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. Dry Dynamics, mostly. Momentum, mostly My favorite things. Some Old Chesnuts Focus of Talk 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 Ferrel 1859 ERA-40

6. Zonal Average Meridional Wind Ferrel 1859 ERA-40

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

8. Eddy Meridional Temp. Flux ERA-40

9. Eddy Meridional Momentum Flux ERA-40

10. Eddy Meridional Momentum Flux TransientTotal StationaryStationary - 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 In steady state, this term is zero, by mass continuity. Let’s make this part of the drag’. So in steady state,

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

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 Momentum Lorenz (1952) Ferrel 1859

20. Role of Eddies in Momentum Lorenz (1967) Ferrel 1859

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

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

23. Momentum is Funny Stuff This can be achieved, if the eddies are able to propagate out of the source region. 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. 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. 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. Consider the following picture of the temperature and pressure variations on a height surface associated with a westward tilting wave. How did the eddy heat flux end up in the momentum Budget? LHLHWCWC

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

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

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

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 Tanaka, et al. 2006, JMSJ Transient Stationary Hadley Cell Eddy-Driven Cell

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. N H S H Tanaka, et al. 2006 Total 4-7 1-3 >8 1-3 Form Drag by Zonal Wavenumber

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. Subtropical Jet Eddy-Driven Jet

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

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

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

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

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

51. Positive Eddy Feedback Lorenz & Hartmann, 2001 Z=uM=-d/dy(u’v’) Vertical mean zonal wind and eddy momentum forcing of first EOF (N-S shift) are coherent across a broad range of frequencies and forcing leads wind, except for very long periods where they come into phase.

52. Positive Eddy Feedback Lorenz & Hartmann, 2001 Z=u is redM=-d/dy(u’v’) is whiter

53. Positive Eddy Feedback Lorenz & Hartmann, 2001 Z=uM=-d/dy(u’v’) Clues a. M remembers Z b. High-frequency eddies produce low-frequency forcing. a b synoptic = 2-7 days

54. Simple Model of Positive Eddy Feedback Lorenz & Hartmann, 2001 M=-d/dy(u’v’) b. High-frequency eddies produce low- frequency forcing, because they respond to zonal flow. Linear System Assume part of momentum forcing depends on zonal wind. Choose b to explain long-term memory, then z without feedback can be computed.

55. Why is Transient Eddy Feedback Positive? Are Eddy-Driven Jets Self-Sustaining? Yu & Hartmann 1993 Wave source is baroclinic instability, which produces wave energy near the surface where the meridional temperature gradient is large. Waves propagate upward in westerly winds Form drag produces a huge downward zonal momentum flux A thermally direct overturning circulation develops to balance the momentum budget. If waves can propagate out of baroclinic zone they can bring in angular momentum. Diabatic heating must balance heating by overturning cell.

56. Why is Transient Eddy Feedback Positive? Are Eddy-Driven Jets Self-Sustaining? Yu & Hartmann 1993

57. Why is Transient Eddy Feedback Positive? Are Eddy-Driven Jets Self-Sustaining? Yu & Hartmann 1993

58. Why is Transient Eddy Feedback Positive? Are Eddy-Driven Jets Self-Sustaining? So the eddy source and eddy momentum flux convergence can just follow the jet. The meridional cell forced by the form drag of the growing eddies also follows the eddy source, which is the jet. Remaining problem is to bring along the diabatic heating that sustains the meridional cell associated with the form drag. If the heating is driven by the departure from equilibrium forced by the meridional circulation, this is not a problem, the heating couplet follows the circulation.

59. Are Meridional Displacements of Eddy-Driven Jets Self- Sustaining? Use momentum (ignore tendency) and continuity, To sustain jet in new location, need to move diabatic heating with wave driving.

60. Are Meridional Displacements of Eddy-Driven Jets Self- Sustaining? To sustain jet in new location, need to move diabatic heating with wave driving. Works fine in simple models with Newtonian heating, if baroclinic zone is broad Eddy momentum driving can define shape of heating.

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

62. SAM & Precip Sen Gupta & England, 2006 45 30 60

63. Why is Transient Eddy Feedback Positive? Are Eddy-Driven Jets Self-Sustaining? Yu & Hartmann 1993

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

65. SAM & Precip Sen Gupta & England, 2006 45 30 60

66. Parameterizing Eddies Lorenz (1967) Ferrel 1859

67. Conclusion Thomson 1857 We can explain in simple terms that eddy momentum fluxes are associated with the growth, propagation and absorption of waves. It is hard to imagine a climate of Earth, in which eddies do not move momentum poleward. The interaction of eddies with jets and diabatic heating produces interesting variability, about which we are still learning.