1. A&OS C110/C227: Review of thermodynamics and dynamics IV
Robert Fovell
UCLA Atmospheric and Oceanic Sciences

2. Notes Everything in this presentation should be familiar
Please feel free to ask questions, and remember to refer to slide numbers if/when possible
If you have Facebook, please look for the group “UCLA_Synoptic”. You need my permission to join. (There are two “Robert Fovell” pages on FB. One is NOT me, even though my picture is being used.)

3. Question for thought
Temperature differences make pressure differences, and pressure differences drive winds.
The purpose of winds is to “blow themselves out”, to reduce the temperature difference
The ideal situation is for the atmosphere to push warm air towards the cold place and cold air towards the warm place simultaneously
Consider the near-surface wind. Assume air can move only in one direction. Which is “easier” to accomplish: warm towards cold or cold towards warm?

4. The sea-breeze circulation or “one-cell” model

5. Step I • Start with no pressure difference between sea and land
• Heating increases temperature and thickness of air over land (hypsometric)
• Pressure difference starts moving air from warm column into cold column

6. Step II
• The flow of air aloft from the warm to the cold column implies vertical motions
• Air rises in warm column, and cools adiabatically as a result
• Air sinks in the cold column, and is subject to compression warming

7. Step III
• The column mass changes imply surface pressure changes, owing to hydrostatics
• Surface pressure beneath the warm column drops, as mass is lost above it
• Surface pressure beneath the cold column rises as mass flows into it

8. Step IV
• The surface pressure gradient encourages air to flow from the cold towards warm
• The “one-cell” circulation, driven by a temperature difference, is completed
• Note the importance of vertical motions in reducing the temperature difference
Land breeze

9. Thermally direct
This circulation is established spontaneously in response to the temperature difference that develops between land and sea. It does not need to be forced
This circulation is termed thermally direct
Note the thermally direct circulation consists of warmer air rising and colder air sinking, which works against the original temperature difference
Note also the near-surface wind is directed from cold towards warm

10. Hemispheric meridional (three-cell) circulation model

11. Hemispheric one-cell model
• Apply the one-cell sea-breeze model to the entire northern hemisphere
• This would suggest surface low pressure and rising air over the warm equator
and surface high pressure and sinking air over the cold pole

12. Three-cell step I
• Earth’s rotation breaks the single cell circulation into three cells, named the
polar, Ferrel and Hadley cells
• Sinking air and surface high pressure are created near 30˚N
• Rising air and surface low pressure are established near 60˚N

13. Three-cell step II • The polar and Hadley cells are thermally direct
• Note the middle (Ferrel) cell is thermally indirect. It is forced, the “middle cog”
• The surface pressure gradients are now as shown. What would the geostrophic
winds be?

14. Three-cell step III
• The Coriolis force opposes PGF, acts to the right of the winds in the N hemisphere
• The geostrophic winds would be easterly (east to west) between the pole and
60˚N, and between 30˚N and the equator
• The midlatitude winds are westerly

15. Surface winds – plan view
• The polar easterlies and midlatitude westerlies have been drawn in geostrophic
balance, but not the tropical north-east trade winds.
• The trade winds are depicted with a component from H to L pressure. Why?

16. The geostrophic wind Recall the geostrophic wind equations
The Coriolis parameter f is a function of latitude, and vanishes at f = 0˚ (equator)
Geostrophic balance cannot be maintained in the tropics. f is too small.

17. What f is and means… f is the vertical component
of Earth’s rotation vector

18. What f is and means…

19. What f is and means…

20. The “thermal wind”: basic concept

21. Winds above the surface
Earth’s rotation produces a three-cell per hemisphere structure, with polar easterlies and midlatitude westerlies in geostrophic balance, and tropical NE trades with a component from H towards L
Note surface friction was not included in that simple picture
How do the winds vary with height above the surface?
Keep in mind the following:
Temperature differences make pressure differences, and pressure differences drive winds
Temperature differences ALSO make pressure differences vary with altitude… which results in vertical wind shear
Wind shear is the change of wind speed and/or direction over a distance
The relationship between horizontal temperature variations and how the horizontal wind changes with height is called the thermal wind relationship
The thermal wind is the vertical shear of the geostrophic wind. The concept is only valid when and where geostrophic balance is

