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Diagnostics MJR 1 ECMWF Training Course 2009 – NWP-PR Atmospheric Variability: Extratropics Mark Rodwell 19 March 2009

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Diagnostics MJR 2 Talk Outline Free Barotropic Rossby Waves Observations Theory The Rossby Wave Source Theory Explaining the extra-tropical response to the aerosol change Diabatic Processes Potential Vorticity Explosive growth of cyclones Causes of forecast busts Precipitation Deterministic verification Combined prediction systems

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Diagnostics MJR 3 Free Barotropic Rossby Waves

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Rossby Wave MJR 4 Rossby waves. Upper tropospheric v Ψ, v χ & RWS 24 May 25 May 26 May 27 May 2008 Group Velocity Phase Velocity Contour 8ms s -2

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Rossby Wave MJR 5 The Vorticity Equation x z y is the unit vertical vector and is the horizontal curl operator Motivation (2D flow) : Curl of the 3D momentum equation in absolute frame of reference: Shallow atmosphere approximation & assuming non-divergent, horizontal, barotropic, frictionless flow:

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Rossby Wave MJR 6 Free Barotropic Rossby Waves We obtain the dispersion relation Where Rossby waves get advected downstream and propagate upstream The larger the spatial scale of the wave, the faster the upstream propagation For stationary waves Mid-latitude stationary zonal wavenumbers Seeking wave-like solutions … Non-divergent barotropic vorticity equation Where

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Rossby Wave MJR 7 Rossby waves. Upper tropospheric v Ψ, v χ & RWS 24 May 25 May 26 May 27 May 2008 Contour 8ms s -2 Group Speed Phase Speed 10ms -1 agrees well with theory

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Rossby Wave MJR 8 Stationary Rossby Waves: Vorticity advection Advection by Anomalous Rotational WindAdvection of Anomalous Vorticity s -2 Non sig. Sig. 10% Upstream Propagation Downstream Advection 40-year mean response to change in aerosol climatology deduced using seasonal-mean data. Results are very similar when daily data are used. Anomalies integrated hPa.

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Rossby Wave MJR 9 The Rossby Wave Source

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Rossby Wave MJR 10 Upper Troposphere Divergent Wind Anomaly New minus Old aerosol. Anomaly is integrated between 100 and 300 hPa

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Rossby Wave MJR 11 The Rossby Wave Source When divergent winds are not neglected in the vorticity equation For use in complex GCMs, it is found here to be useful to vertically integrate this equation between 100 and 300 hPa Application to barotropic models: Sardeshmukh and Hoskins (1988)

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Rossby Wave MJR 12 JJA Balance in Vorticity Equation New-Old Rossby Wave Source Advection by Anomalous Rotational WindAdvection of Anomalous Vorticity s -2 Non sig. Sig. 10% Upstream Propagation Downstream Advection 40-year mean response to change in aerosol climatology deduced using seasonal-mean data. Results are very similar when daily data are used. Anomalies integrated hPa. The Rossby Wave Source is indeed seen as the tropically induced source of the extratropical stationary Rossby wave response Wave Initiators

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Rossby Wave MJR 13 JJA New-Old RWS, v χ,Ψ and mean ζ s -2 Rossby wave paths agree beautifully with those predicted by Hoskins and Ambrizzi (1995)

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Rossby Wave MJR 14 JJA Precipitation, v925 and Z500. New-Old mm day % Sig.

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Rossby Wave MJR 15 DJF New-Old RWS, v χ,Ψ and mean ζ s -2 Extratropical RWS anomaly coincides with precipitation changes. Is upper tropospheric divergent wind directly related to local physics? Rossby wave path agrees with that shown by Hoskins and Ambrizzi (1993)

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Rossby Wave MJR 16 Diabatic Processes

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Rossby Wave MJR 17 Adiabatic & Diabatic Contributions to RWS θ=320K θ=340K 30 o N90 o N60 o N hPa Account for adiabatic stretching by considering Potential Vorticity (P): Stretching, Tilting & Advection by Diabatic Processes (+ Friction) ADIABATIC + DIABATIC When averaging over a long period PV absorbs the adiabatic stretching

