Comparison between LETKF and EnVAR with observation localization

Transcription

1 Comprson beeen LETKF nd EnVAR h observon loclzon * Sho Yoo Msru Kun Kzums Aonsh Se Orguch Le Duc Tuy Kb 3 Tdsh Tsuyu Meeorologcl Reserch Insue JAMSTEC 3 Meeorologcl College 6..7 D Assmlon Semnr n RIKEN/AICS

2 Bcground covrnce o o solve o o clcule 3DVAR4DVAR Ssc Implcly Wh don o M nd EnKF Ensemble-bsed Eplcly Ensemble ppromon ybrd-4dvar Ensemble-bsed Implcly Wh don o M nd EnVAR Ensemble-bsed Implcly Ensemble ppromon Ensemble-bsed vronl d ssmlon Inroducon T T M M J y R y B T M M J J y R B Cos Funcon Byesn ssmlon provdes Anlyss rom Frs guess nd Observon y. es mmum lelhood vlue hen cos uncon J s mnmum ( J=). Severl mehods re clssed usng ho o solve J=. Bcground erm Observon erm Grden EnVAR provdes nlyss mplcly hou don models /33

3 Inroducon Why s J= solved mplcly? 3/33 Cos Funcon J Bcground erm T B M Observon erm T y R M y J b J o Qudrc uncon o - Qudrc uncon o (M ( )) (M ( ))-y Gussn ppromon Observon (M ( )) erm s srcly s ppromed reed o qudrc uncon o by ssumng lner (M ( )) J E Im Implc mehod s beer becuse observon operor re srcly reed J= s chnged cn be solved by solvng eplcly J= e.g. mplcly EnKF

4 Inroducon Prevous sudes bou EnVAR 4/33 Zupns (5) Zupns e l. (8) EnVAR mehod s suggesed Lu e l. (8 9) Buehner (3) 4D-EnVAR s compred o oher mehods Gussn ppromon Splly loclzed bcground covrnce un e l. (4) 4D-EnKF s suggesed Any me nlyss n ssmlon ndo s provded Assmlon ndo Lu e l. (8) 3D-EnKFEnVAR 4D-EnKFEnVAR n- me n n- me In hs sudy 4D-EnVAR s compred o 4D-EnKF (LETKF) n

5 Conens 5/33. Inroducon. Formulon o EnVAR h observon loclzon 3. Comprson beeen LETKF nd EnVAR. Sngle-observon ssmlon. OSSEs h SPEEDY model 3. Rel observon d ssmlon h JMANM

6 OSSE Observon sysem smulon epermens h SPEEDY model Number o members: Assmlon ndo: 6 hours Loclzon rdus: σ =(m) σ V =.(sgm) Observons: U V T R Ps Inlon: Mulplcve (=.) Anlyss me: Cener o he ndo (=3h) Observon me: =h 3h 5h Posons o observons 6/33 Bs o specc humdy 6-hour orecs (g/g) o nure run RMSE o specc humdy 6-hour orecs (g/g) o nure run Number o orecs-nlyss cycles (every 6 hour) Bs nd RMSE o EnVAR re smller hn hose o LETKF

7 Formulon 7/33 EnVAR ormulon Mulplcve nlon Bcground Anlyss error covrnce B T L M : nlyss pons : observon pons : me slos : ensemble members Anlyss vluble s rnsormed rom o J Grden o J Then M Loclzon Perurbon o L R y Observon error vrnce - Observon loclzon - Derved rom Bcground loclzon - Globlly dened J Observon operor (non-lner) Smlr o LETKF Deren rom LETKF

8 EnVAR hou loclzon Formulon Weghed summon o ensemble perurbons s dded o rs guess ) ( y R M J C: Zupns e l. (8) T T J y R y B y R J B y R M J M B 8/33 Cos uncon: Componens ormulon: Appromon o B usng ensemble ere Solve or nd gn : grd pons(-n) : obs. pons(-k) : me slos(-t) : members(-m)

