Thickness and Thermal Wind aalopez /aos101/wk12.html aalopez /aos101/wk12.html

Thickness and Thermal Thickness and Thermal WindWind

http://www.aos.wisc.edu/~aalopez/aos101/wk12.html



PressurePressure• 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

ThicknessThickness

A Thought Experiment:A Thought Experiment:

Start with a column of Start with a column of air.air.


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

1000mb


The top of this column The top of this column is quite high—let’s say is quite high—let’s say that its pressure is that its pressure is 500mb.500mb.

1000mb

500mb


This column has some This column has some thicknessthickness: it is some : it is some distance between distance between 1000mb and 500mb.1000mb and 500mb.

1000mb

500mb


If we If we heatheat the column the column of air, it will expand, of air, it will expand, warm air is less dense.warm air is less dense.

The The thicknessthickness of the of the column will increase.column will increase.

500mb is now 500mb is now farther farther from the ground.from the ground. 1000mb

500mb

Warmer


If we If we coolcool the column the column of air, it will shrink, of air, it will shrink, cool air is more dense.cool air is more dense.

The The thicknessthickness of the of the column will decrease.column will decrease.

500mb is now 500mb is now closer to closer to the ground.the ground. 1000mb

500mb

Colder


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


It wouldn’t have mattered It wouldn’t have mattered whichwhich pressure we had chosen. They are pressure we had chosen. They are allall higher above the ground when it higher above the ground when it is warmer….is warmer….

……which is which is what this what this figure is figure is trying to trying to show.show.

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

700mb

……whereas whereas it is quite it is quite low to the low to the ground ground near the near the poles.poles.

700mb

See how “thick” these layers are.

These layers are much less “thick”.

General Circulation ReviewGeneral Circulation Review

Conceptual CirculationConceptual Circulation

Let’s think about what Let’s think about what thickness means near a thickness means near a polar polar

frontfront, where cold air and , where cold air and warm air are meeting.warm air are meeting.

This is a cross section of the This is a cross section of the atmosphere.atmosphere.

North

COLDSouth

WARM

Cold air is coming from the north. Cold air is coming from the north. This air comes from the polar high This air comes from the polar high near the North Pole.near the North Pole.

North

COLDSouth

WARM

Warm air is coming from the south. Warm air is coming from the south. This air comes from the subtropical This air comes from the subtropical high near 30°N.high near 30°N.

North

COLDSouth

WARM

These winds meet at the These winds meet at the polar frontpolar front..

North

COLDSouth

WARM

POLAR FRONT

Now, think about what we just Now, think about what we just learned about how temperature learned about how temperature controls the THICKNESS of the controls the THICKNESS of the atmosphere.atmosphere.

North

COLDSouth

WARM

POLAR FRONT

On the warm side of the front, On the warm side of the front, pressure levels like 500mb and pressure levels like 500mb and 400mb are going to be very high 400mb are going to be very high above the ground.above the ground.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

On the cold side of the front, On the cold side of the front, pressure levels like 500mb and pressure levels like 500mb and 400mb are going to be very low to 400mb are going to be very low to the ground.the ground.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

Above the front, the thickness of the Above the front, the thickness of the atmosphere changes rapidly.atmosphere changes rapidly.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

Now, let’s think about the pressure Now, let’s think about the pressure gradient force above the front.gradient force above the front.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

Let’s draw a line from the cold side of Let’s draw a line from the cold side of the front to the warm side.the front to the warm side.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B

What is the pressure at point A?What is the pressure at point A?

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B

The pressure at point A is less than The pressure at point A is less than 400mb, since it is higher than the 400mb, since it is higher than the 400mb isobar on this plot. Let’s 400mb isobar on this plot. Let’s estimate the pressure as 300mb.estimate the pressure as 300mb.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B300mb

What is the pressure at point B?What is the pressure at point B?

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B300mb

The pressure at point B is more than The pressure at point B is more than 500mb, since it is lower than the 500mb, since it is lower than the 500mb isobar on this plot. Let’s 500mb isobar on this plot. Let’s estimate the pressure as 600mb.estimate the pressure as 600mb.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B300mb

600mb

The pressure gradient force between The pressure gradient force between point B and point A is point B and point A is hugehuge!!

