Generalized vertical Coordinate Ocean Generalized vertical Coordinate Ocean ModelModel

for Multi-Scale, Non-Boussinesq or Boussinesq Applicationsfor Multi-Scale, Non-Boussinesq or Boussinesq Applications

Y. Tony Song Y. Tony Song Jet Propulsion Laboratory, California Institute of Jet Propulsion Laboratory, California Institute of

TechnologyTechnology

Sponsored by NASA and ONR

MotivationMotivation• How may ocean How may ocean

models do we have?models do we have?

• A lot; they differ simply A lot; they differ simply by their coordinate by their coordinate formulation.formulation.

• All of them solve the All of them solve the same ocean equationssame ocean equations

Generalized vertical Coordinate Equations

zz BH

Understanding/predicting ocean dynamics Understanding/predicting ocean dynamics needs both observations and modelsneeds both observations and models

• Satellite observationsSatellite observations give synoptic view give synoptic view of the global oceanof the global ocean

• Based on remote Based on remote sensing technologysensing technology

• With amazing With amazing accuracyaccuracy

• Ocean modelsOcean models give 3-dimensional give 3-dimensional structure of the oceanstructure of the ocean

• Based on computer Based on computer technologytechnology

• With possible errors With possible errors (inconsistent with (inconsistent with satellite measurements)satellite measurements)

Problems:Problems:

• T/P & Jason provide SSH, representing T/P & Jason provide SSH, representing volume changes (volume changes (heat expansionheat expansion), but ), but most models are incompressible most models are incompressible (Boussinesq).(Boussinesq).

• GRACE measures ocean bottom GRACE measures ocean bottom pressure, representing water pressure, representing water mass mass changes, changes, but most models are not mass but most models are not mass conserving.conserving.

Model Errors:Model Errors:

1.1. Numerical Error:Numerical Error: Conventional single-coordinate model Conventional single-coordinate model has difficulties to represent multi-scale has difficulties to represent multi-scale ocean dynamics & topography ocean dynamics & topography accurately.accurately.

2.2. Representation Error:Representation Error:Boussinesq approximations do not Boussinesq approximations do not represent real ocean physics (e.g. heat represent real ocean physics (e.g. heat expansion & freshwater flux) and is expansion & freshwater flux) and is inconsistent with T/P and GRACE data.inconsistent with T/P and GRACE data.

Reduce representation errors Reduce representation errors by by non-Boussinesqnon-Boussinesq formulationformulation

Reduce numerical errors by the generalized

coordinate

The New Model Configuration

SCRUM (Song&Haidvogel

1994)

Non-Boussinesq

ROMS

(Song 2002)

GCOM

Two analytical s/sp—coordinate systems

shallow deep

5000m

10mh

S-coordinate (Song&Haidvogel 1994):

Sp-coordinate (Song 2002):

)()()()1( 0' sCppsppspp cbcbs

)()()1( sChHshsz cc

Z-levels

S-levels BBL

SBL

Default Model Structure•All-in-one capability in general coordinate All-in-one capability in general coordinate systemsystem

•Truly compressible ocean model (Truly compressible ocean model (non-non-BoussinesqBoussinesq))

Flexible for coupling

Open Ocean

Hz—depth metricBz—Boussinesq

factor

Heat expansion /contractio

n

Sea Surface

JPL Compressible Ocean Model

GRACE

• Topography-following & non-Boussenesq

• Consistent with GRACE and T/P observations

Bottom

TOPEX

H L

Study 1. Bottom Pressure Waves Detected in Tropical Pacific (Song & Zlotnicki, GRL 2003)

Tropical Instability Eddy

Thermocline

Bottom Pressure Waves

More comparison with T/P dataMore comparison with T/P data

Study 2. Simulating ENSO with non-Boussinesq/Boussinesq

0.5°C Difference

due to Boussines

q

Simulated almost all the ENSO

events

Study 3. Multi-Scale Modeling System for Coastal Oceans

Basin-scale 50-km in p-coordinate

Regional scale 10-km in z-

Coastal scale 1-km

Coastal can not be cut off from open ocean, therefore multi-scale modeling capability is needed

Ocean color

SummarySummary• A new model with combined topography-A new model with combined topography-

following and non-Boussineq features is following and non-Boussineq features is developed for better representing T/P & developed for better representing T/P & GRACE data.GRACE data.

• Using the new model, we detected ocean Using the new model, we detected ocean bottom pressure waves in Tropical Pacific.bottom pressure waves in Tropical Pacific.

• We have also developed a multi-scale We have also developed a multi-scale coastal ocean modeling system for the coastal ocean modeling system for the coastal region off Southern California & coastal region off Southern California & Mexico.Mexico.

Related PublicationsRelated PublicationsSong, Y. T. and D. B. Haidvogel, A semi-implicit ocean circulation model using a Song, Y. T. and D. B. Haidvogel, A semi-implicit ocean circulation model using a

generalized topographygeneralized topography-following coordinate. -following coordinate. J. Comput. PhysJ. Comput. Phys., 115, 228-244, 1994. ., 115, 228-244, 1994.

Song, Y. T., A Song, Y. T., A general pressure gradientgeneral pressure gradient formulation for ocean models, Part I: Scheme formulation for ocean models, Part I: Scheme design and diagnostic analysis. design and diagnostic analysis. Mon. Wea. RevMon. Wea. Rev., 126, 3213-3230, 1998.., 126, 3213-3230, 1998.

Song, Y. T. and D. Wright, A Song, Y. T. and D. Wright, A general pressure gradientgeneral pressure gradient formulation for ocean models, formulation for ocean models, Part II: Energy, momentum, and bottom torque consistency. Part II: Energy, momentum, and bottom torque consistency. Mon. Wea. RevMon. Wea. Rev., 126, ., 126, 3231-3247, 1998.3231-3247, 1998.

Song, Y. T., Computational design of the Song, Y. T., Computational design of the general coordinategeneral coordinate ocean model for multi-scale ocean model for multi-scale compressiblecompressible or incompressible flow applications, or incompressible flow applications, J. Atmos., Ocean Tech.J. Atmos., Ocean Tech., , submitted, 2002.submitted, 2002.

Song, Y. T. and V. Zlotnicki, Ocean bottom pressure waves detected in the Tropical Song, Y. T. and V. Zlotnicki, Ocean bottom pressure waves detected in the Tropical Pacific, Pacific, GRLGRL, submitted, 2003., submitted, 2003.