22. Thermal wind I
• Suppose the 1000 mb isobar has no N-S tilt, and therefore no PGF
• The mb layer T is higher to the S, so the PGF points to the N at 750 mb
• The 750 mb geostrophic wind is westerly, as shown at right
• The horizontal T difference has already caused a westerly vertical wind shear

23. Thermal wind II
• The mb layer is ALSO warmer to the south, so it is thicker there
• This means the 500 mb isosurface has greater tilt, and larger PGF, than at 750 mb
• Therefore, the 500 mb geostrophic wind is even more westerly than at 750 mb
• The effects of horizontal temperature differences are cumulative

24. Thermal wind III
• The mb layer is still warmer and thicker to the south
• Westerly wind speed continues to increase with height
• Where it is warmer to the south, the vertical shear is westerly

25. Thermal wind IV
• Suppose the mb layer is warmer and thicker to the N. (How? Why?)
• The 100 mb layer has less tilt than the 250 mb layer
• 100 mb PGF is smaller, and the wind, though still westerly, is weaker in magnitude
• Where it is warmer to the north, the vertical shear is easterly

26. Thermal wind V
•The mb layer can be warmer at the pole because it resides in the
stratosphere, while the tropical layer is still below the tropopause
• In the stratosphere, T ceases decreasing with height, and may increase
• Note the fastest westerly wind resides where the N-S T difference vanishes

27. Jet stream I
The tropical atmosphere is relatively warm, so the troposphere is deep and the tropopause is high
Minimum T is reached at the tropopause and it’s quite cold (-80˚C)

28. Jet stream II
Suppose the troposphere contains the same mass above equator and pole (not quite true)
Surface pressure ~ same, too
The colder polar troposphere needs to be thinner, so its tropopause is lower
As drawn, T in the polar stratosphere does not increase with height, but at least it stops decreasing

29. Jet stream III
Note the level where the polar air T equals tropical air T. Above that level, the polar air is actually warmer, even in winter.
At that level, the N-S temperature gradient vanishes. That is the level where the midlatitude (subtropical) jet stream is found

30. Recap This explains why a jet stream would be found at a height where
the horizontal temperature gradient vanishes. It does not explain
why jet streams tend to be concentrated in space.

31. Zonal wind variation with latitude and pressure (height)
Including NCEP/NCAR Reanalysis plots obtained from

32. Zonal wind vs. pressure/latitude
Data from the NCEP/NCAR Reanalysis, representing long term means from 1950 to 2010
“Zonal wind” means the west-east component, westerly is positive, easterly is negative
First plot will also be averaged through the year (January to December), creating an annual average
South pole is at left, north pole at right
Things we will note
Westerly winds near surface in midlatitudes of both hemispheres that increase with height through troposphere
Westerly jet at about 200 mb level in both hemispheres at 30-40˚ latitude. Westerly winds decrease farther aloft
Weak easterly flow above equator through a very deep layer
Polar surface easterlies very difficult to see.
27 m/s or 60 mph

36. C W W C

37. Two vertical profiles of zonal wind U

38. Questions for thought Zonal wind vs. height for two times of year
Height #5 is the tropopause, and J means jet max
In the profile at left there is an easterly jet at height #1. It is westerly at height #1 in the profile at right.
At which heights (1-5) does the horizontal temperature gradient vanish for each profile?
Which profile most likely represents summer, and why?

39. The “thermal wind”: temperature advection

40. Problem
Suppose the geostrophic wind at level p is from the south, at 10 m/s.
Suppose the horizontal temperature gradient is purely N-S, with colder air to the north
Questions will be:
In a N-S vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
In an E-W vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
In a plan view, draw the geostrophic winds at p and p-∆p, the shear vector, and isotherms of layer mean temperature
Determine the sense of temperature advection: cold, warm or no advection

41. Question 1: In a N-S vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
• The geostrophic wind at level p is from the S. This means the PGF points W.
• Thus, isobaric surface p does NOT tilt in the N-S direction, since the N-S PGF
component is zero.
• The zonal component of the geostrophic wind at level p is zero.

