Thickness and the Thermal Wind

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Thickness and the Thermal Wind

• AOS 101 Discussions 301/303
• April 14th / April 16th, 2008

Discussion Leader Brian Miretzky
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Review

• Turn in hw 8
• Go over hw 7
• Parcel Path is an instantaneous view of what
  might happen to a parcel as it rises up at the
  next moment
• In future times the profile of the atmosphere
  will likely be different
• Lake Mendota declared ice free April 10th, no 70
  degree day yet this week?

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Hydrostatic Balance

• Known that pressure decrease with height
• Thus we have a vertical pressure gradient force
  pointing?...
• Upward
• This is counteracted with the gravitational force
  point downward, which may lead to hydrostatic
  equilibrium.
• Often we take this to be the case in our
  atmosphere.
• ?P ? g ?z

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Hypsometric Equation

• Combining the previous equation with the ideal
  gas law allows us to formulate the hypsometric
  equation
• Z2-Z1 (RT)/g ln(P2 P1)
• This gives a way to calculate the thickness of an
  atmospheric layer.
• One assumption made here is that gravity which
  actually does slightly decrease the farther away
  from Earth is the same all the time in this
  equation. This allows us to reference our Z
  (geopotential height) to z (geometric height)

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Thickness

• Before we make sure the equation makes physical
  sense lets explore what we mean by thickness in
  terms of previously discussed atmospheric
  characteristics
• Lets start with a statement

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Upper Tropospheric Pressure Surfaces
The height of a pressure surface above ground is
analogous to the pressure. As an example, a low
height of the 500 mb surface is analogous to
lower pressure. This will be very important when
we analyze upper tropospheric data.
Figure A 3-dimensional representation of the
height of the 500 mb surface (in meters)
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A Thought Experiment

• Start with a column of air.

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A Thought Experiment

• The base of this column is at the surface, so
  lets say its pressure is about 1000mb.

1000mb
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A Thought Experiment

• The top of this column is quite highlets say
  that its pressure is 500mb.

500mb
1000mb
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A Thought Experiment

• This column has some thickness there is some
  distance between 1000mb and 500mb.

500mb
1000mb
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A Thought Experiment

• If we heat the column of air, it will expand
  because warm air is less dense.
• The thickness of the column will increase.
• 500mb is now farther from the ground.

500mb
1000mb
Warmer
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A Thought Experiment

• If we cool the column of air, it will shrink,
  cool air is more dense.
• The thickness of the column will decrease.
• 500mb is now closer to the ground.

500mb
1000mb
Colder
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A Thought Experiment

• In fact, temperature is the ONLY factor in the
  atmosphere that determines the thickness of a
  layer!

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A Thought Experiment

• It wouldnt have mattered which pressure we had
  chosen. They are all higher above the ground
  when it is warmer.

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• which is what this figure is trying to show.

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• In the tropics, 700mb is quite high above the
  ground

700mb
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• whereas it is quite low to the ground near the
  poles.

700mb
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These layers are much less thick.
While these have a greater thickness.
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Lets think about what this means near a polar
front, where cold air and warm air are meeting.
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• This is a cross section of the atmosphere.

North COLD
South WARM
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• Cold air is coming from the north. This air
  comes from the polar high near the North Pole.

North COLD
South WARM
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• Warm air is coming from the south. This air
  comes from the subtropical high near 30N.

North COLD
South WARM
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• These winds meet at the polar front.

POLAR FRONT
North COLD
South WARM
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• Now, think about what we just learned about how
  temperature controls the THICKNESS of the
  atmosphere.

POLAR FRONT
North COLD
South WARM
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• On the warm side of the front, pressure levels
  like 500mb and 400mb are going to be very high
  above the ground.

400mb
500mb
POLAR FRONT
North COLD
South WARM
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• On the cold side of the front, pressure levels
  like 500mb and 400mb are going to be very low to
  the ground.

400mb
500mb
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• Above the front, the thickness of the atmosphere
  changes rapidly.

400mb
500mb
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• Now, lets think about the pressure gradient
  force above the front.

