The Inverse Regional Ocean Modeling System

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. MillerScripps Institution of Oceanography

Chua B. and A. BennettOregon 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)

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

Ensemble Ocean Prediction

Stability Analysis Modules

ROMS Block Diagram NEW Developments

Arango et al. 2003Moore et al. 2003Di 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 Matrixµ TºR GPG

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 0-500mCurrents 0-150mSSH

Model Configuration:Open boundary cond.nested in CCS grid

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

SSH [m]

1st GUESS day=5

TRUE day=5

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=5

ASSIMILATION Results ERRORor

RESIDUALSSea Surface Temperature [C]

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

before assimilation

observation number

Normalized Observation-Model Misfit

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

TS

VU

after assimilation

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

observation number

SKILL = 1 – (SST RMS error)

daysassimilation 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

orRESIDUALS

Velocity (V)ASSIMILATION Results

1st GUESS day=5

AHV=4550AHT=4550

AHV=0AHT=0

AHV=4550AHT=1000

AHV=4550AHT=0

TANGENT LINEAR INSTABILITY SST[C]

TANGENT LINEAR INSTABILITY

TLMAHV=4550AHT=4550

TLMAHV=4550AHT=1000

TLMAHV=0AHT=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

…end

Vzeta

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 - dimensionalzeta =

81.303

temp =

88.112

salt =

97.177

u =

96.591

v =

95.9

TOTAL non-dimnensional=98%

Strong - dimensionalzeta =

84.374

var_red =

92.131

var_red =

94.522

var_red =

86.654

var_red =

88.683

TOTAL = 92%