9 EnVAR h observon loclzon Formulon M B l l l L / ~ L M B l l l L L L / / l l y R M J ~ ~ ~ ~ ~ l l l y R M J l: grd pons(-n) : obs. pons(-k) : me slos(-t) : members(-m) The number o ensemble members s usully oo smll o me nlyss h lrge degree o reedom. Loclzon requred or ncresng degree o reedom o Then cos uncon: Grden o cos uncon: Loclzon cor (I grd s r rom grd s smll or.) o s hs clculed? 9/33 Mulplcve nlon prmeer

10 EnVAR h observon loclzon Formulon ~ ~ ~ l l l y R M J N N N l N N l l N N l l l L L L / / / ~ ~ /33 l: grd pons(-n) : obs. pons(-k) : me slos(-t) : members(-m) ere Usng ollong equon l l l L / ~ I nd re compleely on he sme pon s sme s. (Then depends only on he vluble on he grd.) / L l

11 Formulon o o solve J= /33 ~ J ~ l J M ~ l R y / l Ll L l / l L / l ~ J ~ J M l ~ No ndependen or nlyss pons l M L R Independenly clculed or every nlyss pons R L y y Usng ollong equon / / L L l L l l L / l ~ l l Observon loclzon Appromed ne cos uncon s dened l: grd pons(-n) : obs. pons(-k) : me slos(-t) : members(-m)

12 Formulon Summry o EnVAR ormulon /33 Anlyss J J T M M L y R Observon error vrnce L y R Anlyss perurbon J M T M δ / U Loclzon cer U L R Observon operor U Egenvlue decomposon o essn mr o J Mnmzon o globlly dened J h observon loclzon U : nlyss pons : observon pons : me slos : ensemble members

13 Formulon [] (Locl or Globl) LETKF Derence beeen LETKF nd EnVAR EnVAR EnVAR clcules drecly I s lner nd nlyss pon s sme s observon pon EnVAR=LETKF LETKF EnVAR Clculed h nlyss pon Independenly or ech nlyss [] Grden o (round Frs guess or Anlyss) δ n EnVAR s round nlyss I s lner EnVAR=LETKF 3/33 Clculed h observon pon or ll nlyss Observon pon Anlyss pon : nlyss pons : observon pons : me slos : ensemble members

14 4/33 Sngle-observon ssmlon Comprson o LETKF (Lner cse) Number o members: Loclzon rdus: σ=(m) σv=.(sgm) Observons: σ=.835 Frs guess o relve humdy nd horzonl nd U=-9.8 m s- Anlyss-Frs guess (LETKF) U=-.9 m s- Anlyss-Frs guess (EnVAR) U=-.9 m s- Incremen o EnVAR s sme s LETKF observon pon bu smller r rom observon pon ( severer loclzon)

15 Sngle-observon ssmlon Why s EnVAR loclzon severer hn LETKF? 5/33 Observon loclzon o hs EnVAR s derved rom bcground loclzon bu h o LETKF s no. e.g. In o nlyss pons nd one observon K y nd Bcground loclzon K K Then B B R LB B R K (Greybush e l. ) K K Observon loclzon o LETKF K K B B B R B R B LB B R / L LB R B B B R B R Bloclzon Rloclzon K Thereore bcground L loclzon s severer

16 6/33 Sngle-observon ssmlon Comprson o LETKF (Non-lner cse) Number o members: Loclzon rdus: σ=(m) σv=.(sgm) Observons: σ=.835 Frs guess o relve humdy nd horzonl nd R=53. % Anlyss-Frs guess (LETKF) R=44. % Anlyss-Frs guess (EnVAR) R=39.6 % EnVAR nlyss s closer o observon hn LETKF

17 OSSE Observon sysem smulon epermens h SPEEDY model Number o members: Assmlon ndo: 6 hours Loclzon rdus: σ =(m) σ V =.(sgm) Observons: U V T R Ps Inlon: Mulplcve (=.) Anlyss me: cener o he ndo Observon me: =h 3h 5h Posons o observons 7/33 Bs o specc humdy 6-hour orecs (g/g) o nure run RMSE o specc humdy 6-hour orecs (g/g) o nure run Number o orecs-nlyss cycles (every 6 hour) EnVAR s beer cused by derence o ho o clcule nd δ

18 OSSE O-F sgrm Observon-Forecs (O-F) hsogrm n ll EnVAR nlyss 8/33 Specc humdy ssmlon: Lner bu non-gussn probbly dsrbuon

