Meteorologische Modellierung

Transcription

1 Morologsch Modllrg Irodco o Nmrcl Modlg of h Globl mosphrc Crclo Fr L Ol 0. Irodco: Whr/wh s h problm d bscs. h lr volo dcy qo dscrzo m. O-dmsol lr dvco dscrzo m d spc. O-dmsol lr dffso d o-dmsol lr rspor qo 4. Nolr dvco d d olr rspor qo Brgrs-qo 5. Mor dmsos grds 6. Dsg of mosphrc grl crclo modl GCM 7. mpl: qg broropc chl whr prdco smsr Fr L

2 Rfrcs D. R. Drr: Nmrcl Mhods for Wv Eqos Gophyscl Fld Dymc Sprgr 999 ISBN: G.J. Holr & R.. Wllms: Nmrcl Prdco d Dymc Morology Scod Edo Joh Wly & Sos 980 ISBN: D. Rdll: Irodco o mosphrc Modlg hp://w.mos.colos.d/grop/dv/604.hml Fr L Irodco o Nmrcl Modlg 0. Irodco: h Problm d Bscs Fr L

3 h Problm Nolr qs-lr copld prl dffrl qos who ow lyc solo Empl: wo dmsol flow P v fv F v.. y v v v P v f Fy v... y y v v y y v F v... y Eq. of moo Eq. of moo Coy q. Frs lw of hrmodymcs P R P0 P R c p Fr L Eq. of s Po. mprr h Problm h Problm Empl: Frs lw -d p=cos. F... locl chg wh m dvco dffso ohr forcg frs drvv m frs drvv spc Scod drvv spc? Fr L

4 { Nmrcl Solo of Prl Dffrl Eqos From hory h qos o h mrcs: coos fcos -> dscr vls b dffrl grl qos -> lgbrc qos ss: choc of h dscrzo b clclo rprso of h drvvs pprochs lgorhms: - grd po mhods f dffrcs - srs pso spcrl mhod d f lms Evlo of mhod: - cosscy ccrcy covrgc d sbly Fr L Empl: h Empl: Grd Po Mhod h Grd Po Mhod coos fco -> dscr vls s s = y z s s s - s s + s s dfs h rsolo Fr L 4

5 { Empl: h Grd Po Mhod s s = y z s s b drvvs -> f dffrcs.g. from ylor-pso d s s s s s... ds from from d ds d ds from d s s s s s... ds s s s s d ds s s... s s... s... Fr L Forwrd dffrcs Bcwrd dffrcs Crl dffrcs s - s s + s Empl: Srs Epso -h Spcrl Mhod s * s * s s + s * s s = y z s * dffrbl orhogol Bss- fcos Forr-srs; Lgdr Polyomls. h rsolo s gv by h mbr of mods d drvvs -> lycl drvvs of h bss-fcos ds Fr L d ds * s 5

6 Empl: Srs Epso F Elms mpl F s s s s = y z s=f s+bf s+. F F rbrry fco whch s oly loclly o zro Drvvs -> dpdg o h fco Fr L s F s s F s s Evlo: Cosscy h dscrzo ms covrg o h dffrl: lm s0 s d ds Empl: forwrd dffrc: Cosscy from ylor-pso: s s s s s d d s s s s s... ds ds s s s d d s... s ds ds s s s d d lm lm s s s 0 0 ds ds Fr L s... d ds 6

7 Evlo: ccrcy ccrcy: Smlls powr of s h dvo from h rh : ccrcy ordr of ccrcy of h dscrzo Empl: forwrd dffrcs ylor-pso s s s s s => forwrd dffrcs r of frs ordr ccrcy d d s s s s s... ds ds s s s d d s... s ds ds d O s s ds b mosly: ccrcy ordr of ccrcy of h schm Cosdrg h whol qo.. cldg h rgh hd sd s.g. Sco Evolo dcy qo Fr L Evlo: Covrgc Covrgc: Covrgc of h rror o 0 for smll s: lm s0 0 Error: Dvo of h mrcl solo from h rh lycl solo; Error msr Norm Empls Ecld qdrc Norm: b Mmm Norm: N / m N Fr L 7