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Rossby Wave MJR 18 SYNOP Precipitation Anomaly Summer 2007 Based on 24hr accumulations and our new global SYNOP climatology for the years mm/day Total rainfall was double the climatological mean

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Rossby Wave MJR 19 Components of a Predictable Signal Europes wet summer of 2007 could have been the unlucky mean of unpredictable variability. But if not, then this schematic shows some likely building blocks to predictability mm/day TROPICAL PHYSICS? LOCAL PHYSICS? PHYSICS ALONG WAVE? DYNAMICAL WAVES? SCHEMATIC

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Rossby Wave MJR 20 Terms in PV QuadraticDiabatic (residual) Results are based on 0 and 12Z analyses. An over-bar indicates the climatological mean and a prime indicates the instantaneous 2007 departure from the climatological mean. (June 1 to August 13) Clearer view of Rossby wave? Agreement with rainfall anomalies. Important for sustaining wave? UNIT = Km 2 kg -1 s -2

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Rossby Wave MJR 21 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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Rossby Wave MJR 22 Analysis of winter storm Lothar PV=2 SURFACE V 850 CYCLONE KURT LOW-LEVEL CYCLONE LOTHAR 0Z, 26 DEC1999 TROPOPAUSE FOLD NOW ALSO ASSOCIATED WITH LOTHAR Wernli et al. (2002) Fig. 7b

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Rossby Wave MJR 23 Analysis of winter storm Lothar 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 Wernli et al. (2002) Fig. 7c

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Rossby Wave MJR 24 RWS, v χ and Meridional wind anomalies RWS shade interval s -2. Meridional wind contour interval 8 ms hPa integrals 30 May 5 June 6 June Classic example that led to a forecast bust over Europe a few days later What is the diabatic forcing? How well does the (first guess) forecast represent this forcing? What are the implications of observation rejection? Look at developments like this from PV perspective.

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Rossby Wave MJR 25 Precipitation

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Rossby Wave MJR 26 Deterministic Scores: Z500, θ PV=2 & Precip

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Rossby Wave MJR 27 Extratropical Deterministic Precip Scores D+5 forecast in 2008 as good as D+1 forecast in 1995 Area = [SP--30 o S & 30 o N--NP] 24h Accumulated Precipitation Forecast Scored against SYNOP Observations

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Rossby Wave MJR 28 ECMWF Meteogram of Precipitation Mumbai ENSEMBLE CONTROL FORECAST HIGH RESOLUTION DETERMINISTIC FORECAST ENSEMBLE PREDICTION SYSTEM Highly useful product but … … What should I believe? At D+2? At D+5?

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Rossby Wave MJR 29 Combined Prediction System – Concept Combining a 10-member ensemble of equally likely members (orange squares) with a single more accurate forecast (yellow rectangle)

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Rossby Wave MJR 30 Combined Prediction System - Theory K = number of forecast systems ( K 3 here) w k is the weight applied to system k (independent of location) Find weights that maximize Brier Skill Score Apply in cross-validated mode (date for year y applied in year y+1) B = Brier Skill Score averaged over all stations n = number of dates M j = set of stations reporting on date j m j = number of stations in M j p ij = CPS probability v ij = verification (0 or 1) b clim = b clim (location,month) (from climatology)

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Rossby Wave MJR 31 Combined Prediction System - Weights

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Rossby Wave MJR 32 Combined Prediction System - Results

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Rossby Wave MJR 33 Combined Meteogram Mumbai

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Rossby Wave MJR 34 Summary Free Barotropic Rossby Waves Propagate upstream and get advected downstream Larger waves can become stationary (e.g. Blocking) The Rossby Wave Source How the (tropical) divergent flow can influence the extratropics Diabatic Processes May be important for maintaining anomalous flow over a season Clearly important for explosively growing cyclones Poor representation (over North America) may lead to forecast busts Precipitation Deterministic scores show improving trends Combined prediction systems can improve probabilistic forecasts

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