weak constraint 4dvar in the r egional o cean m odeling s ystem ( roms ): development and...
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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%