8 Evlo: Sbly mos mpor for prccl s Sbly: schm s sbl f h dffrc bw h mrcl d h lycl solo s bodd: C or: schm s sbl f h mrcl d h lycl solos dvrg wh m: If s bodd: Sbly my dpd o s C Sbly lyss: vros mhods.g.: Drc hrsc Ergy Mhod d Vo Nm Mhod s dvco qo sbl sbl Irrlo L Eqvlc horm: For coss schm sbly s cssry d sffc codo for covrgc. Fr L 0. Irodco: h Problm d Bscs 0. Irodco: h Problm d Bscs Smmry: Rso o do mrcs: No lyc solo of h problm Mhods: Grd po mhod spcrl mhod f lms F Dffrcs: forwrd bcwrd crl Evlo: cosscy ccrcy covrgc d sbly Fr L 8

9 Irodco o Nmrcl Modlg. h Lr Evolo Dcy Eqo Dscrzo m Fr L h Lr Evolo Dcy Eqo qo: F o: wh mgry.. =b d compl = R + I oscllo qo rsls:.g. rl oscllo: v fv f wh v f sc R ; Im Fr L 9

10 { qo: lycl Solo F solo: p F Dscrbs h pol dcy of l prrbo = 0 -F/ 0 =l vl o h sory solo F/. m scl: / l vl problm 0 dd; q. s frs ordr m mpl: 0 =0 F= =0.05 Fr L Nmrcl Solo F Dscrzo m: -> 0 + : msp; : gr coos dscr msp ms b chos dqly physclly mgfl! Fr L 0

11 { { Nmrcl Solo F + - b Drvvs -> f Dffrcs Bcwrd dffrcs - + Impropr sc ow d + dd Forwrd dffrcs wo lvl schm Eschr-Vrfhr Crd dffrcs hr lvl schm Zwschr-Vrfhr Fr L Nmrcl Solo F c dlg wh h rgh hd sd h g grl: qo f ; dscrzo wo lvl f Choc of f: f Eplc Elr f Implc fl fl Sm-mplc f l =olr pr; f l =lr pr Fr L

12 Eplc Elr Dscrzo: f f g grd.. compd from volo dcy qo: F Fr L Dscrzo: Implc f f g grd +.. compd from + b sd r-rrgm of h qo s cssry o ob +! volo dcy qo: F F Fr L

13 wo Lvl Schm: Eplc Elr F F lm 0 Cosscy?... lm lm Ys from ylor-pso: ccrcy ordr of h dscrzo: frs ordr Error gos wh Fr L wo Lvl Schm: Eplc Elr F F ccrcy ordr of h schm? Err sz: sr h lyc solo ylor-pso:! Isr h ylorpso:! Err! Err => Err= O hr wh F=0 Sc Fr L

14 wo Lvl Schm: Eplc Elr Sbly F=0 lyclly: F F? p 0 p 0 mrclly: 0 0 => mpld crss/dmshs wh fcor => for sbl for b for +/- mps => choc of sch h /! bodd sbl Covrgc lm 0? Ys from L qvlc horm 0 No: Fr L p O wo Lvl Schm: Implc F F Cosscy? ys l plc ccrcy Ordr? Frs ordr schm.. rror grows wh Sbly? wh F=0: => mpld dmshs wh fcor => C For ll sc < => mplc lwys sbl b >/ o ppropr o h problm! Covrgc? Ys Fr L 4

15 5 wo Lvl Schm: Cr-Ncolso Cosscy? ccrcy Ordr? F g g ys l plc d mplc g = : plc; g = 0 : mplc Err g g ] [ Isr lycl solo: ylor-pso:! Isr ylor-pso: ]! [! g g Err! g Err => for g= 0. m.: Err= O; for g=0.5: Err=O wh F=0 =0 for = d g=0.5 } Fr L wo Lvl Schm: Cr-Ncolso F g g Sbly? wh F=0: g g g g For ll < domor > mror b: >/ o ppropr o h problm => mpld chgs wh fcor g g => => lwys sbl for g < g g => Covrgc C Fr L

