Initialization and Ensemble generation for Seasonal Forecasting

1. Initialization and Ensemble generation for Seasonal Forecasting Magdalena A. Balmaseda

2. Outline • The importance of the ocean initial conditions in seasonal forecasts • A well stablished case: ENSO in the Equatorial Pacific • A tantalizing case: NAO forecasts • Ocean Model initialization • Why Ocean Data Assimilation? • The ECMWF data assimilation system From historical ocean reanalysis to real time ocean forecasts Impact of data assimilation • Other initialization strategies • Ensemble Generation: Sampling Uncertainty • Seasonal forecasts versus Medium range: different problems, different solutions? • The ECMWF ensemble generation system. • Other ensemble generation strategies

3. 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 • Higher heat capacity (Thermodynamic argument) • Predictable dynamics • Oceanic point of view: Initial value problem • Prediction of tropical SST

4. Need to Initialize the subsurface of the ocean

5. T anomaly@ 90m: Autumn 2005 Anomalies below the mixed layer. They can reemerge Seasonal Forecasts for European Winters SST anomaly Autumn 2005 SST anomaly Winter 2005/6

6. atmos obs atmos reanalysis initial conditions Reliable probability forecasts land,snow…? ensemble generation atmos DA AGCM Probabilistic forecast SST analysis calibration OGCM ocean DA initial conditions ocean reanalysis Tailored products sea-ice? ocean obs End to End Forecasting System

7. Initialization Data Assimilation Different Strategies

8. Real time Probabilistic Coupled Forecast time Ocean reanalysis Consistency between historical and real-time initial initial conditions is required Quality of reanalysis affects the climatological PDF Main Objective: to provide ocean Initial conditions for coupled forecasts Coupled Hindcasts, needed to estimate climatological PDF, require a historical ocean reanalysis

9. 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 is surface fluxes is large.

10. Equatorial Atlantic: Taux anomalies Equatorial Atlantic upper heat content anomalies. No assimilation Equatorial Atlantic upper heat content anomalies. Assimilation Uncertainty in Surface Fluxes:Need for Data Assimilation ERA15/OPS ERA40 • 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: • Does assimilation of ocean data constrain the ocean state? • Does the assimilation of ocean data improve the ocean estimate? • Does the assimilation of ocean data improve the seasonal forecasts

11. 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 is surface fluxes is large. • + Assimilation of ocean data into an ocean model • Which data? (SST, Subsurface Temperature, Salinity, Sea Level) • Which instruments?(TAO,XBTs,ARGO) • Which method? (OI,3Dvar,4Dvar,EnKF,…) • Which frequency, error statistics, balance relationships…?

12. Data coverage for Nov 2005 Ocean Observing System Data coverage for June 1982 Changing observing system is a challenge for consistent reanalysis. Today’s Observations will be used in years to come ▲Moorings: SubsurfaceTemperature ◊ ARGO floats: Subsurface Temperature and Salinity + XBT : Subsurface Temperature

13. ARGO floats XBT (eXpandable BathiThermograph) Moorings Satellite SST Sea Level Real Time Ocean Observations

14. ECMWF System-3 • Ocean model: HOPE (~1x1) • Assimilation Method OI • Assimilation of T + Balanced relationships (T-S, ρ-U) • 10 days assimilation windows, increment spread in time • New Features • ERA-40 fluxes to initialize ocean • Retrospective Ocean Reanalysis back to 1959. • Multivariate on-line Bias Correction . • Assimilation of salinity data. • Assimilation of altimeter-derived sea level anomalies. • 3D OI • http://www.ecmwf.int/products/forecasts/d/charts/ocean

15. Multivariate Formulation • From , a salinity increment by preserving the water mass characteristics (Troccoli et al, MWR,2002) • S(T) scheme: Temperature/Salinity relationship is kept constant • From ,velocity is also updated by introducing dynamical constraints (Burgers et al, JPO 2002) • It prevents the disruption of the geostrophic balance and the degradation of the circulation. Important close to the equator.

16. Tanal Sanal Tmodel Smodel A) Lifting of the profile B) Applying salinity Increments Updating Salinity: S(T) SCHEME S Troccoli et al, MWR 2002

17. T/S conserved T/S conserved OI CH96 T/S Changed OI Assimilation of S(T) not S(z) System 3: Assimilation of Temperature, Salinity and Sea Level

18. PIRATA Impact of data assimilation on the mean Assim of mooring data CTL=No data Large impact of data in the mean state: Shallower thermocline

19. Why a bias correction scheme? • A substantial part of the analysis error is correlated in time. • Changes in the observing system can be damaging for the representation of the inter-annual variability. • Part of the error may be induced by the assimilation process. What kind of bias correction scheme? • Multivariate, so it allows to make adiabatic corrections (Bell et al 2004) • It allows time dependent error (as opposed to constant bias). • First guess of the bias non zero would be useful in early days (additive correction rather than the relaxation to climatology in S2) Generalized Dee and Da Silva bias correction scheme Balmaseda et al (2006)

20. 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)

21. DataAssimilation improves the interannual variability of the ocean analysis No Data Assimilation Assimilation:T+S Assimilation:T+S+Alt Correlation with OSCAR currents Monthly means, period: 1993-2005 Seasonal cycle removed

22. No Data Assimilation Data Assimilation No Data Assimilation Data Assimilation Impact of Data Assimilation Forecast Skill Ocean data assimilation also improves the forecast skill (Alves et al 2003)

