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More on Ocean-Atmosphere (General Circulation) Models

More on Ocean-Atmosphere (General Circulation) Models. Outline. Overview of the “fluid dynamics” part of Climate models Two applications of climate models to non Global Warming problems…. !! Not examinable !!. Model (prognostic) variables. Newton’s law+mass conservation

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More on Ocean-Atmosphere (General Circulation) Models

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  1. More on Ocean-Atmosphere (General Circulation) Models

  2. Outline • Overview of the “fluid dynamics” part of Climate models • Two applications of climate models to non Global Warming problems… !! Not examinable !!

  3. Model (prognostic) variables Newton’s law+mass conservation • 3 components of velocity (u,v,w) • Pressure (Oce.) & Geopotential (Atm.) 1st Law of Thermodynamics • Temperature “Tracer” conservation • Moisture (Atm.) & Salinity (Oce.)

  4. Eulerian approach: budgets applied to fixed volume elements z y x δx, δy and δz are the model grid box dimensions

  5. Newton’s Law in east-west (x) direction:Pressure force z y x P(x)δzδy P(x+δx)δzδy δx, δy and δz are the model grid box dimensions

  6. Newton’s Law in east-west (x) direction:fluid transport of momentum z y ρ(x)u(x)δzδy times u(x) x ρ(x+δx)u(x+δx)δzδy times u(x+δx)

  7. Newton’s law in east-west (x) direction:fluid transport of momentum z ρ(z+δz)w(z+δz)δxδy times u(x,y,z+δz) y x ρ(z)w(z)δxδy times u(x,y,z) NB: Non linear & couples the boxes

  8. Horizontal resolution • Atmospheric & Oceanic models (when used in climate mode) are run at ≈δx=δy=2°(i.e., 200km X 200km) horizontal resolution. … but, oceanic storms are smaller than 2° so must be parameterized. Atmospheric storms have a length scale of 10° and are represented. NB: A “coupler” might be needed if O/A not run on same grid

  9. Horizontal grid • Problems with convergence of meridians at the poles… As Δx becomes small, the time step must become small in order to avoid numerical instabilities… too expensive!

  10. Ocean modeller solution… Rotate grid and put poles over continents! … but does not work for the atmosphere…

  11. A possible solution: the “Cube-Sphere” Snapshot of Atmospheric temperature (500mb) on a water world “Corners” Sea level (m)

  12. Vertical coordinates Atmosphere ~20 levels Ocean ~15 levels

  13. Time discretization & computer performances • Timestep δt is a few minutes for the Atmosphere and about 1h for the ocean. • Atmosphere is the most expensive to run and typically is the bottle neck of climate models (Feynman’s “Dry & Wet fluid”). • 1 week of computer time ≈ 50 yrs of simulated climate.

  14. Total number of variables… • About 6X15X180X90≈1-2 million for Oceans and Atmosphere. • Coupled O-A General Circulation Models are thus very large systems of coupled, non linear, ordinary differential equations.

  15. ΔT Ψ … Lorenz (1963)

  16. Which of the Oceans and the Atmosphere transport more energy poleward?

  17. Net energy loss at TOA in Extra-Tropics Total poleward energy transport = + Net energy gain at TOA in Tropics Atmosphere Ocean NB: In lectures we considered the integrated value, which is … zero!

  18. Poleward heat transport (by either Ocean or Atmosphere) is small… Energy exchanged at top-of-atmosphere : Planetary albedo Solar constant

  19. High energy air parcels are carried poleward by winds Warm water parcels are carried poleward by currents

  20. Trenberth & Caron, 2001

  21. Simplify the problem… -No continents -Flat ocean bottom

  22. Simplify the problem… What is the relative contribution of ocean & atmosphere in a waterworld…? ? -No continents -Flat ocean bottom

  23. Coupled (O/A) GCM in water world geometry Atmosphere Ocean NB: Quite different results with polar islands!

  24. Insights from water world • The energy carried by ocean and atmosphere is similar in middle latitudes • … but the mass flowing across latitudes per second is greater in the atmospherere than in the ocean

  25. Insights from water world • The energy carried by ocean and atmosphere is similar in middle latitudes • … but the mass flowing across latitudes per second is greater in the atmospherere than in the ocean!

  26. Comparison Water World / Real World Continuous curves: Water world (coupled model) Broken curves: Real World (Observations)

  27. Is the Gulf Stream responsible for mild European Winters?

  28. WARM! COLD! Eddy surface air temperature from NCAR reanalysis (January, CI=3K) “Every West wind that blows crosses the Gulf Stream on its way to Europe, and carries with it a portion of this heat to temper there the Northern winds of winter. It is the influence of this stream upon climate that makes Erin the “Emerald Isle of the Sea”, and that clothes the shores of Albion in evergreen robes; while in the same latitude, on this side, the coasts of Labrador are fast bound in fetters of ice.” Maury, 1855. Lieutenant Maury “The Pathfinder of the Seas”

  29. Model set-up (Seager et al., 2002) • Full Atmospheric model • Ocean only represented as a motionless “slab” of 50m thickness, with a specified “q-flux” to represent the transport of energy by ocean currents Atmosphere

  30. Seager et al. (2002)

  31. Seager et al. (2002)

  32. Conclusions • Climate models offer a large space to use one’s imagination. • Basic climate questions are still debated and the field is open.

  33. I leave it to Jenny… • …but will be back for Lecture 22. • Office hours: Tuesdays, 5-6pm in Huxley Room 726 until end of Term 2.

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