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**PV Diagnostics Meteorological Training Course 25 April 2006**

Mark Rodwell PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Structure of Talk What is PV? Insight into Dynamics Verification**

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

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What is PV? PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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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 ‡ 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. PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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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 EG: A PARCEL OF AIR STARTS SPINNING (RELATIVE VORTICITY) IF MOVED TO A DIFFERENT LATITUDE PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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Vorticity II 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? ‡ The non-divergent barotropic vorticity equation was used in the first numerical prediction models PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Ertel Potential Vorticity (EPV) I**

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 to and so we do not need to assume barotropic flow. ‡ The behaviour of the material circuit contributes nothing. PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Ertel Potential Vorticity (EPV) II**

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: ‡ Some 2D convergence may be accompanied by an increase in density rather than stretching and the (in EPV) takes account of this. PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Isentropic Potential Vorticity (IPV) I**

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

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Insight in Dynamics PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Importance of Static Stability at the Tropopause**

LARGE INCREASE IN /p (AND THUS PV) AT THE TROPOPAUSE CAN DEFINE THE TROPOPAUSE BY A VALUE OF PV Copyright Federation Francaise de Parachutisme (1999) PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Dynamic Tropopause at 2PV units**

STRATOSPHERE (HIGH PV) TROPOPAUSE (PV=2 ISO-SURFACE) TROPOPAUSE FOLD TROPOSPHERE (LOW PV) Massacand (1996) PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Flow “Induced” by an IPV Anomaly (Cyclonic)**

MORE STABLE COLD WARM LESS STABLE DYNAMIC TROPOPAUSE ⊙ ⊗ IPV’ VORTICITY AND STABILITY ANOMALIES TYPICALLY HAVE THE SAME SENSE AS IPV TONGUE OF STRATOSPHERIC AIR COLD ADVECTION, LESS STATIC STABLITY AND ANTICYCLONIC IPV ON SURFACE WEAKER TROPOSPHERIC STABILITY ALLOWS CONVECTION WHICH CAN LOWER OR DAMP THE IPV ANOMALY TO MAINTAIN THERMAL WIND BALANCE Hoskins, McIntyre and Robertson (1985) Fig. 9a. in K, PV in PV units PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Circularly Symmetric Flows “Induced by” Simple Isolated IPV Anomalies**

100 200 300 hPa 1000 600 800 400 ISENTROPES (CI = 5K) AND AZIMUTHAL WIND (CI=INTERVAL 3ms-1) WARM ⊙ ⊗ UPPER-LEVEL CYCLONIC IPV ANOMALY (STIPPLED) SURFACE TEMPERATURE ANOMALY (+1OK) 100 200 300 hPa 1000 600 800 400 5 4 3 2 1 } WARM CAN BE INTERPRETTED AS A CYCLONIC IPV ANOMALY ⊗ ⊙ WARM Hoskins, McIntyre and Robertson (1985) r=1667km r=0 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Isentropic Potential Vorticity (IPV) II**

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

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**Cut-off Lows and Blocking Highs**

IPV on 330K for consecutive days. 1-2PVU filled in black CUT-OFF LOW ADVECTION OF LOW IPV IPV A BETTER WAY OF DEFINING “CUT-OFF” THAN 500hPa HEIGHT BLOCKING HIGH CUT-OFF LOWS AND BLOCKING HIGHS HAVE SIMILAR (OPPOSITE) STRUCTURES CONVECTIVE HEATING DAMPS CYCLONE FASTER THAN RADIATIVE COOLING DAMPS ANTICYCLONE Hoskins, McIntyre and Robertson (1985) Fig. 11 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**PV Modification PV and accumulated tendencies of PV**

