Weak Constraint 4DVAR in the R egional O cean M odeling S ystem ( ROMS ): Development and application for a baroclinic coastal upwelling system Di Lorenzo, E. Georgia Institute of Technology Arango, H. Rutgers University Moore, A. and Powell B. UC Santa Cruz Cornuelle, B and A.J. Miller Scripps Institution of Oceanography

Australia Asia USA Canada Pacific Model Grid SSHa (Feb. 1998) Regional Ocean Modeling System (ROMS)

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 3) PSAS Ensemble Ocean Prediction Stability Analysis Modules ROMS Block Diagram NEW Developments Arango et al Moore et al Di Lorenzo et al. 2006

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

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

Coastal Baroclinic Upwelling System Model Setup and Sampling Array section

An example of Representer Functions for the Upwelling System Computed using the TL-ROMS and AD-ROMS

Comparison of the IOM assimilation solutions with TRUE and BACKGROUND Coastal Baroclinic Upwelling System Model Setup

Comparison of SKILL score of IOM assimilation solutions with independent observations HIRES: High resolution sampling array COARSE: Spatially and temporally aliased sampling array

RP-ROMS with CLIMATOLOGY as BASIC STATE RP-ROMS with TRUE as BASIC STATE RP-ROMS WEAK constraint solution Instability of the Representer Tangent Linear Model (RP-ROMS) SKILL SCORE

Replacing the RP-ROMS with NL-ROMS in the outer loop

PROGRESS Developed and tested weak constraint 4DVAR in ROMS The system is able t`o initialize the forecast extracting dynamical information from the observations. PENDING ISSUES Tangent Linear Dynamics are unstable in realistic settings. Background and Model Error COVARIANCE functions are Gaussian and implemented through the use of the diffusion operator. Preconditioning Posterior Statistics

Arango, H., A. M. Moore, E. Di Lorenzo, B. D. Cornuelle, A. J. Miller, and D. J. Neilson, 2003: The ROMS tangent linear and adjoint models: A comprehensive ocean prediction and analysis system. IMCS, Rutgers Tech. Reports. Moore, A. M., H. G. Arango, E. Di Lorenzo, B. D. Cornuelle, A. J. Miller, and D. J. Neilson, 2004: A comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of a regional ocean model. Ocean Modelling, 7, Di Lorenzo, E., A. M. Moore, H. G. Arango, B. D. Cornuelle, A. J. Miller, R. D. Powell, B. S. Chua, and A. F. Bennett, 2006: Weak and Strong Constraint Data Assimilation in the inverse Regional Ocean Modeling System (ROMS): development and application to a baroclinic coastal upwelling system. Ocean Modelling, in press. References

Application of IOM in realistic settings: 1)California Current System: produce a long term reanalysis of the CalCOFI Hydrography from )Intra American Seas: implement a real time forecasting system

TRUE Mesoscale Structure SSH [m] SST [C] ASSIMILATION Setup California Current 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] 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=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  observation number Error Variance Reduction STRONG Case = 92% WEAK Case = 98%