ROMS/TOMS TL and ADJ ROMS/TOMS TL and ADJ Models: Models: Tools for Generalized Tools for Generalized Stability Analysis and Data Stability Analysis and Data Assimilation Assimilation Andrew Moore, CU Andrew Moore, CU Hernan Arango, Rutgers U Hernan Arango, Rutgers U Arthur Miller, Bruce Cornuelle, Arthur Miller, Bruce Cornuelle, Emanuele Di Lorenzo, Doug Neilson Emanuele Di Lorenzo, Doug Neilson UCSD UCSD
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ROMS/TOMS TL and ADJ Models: Tools for Generalized Stability Analysis and Data Assimilation
ROMS/TOMS TL and ADJ Models: Tools for Generalized Stability Analysis and Data Assimilation. Andrew Moore, CU Hernan Arango, Rutgers U Arthur Miller, Bruce Cornuelle, Emanuele Di Lorenzo, Doug Neilson UCSD. Major Objective. - PowerPoint PPT Presentation
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ROMS/TOMS TL and ADJ Models:ROMS/TOMS TL and ADJ Models:Tools for Generalized Stability Tools for Generalized Stability Analysis and Data AssimilationAnalysis and Data Assimilation
Andrew Moore, CUAndrew Moore, CUHernan Arango, Rutgers UHernan Arango, Rutgers U
Arthur Miller, Bruce Cornuelle, Arthur Miller, Bruce Cornuelle, Emanuele Di Lorenzo, Doug Neilson Emanuele Di Lorenzo, Doug Neilson
UCSDUCSD
Major ObjectiveMajor Objective
• To provide the ocean modeling To provide the ocean modeling community with analysis and community with analysis and prediction tools that are available in prediction tools that are available in meteorology and NWP, using a meteorology and NWP, using a community OGCM (ROMS).community OGCM (ROMS).
OverviewOverview
• NL ROMS: NL ROMS: 0 0S t S
• Perturbation: Perturbation: 0S S s
OverviewOverview
• NL ROMS:NL ROMS:
• TL ROMS:TL ROMS: 0
|Ss t S s As
• AD ROMS:AD ROMS: † †Ts t A s
( ) (0, ) (0)s t R t s
† †(0) ( ,0) ( )Ts R t s t
(TL1)
(AD)
0 0S t S
OverviewOverview
• Second TLM: Second TLM:
0 0( ) ( )S t S A S S (TL2)
• TL1= Representer ModelTL1= Representer Model
• TL2= Tangent Linear Model TL2= Tangent Linear Model
Current Status of TL and ADCurrent Status of TL and AD
• All advection schemesAll advection schemes
• Most mixing and diffusion schemesMost mixing and diffusion schemes
• Dynamics/sensitivity/stability of flow Dynamics/sensitivity/stability of flow to naturally occurring perturbationsto naturally occurring perturbations
• Dynamics/sensitivity/stability due to Dynamics/sensitivity/stability due to error or uncertainties in forecast error or uncertainties in forecast systemsystem
Transport Singular VectorTransport Singular Vector
North East North AtlanticNorth East North Atlantic
• 10 km resolution10 km resolution
• 30 levels in vertical30 levels in vertical
• Embedded in a model of N. AtlanticEmbedded in a model of N. Atlantic
• Wilkin, Arango and HaidvogelWilkin, Arango and Haidvogel
SSTSV t=0
SV t=5
SummarySummary
• Eigenmodes: natural modes of Eigenmodes: natural modes of variabilityvariability
• Adjoint eigenmodes: optimal Adjoint eigenmodes: optimal excitations for eigenmodesexcitations for eigenmodes
• Pseudospectra: response of system to Pseudospectra: response of system to forcing at different freqs, and forcing at different freqs, and reliability of eigenmode calculationsreliability of eigenmode calculations
• Initial conditions: Initial conditions: (0)S I i
• Observations: Observations: d H S • For simplicity, assume error-free b.c.sFor simplicity, assume error-free b.c.s
• Cost func:Cost func: 1 1 1Tf iJ f C f i C i C
• Minimize J using indirect representer methodMinimize J using indirect representer method
• (Egbert et al., 1994; Bennett et al, 1997)(Egbert et al., 1994; Bennett et al, 1997)
( ) ( )S t S F t f t
OSU Inverse Ocean Model OSU Inverse Ocean Model System (IOM)System (IOM)
• Chua and Bennett (2001)Chua and Bennett (2001)
• Provides interface for TL1, TL2 and Provides interface for TL1, TL2 and AD for minimizing J using indirect AD for minimizing J using indirect representer methodrepresenter method
• Initial cond: Initial cond: (0)FS I• Outer loop, n Outer loop, n
1 1 1( ) ( ) ( )n n n n nF FS t S A S S F t
TL2• Inner loop, m Inner loop, m
AD† ( ) 0ms T † 1 † ;n T T nm m ms t A s H
1 † ;nm m f ms t A s C s †(0) (0)m i ms C s TL1
1T n T n
m m FH s C d H S
1 1 1 †( ) ( ) ( )n n n n nf mS t S A S S F t C s TL2†(0) (0)n
• Greens function assimilationGreens function assimilation
• IOM interface (IROMS) (NL, TL1, TL2, IOM interface (IROMS) (NL, TL1, TL2, AD)AD)
PublicationsPublications
• Moore, A.M., H.G Arango, E. Di Lorenzo, B.D. Moore, A.M., H.G Arango, E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. Neilson, 2003:Cornuelle, A.J. Miller and D. Neilson, 2003: A A comprehensive ocean prediction and analysis comprehensive ocean prediction and analysis system based on the tangent linear and adjoint of system based on the tangent linear and adjoint of a regional ocean modela regional ocean model. . Ocean Modelling,Ocean Modelling, Final Final revisions.revisions.
• H.G Arango, Moore, A.M., E. Di Lorenzo, B.D. H.G Arango, Moore, A.M., E. Di Lorenzo, B.D. Cornuelle, A.J. Miller and D. Neilson, 2003:Cornuelle, A.J. Miller and D. Neilson, 2003: The The ROMS tangent linear and adjoint models: A ROMS tangent linear and adjoint models: A comprehensive ocean prediction and analysis comprehensive ocean prediction and analysis system. system. Rutgers Tech. Report, Rutgers Tech. Report, In preparation.In preparation.
What next?What next?
• Complete 4DVar driverComplete 4DVar driver
• Interface barotropic ROMS to IOMInterface barotropic ROMS to IOM
• Complete 3D Picard iteration test Complete 3D Picard iteration test (TL2)(TL2)
• Interface 3D ROMS to IOMInterface 3D ROMS to IOM
SCB ExamplesSCB Examples
Confluence and diffluenceConfluence and diffluence