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Ensemble Data Assimilation without Ensembles with Application to Ocean Data Assimilation or Flow-Adaptive Background-Error-Covariance Modeling for Data Assimilation using Information from a Single Model Trajectory or E unus pluribum

  1. Ensemble Data Assimilation without Ensembles with Application to Ocean Data Assimilation or Flow-Adaptive Background-Error-Covariance Modeling for Data Assimilation using Information from a Single Model Trajectory or E unus pluribum Christian Keppenne 1 , Michele Rienecker 2 , Robin Kovach 1 , Guillaume Vernieres 1 1 SSAI inc. 2 NASA GSFC 6 th WMO Symposium on Data Assimilation College Park, MD, October 7-11 2013 1

  2. 2001-2008: Ocean EnKF in GMAO NSIPP-1 S/I Prediction system  ODAS EnKF CGCM forecast OGCM run LSM-AGCM-OGCM coupling Poseidon isopycnal OGCM  ARIES AGCM  ODAS EnKF run prior to AGCM coupling  2009-present: GEOS iOdas used with GEOS-5 CGCM  iOdas focus  Seasonal-interannual-decadal forecast initialization  Retrospective ocean reanalysis (1950-present)  Coupled data assimilation  Global eddy resolving ocean data assimilation + coupled DA GEOS iOdas CGCM forecast CGCM run 2 ADAS replay

  3. NASA GMAO Integrated Ocean Data Assimilation System (GEOS iOdas) GEOS-5 coupled modeling system NASA GEOS-5 AGCM  NASA GOCART chemistry + aerosol + radiation model  GEOS-5 catchment LSM  GFDL MOM5 OGCM  LANL CICE  NASA NOBM ocean biology model  GEOS analysis system GEOS DAS atmospheric analysis system  iOdas  Production ocean analysis with: MOM ½ ° x ½ ° - ⅙ ° x L40  CICE ½ ° x ½ x 5  AGCM + GOCART 1¼ ° x 1 ° x L72 (Ganymed 4)   4 hours wallclock time/month to run CGCM on 360 cores  7-8 hours wallclock time/month with ocean analysis 3

  4. iOdas background error-covariance modeling options Multiple trajectory methods  hybrid particle filter EnKF (HPEnKF)  Steady state Ensemble (aka asymptotic EnKF, EnOI, SE*K)  Single trajectory methods  SAFE (Space Adaptive Forecast error Estimation)  FAST (Flow Adaptive error Statistics from a Time series  Ocean DA is about updating fields of unobserved variables   Need reliable cross-field covariances 4

  5. GEOS iOdas ocean EnKF Forecast ensemble augmented with time lagged instances: (e.g., EnKF 16x11: current ensemble + 10 previous lags) EnKF with particle pre-filter step (HPEnKF) (Keppenne et al., 2013a: manuscript)  prefilter step  x p : ensemble member that minimizes RMS OMF  x p : ensemble mean x p x p  D p = x p - x p D p Y x m  EnKF analysis step x m Y 5

  6. AMJ 2006 Vertically integated RMS (passive) ARGO S OMF in 3 ° x 3 ° bins: Difference with control T OI analysis ocean DA needs reliable cross-field covariances! control RMS OMF – EnKF-16x11 RMS OMF: z<200m EnKF 16 better control better GEOS 5 CGCM AGCM 288x181x72  control RMS OMF – HPEnKF-16x11 RMS OMF: z<200m OGCM 720x410x40  HPEnKF 16 better ARGO T assimilated (active)  ARGO S passive  control better Control: Univariate T OI  EnKF 16x11: T, S, u, v update  HPEnKF 16x11: T, S, u, v update  control RMS OMF – EnKF-16x11 RMS OMF: z>200m EnKF 16 better control better control RMS OMF – HPEnKF-16x11 RMS OMF: z>200m HPEnKF 16 better control better 6

  7. ARGO T assimilation experiment AMJ 2006 Vertically integated RMS (passive) S OMF in 3 ° x3 ° boxes T OI control EnKF 16x11 Production analysis with EnOI (50 forecast error anomaly EOFs) [Vernieres et al. 2012: NASA tech. report 2012] 1993-2005 0-300m 2006-2012 0-300m HPEnKF 16x11 1993-2005 300-1000m 2006-2012 300-1000m 7

  8. Want something  faster than EnKF/HPEnKF  able to flow-adaptively update unobserved model fields  that works as well as EnOI What’s really nice about ensemble assimilation methods? Adaptively estimates background errors amplitudes  Not when using covariance inflation  Adaptively estimates background error distribution for  Fields of observed quantities  Alternative methods can do that too  Fields of unobserved quantities  Yes, but large ensembles are needed for proper <t, s>  (or other ocean variable pairs) covariance estimates 8

  9. Ensemble data assimilation without ensembles Flow-adaptive error covariance estimation without ensemble integration 2 approaches built in GEOS iOdas (Keppenne et al 2013b, Joatech, submitted)  Ensemble in time (FAST)  Ensemble in space (SAFE)

