1 ipv and the dynamic tropopause john w. nielsen-gammon texas a&m university 979-862-2248...

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IPV and the Dynamic Tropopause

John W. Nielsen-GammonTexas A&M University

979-862-2248 [email protected]

COMETFeb. 20, 2002

IPV and the Dynamic TropopauseJohn W. Nielsen-Gammon 2

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

gp

fPR /

)(

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Mathematical Definitions of PV

• Rossby:

• Ertel:

Vorticity times static stability

gp

fPR /

)(

gp

f

pfgP

/

)()(

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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)

280

310

330

350

380

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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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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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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 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

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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

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• 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

Superposition?Superposition?

AmplificationAmplification

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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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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

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

1 ipv and the dynamic tropopause john w. nielsen-gammon texas a&m university 979-862-2248...

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