Initialization Techniques in Seasonal Forecasting

1. Initialization Techniques in Seasonal Forecasting Magdalena A. Balmaseda

2. Outline • The importance of the ocean initial conditions in seasonal forecasts • A well established case: ENSO in the Equatorial Pacific • Other examples of SST forcing • 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

3. The basis for extended range forecasts • Forcing by boundary conditions changes the atmospheric circulation, modifying the large scale patterns of temperature and rainfall, so that the probability of occurrence of certain events deviate significantly from climatology. • Important to bear in mind the probabilistic nature of SF • How long in advance?: from seasons to decades • The possibility of seasonal forecasting has clearly been demonstrated • Decadal forecasting activities are now starting. • The boundary conditions have longer memory, thus contributing to the predictability. Important boundary forcing: • SST: ENSO, Indian Ocean Dipole, Atlantic SST • Land: snow depth, soil moisture • Atmospheric composition: green house gases, aerosols,… • Ice?

4. COUPLED MODEL Atmosphere model Atmosphere model Atmosphere model Ocean model Ocean model Ocean model PROBABILISTIC CALIBRATED FORECAST ENSEMBLE GENERATION Forward Integration Forecast Calibration Initialization End-To-End Seasonal forecasting System Tailored Forecast PRODUCTS OCEAN

5. ENSO and Indian Ocean SST influcences Goddard et al 1999

6. Gianini, Batisti, Held and Sobel 2008

8. Importance of Initialization • Atmospheric point of view: Boundary condition problem • Forcing by lower boundary conditions changes the PDF of the atmospheric attractor “Loaded dice” • Oceanic point of view: Initial value problem • Prediction of tropical SST: need to initialize the ocean subsurface. • Emphasis on the thermal structure of the upper ocean • Predictability is due to higher heat capacity and predictable dynamics • A simple way is to run and ocean model with surface fluxes. But uncertainty in the fluxes is too large to constrain the solution. • An alterative to combine model+forcing fluxes + ocean observations using a data assimilation system. The challenge is to initialize the thermal structure • Without disrupting the dynamical balances (wave propagation is important) • While preserving the water-mass characteristics

9. Need to Initialize the subsurface of the ocean

10. T anomaly@ 90m: Autumn 2005 SST anomaly Winter 2005/6 Anomalies below the mixed layer re-emerge and Do they force the Atmosphere? A tantalizing case: SF of NAO and European Winters SST anomaly Autumn 2005

11. 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: • Initialization of SST and ocean subsurface. • Land/ice/snow potentially important. Not much effort so far … • Atmospheric initial conditions play a secondary role. We choose a metric, forecasts of SST from 1-6 months.

12. Ocean reanalysis Real time Probabilistic Coupled Forecast time Coupled Hindcasts, needed to estimate climatological PDF, require a historical ocean reanalysis Dealing with model error: Hindcasts Consistency between historical and real-time initial conditions is required. Hindcasts are also needed for skill estimation

13. 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.

14. 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

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

16. 1982 1993 2001 XBT’s 60’s Satellite SST Moorings/Altimeter ARGO TRITON 1998-1999 PIRATA Time evolution of the Ocean Observing System

17. 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

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. Ocean Reanalysis activities at ECMWF Main Objective: Initialization of seasonal forecasts Historical reanalysis brought up-to-date=> Useful to study and monitor climate variability • Currently Operational: ORA-S3 (HOPE/OI) • Next Operational System: NEMO-NEMOVAR • ERA-40 daily fluxes (1959-1989) and ERA-Interim thereafter • Retrospective Ocean Reanalysis back to 1958 • Multivariate offline+on-line Bias Correction (pressure gradient, Temp,Sal, offline from recent period ) • Assimilation of temperature, salinity, altimeter sea level anomalies an global sea level trendsusing 3D-var • Balance constrains (T/S and geostrophy) • Sequential, 10 days analysis cycle, Incremental Analysis Update • 5 ensemble members

