Turbulence Eddy Dissipation Rate forecast based on COSMOEU

Turbulence (Eddy Dissipation Rate) forecast based on COSMO-EU 1. introduction/motivation 2. extended turbulence scheme 3. comparison of model output (EDP) and measurement (EDR) 4. abstract and outlook Turbulence forecast for aviation WV 2 Axel Barleben

1. introduction/motivation Department Aviation Meteorology of DWD - is responsible for the meteorological support of the Civil Aviation in Germany - the German Meteorological Service Deutscher Wetterdienst (DWD) is a federal authority under the Federal Ministry of Transport, Building and Urban Affairs - DWD operates five regional advisory centres for IFR and VFR traffic - three of them act as Meteorological Watch Offices for aviation weather watch and warning (MWO) resulted from the german airspace structure (3 Flight Information Regions up to FL 245, 2 Upper air Information Regions above Fl 245) FIR Bremen FIR Langen München Turbulence forecast for aviation WV 2 Axel Barleben

1. introduction/motivation products containing turbulence forecast support for prediction ? - SIGMET (severe turb FIR/UIR) - General advices about CAT-prone areas - Threshold values of horizontal/vertical wind shear of Richardson number of Ellrod-index - CAT(Maximum)%, WAFC - SWC WAFC - GAMET/AIRMET (moderate turb) - AIREP (observation) PIREP (obs) - reports (mod, sev for FIR) - Low Level SWC Central Europe (up to FL 245) - wind shear (up to 1600 ft gnd , rep or exp) (METAR/COMMENTS/WARNING) - briefing for pilots Turbulence forecast between surface and FL 450 with accuracy 1000 ft appropriate forecast tools ? Valid usual method : turbulence is predicted (SIGMET) after turbulence is observed(PIREP) => require an improvement of turbulence forecast method Turbulence forecast for aviation WV 2 Axel Barleben

1. introduction/motivation eddy dissipation rate [m**(2/3)/s] ICAO ANNEX 3 Appendix 6 /4. 2. 6 Criteria related to phenomena included in SIGMET and AIRMET: SEV TURB EDR > 0. 7 MOD TURB 0. 4< EDR <= 0. 7 ? -strategic decision of DWD (aeronautical meteorological department) after preliminary studies -development Eddy Dissipation Parameter derived from local model COSMO-EU -measurement of atmospheric turbulence , not directly -not available over Europe -alternative indicator of turbulence is the Derived Equivalent Vertical Gust Velocity (DEVG available , low quantity ) Turbulence forecast for aviation WV 2 Axel Barleben

Current thresholds derived from comparison EDR/PIREPS 1. introduction/motivation Julia M. Pearson, R. Sharman Calibration of in situ eddy dissipation rate (EDR) severity thresholds based on comparisons to turbulence pilot reports (PIREPs) 16 th Conference ARAM, Austin, 2013 Pearson, Sharman 2013 0. 014 lgt , 0. 124 mod , 0. 345 sev Pettegrew et al. 2010 : PIREP/ACARS => 0. 15 lgt , 0. 35 mod , 0. 55 sev ICAO ANNEX 3 Appendix 6 SEV TURB EDR > 0. 7 MOD TURB 0. 4< EDR <= 0. 7 for example: sev turb edr 076 final aim => EDP (from model output) reproduce the EDR (measurement) Turbulence forecast for aviation WV 2 Axel Barleben

2. extended turbulence scheme COSMO-EU -for operational NWP -nested within GME on a 665 x 657 grid with 40 layers mesh size 7 km -based on the primitive hydro thermo dynamical equations -describing compressive no hydrostatic flow -formulated in rotated geographical coordinates -generalized terrain-following vertical coordinate - turbulence scheme (Raschendorfer, DWD) prognostic level 2. 5 closure for the prognostic tke–equation http: //www. cosmo-model. org/ content/model/documentation/ core/default. htm tke - direct model output (DMO) Turbulence forecast for aviation WV 2 Axel Barleben

2. extended turbulence scheme Kolmogorov (1941) tke is only a function of edr Lp - turbulence length scale α – dissipation constant ³√ Turbulence forecast for aviation Eddy Dissipation Parameter WV 2 Axel Barleben

