Hernan G. Arango

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ROMS/TOMS StatusAlgorithms, Adjoint and
Applications

• Hernan G. Arango
• Institute of Marine and Coastal Sciences
• Rutgers University

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Collaborators
Hernan G. Arango IMCS, Rutgers
Alexander F. Shchepetkin IGPP, UCLA
Bruce D. Cornuelle SIO, UCSD
Arthur J. Miller SIO, UCSD
Emanuele Di Lorenzo Georgia Tech
Andrew M. Moore PAOS, U. Colorado
Meinte Blaas Delft Hydraulics
Christopher R. Sherwood USGS, WHOI
Richard P. Signell USGS, WHOI
John C. Warner USGS, WHOI
W. Paul Bissett FERI
Katja Fennel IMCS, Rutgers
Hartmut Frenzel IGPP, UCLA
Kate S. Hedstrom ARCS/UAF
Mark G. Hadfield NIWA
John L. Wilkin IMCS, Rutgers
W. Paul Budgell IMR, Norway
Xavier J. Capet IGPP, UCLA
Pierrick Penven U. of Cape Town
Yuliya Kanarska IGPP, UCLA
Patrick Marchesiello IRD, Bretagne
Yusuke Uchiyama IGPP, UCLA
David Robertson IMCS, Rutgers
Tal Ezer Princeton U.
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Long-Term Goals

• To design, develop, and test an expert ocean
  modeling system for high-resolution scientific
  and operational applications over a wide range of
  scales from estuaries to regional to global.
• To improve US Navy ocean modeling capabilities
  for re-locatable, coastal, atmosphere-ocean
  prediction.
• To provide the ocean modeling community with
  analysis and prediction tools that are available
  in meteorology and Numerical Weather Prediction
  (NWP) .

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Objectives

• To explore the factors that limit the
  predictability of the circulation in regional
  models in a variety of dynamical regimes.
• To build 4D variational assimilation platforms
  strong and weak constraint 4DVAR.
• To build a Generalized Stability Theory (GST)
  analysis platforms eigenmodes, EOFs, optimal
  perturbations, forcing singular vectors,
  stochastic optimals, pseudospectra.
• To build an ensemble prediction platform by
  perturbing forcing, initial, and boundary
  conditions with GST singular vectors.

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ROMS/TOMS Framework
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Accomplishments

• ROMS/TOMS version 2.2 released to full user
  community and version 3.0 released beta testers
  on May 26, 2005. Currently, ROMS and TOMS are
  identical.
• Rewrote tangent linear (TLM), representer (RPM)
  and adjoint (ADM) models in Fortran 90 to improve
  the efficiency and multiple levels of nesting.
• Parallelized TLM, RPM and ADM.
• Designed a single makefile structure to
  facilitate compiling in any computer architecture

477 files, 340514 lines of code, 1093905 words,
13440936 characters

• Continued to develop web-based documentation

http//www.ocean-modeling.org/ http//marine.rutge
rs.edu/po/models/roms/index.php
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New Capabilities

• Dynamic-thermodynamic Sea-Ice model using
  elastic-viscous-plastic rheology (Budgell,
  Hedstrom, Curchitser)
• Updated COARE bulk parameterization (Hedstrom)
• Boundary layer salt flux, E-P (Goodman)
• Craig and Banner wave breaking surface flux
  (Warner)
• Scott Doneys biological model (Fennel)
• Positive definite tracer advection (Warner)
• Wetting and drying capabilities (Warner)
• Near-shore radiation stresses (Warner)

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Wetting and Drying
Suisun Bay, Northern San Francisco Bay, CA
To Sacramento
To Golden Gate
(Warner)
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Radiation Stresses

• Nearshore radiation stress terms as derived by
  Mellor (JPO, 2003) have been implemented into the
  momentum equations and the diagnostics.
  Algorithms are currently being tested.

• Coupling of ROMS to SWAN using the MCT is near
  completion. This will enhance existing coupling
  capabilities.

(Warner)
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4D Variational Data Assimilation Platforms (4DVAR)

• 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
• Indirect Representer Method inner and outer
  loops, NLM, TLM, RPM, ADM (Egbert et al., 1994
  Bennett et al, 1997)

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Strong Constraint 4DVAR from IOM
(Di Lorenzo et al., 2005)
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Strong and Weak Constraint 4DVAR
(Southern California Bight)
Normalized Misfit
Datum
0-500 m data
CalCOFI Sampling grid
Annual Climatology
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Intra-Americas Seas (IAS) Applications
(Moore, Milliff, Arango)

• Develop a real-time data assimilation and
  prediction system for the IAS based on a
  continuous upper ocean monitoring system
• Demonstrate 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)
• Develop much needed experience in both the
  assimilation of disparate ocean data and ocean
  prediction in regional ocean models.

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Intra-Americas Seas Observation Types
plus satellite data (SSH, SST) and radar
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Intra-Americas Sea (IAS) Application

• Climatological heat fluxes, daily NCEP winds
• NATL boundary conditions

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Adjoint Sensitivity

• Given the model state vector
• 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
• We will define sensitivity as
  etc.

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Sensitivity of Yucatan Transport to Perturbations
in Free-Surface
5 days
15 days
20 days
25 days
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Intra-Americas Sea Optimal Pertubations
Initial
Final
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Final Remarks

• Are we closer to operational weather prediction
  systems?
• Maintenance of TLM, RPM, and ADM models.
• At early stages, the perturbations and forecast
  error are linear. Therefore, the GST tools are
  powerful to study such systems.
• The presence of open boundary conditions
  represents a considerable technical challenge for
  GST and 4DVAR applications.
• Linearization of physics.
• Modeling background error covariance.
• Training and documentation.
• 2005 ROMS/TOMS Workshop Adjoint Modeling and
  Applications, Scripps Institution of
  Oceanography, La Jolla, October 24-26, 2005.

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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_a
  djoint.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
• 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, doi10.1029/2003JCC002218.
• http//marine.rutgers.edu/po/Papers/Wilki
  n_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

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Background Material
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Overview
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Tangent Linear and Adjoint Based GST Drivers

• Singular vectors

• Forcing Singular vectors

• Stochastic optimals

• Pseudospectra

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Two Interpretations

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

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GSA on the Southern California Bight (SCB)
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Eigenmodes
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diffluence
Optimal Perturbations

• A measurement of the fastest growing of all
  possible perturbations over a given time interval

confluence
SCB maximum growth of perturbation energy over 5
days
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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
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Open Boundary Sensitivity errors growth quickly
and appear to propagate through the model domain
as coastally trapped waves.
Singular Vectors
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Ensemble Prediction

• 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)
• ensemble mean
• ensemble spread
• Adjoint based perturbations excite the full
  spectrum

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Ensemble Prediction
For an appropriate forecast skill measure, s
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Data Assimilation Overview

• Cost Function

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Minimization

• Perfect model constrained minimization (Lagrange
  function)

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4D Variational Data Assimilation Platforms (4DVAR)

• 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
• Indirect Representer Method inner and outer
  loops, NLM, TLM, RPM, ADM (Egbert et al., 1994
  Bennett et al, 1997)

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Forward and Adjoint MPI Communications
(with respect to TILE R)
Forward
Adjoint