJF 1977/78 on 500-hP height field in decmetres. integrtions of GCMs (Pittlwl nd Hmeed, 1991; Wllnd nd Simmonds, 1997). All numericl model results will lso e tested using the student-t test for significnce of differences in men of two smples with estimted vrinces sed on memers. Studies compring how well GCMs simulte snow cover extent nd snow mss (during Atmospheric Model Intercomprison Project (AMIP) period) with oservtionl dtsets hve concluded tht GCMs ccurtely represent lrge-scle winter men snow cover. However, GCMs re poorer in reproducing internnul vriility (Foster et l., 1996; Frei nd Roinson, 1998). In most GCMs, including the GISS GCM used in our experiment, the men winter snow cover extent is within 5% of the men oserved winter snow cover extent (Frei nd Roinson, 1998). In generl snow cover in the GISS GCM is deficient during DJF when compred to oservtions. The lck of snow cover is more pronounced in Eursi thn in North Americ. In Eursi, west

8 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 41 Fig. 4 () First EOF of se level pressure sed on dt of 24 winters (DJF) 1972/ /96. Also shown is frction of vrince ttriuted to the first EOF. () Percent correltion etween oserved Eursin DJF snow cover nd oserved NH DJF se level pressure. Light shding indictes correltion vlues with 95% sttisticl significnce nd drk shding indictes correltion vlues with 99% sttisticl significnce. Correltion mp cptures three pole pttern of dominnt EOF in se level pressure fields. of 90 E, men snow cover is present only polewrd of 50 N while the oservtions show snow cover to extend closer to 40 N, with the exception of western Europe. Model simulted snow cover in estern Asi nd North Americ is frther equtorwrd, ner the oserved snow line. Besides compring snow extent nd snow mss other studies hve explored snow-climte feedcks (Cess et l., 1991; Rndll et l., 1994). These studies hve shown tht the snowclimte feedck (descried s whether snow cover response to forced climte chnge mplifies or dmpens tht climte chnge) cn vry considerly mong the GCMs from wek negtive feedcks to strong positive feedcks. However most GCMs exhiit positive snow-climte feedck including the GISS GCM. The tmospheric GCM Model II is n updted, 4 ltitude 5 longitude 9 levels resolution version of Model II devel-

9 42 / Judh Cohen nd Dr Entekhi Fig. 5 Oserved snow cover frequency in percent for Decemer, Jnury, Ferury 1977/78. oped t the Ntionl Aeronutics nd Spce Administrtion (NASA) GISS (Hnsen et l., 1983). Model II hs een used to simulte the impcts of trnsient increses nd equilirium douling of CO 2 (Hnsen et l., 1988). Model improvements incorported into Model II relte to the improved lnd surfce hydrology scheme of Rosenzweig nd Armopolous (1997), convective prmetriztion (Del Genio nd Yo, 1993; Del Genio et l., 1996), more relistic oundry lyer (Hrtke nd Rind, 1997), fourth order differencing scheme for momentum dvection, qudrtic upstrem scheme for dvecting het nd moisture, cloud liquid wter udget, more sophisticted ground hydrology nd vrying cloud opticl thickness (Druyn et l., 1995). The ledo of snow cover cn vry etween 0.5 nd 0.85 depending on the ge of the snow nd whether melting hs occurred. Snow cover my only contriute to frction of the surfce ledo depending on whether vegettion is present nd on the depth of the snow nd the height of the vegettion. In the model the presence of snow cover does not lter the surfce roughness. Precipittion, with surfce tempertures t or elow freezing, flls s snow nd is dded to the existing snow cover. Snow is mintined s long s surfce tempertures remin elow freezing. When surfce tempertures rech 0 C, dditionl heting goes into melting the snow; melted snow goes directly into the surfce runoff. The grid resolution eing employed here (4 5 9 levels) is not s fine s in some other models. Nevertheless, compred with other models run in the AMIP intercomprisons, the model performs well compred with other mjor GCMs (Gtes et l., 1999), especilly with regrds to precipittion, importnt in simulting relistic snow cover. For exmple, Lu et l. (1996) found tht the GISS model ws rnked pproximtely fifth out of 28 GCMs in its ility to simulte components of the hydrologic cycle. Boyle (1998), in ssessing the AMIP models sesonl precipittion cycle, noted tht model with low resolution such s GISS ppers to perform etter thn models with more thn doule the numer of grid points. They concluded tht the Mx Plnk Institute (MPI) model (with finer horizontl resolution nd doule the numer of verticl levels) nd GISS hve distriutions of precipittion through the yer tht mtch the oservtions firly well nd tht mtch ech other. The GISS model is lso documented s compring fvourly with the oservtions for snow cover nd snow mss reltive to other GCMs (Foster et l., 1996). From the oservtionl nlysis presented erlier, it ws shown tht the dominnt mode of vriility for the NH winter is importnt in snow-climte reltionships. The GISS model is documented s eing le to simulte the dominnt mode of vriility s oserved (Shindell et l., 1999). Perturtion nd Control Experiments In this section, the regionl to glol responses of the tmosphere to perturtions re investigted using the GISS GCM with sesonl climte SSTs (Hnsen et l., 1983). A six-yer simultion ws mde with the GISS GCM. From this six-yer (12-month) simultion, six control nd six perturtion ensemle memers were initilized y the tmospheric conditions on dys smpled from different GCM yers. The control simultion nd the perturtion simultion only vried in the prescried snow cover, s descried elow, in order to study the sensitivity of the tmospheric generl circultion in the extrtropics to the vriility of sesonl snow cover nomlies. Ech ensemle simultion ws crried out from Decemer to Ferury.

