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The General Circulation of the Atmosphere and its Variability

The General Circulation of the Atmosphere and its Variability. Dennis L. Hartmann Dynamics Seminar October 18, 2007. Thomson 1857. Outline of Talk. • Description of the General Circulation in classical terms • Review of some of the advances in the past 25-40 years

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The General Circulation of the Atmosphere and its Variability

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  1. The General Circulation of the Atmosphere and its Variability Dennis L. Hartmann Dynamics Seminar October 18, 2007 Thomson 1857

  2. Outline of Talk • Description of the General Circulation in classical terms • Review of some of the advances in the past 25-40 years • Discussion of theories of Dynamical Variability in the Atmosphere Thomson 1857

  3. Focus of Talk • Dry Dynamics, mostly. • Momentum, mostly • My favorite things. • Some Old Chesnuts Ferrel 1856

  4. Zonal Average Views • Zonal Average Climatology • Zonal Average of x = [x] • x - [x] = x* = deviation from the zonal average • Time average of x = x • x - x = x’ = deviation from time average Ferrel 1859

  5. Zonal Average Zonal Wind ERA-40 Ferrel 1859

  6. Zonal Average Meridional Wind ERA-40 Ferrel 1859

  7. Eddy Covariances Zonal Average of Product Zonal Average of Eddy Product Product of Zonal Averages Maury 1855

  8. Eddy Meridional Temp. Flux ERA-40

  9. Eddy Meridional Momentum Flux ERA-40

  10. Transient Total Eddy Meridional Momentum Flux Stationary Stationary - JJA ERA-40

  11. Eddy-Driven Jets • When you see surface westerlies with westerlies above, as in midlatitudes, these westerlies are driven by large-scale eddy momentum fluxes. • The observed mean meridional circulations export mass-averaged westerly relative angular momentum.

  12. Zonal-mean Momentum Expand total derivative and use continuity in p-coord. Multiply by a cos and average over longitude.

  13. Zonal-mean Momentum Next, integrate this over the mass of the atmosphere.

  14. Zonal-mean Momentum Let’s make this part of the drag’. In steady state, this term is zero, by mass continuity. So in steady state,

  15. Steady, Mass-integrated Zonal-mean Momentum Equation Meridional eddy flux of zonal momentum Mass-integrated mean zonal wind advection

  16. Steady, Mass-integrated Zonal-mean Momentum Advection Peaks at around 30N, so both Hadley and Ferrel Cells export relative angular momentum

  17. Steady, Mass-integrated Zonal-mean Momentum Advection Eddies and MMC export relative angular momentum from the tropics and the eddies import relative angular momentum into extratropics, and focus it above the surface westerlies.

  18. Conclusion: Eddies must move momentum poleward • If we have a climate with easterlies in the tropics and westerlies in midlatitudes, and eddies dominate the circulation in between, then eddies must transport westerly momentum poleward.

  19. Role of Eddies in MomentumLorenz (1952) Ferrel 1859

  20. Role of Eddies in MomentumLorenz (1967) Ferrel 1859

  21. Consider a non-divergent, barotropic fluid Momentum is Funny Stuff Enstrophy Equation Steady Enstrophy Equation

  22. Steady Enstrophy Equation Momentum is Funny Stuff If source F* adds enstrophy, eddy vorticity flux must be up-gradient (normally northward) to maintain steady state. Zonal Wind Equation That would tend to accelerate the flow in the region where the source of eddy enstrophy is located.

  23. Momentum is Funny Stuff If angular momentum is conserved, there must also be an easterly acceleration somewhere else, to balance out the westerly acceleration produced in the eddy source region. This can be achieved, if the eddies are able to propagate out of the source region. N.B. Wave propagation goes in the opposite direction to the momentum flux, so if waves propagate out of region, momentum is transported in.

  24. Barotropic Cartoon

  25. Momentum is Funny Stuff + - - + + - + Where is eddy source, and sink ?

  26. Momentum is Funny Stuff In quasi-geostrophic, baroclinic case, = Eliassen-Palm Flux Vector How did the eddy heat flux end up in the momentum Budget?

  27. How did the eddy heat flux end up in the momentum Budget? • The eddy heat flux represents the form drag in a hydrostatic and quasi-geostrophic wave that tilts westward with height. • ‘Easy’ to visualize by thinking in potential temperature coordinates.