2. extended turbulence scheme prognostic tke–equation in principle and simplify - new turbulence scheme Raschendorfer, M. : Further steps towards a scale separated turbulence scheme. 13 th COSMO General Meeting, Rome, Italy, 2011 wake vortices by SSO (sub grid scale orography) blocking horizontal shear vortices shallow and deep convection patterns time tendency of tke transport = (advection diffusion) shear production buoyancy + production + by the mean flow eddyshear production + by sub grid scale + dissipation rate (EDR) circulations labile : > 0 stable : < 0 neutral : = 0 Turbulence forecast for aviation WV 2 Axel Barleben

2. extended turbulence scheme scale separation approach and turbulence scheme Sub grid scale Kinetic Energy = Turbulent Kinetic Energy + non turbulent Circulation phrased as Sc , scale interaction terms of Kinetic Energy SKE = TKE + CKE Equilibrium of energy production (source terms Qc) and scale interaction term Turbulence forecast for aviation TKE similar to parameterization edr WV 2 Axel Barleben

2. extended turbulence scheme TKE-production by separated horizontal (vertical) shear modes: Equilibrium of production and scale transfer towards turbulence - effective scaling parameter du 2 du 1 dv 1 du 3 dv 2 dw 1 dw 3 dv 3 dw 2 partial derivatives from components of velocity HSH=DEF**2+DIV**2 ; ELD=VSH*(DEF-DIV) = (HSH+TSV) Turbulence forecast for aviation DST=du 1 -dv 2 DSH=dv 1+du 2 DIV=-(du 1+dv 2) DEF=SQRT(DST**2+DSH**2) VSH=du 3**2+dv 3**2 TSV~VSH TSV=VSH+dw 1**2+dw 2**2+dw 3**2 WV 2 Axel Barleben

2. extended turbulence scheme TKE-production by separated wake modes due to SSO: - blocking Term according Lott und Miller (1997) - describe breaking gravity wave after vertical propagation (and no horizontal) - is estimated currently (SSO-scheme COSMO-EU) - momentum sink due to friction of sub grid scale orography Equilibrium of production and loss by scale transfer Turbulence forecast for aviation WV 2 Axel Barleben

2. extended turbulence scheme TKE-production by convection (thermal circulations) moist convection according Tiedke (1987) mass flux convection scheme is installed in COSMO-EU TKE-production can be derived directly vertical velocity scale of circulation virtual potential temperature of ascending air virtual potential temperature of descending air Equilibrium of production and loss by scale transfer Turbulence forecast for aviation WV 2 Axel Barleben

3. comparison of EDP and EDR max. EDR is measured by commercial aircrafts available over the USA COSMO-EU => COSMO-US was nested over US domain COSMO-US : dlam/dphi = 0. 0625 ie = 353 je = 314 ke = 40 philu = -9. 075 (startlat) lamlu = -12. 608 (startlon) pollon = -86. 0 pollat = -53. 0 dt = 40 Data structure winter 2010/11 (01. 10 -31. 3) 495 GB grib 1 COSMO-US 62 GB net. CDF ACARS from MADIS archive Events MOG/No. Turb max. EDR Turbulence forecast for aviation all 6. 318. 975 1. 473. 862 23% / 77 % >2000 m 5. 049. 488 683. 003 14% / 86 % >6400 m 4. 140. 997 187. 522 5% / 95 % WV 2 Axel Barleben

Share of the 5 % (events from in all) moderate or greater turbulence above 6400 m 3. comparison of EDP and EDR Climatology of Upper-Level Turbulence over th e Contiguous United States J. K. WOLFF , R. D. SHARMAN, Journ. Appl. Meteor. and Clim. , Vol 47, 2008 Turbulence in clouds (convection, CIT) and near lower shear zone of jet 10 -20 -times more likely as near core of jet and upper shear zone , of prime importance Turbulence forecast for aviation PIREP database FIG. 14. Vertical profile of the yearly averaged MOG/total divided by the globally averaged MOG/total background value of 0. 32 stratified by in cloud and clear air as well as by season (October–March, dashed lines; April–September, thin solid lines; yearly average, thick solid lines). WV 2 Axel Barleben

