Predictability Training Course, April 2006 Initialization and Ensemble generation for Seasonal Forecasting Magdalena A. Balmaseda

Predictability Training Course, April 2006 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 Outline

Predictability Training Course, April 2006 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

Predictability Training Course, April 2006 Need to Initialize the subsurface of the ocean

Predictability Training Course, April 2006 Seasonal Forecasts for European Winters SST anomaly Autumn 2005 SST anomaly Winter 2005/6 Anomalies below the mixed layer. They can reemerge T 90m: Autumn 2005

Predictability Training Course, April 2006 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

Predictability Training Course, April 2006 Initialization Data Assimilation Different Strategies

Predictability Training Course, April 2006 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

Predictability Training Course, April 2006 Most common practice: Uncoupled initialization of ocean and atmosphere Atmosphere Initialization (from NWP or AMIP): atmos model +(atmos obs+assimilation system)+prescribed SST Ocean Initialization: ocean model + ocean obs +assimilation system+ prescribed surface fluxes So far mainly subsurface Temperature, and altimeter. Salinity from ARGO is used in the new ECMWF system. Atmospheric Fluxes are a large source of systematic error in the ocean state. Data Assimilation struggles to correct the systematic error

Predictability Training Course, April 2006 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.

Predictability Training Course, April 2006 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:  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

Predictability Training Course, April 2006 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…?

Predictability Training Course, April 2006 Data coverage for Nov 2005 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 Data coverage for June 1982 Ocean Observing System

Predictability Training Course, April 2006 Real Time Ocean Observations ARGO floats XBT (eXpandable BathiThermograph) Moorings Satellite SST Sea Level

Predictability Training Course, April 2006 Sea Level Evolution during the 1997/1998 El Nino Courtesy of NASA

Predictability Training Course, April 2006 Time evolution of the Ocean Observing System XBT’s 60’s Satellite SST Moorings/Altimeter ARGO PIRATA TRITON

Predictability Training Course, April 2006

New Features ERA-40 fluxes to initialize ocean Retrospective Ocean Reanalysis back to Multivariate on-line Bias Correction. Assimilation of salinity data. Assimilation of altimeter-derived sea level anomalies. 3D OI 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

Predictability Training Course, April 2006 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. Multivariate Formulation

Predictability Training Course, April 2006 Updating Salinity: S(T) SCHEME S A) Lifting of the profile Tanal Tmodel B) Applying salinity Increments Sanal Smodel Troccoli et al, MWR 2002

Predictability Training Course, April 2006 System 3: Assimilation of Temperature and Salinity T/S Changed T/S conserved Assimilation of S(T) not S(z)

Predictability Training Course, April 2006 System 3: Assimilation of Temperature and Salinity Contribution To ENACT: Assimilation of salinity along T surfaces are orthogonaland (TM #458, Haines et al MWR) Nice property:

Predictability Training Course, April 2006 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)

Predictability Training Course, April 2006 System 3: Assimilation of Sea Level Anomalies from altimeter Based on Cooper and Haines 1996 (basically translate SLA into increment of T and S) Ingredient : We tried ‘external’ mean sea level products (CLS, Nasa, …) but the choice of the reference global mean is not trivial and the system can be quite sensitive to this choice Observed SLA from T/P+ERS+GFO Respect to 7 year mean of measurements A Mean Sea Level

Predictability Training Course, April 2006 System3: Assimilation of Altimeter Data How to extract T/S information from Sea Level? How to combine Sea level and subsurface data? Cooper and Haines, 1999

Predictability Training Course, April 2006 Impact of data assimilation Assim of mooring data CTL=No data Large impact of data in the mean state: Shallower thermocline PIRATA

Predictability Training Course, April 2006 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)

Predictability Training Course, April The systematic error may be the result of the assimilation process Assim incr (C.I=0.05 C/10 days) Vertical velocity (C.I=0.5m/day) control assim Mean Analysis – Obs NINO 3 100m 200m

Predictability Training Course, April 2006 Bias evolution vector-equation Some notation (Temperature,Salinity,Velocity) prescribed (constant/seasonal) k f kk f k b bbb ; 1  

