outline

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

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

Δ−+

= θζ

COMETFeb. 20, 2002

Mathematical Definitions of PV

• Rossby:

• Ertel:

Vorticity times static stability

Δ−+

= θζ

( ) gp

ζθζ θ

θ ΔΔ−

+≈⎟⎟

⎞⎜⎜⎝

⎛∂

∂+−=

COMETFeb. 20, 2002

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

PV Cross Section Pole to Pole at 80W

COMETFeb. 20, 2002

PV and Westerlies (m/s)

COMETFeb. 20, 2002

PV and Absolute Vorticity (*10-5 s-1)

COMETFeb. 20, 2002

PV and Potential Temperature (K)

COMETFeb. 20, 2002

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

PV Contours: 0, 0.25, 0.5, 1, 2, 4, 8

COMETFeb. 20, 2002

PV Contours: 0, 0.25, 0.5, 1, 2, 4, 8

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

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?

COMETFeb. 20, 2002

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

The PV Conundrum

• Maps of mean PV between pressure surfaces– Encapsulates the PV distribution– Cannot diagnose evolution or

dynamics

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

The 1.5 PVU contour on the 320 K isentropic surface is…

COMETFeb. 20, 2002

…identical to the 320 K contour on the 1.5 PVU (tropopause) surface!

COMETFeb. 20, 2002

Color Fill Version of Tropopause Map

COMETFeb. 20, 2002

Tropopause Map with Jet Streams

COMETFeb. 20, 2002

Tropopause Map, hour 00

COMETFeb. 20, 2002

Tropopause Map, hour 48, with jets

COMETFeb. 20, 2002

Midway Point

• Play with some PV• Watch a movie

COMETFeb. 20, 2002

QuickTime™ and aGIF decompressorare needed to see this picture.

COMETFeb. 20, 2002

PV Dynamics: The Short Course

High PV / Stratosphere / Low Theta on Tropopause

Low PV / Troposphere / High Theta on Tropopause

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

PV Anomaly: A Wave on the Tropopause

COMETFeb. 20, 2002

PV Anomaly: Anomalous Winds

Think of each PV anomaly as a cyclonic or anticyclonic vortex

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

PV Anomaly: What will the total wind field be?

Short Wave

Planetary Wave

COMETFeb. 20, 2002

Wave Propagation

• Individual waves propagate upstream

• Short waves move slower than jet• Long waves actually retrogress

COMETFeb. 20, 2002

The Making of a Rossby Wave Packet

• Trough amplifies downstream ridge

• Ridge amplifies downstream trough, weakens upstream trough

• Wave packet propagates downstream

COMETFeb. 20, 2002

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”

COMETFeb. 20, 2002

Tropopause, Feb. 10, 2001, 00Z

Superposition?Superposition?

AmplificationAmplification

COMETFeb. 20, 2002

500 mb, Feb. 10, 2001, 00Z

COMETFeb. 20, 2002

500 mb, Feb. 10, 2001, 06Z

COMETFeb. 20, 2002

500 mb, Feb. 10, 2001, 12Z

COMETFeb. 20, 2002

500 mb, Feb. 10, 2001, 18Z

COMETFeb. 20, 2002

500 mb, Feb. 11, 2001, 00Z

COMETFeb. 20, 2002

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

MSLP (mb), 950 mb theta-e (K), 700-950 mb PV, 300 K 1.5 PV contour

COMETFeb. 20, 2002

Surface, Feb. 10, 2001, 06Z

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

Diabatic Processes: Diagnosis

• Low-level PV increases• Upper-level PV decreases• Tropopause potential temperature

increases

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

Forecasting Applications (1):Evolution

• Can directly diagnose evolution– Motion of upper-level systems– Intensification and weakening– Formation of new troughs and ridges

downstream

COMETFeb. 20, 2002

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?

COMETFeb. 20, 2002

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

COMETFeb. 20, 2002

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?

COMETFeb. 20, 2002

Summary

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

outline

pv conundrummaps of

pv distributioncannot

mbwhats pv

pv positive

cutoffshigh pv

pv gradientswaves

pv field

ridgeforget pv

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