1. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization and Ensemble generation for Seasonal Forecasting Magdalena A. Balmaseda

2. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting The importance of the ocean initial conditions in seasonal forecasts A well established case: ENSO in the Equatorial Pacific A tantalizing case: NAO forecasts Ocean Model initialization Ocean initialization: requirements Standard practice: assessment Other initialization strategies: assessment Role of ocean initialization into context Ensemble Generation: Sampling Uncertainty Seasonal forecasts versus Medium range: different problems, different solutions? The ECMWF ensemble generation system. Other ensemble generation strategies Outline

3. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting The Basis for Seasonal Forecasts Atmospheric point of view: Boundary condition problem Forcing by lower boundary conditions changes the PDF of the atmospheric attractor Loaded dice The lower boundary conditions (SST, land) have longer memory oHigher heat capacity (Thermodynamic argument) oPredictable dynamics Oceanic point of view: Initial value problem Prediction of tropical SST: need to initialize the ocean subsurface. Examples: oA well established case is ENSO oA more tantalizing case is the importance subsurface temperature in the North Subtropical Atlantic for seasonal forecasts of NAO and European Winters.

4. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Need to Initialize the subsurface of the ocean

5. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting A tantalizing case: SF of NAO and European Winters SST anomaly Autumn 2005 SST anomaly Winter 2005/6 T anomaly@ 90m: Autumn 2005 Anomalies below the mixed layer re-emerge and Do they force the Atmosphere?

6. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Probabilistic forecast calibration Reliable probability forecasts Tailored products End to End Forecasting System atmos DA atmos obs SST analysis ocean DA ocean obs ocean reanalysis atmos reanalysis land,snow…? sea-ice? initial conditions initial conditions AGCM OGCM ensemble generation

7. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Coupled Hindcasts, needed to estimate climatological PDF, require a historical ocean reanalysis Real time Probabilistic Coupled Forecast time Ocean reanalysis Quality of reanalysis affects the climatological PDF Consistency between historical and real-time initial initial conditions is required Main Objective: to provide ocean Initial conditions for coupled forecasts

8. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Creation of Ocean Initial conditions Ocean model driven by surface fluxes: Daily fluxes of momentum, Heat (short and long wave), fresh water flux From atmospheric reanalysis ( and from NWP for the real time). but uncertainty in surface fluxes is large.

9. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Equatorial Atlantic: Taux anomalies Equatorial Atlantic upper heat content anomalies. No assimilation Equatorial Atlantic upper heat content anomalies. Assimilation ERA15/OPS ERA40 Uncertainty in Surface Fluxes: Need for Data Assimilation Large uncertainty in wind products lead to large uncertainty in the ocean subsurface The possibility is to use additional information from ocean data (temperature, others…) Questions: 1.Does assimilation of ocean data constrain the ocean state? 2.Does the assimilation of ocean data improve the ocean estimate? 3.Does the assimilation of ocean data improve the seasonal forecasts

10. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Real Time Ocean Observations ARGO floats XBT (eXpandable BathiThermograph) Moorings Satellite SST Sea Level

11. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Time evolution of the Ocean Observing System XBTs 60s Satellite SST Moorings/Altimeter ARGO 19821993 2001 1998-1999 PIRATA TRITON

12. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Data coverage for Nov 2005 Changing observing system is a challenge for consistent reanalysis Todays Observations will be used in years to come Moorings: SubsurfaceTemperature ARGO floats: Subsurface Temperature and Salinity + XBT : Subsurface Temperature Data coverage for June 1982 Ocean Observing System

13. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Impact of data assimilation on the mean Assim of mooring data CTL=No data Large impact of data in the mean state: Shallower thermocline PIRATA

14. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting ORA-S3 Main Objective: Initialization of seasonal forecasts Historical reanalysis brought up-to-date (11 days behind real time) Source of climate variability Main Features ERA-40 daily fluxes (1959-2002) and NWP thereafter Retrospective Ocean Reanalysis back to 1959 Multivariate on-line Bias Correction (pressure gradient) Assimilation of temperature, salinity, altimeter sea level anomalies an global sea level trends. 3D OI, Salinity along isotherms Balance constrains (T/S and geostrophy) Sequential, 10 days analysis cycle, IAU Balmaseda etal 2007/2008

15. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting System 3: Assimilation of Temperature, Salinity and Sea Level T/S conserved T/S Changed T/S conserved Assimilation of S(T) not S(z)

16. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting The Assimilation corrects the ocean mean state Mean Assimation Temperature Increment Free model Data Assimilation z (x)Equatorial Pacific Data assimilation corrects the slope and mean depth of the equatorial thermocline

17. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting The Assimilation corrects the ocean mean state Western PacificEquatorial Indian Analysis minus Observations DATA ASSIM NO DATA ASSIM

18. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting CNTL:No data (1993-2001)Assimilation of T (1993-2001) Data Assimilation Improves the Interannual variability of the Analysis Correlation of SL from System2 with altimeter data (which was not assimilated)

19. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Correlation with OSCAR currents Monthly means, period: 1993-2005 Seasonal cycle removed No Data Assimilation Assimilation:T+S Assimilation:T+S+Alt Data Assimilation improves the interannual variability of the ocean analysis

20. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Ocean data assimilation also improves the forecast skill (Alves et al 2003) Data Assimilation No Data Assimilation Impact of Data Assimilation Forecast Skill

21. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Progress is not monotonic: Need good coupled models to gauge the quality of initial conditions Skill can be limited by the quality of the coupled model So far so good, but: a) ERA15/OPS fluxes S2 NO Asim S2 Assim b) ERA40/OPS fluxes DEM NO Assim DEM Assim

22. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Impact on ECMWF-S3 Seasonal Forecast Skill S3 Nodata S3 Assim

23. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization into context Ocean Initial Conditions Versus Coupled Model S2 S2ic_S3model S3

24. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Some general considerations on initialization

25. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization Problem: Production of Optimal I.C. Optimal Initial Conditions: those that produce the best forecast. Need of a metric: lead time, variable, region (i.e. subjective choice) In complex non linear systems there is no objective searching algorithm for optimality. The problem is solved by subjective choices. Theoretically: I.C. should represent accurately the state of the real world. I.C. should project into the model attractor, so the model is able to evolve them. In case of model error the above 2 statements may seem contradictory Practical requirements: If forecasts need calibration, the forecast I.C. should be consistent with the I.C. of the calibrating hindcasts. Need for historical ocean reanalysis Current Priorities: oInitialization of SST and ocean subsurface. oLand/ice/snow potentially important. Not much effort so far … oAtmospheric initial conditions play a secondary role. We choose a metric, forecasts of SST from 1-6 months.

26. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Perceived Paradigm for initialization of coupled forecasts Real worldModel attractor Medium range Being close to the real world is perceived as advantageous. Model retains information for these time scales. Model attractor and real world are close? Decadal or longer Need to initialize the model attractor on the relevant time and spatial scales. Model attractor different from real world. Experiments: Uncoupled SST + Wind Stress + Ocean Observations (ALL) Uncoupled SST + Wind Stress (NO-OCOBS) Coupled SST (SST-ONLY) (Keenlyside et al 2008, Luo et al 2005) Seasonal? Somewhere in the middle? At first sight, this paradigm would not allow a seamless prediction system.

27. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Impact of real world information on skill: NINO3.4 RMS ERROR ALL NO-OCOBS SST-ONLY Adding information about the real world improves ENSO forecasts From Balmaseda and Anderson 2009

28. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting NINO-W EQATL EQ3 STIO WTIO Reduction (%) in SST forecast error Range 1-3 months In Central/Western Pacific, up to 50% of forecast skill is due to atmos+ocean observations. Sinergy: > Additive contribution Ocean~20% Atmos ~25% OC+ATM~55% Impact of real world information on skill:

29. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Relation between drift and Amplitude of Interannual variability. Upwelling area penetrating too far west leads to stronger IV than desired. Western Pacific Relation between drift and Amplitude of Interannual variability. Possible non linearity: is the warm drift interacting with the amplitude of ENSO? Impact of Initialization Drift and Variability depend on Initialization !! More information corrects for model error, and the information is retained during the fc. Need more balanced initialization methods to prevent initialization shock hitting non linearities Eastern Pacific ALL NO-OCOBS SST-ONLY DRIFT VARIABILITY

30. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization Shock and non linearities Forecast lead time phase space Model Attractor (MA) non-linear interactions important Real World (RW) Initialization shock a b c

31. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization shock and non linearities Forecast lead time phase space Model Attractor (MA) non-linear interactions important Real World (RW) Empirical Flux Corrections

32. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initialization Advantages: It is possible The systematic error during the initialization is small(-er) It can be used in a seamless system Disadvantages: Model is different during the initialization and forecast Possibility of initialization shock No synergy between ocean and atmospheric observations Full Coupled Initialization: No clear path for implementation in operational systems Need of a good algorithm to treat systematic error. Problem with different time scales Simplified coupled models? Initialization of slow time scales only, limited number of modes. Weakly-coupled initialization? Atmosphere initialization with a coupled model Ocean initialization with a coupled model. Ocean initialization in anomaly mode with a coupled model (DePreSyS) Uncoupled: Most commonOther Strategies

33. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Data Assimilation Observation space Model space The transformation from observation to model space should be scale dependent. Initialization of the model attractor does not mean neglecting observations. The challenge for a seamless prediction system is the consistent/simultaneous initialization of the different time scales.

34. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Delayed Ocean Analysis ~12 days Real Time Ocean Analysis ~Real time ECMWF: Weather and Climate Dynamical Forecasts ECMWF: Weather and Climate Dynamical Forecasts 18-Day Medium-Range Forecasts 18-Day Medium-Range Forecasts Seasonal Forecasts Seasonal Forecasts Monthly Forecasts Monthly Forecasts Ocean model Atmospheric model Wave model Atmospheric model Ocean model Wave model

35. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting D1 Time (days) 111210987654321 BRT ocean analysis: D1-12NRT ocean analysis: D1 Assimilation at D1-12 Assimilation at D1-5 Operational Ocean Analysis Schedule BRT ( Behind real time ocean analysis): ~12 days delay to allow data reception For seasonal Forecasts. Continuation of the historical ocean reanalysis NRT (Near real time ocean analysis):~ For Var-EPS/Monthly forecasts

36. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting ENSEMBLE GENERATION Representing Uncertainty without disrupting Predictability Seasonal versus Medium Range Source of Uncertainty Different Strategies

37. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Initial pdf forecast pdf Tangent propagator Medium Range: Singular Vectors Ensemble Generation Are Singular Vectors a valid approach for Seasonal Forecasts? We need the TL& Adjoint of the full coupled model is required. BUT… 1.The linear assumption would fail for the atmosphere at lead times relevant for seasonal (~>1month). Besides 2.Uncertainty in the initial conditions may not be the dominant source of error (See later)

38. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Ensemble Generation Sampling Uncertainty in Initial Conditions : Random sampling of initial uncertainty (as opposed to optimal) ECMWF burst mode ensemble Lag ensemble (NCEP) Simplified problem (Moore et al 2003) (academic, non operational) Full Ocean GCM and a simplified atmosphere Measure growth only on SST Breeding techniques Sampling Uncertainty in Model Formulation: Stochastic physics (operational) Stochastic optimals (academic) Perturbed parameters (climate projections) Multimodel ensemble (EUROSIP)

39. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Ensemble Generation In the ECMWF Seasonal Forecasting System 1.Uncertainty in initial conditions: Burst ensemble: (as opposed to lag-ensemble) 40-member ensemble forecast first of each month Uncertainty in the ocean surface 40 SST perturbations Uncertainty in the Ocean Subsurface 5 different ocean analysis generated with wind perturbations + SV for atmospheric initial conditions Impact during the first month 2.Uncertainty in model formulation: Stochastic physics Multi-model ensemble (EUROSIP)

40. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting - Create data base with errors of weekly SST anomalies,arranged by calendar week: Error in SST product: (differences between OIv2/OI2dvar) Errors in time resolution: weekly versus daily SST -Random draw of weekly perturbations, applied at the beginning of the coupled forecast. Over the mixed layer (~60m) -A centred ensemble of 40 members 1.1 Uncertainties in the SST SST Perturbations

41. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting 1-3 months decorrelation time in wind ~6-12 months decorrelation time in the thermocline - Create data base with errors in the monthly anomalous wind stress, arranged by calendar month: (differences between ERA40-CORE) -Random draw of monthly perturbations, applied during the ocean analyses. -A centered ensemble of 5 analysis is constructed with: -p1 -p2 0 +p1 +p2 1.2 Uncertainties in the ocean Subsurface Wind perturbations +p1/-p1 Effect on Ocean Subsurface (D20)

42. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting 1.2 Uncertainty in the ocean subsurface: wind perturbations ERA40-CORE (1958-1979) ERA40-CORE (1980-2000) Ocean Subsurface: Data assimilation C.I=0.2 C Ocean Subsurface: No Data assimilation

43. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting 1.3 Uncertainty in the Atmospheric initial conditions The atmosphere model is also perturbed using singular vectors (SV): Same as for the medium range and monthly forecasting system The SV affect the spread of the seasonal forecasts: Mainly during the first month Mainly in mid-latitudes It makes the medium-range, monthly and seasonal forecasting systems more integrated

44. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting ECMWF stochastic physics scheme: is a stochastic variable, constant over time intervals of 6hrs and over 10x10 lat/long boxes Buizza, Miller and Palmer, 1999; Palmer 2001 Stochastic forcing 2.1) Uncertainties in deterministic atmospheric physics? The Stochastic Physics is a probabilistic parameterization, but it does not intend to sample uncertainty in the parameters, nor model error

45. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting The spread by different methods converge to the same asymptotic value after after 5-6 months. SST and Lag-averaged perturbations dominate spread at ~1month lead time. With DA, the wind perturbations grow slowly, and notably influence the SST only after 3m. Without DA, the initial spread (<3m) is larger. The asymptotic value is slightly larger Is the level of spread sufficient? SPSTST From Vialard et al, MWR 2005 Wind Perturbations (WP) SST Perturbations(ST) Stochastic Physics (SP) Ensemble Spread Wind Perturbations No DA (WPND) All(SWT) Lag-averaged(LA)

46. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Forecast System is not reliable: RMS > Spread To improve the ensemble generation we need to sample other sources of error: a) Model error: multi-model, physical parameterizations b) To design optimal methods: Stochastic Optima, Breeding Vectors, … A.Can we reduce the error? How much? (Predictability limit) Is the ensemble spread sufficient? Are the forecast reliable? B.Can we increase the spread by improving the ensemble generation?

47. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Persistence ECMWF ensemble spread RMS error of Nino3 SST anomalies EUROSIP ECMWF-UKMO-MeteoFrance 2.1) Sampling model error: The Real Time Multimodel

48. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting 2.2) Sampling model error: The Real Time Multimodel Persistence ECMWF ensemble spread RMS error of Nino3 SST anomalies Bayesian Calibration EUROSIP ECMWF-UKMO-MeteoFrance

49. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Consider a stochastically forced linear ENSO oscillator: Which are the patterns of f(t) that maximize the variance of s? f(t) is coherent in space and white in time. Alternative methods: Stochastic Optimals Linear Theory: (Farrell and Ioannou, 1993)

50. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Variance about ensemble mean, V: Ps are EOFs of C. Qs are stochastic optimals of Z (Farrell and Ioannou, 1993). Alternative methods: Stochastic Optimals

51. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Example of Stochastic Optimals for and Intermediate Coupled Model for the Tropical Pacific (Zabala-Garay et al,2003)

52. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting Alternative methods: Breeding vectors Bred vectors Toth and Kalnay (1996) The differences between the control forecast and perturbed runs Tuning parameters Size of perturbation Rescaling period (important for coupled system) No theoretical problems with different time scales. Applied to the CZ model by Cai et al. (2002)

53. Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting NASA/NSIPP BV vs. NCEP/CFS BV Z20 EOF2 Z20 EOF1 SST EOF1 NCEPNSIPP Results by Yang et al 2005 Alternative methods: Breeding vectors