AOSS 401, Fall 2007 Lecture 12 October 3 , 2007

1. AOSS 401, Fall 2007Lecture 12October 3, 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 • Homework • Homework and some review questions were posted last night. • Homework due Monday • We will go over the review questions on Friday • Think about them • Exam next Wednesday • Today’s lecture is the last fundamentally new material that will be on the exam • Friday we will talk about vertical velocity some more • Friday and Monday we will look at the material in different ways and more thoroughly • Also have your questions • Mid-term evaluation • “students will be notified soon thereafter that they can fill out the midterm evaluations between October 8 and October 14”

3. Material from Chapter 3 • Balanced flow • Examples of flows • Stratospheric Vortex • Ozone hole • Surface Flow • Friction • Thermal wind

4. 1.4X10-4 s-1 1.0X10-4 s-1 0.0 s-1 Picture of Earth f=2Ωsin(Φ)

5. Ω k Maximum rotation of vertical column. Picture of Earth Ω k Ω No rotation of vertical column. k

6. Rotation • When a fluid is in rotation, the rotation comes to define the flow field; it provides structure. • That structure aligns with the vector that defines the angular velocity. • So if the flow is quasi-horizontal, then how the flow aligns in the vertical is strongly influenced by the rotation and its projection in the vertical. • On a horizontal surface the curvature of the flow is important

7. And on the Earth. • Tropics are more weakly influenced, defined by rotation than middle latitudes. • This also influences the vertical structure of the dynamical features.

8. Length scales • Planetary waves: 107 meters, 10,000 km • Have we seen one of these in our lectures? • Synoptic waves: Our large-scale, middle-latitude, 106 meters, 1000 km • What’s a synoptic wave? What does synoptic mean? • Hurricanes: 105 meters, 100 km • Fronts: 104 meters, 10 km • Cumulonimbus clouds: 103 meters, 1 km • Tornadoes: 102 meters, 0.1 km • Dust devils: 1 - 10 meters

9. Returning to our mid-latitude, large-scale flow. • We saw last lecture that we could define natural coordinates that were (potentially) useful for determining the motion from maps of thermodynamic fields. That is, the pressure gradient or its analogue, geopotential height. • We saw that, while a powerful constraint, geostrophy is formally true only when the lines of geopotential are straight. • It’s also a balance, steady state. • Hence, while seductive, this is not adequate.

10. How do these natural coordinates relate to the tangential coordinates? • They are still tangential, but the unit vectors do not point west to east and south to north. • The coordinate system turns with the wind. • And if it turns with the wind, what do we expect to happen to the forces? Ω a Φ = latitude Earth

11. Looking down from above

12. Looking down from above

13. Looking down from above

14. Looking down from above

15. Looking down from above

16. Balanced flows in natural coordinates(balanced, here, means steady)

17. Cyclostrophic FlowHow do we get this kind of flow? Pressure gradient force Low Low Do we have this balance around a high? Centrifugal force

18. Gradient FlowWhat forces are being balanced? Definition of normal, n, direction Low High n n

19. Gradient Flow Definition of normal, n, direction Low High n R<0 R>0 n

20. Gradient FlowSolution must be real Low ∂Φ/∂n<0 R>0 Always satisfied High ∂Φ/∂n<0 R<0 Trouble! pressure gradient MUST go to zero faster than R

21. What does this mean physically • For a high, the pressure gradient weakens towards the center of the high. If pressure weakens, then wind speed weakens. Hence, highs associated with relatively weak winds. • For a low, there is no similar constraint. Hence lows can spin up into strong storms.

22. Gradient Flow(Solutions for Lows, remember that square root.) Pressure gradient force NORMAL ANOMALOUS Low Low V V Coriolis Force Centrifugal force

23. Gradient Flow(Solutions for Highs, remember that square root.) Pressure gradient force NORMAL ANOMALOUS High High V V Coriolis Force Centrifugal force

24. Why do we call these flows anomalous? • Where might these flows happen?

25. Normal and Anomalous Flows • Normal flows are observed all the time. • Highs tend to have slower magnitude winds than lows. • Lows are storms; highs are fair weather • Anomalous flows are not often observed. • Anomalous highs have been reported in the tropics • Anomalous lows are strange –Holton “clearly not a useful approximation.”

26. Balanced flow: an application of all that we know

27. Geopotential, 50 hPa surface Pressure units: hPa mbar inches of Hg Length scale? >1,000 km ~10,000 km

28. What about the wind? Pressure gradient Coriolis force What’s the latitude? Centrifugalforce Wind

29. Wind

30. What would happen if I put dye in the low?

31. So we observe that what happens in this low stays in this low.

32. Ozone, October 23, 2006

33. Summary from ozone hole • Ozone hole movie • Cyclonic polar low isolates air from rest of Earth. • Extreme cold temperature cause nitric acid and water clouds which changes basic chemical environment of atmosphere. • Return of sun destroys ozone in isolated air with changed chemical environment.

34. Let’s move down to the surface. • At 1000 mb • How are things different? • How would we have to modify the equations?

35. Geostrophic and observed wind 1000 mb (land)

36. Geostrophic and observed wind 1000 mb (ocean)

37. Think about this in terms of natural coordinates.

38. Our geostrophic flow. north Φ0+ΔΦ Φ0 Φ0+2ΔΦ Δn Φ0+3ΔΦ east south west

39. We have said that what’s going on near the surface is related to viscosity.

40. So what does it say if our wind crosses the height contours? north Φ0 Δn ? Φ0+ΔΦ Φ0+2ΔΦ Φ0+3ΔΦ east south west

41. So what does it say if our wind crosses the height contours?(Staying in natural coordinates.) n t north Φ0 ΔΦ Φ0+ΔΦ Φ0+2ΔΦ Φ0+3ΔΦ east south west

42. So what does it say if our wind crosses the height contours?(Staying in natural coordinates.) n t angle, α north Φ0 v ΔΦ Φ0+ΔΦ u Φ0+2ΔΦ Φ0+3ΔΦ east south west

43. Friction force

44. Friction force

45. Balance of forces (northern hemisphere)(Staying in natural coordinates.) n t angle, α north Φ0 ΔΦ Φ0+ΔΦ Φ0+2ΔΦ Φ0+3ΔΦ east south west

46. Balance of forces (northern hemisphere)(Staying in natural coordinates.) n t angle, α north Φ0 ΔΦ Φ0+ΔΦ Φ0+2ΔΦ Φ0+3ΔΦ angle, α, as well? east south west

47. Angle in terms of forces

48. Can also be derived from Looks like a great homework problem!

49. Some basics of the atmosphere Troposphere ------------------ ~ 2 Mountain Troposphere ------------------ ~ 1.6 x 10-3 Earth radius Troposphere: depth ~ 1.0 x 104 m This scale analysis tells us that the troposphere is thin relative to the size of the Earth and that mountains extend half way through the troposphere.

50. Structure of the atmospheric boundary layer (Vertical length scales) Free Atmosphere PBL height Planetary (Convective) Boundary Layer (PBL) k { ~ 102-3 m Blending height Atmospheric Surface Layer (ASL) n ~ 10 1~2 m Wind profile Roughness sublayer ~ 10 -1~1 m Inertial sublayer ~ 10-3 m Transition layer Interfacial sublayer Viscous sublayer from Bob Su ( www.itc.nl )