16 6 Fr L wo Lvl Schm: 4h ordr Rg- 4 6 f d d Grl qo: Rg- 4h ordr: wh 4 f f f f Dcy qo: o o plcly dpd f F f Ordr: Err=O 4 Sbly: Sbl for Fr L wo lvl schm: 4h ordr Rg f f f f Id: vrg of gs for dffr + / + / / + / + f= / f+ /= / f+ /= / f+ = 4 / wh rfcl bs pos + Epsv sc f ds o b compd 4 ms

17 hr Lvl Schms Grl: hr lvl schms do o oly cosdr m d + b lso m -..g. From ylor-pso: d d d d d d 6 d d d d d d 6 d d... d d => Dscrzo s coss d Ordr Err=O Dcy qo: F Lp frog Fr L Lp Frog F F.. vlo of h grd for sp - -> + chroology: Sp : Δ - d/d = F - + Sp +: Δ - - d/d = F - + wo m lvls r dd - d! Fr L 7

18 8 Fr L Lp Frog F F Sbly Compol Mod? 0: wh F ssmpo: chgs ch m sp by fcor λ.. wo solos: / For ->0 : λ = physcl sc corrc; λ =- physcl For > 0: physcl mod 0 < λ < o compol Mod λ < -.. oscllg sbly! Lp Frog o sd for dmpd dsspv sysms! Lp Frog: Usbl Compol Mod Lp-Frog lzo 0 =0 ; <0 = = 0 - = 0- > 0 = = - = = +4 < =4 4 = - > 4 Fr L

19 hr Lvl Schm: dms-bshforh F grd by vrgg grd from d grd from rpold + =+-- coss d d ordr Err=O sbly compol mod? wh F 0:.. wo solos: / 4 for ->0 : λ = physcl corrc solo; λ =0 physcl for > 0: physcl mod 0 < λ < dmpd compol mod 0 Fr < λ < L dmpd => sbly! h Lr Evolo Dcy Eqo. h Dcy Eqo: Dscrzo m Smmry: Dcy lr volo qo: frs ordr m l vl Schms: mplc plc sm-mplc wo-lvl hr-lvl Spcfc schms: Elr Cr-Ncolso Rg- Lpfrog dms-bshford Compol mod Lpfrog sbl for dsspv sysms! Fr L 9

20 Irodco o Nmrcl Modlg. O-Dmsol Lr dvco Dscrzo m d Spc Fr L h Lr -d dvco Eqo qo: =cos. hyprbolc frs ordr m d spc: l d bodry codos dd b c d f 0 hyprbolc: b -4c > 0 prbolc: b -4c = 0 llpc: b -4c < 0 lycl solo: f wh y fco f mpl: p Fr L Sprposo of wvs wh wv mbr d phs vlocy 0

21 Nmrcl Solo: Spcrl Mhod Id: rsformo of o w bss fcos whch r dffrbl orhogol fcos of => drvos spc c b clcld lyclly. Empl: Forr-srs N p N = m dpd compl Forr coff.; N = cosdrd mods rsolo N<< => mgh o b prfcly rprsd Isr o dvco qo: => N N p N N p => N+ copld ordry dffrl qos Fr L Spcrl Mhod Smlr o h volo dcy qo b wh mgry = d compl oscllo qo lycl solo: p 0 => compl solo of h dvco q: 0 p s pcd => locl: oscllo globl: o dsprsv wvs wh phs vlocy Fr L

22 Spcrl Mhod: Eplc slowr d -dpd Fr.. L mrcl dsprso Nmrcl solo: log o volo dcy q. b: dffr chrcrscs mpl: plc Elr Sbly? p wh o wv oly d omd d rc mpldcrss wh lwys sbl N b Phs rror sc lycl ly Spcrl Mhod: Implc mpl: mplc Sbly? p wh d rc mplddcrss b Phs rror N sc lycl ly slowr d -dpd Fr L.. mrcl dsprso lwys sbl b -dpd dmpg.. mrcl dffso

