RSM 51-HOURS FORECAST. Fig Schematic illustration of the 4D-Var 6hour cycle design.

Transcription

1 3.6 Reginl nlysis 3.6. Intductin In June 3, JA hs ls implemented the 4-Dimensinl Vitinl dt ssimiltin (4D-V system f the Reginl Spectl del (RS insted f the 3-Dimensinl Optiml Intepltin (3D-OI system with physicl initiliztin f ssimilting Rd-Ringuge Anlyzed Pecipittin dt. suppt sht-tem fecst up t dys, RS mkes fecsts ve Est Asi e with km hizntl eslutin nd 4 veticl levels up t hp nd ls pvide the ltel undy cnditin f S. he 4D-V system f RS hs 6-hu ssimiltin windw, i.e., ± 3 hus t 4 initil times (, 6,, nd 8. Assimilted dt e SYNOP, EP, PIO, Wind Pfile, SHIP, BOY, Aicft, AW, SAE, AOVS nd Rd-Ringuge Anlyzed Pecipittin. he design f the 4D-V cycle is illustted in Fig OBS -OBS -OBS -OBS -OBS -OBS -OBS R-A dt R-A dt R-A dt R-A dt R-A dt R-A dt :get nlysis -OBS :nventinl sevtin dt (time R-A :Rd-Ringuge Anlyzed Pecipittin INNER OOP 6-HOR ASSIIAION WINDOW (ne-hu pecipittin munt OER OOP 3-HOR FOREAS RS 5-HORS FOREAS Fig Schemtic illusttin f the 4D-V 6hu cycle design Bsic fmultin 4D-V seeks the mdel tecty in phse spce tht minimises the diffeence etween mdel nd sevtins in n ssimiltin windw. he diffeence is mesued y cst functin. he cst functin is given y J ( x = ( x x B ( x x + ( H ( x y O ( H ( x y + J c (3.6. whee the supescipt indictes the tnspse f vects mtices, dentes the fist guess f the mdel stte viles t the eginning f the ssimiltin windw nd the ltel undy cnditin in the ssimiltin windw, the clumn vect cnsisting f sevtinl dt ville in the ssimiltin windw. is the clumn vect cnsisting f mdel stte viles t ll time levels in the ssimiltin windw, which is detemined y the mdel, the initil cnditin nd ltel undy cnditin. x x x y x x x = x N = ( x (

2 whee{ x } is the clumn vect cnsisting f the mdel stte viles t time level i, nd ( is the pedictin i equtin f the mdel s functin f initil cnditin nd ltel undy cnditin. he ttl nume f the time levels in the ssimiltin windw is N+. seved viles nd intepltes fm mdel gid pints t sevtin pints. H ( is the sevtin pet tht cnvets mdel stte viles t nd O e the e cvince mtices f x nd y clled the ckgund e cvince mtices nd the sevtin e cvince mtix, espectively, nd J c is the penlty tem f suppessing gvity wve nise. he vlue f the cst functin is clculted y fwd integtin f the mdel. he penlty tem is given s B J c D = t D t (3.6.3 whee dentes the penlty pmete, ( D t the clumn vect cnsisting f the petutin f the time tendency f the hizntl divegence t ll mdel gid pints nd ll time levels. he time tendency is ppximted y tw-time level finite diffeence scheme. inimiztin f the cst functin using smth ptimiztin lgithm equies the gdient f the cst functin with espect t the initil cnditin nd the undy cnditin x. It is witten s fllws. H D D ( [ ( ] + x J = B x x + O H x y (3.6.4 x x x t t he tnspse f the Jcin mtices f the mdel, ( x, e the ppgt mtices f the dint mdel. he sic stte t ech time level, which is necessy f the ckwd integtin f the dint mdel, is pvided y fwd integtin f the iginl mdel Eqs. ( Bckgund e cvince ( ntl vile RS is hydsttic spectl mdel with sigm-pessue hyid veticl cdinte. he pedicted viles e wind, vitul tempetue, sufce pessue nd specific humidity in spectl spce. he cntl viles f the 4D-V system e unlnced wind ( u, v, vitul tempetue, sufce pessue p, nd specific humidity q in gid spce t the eginning f the ssimiltin windw, nd the undy cnditins f them t the eginning nd end f the ssimiltin windw. he unlnced wind is clculted y sutcting wind cmpnent explined y pessue gdient fce fm the full wind s fllws. v s u v u = v xx yx xy yy u v g g (

