IPV and the Dynamic Tropopause

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IPV and the Dynamic Tropopause

• John W. Nielsen-Gammon
• Texas AM University
• 979-862-2248 n-g_at_tamu.edu

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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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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

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Mathematical Definitions of PV

• Rossby
• Ertel
• Vorticity times static stability

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Units of Potential Vorticity

• 1 PVU equalsyou dont 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)
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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
• Vertical tropopause

• Flat PV gradients
• Boring
• No wind or vorticity variations
• Stratification high where PV is large
• Flat 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

• 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
• 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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Whats PV Got that Traditional Maps Havent 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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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

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), 700-950 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
• Its 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
• Wheres 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

• Definition of PV
• IPV maps and tropopause maps
• Diagnosis of evolution using PV
• Dynamics using PV
• Forecasting applications of PV