LETKF compared to 4DVAR for assimilation of surface pressure observations in IFS

Transcription

1 LETKF compred to 4DVAR for ssimiltion of surfce pressure oservtions in IFS Pu Escrià, Mssimo Bonvit, Mts Hmrud, Lrs Isksen nd Pul Poli Interntionl Conference on Ensemle Methods in Geophysicl Sciences Toulouse, 2-6 Novemer 202 Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

2 Index 2 LETKF equtions Only Surfce Pressure Dt (PSFC) ssimilted Surfce Pressure is correction Infltion LETKF ginst 4DVAR LETKF Smoother Summry nd Discussion Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

3 LETKF equtions 3 Description of method in (Hunt et l., 2007) Ojective: minimiztion of J (s 4DVAR) J(x) (x x ) T (P ) (x x ) (y H(x)) R o T (y o H(x)) Ensemle prediction for ckground stte nd error estimtion: x x T P ( k ) X ( X ) Anlysis solved in the suspce S, spce of ensemle perturtions (w S): x x X w Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

4 Pu Escrià Interntionl Conference on Ensemle Methods, Novemer Lineriztion of H ssuming tht perturtions re very smll w.r.t the men: Reformultion of J in S (now J*): Minimiztion of J* hs nlyticl solution: LETKF equtions ] [ ] [ ) ( ) ( * w Y y y R w Y y y w w k w J o T o T ] ) ( ) [( ) ( ) ( T w o T w Y R Y I k P y y R Y P w

5 LETKF equtions 5 The nlysis stte is: Anlysis ensemle chosen using the Symmetric Squre Root method: Ensemle of nlysis sttes is finlly computed s: Done independently for ech grid point x i x X ( w w i ) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

6 Only Surfce Pressure Dt (PSFC) ssimilted 6 First check of performnce of different schemes in consistent environment A similr simplified configurtion is used in the ERA-20C renlysis Opertionl nlysis cn e used s truth (could fvour 4DVAR scheme) It skips the (open) LETKF prolems when ssimilting ll the oservtions: ) Loclistion of stellite rdinces ) B rnk deficiency degrdes fitting of oservtions when their numer increses Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

7 Only Surfce Pressure Dt (PSFC) ssimilted 7 ~ os within 2 hour ssimltion window (ll ville types) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

8 PSFC is correction 8 PSFC hs een corrected y opertionl (Drsko s) is correction scheme in LETKF (MSLP RMSE t SH with respect to opertionl nlysis) LETKF No BC LETKF BC Experimentl results re very sensitive to PSFC is correction Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

9 Infltion 9 Ad hoc fctor introduced in LETKF (nd EnKF in generl) ecuse ckground error is known to e underestimted due to model nd oundry condition errors, non-linerities, non-gussinities, etc Infltion pplied in our EnKF is multiplictive nd it is sed on the relxtionto-prior spred scheme (Whitker, 202): ( ) Severl schemes for dditive nd multiplictive infltion re implemented in IFS-EnKF Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

10 Infltion 0 α = 0.90 good for surfce nd low troposphere (MSLP RMSE & BIAS t NH) Wek sensitivity to infltion fctor Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

11 Infltion 4DVAR/EDA lso enefits from infltion (here MSLP RMSE t NH) EDA clirted EDA no clirted Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

12 Infltion 2 REDNMC coefficient for 4DVAR experiments, α =.4 After tuning (experiment fqm): i ( i o i ) o NH, α =.04 TR, α = 0.79 SH, α =.32 Equilirium Overdispersion Underdispersion Comprison well tuned for NH Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

13 LETKF ginst 4DVAR 3 The im is to compre LETKF, 4DVAR nd hyrids in ERA-20C like surfce pressure only ssimiltion (PSFC) experiments Verifiction metrics: ) Anlyses: Temporl series of MSLP, T2m, U0m, V0m nd Z500 RMSE & BIAS Verticl profiles of T, Z, U nd V RMSE (50 hp top) MSLP RMSE sptil mps ) Forecsts: MSLP nd Z500 RMSE y forecst rnge All results re verified ginst opertionl nlysis (truth) Verifiction for Northern Hemisphere (LAT > 20º N) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

14 LETKF ginst 4DVAR 4 Configurtion of experiments Nme Anlysis Method B mtrix 549 4DVAR Full Rnk Sttic 580 4DVAR Full Rnk Sttic fqm 4DVAR / EDA fr3m 4DVAR / LETKF Full Rnk Dynmic Vrince Full Rnk Dynmic Vrince fqi2 LETKF Low Rnk Full Dynmic Win leng Initil Dt PSFC BC Loop Trunc Loop Iter Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202 Ens mem 2 ERA Vr 95/59 35/50 N/A 24 ERA Vr 95/59 35/50 N/A 2 ERA Vr 95/59 70/ ERA Vr / Drsko s 95/59 70/ Cold Drsko s N/A N/A 60 Os ssimilted Resolution Levels Plotted Period WllTime wrt fqi2 PSFC (Surfce Pressure dt) T59 ~.5 x.5 deg

15 LETKF ginst 4DVAR 5 MSLP RMSE & BIAS of nlyses t Northern Hemisphere LETKF performs generlly etter thn ny other scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

