Weak Constraint 4DVAR in the Regional Ocean Modeling System (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. MillerScripps Institution of Oceanography

Australia

Asia

USA

Canada

Pacific Model Grid SSHa

(Feb. 1998)

Regional Ocean Modeling System (ROMS)

OCEAN INIT IALIZE

FINALIZE

RUN

S4DVAR_OCEAN

IS4DVAR_OCEAN

W4DVAR_OCEAN

ENSEMBLE_OCEAN

NL_OCEAN

TL_OCEAN

AD_OCEAN

PROPAGATOR

KERNELNLM, TLM, RPM, ADM

physicsbiogeochemicalsedimentsea ice

Optimal pertubations

ADM eigenmodes

TLM eigenmodes

Forcing singular vectors

Stochastic optimals

Pseudospectra

ADSEN_OCEAN

SANITY CHECK S

PERT_OCEAN

PICARD_OCEAN

GRAD_OCEAN

TLCHECK _OCEAN

RP_OCEAN

ESMF

AIR_OCEAN

MASTER

ean M ode

earch C o m

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. 2003Moore et al. 2003Di 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 Setupand 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 BACKGROUNDCoastal 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, 227-258.

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 1950-2006

2) Intra American Seas: implement a real time forecasting system

TRUE Mesoscale Structure

SSH[m]

SST[C]

ASSIMILATION SetupCalifornia Current

Sampling:(from CalCOFI program)5 day cruise 80 km stations spacing

Observations:T,S CTD cast 0-500mCurrents 0-150mSSH

Model Configuration:Open boundary cond.nested in CCS grid

20 km horiz. Resolution20 vertical layersForcing NCEP fluxesClimatology initial cond.

SSH [m]

WEAK day=5

STRONG day=5

TRUE day=5

ASSIMILATION Results

1st GUESS day=5

WEAK day=5

STRONG day=5

ASSIMILATION Results

ERRORor

RESIDUALS

SSH [m]

1st GUESS day=5

WEAK day=0

STRONG day=0

TRUE day=0

Reconstructed Initial Conditions

1st GUESS day=0

Normalized Observation-Model Misfit

Assimilated data:TS 0-500m Free surface Currents 0-150m

TS

VU

observation number

Error Variance ReductionSTRONG Case = 92%WEAK Case = 98%