19 OSSE Specc humdy ssmlon 9/33 LETKF EnVAR Bs o specc humdy 6-hour orecs (g/g) o nure run Thc: relve humdy ssmlon (CTL) Thn: specc humdy ssmlon RMSE o specc humdy 6-hour orecs (g/g) o nure run EnVAR s beer hn LETKF nd relve humdy ssmlon s beer hn specc humdy ssmlon

20 OSSE EnVAR h loclly dened cos uncon Locl J s mnmzed mplcly Bs o specc humdy 6-hour orecs (g/g) o nure run Clclon me (sec) /33 > 6 RMSE o specc humdy 6-hour orecs (g/g) o nure run Blc: LETKF Red: EnVAR h Globl J Blue: EnVAR h Locl J Globlly dened clculed h observon pon Loclly dened clculed h nlyss pon Smlr o LETKF Globl J hs good mpc

21 OSSE EnVAR h he specc number o eron /33 Bs o specc humdy 6-hour orecs (g/g) o nure run -3 RMSE o specc humdy 6-hour orecs (g/g) o nure run Blc: LETKF Red: EnVAR (CTL) Green: EnVAR (sop er 5 erons) Blue: EnVAR (sop er erons) EnVAR h 5 erons s beer hn LETKF (clculon me s -3 mes s long s LETKF)

22 Summry o OSSEs /33 We developed EnVAR h observon loclzon nd compred o LETKF EnVAR nlyss s closer o rue vlue hn LETKF becuse globlly dened cos uncon s mnmzed Severl mes longer clculon me hn LETKF Non-lner observon operor s srcly reed n EnVAR (Gussn ppromon should no be used) Observon loclzon o hs EnVAR s sme s bcground loclzon ( severer hn loclzon o LETKF) Is EnVAR lso beer hn LETKF n rel obs. d ssmlon?

23 Rel d ssmlon 3/33 Locl Rnll on 8 July 3 5 6JST 6 7JST 7 8JST 8 9JST 9 JST JST Anlyzed precpon MSM (nl: 5JST) - To precpon sysems ere genered. - Accure orecs s dcul. (even hough he nl condon ncluded rnll) MSM (nl: 8JST) Dense observons re epeced o mprove orecss

24 Rel d ssmlon Assmled Dense Observons 4/33 Observon Elemens Frequency Surce (JMA Surce observon nd AMeDAS) U V T every mnues GNSS PWV every mnues Rdr Rdl nd every mnues Ksh ned Nr Rdosonde U V T R every 3 hours Tsuub Ur Yoosu Ryou Mru Seng orzonl loclzon: m Vercl loclzon:. lnp (PWV s no loclzed verclly) Mulplcve nlon prmeer:. Observon error: U V: m/s T: K R: % PWV: 5 g/m Rdl nd: 3 m/s Surce nd (m/s) 7/8 8JST GNSS PWV (g/m ) 7/8 8JST :Rdr :Sonde

25 Rel d ssmlon Flo o Assmlon Epermens 5/33 Boundry condon: JMA GSM Forecs + Weely Ensemble Perurbon 376 9JST JST 378 6JST 378 9JST 378 JST 378 5JST 378 8JST Ouer Grd nervl: m Grd number: Ensemble sze: 5 Anlyss ndo: 3 hour (Operonl Observons used n JMA Meso-DA every 3 mnues) Donsclng 9JST- 5 Members Boundry Condon every 3 mnues Inner Grd nervl: m Grd number: 6 Ensemble sze: 5 Anlyss ndo: hour 5JST 6JST 7JST 8JST Eended Forecs : Ensemble Forecss : Anlyss (LETKF or EnVAR) Domn Trge: Locl rn ner Toyo n JST

26 Rel d ssmlon 9JST Comprson o -h Rnll n 8-9 JST 8JST 9JST 6/33 EnVAR EnVAR-NPWV (/o PWV d) EnVAR-NSONDE (/o Sonde d) LETKF NDA (/o ny d) Anlyzed precpon Good mpcs o PWV nd Sonde d ssmlon Domn o clcule he score Trge o sensvy

