1. Call Passcode 69801

2. Potential Vorticity and Its Application in Operations
Philip N. Schumacher
11 December 2007
This talk is based on work done with Dr. Martin Baxter of Central Michigan University and Josh Boustead of WFO OAX.

3. Overview What is potential vorticity and why care.
Tropopause maps and its relationship to synoptic scale forcing
Potential vorticity distribution and TROWALs.
Internal potential vorticity anomalies.
PV and its impact on the warm conveyor belt.
The future - using PV to analyze model differences.

4. What is potential vorticity
Potential vorticity – conserved for frictionless and adiabatic flow.
(from Holton 1979)
A property of a stably stratified fluid – the atmosphere and oceans.

5. PV in the atmosphere PV has characteristics within the atmosphere.
Troposphere – PV ~1 PVU
Stratosphere – PV ~10 PVU
Tropopause – PV gradient separating the troposphere and stratosphere
Internal PV anomalies – Values can reach stratospheric levels.
More on these later.

6. Defining the tropopause
WMO definitition – lapse rate of -2˚C/km.
Dynamic tropopause (Morgan and Nielsen-Gammon 1998). The level where the PV exceeds some critical value.
Usually between 1 and 2 PVU.
The pressure of the dynamic tropopause is generally defined as the last time PV exceeds the critical value (moving up in the atmosphere).
Removes internal anomalies.

7. Tropopause undulations
Downward extension of the tropopause due to descent at and above the tropopause.
Macroscale features covering over 1000 km horizontally.
Characterized by:
a warm pool on an upper-level (e.g., 200 hPa) pressure surface
high static stability (~ 10 K per 50 hPa)
high IPV (> 2 PVU)
Otherwise known as short-wave troughs.

8. From Hirschberg and Fritsch (1991, MWR)
WAA W
200 hPa heights and temperatures
Cross section of temperature advection 10-1 K h-1) S
IPV
less stable
300 hPa static stability (10-3 K hPa-1)
250 hPa IPV (PVU units)
From Hirschberg and Fritsch (1991, MWR)

9. Finding tropopause undulations
Try looking at individual pressure surfaces.
But which gradients are important and at what level?
300 mb
350 mb
450 mb
400 mb

10. Let’s take another look!
If we trace the 1.5 PVU line, we find that different waves are available at different levels.
What if we plot pressure on a PV surface (1.5 PVU)?
Then multiple short-waves are visible on one map! 1 2 3 4

11. Hirschberg and Fritsch (1991, MWR)
Note ascent ahead of the undulation, subsidence behind. So positive PV advection is forcing for large-scale ascent.
Hirschberg and Fritsch (1991, MWR)

12. So what is the advantage?
All of these can be associated with synoptic-scale forcing for ascent:
Positive PV advection
Vorticity advection increasing with height
Convergence of Q-vectors

13. Let’s compare 0900 – 2300 UTC 28 Feb 2007 300-500 mb Q-vectors
700 mb Fgen
1.5 PV sfc pressure
700 mb Fgen
500 mb vorticity
700 mb
Fgen
Mosaic base reflectivity

14. Review
Q-vectors did not isolated the second wave moving into central Nebraska.
500 mb vorticity grid is more “noisy” to examine.
Can be difficult to discern subtle features. This is a big advantage in summer.

15. Other advantages
Q-vectors have be smoothed and on low-resolution grids.
Even smoothed fields on grids < 50 km resolution are too noisy.
RUC 80 km RUC 40 km

16. One other advantage
The “influence” of a wave on lower level circulations is related to:
Rossby depth – h ~ fL/N
f - Coriolis
L – horizontal scale of anomaly
N – Brunt-Väisälä frequency (stability)
N = (g/)(/z)
For a given wave the less stable the atmosphere, the deeper into the atmosphere it influences the winds and ageostrophic circulation.
Stability is why “weaker” waves in summer have a big influence on vertical motion.