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B300mb

600mb

Therefore, all along the polar front, Therefore, all along the polar front, there will be a strong pressure there will be a strong pressure gradient force aloft, pushing gradient force aloft, pushing northward.northward.

North

COLDSouth

WARM

POLAR FRONT

500mb

400mb

500mb

400mb

A

B300mb

600mb

Key Points:Key Points:

This strong pressure gradient force This strong pressure gradient force happens:happens: Aloft (above the surface)Aloft (above the surface) Directly above the Polar FrontDirectly above the Polar Front

Also, this force pushes toward the Also, this force pushes toward the north (in the Northern Hemisphere).north (in the Northern Hemisphere).

Polar Front and The JetPolar Front and The Jet

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

Polar Front and The Polar JetPolar Front and The Polar Jet

Suppose we Suppose we have a polar have a polar front at the front at the surface.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.


All along the All along the front, there front, there is a strong is a strong pressure pressure gradient gradient force force pushing pushing northward.northward.


Winds aloft Winds aloft are in are in geostrophic geostrophic balance…balance…


……so the true so the true wind will be wind will be a WEST a WEST wind, wind, directly directly above the above the polar front.polar front.

Another View:Another View:

Here’s the same diagram, shown Here’s the same diagram, shown from a slightly different angle, which from a slightly different angle, which might make this all more clear.might make this all more clear.

In Perspective:In Perspective:Here is the polar front

at the surface.

In Perspective: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:In Perspective:The midlatitude jet

stream is found directly above the

polar front.

Conclusions:Conclusions:

The Midlatitude Jet Stream is found The Midlatitude Jet Stream is found directly above the polar front, with directly above the polar front, with cold air to the LEFT of the flow.cold air to the LEFT of the flow.

This is because of the changes in This is because of the changes in THICKNESS associated with the polar THICKNESS associated with the polar front.front.

This process is known as the This process is known as the THERMAL WIND RELATIONSHIP.THERMAL WIND RELATIONSHIP.

Thermal WindThermal Wind

The strength and The strength and direction of the direction of the wind changes with wind changes with altitude above the altitude above the frontfront

Upper level geostrophicwind

LowerLevelGeostrophicwind

Thermal Wind

Backing and Veering of Backing and Veering of WindWind

Lower levelGeo winds Upper

LevelGeo wind

Thermal Wind

If winds rotate clockwiseFrom lower level to upperLevel veering !

Thermal Wind

Upper Level Geo Wind

LowerLevelGeo Wind

If winds rotate counter-Clockwise with height Backing !

Backing or Veering?Backing or Veering?

Find the lower level Find the lower level geostrophic windsgeostrophic winds

Track angle (shortest) Track angle (shortest) FROM lower level wind FROM lower level wind to upper level windto upper level wind

Did you go clockwise?Did you go clockwise? Did you go Did you go

counterclockwise?counterclockwise?

CLOCKWISE CLOCKWISE

VEERINGVEERING

COUNTERCLOCKWICOUNTERCLOCKWISE SE BACKING BACKING

Cold or Warm Advection?Cold or Warm Advection?

Thermal wind Thermal wind always travels with always travels with COLDER AIR ON ITS COLDER AIR ON ITS LEFT !LEFT !

Recall thatCold advection bringsCold 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

V V

V

1 T

2

Cold

Warm

VV

V

1

T

2

Cold

Warm

VV

V

1T

2

Warm

Cold

No thermal advection:

Thermal wind is parallel to low level wind, so geostrophic wind at lower and upper levels are parallel

Cold Air Advection:

Thermal wind is to the left of the low level wind, so geostrophic wind must back with height => CAA

Warm Air Advection:

Thermal wind is to the right of the low level wind, so geostrophic wind must veer with height => WAA

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.

In the presence of a horizontal temperature gradient, the tilt of pressure surfaces increases with height.

cold warm

ug

p=p1

p=p2

Thermal Equation (Cont)

Thermal wind relationshipThe change in the Geostrophic Wind is directly proportional to the horizontal temperature gradientThis 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.

http://www.aos.wisc.edu/%7Eaalopez/aos101/wk11.html#geo

http://www.aos.wisc.edu/%7Eaalopez/aos101/wk11.html#geo

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.

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Thickness and Thermal Wind aalopez /aos101/wk12.html aalopez /aos101/wk12.html