23 Spcrl Mhod: Lp Frog Lp frog: Rcll: chroology: d/d=- Sp : Δ - + d/d=- Sp +: Δ Fr L Lp frog: Sbly? Spcrl Mhod: Lp Frog wh 0 wosolos physcl d 'compol' - mod b wh compol - mod80 o of phs boh mods rl c phsrror : rc fsr 6 Lpfrog ppropr b mrcl dsprso; compol mod bohrs Fr L

24 Lp Frog: Compol Mod qo: wh =0 dvco of h zol m 0 Lpfrog b mpld chg l codo: =0= problm: Δ dd b ow mos css compd wh Elr. l Δ= 0 +E E=smll rror compl solo : 0 E physclmod : 0 E b compol mod - : 0 v Δ corrc E h compol mod s drmd by h lzo rror E oly Fr L E Lp Frog: Robr-ssl Flr Modfco of h lp frog schm: Compo of or -Δ by wghd vrgs of +Δ d -Δ Clclo rol:... * * * * f * ; flr cos. sp d/d = f Δ *- + * sp + Δ d/d = f *- + * Fr L 4

25 5 Fr L Lp Frog wh Robr-ssl Flr b * * * Sbly? * * + from sr o b pls rrrg: * * old Mr-formlo: w rso-mr X X Egvl problm 0 Egvls λ from / / => For <- γ h schm s lwys sbl! For ->0 : λ = physcl rl; λ = γ- compol dmpd For > 0 : λ < λ <.. boh mods dmpd srogr for compol Dmpg dpd lrgr srogr dmp.: Nmrcl dffso Nmrcl dsprso dpd phs rror Grd Po Mhod: F Dffrcs Dscrzo spc d m.. spc d m drvvs r ppromd by dffrcs. wo lvl schms plc: crd dffrcs dowsrm >0 psrm >0 = m; = spc Fr L

26 6 F Dffrcs wo lvl schm Eschr-Vrfhr: ccrcy d ordr!!!!!!!!! O O Err Err Err Err crd dffrcs: d ordr Δ s ordr Δ Fr L!!!! O O Err Err Err!!!! O O Err Err Err F Dffrcs wo lvl schm: ccrcy d ordr b Dowsm: c Upsm: s ordr Δ d Δ s ordr Δ d Δ Fr L

27 7 F Dffrcs: Sbly wo lvl schm: Sbly crd dffrcs:. Ergy Mhod grl: sclr qdrc orm for h ol rgy E h spc s of h sysm d show h E rms bodd wh m. E Hr: sqr d sm p: cyclc bodry codos: Schwrz sch qly: => sbl dvg: pplcbl lso for o lr problms. Dsdvg: dfo of E dd Fr L Fr L F Dffrcs: Sbly wo lvl schm: Sbly crd dffrcs:. Vo Nm Mhod Grl: Lrz h problm. Rplc dpdc spc by Forr pso lycl. Ivsg h mplfco fcor of o m sp + =. h schm s sbl f. Hr: lrdy lr Forr-pso: Isr o : dvg: Rlvly sy. Dsdvg: Lrzo lr -> oly o o cosdr s s s rc wh Nmrcl solo :. mplfco fcor > => sbl =>. Phs rror sc =lycl solo

28 F Dffrcs: Sbly wo lvl schm: Sbly lyss b Dowsrm: Vo Nm mhod Isr o : wh Nmrcl solo : ; vsg + = cos s cos s rc cos =>. mplfco fcor > => sbl. Phs rror sc =lycl solo Fr L F Dffrcs: Sbly wo lvl schm: Sbly lyss c Upsrm: Vo Nm mhod Isr o : wh cos ; vsg => Upsrm sbl for 0 Cor-Frdrch-Lvy crro = Cor-mbr Fr L + = cos s s rc cos Sbl for cos sc cos

