Gilbert Brunet Recherche en Prévision Numérique (RPN) Direction de la Recherche en M étéorologie

1. Deux Défis de Recherche en Prévision Numérique: 1) Les Transitions Extra-Tropicales des Ouragans; 2) Prévisions saisonnières avec un modèle simplifié. Gilbert Brunet Recherche en Prévision Numérique (RPN) Direction de la Recherche en Météorologie Service Météorologique du Canada Environnement Canada Québec, Canada Juin 2003, Laboratoire de Météorologie Dynamique, Paris

2. Introduction • 1) Historique et activité de recherche et développement à RPN http://www.cmc.ec.gc.ca/rpn/ • 2) Diagnostique des processus ondulatoires d’un ouragan simulé • 3) Prévision saisonnière à l’aide d’un modèle de circulation générale simplifié

3. Numerical Weather PredictionV. Bjerknes (1904) and L.F. Richardson (1922) • Numerical weather prediction is based on the mathematical laws of fluid, Horizontal Momentum Vertical Momentum Continuity Thermodynamic Moisture State • The NWP problem needs to be discretised and solved on super computer with sophisticated mathematical algorithms and technics

4. L.F. Richardson La prévision numérique du temps et du climat, M. Rochas et J.-P. Javelle.

5. The Starting Point: the 50’s and 60’s • Provides initial conditions for NWP models: Correct a forecast by direct insertion of observations (Cressman, 1959) • lead to inconsistencies in the 3D meteorological fields • Univariate statistical interpolation (Gandin, 1963) • Increased computer power permitted a return to more general primitive equations (PE) grid-point models (e.g. the Schumann & Hovermale model implemented in the U.S. in 1966) • The first successful integrations of a global spectral PE model were performed (Robert, 1969)

6. Contributions during the 1990’s • SI-SL method implemented in spectral models (Ritchie et al.) • Unified GEM (SI-SL, global, uniform or variable resolution, non- hydrostatic and hydrostatic) model (Staniforth, Côté, Gravel) • Ensemble Kalman Filter (Houtekamer and Mitchell, MRB)

7. Next supercomputer (2003): 800 processors (IBM Power4)

8. Contributions during the 1990’s • First SI-SL fully non-hydrostatic model (became MC2) developed (Tanguay, Laprise, Robert) • MC2 internationally recognized for mesoscale modelling (Benoit et al.)

9. Increasing computer power • Increasing computer power • 1960 ’s - Bendix G20, IBM370. • 1970’s: Control Data 7600, Control Data 176 • 1980’s: Cray 1S, Cray XMP-2/8, Cray XMP-4/16 • 1990’s: NEC SX-3/44, SX-3/44R, SX-4/64M2, SX-5/32M2 and SX-6/10M8 • 2000’s: IBM Power4 Cluster (100M8)

10. Trend in skill 1958-2002

11. Performance of the global medium-range 100km resolution GEM forecast system(Historical evolution of the 500hPA 24H-forecast standard deviation error on North Hemisphere) North Hemisphere

12. Performance of the global long-range 100km resolution GEM forecast system(Historical evolution of the 500hPA 120H-forecast standard deviation error on North Hemisphere)

13. Wave Activity Diagnostics in a Simulated Hurricane Yongsheng Chen Gilbert Brunet M.K. Yau

14. Background and Motivation • Recent studies have shown that inner spiral bands have characteristics of vortex Rossby waves • Vortex Rossby waves (VRW) and gravity waves are mixed • Apply Empirical Normal Mode (ENM) method to separate the waves to isolate the effect of VRW on a simulated hurricane -Chen and Yau 2001 (6 km grid size, 24 h simulation sampled every 2 minutes) Chen, Brunet and Yau 2003: Spiral Bands in a Simulated Hurricane. Part II: Wave Activity Diagnostics. Journal of Atmospheric Sciences: Vol. 60, No. 10, pp. 1239–1256.

15. PV and W evolution (z=2km)

16. Empirical Normal Mode (ENM) method • principal component analysis • takes advantage of wave activity conservation law • decomposes simultaneously wind and thermal fields into dynamically consistent and orthogonal modes with respect to wave activities • used to study Rossby waves (Brunet 1994, Brunet and Vautard 1996, Zadra et al. 2002) and gravity waves (Charron and Brunet 1999)

17. Derivation of wave activity equation: Hydrostatic primitive equations in storm-following isentropic coordinates

18. Derivation of wave activity equation (cont.): • Assume small amplitude, linearization • Basic state = time-azimuthal mean • Azimuthal-invariant pseudo-momentum density conservation • Time-invariant pseudo-energy density conservation

19. Jg Jv ~ -u’ v’ inward momentum trans. ~ -u’ T’ inward heat trans. Derivation of wave activity equation (cont.): Pseudo-momentum equation:

20. Derivation of wave activity equation (cont.): Pseudo-energy equation: KE PE DS

21. ENM Matrix Notation The norm of C and n are pseudo-momentum ENM extracts modes which conserve wave activities (J and A) when dynamics is linear EOF ~ ENM

22. 00h 06h 12h 18h PV at 6 km

23. >0 <0 Basic State

24. Model data analysis • Procedures • vertical interpolation from  coordinates to  coordinates • remove basic state(time-azimuthal mean) • azimuthal decomposition • find ENM modes (time series + spatial patterns) • wave modes kinematics and dynamics

25. J A J A Wavenumber 1 and 2, ENM mode J and A spectra • J and A change sign • Period and phase speed • Retrograde and prograde waves • Unstable mode?

