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Prediction of Ocean Circulation in the Gulf of Mexico and Caribbean Sea An application of the ROMS/TOMS Data Assimilation Models Hernan G. Arango (IMCS,

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Presentation on theme: "Prediction of Ocean Circulation in the Gulf of Mexico and Caribbean Sea An application of the ROMS/TOMS Data Assimilation Models Hernan G. Arango (IMCS,"— Presentation transcript:

1 Prediction of Ocean Circulation in the Gulf of Mexico and Caribbean Sea An application of the ROMS/TOMS Data Assimilation Models Hernan G. Arango (IMCS, Rutgers University) Emanuele Di Lorenzo (Georgia Institute of Technology) Arthur J. Miller, Bruce D. Cornuelle (Scripps Institute of Oceanography, UCSD) (Scripps Institute of Oceanography, UCSD) Andrew M. Moore (PAOS, Colorado University)

2 Gulf of Mexico and Caribbean Seas plus satellite data (SSH, SST) and radar Ocean Observations

3 ROMS/TOMS Ocean Modeling Framework

4 Gulf of Mexico Ocean Model Grid Ocean Modeling of North Atlantic

5 Ocean Model Surface Currents and Sea Level

6 Ocean Modeling Applications in Develop a real-time data assimilation and prediction system for the Gulf of Mexico and Caribbean Seas based on a continuous upper ocean monitoring systemDevelop a real-time data assimilation and prediction system for the Gulf of Mexico and Caribbean Seas based on a continuous upper ocean monitoring system Demonstrate the utility of variational data assimilation in a real-time, sea-going environmentDemonstrate the utility of variational data assimilation in a real-time, sea-going environment Demonstrate the value of collecting routine ocean observations from specially equipped ocean vessels (Explorer of the Seas)Demonstrate the value of collecting routine ocean observations from specially equipped ocean vessels (Explorer of the Seas) Develop much needed experience in both the assimilation of disparate ocean data and ocean prediction in regional ocean models.Develop much needed experience in both the assimilation of disparate ocean data and ocean prediction in regional ocean models. Add platform oceanic measurements (a possibility)Add platform oceanic measurements (a possibility) Gulf of Mexico and Caribbean Seas

7 Ensemble Prediction For an appropriate forecast skill measure, s

8 Example from the Caribbean model run, of sensitivity of the transport through the Yucatan Strait given a particular realization of the circulation. In this case the maximum transport at time t N, indicated by the strong gradients in sea surface height (SSH), is sensitive to a pattern of Kelvin waves at previous time t 0. These types of sensitivity, computed using the non-linear and Adjoint models of ROMS, will be applied for the Florida Strait to explore how different topographic shapes affect the transport during different circulation regimes. Ocean Adjoint Modeling Applications

9 4D Variational Data Assimilation Platforms (4DVAR) Strong Constraint (S4DVAR) drivers: Strong Constraint (S4DVAR) drivers:  Conventional S4DVAR: outer loop, NLM, ADM  Incremental S4DVAR: inner and outer loops, NLM, TLM, ADM (Courtier et al., 1994)  Efficient Incremental S4DVAR (Weaver et al., 2003) Weak Constraint (W4DVAR) - IOM Weak Constraint (W4DVAR) - IOM  Indirect Representer Method: inner and outer loops, NLM, TLM, RPM, ADM (Egbert et al., 1994; Bennett et al, 1997)

10 Strong Constraint 4DVAR from IOM (Di Lorenzo et al., 2005)

11 Normalized Misfit Datum Assimilated data: TS 0-500m Free surface Currents 0-150m Strong Constraint 1 st Guess True Synthetic Data SST T S VU  Weak Constraint Strong and Weak Constraint 4DVAR (Southern California Bight) 0-500 m data CalCOFI Sampling grid Annual Climatology

12 Given the model state vector: Given the model state vector: Consider a Yucatan Strait transport index,, defined in terms of space and/or time integrals of : Consider a Yucatan Strait transport index,, defined in terms of space and/or time integrals of : Small changes in will lead to changes in where: Small changes in will lead to changes in where: We will define sensitivity as etc. We will define sensitivity as etc. Adjoint Sensitivity + …

13 Publications Arango, H.G., Moore, A.M., E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. Neilson, 2003: The ROMS Tangent Linear and Adjoint Models: A comprehensive ocean prediction and analysis system, Rutgers Tech. Report. http://marine.rutgers.edu/po/Papers/roms_adjoint.pdf http://marine.rutgers.edu/po/Papers/roms_adjoint.pdfhttp://marine.rutgers.edu/po/Papers/roms_adjoint.pdf Di Lorenzo, E., A.M. Moore, H.G. Arango, B. Chua, B.D. Cornuelle, A.J. Miller and A. Bennett, 2005: The Inverse Regional Ocean Modeling System: Development and Application to Data Assimilation of Coastal Mesoscale Eddies, Ocean Modelling, In preparation. Moore, A.M., H.G Arango, E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. 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. http://marine.rutgers.edu/po/Papers/Moore_2004_om.pdf http://marine.rutgers.edu/po/Papers/Moore_2004_om.pdfhttp://marine.rutgers.edu/po/Papers/Moore_2004_om.pdf Moore, A.M., E. Di Lorenzo, H.G. Arango, C.V. Lewis, T.M. Powell, A.J. Miller and B.D. Cornuelle, 2005: An Adjoint Sensitivity Analysis of the Southern California Current Circulation and Ecosystem, J. Phys. Oceanogr., In preparation. Wilkin, J.L., H.G. Arango, D.B. Haidvogel, C.S. Lichtenwalner, S.M.Durski, and K.S. Hedstrom, 2005: A Regional Modeling System for the Long-term Ecosystem Observatory, J. Geophys. Res., 110, C06S91, doi:10.1029/2003JCC002218. http://marine.rutgers.edu/po/Papers/Wilkin_2005_jgr.pdf http://marine.rutgers.edu/po/Papers/Wilkin_2005_jgr.pdfhttp://marine.rutgers.edu/po/Papers/Wilkin_2005_jgr.pdf Warner, J.C., C.R. Sherwood, H.G. Arango, and R.P. Signell, 2005: Performance of Four Turbulence Closure Methods Implemented Using a Generic Length Scale Method, Ocean Modelling, 8, 81-113. http://marine.rutgers.edu/po/Papers/Warner_2004_om.pdf http://marine.rutgers.edu/po/Papers/Warner_2004_om.pdfhttp://marine.rutgers.edu/po/Papers/Warner_2004_om.pdf

