1. 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

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

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

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

5. 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.

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

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

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

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

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

11. More comparison with T/P data

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

13. 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

14. Summary A new model with combined topography- following and non-Boussineq features is developed for better representing T/P & GRACE data. 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. 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. 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.