20. Estimating Bias Correction From Argo Period The offline bias correction is estimated from Argo. The correction is applied during the data assimilation process in the production of long climate reanalysis (from 19570901 to present)

21. Equatorial Pacific (x) Mean Assimation Temperature Increment z The Assimilation corrects the ocean mean state Data assimilation corrects the slope and mean depth of the equatorial thermocline Free model Data Assimilation

22. Fit to subsurface temperature data (RMS) EQ Central Pacific EQ Indian Ocean CONTROL ASSIM: T+S ASSIM: T+S+Alti TROPICAL Pacific GLOBAL Altimeter Improves the fit to InSitu Temperature Data

23. Improves the Interannual Variability ASSIM TS T+S+Alti CONTROL (no ASSIM) Correlation with altimter data.

24. 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)

25. Impact on ECMWF-S3 Seasonal Forecast Skill S3 NodataS3 Assim Balmaseda et al 2008

26. From Balmaseda and Anderson 2009 See also Fujii et al 2008 • No observation system is redundant • Not even in the Pacific, where Argo, moorings and altimeter still complement. Lessons for other basins? • The altimeter is the only OS contributing to the North Subtropical Atlantic. Argo is the only OS contributing the skill on the Indian Ocean. • There are obvious problems in the Eq Atlantic: model error, assimilation, and possibly insufficient observing system Assessing the Ocean Observing System • A decade agoseasonal forecasts skill was considered a “blunt” tool to measure quality of ocean analysis: coupled models were not discerning enough. • Improvements in the coupled ocean – atmosphere models also translate on the ability of using SF as evaluation of ocean initial conditions. There are now several examples showing the positive impact of data assimilation on the skill of seasonal forecast. • There are even results from observing system experiments showing impact on seasonal forecast skill. Important to bear in mind: • The assessment depends on the quality of the coupled model • Need records long enough for results to be significant => any observing system needs to stay in place for a long time before any assessment is possible. • So far impact on forecasts of SST only. Impact on atmospheric variables next

27. Perceived Paradigm for initialization of coupled forecasts Real world Model 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. Seasonal? Somewhere in the middle? At first sight, this paradigm would not allow a seamless prediction system. • Experiments: • Uncoupled SST + Wind Stress + Ocean Observations (ALL) • Uncoupled SST + Wind Stress (Atmos+SST) • Coupled with observed SST interface (SST only)

28. Relation between drift and Amplitude of Interannual variability. • Upwelling area penetrating too far west leads to stronger IV than desired. Impact of external “real world” information ALL ATMOS+SSTSST only • Need better (more balanced) initialization • More information corrects for model error, and the information is retained during the fc. • Model errors that can not be corrected by initialization (intraseasonal variability) • Relation between drift and Amplitude of Interannual variability. • Possible non linearity: is the warm drift interacting with the amplitude of ENSO? • Other source of errors: even with the correct “mean state” the I.V amplitude is small. MJO?

29. Impact of “real world” information on skill: NINO3.4 RMS ERROR ALLATMOS+SSTSST only The additional information about the real world improves the forecast skill, execept in the Equatorial Atlantic However… optimal use of the observations may require more sophisticated assimilation techniques, able to map the observation space into the model space From Balmaseda and Anderson 2009

30. Half of the gain on forecast skill is due to improved ocean initialization S1 S2 S3 A decade of progress on ENSO prediction Initialization into Context • Steady progress: ~1 month/decade skill gain • How much is due to the initialization, how much to model development?