29 9 Fr L F Dffrcs: Upsrm O lvl schm: Upsrm cos cos s rc wh Nmrcl solo o wv : wh > 0 - < => Nmrcl dffso for μ<; srogr dmpg for lrgr ; OμΔ - Phs rror -dpd => Nmrcl dsprso slowr; OΔ For smll Δ:... cos cos s rc Error Fr L F Dffrcs: Lp Frog hr lvl schm: Lpfrog Sbly: s Sbl rl; = for / Cor-Frdrch-Lvy crro Phs rror => Nmrcl dsprso Compol Mod - => Robr-ssl Flr... 6 s s rc d s s for wh Vo Nm mhod + = ; vsg + = physcl mod

30 Sm- Lgrg Mhod Id: Drg dvco h propry hr of prcl/volm rms cos: d 0 d => Nw dsrbo from prcl r-dsrbo by dvco Eplc: Nw prcl posos from vlocs Implc: Old prcl posos from vlocs ypclly fd grd => rpolo Sm-Lgrg =>dffso + = Fr L O-Dmsol Lr dvco Smmry Nmrcl mhods: Spcrl f dffrcs d sm-lgrg Sbly lyss: Ergy mhod Vo Nm mhod Nmrcl dffso: mpld dmpg wv mbr dpd Nmrcl dsprso: Error phs vlocy wv mbr dpd Impor prmr: Cor-mbr / Cor-Frdrch-Lvy crro Fr L 0

31 Irodco o Nmrcl Modlg. O-Dmsol Lr Dffso d O-Dmsol Lr rspor Eqo Fr L h Lr Dffso Eqo H Eqo qo o dmsol: prbolc frs ordr m scod ordr spc =cos.= Dffso coff. Il d bodry vls dd lyc solo: dmpd wv wv mbr : 0 p p Epol dcy of h mpld dpd o h shorr h fsr Fr L

32 Nmrcl Solo: Spcrl Mhod N N p s Forr-srs: p p N N N N Isr => => N copld ordry dffrl qos Nmrcl solo smlr o dcy qo Fr L Fr L Grd Po Mhod: F Dffrcs Dscrzo for scod drvv spc: from dscrzo of O b from ylor pso

33 F Dffrcs Possbl dscrzos wo lvl schms Eplc forwrd m crd spc; FCS: b Implc: c Cr-Ncolso: g g wh No: Lp frog s sbl Fr L Fr L F Dffrcs Forwrd m Crd Spc; FCS!!! O Err Err Err s 4 cos => sbl for 4 For smll Δ: 4 lycl:... p ccrcy/ordr: Sbly: Vo Nm mhod + = d covrgc

34 h Lr rspor Eqo dvco d Dffso qo o dmsol: d ordr prbolc lycl solo: dmpd rvlg wv 0 p p Fr L F Dffrcs Prvos owldg: FCS mpropr for dvco; Lp frog mpropr for dffso => md schm: Lp frog für dvo FCS für Dffso Mor grl: m splg mhod: Prog of dcs d dffr mrcl rms Clm modls ECHM PlSm: dbc pr lp frog d dbc prs Elr or mpl. Fr L 4

35 5 Fr L F Dffrcs m splg Lp frog d FCS.. sbl for or Sbly Vo Nm mhod + = d s cos 4 s cos 4 s +=physcl... cos 4 / wh.. lycl s cos 4 s rc dpd o -d Lr Dffso d -d Lr rspor Eqo Smmry Dffso qo h qo Spcrl: l dcy qo Grd po: FCS b rspor qo m spg mhod Fr L

36 Irodco o Nmrcl Modlg 4. Nolr dvco d -d Nolr rspor Eqo Brgrs Eqo Fr L h Nolr dvco Eqo Ivscd Brgrs Eqo d qo o dmsol: 0 0 d Solo: f wh y fco f L lr dvco b f dpds o slf mplc qo Solvbl for prccl s fw spcl css oly..g. Plzm 964 lls: Il codo: 0 s Solo: ~ s s wh I ~ s I = frs d Bssl fco forml gomrcl solo c b cosrcd by sg h mhod of chrcrscs Fr L 6