14 Background Material

15 Overview Let’s represent NLM ROMS as:Let’s represent NLM ROMS as: The TLM ROMS is derived by considering a small perturbation s to S. A first-order Taylor expansion yields:The TLM ROMS is derived by considering a small perturbation s to S. A first-order Taylor expansion yields: A is real, non-symmetric Propagator Matrix The ADM ROMS is derived by taking the inner-product with an arbitrary vector, where the inner-product defines an appropriate norm (L2-norm):The ADM ROMS is derived by taking the inner-product with an arbitrary vector, where the inner-product defines an appropriate norm (L2-norm):

16 Tangent Linear and Adjoint Based GST Drivers Singular vectors: Singular vectors: Forcing Singular vectors: Forcing Singular vectors: Stochastic optimals: Stochastic optimals: Pseudospectra: Pseudospectra: and Eigenmodes of Eigenmodes of

17 Two Interpretations Dynamics/sensitivity/stability of flow to naturally occurring perturbations Dynamics/sensitivity/stability of flow to naturally occurring perturbations Dynamics/sensitivity/stability due to error or uncertainties in the forecast system Dynamics/sensitivity/stability due to error or uncertainties in the forecast system Practical applications: Practical applications:  Ensemble prediction  Adaptive observations  Array design...

18 GSA on the Southern California Bight (SCB) Free-SurfaceSST and Surface currents

19 Eigenmodes SCB coastally trapped waves TLM eigenvectors (A): normal modes TLM eigenvectors (A): normal modes ADM eigenvectors (A T ): optimal excitations ADM eigenvectors (A T ): optimal excitations Real PartImag Part

20 diffluence Optimal Perturbations A measurement of the fastest growing of all possible perturbations over a given time intervalA measurement of the fastest growing of all possible perturbations over a given time interval SCB maximum growth of perturbation energy over 5 days confluence

21 Stochastic Optimals Provide information about the influence of stochastic variations (biases) in ocean forcing SCB patterns of stochastic forcing that maximizes the perturbation energy variance for 5 days

22 Open Boundary Sensitivity: errors growth quickly and appear to propagate through the model domain as coastally trapped waves. Singular Vectors

23 Ensemble Prediction Optimal perturbations / singular vectors and stochastic optimal can also be used to generate ensemble forecasts.Optimal perturbations / singular vectors and stochastic optimal can also be used to generate ensemble forecasts. Perturbing the system along the most unstable directions of the state space yields information about the first and second moments of the probability density function (PDF):Perturbing the system along the most unstable directions of the state space yields information about the first and second moments of the probability density function (PDF):  ensemble mean  ensemble spread Adjoint based perturbations excite the full spectrumAdjoint based perturbations excite the full spectrum

24 Data Assimilation Overview Cost Function: Cost Function: wheremodel,background,observations, background error covariance, inverse background error covariance, inverse observations error covariance Model solution depends on initial conditions ( ), boundary conditions, and model parameters Model solution depends on initial conditions ( ), boundary conditions, and model parameters Minimize J to produce a best fit between model and observations by adjusting initial conditions, and/or boundary conditions, and/or model parameters. Minimize J to produce a best fit between model and observations by adjusting initial conditions, and/or boundary conditions, and/or model parameters.

25 Minimization Perfect model constrained minimization (Lagrange function): Perfect model constrained minimization (Lagrange function): We require the minimum of at which:,,,,,, yielding A T is the transpose of A, often called the adjoint operator. It can be shown that:A T is the transpose of A, often called the adjoint operator. It can be shown that: The adjoint equation solution provides gradient information

26 4D Variational Data Assimilation Platforms (4DVAR) Strong Constraint (S4DVAR) drivers: Strong Constraint (S4DVAR) drivers:  Conventional S4DVAR: outer loop, NLM, ADM  Incremental S4DVAR: inner and outer loops, NLM, TLM, ADM (Courtier et al., 1994)  Efficient Incremental S4DVAR (Weaver et al., 2003) Weak Constraint (W4DVAR) - IOM Weak Constraint (W4DVAR) - IOM  Indirect Representer Method: inner and outer loops, NLM, TLM, RPM, ADM (Egbert et al., 1994; Bennett et al, 1997) RP:

27 Forward and Adjoint MPI Communications Forward Adjoint

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