Andy Moore Dept. of Ocean Sciences UC Santa Cruz

1. Assessing the Information Content and Impact of Observations on OceanCirculation Estimates using 4D-Var Andy Moore Dept. of Ocean Sciences UC Santa Cruz

2. Acknowledgements • Office of Naval Research • National Science Foundation • National Ocean Partnership Program • 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

3. Outline • ROMS 4D-Var • Information content of observations • Observation impacts • Predictability

4. ROMS 4D-Var (Moore et al, 2011a) http://myroms.org • Incremental (linearize about a prior) (Courtier et al, 1994) • Primal & dual formulations (Courtier 1997) • Primal – Incremental 4-Var (I4D-Var) • Dual – PSAS (4D-PSAS) & indirect representer (R4D-Var) (Da Silva et al, 1995; Egbert et al, 1994) • Strong and weak (dual only) constraint • Preconditioned, Lanczos formulation of conjugate gradient (Lorenc, 2003; Tshimanga et al, 2008; Fisher, 1997) • Diffusion operator model for prior covariances (Derber & Bouttier, 1999; Weaver & Courtier, 2001) • Multivariate balance for prior covariance (Weaver et al, 2005) • Adjoint of dual 4D-Var (obs impact, obs sensitivity, OSEs) (Langland and Baker, 2004; Gelaro et al, 2007) • Physical and ecosystem components • Parallel (MPI)

5. ROMS 4D-Var (Moore et al, 2011a) http://myroms.org • Incremental (linearize about a prior) (Courtier et al, 1994) • Primal & dual formulations (Courtier 1997) • Primal – Incremental 4-Var (I4D-Var) • Dual – PSAS (4D-PSAS) & indirect representer (R4D-Var) (Da Silva et al, 1995; Egbert et al, 1994) • Strong and weak (dual only) constraint • Preconditioned, Lanczos formulation of conjugate gradient(Lorenc, 2003; Tshimanga et al, 2008; Fisher, 1997) • Diffusion operator model for prior covariances (Derber & Bouttier, 1999; Weaver & Courtier, 2001) • Multivariate balance for prior covariance (Weaver et al, 2005) • Adjoint of dual 4D-Var (obs impact, obs sensitivity, OSEs) (Langland and Baker, 2004; Gelaro et al, 2007) • Physical and ecosystem components • Parallel (MPI)

6. Lanczos Factorization Cornelius Lanczos (1893-1974) A is the Hessian or stabilized representer matrix. m is the number of inner-loops

7. Mesoscale eddies The California Current

8. Conclusions Information content: • Much of the current observational data • is redundant (>90%). • In situ observations represent ~10% of • total obs, but often exert considerable impact • on the coastal circulation. • Satellite obs exert the largest control on • predictability of coastal circulation. Observation impact: Observation sensitivity & predictability:

9. fb(t), Bf bb(t), Bb xb(0), B Previous assimilation cycle ROMS: California Current System (CCS) 4D-Var applied sequentially every 7 days: Jul 2002-Dec 2004. COAMPS forcing ECCO open boundary conditions 3km, 10 km, 30km, 30 or 42 levels Veneziani et al (2009) Broquet et al (2009ab, 2011)

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

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

12. Sequential 4D-Var (2002-2004) Observations Observations Observations prior prior prior 4D-Var Analysis 4D-Var Analysis 4D-Var Analysis Posterior Posterior Posterior 7 days Forecast Forecast Forecast

13. Maximum Likelihood Estimate Circulation estimate from 4D-Var: Posterior Gain Obs operator Prior Obs Obs Cov Prior Cov TLM at obs points Prior hypotheses

14. Information Content of Obs Degrees of freedom of obs (dof): Cardinali et al, 2004; Desroziers et al., 2009 Bennett & McIntosh, 1982 Tr{KG}/Nobs vs assimilation cycle (courtesy of Lanczos vectors) upper & lower bounds 30km Only ~10% of obs contain independent info At 10km resolution, dof~1-2% of Nobs (Moore et al, 2011b)

15. Observation Impacts 7day average transport 10km ROMS Transport increment = (Posterior-Prior) (Langland & Baker, 2004; Gelaro et al., 2007) KT

16. Prior alongshore transport (CC+CUC+CJ) Poleward Equatorward Prior cross-shore transport Offshore Onshore

17. Analysis Cycle – Transport Increments Poleward Alongshore transport Tangent Linear Assumption Holds! Equatorward Offshore Cross-shore transport Onshore

18. rms Analysis Cycle – Observation Impacts 10km ROMS Poleward Alongshore transport Equatorward Cross-shore transport Offshore Onshore (Moore et al, 2011c)

19. IGW IGW Adjoint CTW (GT) Adjoint CTW (GT) IGW IGW CTW (G) CTW (G) IGW IGW Gyre Circulation Alongshore Transport Impacts Sv (10-5) SSH SST

20. Alongshore Transport Impacts Sv (10-3) Sv CTD Salinity Argo Salinity

21. Predictability 14 day forecast ensemble 4D-Var 7 day forecast ensemble time t0+14 t0 t0+7 Predictability due to assimilating observations during [t0,t0+7]: Obs Sensitivity using (4D-Var)T

22. Example: 37N Transport Predictability (Moore et al, 2011d) 30km ROMS implies 4D-Var increases predictability

23. Conclusions • Much of the current observational data • is redundant (>90%). • Caveat: Dependent on prior hypotheses. • In situ observations represent ~10% of • total obs, but often exert considerable impact • on the coastal circulation (transport). • Caveat: Dependent on prior hypotheses. • Recommendation: Decimate satellite data. • Satellite obs exert the largest control on • predictability coastal circulation (transport). • Caveat: Dependent on prior hypotheses.