10 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 43 c Fig. 6 () Men snow mss for Decemer, Jnury, Ferury in kg m 2 (LWE) or cm (depth) for the incresed snow cover simultion minus the control simultion. () Men surfce ledo for Decemer, Jnury, Ferury in percent for the incresed snow cover simultion minus the control simultion. (c) Men sored shortwve rdition for Decemer, Jnury, Ferury in W m 2 for the incresed snow cover simultion minus the control simultion. Two types of integrtion re mde: control simultion nd n incresed snow cover simultion. The incresed snow cover simultion is sed on the oserved snow cover from the positive-nomlous DJF 1977/78 seson (see Fig. 5). Prescried snow cover is held fixed for the entire three-month integrtion. Snow cover is prescried t the liquid wter equivlent (LWE) of 50 kg m 2 or 50 mm t ll lnd points etween 36 N nd 60 N, to mtch the oserved winter snow cover. The LWE of 50 mm is the NH verge for snow depth during DJF (Bmzi nd Kinter, 1997). Annully, 36 N roughly corresponds to the oserved 20% frequency in Eursi nd 25% frequency in North Americ of snow cover occurrence during winter (Mtson et l., 1986). It hs lso een oserved tht snow cover nomlies in winter tend to persist from Decemer through Ferury (Iwski, 1991; Wllnd nd Simmonds, 1997), justifying keeping snow cover fixed for the entire three-month integrtion. Becuse WN98 performed GCM sensitivity to decresed snow cover, n incresed snow cover experiment offers good complement to their work. It lso llows explortion of climte response symmetry.

11 44 / Judh Cohen nd Dr Entekhi Fig. 7 Men surfce ir temperture for Decemer, Jnury, Ferury in C for ) the control simultion ) the incresed snow simultion minus the control simultion. Anomlous snow cover cooled surfce tempertures y 1 3 C. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. In Fig. 6, the snow mss for the control simultion nd the difference in snow mss etween the incresed snow simultion nd the control re presented. The incresed snow cover produces lrge chnges in the ground ledo cross the mjor continents in the mid-ltitudes (see Fig. 6). Higher ledo reflects more incoming shortwve (SW) rdition nd therefore sustntilly less SW rdition is sored t the surfce (see Fig. 6). The nomlous snow cover results in net cooling. The negtive net heting trnsltes to cooling on the order of 1 3 C over the nomlous snow cover which is the locl thermodynmic response forced y snow cover (see Fig. 7). So even though chnges in the snow cover nd ground ledo re quite lrge etween the two model integrtions, surfce temperture differences compre more resonly with those which might e expected from internnul vriility (Hnsen nd Leedeff, 1987). The nomlous equtorwrd snow cover nd the nomlous southwrd cooling produces n equtorwrd shift in the region of the strongest ltitudinl temperture grdient. This shift in the temperture grdient could potentilly influence mid-tropospheric circultion since the zonl wind is function of the ltitudinl temperture grdient (the sis of the therml wind eqution). In terms of the tmosphere s response to the perturtions, the SLP fields in Fig. 8 show tht higher pressures re produced over the nomlous snow cover, due to colder surfce tempertures. Lower pressures re found in the North Atlntic in response to the nomlous presence of snow cover nd consistent with the oservtionl nlysis presented in Section 2. Lower pressures in the region of the sutropicl high produce relxed ltitudinl SLP grdient in the North Atlntic. In contrst, SLPs re mostly unchnged over the Pcific ocen, gin consistent with the insignificnt correltions oserved in the North Pcific etween snow cover nd SLP. So despite similr forcings for the North Atlntic nd North Pcific, the forcings from incresed snow cover re only significnt in the North Atlntic. In Fig. 9, surfce wind vectors show incresed cyclonic circultion in the region of the Azores high nd slight increse in the nticyclonic circultion ssocited with the Icelndic low. Also, nomlous esterly flow develops cross the North Atlntic. All of the ove-mentioned nomlies, cused y incresed snow cover re similr to oservtions during negtive phses of the NAO nd similr to the nomlous synoptic conditions ssocited with the dominnt EOF of SLP fields.

