AOSS 401, Fall 2006 Lecture 18 October 24 , 2007

1. AOSS 401, Fall 2006Lecture 18October 24, 2007 Richard B. Rood (Room 2525, SRB) rbrood@umich.edu 734-647-3530 Derek Posselt (Room 2517D, SRB) dposselt@umich.edu 734-936-0502

2. Class News • Final exam will be last day of class • Derek and I decided to think about good homework problems for another day. • No homework posted today.

3. Material from Chapter 4 • Vorticity, Vorticity, Vorticity • Relative and planetary vorticity • Mid-latitude disturbances • Vorticity, divergence, in 3-D

4. Weather • National Weather Service • http://www.nws.noaa.gov/ • Model forecasts: http://www.hpc.ncep.noaa.gov/basicwx/day0-7loop.html • Weather Underground • http://www.wunderground.com/cgi-bin/findweather/getForecast?query=ann+arbor • Model forecasts: http://www.wunderground.com/modelmaps/maps.asp?model=NAM&domain=US

5. Two important definitions • barotropic – density depends only on pressure. And by the ideal gas equation, surfaces of constant pressure, are surfaces of constant density, are surfaces of constant temperature. • baroclinic – density depends on pressure and temperature.

6. Absolute (or total) Vorticity

7. Relative and planetary vorticity • Planetary vorticity is cyclonic is positive vorticity • Planetary vorticity, in middle latitudes, is usually larger than relative vorticity

8. We derived the vorticity equation TERMS DIVERGENCE TILTING SOLENOIDAL or BAROCLINIC

9. Comments on the terms • There are important dynamical features in the atmosphere where all of these terms are important. • Baroclinic terms are due to there being gradients of temperature on pressure surfaces. (Are they explicitly there in pressure coordinates?) Like a thermodynamic “source” of rotation.

10. Tilting Term rotation in, say, (y, z) plane, “vorticity” in x plane as the wheel is turned there is a component of “vorticity” in the z plane

11. Divergence influence on vorticity

12. Divergence influence on vorticity

13. Scale factors for “large-scale” mid-latitude

14. Assume balance among terms of 10-10s-2

15. A nuance on vorticity and the scaled equation: potential vorticity

16. A simple version of potential vorticity Integrate with height,z1 z2 over a layer of depth H.

17. A simple version of potential vorticity This is the potential vorticity under the set of assumptions that we used to derive the equation. Constant density, constant temperature  so only in a shallow layer might this be relevant to the atmosphere. Potential vorticity is a measure of absolute vorticity relative to the depth of the vortex.

18. Relative vorticity with change of depth

19. Vorticity and depth • We can see that there is a relationship between depth and vorticity. • As the depth of the vortex changes, the relative vorticity has to change in order to conserve the potential vorticity. • This is the play between relative and planetary vorticity.

20. Scaled vorticity equation

21. An observation • The vorticity is dominated by the geostrophic component of the wind. • The divergence requires the wind to be away from geostrophic balance. • Generally vg/va >= 10

22. Let’s explicitly map these ideas to the Earth

23. Local vertical / planetary vorticity

24. relative vorticity/planetary vorticity relative vorticity planetary vorticity

25. Compare relative vorticity to planetary vorticity for large-scale and middle latitudes planetary vorticity is usually larger than relative vorticity

26. Relative and planetary vorticity • Planetary vorticity is cyclonic is positive vorticity • Planetary vorticity, in middle latitudes, is usually larger than relative vorticity • A growing cyclone “adds to” the planetary vorticity. • Lows intense • A growing anticyclone “opposes” the planetary vorticity. • Highs less intense

27. Compare relative vorticity to planetary vorticity andto divergence Flow is rotationally dominated, but divergence is crucial to understanding flow.

28. Consider our simple form of potential vorticity From scaled equation, with assumption of constant density and temperature.

29. Fluid of changing depth

30. Two things that we have learned about vorticity. • Convergence and divergence in a column of fluid, impacts the vorticity throughout the column. • Specifically, divergence above causes low pressure at the surface. • Stretching and shrinking of a column of vorticity will change the relative vorticity.

31. Possible development of a surface low. pressure surfaces Earth’s surface

32. Lets return to our simple problem warming pressure surfaces cooling Earth’s surface

33. Lets return to our simple problem pressure / height surfaces rise pressure / height surfaces sink warming cooling Earth’s surface

34. Lets return to our simple problem PGF H warming L cooling Earth’s surface

35. Lets return to our simple problem PGF H warming L mass leaves column / low forms at ground cooling L Earth’s surface

36. Lets return to our simple problem PGF H warming L mass leaves column / low forms at ground cooling H L mass enters column / high forms at ground Earth’s surface

37. Lets return to our simple problem PGF H warming L mass leaves column / low forms at ground cooling H PGF L mass enters column / high forms at ground Earth’s surface

38. Mass continuity? • What are the implications of mass continuity? • What is your law, your equation, your tool to answer that question?

39. Temperature • Assuming the air moves isentropically, what happens to the temperature? • What is your law, your equation, your tool to answer that question?

40. Lets return to our simple problem PGF H warming L cooling H PGF L Earth’s surface

41. Simple Thermal Circulation • There is the sense of the air moves to counter the heating. • If the heating ended, then the circulation would end, acting to bring back the original equilibrium situation. • This sort of low is cause by heating, is called a “thermal” low, warm core. It tends to damp out.

42. Lets return to our simple problem H L PGF warm core cold core H PGF L Earth’s surface

43. Simple Thermal Circulation • This sort of low is cause by heating, is called a “thermal” low, warm core. It tends to damp out. • Remember the question about the hurricane being warm core. • What about the divergence and convergence?

44. Lets return to our simple problem DIVERGENCE CONVERGENCE PGF L H warm core cold core L H PGF CONVERGENCE DIVERGENCE Earth’s surface

45. Simple Thermal Circulation • What about the divergence and convergence? • Convergence and Divergence are aligning over top of each other in the vertical. • Again, in this case there is a tendency for the circulation to damp out.

46. Back to the earth again

47. Still in the atmosphere

48. Flow over a hill HILL

49. Derived a simple form of potential vorticity From scaled equation, with assumption of constant density and temperature.

50. Flow over a hill(long in the north-south)(can’t go around the hill) west east