SO441 Synoptic Meteorology

1. SO441 Synoptic Meteorology Lesson 6: Potential vorticity

2. 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

3. 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.

4. 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

5. 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?

6. 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)

7. 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