12 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 45 Fig. 8 Men se level pressure for Decemer, Jnury, Ferury in hp 1000 for () the control simultion () the incresed snow simultion minus the control simultion. Higher pressure is evident over the nomlous snow cover with lower pressure over the North Atlntic etween N cused y chnges in the generl circultion. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. Men 500-hP heights (see Fig. 10) re lower over the midltitudes with two nomly centres, the mjor one centred over the North Atlntic stretching from centrl estern North Americ to western Europe nd the other over centrl nd estern Eursi. This is function of oth the colder tempertures nd the lowered surfce pressures. The lower heights over the North Atlntic re rotropic response to the lower se level pressure in the sme region. However, the lower heights over the continents re roclinic response. So, despite higher se level pressure over the mid-ltitude continentl regions, mid-upper tropospheric heights re lower in response to the colder tmospheric column. Mid-tropospheric heights re slightly higher over the Arctic. The higher heights over the Arctic nd lower heights cross the mid-ltitude North Atlntic nd Asi with incresed snow cover re consistent with oservtionl nlysis. Winds t 200-hP lso indicte tht the incresed snow produces two centres of nomlous cyclonic circultion, one over estern North Americ nd one over western Europe (not shown). The differences in the 200-hP zonl wind (see Fig. 11) show tht incresed snow cover enhnces the mgnitude of the Atlntic zonl jet long the Western Atlntic nd strengthens the southwestern flnk of the jet, therey incresing zonl wind speeds t lower ltitudes reltive to higher ltitudes. In Fig. 11, the upper-level zonl winds re wekened over Hudson By extending to Scndinvi, indicting southwrd shift in momentum. This southwrd shift of momentum in the zonl jet is similr to tht oserved in the westerly phse of the zonl-men wind index (greter positive westerly nomlies re oserved t 35 N reltive to 55 N). Anomlous cooling long the southern hlf of the mid-ltitudes would tend to shift the region of the strongest ltitudinl temperture grdient south. Since the zonl jet overlies the polr front, corresponding southwrd shift in the zonl jet ccompnies the cooling ssocited with the nomlous snow cover. Therefore, during yers with extensive snow cover, noticele shift in momentum from 55 N to 35 N is produced s oserved in the zonl-men wind index. The significnt southwrd shift nd strengthening of the Atlntic jet is not duplicted in the Pcific jet, consistent with other modelling results nd the oservtionl nlysis. Tle 2 lists the 500-hP zonl men wind t 35 N nd 55 N. The difference etween these two vlues constitutes

13 46 / Judh Cohen nd Dr Entekhi Fig. 9 Men surfce wind vectors for Decemer, Jnury, Ferury for () the control simultion () the incresed snow simultion minus the control simultion. Anomlous esterly flow south of Icelnd nd Greenlnd nd nomlous westerly flow centred round 40 N is produced y nomlous low pressure in the North Atlntic N with incresed snow cover. the zonl-men wind index in the model climte. The vlues of this index in the control nd perturtion ensemle experiments re sttisticlly distinct nd consistent with internnul differences in the oserved vlues of this index. The differences in the 500-hP zonl wind show tht incresed snow cover shifts the zonl jet southwrd, incresing zonl wind speeds t lower ltitudes reltive to higher ltitudes. This southwrd shift in the zonl jet is similr to tht oserved in the westerly phse of the zonl-men wind index. Reltive vorticity, presented in Fig. 12, indictes tht on the northern edge of the jet the reltive vorticity is positive or cyclonic, while on the southern edge it is negtive or nticyclonic. The men jet extends from the estern United Sttes to the British Isles. North of the jet, men positive reltive vorticity helps to mintin low pressure in the region while south of the jet, men negtive reltive vorticity helps to mintin the sutropicl high. With more extensive snow cover, southwrd shift in the zonl jet increses cyclonic vorticity in nd from estern North Americ cross the Atlntic into western nd southern Europe. While to the north, incresed snow cover results in nd of nomlous nticyclonic circultion from southern Greenlnd into Scndinvi. An importnt impct of the winter-time perturtion of snow cover is ltering the position nd strength of the storm trcks. There re two common techniques for dignosing storm trcks, one uses SLP nd the other uses the root men squre (RMS) of filtered 500-hP heights. Here we use the filtered 500-hP RMS to illustrte chnges in storm trcks; the SLP sed technique (not shown) shows good greement with tht derived from 500-hP heights. With incresed cyclonic

