Jim Steenburgh Atmos 5110 University of Utah jim.steenburgh@utah

1. PV Jim Steenburgh Atmos 5110 University of Utah jim.steenburgh@utah.edu

2. What is PV thinking? • The use of potential vorticity conservation and “invertability” for understanding atmospheric dynamics and the evolution of large-scale weather systems

3. PV is conserved following fluid motion for adiabatic, frictionless flow Provides a tool for understanding cyclone evolution over complex terrain Components Absolute Vorticity Static Stability Potential vorticity (PV) review + p 

4. Units of K kg-1 m2 s-1 Define 1 PVU = 10-6 K kg-1 m2 s-1 PV is typically higher in the stratosphere (>2 PVU) and lower in the troposphere (< 2 PVU) Dynamic Tropopause – Tropopause defined using PV (I use 2 PVU, others 1.5) Potential vorticity (PV) review Stratosphere ( > 2 PVU) Dynamic Tropopause 2 PVU Troposphere ( < 2 PVU)

5. Example Stratospheric Reservoir Dynamic Tropopause Tropopause Undulation PV “Wall” Not quite a fold Troposphere

6. Summary of terms • Dynamic tropopause – tropopause defined using potential vorticity (i.e., 1.5 or 2.0 PV surface) • Stratospheric reservoir – region of high PV in the stratosphere • Tropopause undulation – wave-like undulation in the tropopause • Tropopause fold – area where stratospheric air folds under tropospheric air

7. Dynamic trop height is high in tropics, low in high latitudes Dynamic trop pressure is low in tropics, high in high latitudes Dynamic trop potential temperature is high in tropics, low in high latitudes On an isentropic surface (e.g., 320) PV increases toward the poles If adiabatic/frictionless, PV conserved on an isentropic surface and potential temperature conserved on a PV surface (e.g., the dyn trop) Mean distribution of PV in the atmosphere (Bluestein 1993)

8. Dynamic tropopause analysis • An analysis of variables (e.g., wind, pressure) on the dynamic tropopause • Advantages • Jets (subtropical and polar) are frequently at differing pressure levels, but are typically near the dynamic tropopause • Tropopause pressure or potential temperature can be used to identify PV “anomalies” & upper-level troughs and ridges • Contain a huge amount of information about the upper-levels on a single map

9. Synoptic application • Regions of high tropopause pressure (low potential temperature) are cyclonic PV anomalies and accompanied by upper-level troughs/cyclones • Regions of low tropopause pressure (high potential temperature) are anticyclonic PV anomalies and accompanied by upper-level ridges/anticyclones • Rising tropopause pressure is an indication of a developing trof or weakening ridge • Falling tropopause pressure is an indication of a weakening trof or developing ridge • Strong jets are usually found in regions of large tropopause pressure gradients (a.k.a. the PV Wall).

10. Dynamic tropopause pressure

11. Dynamic tropopause potential temperature

12. PV on an isentropic surface (315 K)

13. JIM Real-time Examples

14. Key components of PV thinking • Since PV and potential temperature are “conserved” their evolution is dominated by advective processes • Easy to conceptualize what is happening • PV can be “inverted” to deduce all other kinematic and themodynamic fields (e.g., wind and temperature) • PV non-conservation can be used to better understand how diabatic processes influence large-scale dynamics

15. Following Bluestein Vol. II, sec 1.9, PV can be inverted if we assume a suitable “balance conditions” Cyclonic PV anomalies induce a cyclonic circulation Anticyclonic PV anomalies induce an anticyclonic circulation What is inversion? - + + - Hoskins et al. (1985) [following Thorpe 1985)

16. The induced cyclonic circulation and temperature anomalies are strongest near the PV anomalie and spread horizontally and vertically Vertical penetration is inversely proportional to stability High stability = weak penetration Low stability = strong penetration What is inversion? - + + - Hoskins et al. (1985) [following Thorpe 1985)

17. A warm thermal anomaly at the earth’s surface acts like a cyclonic PV anomaly and induces a cyclonic circulation A cold thermal anomaly at the earth’s surface acts like an anticyclonic PV anomaly and induces an anticyclonic circulation Circulations penetrate horizontally and vertically (latter inversely proportional to static stability) What is inversion? - + - + Hoskins et al. (1985) [following Thorpe 1985)

18. Upper-level PV anomaly and surface thermal anomaly become “phase locked” and mutually amplify Upper-level PV anomaly overtakes low-level frontal zone Cyclonic circulation associated with upper-level PV anomaly produces a warm tongue/anomaly Cyclogenesis from a PV-thinking perspective

19. Two anomalies become phase locked, mutually amplify, and cyclogenesis occurs Cyclonic circulation induced by surface warm anomaly advects high PV air aloft equatorward enhancing upper level PV anomaly Cyclonic circulation induced by upper-level PV anomaly amplifies surface thermal anomaly Overall cyclonic circulation amplifies Cyclogenesis from a PV-thinking perspective

20. Cyclogenesis from a PV-thinking perspective • Cyclone building blocks • Upper-level cyclonic PV anomaly associated with tropopause depression • Diabatically generated cyclonic PV anomaly associated with condensation • Warm anomaly at ground (eventually the frontal wave) • Davis and Emanuel (1991) use “piecewise” inversion to quantify contributions from these building blocks PV “Destroyed” PV “Generated”

21. Real-world example (Davis and Emanuel 1991) Surface potential temperature with 925 mb winds induced from upper level PV anomaly Acts to amplify surface thermal anomaly as cyclogenesis ensues

22. Real-world example (Davis and Emanuel 1991) Tropopause potential temperature with tropopause winds induced by surface thermal anomaly AND low-level cyclonic PV induced by diabatic heating Amplifies upper-level anomaly (example of phase locking)

23. Real-world example (Davis and Emanuel 1991) Surface potential temperature with 925 mb winds induced from “interior” PV anomaly Acts initially to amplify surface thermal anomaly & then propagate anomaly in later stages

24. Real-world example (Davis and Emanuel 1991) Surface potential temperature with 925 mb winds induced from diabatically generated cyclonic PV anomaly Acts to amplify surface thermal anomaly