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

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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

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

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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)

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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)

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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)

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

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The California Current Mesoscale eddies

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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:

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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.

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

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

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

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

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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)

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

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

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

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

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

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

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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

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

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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.

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