31. Initialization into context (2): Information about the state of the real world

32. e Model Attractor (MA) c non-linear interactions important b phase space Real World (RW) Forecast lead time Initialization Shock and Skill Initialization shock d a: perfect initialization and perfect model b: no initialization shock. Best skill c: Initialization shock. Good skill until lead time L d: model attractor ini. No initialization shock e: initialization shock+ Non linearities Different convergence a L

33. Initialization Shock not opposite to Forecast Skill • It is possible to have real world initializationwithout initialization shock and “best skill” • The impact of initialization shock on skill depends on the lead time. • At seasonal time scales , the benefits of real-world initialization in forecasts skill are clear, in spite of initialization shock. The Equatorial Atlantic is an exception (Balmaseda and Anderson 2009). • At decadal time scales we don’t know yet, since it is difficult to quantify skill. • Anomaly Initialization does not imply Model Attractor Initialization. • Coupled Data Assimilation does not imply Anomaly Initialization

34. EasyINIT workshop on Initialization Inventory of strategies (see table) Need to be assessed and evaluated Nudging of anomalies from other reanalysis may not the best, but a practical solution to study sensitivities and to get started Relation between initialization strategy and forecast strategy Coupled initialization probably the long term solution, but more difficult to start with. Use all possible observational information unless there is a good reason why not. http://www.knmi.nl/samenw/easyinit/

35. Assimilation mainly of ocean observations. Not intention to initialize the fast time scales of the atmospheric component. The atmospheric observations are either neglected or binned in long windows. They can also be used indirectly via nudging to existing atmospheric reanalysis. The aim is to produce better (more balanced) initial conditions rather than an accurate estimation of the ocean variability. Observations are used to correct both the mean and the variability. Existing efforts Coupled 4D-var (Suguira et al 2008). Both ocean and atmospheric observations (binned). 9 months assimilation cycle. Control vector: coupling coefficients and ocean initial conditions. Coupled EnKF (Zhang et al 2007). Only ocean observations are used directly. Atmospheric information is nudged during the integration. Ocean Data Assimilation with a coupled model. (Fujii et al 2009) Atmospheric model is free (AMIP). Spectral control of SST variability. Free at time scales < 1month. Coupled model+SST constraint : Luo et al 2005, Kynleeside et al 2005 Coupled Data Assimilation: MEAN+ ANOMALY

36. Coupled 4Dvar: log (αE) – From Sigiura et al. (2008) ODA+CGCM: Precip. From Fujii etal 2009 Coupled- EnKF: Forecast RMSE of Niño-3 SST From Tony Rosati Examples of Coupled Data Assimilation: MEAN+ ANOMALY Forcast lead (months) 3Dvar 1.0 CDA -EnKF Initial month

37. Observational information is used to initialize only the anomalies, which are superimposed into the model climate. It assumes quasi-linear regime. Observational information is used either directly or from existing reanalysis. Usually only the ocean component is initialized. Background given by the coupled model To obtain observational anomalies an observational climatology is assumed. In poor observed areas the time sampling for the climatology may be limited Two flavours One-Tier anomaly initialization (Smith et al 2007). Ocean observations are assimilatated directly. Background error covariance formulation derived from coupled model. Emphasis on large spatial scales Two-Tier anomaly initialization (Pohlmann et al 2009). Nudging of anomalies from existing ocean re-analysis. The spatial structures are those provided by the source re-analysis. Special case when only SST anomalies are used. (Keenlyside et al 2008) 2) ANOMALY INITIALIZATION

38. Model Attractor (MA) non-linear interactions important phase space Empirical Flux Corrections Real World (RW) Forecast lead time Initialization Shock and non linearities b a

39. Combine project –Strategies for dealing with systematic errors in a coupled ocean-atmosphere forecasting systemProject concept Nature climate Flux correction Normal initialisation Anomaly initialisation Model climate Linus Magnusson et al.

40. Nino3.4 SST forecasts November 1995 – November 1998 Control Anomaly Initialisation U-flux correction 99 96 97 98 Linus Magnusson et al.

41. ENSEMBLE GENERATION Representing Uncertainty without disrupting Predictability Seasonal versus Medium Range Sources of Uncertainty Different Strategies

42. 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)

43. 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 (NASA system) • Sampling Uncertainty in Model Formulation: • Stochastic physics (operational) • Stochastic optimals (academic) • Perturbed parameters (climate projections) • Multimodel ensemble (operational)

44. 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)

45. 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

46. 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

47. 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, …

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

49. 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

50. 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 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. ”