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

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

2. 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

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

4. 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.

5. Model Errors: • 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.

6. 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)

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

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

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

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

11. More comparison with T/P data

12. Study 2. Simulating ENSO with non-Boussinesq/Boussinesq Simulated almost all the ENSO events 0.5°C Difference due to Boussinesq

13. 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-coordinate

14. Summary • A new model with combined topography-following 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.

15. 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 multi-scale 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.