3 whee ( u,v g g dente the gestphic wind nd { } viles { u, v, (, p q v s, } e uncelted with ech the. e egessin cefficients. It is ssumed tht the cntl i ( Veticl celtin he cntl viles nmlized y thei ckgund e stndd devitins e expnded in the eigenvects f the ckgund e veticl celtin mtices tht e ssumed t e hmgeneus in the hizntl diectin: x x K σ ~ x = σ ~ K x K (3.6.6 whee xk dentes ne f the cntl viles t gid pint t the k -th level, σ k the ckgund e stndd devitin f xk, the thgnl mtix cnsisting f the eigenvects, ~ xk the k -th expnsin cefficient, nd K the nume f veticl levels. It is ssumed tht the ckgund e stndd devitins e hizntlly hmgeneus. (c Hizntl celtin he hizntl celtins f the expnsin cefficients e ls ssumed t e hizntlly hmgeneus. hen the hizntl celtin mtix f the whee (k = N is the N O k -th cefficient is witten s N ( k N ( N Hizntl gid 3 Fig Hmgeneus cvince - celtin mtix etween the k -th expnsin cefficients t the gid pints in tw ws tht lie in the znl diectin nd e septed y ( y f gid pints in the znl nd meidinl diectins, espectively, nd in the meidinl diectin. nd N dente the numes y the meidinl gid intevl. Hizntl celtin functins e ssumed t e f Gussin type. hen the su celtin mtices { } e pptinl t : ( y = exp η ( =,,, N ( (3.6.8 y ε =, ε exp ( k (3.6.9 η = - 3 -

4 (k whee η is the meidinl celtin length f the k -th expnsin cefficient. he hlesky decmpsitin mtix ( k f is ls witten y the hlesky decmpsitin mtix f : =, = N O NN (3.6. whee { } e scls clculted fm the scl cefficient in Eq. (3.6., = ε, ( ( =,3, N =, = ( =,, N (3.6. (3.6. k k k k l = l ( ( ( ( + ε + + l ( =, 3,,N, l =,,,N (3.6.3 = the tens pduct, nd the -lwe tingul mtix tht stisfies the fllwing equtin. = (3.6.4 he ckgund e sttistics wee tined fm diffeences etween 8- nd 6-hu fecsts f the sme vlid time using the N methd (Pish nd Dee, 99. he elements f the celtin mtix slute vlues wee less thn. wee neglected t sve cmputtinl time. f which Adint mdel While fwd mde mdel in the 4D-VAR hs ll physics included, the dint mdel cuently hs dynmicl pcesses, hizntl diffusin, nd physics f fu pcesses: lge scle cndenstin nd evptin, mist cnvective dustment, simplified veticl diffusin, nd lng-wve ditin, ut cnvective pmeteiztin is nt implemented. he lgithm f 4D-V system is designed f the pllel cmpute with distiuted memy. An incement ppch (utie et l., 994 will e used t sve cmputtinl time nd memy f cmpute. he ute lp mdel is RS with hizntl eslutin f km nd 4 veticl levels. he inne lp mdel f clculting nlysis incements is 4km vesin f RS, which is esnle expense f petinl pplictin

5 3.6.4 Osevtins t e ssimilted Assimilted sevtinl typicl dt e disnde, pilt lln, wind pfile, icft, ship, uy, gesttiny stellite, pl it stellite nd Rd-Ringuge Anlyzed Pecipittin. hei elements e sufce pessue, (wind velcity u, v-cmpnents, tempetue, eltive humidity, nd ne-hu pecipittin munt. le 3.6. shws the sevtin e tles used in the eginl nlysis (tp hp. he tle mens diect sevtins ( nd emte-sensing sevtins (. he e t n ity pessue level is linely inteplted in the lgithm f pessue (lg(p. le 3.6. he sevtin e tles used in the petinl eginl nlysis. Ps, u, v, nd RH dente sufce pessue, (wind velcity u, v-cmpnents, tempetue nd eltive humidity espectively. ( sevtinl e (diect sevtin element Ps u v level (hp (m/s (m/s (K RH (% ( sevtinl e (emte sensing element Ps u v level (hp (m/s (m/s (K hp hp hP hP hP hP hP hP hP hP hp hp hp hp hP hP hP hP hp hp RH (% Osevtin e f pecipittin σ σ 3σ ( ( >, σ is given s fllws. ( mm h ( mm / h mm / h / σ > (3.6.5 whee is ne-hu pecipittin munt pvided y the mdel nd is seved ne-hu pecipittin munt. Refeence utie, P., J.-N. heput nd A. Hllingswth, 994: A sttegy f petinl implementtin f 4D-V, using n incementl ppch. Qut. J. Ry. ete. Sc.,, Pish, D. nd J. Dee, 99: he Ntinl etelgicl ente s spectl sttisticl intepltin nlysis system. n. We. Rev.,,