  28. How did the eddy heat flux end up in the momentum Budget? • Consider the following picture of the temperature and pressure variations on a height surface associated with a westward tilting wave. C L W H C L W H

  29. How did the eddy heat flux end up in the momentum Budget? • Add potential temperature perturbation. L H L H

  30. How did the eddy heat flux end up in the momentum Budget? • Sketch in dz necessary to get back to a constant potential temperature surface; dz ~ -dtheta L H L H

  31. How did the eddy heat flux end up in the momentum Budget? • Now let’s focus in on the resulting form drag. In westward- tilting wave, atmosphere above exerts an eastward torque on atmosphere below, and vice-versa. Height of theta surface, material surface. H L L H L H

  32. Eliassen-Palm Cross Sections = Eliassen-Palm Flux Vector Heat Flux part dominates climatology of E-P Cross-Sections Tanaka, et al. 2006, JMSJ

  33. How did the eddy heat flux end up in the momentum Budget? • In middle latitudes, baroclinic eddies have poleward heat fluxes that are associated with • eddy energy production, • upward wave propagation and • huge form drag that moves momentum from the upper to the lower troposphere.

  34. The Residual or Lagrangian Circulation Use momentum (ignore tendency) and continuity, Mean sinking is the meridional gradient of the drag integrated down to that level. Thermo not used.

  35. Zonal Mean Circulations = Residual or Lagrangian Circulation Heat Flux part dominates climatology of E-P Cross-Sections Tanaka, et al. 2006, JMSJ

  36. Stationary and Transient Driving of Lagrangian Circulation Hadley Cell Stationary Eddy-Driven Cell Transient Tanaka, et al. 2006, JMSJ

  37. If the eddy heat flux and form drag are so dominant in the momentum budget, are lateral eddy momentum fluxes really that important? They have to be. • Variability of eddy-driven jets is an important part, perhaps the most important part, of extratropical variability. • ‘Easiest’ place to see this is in the Southern Hemisphere.

  38. Southern Hemisphere Eddy-Driven Jet. Lots of Ocean, not much topography, fairly zonally symmetric, most of form drag from high wavenumbers. Clear, almost seasonally invariant eddy-driven jet.

  39. Southern Hemisphere Eddy-Driven Jet. Form Drag by Zonal Wavenumber N H 1-3 S H >8 4-7 Total 1-3 Tanaka, et al. 2006

  40. Southern Hemisphere Eddy-Driven Jet. Lots of Ocean, not much topography, fairly zonally symmetric, most of form drag from high wavenumbers. Clear, almost seasonally invariant eddy-driven jet. Eddy-Driven Jet Subtropical Jet

  41. Southern Hemisphere Eddy-Driven Jet. Eddy-Driven Jet Subtropical Jet Lorenz & Hartmann, 2001

  42. Southern Hemisphere Eddy-Driven Jet. Lots of Ocean, not much topography, fairly zonally symmetric, most of form drag from high wavenumbers. Clear, almost seasonally invariant eddy-driven jet. Primary mode of low-frequency variability is North-South movement of the Eddy-Driven Jet.

  43. Southern Hemisphere Eddy-Driven Jet. Hartmann and Lo, 1998

  44. Southern Hemisphere Eddy-Driven Jet. First EOF of zonal wind almost independent of season. Amplitude of EOF 1 is slowly varying, with most variance > 20 days Hartmann and Lo, 1998

  45. Southern Hemisphere Eddy-Driven Jet. First EOF represents N-S shift of eddy driven jet. 1.5 standard deviation of PC-1 corresponds to 10˚ latitude shift of surface westerlies. Hartmann and Lo, 1998

  46. Southern Hemisphere Eddy-Driven Jet. Momentum Budget of Meridional Eddy-Jet Meandering Residual Circ. Barotropic ‘Baroclinic’ aka Form Drag Drag determined as residual Hartmann and Lo, 1998

  47. Momentum Budget of Meridional Eddy-Jet Meandering Barotropic ‘Baroclinic’ aka Form Drag Total Eddy Forcing Residual Circ. Drag determined as residual Hartmann and Lo, 1998

  48. Southern Hemisphere Eddy-Driven Jet. Lots of Ocean, not much topography, fairly zonally symmetric, most of form drag from high wavenumbers. Clear, almost seasonally invariant eddy-driven jet. Primary mode of low-frequency variability is North-South movement of the Eddy-Driven Jet. Eddy fluxes and residual circulation adjust to new position of jet, so that net tendency is small and jet is stable in new position. Despite being relatively small in climatology, meridional momentum flux convergence seems to play a central role in N-S movement of eddy-driven jet.

  49. Southern Hemisphere Eddy-Driven Jet. Lots of Ocean, not much topography, fairly zonally symmetric, most of form drag from high wavenumbers. Clear, almost seasonally invariant eddy-driven jet. Primary mode of low-frequency variability is North-South movement of the Eddy-Driven Jet. Eddy fluxes and residual circulation adjust to new position of jet, so that net tendency is small and jet is stable in new position. But, are the eddies passive or active, and do eddies add a positive feedback that adds persistence to departures of the eddy-driven jet position?

  50. Positive Eddy Feedback Focus on vertical average momentum balance and meridional wave propagation. Lorenz & Hartmann, 2001

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