ROMS/TOMS Tangent ROMS/TOMS Tangent Linear and Adjoint ModelsLinear and Adjoint Models

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

• In addition to IOM, provide the ocean In addition to IOM, provide the ocean modelling community with analysis modelling community with analysis and prediction tools available in and prediction tools 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: 0 0S t S

• 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)

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

• All boundary conditionsAll boundary conditions

• Orthogonal curvilinear gridsOrthogonal curvilinear grids

• All equations of stateAll equations of state

• Coriolis, pressure gradient, etc.Coriolis, pressure gradient, etc.

Picard Iteration Test (TL2):Picard Iteration Test (TL2):

11

2

3

4

5

1

2

3

4 5

• 6 month integration time

2~ ~ 1.5oR U L

• 50 Picard iterations

•

1

2

34 5

Available Drivers (TL1, AD)Available Drivers (TL1, AD)

• Singular vectors:Singular vectors:

andand• Eigenmodes of Eigenmodes of

• Forcing Singular vectors:Forcing Singular vectors:

• Stochastic Stochastic optimals: optimals:

• Pseudospectra: Pseudospectra: 1HI A I A

( ,0) (0, )TR t XR t

(0, )R t ( ,0)TR t

0 0

( , ) ( , )

T

R t dt X R t dt

| '|/ '

0 0

( , ) ( , ) 'ct t t Te R t XR t dt dt

Southern California Bight Southern California Bight (SCB)(SCB)• Model grid Model grid

1200kmX1000km1200kmX1000km

• 10km resolution, 10km resolution, 20 levels20 levels

• Di Lorenzo et al. Di Lorenzo et al. (2003)(2003)

SCB ExamplesSCB Examples

PseudospectrumPseudospectrum

Singular VectorsSingular Vectors

• Energy norm, 5 day growth timeEnergy norm, 5 day growth time

Confluence and diffluenceConfluence and diffluence

Boundary sensitivityBoundary sensitivity

Seasonal DependenceSeasonal Dependence

Stochastic OptimalsStochastic Optimals

Drivers under developmentDrivers under development

• Ensemble prediction (SVs, FSVs, SOs, Ensemble prediction (SVs, FSVs, SOs, following NWP)following NWP)

• 4D Variational Assimilation (4DVar)4D Variational Assimilation (4DVar)

• 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

Boundary sensitivityBoundary sensitivity

Stochastic OptimalsStochastic Optimals