Conservation of PV

1. Conservation of PV 1 PVU = 10-6 m2 K kg-1 s-1 There is a “potential” to create relative vorticity by changing latitude or by changing the thickness of isentropic layers A parcel of air flowing from a cold, statically stable region to a warm, less stable region will acquire positive relative vorticity through PV conservation (or stretching).

2. Climatological PV and theta (zonally averaged, northern winter) Theta: dashed contours with intervals 30K PV: solid contours, units: PVU PV increases northward and upward. Hoskins 1990

3. Penetration depth f =Coriolis parameter L=characteristic length scale N= Brunt-Vaisala frequency Positive PV anomaly: - Cyclonic flow - Magnitude maximum at anomaly level - Circulation extends above and below anomaly - Depth of circulation called the “penetration depth” Negative PV anomaly: - Anticyclonic flow - Magnitude maximum at anomaly level - Circulation extends above and below anomaly - Depth of circulation called the “penetration depth”

4. Low level PV anomalies Warm anomaly at surface associated with low pressure system Positive vorticity Note fake isentropes below ground (positive static stability!)

5. Cyclogenesis from a PV perspective The nature of propagation of an upper-level PV anomaly Consider the (x,y) projection of an upper air PV anomaly (this is equivalent to a trough, since cold air is present beneath the anomaly) The anomaly will propagate westward with a new (negative) anomaly developing to the east due to advection of PV. This is equivalent to the westward propagation of Rossby waves due to advection of planetary vorticity

6. Cyclogenesis from a PV perspective The nature of propagation of a low-level PV anomaly Consider the (x,y) projection of An lower atmosphere PV anomaly (a wave in the potential temp field) The anomaly will propagate eastward due to thermal advection.

7. Cyclogenesis from a PV perspective Upper level PV anomaly Lower level PV anomaly Each anomaly has a circulation associated with it that extends some depth through the troposphere For development of a cyclone, these circulations must come into phase and reinforce one another – but how, since they propagate in opposite directions?

8. Consider an upper-level positive PV anomaly propagating over a low-level baroclinc zone WTA • Upper positive PV anomaly is associated with a cyclonic circulation below it (determined by the penetration depth); • The resultant low-level circulation induces a warm anomaly to its east through warm thermal advection (WTA).

9. The warm anomaly acts as a positive PV anomaly near the surface. It has its own cyclonic circulation, which extends upward to some extent (determined by the penetration depth) • The resultant upper-level circulation is to the east of the original positive PV anomaly.

10. PPVA • This circulation induces positive PV advection (PPVA) to its west , which is in the eastern half of the original upper-level positive PV anomaly.

11. The effect is to strengthen the upper level positive PV anomaly and reduce its westward propagation tendency. • The upper level anomaly has increased influence on lower level thermal advection, strengthening the lower level anomaly and reducing its eastward propagation tendency.

12. Ut • The upper-level and low-level circulations are phase locked and amplify each other. • Cyclone development can not occur unless there is an up-shear vertical tilt.

13. Diabatic processes and the PV perspective (290-292 of Martin) Diabatic processes are associated with the creation or destruction of PV. In pressure coordinates: Where ηa is the 3D absolute vorticity vector, and is the heating rate. Neglecting the horizonal components: PV is increased when the vertical gradient of diabatic heating is positive.

14. Maximum Heating Rate

15. A diabatic heating maximum occurs downstream of the upper level PV anomaly where air is rising most vigorously and in the middle troposphere where the maximum condensation occurs. Erodes upper level PV anomaly Strengthens low-level PV anomaly

16. In an extratropical cyclone diabatic heating builds ridge aloft and strengthens cyclone at surface

17. Stratiform Precipitation Stratiform Precipitation Height (km) B Spin up the mid-level cyclonic circulation A Heating Spin down the low-level cyclonic circulation Schumacher et al. 2004