17. Let’s go back to our tropopause map
If stability is constant, then waves 1 and 2 will have the biggest influence because they extend lower in the atmosphere. 1 4 3 2

18. Comparing a tropopause map to a constant pressure map
1800 UTC 17 January 1996
Tropopause map mb isotachs
Potential temperature (yellow), wind, and potential temperature advection (shaded)
Wind speed (shaded), height (white)

19. Distribution of PV and how it influences precipitation with TROWALS
How PV is organized near the tropopause can also influence where precipitation falls.
TROWALs are areas with low stability and ample moisture.
Determining where precipitation is favored within a TROWAL is critical to warning decisions and QPF/snowfall forecasts.

20. PV around 400 mb From Martin 1998
PV anomaly attached to polar vortex. Isolated southern stream PV anomaly.

21. 309 K Equivalent Temperature Surface
From Martin 1998

22. Snowfall totals from 19-20 January 1995.
Heavy snow north of pressure ridge.
Snowfall totals from January 2001.
Heavy snow south of pressure ridge.

23. Standard maps - 0000 UTC 20 Jan 1996 from Martin
Sfc mb
Notice the strong gradient along both the cold front and warm front up to 500 mb.
700 mb mb

24. 850 mb and 700 mb 1200 UTC 29 January 2001
850 mb mb

25. 300 mb and 500 mb UTC 29 January 2001
500 mb mb

26. Cross-section of frontogenesis
Both cross-sections run from west to east.
Frontogenesis (lower left) Frontogenesis (yellow lines), PV (shaded)

27. Conceptual Model of Physical Processes within the Trowal
from Moore et al. (2005)
Frontogenetical circulation
Frontogenetical zone
Isobars on an isentropic surface e
For cases where PV anomaly is attached to the polar vortex.
System-relative flow

28. Conceptual model for frontal circulation within a TROWAL associated with an isolated PV anomaly
Mid-level frontogenesis

29. Example from 1900 UTC 27 Nov 2005 – 1800 UTC 28 Nov 2005
Shaded – Pressure on the 1.5 PVU surface
Red solid lines – Pressure on the 1.5 PVU surface.
Dashed black lines – Pressure on the 310 K theta-E surface
0.5 reflectivity

30. Induced flow by PV anomalies
PV anomalies can induce flow away from where they are located.
The strength of the flow is determined by the size of the anomaly (wave) and the vertical stability.
Less stable – more influence
Larger wave – more influence

31. Non-conservation of PV
dθ/dt > 0
PV is produced below areas where diabatic heating is maximized. PV is destroyed above areas where diabatic heating is minimized
dθ/dt >> 0
dθ/dt > 0
PV decreased
PV increased

32. Effect of non-conservation
From Martin (2006)
Destruction of PV near the tropopause by latent heat release can increase amplitude of an upper level wave.
Production of PV below the tropopause by latent heat release can induce mid- or low level circulations (i.e. mesocyclone vortices).
Both can influence weather downstream.

33. PV inversions Given PV distribution through the atmosphere you can:
Determine the balanced wind field at all levels.
Determine the height field at all levels.
Recovers only the balanced wind (divergence is ignored).
From Baxter (2006)

34. SO WHAT???
Piecewise PV inversions (where the power is): Isolate anomalies or layers. Can determine the influence of individual anomalies throughout the atmosphere. Can create new conceptual models – and more!

35. Result of a piecewise inversion
From Baxter (2006)

36. Influence of PV anomalies on the low level jet/warm conveyor belt
950 mb QGPV anomaly
QGPV (shaded) and induced geostrophic wind.
From Lackmann (2002)
950 mb height and wind anomaly from interior QGPV.
Full PV and geostrophic wind.