400mb
500mb
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• Lets draw a line from the cold side of the front
  to the warm side.

400mb
A
500mb
B
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• What is the pressure at point A?

400mb
A
500mb
B
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• The pressure at point A is less than 400mb, since
  it is higher than the 400mb isobar on this plot.
  Lets estimate the pressure as 300mb.

400mb
A
500mb
B
300mb
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• What is the pressure at point B?

400mb
A
500mb
B
300mb
400mb
500mb
POLAR FRONT
North COLD
South WARM
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• The pressure at point B is more than 500mb, since
  it is lower than the 500mb isobar on this plot.
  Lets estimate the pressure as 600mb.

400mb
A
500mb
B
300mb
400mb
600mb
500mb
POLAR FRONT
North COLD
South WARM
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• The pressure gradient force between point B and
  point A is huge!

400mb
A
500mb
B
300mb
400mb
600mb
500mb
POLAR FRONT
North COLD
South WARM
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• Therefore, all along the polar front, there will
  be a strong pressure gradient force aloft,
  pushing northward.

400mb
A
500mb
B
300mb
400mb
600mb
500mb
POLAR FRONT
North COLD
South WARM
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Key Points

• This strong pressure gradient force happens
• Aloft (above the surface)
• Directly above the Polar Front
• Also, this force is directed toward the north (in
  the Northern Hemisphere).

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Polar Front and The Jet

• So, how does this all cause the midlatitude jet
  stream?

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Polar Front and The Polar Jet

• Suppose we have a polar front at the surface.

This purple line is the polar front at the
surface. As well learn, this is NOT how fronts
are correctly drawn, but it will work for now.
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Polar Front and The Jet

• All along the front (aloft), there is a strong
  pressure gradient force pushing northward.

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Polar Front and The Jet

• Winds aloft are in geostrophic balance

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Polar Front and The Jet

• so the true wind will be a WESTERLY wind (a wind
  from the west), directly above the polar front,
  balancing the Coriolis force and the pressure
  gradient force

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Another View

• Heres the same diagram, shown from a slightly
  different angle, which might make this all more
  clear.

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In Perspective
Here is the polar front at the surface.
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In Perspective
Remember, its a polar front because it is where
warm air from the south meets cold air from the
north.
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In Perspective
The midlatitude jet stream is found directly
above the polar front.
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Some Conclusions

• The Midlatitude Jet Stream is found directly
  above the polar front, with cold air to the LEFT
  of the flow.
• This is because of the changes in THICKNESS
  associated with the polar front.
• The change in geostrophic wind with height is
  directly proportional to the horizontal
  temperature gradient!
• This process is known as the THERMAL WIND
  RELATIONSHIP.

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Thermal Wind
The thermal wind describes the vertical
geostrophic wind shear (i.e., the change of
geostrophic wind with height, or simply the
difference between two geostrophic wind vectors
with height) Remember The thermal wind, isnt
actually an observed wind!
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Thermal Wind
The most important result of the thermal wind
relationship is that Large temperature
gradients at the surface correspond to strong
winds aloft!
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Thermal Wind
The direction and strength of the thermal wind
tells us about the temperature structure of the
atmosphere A strong thermal wind means that the
temperature gradient is strong (and thus, the
geostrophic wind shear is also strong) Also, the
thermal wind always points in a direction with
cold air to the left!
Lower geo. wind
Upper geostrophic wind
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Backing vs. Veering
In the example to the right, the geostrophic wind
direction changes clockwise with height. This is
called veering of the geostrophic wind.
Veering of the geostrophic winds with height
always results in warm air advection, like the
picture to the right suggests.
Lower geo. wind
Upper geostrophic wind
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Backing vs. Veering
Now, in the example to the right, the geostrophic
wind direction changes counter-clockwise with
height. This is called backing of the
geostrophic wind. Backing of the geostrophic
winds with height always results in cold air
advection, like the picture to the right suggests.
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Now, lets look for some examples of the thermal
wind relationship in todays weather . . .