Richard B. Rood (Room 2525, SRB) rbrood@umich 734-647-3530 Cell: 301-526-8572

1. AOSS 401Geophysical Fluid Dynamics:Atmospheric DynamicsPrepared: 20131203Description / Analysis / Tropics Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Cell: 301-526-8572 Special thanks to Derek Posselt

2. Class News • Ctools site (AOSS 401 001 F13) • Second Examination on December 10, 2013 • Homework • Homework due November 26, 2013 • Rest of lectures • Tropics • Reviews

3. Weather • National Weather Service • Model forecasts: • Weather Underground • Model forecasts: • NCAR Research Applications Program

4. Equations of motion(z, height, as vertical coordinate) tangential coordinate system on Earth’s surface (x, y, z) = (+ east, + north, + local vertical)

5. Equations of motion(p, pressure, as a vertical coordinate) tangential coordinate system on Earth’s surface (x, y, p) = (+ east, + north, pressure is vertical coordinate)

6. The quasi-geostrophic (QG) equations momentum equation geostrophic wind continuity equation thermodynamicequation

7. Vorticity Advection Thickness Advection Geopotential tendency equation • Linear partial differential equation for geopotential tendency. • Given a geopotential distribution at an initial time, can compute geopotential distribution at a later time. • The right hand side is like a forcing.

8. QG-omega equation Combine all QG equations • Link between vertical derivative of vorticity advection (divergence/stretching) and vertical motion

9. What is our strategy for exploring complex unsolvable equations?

10. What are the differences between the tropics and the middle latitudes on Earth? • Tropics: • The area of the tropics – say + and – 30 degrees latitude is half the area of the Earth. • Might say the tropics is + and – 20 degrees of latitude, and subtropics are between 20 and 30 degrees of latitude. • The importance of rotation, the Coriolis parameter. • What else is different?

11. Picture of Earth: What can you say about this figure?

12. Differences between the tropics and middle latitudes • The contrast between summer and winter is not as large as at middle and high latitudes. • There is lot of solar heating. • There is a lot of water! • What is the “physical” difference between water and land? • Sea surface temperature is important to dynamics. • What happens to water when it is warm?

13. Coriolis force • The coriolis parameter decreases to zero at the equator. • Approximated by b X distance from the equator. • We see from our wave equation and the conservation of vorticity that b is a parameter of central importance to the dynamics • Advection of planetary vorticity.

14. Let’s think about the Coriolis parameter

15. Coriolis parameter in the tropics What latitude is Coriolis parameter, say, 10% of mid-latitude value?

16. Perturbation equation: Barotropic Rossby wave at middle latitudes

17. Wave like solutions

18. Recalling our simple wave solution and comparing advection of planetary and relative vorticity. (mid-latitudes)

19. Coriolis force • Can we say that the advection of planetary vorticity is less important in the tropics? • We will come back to this.

20. Let’s think about waves some more • Some fundamental ideas. • Waves have some sort of restoring force • Buoyancy waves: gravity • Rossby waves: The gradient of planetary vorticity • Think about the conservation of potential vorticity • Waves tend to grow and decay at the expense of the “energy” in the mean state. • Waves tend to respond to out of balance situations. • Waves tend to move things towards equilibrium • Waves propagate • So they can communicate things happening in one part of the fluid to far away places.

21. In middle latitudes: • How do the Rossby waves that cause weather, the synoptic waves, get their energy?

22. Energetics of Mid-latitude Cyclone Development • The jet stream is commonly associated with strong temperature gradients in the middle/lower troposphere (thermal wind relationship) • Mid-latitude cyclones develop along waves in the jet stream • Mid-latitude cyclones are always associated with fronts (Norwegian cyclone model) • There is a link between temperature gradients and cyclone development…

23. Barotropic/baroclinic atmosphere • Energetics: • Baroclinic = temperature contrast = density contrast = available potential energy • Extratropical cyclones intensify through conversion of available potential energy to kinetic energy

24. Energetics in mid-latitude wave Ability to convert potential energy to kinetic energy directly related to tilt with height (offset) of low/high pressure

25. Tropics and middle latitudes • In middle latitudes the waves grow from the energy available in the baroclinic atmosphere. • horizontal temperature gradients • scale is large • latent heat release is on scales small compared to baroclinic energy convergence. • In the tropics the horizontal temperature gradients are small.

26. An estimate of the January mean temperature mesosphere stratopause note where the horizontal temperature gradients are large stratosphere tropopause troposphere south summer north winter

27. Tropics and middle latitudes • Baroclinicity is less important in the tropics • Latent heat release is generally more important. • What does this mean?

28. Vertical Velocity • I emphasize the importance and the complications of the vertical velocity. • It is small, very small, but it is at the center of converting potential energy to kinetic energy. (thermodynamics to motion) • How do we calculate vertical velocity? • Something small in an environment full of big things.

29. Vertical velocity: Omega equation • Kinematic method • Horizontal advection • Diabatic method • Omega equation

30. Characteristics of large-scale vertical velocity • In all of the estimates for vertical velocity what is missing? • The answer is _______________ • The vertical velocity in this large-scale, mid-latitude description of dynamics is exactly what is needed to maintain what balances ____________ ?

31. Importance of latent heat release • Diabatic processes are more important in the tropics. • Hence, vertical velocity is more strongly related to diabatic heating than to temperature advection. • What about divergence? • The scale of the forcing of motions is small • Related to the phase change of water.

32. Estimating the vertical velocity: Diabatic Method Start from thermodynamic equation in p-coordinates: If you take an average over space and time, then the advection and time derivatives tend to cancel out. Diabatic term

33. Picture of Earth: What can you say about this figure?

34. Inter-tropical Convergence Zone (ITCZ)

35. ITCZ Circulation This is one place where heat is the direct driver of motion.

36. A couple of things to note • The winds at the surface in the tropics are, on average, easterly, from the east, towards the west. • Go back to our mid-latitude wave: • What does this say about waves in the tropics? • Well, it says, they are different! • (Not that they don’t exist!)

37. ITCZ: Seasonal differences

38. ITCZ: Seasonal differences What is happening here and here?

39. South American Seasonal Cycle CONVECTION GOES WILD

40. Cloud Liquid Water: Average NOTE: Remarkable areas with no clouds! No rain!

41. Vertical circulation around the ITCZ What is the direction of the zonal wind?

42. ITCZ: Seasonal differences What is happening here and here?

43. Monsoonal Flow

44. Lets return to an old problem DIVERGENCE CONVERGENCE PGF L H warm core cold core L H PGF CONVERGENCE DIVERGENCE Earth’s surface OCEAN LAND SUMMER TIME

45. Thermal circulation PGF H L cooling warming H PGF L Earth’s surface Earth’s surface OCEAN LAND SUMMER TIME

46. Monsoonal Circulation • Driven by land-sea temperature contrast. • Reversal of flow from summer to winter. • Tremendously important to precipitation. • South and East Asian monsoon among most important of circulation features.

47. Circulation features of the tropics • Inter-tropical convergence zone • Hadley circulation • Monsoonal circulations • Madden-Julian Oscillation • African easterly waves • Walker circulation • El Nino and La Nina

48. Madden-Julian Oscillation OLR = outgoing longwave radiation. Cold is the top of the clouds. Cold is the top of the hot towers.

49. African easterly waves

50. African easterly waves That’s north Africa. It’s summer. What is happening here and here?