37. Impact of LHR and PV generation along cold frontal precip bands
A strip of PV will be produced in the lower trop
An associated cyclonic circulation will result, enhancing the cyclonic shear across the frontal zone and contributing substantially to the strength of the cold frontal LLJ
This strengthening of the LLJ can result in enhanced downstream moisture transport
Martin (2006), after Lackmann (2002)

38. Some results of a Partners Project with WFO OAX and Dr
Some results of a Partners Project with WFO OAX and Dr. Martin Baxter from Central Michigan University
What role does convection play in the physical processes that create banded snowfall?
Does warm-sector convection aid or inhibit the development of banded snowfall?
How can convection influence the balance of processes that create banded snowfall?
Is convection always the dominant source of model forecast errors in these situations?
Previous work by Brennan and Lackmann (2006), Mahoney and Lackmann (2007), and Baxter (2006) examine the role of N-S oriented convection, our cases feature E-W oriented convection

39. Three Cases Were Selected
We’ll look at two cases involving diabatically generated PV anomalies that were E-W oriented along and north of warm frontal boundaries
Jan (OAX)
Feb (OAX/FSD)
48 hour simulations were performed using the WRF-ARW
Horizontal Domains: km, two-way nesting
Vertical Resolution: 50 levels, model top of 100 mb
Initial and Lateral Boundary Conditions: NARR - 32 km, 45 layers, updated every 3 hrs
Lin et al., RRTM, Dudhia, Monin-Obukov, Thermal Diffusion, YSU PBL, Kain-Fritsch (on two outermost domains only)
WRF-ARW simulations were compared with NARR data
Piecewise inversion performed on the NARR and WRF were done in two layers, 400 to 200 mb and 900 to 450 mb every 50 mb for each inversion

40. Case #1 Jan 4-5, 2005 Winter Storm
Long duration winter storm for the OAX CWA
Initial precipitation on the 4th was in response to strong WAA
The second round of precipitation on the 5th was due to strong dynamical forcing
Little in the way of frontogenesis with this system
Two events added up to large snowfall totals across eastern Nebraska and western Iowa.
We’ll be focusing on the 5 January.

41. Event Total Precipitation
COOP Data
WRF-48 hr Total

42. Surface Analysis 1800 UTC 5 Jan

43. Central Plains Radar Mosaic
Valid 1500 UTC 5 Jan
Valid 1800 UTC 5 Jan

44. 3-hr Accumulated Precipitation Valid 1500 UTC 5 Jan
NARR Data
WRF-ARW Data

45. Operational NAM/GFS 12-hr Accumulated Precipitation valid 0000 UTC 6 Jan

46. PV Comparison

47. NARR-WRF Difference Shaded – PV around 700 mb from NARR.
Red lines – NARR – WRF PV difference around 700 mb.
Wind barbs – Narr – WRF wind vector difference at 700 mb

48. Induced 700 hPa Height and Wind Perturbation Inversion from 400 to 200 hPa

49. Induced 700 hPa Height and Wind Perturbation Inversion from 900 to 450 hPa
NARR
WRF

50. PV Anomalies (700 mb) – 18 Z 5th NARR WRF
“Assumed” flow based on position of PV anomalies
Notice the PV in MO/IL associated with the convection in the NARR

51. Summary Jan 3-5 Winter Storm
The influence of the upper-level PV anomalies on the low-mid level fields was similar in the NARR & WRF
Evaluation of the low-mid level PV anomalies helps us to understand forecast errors and how they can be modified
The more E-W orientation of the 700 mb PV anomaly in the WRF led to an incorrect focus for precipitation. While the convection in the NARR led to a different PV structure resulting in greater temperature advection in Northern IA and increased westerly flow over MO/AR/OK .

52. February 13-14, 2004 Winter Storm
Heavy snow and freezing rain fell in the mid-Missouri River Valley into southern Iowa
Heavy rainfall occurred the mid-Mississippi Valley into the lower Ohio Valley
Strong polar jet along the U.S.- Canadian border remained stationary over 24 h
Northern Plains was in the right entrance of the upper level jet
Southern stream wave was moving into Texas and the lower Mississippi Valley
Broad baroclinic zone extended from the lower Mississippi Valley into the Missouri Valley.
A large-scale warm advection and frontogenesis was observed within this baroclinic zone.

