Generalized vertical Coordinate Ocean Model for MultiScale NonBoussinesq

Generalized vertical Coordinate Ocean Model for Multi-Scale, Non-Boussinesq or Boussinesq Applications Y. Tony Song Jet Propulsion Laboratory, California Institute of Technology Sponsored by NASA and ONR

Motivation • How may ocean models do we have? • A lot; they differ simply by their coordinate formulation. • All of them solve the same ocean equations Generalized vertical Coordinate Equations

Understanding/predicting ocean dynamics needs both observations and models • Satellite observations • Ocean models • Based on remote sensing • Based on computer give synoptic view of the global ocean technology • With amazing accuracy give 3 -dimensional structure of the ocean technology • With possible errors (inconsistent with satellite measurements)

Problems: • T/P & Jason provide SSH, representing volume changes (heat expansion), but most models are incompressible (Boussinesq). • GRACE measures ocean bottom pressure, representing water mass changes, but most models are not mass conserving.

Model Errors: 1. Numerical Error: Conventional single-coordinate model has difficulties to represent multi-scale ocean dynamics & topography accurately. 2. Representation Error: Boussinesq approximations do not represent real ocean physics (e. g. heat expansion & freshwater flux) and is inconsistent with T/P and GRACE data.

The New Model Configuration Reduce representation errors by non-Boussinesq formulation Reduce numerical errors by the generalized coordinate GCOM SCRUM (Song&Haidvogel 1994) Non-Boussinesq ROMS (Song 2002)

Two analytical s/sp—coordinate systems S-coordinate (Song&Haidvogel 1994): Sp-coordinate (Song 2002): shallow 10 m deep h 5000 m

Default Model Structure • All-in-one capability in general coordinate system • Truly compressible ocean model (non-Boussinesq) Z-levels Hz—depth metric Bz—Boussinesq factor S-levels SBL Flexible for coupling Open Ocean BBL

JPL Compressible Ocean Model • Topography-following & non-Boussenesq • Consistent with GRACE and T/P observations TOPEX Sea Surface Heat expansion /contraction Bottom GRACE

Study 1. Bottom Pressure Waves Detected in Tropical Pacific (Song & Zlotnicki, GRL 2003) Tropical Instability Eddy The rmo cline H L Bottom Pressure Waves

More comparison with T/P data

Study 2. Simulating ENSO with non-Boussinesq/Boussinesq Simulated almost all the ENSO events 0. 5°C Difference due to Boussinesq

Study 3. Multi-Scale Modeling System for Coastal Oceans Coastal can not be cut off from open ocean, therefore multi-scale modeling capability is needed Coastal scale 1 km Ocean color Regional scale 10 -km in z- Basin-scale 50 -km in p-

Summary • A new model with combined topographyfollowing and non-Boussineq features is developed for better representing T/P & GRACE data. • Using the new model, we detected ocean bottom pressure waves in Tropical Pacific. • We have also developed a multi-scale coastal ocean modeling system for the coastal region off Southern California & Mexico.

Related Publications Song, Y. T. and D. B. Haidvogel, A semi-implicit ocean circulation model using a generalized topography-following coordinate. J. Comput. Phys. , 115, 228 -244, 1994. Song, Y. T. , A general pressure gradient formulation for ocean models, Part I: Scheme design and diagnostic analysis. Mon. Wea. Rev. , 126, 3213 -3230, 1998. Song, Y. T. and D. Wright, A general pressure gradient formulation for ocean models, Part II: Energy, momentum, and bottom torque consistency. Mon. Wea. Rev. , 126, 3231 -3247, 1998. Song, Y. T. , Computational design of the general coordinate ocean model for multiscale compressible or incompressible flow applications, J. Atmos. , Ocean Tech. , submitted, 2002. Song, Y. T. and V. Zlotnicki, Ocean bottom pressure waves detected in the Tropical Pacific, GRL, submitted, 2003.