37 h Mhod of Chrcrscs Lgrg prspcv: dscssg h phs of dvdl prcls pos phs = chrcrscs d from 0 => vlocy of dvdl prcl s cos m d => prcls r movg o srgh ls: => chrcrscs r srgh ls wh slop 0 =0 0 0 d 0 d 0 f 0 =0 vrs spc: chrcrscs cross cr m c => dscos shoc wvs r formd => b fr c o prcl c hv mor h o loco physcl! => physcl solos oly possbl p o = c Fr L Chrcrscs of Plzms Solo = = = =0 lyc solo chrcrscs fr: Plzm G.W. 964: c grl of compl spcrl qos for sdy o-dmsol flow. lls Fr L 7

38 h Nolr dvco Eqo h olr rm: Empl: s L S-srs wvs wh m dpd mplds 0 No lr rm fr srg s-srs: s => Ergy/momm s rdsrbd wh h wv spcrm Fr L s cos s[ cos ] s[ ] h o lr wv-wv rco of h wvs d forcs wvs wh wv mbr + d -. Grd Po Mhod: lsg Problm: Wh f mbr of grd pos.g. 0-M wvs wh wv mbrs > M/ g rroosly rprd s M- Empl: M=4; = => fls wv wh = = 0 4 Fr L 8

39 lsg: Cosqc for Ergy Empl: l 0 0 s 0 cos =>. Ergy: E0 s d Ergy chg: E d d d wh 0 s cos 0 s E B Wh rsolo M= s ls g s s d 0 => lyclly h ol rgy s cosrvd E s 0 => Ergy crs d o lsg from lmd rsolo Fr L 0 0 s s d Nolr Isbly ch m lvl shor wvs + my b forcd whch polly r o rsolvd d hrfor rroosly rprd. hs lds o rlsc crs of wv mplds.. rgy prclr h shor wv pr of h spcrm d flly o blow p of h mrcl solo. hs mchsm s prcpl dpd of h m sp lgh or h grd sz. Nolr sbly Fr L 9

40 40 Solos rfcl lmo of shor wvs Dffsv schms.g. psrm Eplc dffso ppropr dscrzo of o lr rms Nolr Isbly Fr L Fr L lyclly:.. ol rgy ~ s cosrvd d 0 If hs wold lso b h cs mrclly => o o lr sbly Solo: Dscrzo of h o lr rm s ry: 0 d d E 0 mpl: Pos cyclc bodry codos: No ppropr Dscrzo of h Nolr rm

41 4 E d ry: B: Sll rsfr of rgy o wrog wvs physcl 0 6 mpl: pos cyclc bodry codos ppropr E rd ry: ppropr Dscrzo of h Nolr rm Fr L 6 opos wo lvl Elr: 6 hr lvl Lp frog: Co: slghly sbl d o -dscrzo b lr sbly my occr => md h CFL crro F Dffrcs Fr L

42 0 sz: rsformo of o w bss fcos whch r dffrbl N orhogol fcos of.g. Forr-srs: p => lf hd sd: => rgh hd sd: Spcrl Mhod N N N N p p F p wh = + d F l l L ll l p p N L =m-n-n; L =mn+n.. L =-N L =N for 0 d L =-N L =+N for < 0 Fr L Sc corbos o wvmbrs -N o N r obd rco coffcs Spcrl Mhod N N N N p F p wh F l l L ll l L =m-n-n; L =mn+n wh N N F p N N F p rsolvd wvs N N F p rsolvd wvs Nglcg h rsolvd wvs lds o N copld ordry dffrl qos ODE s: L F ll l l l L =m-n-n; L =mn+n -N N o b solvd sg commo mhods C off: o lsg b o cosrvg moms hghr h Fr L 4

43 4 Fr L spcrl mhod vrss f dffrcs: spcrl: c spl drvvs b mrcl ffor gos wh N f dffrcs: mrcl ffor gos wh N b spl drvvs o c Improvm by combo: h spcrl rsform mhod Id: comp drvvs d lr rms spcrl spc d o lr rm o corrspodg grd N+ grd pos o vod lsg. h ffor gos wh N ln sg fs forr rsform ff. No lr dvco: Sp : rsform o grd po dom vrs Forr rsformo v ff Sp : comp o grd pos Sp : rsform o spcrl spc v ff Sp 4: comp h -drvv of spcrl spc d do h m sppg Sp :. 0 0 h Spcrl rsform Mhod Fr L h Vscd Brgrs Eqo: dvco d Dffso qo o dmso: Vros pplcos o dscrb procsss scc d chology smpl wy.g. rod rffc d mpor s bd for mrcl schms. Nmrcl Solo: Spcrl or f dffrcs wh h ow schms. I mos css by sg m splg sprg dvco d dffso forml lyc solo sg Col-Hopf rsformo: z z z l l l l z z z z z d G d G ; p ; p => d G ; 0 0 Lr h qo