  10. Flow Adaptive error Statistics from a Time series (FAST) Ensemble of lagged state instances sampled along same trajectory         X x x , j 0 , , n 1 , ( 11 a )  k k j ( k ) 1   n 1  x x , ( 11 b )  ( k )  k j j 0 n High pass filtered ensemble         0  X x x , j 0 , , n 1 , ( 12 )   k k j k j      0 0 x x ( 1 ) x , ( 13 )  k k k 1 x : original trajectory  x 0 : low-pass filtered trajectory (SMA or IR filter)  Resampling to compensate window centering effect          n 1    b    X x x , j 0 , , n 1 , ( 14 a )   k k j  ij k i i 0               X x x , j 0 , , n 1 , ( 14 b )  k k j b ij : random weights  10

  11. a) Active Argo T RMS OMF 2010-2011 (0-3000m) EnOI 0 order 1 st order 2 nd order FAST b) Passive Argo S (0-3000m) EnOI 20 leading EOFs last 20 state vectors EnOI 0 order 1 st order 2 nd order last 20 1 st order time differences FAST last 20 2nd order time differences FAST 20 lags 11

  12. Space Adaptive Forecast error Estimation (SAFE)  Treat state variables in nearby grid cells as if they were from other ensemble members (spatial ensemble analogy)  Other computations essentially same as in EnKF except distance-dependent weighted mean instead of arithmetic mean (done with Gaussian filter)  Coastlines introduce difficulties in the ocean (handled with aforementioned Gaussian averaging) 12

  13. Space Adaptive Forecast error Estimation (SAFE)   observed: v vv vw P P     x [ v , w ], P , unobserved: w wv ww   P P 1: estimate background error variance of observed field v at each  gridpoint (Gaussian filter ( Q ) replaces arithmetic ensemble mean)   ),   Q  Q σ 2 2 vv diag ( P ) ( v ( v ) vv 2: assimilation increment D v for observed field v  3: estimate cross-field covariances < v , w > at every grid point     ).  vw  Q  Q  Q 2 ( v ( v ) w ( w ) 4: project D v onto fields of unobserved variables at every gridpoint  approximation: 13

  14. 5-day lead active Argo T RMS OMF 2010-2011 5-day lead passive Argo S RMS OMF 2010-2011 a) b) 0 0 200 200 400 400 600 600 800 800 1000 1000 1200 1200 1400 1400 SAFE SAFE FAST FAST EnOI EnOI 1600 1600 T OI T OI 1800 1800 -0.25 -0.20 -0.15 -0.10 -0.05 0.0 -0.06 -0.04 -0.02 0.0 0.02 0.04 0.06 (PSU) (ºC) RMS OMF reduction over no-assimilation control  observed T  unobserved S 14

  15. a) e) i) 100 W-E W-E W-E 0.5 150 200 250 300 170W 160W 150W 140W 130W 120W 110W 0.0 170W 160W 150W 140W 130W 120W 110W 170W 160W 150W 140W 130W 120W 110W b) f) j) 100 S-N S-N S-N 150 200 -0.5 250 300 20S 10S EQ 10N 20N 20S 10S EQ 10N 20N 20S 10S EQ 10N 20N TT EnOI/T OI TT SAFE TT FAST c) g) k) 100 W-E W-E W-E 150 0.05 200 250 300 170W 160W 150W 140W 130W 120W 110W 170W 160W 150W 140W 130W 120W 110W 170W 160W 150W 140W 130W 120W 110W 0.0 d) h) l) 100 150 S-N S-N S-N 200 250 -0.05 300 20S 10S EQ 10N 20N 20S 10S EQ 10N 20N 20S 10S EQ 10N 20N TS EnOI TS SAFE TS FAST 15

  16. a) f) k) 100 Jan 1 2010 Jan 1 2010 Jan 1 2010 150 200 250 300 b) l) g) 100 Apr 1 2010 Apr 1 2010 Apr 1 2010 150 200 250 300 0.05 c) m) h) 100 Jul 1 2010 Jul 1 2010 Jul 1 2010 150 200 0.0 250 300 d) n) i) 100 Oct 1 2010 Oct 1 2010 Oct 1 2010 -0.05 150 200 250 300 e) o) j) 100 Jan 1 2011 Jan 1 2011 Jan 1 2011 150 200 250 300 170W 160W 150W 140W 130W 120W 110W 170W 160W 150W 140W 130W 120W 110W 170W 160W 150W 140W 130W 120W 110W TS EnOI TS FAST TS SAFE 16

  17. 2011 control run RMS S OMF - 5-day lead Argo S RMS OMF from runs with ARGO T assimilation (0-300m) SAFE EnOI a) c) b) d) FAST T OI 17

  18. 2011 control run RMS S OMF - 5-day lead Argo S RMS OMF from runs with ARGO T assimilation (300-3000m) SAFE EnOI a) c) b) d) FAST T OI 18

  19. Application to sea ice concentration assimilation  1 st generation system (used in GMAO ocean reanalysis)  Assimilation of NSIDC ice fraction (aice)  ice fraction innovation: NSIDC - CICE model state  SAFE to estimate <aice, T> and <aice, S> covariances (can also use FAST, EnOI)  Incremental update of MOM T, S ocean fields OGCM: MOM4.1 tripolar grid 720x410x40  CICE 4.1 720x410x5  AGCM: Fortuna 2.5 288x181x72  iOdas-503  19

  20. 1 st . Generation iODAS sea ice assimilation 01/01/2011 NSIDC control FAST aice OI SAFE EnOI CGCM MERRA replay SAFE NH ice SH ice FAST EnOI aice OI 20

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