Transcript Thickness and Thermal Wind

Thickness and Thermal Wind
http://www.aos.wisc.edu/~aalopez
/aos101/wk12.html
Pressure
• Pressure is the weight of
molecules ABOVE you
• Fewer molecules above
you as you go up causes
pressure to decrease with
altitude
• Temp, density, volume
change because of
pressure change – do not
cause the pressure change
as a parcel rises
Thickness
A Thought Experiment:

Start with a column of air.
A Thought Experiment:

The base of this column is
at the surface, so lets say
its pressure is about
1000mb.
1000mb
A Thought Experiment:

The top of this column is
quite high—let’s say that
its pressure is 500mb.
500mb
1000mb
A Thought Experiment:

This column has some
thickness: it is some
distance between 1000mb
and 500mb.
500mb
1000mb
A Thought Experiment:

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If we heat the column of
air, it will expand, warm
air is less dense.
The thickness of the
column will increase.
500mb is now farther
from the ground.
500mb
1000mb
Warmer
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
A Thought Experiment:

In fact, temperature is the ONLY factor in
the atmosphere that determines the
thickness of a layer!
A Thought Experiment:

It wouldn’t have mattered which pressure
we had chosen. They are all higher above
the ground when it is warmer….

…which is
what this
figure is
trying to
show.

In the
tropics,
700mb is
quite high
above the
ground…
700mb

…whereas it
is quite low
to the
ground near
the poles.
700mb
These layers
are much
less “thick”.
See how
“thick” these
layers are.
General Circulation Review
Conceptual Circulation
Let’s think about what thickness
means near a polar front, where
cold air and warm air are
meeting.

This is a cross section of the atmosphere.
North
COLD
South
WARM

Cold air is coming from the north. This air
comes from the polar high near the North
Pole.
North
COLD
South
WARM

Warm air is coming from the south. This
air comes from the subtropical high near
30°N.
North
COLD
South
WARM

These winds meet at the polar front.
POLAR
FRONT
North
COLD
South
WARM

Now, think about what we just learned
about how temperature controls the
THICKNESS of the atmosphere.
POLAR
FRONT
North
COLD
South
WARM

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

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

Above the front, the thickness of the
atmosphere changes rapidly.
400mb
500mb
400mb
500mb
POLAR
FRONT
North
COLD
South
WARM

Now, let’s think about the pressure
gradient force above the front.
400mb
500mb
400mb
500mb
POLAR
FRONT
North
COLD
South
WARM

Let’s 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

What is the pressure at point A?
400mb
A
500mb
B
400mb
500mb
POLAR
FRONT
North
COLD
South
WARM

The pressure at point A is less than
400mb, since it is higher than the 400mb
isobar on this plot. Let’s estimate the
pressure as 300mb.
400mb
A
500mb
300mb
B
400mb
500mb
POLAR
FRONT
North
COLD
South
WARM

What is the pressure at point B?
400mb
A
500mb
300mb
B
400mb
500mb
POLAR
FRONT
North
COLD
South
WARM

The pressure at point B is more than
500mb, since it is lower than the 500mb
isobar on this plot. Let’s estimate the
pressure as 600mb.
400mb
A
500mb
300mb
B
400mb
600mb
500mb
POLAR
FRONT
North
COLD
South
WARM

The pressure gradient force between point
B and point A is huge!
400mb
A
500mb
300mb
B
400mb
600mb
500mb
POLAR
FRONT
North
COLD
South
WARM

Therefore, all along the polar front, there
will be a strong pressure gradient force
aloft, pushing northward.
400mb
A
500mb
300mb
B
400mb
600mb
500mb
POLAR
FRONT
North
COLD
South
WARM
Key Points:

This strong pressure gradient force
happens:
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Aloft (above the surface)
Directly above the Polar Front
Also, this force pushes toward the north
(in the Northern Hemisphere).
Polar Front and The Jet

So, how does
this all cause
the
midlatitude jet
stream?
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 we’ll learn, this is NOT
how fronts are correctly
drawn, but it will work for
now.
Polar Front and The Jet
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All along the
front, there is
a strong
pressure
gradient force
pushing
northward.
Polar Front and The Jet
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Winds aloft
are in
geostrophic
balance…
Polar Front and The Jet

…so the true
wind will be a
WEST wind,
directly above
the polar
front.
Another View:

Here’s the same diagram, shown from a
slightly different angle, which might make
this all more clear.
In Perspective:
Here is the polar front at
the surface.
In Perspective:
Remember, it’s a polar
front because it is where
warm air from the south
meets cold air from the
north.
In Perspective:
The midlatitude jet
stream is found directly
above the polar front.
Conclusions:
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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.
This process is known as the THERMAL
WIND RELATIONSHIP.
Thermal Wind

The strength and
direction of the wind
changes with altitude
above the front
Lower
Level
Geostrophic
wind
Thermal Wind
Upper level geostrophic
wind
Backing and Veering of Wind
If winds rotate clockwise
From lower level to upper
Level  veering !
Thermal Wind
Lower level
Geo winds
Upper
Level
Geo wind
If winds rotate counterClockwise with height 
Backing !
Lower
Level
Geo Wind
Upper Level
Geo Wind
Thermal Wind
Backing or Veering?
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Find the lower level
geostrophic winds
Track angle (shortest)
FROM lower level
wind to upper level
wind
Did you go clockwise?
Did you go
counterclockwise?

CLOCKWISE 
VEERING

COUNTERCLOCKWISE
 BACKING
Cold or Warm Advection?

Thermal wind always
travels with COLDER
AIR ON ITS LEFT !
Recall that
Cold advection brings
Cold air into warm region
Definition of the thermal wind

The thermal wind (VT) is not a wind at
all, but a vector difference between the
geostrophic wind at one level and the
geostrophic wind at another level, i.e., it is
a wind shear :

VT = Vupper level - Vlower level
Cold
No thermal advection:
Thermal wind is parallel to low level wind, so
geostrophic wind at lower and upper levels are
parallel
V1
VT
V2
Warm
Cold
V2
Cold Air Advection:
Thermal wind is to the left of the low level wind, so
geostrophic wind must back with height => CAA
VT
V1
Warm
Cold
Warm Air Advection:
V1
Thermal wind is to the right of the low level wind, so
geostrophic wind must veer with height => WAA
VT
V2
Warm
Thermal Wind Equation

Thickness is proportional to the mean
temperature in the layer. Lines of equal z
(isobars of thickness) are equivalent to the
isotherms of mean temperature in the
layer.
Thermal Equation (Cont)
In the presence of a horizontal temperature gradient,
the tilt of pressure surfaces increases with height.
ug
p=p2
p=p1
cold
warm
Thermal wind relationship
The change in the Geostrophic Wind is directly proportional to the
horizontal temperature gradient
This is the Thermal (temperature) Wind relationship (refer to fig 3.8 in the
book)
Thermal Wind

A horizontal thermal gradient creates
a PGF at upper levels. As you increase
in altitude, the pressure gradient
between the warm column and the
cool column increase. Last week we
saw that wind in geostrophic balance,
balances the PGF and Coriolis force.
As the PGF increases the magnitude
of the wind will increase and so will
the Coriolis force. In this figure, the
size of the green circles represent the
magnitude of the geostrophic wind
and the x in the circle represents the
tail end of the directional arrow, so
we are looking at an arrow pointing
into away from us.

The vertical change in geostrophic wind is called the
geostrophic vertical shear. Since the geostrophic
vertical shear is directly proportional to the horizontal
temperature gradient, it is also called the Thermal
Wind
So the Thermal wind is not an actual wind, but the
difference between two winds at different levels.