27 Rel d ssmlon Are Frcons Sll Scores mproved? 7/33 FSS O F O F 9JST- 5JST 6JST 7JST 8JST O F : number densy o observed rnll n -h rcon : number densy o orecs rnll n -h rcon All our orecss rom EnVAR nlyses re beer hn NDA srong rn ghresoluon rn poson

28 Rel d ssmlon Impc o Dense Observons 8/33 Rnll n 8-9 JST EnVAR EnVAR-NPWV (/o PWV d) EnVAR-NSONDE (/o Sonde d) [EnVAR] [NDA] [EnVAR] [EnVAR-NPWV] - PWV d grely mproved rnll orecss. - Rdosonde d lso mproved e rn orecss. [EnVAR] [EnVAR-NSONDE] Boh PWV nd rdosonde d could mprove rnll orecss

29 Rel d ssmlon EnVAR v.s. LETKF Rnll n 8-9 JST EnVAR LETKF [EnVAR] [NDA] 9/33 - Derence beeen EnVAR nd LETKF s smll Tme seres o RMS o (O A) nd (O F) o PWV n he orecs-nlyss cycles [EnVAR] [LETKF] In EnVAR srong rnll (> 5 mm/hr) orecss re slghly beer hn h o LETKF

30 Rel d ssmlon Correlon beeen Rnll nd Inl Ses Correlon beeen J nd n CORR( ) m J m m J m( ) m( ) J J ( ) ( ) m m m m 3/33 m er vpor nd nds o EnVAR nlyss : grd number m: ensemble member Lrge grden J m m : -h rnll (8 9JST) verged n hs re ( ) : vrbles n m hegh 8JST I nds pon o he drecon o vecors n hs gure rnll becomes sronger Lo-level convergence s correled o rnll nensy Convergence Posve correlon o er vpor Correlon beeen rnll nd m er vpor nd nds clculed by 5-member EnVAR

31 Rel d ssmlon 3/33 Derence o Lo-level vrbles [EnVAR] [EnVAR-NSONDE] [EnVAR] [EnVAR-NPWV] m er vpor nd nds o EnVAR nlyss Convergence Posve ncremen o er vpor [EnVAR] [LETKF] Locl ron? Derence o m er vpor nd nds Convergence Convergence Incremen o lo-level er vpor nd convergence mes rnll sronger Posve correlon o er vpor Correlon beeen rnll nd m er vpor nd nds clculed by 5-member EnVAR

32 Summry o Rel D Assmlon 3/33 We ssmled dense obs. or he locl rnll ner Toyo Impc o dense PWV nd Rdosonde obs. PWV mproved rnll orecs hrough correcng lo-level er vpor Sonde obs. mproved rnll orecs hrough correcng lo-level nds Comprson beeen LETKF nd EnVAR EnVAR cn me he nlyss hch s closer o obs. hn LETKF Improvemen o rnll orecs by usng EnVAR s smll Correlon o rnll bsed on ensemble orecss Lo-level er vpor nd convergence mde locl rnll sronger Are hese mpcs generl? Vercon n longer perod requres

33 Summry (EnVAR v.s. LETKF) Formulon Non-lner observon operor s more srcly reed n EnVAR Observon loclzon o EnVAR s sme s bcground loclzon ( severer hn loclzon o LETKF) OSSEs Anlyss o hs EnVAR lzon re more ccure hn LETKF becuse globlly dened cos uncon s mnmzed Rel observon d ssmlon PWV ssmlon n boh EnVAR nd LETKF mproved rnll orecs EnVAR nlyss s closer o obs. hn LETKF Improvemen o rnll orecs by usng EnVAR s smll n hs cse 33/33 Our reserch s suppored n pr by Sregc Progrm or Innovve Reserch (SPIRE) Feld 3 (proposl number: hp4 nd hp54) nd Toyo Meropoln Are Convecon Sudy or Ereme Weher Reslen Ces (TOMACS). SPEEDY-LETKF (hps://code.google.com/p/myosh/) nd he source code developed by Numercl Predcon Dvson n JMA re used n hs sudy. GNSS d ere provded rom he nd Lborory Meeorologcl Selle nd Observon Sysem Reserch Deprmen n MRI. Rdosonde observons ere conduced s pr o TOMACS progrm. The oher observon d ere rom JMA.