44 Nmrcl Solo of Brgrs Eqo sg dffr Fr L Nolr dvco d -d Nolr rspor Eqo Brgrs Eqo Smmry Vscd d vscd Brgrs qo lsg No lr sbly Ergy cosrvg dscrzo Spcrl rsform mhod Fr L 44

45 Irodco o Nmrcl Modlg 5. Mor Dmsos Grds Fr L hr Dmsos wh Sclr d Vcor Flds Problm: o oly o dmso d vrbl b hr yz dmsos d vros copld vrbls sclrs d vcors. ypclly: Sclrs mprr hgh vorcy dvrgc c. d d flow vw Nmrcs: Grd po modls: dscrzo sg sggrd grds.g. sclrs shfd comprd o vcors. Sm- Spcrl modls: o lr rms d prmrzos o corrspodg Gss grds wh sggrg h vrcl. Fr L 45

46 Grds Horzol: clsscl grds ccordg o rw =sclr v=flow v v v v v v v Fr L v E = wo shfd C-grds Grds Vrcl: sggrd z w v w v w w vrclly sggrd o ll ohr vrbls v horzolly or or v grd pos Fr L 46

47 47 Fr L Grds Globl grds clsscl : lo-l grd Nw: Icoshdro - v v Sggrd grd: Dscrzo sg ppropr vrgg: z w + w Empl: dvco -drco o C-grd: Vrcl dvco: z w z w z w or br z w w z w or Grds: Dscrzos Fr L

48 Mor Dmsos Grds Smmry Grds fr rw BCDE Sggrd grd Lo-l- d coshdrl-grds Fr L Irodco o Nmrcl Modlg 6. Dsg of mosphrc Grl Crclo Modl GCM Fr L 48

49 mosphrc Grl Crclo Modl GCM Procsss: dbc: mos mosphrc fld dymcs Dbc: forcg sorcs d dsspo ss Vrbls: progosc dymc vrbls ECHM bodry codos prlly progosc Rprso qos: dbc: rsolvd scls; bsd o fdml lws ppromd;.g. prmv q. Dbc: rsolvd scls; prmrrzd.. ld o h progosc vrbls rsolvd scls Fr L mosphrc Grl Crclo Modl GCM Nmrcs Rprso d dscrzo: Horzol: spcrl rsform mhod Lgdr polyomls or grd po f dff.; sm-lgrg rcr rspor q Vrcl: m: Rsolo: sggrd grd z- p- σ- d/or θ-sysm mosly md: p op d σ grod m splg mhod; dbc: mosly lpfrog wh ssl flr; smmplc dvrgc q.; dbc: plc or mplc.g. dffso Horzol: bo 0-500m Vrcl: bo 0-00 lvls; 0-0/00m m: som ms Fr L 49

50 mosphrc Grl Crclo Modl GCM Nmrcs Ip: Il flds or rsr fls d bodry codos Op: Progosc vrbls ddcd prmrs hsory rsr fls Wor flow: Ilzo: rd bodry codos z 0 lbdo SS c c. S l codos.g. orml mod lzo for NWP sr d for clm or rd hsory rsr fls m sppg: pd bodry codos.g. rdo SS b comp dbc d dbc dcs c pd progosc vrbls d wr op rmo: wr hsory rsr fls for coo Fr L Dsg of mosphrc Grl Crclo Modl GCM Smmry m splg mhod dbc/dbc Rsolvd d rsolvd procsss -> prmrzos Progosc d dgosc vrbls Bodry l codos Fr L 50