14 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 47 Fig. 10 Men 500-hP heights for Decemer, Jnury, Ferury in decmetres 560 for () the control simultion () the incresed snow simultion minus the control simultion. Colder tempertures produce lower heights over the nomlous snow cover. Lower heights lso result over the North Atlntic due to lower se level pressures. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. circultion south of the Icelndic low, southwrd shift in the Atlntic jet, nd corresponding southwrd shift in cyclonic reltive vorticity, the storm trcks lso exhiit southwrd shift. Shown in Fig. 13 is the RMS field of the filtered 500- hp heights ( ndpss filter ws used tht retins 2 8 dy fluctutions following the technique of Trenerth, 1991). Similr to oservtion, the men Atlntic storm trck position egins in the northestern United Sttes, continues in northesterly direction cross the North Atlntic ending long the cost of Scndinvi. With incresed snow cover there is no chnge in the entrnce region of the Atlntic storm trcks, however, the mgnitude is incresed while the exit region is shifted south cross western Europe nd the Mediterrnen. The model result of more southwrd storm trck is consistent with the oservtionl nlysis of lower SLPs nd mid-tropospheric heights cross the mid-ltitude North Atlntic from the estern United Sttes into western nd southern Europe. With southwrd shift in the zonl jet, cyclonic vorticity nd the storm trcks, wetter thn norml conditions develop cross southern Europe nd the Mediterrnen nd drier thn norml conditions cross northern Europe (see Fig. 14). This is consistent with the oserved correspondence etween the ltitudinl pressure-sed NAO index nd wether conditions over Europe nd djcent regions (Hurrell, 1995). 4 Discussion Snow cover hs higher ledo thn ny other nturlly occurring surfce condition. As snow cover extends nomlously equtorwrd towrds regions with higher incident solr rdition, its high ledo produces locl cooling. This cooling, in ddition to ltering the climte loclly, my force thermodynmicl nd dynmicl chnges remotely. For this reson we explore snow-climte teleconnections. Previous studies hve shown snow-climte reltionships to e regionl. Here we demonstrte tht the locl forcing of snow cover nomlies cn led to snow-tmosphere teleconnection on lrger, hemispheric scle. The two most importnt results tht seprte our results from previous studies on snow-climte forcings re: 1) the ssocition of snow-climte forcings (more so thn SSTs) with the dominnt mode of vriility for the NH during winter; nd 2) we present oth oserv-

15 48 / Judh Cohen nd Dr Entekhi Fig. 11 Men zonl wind for Decemer, Jnury, Ferury in m s 1 t 200 hp for () the control simultion () the incresed snow simultion minus the control simultion. Anomlous esterly flow south of Icelnd nd Greenlnd nd nomlous westerly flow centred round 40 N re produced y nomlous low pressure in the North Atlntic N with incresed snow cover. The North Atlntic Jet is suppressed southwrd with incresed snow cover. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. TABLE 2. Zonl men wind index, defined s the 500-hP zonl wind t t 55 N minus the zonl wind t 35 N. The men of ech set of six ensemles re shown in m s 1. The confidence level tht the two men estimtes re sttisticlly different is included in prenthesis. Confidence limits re computed using t-test for differences of mens for two smll smples (Johnson, 1994). Model Simultion Wind t 35 N Wind t 55 N Zonl-Men Wind Index control incresed snow 19.0 (>95%) 10.3 (>90%) 8.7 (>95%) tionl nd numericl evidence tht Eursin snow cover nomlies result in dynmicl tmospheric response in the North Atlntic sector more so thn in the North Pcific