42. Question 1: In a N-S vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
• However, it is colder to the N, so there is a westerly geostrophic wind at p-∆p
• Thus, there is a vertical shear in the west-east wind
• Westerly vertical shear occurs when it is colder to the N

43. Question 2: In an E-W vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
• The geostrophic wind at level p is from the S. This means the PGF points W.
• How does isobaric surface p-∆p tilt?

44. Question 2: In an E-W vertical cross-section, sketch isobaric surfaces p and p-∆p. Also sketch the west-east component of the geostrophic wind at levels p and p-∆p
• The problem states there is NO temperature gradient in the W-E direction
• Therefore, there is no thickness variation from W to E
• The thermal wind concept says there is no shear in the N-S wind between levels
p and p-∆p, so the PGF at level p-∆p is the same as at level p
• There is a wind at both levels. There is no shear in this component between them.

45. Question 3: In a plan view, draw the geostrophic winds at p and p-∆p, the shear vector, and isotherms of layer mean temperature
• The geostrophic wind at level p is from the south, as shown
• What does the geostrophic wind at level p-∆p look like?

46. Question 3: In a plan view, draw the geostrophic winds at p and p-∆p, the shear vector, and isotherms of layer mean temperature
• The geostrophic wind at level p-∆p has a component of PGF pointing W, yielding
a southerly wind component, AND also a PGF component pointing N,
representing a westerly wind component
• As a consequence, the wind at p-∆p is from the southwest

47. Question 3: In a plan view, draw the geostrophic winds at p and p-∆p, the shear vector, and isotherms of layer mean temperature
• The shear vector is drawn from the head of the lower level wind vector to the
head of the upper level wind vector.
• What do the isotherms of layer mean T look like? Keep in mind the temperature
gradient was purely N-S in this problem

48. Question 3: In a plan view, draw the geostrophic winds at p and p-∆p, the shear vector, and isotherms of layer mean temperature
• Isotherms of layer mean temperature are parallel to the shear vector, with
cold air to the LEFT

49. Question 4: Determine the sense of temperature advection: cold, warm or no advection
• Note the wind at both levels has a component blowing from warm towards cold.
This is WARM ADVECTION
• Note further that the component of the wind DOING the advection is constant with
height. The shear vector shows that what changes between the levels is
parallel to the isotherms, and so isn’t doing any advecting!

50. A closer look…
• There are three independent pieces of information in this problem: the geostrophic
wind at the lower level, at the upper level, and the orientation of the T gradient
• Given two of those, you can determine the third
• Example: given one wind and shear vector, you know lower level wind and the
isotherms. Given isotherms and one wind, you can get the other wind

51. Important information I
In the example problem the winds turned clockwise with height. This is called veering, and is associated with warm advection
When the wind turns counterclockwise with height, that is called backing and is associated with cold advection
Note again the wind component doing the temperature advection does not change magnitude with height!
BUT the thermal wind is the vertical shear of the geostrophic wind. If the wind is not geostrophic, the thermal wind concept does not strictly apply
The wind is NOT geostrophic when
The isobars are curved
Friction is acting, as near the real surface
Coriolis force is unimportant (spatial/temporal scales are too small)
You are too close to the Equator

52. Important information II
In particular, note that the wind ALMOST ALWAYS veers with height near the surface, due to FRICTION
Friction slows the wind, reducing Coriolis force and permitting the large-scale wind to flow with a component towards L pressure
As one ascends from the surface, friction lessens, so the wind moves clockwise towards geostrophic balance
This near-surface veering does NOT necessarily mean warm advection is occurring
When friction is important, the wind isn’t geostrophic!
When the wind isn’t geostrophic, one needs to replace the actual wind with a geostrophic version to apply the thermal wind concept

53. Computing shear and T gradients
• Let the thermal wind (vertiical shear vector) between layers p0 and p1
(p0 > p1) be defined as
• These components can be related to the horizontal gradients of layer mean T as
where f = 2OsinF and Rd = 287 J/(kg K) for dry air

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