Challenges and Advances of Regional Ocean Data Assimilation. Andy Moore Department of Ocean Science University of California Santa Cruz

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1 Challenges and Advances of Regional Ocean Data Assimilation Andy Moore Department of Ocean Science University of California Santa Cruz

2 The Large Scale Ocean Circulation

3 Diverse Approach Global versus Regional Global ECMWF MERCATOR ECCO(2) NASA/GMAO NCOM HYCOM FOAM BLUElink SODA GLORYS Others Regional & Nested MFS HOPS NCOM MODAS FOAM ROMS Methods 3D-Var En-3D-Var 4D-Var Nudging EnKF SEEK MVOI

4 Mature Applications Scientific Ocean analyses Climate variability Climate change ENSO, MOC Eddy variability Coastal upwelling Practical Oil spill (eg. DWH) Search and rescue Contaminant dispersal (eg. Fukoshima) Forecasting (eg.ioos) Fisheries management

5 Overview Part I Challenges Part II Recent Advances

6 Part I - Challenges Space- and time-scales Observations Control vector Correlation functions Tracers in the ocean Initialization shocks

7 The California Current Large Marine Ecosystem

8 Ocean Space- and Time-Scales

9 The California Current Mesoscale eddies

10 The Ocean Sub-Mesoscale

11 Coastal Upwelling & CCLME Upwelling due to wind stress curl Sardines Upwelling due to divergence Anchovies Rykaczewski & Checkley (2007)

12 Apex Predators

13 Other Food Webs

14 Apex Predators

15 Ocean Observations

16 Tagged Marine Mammals Moorings Satellite remote sensing Coastal radars Ships of opportunity ARGO floats Gliders and AUVs

17 Typical 10 day sample of hydrographic obs for ECMWF global ocean analysis

18 Sea Surface Topography

19 z Cooper & Haines (1996) SSH ρ 1 ρ 2 ρ 3 ρ 4

20 z Cooper & Haines (1996) SSH ρ 1 ρ 2 PV conservation ρ 3 ρ 4

21 z Cooper & Haines (1996) Δp s SSH ρ 1 ρ 2 PV conservation ρ 3 ρ 4

22 z Cooper & Haines (1996) Δp s SSH ρ 1 Δh ρ 2 ρ 3 ρ 4 Δ h = g Δ p s ρ(0) ρ( H) ( )

23 The Ocean Control Vector

25 The Ocean Control Vector 4D-Var Cost function: J = J + J b o ( J ) ( J ) o vs time final o initial ROMS, California Current System, 4D-Var, 7 day cycles

26 Prior Error Covariance Modeling

27 Zonal Average Ocean Density Levitus (1982)

28 0m SEC NECC NEC Equatorial Pacific Temperature 100m 200m EUC NEC=N. Eq. Curr. SEC=S. Eq. Curr NECC=N. Eq. Counter Curr. EUC=Eq. Under Curr. 0m Observation 100m Diffusion eqn with a diffusion tensor. 200m 15S EQ 15N Weaver and Courtier (2001) (3D-Var & 4D-Var)

29 Complex Boundaries and Bathymetry Courtesy of Jim Cummings NRL, Monterey (3D-Var) Li et al (2008) (3D-Var)

30 Ocean Color

31 Ocean Tracers Diatoms Silicate Diatoms Silicate Silica test (skeleton) Simon and Bertino (2009) Interpolated Anamorphosis Functions

32 Initialization Shock

33 Initialization Shock ROMS + DARWIN, California Current Courtesy of Kaustubha Raghukumar (UCSC) NMI/DFI and coastally trapped waves?

34 Part II Some Recent Advances The Regional Ocean Modeling System (ROMS) Diagnostic calculations - Obs impact - (4D-Var) T - obs sensitivity - expected errors of functions - towards adaptive sampling

35 ROMS: California Current System (CCS) 4D-Var applied sequentially every 7 days: Jul 2002-Dec ROMS: PE, hydro, sigma 4D-Var: incremental, 1 outer, inner COAMPS forcing ECCO open b.c.s 10km, 42 levels (obs impact) 30 km, 30 levels (obs sensitivity) Veneziani et al (2009) Broquet et al (2009ab, 2011)