sector. Oservtionl nlysis shows significnt reltionship etween nomlous snow cover over Eursi nd the dominnt mode of vriility for the NH winter climte. Snow-climte reltionships re ssocited with the dominnt mode of vriility in oth SLP fields nd mid-tropospheric heights; the SLP nd height pttern closely resemle the NAO or AO mode of vriility. Significnt snow-climte reltionships re predominntly locted in the North Atlntic sector nd re reltively sent from the North Pcific sector. In comprison, SST nomlies exhiit significnt reltionships with the North Pcific climte. SST-climte reltionships resemle modes of vriility whose centres of ction re locted in the North Pcific nd djcent lnd msses, i.e., PNA nd WPP. Results from GCM sensitivity experiment to positive nomlous snow cover re consistent with the oservtionl nlysis. Incresed snow cover produces lower SLPs nd

16 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 49 Fig. 12 Men 200-hP height reltive vorticity for Decemer, Jnury, Ferury in s for () the control simultion () the incresed snow simultion minus the control simultion. With southwrd shift in the North Atlntic Jet, reltive vorticity increses etween N nd decreses north of 55 N with incresed snow cover. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. mid-tropospheric heights cross the mid-ltitude North Atlntic with two negtive nomly centres, one over estern North Americ nd the other over western Europe. Incresed snow cover lso results in nomlous cooling long the southern hlf of the mid-ltitudes which would tend to shift the ltitudinl temperture grdient south. Since the zonl jet overlies the polr front, corresponding southwrd shift in the zonl jet ccompnies the cooling ssocited with the nomlous snow cover. Therefore in the zonl-men wind index, noticele shift in momentum from 55 N to 35 N is oserved. All these circultion chnges re consistent with the dominnt mode of vriility for the NH. The oservtionl nlysis nd the modelling experiment re consistent in showing tht positive-nomlous snow cover is ssocited with n equtorwrd expnsion of the polr vortex. Regionlly this results in higher heights over the Arctic nd lower heights over the mid-ltitude North Atlntic nd djcent lnd msses. This response is the mirror rnge (opposite) to tht found y WN98 with decresed snow cover which resulted in lower heights over the Arctic nd higher heights t mid-ltitudes, further corroorting the snow-climte reltionship presented here. How the surfce cooling nomlies propgte oth verticlly nd horizontlly s height nomlies is not dequtely ddressed in this pper. Future oservtionl nlysis nd numericl experiments re eing plnned to nswer this question etter. WN98 hypothesize tht snow cover nomlies interct with zonl ssymetries nd trnsient eddies to produce height chnges oserved in the tmosphere nd in their GCM. CE99, s possile physicl mechnism for snow-climte forcing, hypothesize tht nomlous cooling y incresed fll Eursin snow cover produces strengthened nd more expnsive Sierin high during winter, which forces the height chnges oserved. A strengthened Sierin high is topogrphiclly constrined to expnd north nd west cross the pole. CE99 demonstrte tht fll Eursin positivenomlous snow cover is correlted with strengthened nd more expnsive Sierin high which is hypothesized to force higher tropospheric heights over the Arctic nd lower heights over the North Atlntic during winter. Shindell et l. (1999) rgue tht oserved chnges in the dominnt mode of vriility for the winter NH occurs through chnges in the index of refrction of propgting wves into the upper troposphere

17 50 / Judh Cohen nd Dr Entekhi Fig. 13 Root men squre filtered 500-hP heights vrince for Decemer, Jnury, Ferury in m for () the control simultion () the incresed snow simultion minus the control simultion. With incresed snow cover the storm trck intensifies long the northestern United Sttes nd shifts south cross Europe nd the Mediterrnen. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. nd the lower strtosphere. It is possile tht ltitudinl temperture grdient chnges forced y snow cover led to nomlous potentil vorticity grdients in the strtosphere which lter the wve refrction index. Chnges in the wve refrction index would lter the mnner in which verticlly propgting tropospheric wve energy is sored y the strtosphere nd therefore could chnge the phse nd/or mgnitude of the AO. Future reserch is needed to test these three different hypotheses nd to formulte new ones. 5 Conclusion Until now, the study of sesonl climte forcings hs primrily focused on ocen-tmosphere reltionships nd teleconnections, with ENSO eing the most widely studied. Here we present oservtionl nd modelling evidence which supports the need to incorporte further lnd surfce into dignosing sesonl climte vriility (soil moisture is currently used). Correltions of snow cover nd SLP fields nd 500-hP heights reproduce the dominnt mode of vriility pttern in the NH low-mid troposphere for DJF. This pttern consists of dipole pttern over the Arctic nd mid-ltitude North Atlntic. Furthermore, numericl modelling experiment forced y vrying sesonl snow cover produced tmospheric nomlies similr to oserved tmospheric nomlies on similr timescles. Here we show tht snow cover cn e significnt forcing mechnism of the NH generl circultion nd tht snow cover vriility helps to explin internnul vriility of the NH generl circultion. Therefore, in light of the modelling experiments presented, snow cover nomlies should e considered s potentilly mplifying tmospheric winter circultion nomlies, prticulrly snow cover nomlies on timescles of seson or longer. The exct mechnisms of how locl surfce heting nomlies trnslte to remote dynmicl chnges is still uncler. We reviewed some hypotheses in Section 4 however, no one rgument hs emerged s conclusive. Existing oservtionl evidence hs shown Eursin snow cover to e skillful leding indictor of NH climte vriility (Wtne nd Nitt, 1999), prticulrly in the North Atlntic (CE99). No oservtionl evidence hs emerged yet for SSTs eing skillful predictor for the climte of the North Atlntic. The GCM results presented here, nd those from WN98, lso demonstrte tht

18 The Influence of Snow Cover on Northern Hemisphere Climte Vriility / 51 Fig. 14 Men lrge scle precipittion for Decemer, Jnury, Ferury in mm dy 1 for () the control simultion () the incresed snow simultion minus the control simultion. Incresed snow cover produces drier conditions cross northern Europe nd wetter conditions cross southern Europe. Also included is shding for 90% (light) 95% (drker) nd 99% (drkest) confidence levels for the sttisticl difference etween the two sets of ensemle simultions. numericl experiments with vrying snow cover cn symmetriclly force climte vriility in the North Atlntic region consistent with the oservtionl evidence. Future nlysis nd experiments will e devised to nswer etter snow-climte cuse nd effect s well s possile feedck mechnisms. Acknowledgments This investigtion ws supported y NSF grnt ATM nd NASA grnt NAG-6441 We would lso like to thnk Drs. Dvid Roinson, Mrtin Hoerling nd Jmes Hurrell for providing us with oserved dt. We would lso like to thnk Dr. In Simmonds nd two nonymous journl reviewers for mny helpful comments. References BAMZAI, A.S. nd J.L. KINTER III Climtology nd internnul vriility of Northern Hemisphere snow cover nd snow depth sed on stellite oservtions. Technicl Report 52, Center for Ocen-Lnd-Atmosphere Studies, Wshington, D.C., 48 pp. BARNETT, T.P.; U. SCHLESE, L. DUMENI nd E. ROECKNER The effect of Eursin snow cover on glol climte. Science, 239: ;, nd M. LATIF The effect of Eursin snow cover on regionl nd glol climte vritions. J. Atmos. Sci. 46: BARNSTON, A.G. nd R. LIVEZEY Clssifiction, sesonlity nd persistence of low-frequency tmospheric circultion ptterns. Mon. Wether Rev. 115: BASIST, A.N.M. CHELLIAH Comprison of tropospheric tempertures derived from the NCEP/NCAR renlysis, NCEP opertionl nlysis, nd the microwve sounding unit. Bull. Am. Meteorol. Soc. 78: BOYLE., J.S Evlution of the nnul cycle of precipittion over the United Sttes in GCMs: AMIP simultions. J. Clim., 11: CESS, R.D.; G.L. POTTER, M.-H. ZHANG, J.-P. BLANCHET, S. CHALITA, R. COLMAN, D.A. DAZLICH, A.D. DELGENIO, V. DYMNIKOV, V. GALIN, D. JERRETT, E. KEUP, A.A. LACIS, H. LETREUT, X.-Z. LIANG, J.F. MAHFOUF, B.J. MCAVNEY, V.P. MELESHKO, J.F.B. MITCHELL, J.-J. MORCRETTE, P.M. NORRIS, D.A. RANDALL, L. RIKUS, E. ROECKNER, J.-F. ROYER, U. SCHLESE, D.A. SHENIN, J.M. SLINGO, A.P. SOKOLOV, K.E. TAYLOR, W.M. WASHINGTON, R.T. WETHERALD nd I. YAGAI.