23. ECMWF: Weather and Climate Dynamical Forecasts 10-Day Medium-Range Forecasts Seasonal Forecasts Monthly Forecasts Atmospheric model Atmospheric model Wave model Wave model Real Time Ocean Analysis ~8 hours New Ocean model Delayed Ocean Analysis ~11 days

24. 1 2 3 4 5 6 7 8 9 10 11 12 BRT ocean analysis: D1-12 NRT ocean analysis: D1 Time (days) Assimilation at D1-12 Assimilation at D1-5 Operational Ocean Analysis Schedule D1 • 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):~ 8 hours delay • For Monthly forecasts

25. North Atlantic: T300 anomaly North Atlantic: S300 anomaly The result of the initialization procedure is a historical reanalysis… That can be used not only to initialize SF, but it is also a very valuable source of information for the study of climate variability…

26. 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 Coupled Anomaly Initialization (DePreSys) Weakly-coupled initialization? Atmosphere + ocean mixed layer Ocean +Atmosphere boundary layer Simplified coupled models? Initialization of slow time scales only, limited number of modes Initialization Uncoupled: Most common Other (potential) Strategies • Major challenge: initialization of different time scales

27. ENSEMBLE GENERATION Representing Uncertainty without disrupting Predictability Seasonal versus Medium Range Source of Uncertainty Different Strategies

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

29. Ensemble Generation • Sampling Uncertainty in Initial Conditions: • Random sampling of initial uncertainty (as opposed to optimal) • ECMWF burst mode ensemble (also used in DEMETER) • 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 (academic, non operational) • Sampling Uncertainty in Model Formulation: • Stochastic physics (operational) • Stochastic optimals (academic) • Perturbed parameters (climate projections) • Multimodel ensemble (operational)

30. Ensemble Generation In the ECMWF Seasonal Forecasting System • 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 • Uncertainty in model formulation: Stochastic physics Multi-model ensemble (EUROSIP)

31. SST Perturbations 1.1 Uncertainties in the SST -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

32. 1-3 months decorrelation time in wind Wind perturbations +p1/-p1 Effect on Ocean Subsurface (D20) ~6-12 months decorrelation time in the thermocline 1.2 Uncertainties in the ocean Subsurface -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

33. Ocean Subsurface: No Data assimilation Ocean Subsurface: Data assimilation ERA40-CORE (1980-2000) ERA40-CORE (1958-1979) 1.2 Uncertainty in the ocean subsurface: wind perturbations C.I=0.2 C

34. 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

35. Stochastic forcing 2.1) Uncertainties in deterministic atmospheric physics? 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 The Stochastic Physics samples neither uncertainty in the parameters, nor model error

36. ST SP From Vialard et al, MWR 2005 Ensemble Spread Wind Perturbations (WP) SST Perturbations(ST) Stochastic Physics (SP) Wind Perturbations No DA (WPND) All(SWT) Lag-averaged(LA) • 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?

37. Can we reduce the error? How much? (Predictability limit) • Can we increase the spread by improving the ensemble generation? Is the ensemble spread sufficient? Are the forecast reliable? 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, …

38. RMS error of Nino3 SST anomalies Persistence ECMWF ensemble spread EUROSIP 2.1) Sampling model error: The Real Time Multimodel EUROSIP ECMWF-UKMO-MeteoFrance

39. RMS error of Nino3 SST anomalies Bayesian Calibration Persistence ECMWF ensemble spread EUROSIP 2.2) Sampling model error: The Real Time Multimodel EUROSIP ECMWF-UKMO-MeteoFrance

40. Linear Theory: Alternative methods: Stochastic Optimals • Consider a stochastically forced linear ENSO oscillator: • f(t) is coherent in space and white in time. • Which are the patterns of f(t) that maximize the variance of s? (Farrell and Ioannou, 1993)

41. Example of Stochastic Optimals for and Intermediate Coupled Model for the Tropical Pacific (Zabala-Garay et al,2003)

42. 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)

43. NASA/NSIPP BV vs. NCEP/CFS BV Alternative methods: Breeding vectors Results by Yang et al 2005 NSIPP NCEP SST EOF1 Z20 EOF1 Z20 EOF2

44. Summary: Initialization • Seasonal Forecasting (SF) of atmospheric variables is a boundary condition problem. • Seasonal Forecasting of SST is an initial condition problem. • Assimilation of ocean observations reduces the large uncertainty(error) due to the forcing fluxes. Initialization of Seasonal Forecasts needs SST, subsurface temperature, salinity and altimeter derived sea level anomalies. • Data assimilation changes the ocean mean state. Therefore, consistent ocean reanalysis requires an explicit treatment of the bias. The bias treatment in the ODA in System 3 allows for longer calibration period. • The separate initialization of the ocean and atmosphere systems can lead to initialization shock during the forecasts. A more balance “coupled” initialization is desirable, but it remains challenging. Beware of the term “coupled data assimilation”

45. Summary: Ensemble generation • The ensemble techniques used in the Medium Range can not be applied directly to the Seasonal Forecast System (SFS)(since the linear assumption would not hold in the atmosphere model for optimization times ~>1month) • The ECMWF SFS uses random sampling (as opposed to optimal sampling) of existing uncertainties, mainly in the initial conditions. • Results suggest that model error is the largest source of forecast error. • There is a variety of techniques to sample model error. Multi-model approach is now operational. • There is ongoing research on exploring optimal ways of sampling model error