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A baroclinic instability test case for dynamical cores of GCMs

A baroclinic instability test case for dynamical cores of GCMs. Christiane Jablonowski (University of Michigan / GFDL) David L. Williamson (NCAR). AMWG Meeting, 3/20/06. Overview. Basic Idea & Design Goals Derivation of the test case & discussion of the initital conditions

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A baroclinic instability test case for dynamical cores of GCMs

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  1. A baroclinic instability test case for dynamical cores of GCMs Christiane Jablonowski (University of Michigan / GFDL) David L. Williamson (NCAR) AMWG Meeting, 3/20/06

  2. Overview • Basic Idea & Design Goals • Derivation of the test case & discussion of the initital conditions • 4 dynamical cores: NCAR CAM3 & DWD’s GME • Results of the test case • Steady-state conditions • Evolution of the baroclinic wave • Uncertainty of the ensemble of reference solutions • Conclusions

  3. The Idea & Design Goals • Goal: development of a dynamical core test case (without physics, dry & prescribed orography) that • is easy to apply • is idealized but as realistic as possible • gives quick results • starts from an analytic initial state, suitable for all grids • triggers the evolution of a baroclinic wave • Designed for primitive equation models with pressure-based vertical coordinates (hybrid, sigma or pure pressure coordinate)

  4. Derivation of the Initial Conditions • Initial data required: u, v, T, ps, s • Find a steady-state, balanced solution of the PE eqns: prescribe u, v and the surface pressure ps • Plug prescribed variables into PE equations and derive the • Geopotential field : based on the momentum equation for v (integrate), calculate surface geopotential s • Temperature field: based on the hydrostatic equation

  5. Initial Conditions • v = 0 m/s • ps = 1000 hPa • u & s

  6. Initial Temperature Field

  7. Perturbation • Overlaid perturbation (at each model level) triggers the evolution of a baroclinic wave over 10 days • Suggested: pertubation of the zonal wind field ‘u’ orthe vorticity and divergence (for models in - form)

  8. Characteristics of the Initial Conditions • Instability mechanisms: • Baroclinic instability - vertical wind shear • Barotropic instability - horizontal wind shear • But: • Statically stable • Inertially stable • Symmetrically stable

  9. Characteristics • Static stability

  10. Characteristics • Symmetric stability & Inertial stability

  11. Test Strategy Step 1: • Initialize the dynamical core with the analytic initial conditions (balanced & steady state) • Let the model run over 30 days (if possible without explicit diffusion) • Does the model maintain the steady state? • Perturb the initial conditions with a small, but well-resolved Gaussian hill perturbation • 10-day simulation: Evolution of a baroclinic wave Step 2:

  12. Model Intercomparison NCAR CAM3: • Eulerian dynamical core (EUL), spectral • Semi-Lagrangian (SLD), spectral • Finite Volume (FV) dynamical core (NCAR/NASA/GFDL) • Icosahedral model GME (2nd order finite difference approach) German Weather Service (DWD):

  13. Resolutions • Default:26 vertical levels (hybrid) with model top ≈ 3hPa.In addition: 18 and 49 vertical levels were tested. • EUL & GME: varying horizontal diffusion coefficients K4, no explicit diffusion in SLD and FV simulations.

  14. Steady-State Test Case • Maintenance of the zonal-mean initial state (u wind) Decentering parameter effect,with =0 EUL is matched Wave number 5 effect

  15. Steady-State Test Case: GME • GME shows a truncation error with wave number 5 • Artifact of computational grid and low-order num. method

  16. Steady-State Test Case as a Debugging Tool • Discovery of a flaw in the SLD dynamical core (old CAM2 version): • systematic decrease in the zonal wind speed over time • Here: plotted for 30 days with an older version of the test case (umax = 45m/s)

  17. Baroclinic Waves: 30-day Animation North-polar stereographicprojection Surface pressure Surface temperature Movie: Courtesy ofFrancis X. Giraldo, NRL, Monterey

  18. Evolution of the Baroclinic Wave • Perturbation gets organized over the first 4 days and starts growing rapidly from day 6 onwards ps T (850 hPa) FV 0.5 x 0.625 L26 dycore

  19. Evolution of the Baroclinic Wave • Explosive cyclogenesis after day 7 • Baroclinic wave breaks after day 9 ps T (850 hPa) FV 0.5 x 0.625 L26 dycore

  20. Convergence with Resolution • Surface pressure starts converging at 1 x 1.25 degrees FV L26 dycore, Day 9

  21. Model Intercomparison at Day 9 • Second highest resolutions, L26 • ps fields visually very similar • Spectral noise in EUL and SLD

  22. Model Intercomparison at Day 9 • ps fields visually almost identical • Differences only at small scales

  23. 850 hPa Vorticity at Day 7 • Differences in the vorticity fields grow faster than ps diff.

  24. 850 hPa Vorticity at Day 9 • Small-scale differences easily influenced by diffusion • Spectral noise in EUL and SLD (L26)

  25. Impact of explicit diffusion • EUL T85L26 with K4 increased by a factor of 10 (1 x 1016 m4/s) • No spectral noise, but severe damping of the circulation

  26. Model Intercomparisons: Uncertainty • Estimate of the uncertainty in the reference solutions across all four models using l2(ps)

  27. Single-Model Convergence • Single-model uncertainty stays well below the uncertainty across models • Models converge within the uncertainty for the resolutions T85 (EUL & SLD), 1x1.25 (FV), GME (55km / ni=128)

  28. Uncertainty in the Relative Vorticity • Estimate of the uncertainty in the reference solutions using l2[ (850 hPa)] • Errors grow faster, but conclusions are the same

  29. Vertical Resolutions • Model runs with 18 and 49 levels at mid-range horizontal resolutions are compared to the default 26-level runs • Uncertainty stays well below the uncertainty across the models

  30. Phase Errors • Phase errors diminish with increasing resolutions • Phase error at lower resolutions is substantial for GME, attributes to the relatively ‘late’ convergence of GME (55 km)

  31. Energy Fixer: SLD Dynamical Core • Baroclinic wave test revealed problem in the energy fixer of the SLD dynamical core (old CAM2 version) SLD problem with the energy fixer corrected

  32. Conclusions • Goal: Development of an easy to use baroclinic wave test case that serves as a debugging tool and and fosters model intercomparisons • Test of the models as they are used operationally (no extra diffusion, no special tuning of parameters) • Established an ensemble of reference solutions and their uncertainty • Models converge within the uncertainty at the resolutions EUL & SLD T85, FV 1 x 1.25, GME (55km/ni=128) • Convergence characteristics the same for T or  variable • Accessibility: We make the ensemble of solutions (ps) available to all interested modeling groups and offer to compute l2(ps) norms

  33. Publications • Jablonowski, C. and D. L. Williamson, 2006a: A Baroclinic Wave Test Case for Dynamical Cores of General Circulation Models: Model Intercomparisons, NCAR Technical Note TN-469+STR, 89 pp. (available online at http://www.library.ucar.edu/uhtbin/cgisirsi/TRm6NSmtE3/0/261320020/503/7631(shortly: also available on NCAR’s CAM3 web page) • Jablonowski, C. and D. L. Williamson, 2006b: A Baroclinic Instability Test Case for Atmospheric Model Dynamical Cores, Quart. J. Roy. Meteor. Soc., in review

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