Thickness and Thermal Wind http www aos wisc

Thickness and Thermal Wind http: //www. aos. wisc. edu/~aalopez /aos 101/wk 12. 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 1000 mb

A Thought Experiment: The top of this column is quite high—let’s say that its pressure is 500 mb 1000 mb

A Thought Experiment: This column has some thickness: it is some distance between 1000 mb and 500 mb 1000 mb

A Thought Experiment: If we heat the column of air, it will expand, warm air is less dense. The thickness of the column will increase. 500 mb is now farther from the ground. 500 mb 1000 mb 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. 500 mb is now closer to the ground. 500 mb 1000 mb 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, 700 mb is quite high above the ground… 700 mb

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

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 500 mb and 400 mb are going to be very high above the ground. 400 mb 500 mb POLAR FRONT North COLD South WARM

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

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

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

Let’s draw a line from the cold side of the front to the warm side. 400 mb A 500 mb B 400 mb 500 mb POLAR FRONT North COLD South WARM

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

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

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

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

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

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

Key Points: This strong pressure gradient force happens: 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 All along the front, there is a strong pressure gradient force pushing northward.

Polar Front and The Jet 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: 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 counter. Clockwise with height Backing ! Lower Level Geo Wind Upper Level Geo Wind Thermal Wind

Backing or Veering? 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 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

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.

Thermal Equation (Cont) In the presence of a horizontal temperature gradient, the tilt of pressure surfaces increases with height. ug p=p 2 p=p 1 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.