SO441 Synoptic Meteorology

Lesson 6: Potential vorticity

Potential Vorticity• Concept of potential vorticity:

– Take a column of air defined by two potential temperature surfaces (θ and θ+Δθ).

– Move this column of air eastward. Force it to go up and over a mountain range.

– What happens to the column of air??• It compresses (“fattens”) as it approaches the mountain, and stretches

again on the other side of the mountain

Figure adapted from http://www-das.uwyo.edu/~geerts/cwx/notes/chap12/pot_vort.html

Potential Vorticity• Mathematically, what is it?

– Measures absolute vorticity (spin) over the depth of a column of air

• What does it mean that potential vorticity is conserved?– Following air motion (Lagrangian perspective!!), absolute vorticity divided by depth of the fluid must

remain constant.

• Return to the scenario of easterly flow (a fluid column moves from west to east):– Along it’s path, potential vorticity must be constant. – f, Earth’s vorticity, is constant (b/c it moves to the east)– But h, depth, decreases as it approaches the mountain

• Thus, relative vorticity zeta must also decrease. A ridge forms.– After passing the mountain, depth increases again

• Thus, relative vorticity zeta must now also increase. A trough forms.

0D fDt h

fPVh

Potential Vorticity

• Physically, potential vorticity is a quantity that is– Useful to measure the “spin up” or “spin down” of

an air column for large-scale, adiabatic motion• The very important conservation property

(that potential vorticity is conserved following the fluid motion) is valid for– Atmospheric motions with no friction or diabatic

effects

Potential Vorticity in the real atmosphere

• Here are the average winter 500 mb heights for the NH (left) and SH (right)– Note the SH is nearly symmetric about the pole, but the NH is much

more wavy (3 mean troughs, to be exact)– Why is this the case? What is different about the flow from NH to SH?

Potential Vorticity in the real atmosphere

• Another property of Potential Vorticity is that the amplification of heights as flow approaches a mountain is most prnounced in the low levels. – So 700 mb (left) is much more wavy than 200 mb (right)

Potential Vorticity in the real atmosphere

• The requirement that potential vorticity be conserved is common in both hemispheres. – Flow crossing the Andes Mountains (which are VERY tall) results in

ridging over Chile and troughing over Argentina, Uruguay, and Brazil

Figure adapted from http://www-das.uwyo.edu/~geerts/cwx/notes/chap12/pot_vort.html