6 3.7 es-scle nlysis 3.7. Intductin he 4-Dimensinl Vitinl dt ssimiltin (4D-V system f the JA es-scle del (S hd een develped since 997 nd hs een petinl in ch with 3-hu ssimiltin windw. he 4D-V system f mes-scle nlysis hs the identicl fmewk f eginl nlysis except f hizntl eslutin nd nlysis dmin. he ute lp mdel f 4D-V is RS with hizntl eslutin f km nd 4 veticl levels, nd the inne lp mdel is km vesin f RS. he nlysis dmin is the sme s the fecst dmin f the S (see Sectin Fmely, initil cnditins f S wee peped y the 3-hu PRE-RN, in which 3D-OI f ssimilting cnventinl dt duing the 3-hu peid ust efe the initil time, nd physicl initiliztin f ssimilting Rd-Ringuge Anlyzed Pecipittin dt wee cnducted t ne-hu intevls. PRE-RN ws eplced with the 4D-V, which cnducts 3-hu cycle nlyses t pepe initil cnditins f S. In ch 6, the S ws executed t pduce 5 hu fecst evey 3 hus t 8 times (, 3, 6, 9,, 5, 8 nd initil time. he mes-scle nlysis fequency ws incesed fm 4 times t 8 times t cnduct 3-hu cycle with 6-hu ssimiltin windw Osevtins t e ssimilted Assimilted sevtinl typicl dt e disnde, pilt lln, wind pfile, icft, ship, uy, gesttiny stellite, pl it stellite nd Rd-Ringuge Anlyzed Pecipittin. e nd me new dt, ttl clumn wte vp (WV nd pecipittin etievls fm dinces f micwve dimete (WR such s SS/I, I, nd ASR-E, sufce wind dt fm scttmetes such s QuikSA nd dpple ds hve een ssimilted t enhnce n ccucy f the initil cnditin. hei elements e sufce pessue, (wind velcity u, v-cmpnents, tempetue, eltive humidity, ne-hu pecipittin munt, in te, pecipitle wte nd dil velcity. Rin te nd ttl clumn pecipitle wte dt etieved fm I, SS/I nd ASR-E dt. I, SS/I nd ASR-E e stellite-ne micwve imges. he dil velcity dt f petinl dpple ds e ssimilted diectly int the mes-scle nlysis. le 3.7. shws the sevtin e tles used in the mes-scle nlysis (tp hp. he tle mens diect sevtins ( nd emte-sensing sevtins (. he e t n ity pessue level is linely inteplted in the lgithm f pessue (lg(p

7 le 3.7. he sevtin e tles used in the petinl mes-scle nlysis. Ps, u, v, nd RH dente sufce pessue, (wind velcity u, v-cmpnents, tempetue nd eltive humidity espectively. ( sevtinl e (diect sevtin element Ps u, v RH level (hp (m/s (K (% ( sevtinl e (emte sensing element Ps u, v level (hp (m/s (K hp..5.8 hp hP hP hP hP hP hP hP hP hp hp hp hp hP hP hP hP hp hp RH (% In de t pvide fecst within ne nd hlf hus fm nlysis times, dt cut-ff time is set t fifty minutes. Becuse f the sht dt cut-ff time, sevel cnventinl sevtin dt such s mst f the veses uppe i epts nd mst f the stellite sevtins, e nt used n ust nlysis time. But the mes-scle nlysis cn use them in next 3-hu cycle with 6-hu ssimiltin windw