ECMWF Slide 1 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 PV Diagnostics Meteorological Training Course 25 April 2006 Mark Rodwell

PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 ECMWFSlide 1

PV DiagnosticsMeteorological Training Course

25 April 2006

Mark Rodwell


What is PV? Momentum Vorticity Potential Vorticity

- Conservation- Lagrangian Sources- Inversion

Insight into Dynamics Tropopause “Induced flow” Cut-off lows and blocking highs Cyclogenesis

Verification Deterministic forecasts Probabilistic forecasts

Structure of Talk


What is PV?


Momentum

In an absolute frame of reference, the momentum equation

can be written as:

(u is 3D absolute wind, p is pressure and is density)

Often spherical polar coordinates are used (k being the local

vertical unit vector), winds are relative to the rotating planet

and the shallow atmosphere approximations‡ are made

forcesbody gradient tendency Other Friction Pressure vection AdEulerian

1 )1().(

uFpuudt

u

dt

ud

‡ Replacing “r” with a constant Earth radius “a” in the spherical metrics and neglecting some of the curvature terms and the local horizontal component of the Earth’s rotation.


Vorticity I

Making the shallow atmosphere approximations, using pressure surfaces and taking of the horizontal momentum equations we get an equation for the local vertical component of absolute vorticity,

(v = horizontal wind relative to the planet and dp/dt)

For barotropic, frictionless, horizontal, non-divergent flow, this reduces to the “non-divergent barotropic vorticity equation”:

i.e. absolute vorticity is conserved following the flow

pk

Friction Tilting Divergence

)2(vppppp Fk

p

vkv

dt

d

vkf pp

)3(0dt

d p EG: A PARCEL OF AIR STARTS SPINNING (RELATIVE VORTICITY) IF MOVED TO A DIFFERENT LATITUDE


The non-divergent barotropic vorticity equation (3) helps:

• Understand (and predict‡) mid-tropospheric flow

• Understand tropical-to-extratropical teleconnections

• Introduce the concept of “potential vorticity”:

- Conservation of absolute vorticity, - Inversion of to determine all other fields:

(Can define a streamfunction such that

Knowing P means we can determine and thus the wind)

Can we define a vorticity-like quantity that is conserved and (nearly) invertible without making approximations?

Vorticity II

‡ The non-divergent barotropic vorticity equation was used in the first numerical prediction models

2PPx

vy

u


For barotropic frictionless flow, (curl of (1))

Using Stoke’s theorem‡, this implies that nS is constant

Assuming adiabatic flow (potential temperature, , is constant),

we can write

Hence

Since , must be perpendicular toand so we do not need to assume barotropic flow.

Ertel Potential Vorticity (EPV) I0 dtud

n

m

n

m

n

VS

EPVconstant

nn

)( 1 p ),( p

‡ The behaviour of the material circuit contributes nothing.

)constant(1

)constant(2

n

)volume(V

S

)||( n

)constantmass,(m

)density(


For adiabatic, frictionless flow, is conserved

even for 3D, non-hydrostatic motions :

EPV is conserved because the creation of vorticity by 2D

convergence into the axis of rotation is balanced, within EPV,

by the accompanying‡ increase in distance between

isentropes (“stretching”).

Generalisation to include diabatic and frictional “sources”

gives:

)(EPV

0EPV

dt

d

Ertel Potential Vorticity (EPV) II

)(1EPV

uFdt

d

‡ Some 2D convergence may be accompanied by an increase in density rather than stretching and the (in EPV) takes account of this.

1

2


Using the shallow atmosphere approximation (as models often do) and assuming adiabatic, frictionless flow we can use (2) and calculate derivatives on isentropic surfaces (replace p with and with ):

Combining with the continuity equation for adiabatic flow:

We get:

Where is conserved following the horizontal

flow on an isentropic surface.