ASIAN MONSOON PLUME OF PARTICLES INITIALLY AT 890hPa FRICTIONAL TENDENCY MOUNTAINS PV and accumulated tendencies of PV CIRCLES DENOTE CONSECUTIVE DAYS DIABATIC TENDENCY SHALLOW HEATING REASONABLE BALANCE ACHIEVED PV CAN INVESTIGATE REASONS FOR PV MODIFICATION TOTAL TENDENCY CAN ASK: IS THERE AN ERROR IN MODEL’S DIABATIC OR FRICTIONAL PARAMETRIZATION? Rodwell and Hoskins (1995) Fig. 7 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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Anomalies a few days after injection of Southern Hemisphere midlatitude air into Cross-Equatorial Jet mmday-1 V850 (a) (b) Precipitation TURNING IS A CONSEQUENCE OF PV ADVECTION Based on 16 injection events (v>8.5ms-1) in JJA V850 from ERA-40 daily. Averaged over 4-8 days after injection Precip: Xie-Arkin pentadal. Pentads starting 2-9 days after injection 10% significance indicated WIND ANOMALY IS VERY ROBUST FOR OTHER THRESHOLDS PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Analysis of winter storm “Lothar”**

TROPOPAUSE FOLDING ASSOCIATED WITH KURT AND ISENTROPIC DOWN-GLIDING(?) 18Z, 25 DEC1999 CYCLONE “KURT” PV=2 SURFACE LOW-LEVEL CYCLONE “LOTHAR” V850 Wernli et al. (2002) Fig. 7a PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Analysis of winter storm “Lothar”**

TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR 0Z, 26 DEC1999 CYCLONE “KURT” PV=2 SURFACE LOW-LEVEL CYCLONE “LOTHAR” V850 Wernli et al. (2002) Fig. 7b PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Analysis of winter storm “Lothar”**

6Z, 26 DEC1999 CYCLONE “KURT” PV=2 SURFACE LOW-LEVEL CYCLONE “LOTHAR” UPPER AND LOWER PV ANOMALIES NEARLY JOIN V850 INTENSE WINDS KILL 50 Wernli et al. (2002) Fig. 7c PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Analysis of winter storm “Lothar”**

“INDUCED” TROPOPAUSE FOLD UPPER-LEVEL +PV ANOMALY DIABATIC PROCESSES WERE ESSENTIAL FOR LOTHAR MOIST ASCENDING AIR LATENT HEAT RELEASE HEATING “PRODUCES” LOW-LEVEL +PV ANOMALY MUTUAL AMPLIFICATION OF PHASE-LOCKED PV ANOMALIES SIMILARITIES TO HOSKINS ET AL (1985) BUT MID-TROPOSPHERIC LATENT HEAT RELEASE TAKES THE PLACE OF SURFACE ANOMALY Wernli et al. (2002) Fig. 14 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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Verification PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Z500 and PV330 European Anomaly Correlations**

Z500 FORECASTS AT D+1 TO D+4 ARE EXTREMELY GOOD THESE DAYS PV, WITH ITS INTERTABILITY, MAY EMBODY MORE OF THE IMPORTANT CIRCULATION AND BE A GOOD WAY TO VERIFY FORECASTS BUT IS THIS REALLY THE WEATHER WE EXPERIENCE? 31 OCT STRONG RAINFALL EVENT OVER ALPS SON 2003, T511, ERA40 climatology PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Forecast and Verifying analyses 31 Oct 2003**

Z500 PV330 FC D+4 Z500 FIELDS VERY SIMILAR AND DO NOT HIGHLIGHT AN ESSENTIAL DIFFERENCE MOIST ADVECTION rEURO = 0.90 rEURO = 0.27 AN PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Anomaly Correlation for Europe August 04-March 05**

Z500 step = 10 step = 4 step = 1 Experimental Mean correlation Operations Experimental significant difference PV MAY BE MORE DISCRIMINATING FOR NEW MODEL VERSION TESTING Operations Forecast day RD esuite archives PT2000 spectrally rather than on reduced Gaussian grid. This led to apparent large improvement at 29r1 (which was spurious) step = 10 step = 4 step = 1 Experimental Mean correlation Operations Experimental significant difference PV=2 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. PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Annual-Mean of Daily Anomaly Correlation Coefficients for Europe**

Z500 PV=2 Pp/c FORECAST IMPROVEMENTS ARE MORE APPARENT WITH PV AND PRECIPITATION PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**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 BRIER SCORE: THIS IS NOT THE CASE FOR THE PV DIAGNOSTIC: THE ENSEMBLE SCHEME IS BETTER EVEN AT DAY+1 Z500 PV=2 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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**Summary What is PV? Insight into Dynamics Verification 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 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006

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