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

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ECMWF Slide 2 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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

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ECMWF Slide 3 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 What is PV?

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ECMWF Slide 4 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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 Earths rotation.

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ECMWF Slide 5 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Vorticity I Making the shallow atmosphere approximations, using pressure surfaces and takingof 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

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ECMWF Slide 6 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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

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ECMWF Slide 7 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 For barotropic frictionless flow,(curl of (1)) Using Stokes theorem, this implies that n S 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. Ertel Potential Vorticity (EPV) I The behaviour of the material circuit contributes nothing.

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ECMWF Slide 8 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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: Ertel Potential Vorticity (EPV) II Some 2D convergence may be accompanied by an increase in density rather than stretching and the (in EPV) takes account of this.

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ECMWF Slide 9 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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. Isentropic Potential Vorticity (IPV) I

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ECMWF Slide 10 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Insight in Dynamics

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ECMWF Slide 11 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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

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ECMWF Slide 12 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Dynamic Tropopause at 2PV units TROPOPAUSE (PV=2 ISO-SURFACE) TROPOSPHERE (LOW PV) STRATOSPHERE (HIGH PV) Massacand (1996) TROPOPAUSE FOLD

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ECMWF Slide 13 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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 IPV COLD ADVECTION, LESS STATIC STABLITY AND ANTICYCLONIC IPV ON SURFACE MORE STABLE COLD WARM LESS STABLE IPV WEAKER TROPOSPHERIC STABILITY ALLOWS CONVECTION WHICH CAN LOWER OR DAMP THE IPV ANOMALY

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ECMWF Slide 14 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Circularly Symmetric Flows Induced by Simple Isolated IPV Anomalies Hoskins, McIntyre and Robertson (1985) hPa hPa UPPER-LEVEL CYCLONIC IPV ANOMALY (STIPPLED) SURFACE TEMPERATURE ANOMALY (+1OK) ISENTROPES (CI = 5K) AND AZIMUTHAL WIND (CI=INTERVAL 3ms -1 ) r=1667kmr=0 WARM CAN BE INTERPRETTED AS A CYCLONIC IPV ANOMALY } WARM

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ECMWF Slide 15 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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 largeat 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 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

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ECMWF Slide 16 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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

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ECMWF Slide 17 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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 MODELS DIABATIC OR FRICTIONAL PARAMETRIZATION? CAN INVESTIGATE REASONS FOR PV MODIFICATION Rodwell and Hoskins (1995) Fig. 7 DIABATIC TENDENCY SHALLOW HEATING FRICTIONAL TENDENCY MOUNTAINS ASIAN MONSOON

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ECMWF Slide 18 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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 V 850 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 TURNING IS A CONSEQUENCE OF PV ADVECTION V 850 Precipitation mmday -1 WIND ANOMALY IS VERY ROBUST FOR OTHER THRESHOLDS

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ECMWF Slide 19 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Analysis of winter storm Lothar Wernli et al. (2002) Fig. 7a PV=2 SURFACE V 850 CYCLONE KURT LOW-LEVEL CYCLONE LOTHAR 18Z, 25 DEC1999 TROPOPAUSE FOLDING ASSOCIATED WITH KURT AND ISENTROPIC DOWN-GLIDING(?)

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ECMWF Slide 20 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Analysis of winter storm Lothar Wernli et al. (2002) Fig. 7b PV=2 SURFACE V 850 CYCLONE KURT LOW-LEVEL CYCLONE LOTHAR 0Z, 26 DEC1999 TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR

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ECMWF Slide 21 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Analysis of winter storm Lothar Wernli et al. (2002) Fig. 7c PV=2 SURFACE V 850 CYCLONE KURT LOW-LEVEL CYCLONE LOTHAR 6Z, 26 DEC1999 UPPER AND LOWER PV ANOMALIES NEARLY JOIN INTENSE WINDS KILL 50

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ECMWF Slide 22 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Analysis of winter storm Lothar 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 INDUCED TROPOPAUSE FOLD UPPER-LEVEL +PV ANOMALY DIABATIC PROCESSES WERE ESSENTIAL FOR LOTHAR MUTUAL AMPLIFICATION OF PHASE-LOCKED PV ANOMALIES

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ECMWF Slide 23 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Verification

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ECMWF Slide 24 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Z 500 and PV 330 European Anomaly Correlations PV, WITH ITS INTERTABILITY, MAY EMBODY MORE OF THE IMPORTANT CIRCULATION AND BE A GOOD WAY TO VERIFY FORECASTS SON 2003, T511, ERA40 climatology Z 500 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

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ECMWF Slide 25 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 r EURO = 0.90r EURO = 0.27 AN FC D+4 PV 330 Z 500 Forecast and Verifying analyses 31 Oct 2003 MOIST ADVECTION Z 500 FIELDS VERY SIMILAR AND DO NOT HIGHLIGHT AN ESSENTIAL DIFFERENCE

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ECMWF Slide 26 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Z 500 PV=2 Operations Experimental significant difference Europe = [12.5 o W-42.5 o E, 35 o N-75 o N]. 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. Experimental Operations Experimental significant difference step = 10 step = 4 step = 1 step = 10 step = 4 step = 1 Operations Forecast day Anomaly Correlation for Europe August 04-March 05 Mean correlation PV MAY BE MORE DISCRIMINATING FOR NEW MODEL VERSION TESTING

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ECMWF Slide 27 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Annual-Mean of Daily Anomaly Correlation Coefficients for Europe FORECAST IMPROVEMENTS ARE MORE APPARENT WITH PV AND PRECIPITATION Z 500 P p/c PV=2

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ECMWF Slide 28 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 Brier Score Difference for event > normal DJF , Ensemble (T255) – Deterministic (T511) IN PROBABILISTIC TERMS, A DETERMINISTIC FORECAST OF Z 500 AT DAY+1 IS AS GOOD AS A FORECAST FROM THE ENSEMBLE PREDICTION SYSTEM Z 500 PV=2 BRIER SCORE: THIS IS NOT THE CASE FOR THE PV DIAGNOSTIC: THE ENSEMBLE SCHEME IS BETTER EVEN AT DAY+1

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ECMWF Slide 29 PV diagnostics, Met.TC, MJ Rodwell, 25 April 2006 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

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