1. Thickness and Thermal Wind
AOS 101 Section 301
April 13th, 2009

2. Pressure vs. Height
Pressure decreases with height, but can also decrease as you move north/south/east/west

3. Pressure vs. Height
300 mb Z Z
500 mb
1000 mb X X
We can imagine pressure surfaces stacked on top of one another

4. Pressure vs. Height Z X
1000 mb
300 mb
500 mb
500 mb everywhere
Pressure Y X
At a given height, there is no pressure gradient if the pressure surface is flat, just like the height surface you are looking at

5. Pressure vs. Height
Pressure
300 mb
500 mb Z Y
300 mb
1000 mb
400 mb
500 mb X X
A pressure gradient only appears when pressure surfaces develop hills and valleys

6. Pressure vs. Height
Height above ground
300 mb
500 mb Z Y
1 km
1000 mb
2 km
3 km X X
When we stay on a pressure surface, we observe that the height of that surface above the ground is low in a region of low pressure, and is high in a region of high pressure.

7. Pressure vs. Height Low Pressure = Low Height
Height above ground
300 mb
500 mb Z Y
1 km
1000 mb
2 km
3 km X X
Low Pressure = Low Height
High Pressure = High Height

8. Thickness
What can cause pressure surfaces to develop hills and valleys?
Consider the how much space warm air occupies compared to cold air…

9. Thickness
Here is a column of air at room temperature

10. Thickness Here is a column of air at room temperature
If I were to cool this column of air …

11. Thickness Here is a column of air at room temperature
If I were to cool this column of air …
It would shrink in size. This is because cold air is more dense than warm air (recall the lecture on buoyancy)
The same amount of air is still there (i.e. it has the same weight, and causes the same amount of pressure beneath it), the column is just shorter when the air is cooled.

12. Thickness Here is a column of air at room temperature
If I were to cool this column of air …
It would shrink in size. This is because cold air is more dense than warm air (recall the lecture on buoyancy)
The same amount of air is still there (i.e. it has the same weight, and causes the same amount of pressure beneath it), the column is just shorter when the air is cooled.
We refer to this phenomenon as the “thickness” of an air column.

13. Thickness
Thickness = the vertical distance between two pressure surfaces
This is entirely dependent upon the temperature of the air between those pressure surfaces:
Cold Air = Low Thickness
Warm Air = High Thickness

14. Thickness
COOL
WARM

15. Thickness
Imagine the atmosphere is a ‘block’ of fluid that pushes down with 1000 mb of pressure at the bottom
1000 mb
800 mb
600 mb
400 mb
200 mb
0 mb

16. Thickness
Imagine the atmosphere is a ‘block’ of fluid that pushes down with 1000 mb of pressure at the bottom
The block starts out at a uniform temperature – the thickness of the atmosphere is the same everywhere.
1000 mb
800 mb
600 mb
400 mb
200 mb
0 mb

17. Thickness Height is the same everywhere Y X 0 mb 200 mb 400 mb 600 mb

18. Thickness Height is the same everywhere Y X 0 mb 200 mb 400 mb 600 mb

19. Thickness Height is the same everywhere Y X 0 mb 200 mb 400 mb 600 mb

20. Thickness
Imagine the atmosphere is a ‘block’ of fluid that pushes down with 1000 mb of pressure at the bottom
The block starts out at a uniform temperature – the thickness of the atmosphere is the same everywhere.
Now we make the block cold on the west side and warm on the east side…
1000 mb
800 mb
600 mb
400 mb
200 mb
0 mb
COLD
WARM

21. Thickness
0 mb
Imagine the atmosphere is a ‘block’ of fluid that pushes down with 1000 mb of pressure at the bottom
The block starts out at a uniform temperature – the thickness of the atmosphere is the same everywhere.
Now we make the block cold on the west side and warm on the east side…
The pressure surfaces develop a steep slope, with the low end on the cold side and the high end on the high side
200 mb
400 mb
600 mb
800 mb
1000 mb

22. Thickness
0 mb
The 1000 mb pressure surface is still flat – there is the same amount of fluid above the surface whether you are on the cold side or the warm side
200 mb
400 mb
Height is the same
everywhere
600 mb
800 mb
1000 mb Y X

23. Thickness
0 mb
The 1000 mb pressure surface is still flat – there is the same amount of fluid above the surface whether you are on the cold side or the warm side
But at upper levels, a pressure gradient appears …
200 mb
400 mb
600 mb
800 mb L H
1000 mb Y X

24. Thickness
0 mb
The 1000 mb pressure surface is still flat – there is the same amount of fluid above the surface whether you are on the cold side or the warm side
But at upper levels, a pressure gradient appears …
Which gets stronger as you go up.
200 mb
400 mb
600 mb
800 mb L H
1000 mb Y X

25. Thickness
0 mb
The 1000 mb pressure surface is still flat – there is the same amount of fluid above the surface whether you are on the cold side or the warm side
But at upper levels, a pressure gradient appears …
Which gets stronger as you go up.
200 mb
400 mb
600 mb
800 mb L H
1000 mb Y X

26. Thickness
0 mb
The 1000 mb pressure surface is still flat – there is the same amount of fluid above the surface whether you are on the cold side or the warm side
But at upper levels, a pressure gradient appears …
Which gets stronger as you go up.
200 mb
400 mb
600 mb
800 mb L H
1000 mb Y X

27. Thickness and Thermal Wind
A temperature gradient forces the geostrophic wind to blow differently at different levels of the atmospher
As you go up in the atmosphere, the geostrophic wind blows more and more strongly keeping cold air to the left
We call this the thermal wind

28. Thickness and Thermal Wind
More technically, the thermal wind is defined as “the difference in the geostrophic wind between two pressure levels”
This vertical change in the geostrophic wind is entirely dependent on thickness: the “thermal wind” points parallel to lines of constant thickness, with low thicknesses to the left

29. 500 mb
850 mb

30. 500 mb
Thermal wind between 850 mb and 500 mb
850 mb

31. WARM
500 mb
Thermal wind between 850 mb and 500 mb
850 mb
COLD

32. Thickness and Thermal Wind
North Pole
The northern hemisphere is typified by cold air to the north and warm air to the south
Equator

33. Thickness and Thermal Wind
The northern hemisphere is typified by cold air to the north and warm air to the south
The height contours at upper levels are typified by low heights to the north, and high heights to the south, consistent with thickness h1 h2 h3 H

34. Thickness and Thermal Wind
This is why anomalously low pressure/height is referred to as a “trough”, and anomalously high pressure/height is referred to as a “ridge” h1 h2 H L h3

37. Thickness and Thermal Wind
Because mid-latitude cyclones mix warm and cold air along their fronts, they create ridges and troughs at upper levels by changing the temperature field:

38. Cyclone pushes warm air in front of it to the east, and pulls down cold air behind it to the west

39. Cyclone at upper levels sits above cold air, appearing slightly west of surface cyclone.

40. Cyclone at upper levels sits above cold air, appearing slightly west of surface cyclone.
As it turns out, this is a good place for the upper level low – it helps the lower level low get stronger, which in turn helps the upper level low get stronger – CYCLOGENESIS
But, that is a story for another time… L L