19 52 / Judh Cohen nd Dr Entekhi Interprettion of snow-climte feedck s produced y 17 generl circultion models. Science, 253: CHEN L.T. nd Z.X. YAN A sttisticl nlysis of the influence of nomlous snow cover over Qinghi-Tietn plteu during winter-spring monsoon of erly summer. In: Proc. Conf. on Medium nd Long Term Hydrometeorologicl Prediction in the Bsin of the Yngtzee River, Vol. 1, Hydro Electric Press, Beijing, 246 pp. CLARK, M.P.; M.C. SERREZE nd D.A. ROBINSON Atmosphteric controls on Eursin snow extent. Int. J. Climtol. 19: COHEN, J Snow cover nd climte. Wether, 49: nd D. ENTEKHABI Eursin snow cover vriility nd Northern Hemisphere climte predictility. Geophys. Res. Let. 26: DEL GENIO, A.D., nd M.S. YAO Efficient cumulus prmeteriztion for long-term climte studies: The GISS scheme. In: The Representtion of Cumulus Convection in Numericl Models, K. Emnuel nd D. Rymond (Eds), Boston, Am. Meteorol. Soc. AMS Monogrph Series.Vol. 24, no. 46, pp ;, W. KOVARI nd K.-W. LO A prognostic cloud wter prmeteriztion for glol climte models. J. Clim. 9: DESER, C., nd M.L. BLACKMON On the reltionship etween tropicl nd North Pcific se surfce temperture vritions. J. Clim. 8: DEWEY, K.F Dily mximum nd minimum temperture forecsts nd the influence of snow cover. Mon. Wether Rev. 105: DEY, B. nd O.S.R.U. BHANU KUMAR An pprent reltionship etween Eursin snow cover nd the dvnced period of the Indin summer. J. Appl. Meteorol. 21: DRUYAN, L.M.; K.P. SHAH, K.-W. K. LO, J.A. MORENGO nd G. RUSSELL Impcts of model improvements on GCM sensitivity to SST forcing. Int. J. Climtol. 15: FOSTER, J.; G. LISTON, R. KOSTER, R. ESSERY, H. BEHR, L. DUMENIL, D. VERSEGHY, S. THOMPSON, D. POLLARD nd J. COHEN Snow cover nd snow mss intercomprison of generl circultion models nd remotely sensed dt sets. J. Clim. 9: FREI, A. nd D.A. ROBINSON Evlution of snow extent nd its vriility in the tmospheric model intercomprison project J. Geophys. Res. 103: GATES, W.L.; J.S. BOYLE, C. COVEY, C.G. DEASE, E.M. DOUTRIAUX, R.S. DRACH, M. FIORINO, P.J. GLECKLER, J.J. HNILO, S.M. MARLAIS, T.J. PHILLIPS, G.L. POT- TER, B.D. SANTER, K.R. SPERBER, K.E. TAYLOR nd D.N. WILLIAMS An overview of the results of the Atmospheric Model Intercomprison Project (AMIP I). Bull. Am. Meteorol. Soc. 80: GUTZLER, D. S., nd R.D. ROSEN Internnul vriility of winter-time snow cover cross the Northern Hemisphere. J. Clim. 5: HAHN, D.G., nd J. SHUKLA An pprent reltionship etween Eursin snow cover nd Indin monsoon rinfll. J. Atmos. Sci. 33: HANSEN, J.; G. RUSSELL, D. RIND, P. STONE, A. LACIS, S. LEBEDEFF, R. REUDY nd L. TRAVIS Efficient three dimensionl glol models for climte studies: Models I nd II. Mon. Wether Rev. 111: nd S. LEBEDEFF Glol trends of mesured surfce ir temperture. J. Geophys. Res. 92: ; I. FUNG, A. LACIS, D. RIND, S. LEBEDEFF, R. REUDY, G. RUSSELL nd P. STONE Glol climte chnges s forecst y Goddrd Institute for Spce Studies three-dimensionl model. J. Geophys. Res. 93: HARTKE, G.J. nd D. RIND Improved surfce nd oundry lyer models for the GISS GCM. J. Geophys. Res. 102: HURRELL, J.W Decdl trends in the North Atlntic Oscilltion: Regionl tempertures nd precipittion. Science, 269: IWASAKI, T Yer-to-yer vrition of snow cover re in the Northern Hemisphere. J. Meteorol. Soc. Jpn. 169: JOHNSON, R.A Miller nd Freunds Proility nd Sttistics for Engineers. Prentice Hll, Englewood Cliffs, New Jersey, 630 pp. KALNAY, E.; M. KANAMITSU, R. KISTLER, W. COLLIN, D. DEAVEN, L. GANDIN, M. IREDELL, S. SAHA, G. WHITE, J. WOOLLEN, Y. ZHU, A. LEETMAA, R. REYNOLDS, M. CHELLIAH, W. EBISUZAKI, W. HIGGINS, J. JANOWIAK, K.C. MO, C. ROPELEWSKI, J. WANG, R. JENNE AND D. JOSEPH The NCEP/NCAR 40-Yer renlysis project. Bull. Am. Meteorol. Soc. 77: KLEIN, W.H Ojective specifiction of monthly men surfce tempertures in the United Sttes during the winter seson. Mon. Wether Rev. 111: Spce nd time vritions in specifying monthly men surfce temperture from the 700m height field. Mon. Wether Rev. 113: nd J.E. WALSH A comprison of pointwise screening nd empiricl orthogonl functions in specifying monthly men surfce temperture from 700m dt. Mon. Wether Rev. 111: LAU, K.