The I nverse R egional O cean M odeling S ystem Development and Application to Variational Data Assimilation of Coastal Mesoscale Eddies. Di Lorenzo, E. Georgia Institute of Technology Moore, A. UC Santa Cruz Arango, H. Rutgers University Cornuelle, B and A.J. Miller Scripps Institution of Oceanography Chua B. and A. Bennett Oregon State University

Australia Asia USA Canada Pacific Model Grid SSHa (Feb. 1998) (source: modeling team Rutgers, UCLA, GaTech, Scripps) Regional Ocean Modeling System (ROMS)

Inverse Regional Ocean Modeling System (IROMS) Chua and Bennett (2001) Inverse Ocean Modeling System (IOMs) Moore et al. (2003) NL-ROMS, TL-ROMS, REP-ROMS, AD-ROMS To implement a representer-based generalized inverse method to solve weak constraint data assimilation problems a representer-based 4D-variational data assimilation system for high-resolution basin-wide and coastal oceanic flows Di Lorenzo et al. (2006)

Non Linear Model Tangent Linear Model Representer Model Adjoint Model Sensitivity Analysis Data Assimilation 1) Incremental 4DVAR Strong Constrain 2) Indirect Representer Weak and Strong Constrain Ensemble Ocean Prediction Stability Analysis Modules ROMS Block Diagram NEW Developments Arango et al Moore et al Di Lorenzo et al. 2006

Best Model Estimate (consistent with observations) Initial Guess ASSIMILATION Goal

STRONG Constraint WEAK Constraint (A)(B) …we want to find the corrections e Best Model Estimate (consistent with observations) Initial Guess ASSIMILATION Goal

Cost Function

4DVAR inversion Hessian Matrix Model x Model

4DVAR inversion IROMS representer-based inversion Hessian Matrix Stabilized Representer Matrix Representer Matrix Model x Model Obs x Obs Representer Coefficients

WEAK CONSTRAINT

TRUE Mesoscale Structure SSH [m] SST [C] ASSIMILATION Setup Sampling: (from CalCOFI program) 5 day cruise 80 km stations spacing Observations: T,S CTD cast 0-500m Currents 0-150m SSH Model Configuration: Open boundary cond. nested in CCS grid 20 km horiz. Resolution 20 vertical layers Forcing NCEP fluxes Climatology initial cond.

SSH [m] 1 st GUESS day=5 TRUE day=5

SSH [m] WEAK day=5 STRONG day=5 TRUE day=5 ASSIMILATION Results 1 st GUESS day=5

WEAK day=5 STRONG day=5 ASSIMILATION Results ERROR or RESIDUALS SSH [m] 1 st GUESS day=5

WEAK day=5 ASSIMILATION Results ERROR or RESIDUALS Sea Surface Temperature [C] 1 st GUESS day=5

WEAK day=0 STRONG day=0 TRUE day=0 Reconstructed Initial Conditions 1 st GUESS day=0

Normalized Observation-Model Misfit Assimilated data: TS 0-500m Free surface Currents 0-150m T S V U  before assimilation observation number

Normalized Observation-Model Misfit Assimilated data: TS 0-500m Free surface Currents 0-150m T S V U  after assimilation Error Variance Reduction STRONG Case = 92% WEAK Case = 98% observation number

SKILL = 1 – (SST RMS error) days assimilation window Initial Guess Climatology Persistence WEAK STRONG forecast

Subsurface Temperature Free Surface Height Salinity Velocity Persistence Initial Guess

Choosing climatology as the 1st guess leads to dynamically unbalanced fields, a strong initial shock, which degrades the quality of assimilated solution. Assimilating the data greatly improves the model trajectory for 10 days after the assimilation window when compared to the 1st guess. We should be able to exploit the long persistence timescale associated with the slow moving California Current eddies. A 5 day assimilation window may be too short to extract the time dependent dynamical information required to improve the model trajectory. Different definition of skill may be more appropriate to isolate the ability of the model to correct and predict the spatial structure of the eddies. Explore and characterize the dynamical sensitivities of the flow field, and the predictability timescales of the California Current. THOUGHTS on the SCB test

PROGRESS Developed and tested assimilation capability of ROMS for a realistic nested model setup (the California Current eddies ROMS can be used with IOM framework  IROMS

WEAK day=5 STRONG day=5 ERROR or RESIDUALS Velocity (V) ASSIMILATION Results 1 st GUESS day=5

A HV =4550 A HT =4550 A HV =0 A HT =0 A HV =4550 A HT =1000 A HV =4550 A HT =0 TANGENT LINEAR INSTABILITY SST [C]

TANGENT LINEAR INSTABILITY TLM A HV =4550 A HT =4550 TLM A HV =4550 A HT =1000 TLM A HV =0 A HT =0 Non Linear Model Initial Guess

PROGRESS Developed and tested assimilation capability of ROMS for a realistic nested model setup (the California Current eddies ROMS can be used with IOM framework  IROMS Tangent Linear Dynamics are very unstable in realistic settings. Need to find the “optimal” combination of increased viscosity/diffusivity and reduced physics to recover stability. Background and Model Error COVARIANCE functions are Gaussian and implemented through the use of the diffusion operator. We are implementing spatially dependent decorrelation length scales and additional dynamical constraint (e.g. geostrophy) PENDING TECHNICAL ASPECTS

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V zeta temp salt

WEAK day=0 WEAK day=5

WEAK day=5 STRONG day=5 CLIMA day=5 TRUE day=5

Velocity FULL

Weak Constraint Results

WEAK - dimensional zeta = temp = salt = u = v = 95.9 TOTAL non- dimnensional=98% Strong - dimensional zeta = var_red = var_red = var_red = var_red = TOTAL = 92%