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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
Units of Potential Vorticity
• 1 PVU equals…you don’t want to know
• Midlatitude Troposphere: -0.2 to 3.0 PVU– Typical value: 0.6 PVU
• Midlatitude Stratosphere: 1.5 to 10.0 PVU– Typical value: 5.0 PVU
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 5
PV Cross Section Pole to Pole at 80W
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 6
PV and Westerlies (m/s)
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 7
PV and Absolute Vorticity (*10-5 s-1)
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 8
PV and Potential Temperature (K)
280
310
330
350
380
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 9
What do PV gradients imply?• Steep PV gradients
– Jet streams• High PV to left of jet
– Vorticity gradients• Same sign as PV
gradients
– Stratification gradients
• High stratification where PV is large
– Vertical tropopause
• Flat PV gradients– Boring– No wind or
vorticity variations– Stratification high
where PV is large– Flat tropopause
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 10
PV Contours: 0, 0.25, 0.5, 1, 2, 4, 8
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 11
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 12
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 13
PV Contours: 0, 0.25, 0.5, 1, 2, 4, 8
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 14
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 15
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 16
Strong PV gradients matter; PV maxes and mins are inconsequential
• Jet stream follows PV gradients
• Waves in the PV field correspond to waves in the jet stream
• PV extrema bounded by strong gradients could mean short waves or cutoffs
• High PV = trough; Low PV = ridge
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 17
Forget PV! The Traditional Geopotential Height Maps Work Fine!
Advantages of Height
• Identification and assessment of features
• Inference of wind and vorticity
• Inference of vertical motion?
Disadvantages of Height
• Gravity waves and topography
• Inference of evolution and intensification
• Role of diabatic processes is obscure
• Need 300 & 500 mb
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 18
What’s PV Got that Traditional Maps Haven’t Got?
Advantages of PV• PV is conserved• PV unaffected by
gravity waves and topography
• PV at one level gives you heights at many levels
• Easy to diagnose Dynamics
Disadvantages of PV• Unfamiliar• Not as easily available• Not easy to eyeball
significant features• Qualitative inference
of wind and vorticity• Hard to diagnose
vertical motion?
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 19
DYNAMICS?
• A given PV distribution implies a given wind and height distribution
• If the PV changes, the winds and heights change
• If you know how the PV is changing, you can infer everything else
• And PV changes only by advection!
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 20
The PV Conundrum
• Maps of mean PV between pressure surfaces– Encapsulates the PV distribution– Cannot diagnose evolution or
dynamics
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 21
The PV Conundrum
• IPV (Isentropic Potential Vorticity) maps– Many isentropic surfaces have
dynamically significant PV gradients– Hard to know which isentropic
surfaces to look at
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 22
The PV Solution: Tropopause Maps
• Pick a PV contour that lies within the (critical) tropopause PV gradient
• Overlay this particular contour from all the different isentropic layers (or interpolate to that PV value)
• Result: one map showing the location of the important PV gradients at all levels
• Contours advected by horizontal wind
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 23
The 1.5 PVU contour on the 320 K isentropic surface is…
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 24
…identical to the 320 K contour on the 1.5 PVU (tropopause) surface!
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 25
Color Fill Version of Tropopause Map
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 26
Tropopause Map with Jet Streams
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 27
Tropopause Map, hour 00
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 28
Tropopause Map, hour 06
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 29
Tropopause Map, hour 12
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 30
Tropopause Map, hour 18
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 31
Tropopause Map, hour 24
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 32
Tropopause Map, hour 30
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 33
Tropopause Map, hour 36
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 34
Tropopause Map, hour 42
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 35
Tropopause Map, hour 48
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 36
Tropopause Map, hour 48, with jets
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 37
Midway Point
• Play with some PV• Watch a movie
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 38
QuickTime™ and aGIF decompressorare needed to see this picture.
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 39
QuickTime™ and aGIF decompressorare needed to see this picture.
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 40
QuickTime™ and aGIF decompressorare needed to see this picture.
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 41
QuickTime™ and aGIF decompressorare needed to see this picture.
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 42
PV Dynamics: The Short Course
High PV / Stratosphere / Low Theta on Tropopause
Low PV / Troposphere / High Theta on Tropopause
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 43
Superposition
• PV field– Basic state– Anomalies
• Associated wind field– Basic state wind– Winds associated with each anomaly
• Add ‘em all up to get the total wind/PV
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 44
PV Anomaly: A Wave on the Tropopause
+
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PV Anomaly: Anomalous Winds
+
Think of each PV anomaly as a cyclonic or anticyclonic vortex
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 46
PV Wind Rules (for Northern Hemisphere)
• Positive anomalies have cyclonic winds
• Negative anomalies have anticyclonic winds
• Winds strongest near anomaly• Winds decrease with horizontal
distance• Winds decrease with vertical distance
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 47
PV Anomaly: What will the total wind field be?
+
+
Short Wave
Planetary Wave
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 48
Wave Propagation
• Individual waves propagate upstream
• Short waves move slower than jet• Long waves actually retrogress
++
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 49
The Making of a Rossby Wave Packet
++
• Trough amplifies downstream ridge
• Ridge amplifies downstream trough, weakens upstream trough
• Wave packet propagates downstream
-+
-+
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 50
Intensification: Two Ways
• Increase the size of the PV anomaly– “Amplification”
• Increase the amount of PV (or number of PV anomalies) within a small area– “Superposition”
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 51
Tropopause, Feb. 10, 2001, 00Z
Superposition?Superposition?
AmplificationAmplification
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Tropopause, Feb. 10, 2001, 06Z
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Tropopause, Feb. 10, 2001, 12Z
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Tropopause, Feb. 10, 2001, 18Z
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Tropopause, Feb. 11, 2001, 00Z
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500 mb, Feb. 10, 2001, 00Z
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500 mb, Feb. 10, 2001, 06Z
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500 mb, Feb. 10, 2001, 12Z
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500 mb, Feb. 10, 2001, 18Z
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500 mb, Feb. 11, 2001, 00Z
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 61
Low-Level Potential Temperature• Acts like upper-level PV
– Locally high potential temperature = cyclonic circulation
– Locally low potential temperature = anticyclonic circulation
• But gradient is backwards– Winds from north intensify upper-level
PV– Winds from south intensify low-level
warm anomaly
COMETFeb. 20, 2002
IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 62
MSLP (mb), 950 mb theta-e (K), 700-950 mb PV, 300 K 1.5 PV contour
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 63
Surface, Feb. 10, 2001, 06Z
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 64
Surface, Feb. 10, 2001, 12Z
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 65
Surface, Feb. 10, 2001, 18Z
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 66
Surface, Feb. 11, 2001, 00Z
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IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 67
Cyclogenesis
• Mutual Amplification– Southerlies assoc. w/ upper-level
trough intensify surface frontal wave– Northerlies assoc. w/ surface frontal
wave intensify upper-level trough
• Superposition– Trough and frontal wave approach
and occlude
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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