53. Event Totals
COOP
WRF
6 hr accum precip ending 18 Z 14th
NARR
WRF

54. Observed vs. Simulated Reflectivity 18Z 14th F024
WRF
Level III Composite

55. NARR-WRF PV and Wind Differences 1800 UTC 14 Feb
Shaded – PV around 700 mb from NARR.
Red lines – NARR – WRF PV difference around 700 mb.
Wind barbs – Narr – WRF wind vector difference at 700 mb

56. 700 mb temperature difference and 700 to 600 mb EPV difference
700mb Temp difference
NARR-WRF
Warm colors = NARR warmer
Cool colors = NARR cooler
700 to 600 mb EPV Difference
NARR-WRF
Warm colors = NARR less stable
Cool colors = NARR more stable
1200 UTC 14 Feb
1800 UTC 14 Feb

57. 700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb
WRF
NARR

58. 700 mb height and wind fields induced by cyclonic PV from 900 to 450 mb
FGEN
FGEN
NARR
WRF
Position of FGEN appears to be a function of cyclonic wind shift line largely determined by the location of diabatically produced low-mid level PV
There were no differences between NARR and WRF when the flow at 700 mb induced by the 200 to 400 mb PV anomalies was examined

59. PV Anomalies (700 mb) – 18 Z 14th NARR WRF
“Assumed” flow based on position of PV anomalies
Different placement of PV on NE/SD border; Much stronger PV in WRF further SE, with different orientation

60. Feb Conclusions
The area of precipitation responsible for the inaccurate generation of low-mid level PV was stratiform.
The development of this precipitation and associated PV led to the formation of a positive feedback between precipitation and the cyclonic circulation associated with the PV
This allowed the mid level frontogenesis band to set up along I-80 later 6-12 h later instead of along the Iowa and Missouri border.

61. How can we apply this? Examine precipitation and 700 mb PV in model.
While convection is most efficient in producing PV, persistent stratiform precipitation can be effective.
Infer induced mid-level wind fields from internal anomaly.
Are wind field differences the result of model precipitation differences?
If so, determine where initial precipitation will develop and which model solution does this favor?
What is the impact on the warm conveyor belt and frontogenesis?

62. Forecasting Tools
Use PV thinking to adjust model guidance by understanding impact of latent heating on moisture transport, cyclogenesis, low-level jets.
AWIPS Procedure
(NWS Raleigh)
QPF (total and/or convective)
Lower-tropospheric PV, wind,
Sea level pressure
Slide from Mike Brennan (NWS-HPC)

63. What about the future?
The effect of internal PV anomalies can be calculated.
WFO FSD and WFO OAX will be testing GEMPAK software to invert PV on output from the WRF-ARW.
Initially will be displayed on web pages but someday in AWIPS????
Can examine how sensitive the forecast is to location and timing of precipitation.

64. Conclusions
Use of tropopause maps provide an easy way to see short-waves at different levels.
Depth of wave into troposphere can help determine its ability to interact with mid-level boundaries.
Can be used with higher resolution grids than Q-vectors can be applied.

65. Conclusion
Distribution of PV near the tropopause can determine where precipitation is favored within a TROWAL.
Favors development of mid-level boundaries.
Diabatically-produced PV can influence strength of warm conveyor belt.
Wind-parallel anomalies can increase moisture transport .
While convection is most efficient, stratiform precipitation can produce significant PV anomalies.
Location of anomalies can determine where the warm conveyor belt is located.
Can determine where mid-level front becomes established several hours later.
Examining mid-level PV (800 – 500 mb) in models can help forecasters understand if precipitation development in the model is resulting in differences.