)0(0)(

vt

0)(

vt

Isentropic Potential Vorticity (IPV) I

0IPV

vt

pg IPV

pg

1 where


Insight in Dynamics


Importance of Static Stability at the Tropopause

Copyright Federation Francaise de Parachutisme (1999)

LARGE INCREASE IN /p (AND THUS PV) AT THE TROPOPAUSE

CAN DEFINE THE TROPOPAUSE BY A VALUE OF PV


Dynamic Tropopause at 2PV units

TROPOPAUSE(PV=2 ISO-SURFACE)

TROPOSPHERE(LOW PV)

STRATOSPHERE(HIGH PV)

Massacand (1996)

TROPOPAUSE FOLD


Hoskins, McIntyre and Robertson (1985) Fig. 9a. in K, PV in PV units

Flow “Induced” by an IPV Anomaly (Cyclonic)DYNAMIC TROPOPAUSE

TONGUE OF

STRATOSPHERIC AIR

TO MAINTAIN THERMAL WIND BALANCE

VORTICITY AND STABILITY ANOMALIES TYPICALLY HAVE THE SAME SENSE AS IPVCOLD ADVECTION,

LESS STATIC STABLITY AND ANTICYCLONIC IPV ON SURFACE

MORE STABLE

COLD

WARM

LESS STABLE

LESS STABLE

IPV’

WEAKER TROPOSPHERIC STABILITY ALLOWS CONVECTION WHICH CAN LOWER OR DAMP THE IPV ANOMALY

⊙ ⊗


Circularly Symmetric Flows “Induced by” Simple Isolated IPV Anomalies

Hoskins, McIntyre and Robertson (1985)

100

200

300

hPa

1000

600

800

400

100

200

300

hPa

1000

600

800

400UPPER-LEVEL CYCLONIC IPV ANOMALY (STIPPLED)

SURFACE TEMPERATURE ANOMALY (+1OK)

ISENTROPES (CI = 5K) ANDAZIMUTHAL WIND (CI=INTERVAL 3ms-1)

r=1667km r=0

WARM

WARM

CAN BE INTERPRETTED AS A CYCLONIC IPV ANOMALY

5

4

3

2

1LARGE

p}

WARM

⊗⊙

⊗⊙


•The vertical penetration, magnitude and phase-speed of the flow

induced by an IPV anomaly increases with its horizontal scale.

•Surface warm anomalies can lead to large effective

and thus large at the surface.

This IPV also “induces” a flow field (“surface charge electric field”).

•The flows “induced” by two (or more) IPV anomalies can be

approximately superposed (“attribution”).

•The induced velocity fields (e.g. by surface and atmospheric IPV

anomalies) can keep Rossby waves in-step.

Isentropic Potential Vorticity (IPV) II

p )(

pg )IPV(

UPPER-LEVEL +PV ADVECTED OVER A LOW-LEVEL BAROCLINIC REGION CAN LEAD TO MUTUAL AMPLIFICATION. MOIST PROCESSES COULD ENHANCE THE SURFACE DEVELOPMENT

Hoskins, McIntyre and Robertson (1985) Fig. 21


Cut-off Lows and Blocking Highs

Hoskins, McIntyre and Robertson (1985) Fig. 11

IPV on 330K for consecutive days. 1-2PVU filled in black

CUT-OFF LOW

BLOCKING HIGH

ADVECTION OF LOW IPV

CUT-OFF LOWS AND BLOCKING HIGHS HAVE SIMILAR (OPPOSITE) STRUCTURES

CONVECTIVE HEATING DAMPS CYCLONE FASTER THAN RADIATIVE COOLING DAMPS ANTICYCLONE

IPV A BETTER WAY OF DEFINING “CUT-OFF” THAN 500hPa HEIGHT


PV Modification

TOTAL TENDENCY

PV

PLUME OF PARTICLES INITIALLY AT 890hPa

CIRCLES DENOTE CONSECUTIVE DAYS

PV and accumulated tendencies of PV

REASONABLE BALANCE ACHIEVED

CAN ASK:

IS THERE AN ERROR IN MODEL’S DIABATIC OR FRICTIONAL PARAMETRIZATION?

CAN INVESTIGATE REASONS FOR PV MODIFICATION

Rodwell and Hoskins (1995) Fig. 7

DIABATIC TENDENCY

SHALLOW HEATING

FRICTIONAL TENDENCY

MO

UN

TAIN

S

ASIAN MONSOON


Anomalies a few days after injection of Southern Hemisphere midlatitude air

into Cross-Equatorial Jet

(a) (b)

Based on 16 injection events (v>8.5ms-1) in JJA 1979-2001V850 from ERA-40 daily. Averaged over 4-8 days after injectionPrecip: Xie-Arkin pentadal. Pentads starting 2-9 days after injection10% significance indicated

TURNING IS A CONSEQUENCE OF PV ADVECTION

V850 Precipitationmmday-1

WIND ANOMALY IS VERY ROBUST FOR OTHER THRESHOLDS


Analysis of winter storm “Lothar”

Wernli et al. (2002) Fig. 7a

PV=2 SURFACE

V850

CYCLONE “KURT”

LOW-LEVEL CYCLONE “LOTHAR”

18Z, 25 DEC1999 TROPOPAUSE FOLDING ASSOCIATED WITH KURT AND ISENTROPIC DOWN-GLIDING(?)



