Transcript IPV and the Dynamic Tropopause

IPV and the Dynamic Tropopause
John W. Nielsen-Gammon
Texas A&M University
979-862-2248 [email protected]
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Outline
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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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Mathematical Definitions of PV
• Rossby:
( f   )
PR 
 p / g
Vorticity divided by theta surface spacing

: Relative vorticity in isentropic coordinates
Minus sign: makes PV positive since pressure decreases
upward
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Mathematical Definitions of PV
• Rossby:
( f   )
PR 
 p / g
  
( f   )
• Ertel: P   g ( f    )  
 p   p   / g
Vorticity times static stability
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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
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PV Cross Section Pole to Pole at 80W
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PV and Westerlies (m/s)
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PV and Absolute Vorticity (*10-5 s-1)
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PV and Potential Temperature (K)
380
350
330
280
310
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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
• Flat PV gradients
– Boring
– No wind or vorticity
variations
– Stratification high
where PV is large
– Flat tropopause
– Vertical tropopause
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PV
Contours:
0, 0.25, 0.5,
1, 2, 4, 8
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PV
Contours:
0, 0.25, 0.5,
1, 2, 4, 8
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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
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• PV extrema bounded
by strong gradients
could mean short
waves or cutoffs
• High PV = trough;
Low PV = ridge
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Forget PV! The Traditional
Geopotential Height Maps Work Fine!
Advantages of Height
Disadvantages of
Height
• Identification and
assessment of features
• Inference of wind and
vorticity
• Inference of vertical
motion?
• Gravity waves and
topography
• Inference of evolution
and intensification
• Role of diabatic
processes is obscure
• Need 300 & 500 mb
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What’s PV Got that Traditional Maps
Haven’t Got?
Advantages of PV
Disadvantages 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
• 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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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!
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The PV Conundrum
• Maps of mean PV between pressure
surfaces
– Encapsulates the PV distribution
– Cannot diagnose evolution or dynamics
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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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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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The 1.5 PVU contour on the 320 K
isentropic surface is…
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…identical to the 320 K contour on
the 1.5 PVU (tropopause) surface!
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Color Fill Version of Tropopause Map
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Tropopause Map with Jet Streams
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Tropopause Map, hour 00
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Tropopause Map, hour 06
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Tropopause Map, hour 12
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Tropopause Map, hour 18
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Tropopause Map, hour 24
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Tropopause Map, hour 30
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Tropopause Map, hour 36
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Tropopause Map, hour 42
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Tropopause Map, hour 48
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Tropopause Map, hour 48, with jets
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Midway Point
• Play with some PV
• Watch a movie
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PV Dynamics: The Short Course
High PV / Stratosphere / Low Theta on Tropopause
Low PV / Troposphere / High Theta on Tropopause
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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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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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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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PV Anomaly:
What will the total wind field be?
Short Wave
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Planetary Wave
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Wave Propagation
• Individual waves propagate upstream
• Short waves move slower than jet
• Long waves actually retrogress
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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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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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Tropopause, Feb. 10, 2001, 00Z
Amplification
Superposition?
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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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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
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MSLP (mb), 950 mb theta-e (K), 700950 mb PV, 300 K 1.5 PV contour
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Surface, Feb. 10, 2001, 06Z
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Surface, Feb. 10, 2001, 12Z
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Surface, Feb. 10, 2001, 18Z
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Surface, Feb. 11, 2001, 00Z
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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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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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Diabatic Processes: Diagnosis
• Low-level PV increases
• Upper-level PV decreases
• Tropopause potential temperature
increases
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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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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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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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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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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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Summary
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Definition of PV
IPV maps and tropopause maps
Diagnosis of evolution using PV
Dynamics using PV
Forecasting applications of PV
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