-M.; J.H. KIM nd Y. SUD Intercomprison of hydrologic processes in AMIP GCMs. Bull. Am. Meteorol. Soc. 77: MANTUA, N. J.; S.R. HARE, Y. ZHANG, J.M. WALLACE nd R.C. FRANCIS A Pcific interdecdl climte oscilltion with impcts on slmon production. Bull. Am. Meteorol. Soc. 78: MATSON, M.; C.F. ROPELEWSKI nd M.S. VARNADORE An tls of stellite derived Northern Hemispheric snow cover frequency. Technicl report, U.S. Deprtment of Commerce, Ntionl Ocenic nd Atmospheric Administrtion, Wshington, D.C., 75 pp. NAMIAS, J Snowfll over the estern United Sttes: Fctors leding to its monthly nd sesonl vritions. Wetherwise, 13: Influences of norml het sources nd sinks on tmospheric ehvior. In: Proc. Int. Symp. on Numericl Wether Prediction, Tokyo, 1960, Meteorol. Soc. Jpn, pp Some empiricl evidence for the influence of snow cover on temperture nd precipittion. Mon. Wether Rev. 113: PITTALWALA, I. nd S. HAMEED Simultion of the North Atlntic Oscilltion in generl circultion model. Geophys. Res. Let. 18: RANDALL, D.A.; R.D. CESS, J.P. BLANCHET, S. CHALITA, R. COLMAN, D.A. DAZLICH, A.D. DELGENIO, E. KEUP, A. LACIS, H. LETREUT, X.-Z. LIANG, B.J. MCAVANEY, J.F. MAHFOUF, V.P. MELESHKO, J.-J. MORCRETTE, P.M. NORRIS, G.L. POTTER, L. RIKUS, E. ROECKNER, J.F. ROYER, U. SCHLESE, D.A. SHEININ, A.P. SOKOLOV, K.E. TAYLOR, R.T. WETHERALD, I. YAGAI nd M.-H. ZHANG Anlysis of snow feedcks in 14 generl circultion models. J. Geophys. Res. 99: REYNOLDS, R.W. nd T.M. SMITH Improved glol se surfce temperture nlysis using optimum interpoltion. J. Clim. 7: nd A high resolution glol se surfce temperture climtology. J. Clim. 8: ROBINSON, D.A.; F. DEWEY nd R. HEIM JR Northern Hemispheric snow cover: An updte. Bull. Am. Meteorol. Soc. 74: ROBINSON, D.R Evluting snow cover over Northern Hemisphere lnds using stellite nd in situ oservtions. In: Proc. 53rd Estern Snow Conference, Willimsurg, Virgini, Am. Meteorol. Soc. ROGERS, J.C Ptterns of low-frequency monthly se level pressure vriility ( ) nd ssocited wve cyclone frequencies. J. Clim. 3: ROSENZWEIG, C. nd F. ABRAMOPOULOS Lnd-surfce model development for the GISS GCM. J. Clim. 10: SERREZE, M.C.; F. CARSE, R.G. BARRY nd J.C. ROGERS Icelndic Low cyclone ctivity: Climtologicl fetures, linkges with the NAO, nd reltionships with recent chnges in the Northern Hemispheric circultion. J. Clim. 10: SHINDELL, D.T.; R.L. MILLER, G. SCHMIDT nd L. PANDOLFO Simultion of recent northern hemisphere climte trends y greenhouse gs forcing. Nture, 398: THOMPSON, D.W.J. nd J.M. WALLACE The Arctic Oscilltion signture in the wintertime geopotentil height nd temperture fields. Geophys. Res. Let. 25: TING, M.; M.P. HOERLING, T. XU nd A. KUMAR Northern Hemisphere teleconnection ptterns during extreme phses of the zonl-men circultion. J. Clim. 9: TRENBERTH, K.E Storm trcks in the Southern Hemisphere. J. Atmos Sci. 48: VERNEKAR, A.D.; J. ZHOU nd J. SHUKLA The effect of Eursin snow cover on the Indin monsoon. J. Clim., 8: WAGNER, A.J The influence of verge snow depth on monthly men

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