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Model Formulation, Numerics and Approximations

Model Formulation, Numerics and Approximations. Vertical coordinates for climate?. What are the remaining liabilities or challenges with z, z*, p, p*, isopycnal, and various approaches to hybrids between coordinates? Will sigma ever be viable for long-term global ocean climate modeling?

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Model Formulation, Numerics and Approximations

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  1. Model Formulation, Numerics and Approximations

  2. Vertical coordinates for climate? • What are the remaining liabilities or challenges with z, z*, p, p*, isopycnal, and various approaches to hybrids between coordinates? • Will sigma ever be viable for long-term global ocean climate modeling? • Are there "coordinate free" approaches that seem viable, and if so how is the vertical resolution distributed? • Do ice-shelves or changing coastlines introduce significant new considerations?

  3. Strengths and Weaknesses of Terrain-following Coordinate Models Strengths: • Topography is represented very simply and accurately • Easy to enhance resolution near surface. • Lots of experience with atmospheric modeling to draw upon. Traditional Weaknesses: • Pressure gradient errors are a persistent problem. • Errors are reduced with better numerics (e.g., Shchepetkin & McWilliams, 2003) • Gentle slopes (smoothed topography) must be used for consistency • Traditional requirement for stability (Beckman & Haidvogel, 1993): • ROMS requirement (Shchepetkin, pers. comm): • Spurious diapycnal mixing due to advection may be very large. (Same issue as Z-coord.) • Diffusion tensors may be especially difficult to rotate into the neutral direction. • Strongly slopes require larger vertical stencil for the isoneutral-diffusion operator. Myth: Near bottom resolution can be arbitrarily enhanced. • Hydrostatic consistency imposes horizontal resolution-dependent constraints on near-bottom vertical resolution, with serious implications for the ability to represent overflows

  4. Maximum Hydrostatically Consistent Horizontal Resolution Horizontal Resolution (in km) Required to Permit 50m Vertical Resolution at Bottom

  5. Maximum Hydrostatically Consistent Horizontal Resolution Horizontal Resolution (in km) Required to Permit 50m Vertical Resolution at Bottom

  6. Maximum Hydrostatically Consistent Horizontal Resolution Horizontal Resolution (in km) Required to Permit 50m Vertical Resolution at Bottom

  7. Common Approximations

  8. Unstructured ocean grids? • Will any be IPCC-ready by AR6? • What are the big issues? • Cost? • Conservation? • Adiabaticity? • Experience?

  9. Pressure gradient errors? • Are there still outstanding issues with pressure gradient force calculations with generalized (i.e. non-P, non-Z, non-in-situ-density) coordinates? • How serious is this issue?

  10. Numerics for Momentum Eqns • Numerical closures for the momentum equations: • Is there anything new? • Is anything new needed?

  11. Tracer advection • What is the state of the art? • What is good enough at which resolutions and for which vertical coordinates? • How serious is the problem in climate models with spurious diapycnal mixing arising from tracer advection at various resolutions?

  12. Scaling to 1000s of PEs • Scaling to 20 pts/PE • At 1° scales to (360/20)x(200/20) ~ 180 PEs • At 1/4° Mercator scales to ~ 3,600 PEs? • At 0.1 ° Mercator scales to ~ 25,000 Pes • Scaling to 10 pts/PE • At 1° scales to (360/10)x(200/10) ~ 720 PEs • At 1/4° Mercator scales to ~ 14,400 PEs? • At 0.1 ° Mercator scales to ~ 100,000 Pes?

  13. Plug & Play Software? • Is this desirable? • What are we willing to give up for this? • Who will pay for it?

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