3. comparison of EDP and EDR statistical evaluation and 5% MOG/ 95% No. Turb turbulence events (MOG) can’t bring a return with this distribution training data set - large number of examples from each class no change of class distribution in the validation data random-sampling to decrease No. Turb-examples sensitivity-test for several distributions best arrangement 40%MOG/60%No. Turb use only for model output statistic confirmed “I have used the 40% MOG (60% null) distribution because it worked well with all the machine learning algorithms” Dissertation : A Domain Analysis Approach to Clear-Air Turbulence Forecasting Using High-Density In-situ Measurements by Jenny A. Abernethy M. S. , University of Colorado, 2004 Turbulence forecast for aviation WV 2 Axel Barleben

3. comparison of EDP and EDR -model output statistic => classical linear regression -is used to relate the response variable (predictand, Y=max. EDR) to the explanatory variables (predictors Xi = p, v, w, tke, . . eld, div, dsh, ri, Qc…) -Maximum likelihood estimates of β 1…βp are founded by least squares fitting initial situation max. EDR/edp >6400 m, 485513 events(40/60) after linear regression step 1 edp_mos=β 0+β 1*DEN after linear regression step 2 edp_mos=β 0+β 1*DEN+β 2*edp Turbulence forecast for aviation WV 2 Axel Barleben

3. comparison of EDP and EDR Simply density is a significant predictor for max. EDR , ? -edp from COSMO only kinematic variable -max. EDR use required input TAS ( ) -use density adjustment for model output because turbulence is higher for more dense air mass -need further source term for tke-equation involved density Qc_? = Qc_? f(den), gravity wave -max. EDR data seem to be biased by flight activities (influence of aircrafts ahead, higher for low level flights) Turbulence forecast for aviation WV 2 Axel Barleben

validation of full set of data about 4 million couples of measurement/model above FL 210. Receiver Operating Characteristic objective from Turbulence Joint Safety Implementation Team (TJSIT) realized forecast 3. comparison of EDP and EDR PODY PODN TSS 0. 43 0. 75 0. 17 0. 62 0. 66 0. 28 edp = edp + C (ϱ/ϱ₀)³ 0. 73 0. 77 0. 50 edp_mos = β₀ +β₁(ϱ/ϱ₀)³edp 0. 74 0. 81 0. 55 III: numerical tests, idea additional source term depend on density IV: MOS with 1 step (predictor) (ϱ/ϱ₀)³edp evsep=0. 12 ( no-turb/yes-turb for III, IV) Turbulence forecast for aviation WV 2 Axel Barleben

4. outlook / abstract Comparison EDR and EDP -useful for verification of turbulence forecast (edp) with real measurement (edr) -appropriate for optimization of turbulence parameterization (scaling factor for QC_SHS, tubulent length scale, density-adjustment) -MOS (no improvement after step 2) needs other or further indices (or combinations) -edp ( tke-equation) because additive correction require further source-terms (advection) -Qc_con only add in case of CIT, “limiting value” ? -FAA-EDR standards, expanded to Europe , understanding (density) -turbulence scheme in global model ICON (20 km, 60 -90 levels) ~ 2014 -thresholds edp ? tendency : light events to strong, severe events to weak -EDP reproduce EDR inexactly -aviation forecaster (DWD) apply EDP and Ellrod-index for turbulence prediction (example 14. 2. 2013) Turbulence forecast for aviation WV 2 p Axel Barleben

4. outlook / abstract COSMO-EU forecast of eddy dissipation parameter ARS: MODERATE TO SEVERE TURB OBS FL 180 -240, FL 360, 6 -8 UTC Figure: forecast EDP COSMO-EU , Maximum level 10 -19 (FL 180 -360), 14. 02. 2013 06 UTC (method : sum up different levels “ 3 d”) several PIREPS reported mod to sev along 10 degree of longitude Turbulence forecast for aviation WV 2 Axel Barleben

third dimension animation of ELD > 6. 0 10**-7 s**-2 (sev turb) 14. 2. 2013, 06 UTC Turbulence forecast for aviation WV 2 Axel Barleben 3. comparison of EDP and EDR