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Hydrostatic Correction for Terrain-Following Ocean Models

This paper discusses the hydrostatic correction method to reduce pressure gradient errors in ocean models, focusing on the accuracy and efficiency of the scheme. Various high-order schemes are compared, showcasing the benefits of the hydrostatic correction approach.

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Hydrostatic Correction for Terrain-Following Ocean Models

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  1. Hydrostatic Correction for Terrain-Following Ocean Models Peter C Chu and Chenwu Fan Naval Postgraduate School Monterey, California 2003 Terrain-Following Ocean Models Users Workshop  4-6 August, 2003, PMEL/NOAA, Seattle WA

  2. How to effectively reduce the sigma error is a challenge task for TOMS.

  3. Pressure Gradient Error

  4. Pressure Gradient Error

  5. Original Thought: High-Order Schemes • Ordinary Five-Point Sixth-Order Scheme (Chu and Fan, 1997 JPO) • Three-Point Sixth-Order Combined Compact Difference (CCD) Scheme (Chu and Fan, 1998 JCP) • Three-Point Sixth-Order Nonuniform CCD Scheme (Chu and Fan, 1999, JCP) • Three-Point Sixth-Order Staggered CCD Scheme (Chu and Fan, 2000, Math. & Comp. Modeling) • Accuracy Progressive Sixth-Order Scheme (Chu and Fan, 2001, JTECH)

  6. Verification of Current Schemes by Ezer, Arango, Shchepetkin (OCEMOD, 2002)

  7. Verification of Current Schemes by Ezer, Arango, Shchepetkin (OCEMOD, 2002)

  8. Verification of Current Schemes by Ezer, Arango, Shchepetkin (OCEMOD, 2002)

  9. How to reduce errors with low computer cost? Hydrostatic Correction • Chu, P.C., and C.W. Fan, 2003: Hydrostatic correction for reducing horizontal pressure gradient errors in sigma coordinate models. Journal of Geophysical Research, J. Geophys. Res.  Vol. 108, No. C6, 3206, 10.1029/2002JC001668.

  10. Finite Volume Consideration

  11. Pressure Gradient

  12. Horizontal Pressure Gradient

  13. Pressure is a linear function of z(or density constantversus z)

  14. Second-Order Scheme Based on the assumption of linear dependence of P on z.

  15. Steep Topography – Hermit Polynomial Integration

  16. Hermit Polynomial Integration

  17. Hydrostatic Correction

  18. Steep Topography – Hermit Polynomial Integration

  19. Hermit Polynomial Integration

  20. Hydrostatic Correction

  21. Verification of Current Schemes by Ezer, Arango, Shchepetkin (OCEMOD, 2002)

  22. HC has the same accuracy as CCD Scheme

  23. HC has the same accuracy as the sixth-order CCD scheme

  24. CPU time (minute) at the end of 5 day runs of the POM seamount test case using the SD and HC schemes

  25. Conclusions • Hydrostatic correction scheme is a simple scheme with high accuracy and efficiency. • The accuracy of the HC scheme is similar to the sixth-order CCD scheme. • The CPU cost is similar to the ordinary second-order scheme.

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