36 Observations (y) CalCOFI & GLOBEC EN3 SST & SSH ~90% TOPP Elephant Seals (APB) Ingleby and Huddleston (2007) ~10% ARGO Data from Dan Costa

37 Obs Impact vs Obs Sensitivity x = x + Kd a b x = x + K d a b 4D-Var Practical Gain matrix OR ( p p ),, a parameters m Obs impact: K T Obs sensitivity: ( K d ) T

38 Observation Impacts on Analysis Increments J = Δ J = 7day average transport Transport increment = (Posterior-Prior) 10km ROMS (Langland & Baker, 2004; Gelaro et al., 2007) ΔJ K T platform p= 1 ΔJ p N obs = ΔJ i= 1 i

39 Prior alongshore transport (CC+CUC+CJ) Poleward J 37N Prior cross-shore transport Equatorward Offshore J 500m Onshore

40 Analysis Cycle Observation Impacts 10km ROMS Alongshore transport Poleward ΔJ 37N Cross-shore transport Offshore Equatorward dof= tr{kg} >90% redundant ΔJ 500m Onshore rms (Moore et al, 2011c)

41 Alongshore Transport Impacts IGW Adjoint CTW (G T ) IGW IGW CTW (G) Gyre Circulation SSH Sv (10-5 )

42 Obs Impact vs Obs Sensitivity x = x + Kd a b x = x + K d a b 4D-Var Practical Gain matrix OR ( p p ),, a parameters m Obs impact: K T Obs sensitivity: ( K d ) T

43 Observation Sensitivity and Observing System Experiments (OSEs) Change in the obs: δ y ( K y) T yields the change in ΔJ (4D-Var) T For OSE, choose: ( H ( )) δ y = Wd= W y xb perts to obs innovation obs prior Diagonal matrix that selects obs to be withheld

44 Observing System Experiments (OSEs) Altimeter data withheld ΔAlongshore transport ΔJ 37N Direct computation of 4D-Var Observation sensitivity using ( K y ) T

45 Posterior Errors Posterior/analysis error covariance: E a ( I KG) B( I KG) T KRK T = + TL model Prior error covariance Obs error covariance Inspired by ensemble 4D-Var, we can show that: E a K K K K = I G B I G + R d d d d T T (4D-Var) T

46 Prior and Posterior Errors: 37N Transport J 37N Alongshore transport ( b σ ) 2 ( a ) 2 J σ ( a ) 2 J σ J Seldom directly observed! Using K instead of ( K d) T

47 The change in the analysis error variance in J(x a ) due to withholding obs: 2 OSEs and Analysis Errors Consider the linear function J(x a )=h T x a (e.g. transport). 2 ( a ) ( a ) T T σ = σ 2 ( ) J J K hbgw d h T Analysis error with obs withheld +2 + T T h K d GBG + R W K d h ( )( T ) ( ) T T h K d W GBG + R W K d h ( ) ( T ) ( ) Analysis error assimilating all observations?

48 OSEs and Analysis Errors Analysis error variance of 37N transport: 2 2 a Apparently there is a missing factor of 2 in( ) ( a σ σ ) J J

49 Summary Future Ocean DA is diverse and mature Many basic challenges still exist: - expansion of control vector (B?) - tracer assimilation - initialization shock & filtering - vertical projection of satellite obs - covariance models - biogeochemical data assimilation - model error - internal tides - quality control & bias correction - air-sea coupling at all scales Sub-mesoscale and deep ocean are poorly observed (and poorly constrained) Assessment of existing & new observing systems using OSEs and OSSEs High res. regional analyses Ensemble DA Continued development of ocean forecasting systems

50 Acknowledgements Hernan Arango Chris Edwards Gregoire Broquet Brian Powell Milena Veneziani James Doyle Dave Foley Anthony Weaver Mike Fisher Dan Costa Patrick Robinson Javier Zavala-Garay Office of Naval Research National Science Foundation National Ocean Partnership Program

Lecture 1: Primal 4D-Var

Lecture 1: Primal 4D-Var Outline ROMS 4D-Var overview 4D-Var concepts Primal formulation of 4D-Var Incremental approach used in ROMS The ROMS I4D-Var algorithm ROMS 4D-Var Priors f b, B f Ensemble 4D-Var