Predictability Training Course, April 2006 Assim incr (C.I=0.05 C/10 days) Bias and circulation Vertical velocity (C.I=0.5m/day) Standard Bias corrected: pressure

Predictability Training Course, April 2006 CNTL:No data ( )Assimilation of T ( ) Data Assimilation Improves the Interannual variability of the Analysis Correlation of SL from System2 with altimeter data (which was not assimilated)

Predictability Training Course, April 2006 Correlation with OSCAR currents Monthly means, period: Seasonal cycle removed No Data Assimilation Assimilation:T+S Assimilation:T+S+Alt Data Assimilation improves the interannual variability of the ocean analysis

Predictability Training Course, April 2006 Ocean data assimilation also improves the forecast skill (Alves et al 2003) Data Assimilation No Data Assimilation Impact of Data Assimilation Forecast Skill

Predictability Training Course, April 2006 Delayed Ocean Analysis ~11 days Real Time Ocean Analysis ~8 hours New ECMWF: Weather and Climate Dynamical Forecasts ECMWF: Weather and Climate Dynamical Forecasts 10-Day Medium-Range Forecasts 10-Day Medium-Range Forecasts Seasonal Forecasts Seasonal Forecasts Monthly Forecasts Monthly Forecasts Atmospheric model Wave model Ocean model Atmospheric model Wave model

Predictability Training Course, April 2006 D1 Time (days) 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):~ 8 hours delay For Monthly forecasts

Predictability Training Course, April 2006 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…

Predictability Training Course, April 2006 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 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 Uncoupled: Most commonOther (potential) Strategies Major challenge: initialization of different time scales

Predictability Training Course, April 2006 ENSEMBLE GENERATION Representing Uncertainty without disrupting Predictability Seasonal versus Medium Range Source of Uncertainty Different Strategies

Predictability Training Course, April 2006 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)

Predictability Training Course, April 2006 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 (QUAM) (quasi-operational) Multimodel ensemble (operational)

Predictability Training Course, April 2006 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)

Predictability Training Course, April 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

Predictability Training Course, April 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)

Predictability Training Course, April Uncertainty in the ocean subsurface: wind perturbations ERA40-CORE ( ) ERA40-CORE ( ) Ocean Subsurface: Data assimilation C.I=0.2 C Ocean Subsurface: No Data assimilation

Predictability Training Course, April 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

Predictability Training Course, April 2006 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 samples neither uncertainty in the parameters, nor model error

Predictability Training Course, April 2006 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)

Predictability Training Course, April 2006 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?

Predictability Training Course, April 2006 Persistence ECMWF ensemble spread RMS error of Nino3 SST anomalies EUROSIP ECMWF-UKMO-MeteoFrance 2.2) Sampling model error: The Real Time Multimodel

Predictability Training Course, April ) Sampling model error: The Real Time Multimodel Persistence ECMWF ensemble spread RMS error of Nino3 SST anomalies Bayesian Calibration EUROSIP ECMWF-UKMO-MeteoFrance

Predictability Training Course, April 2006 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)

Predictability Training Course, April 2006 Variance about ensemble mean, V: P’s are EOFs of C. Q’s are stochastic optimals of Z (Farrell and Ioannou, 1993). Alternative methods: Stochastic Optimals

Predictability Training Course, April 2006 Example of Stochastic Optimals for and Intermediate Coupled Model for the Tropical Pacific (Zabala-Garay et al,2003)

Predictability Training Course, April 2006 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)

Predictability Training Course, April 2006 NASA/NSIPP BV vs. NCEP/CFS BV Z20 EOF2 Z20 EOF1 SST EOF1 NCEPNSIPP Results by Yang et al 2005 Alternative methods: Breeding vectors

Predictability Training Course, April 2006 Summary: Initialization Seasonal Forecasting (SF) of atmospheric variables is a boundary condition problem. Seasonal Forecasting of SST is an initial condition problem (from the ocean point of view). Assimilation of ocean observations is necessary to reduce the large uncertainty 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”

Predictability Training Course, April 2006 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