Wernli et al. (2002) Fig. 7b

PV=2 SURFACE

V850

CYCLONE “KURT”


0Z, 26 DEC1999 TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR



Wernli et al. (2002) Fig. 7c

PV=2 SURFACE

V850

CYCLONE “KURT”


6Z, 26 DEC1999

UPPER AND LOWER PV ANOMALIES NEARLY JOIN

INTENSE WINDS KILL 50



Wernli et al. (2002) Fig. 14

SIMILARITIES TO HOSKINS ET AL (1985) BUT MID-TROPOSPHERIC LATENT HEAT RELEASE TAKES THE PLACE OF SURFACE ANOMALY

MOIST ASCENDING AIR LATENT HEAT RELEASE

HEATING “PRODUCES” LOW-LEVEL +PV ANOMALY

0

Pdt

dP

“INDUCED” TROPOPAUSE FOLD UPPER-LEVEL +PV ANOMALY

DIABATIC PROCESSES WERE ESSENTIAL FOR LOTHAR

MUTUAL AMPLIFICATION OF PHASE-LOCKED PV ANOMALIES


Verification


Z500 and PV330 European Anomaly CorrelationsPV, WITH ITS INTERTABILITY, MAY EMBODY MORE OF THE IMPORTANT CIRCULATION AND BE A GOOD WAY TO VERIFY FORECASTS

SON 2003, T511, ERA40 climatology

Z500 FORECASTS AT D+1 TO D+4 ARE EXTREMELY GOOD THESE DAYS

BUT IS THIS REALLY THE WEATHER WE EXPERIENCE?

31 OCT

STRONG RAINFALL EVENT OVER ALPS


rEURO = 0.90 rEURO = 0.27

AN

FC D+4

PV330Z500

Forecast and Verifying analyses 31 Oct 2003

MOIST ADVECTION

Z500 FIELDS VERY SIMILAR AND DO NOT HIGHLIGHT AN ESSENTIAL DIFFERENCE


Z500

PV=2

OperationsExperimentalsignificant difference

Europe = [12.5oW-42.5oE, 35oN-75oN]. Significance if |avg(COR)| > stdev(COR). (AR1 model accounts for autocorrelation).Operations is 28r1 to 2004/09/27, 28r3 thereafter. Experimental is 29r1. Comparison with own analysis using ERA40 climate.

Ex

pe

rim

en

tal

Ex

pe

rim

en

tal

OperationsExperimentalsignificant difference

step = 10step = 4step = 1

step = 10step = 4step = 1

Operations Forecast day

Anomaly Correlation for Europe August 04-March 05

Me

an

co

rre

lati

on

Me

an

co

rre

lati

on

PV MAY BE MORE DISCRIMINATING FOR NEW MODEL VERSION TESTING


Annual-Mean of Daily Anomaly Correlation Coefficients for Europe

FORECAST IMPROVEMENTS ARE MORE APPARENT WITH PV AND PRECIPITATION

Z500

Pp/c

PV=2


Brier Score Difference for event “> normal” DJF 2001-2004, Ensemble (T255) – Deterministic (T511)

IN PROBABILISTIC TERMS, A DETERMINISTIC FORECAST OF Z500 AT DAY+1 IS AS GOOD AS A FORECAST FROM THE ENSEMBLE PREDICTION SYSTEM

Z500

PV=2

BRIER SCORE:

N

iii vp

Nb

1

2)(1

}1,0{10 ii vpTHIS IS NOT THE CASE FOR THE PV DIAGNOSTIC: THE ENSEMBLE SCHEME IS BETTER EVEN AT DAY+1


What is PV? Momentum Vorticity Potential Vorticity

- Conservation- Lagrangian Sources- Inversion

Insight into Dynamics Tropopause “Induced flow” Cut-off lows and blocking highs Cyclogenesis

Verification Strong rainfall events More discriminating for skill changes Shows early benefit of ensemble forecasts

Summary

Documents

ECMWF Slide 1 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 PV Diagnostics Meteorological Training Course 25 April 2006 Mark Rodwell