26. 75% 10% 75% 10% Wavenumber 1 and 2, ENM mode J and A spectra Jv Jg • Rotational contribution > gravitational contribution • Leading modes are vortex Rossby waves • Spiral rainbands show vortex Rossby wave characteristics Jv Jg

27. Azimuthally propagating waves Mode 1 Mode 2

28. T=0.27h T=1h Wavenumber 2, ENM mode 1 and 2, time series 11.0% 10.5% |a|2 (10-3) (2 /24H)

29. Wavenumber 2, PV ENM mode 1 and 2, spatial patterns Mode 2 cos Mode 1 cos Mode 1 sin Mode 2 sin

30. Wavenumber 1, ENMs average frequencies (2 /24H) Discrete spectrum max Continuous spectrum

31. Wavenumber 1 and 2, mode 1+2, EP flux • Wave-mean-flow interaction: • Acceleration: low and middle troposphere inside/outside the eyewall • Deceleration: upper troposphere in the eyewall

32. Extratropical Transition- Examining mid latitude transition of hurricanes and typhoons (COMPARE PROJECT). 10km/60 levels Kuosym/Sundqvist (MC2, M. Desgagné) 24-72 H Forecast of relative vorticity at 25m (frame every hour) COMPARE ED FLO

33. 2km/40 levels Kong&Yau (MC2, M. Desgagné)16-30 H Forecast of Relative Vorticity at 20m (frame every hour) COMPARE

34. A Grand Challenge project on theEarth Simulator: a full life cycle convective scale simulation of an hurricane • Brunet, Desgagné, Gyakum, Montgomery and Yau • Meteorological Service of Canada numerical research division (RPN), McGill University and Colorado State University • 40 clusters of 16 full SX-6 nodes • 8 vector processors per node Total 5120 PEs • Peak performance 40 Tflops/sec • Memory: 16 Gbytes/node Total: 10 TB • NEC IXS Xbar Interconnec

35. Proposal for the Earth Simulator Project 964 hPa ET Phase 985 hPa Modelling the Full Lifecycle of Hurricane Earl at 1km Resolution with the Canadian MC2 Model Tropical Phase Class2 Hurricane September 1998: Classified as a very active TC period

36. Modelling the Full Lifecycle of Hurricane Earl at 1km Resolution with the Canadian MC2 Model Horizontal grid: rotated Mercator 11400 x 8700 70 levels 8-9 days Forecast (with a possible restart) Memory: 4 Tb CPUs: 45 x 85 (3825) Steps: 115200 X 6 sec. Wall clock: 8-9 days A real challenge for implicit solver and parallel I/O systems

37. Conclusions • ENM analysis shows wavenumber 1 and 2 leading ENMs are Vortex Rossby wave modes (retrograde and prograde) • The divergence of EP fluxes indicates • acceleration of tangential wind in lower and middle troposphere inside and outside the eyewall • deceleration of tangential wind aloft in the eyewall • critical layer signature in the EP flux (dissipative or nonlinear?): a full life cycle convective scale simulation is proposed

38. Historical Seasonal Forecasting with a Simple General Circulation Model Hai Lin McGill University Jacques Derome McGill University Gilbert Brunet Recherche en Prévision Numérique and McGill University

39. Objective • Test if a numerical model of intermediate complexity has skill in seasonal forecasting

40. The Model • Global, primitive equations • Spherical harmonics, T21, 5 levels • Dry • Time-independent forcing

41. The Model Forcing

42. The Model Forcing • Forcing calculated from NCEP/NCAR reanalysis daily data for each month of 1948-1998. • Includes synthesis of all physical forcings: SST, sea-ice, land-surface conditions, etc.

43. DJF 300 hPa 700 hPa

44. The experiment • Actual seasonal prediction we don’t know the forcing for the forecast period • Compute November forcing anomaly. • Add it to DJF forcing climatology. • Constant through DJF.

45. The Experimental Protocol • Perform 3-month forecasts for 51 winters, all started on Dec. 1 • 24-member ensembles • Initial conditions • Dec. 1 observations plus small-amplitude perturbations (scaled anomalies from random winter days)

46. Verification • Compute forecast anomaly (ensemble average): forecast – model climatology • For each point in space, compute temporal correlation over 51 winters: predicted vs observed anomaly

47. Result for actual seasonal prediction • DJF forcing anomaly is forecast from November (persisted). • Mimic a real world seasonal prediction environment.

48. How good is the forcing persistence?

49. Simple GCM DJF GCMII

50. JF SimpleGCM GCMII