16 LETKF ginst 4DVAR 6 T2M RMSE & BIAS of nlyses t Northern Hemisphere LETKF performs generlly etter thn ny other scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

17 LETKF ginst 4DVAR 7 U0m RMSE & BIAS of nlyses t Northern Hemisphere LETKF performs generlly etter thn ny other scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

18 LETKF ginst 4DVAR 8 V0m RMSE & BIAS of nlyses t Northern Hemisphere LETKF performs generlly etter thn ny other scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

19 LETKF ginst 4DVAR 9 Z500 RMSE & BIAS of nlyses t Northern Hemisphere LETKF performs generlly etter thn ny other scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

20 LETKF ginst 4DVAR 20 T RMSE profile of nlyses t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 LETKF est scheme (strong impct of B f-d in sence of oservtions?!) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

21 LETKF ginst 4DVAR 2 Z RMSE profile of nlyses t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 LETKF est scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

22 LETKF ginst 4DVAR 22 U RMSE profile of nlyses t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 LETKF est scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

23 LETKF ginst 4DVAR 23 V RMSE profile of nlyses t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 LETKF est scheme Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

24 LETKF ginst 4DVAR 24 MSLP RMSE. LOW (0 hp) HIGH (2.4 hp) LETKF < > DVAR/EDA In Pcific (few os) LETKF positive impct (flow-dependency of B?!) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

25 LETKF ginst 4DVAR 25 MSLP RMSE of forecsts t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 OPER LETKF nlysis cler overperformnce not in forecst (initil unlnce?!) 4DVAR-24 the est up to H+20 (eneficil enlrge window?!) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

26 LETKF ginst 4DVAR 26 Z500 RMSE of forecsts t Northern Hemisphere 4DVAR-2 4DVAR-24 4DVAR/EDA 4DVAR/LETKF LETKF-6 OPER 4DVAR/LETKF the est from H+20 on (B qulity?!) Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

27 LETKF Smoother 27 LETKF Smoother is simple methodology for douling the length of the ssimiltion window under the ssumption of linerity in forecst error propgtion (Yng et l., 2009) As the weights w re vlid in the whole ssimiltion window, in the eginning of the window, the current nd the ones of the previous window re oth vlid. So one cn pply the future weights to reconstruct the previous nlysis: ~ xt xt X t w t Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

28 Pu Escrià Interntionl Conference on Ensemle Methods, Novemer Due to technicl implementtion in IFS, future weights w t re pplied to previous X t- out of the nlysis window. However this should not ffect the vlidity of Smoother due to linerity of first 3 hours forecst: A coherent Smoother should use the non-inflted ensemle of nlysis (k=), otherwise future oservtions would e weighted differently thn previous: LETKF Smoother t t t t t t t t t t t t t t t s w kw w X x w W kx w X x w X x x,

29 LETKF Smoother 29 PSFC RMSE of nlyses t Southern Hemisphere LETKF-6 LETKF-2 (Smoothed) Positive impct in presence of few oservtions Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

30 LETKF Smoother 30 PSFC RMSE of nlyses t Northern Hemisphere LETKF-6 LETKF-2 (Smoothed) No significnt impct in presence of enough oservtions?! Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

31 LETKF Smoother 3 T RMSE & BIAS profile of nlyses t Southern Hemisphere Bd: Smoother worsens T in the verticl. Unlnced nlysis? Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

32 LETKF Smoother 32 MSLP RMSE of forecsts t Northern Hemisphere LETKF-6 LETKF-2 (Smoothed Initil unlnce reduced with forecst rnge ut n open issue Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

33 Summry 33 This study compres performnces of LETKF, 4DVAR nd hyrids in simplified environment only ssimilting PSFC nd low resolution T59 In this configurtion LETKF nlysis performs generlly the est t NH (comprison well tuned) ssuming the sme computtionl cost Flow-dependent estimtion of B seems to hve specilly positive impct over Pcific nd in the verticl, where few nd no oservtions re ville LETKF nlyses cler overperformnce is not oserved in forecsts proly due to initil unlnce 4DVAR-24 forecst is the est up to H+20 wheres from then on is 4DVAR/LETKF. This suggests is eneficil enlrging window nd incresing flow-dependent signl in B estimtion LETKF smoother hs positive impct in nlysis skill specilly in presence of few oservtions ut t the sme time it cretes importnt unlnces in the verticl Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202

34 Discussion 34 LETKF seems to e powerful ssimiltion tool when only PSFC is ssimilted. Could it e extended to other poor oserved systems such s ocen or pollution modelling? However, work must e done in removing LETKF initil unlnce nd trying other methodologies for covrince infltion LETKF Smoother seems to tke less profit of douling ssimiltion window thn 4DVAR nd it is still n open issue with respect to verticl unlnces Conclusions of comprison cn not e directly extended to ll oservtions ssimilted simultions. Work on this comprison is going on for ll the Gloe A technicl memorndum on this study is going to pper soon. For more discussions: pescri@emet.es Pu Escrià Interntionl Conference on Ensemle Methods, Novemer 202