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

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

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

Data Assimilation b b (t), B b f b (t), B f x b (0), B ROMS Prior Observations + h(t), Q Posterior Circulation 4D-Var (4-dimensional variational method) (Minimum variance estimate)

ROMS 4D-Var 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) (Moore et al, 2011a)

ROMS 4D-Var 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) (Moore et al, 2011a)

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

The California Current Mesoscale eddies

Conclusions 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. Information content: Observation impact: Observation sensitivity & predictability:

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

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

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

Observations 4D-Var Analysis Posterior Observations 4D-Var Analysis Posterior Observations 4D-Var Analysis Posterior prior Sequential 4D-Var ( ) 7 days Forecast

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

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

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

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

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

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

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

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

time t0t0 t Predictability t 0 +7 Predictability due to assimilating observations during [t 0,t 0 +7]: 4D-Var 14 day forecast ensemble 7 day forecast ensemble Obs Sensitivity using (4D-Var) T

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

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.