COMET Feb. 20, 2002 IPV and the Dynamic Tropopause John W. Nielsen-Gammon 1 Outline • PV basics • Seeing the world through PV • Waves and vortices • Nonconservation • Forecasting applications – Short-range forecasting – Tracking disturbances over the Rockies – Understanding the range of possibilities
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COMET Feb. 20, 2002 IPV and the Dynamic Tropopause John W. Nielsen-Gammon1 Outline PV basics Seeing the world through PV Waves and vortices Nonconservation.
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COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 1
Outline• PV basics• Seeing the world through PV• Waves and vortices• Nonconservation• Forecasting applications
– Short-range forecasting– Tracking disturbances over the Rockies– Understanding the range of possibilities
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 2
Mathematical Definitions of PV
• Rossby:
Vorticity divided by theta surface spacing
: Relative vorticity in isentropic coordinates
Minus sign: makes PV positive since pressure decreases upward
gp
fPR /
)(
Δ−+
= θζ
θζ
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 3
Mathematical Definitions of PV
• Rossby:
• Ertel:
Vorticity times static stability
gp
fPR /
)(
Δ−+
= θζ
( ) gp
f
pfgP
/
)()(
θ
ζθζ θ
θ ΔΔ−
+≈⎟⎟
⎠
⎞⎜⎜⎝
⎛∂
∂+−=
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 4
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 68
Diabatic Processes
• Latent heating max in mid-troposphere– PV increases below LH max– PV decreases above LH max
• It’s as if PV is brought from aloft to low levels by latent heating– Strengthens the surface low and the
upper-level downstream ridge
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 69
Diabatic Processes: Diagnosis
• Low-level PV increases• Upper-level PV decreases• Tropopause potential temperature
increases
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 70
Diabatic Processes: Prediction
• Plot low-level equivalent potential temperature instead of potential temperature
• Compare theta-e to the potential temperature of the tropopause
• If theta-e is higher:– Deep tropospheric instability– Moist convection likely, rapid
cyclogenesis
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 71
Forecasting Applications (1):Evolution
• Can directly diagnose evolution– Motion of upper-level systems– Intensification and weakening– Formation of new troughs and ridges
downstream
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 72
Forecasting Applications (2):Model Correction
• Can correct forecast for poor analyses or short-range deviation– Where’s the real trough?– How will it affect the things around it?– How will its surroundings affect its
evolution?
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 73
Forecasting Applications (3):The Rockies• Can track systems over topography
– Vorticity is altered by stretching and shrinking as parcels go over mountains
– Potential vorticity is conserved on isentropic surfaces
– PV shows you what the trough will look like once it leaves the mountains
– Better forecasts, better comparison with observations
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 74
Forecasting Applications (4): Uncertainty
• Can understand the range of possibilities– Could this trough intensify?– Could a downstream wave be
triggered?– How many “objects” must be
simulated correctly for the forecast to be accurate?
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 75
Summary
• Definition of PV• IPV maps and tropopause maps• Diagnosis of evolution using PV• Dynamics using PV• Forecasting applications of PV