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### Initialization Techniques in Seasonal Forecasting

### ENSEMBLE GENERATION

Magdalena A. Balmaseda

Outline

The importance of the ocean initial conditions in seasonal forecasts

A well established case: ENSO in the Equatorial Pacific

A seasonal forecasting system

Ocean Model initialization

The value of observational information: fluxes, SST, ocean observations

The difficulties

The ECMWF Ocean Initialization system ORAS4

Assessment of Initialization strategies

Full Initialization, Anomaly Initialization

Ensemble generation

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 deviates significantly from climatology.
- Important to bear in mind the probabilistic nature of SF
- How long in advance?: from seasons to decades
- 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,…
- Sea-Ice

End-To-End Seasonal forecasting System

COUPLED MODEL

Atmosphere model

Atmosphere model

Atmosphere model

Ocean model

Ocean model

Ocean model

PROBABILISTIC CALIBRATED FORECAST

ENSEMBLE GENERATION

Forward Integration

Forecast Calibration

Initialization

Tailored Forecast PRODUCTS

OCEAN

Dealing with model error: Hindcasts

Ocean reanalysis

Real time Probabilistic Coupled Forecast

time

Coupled Hindcasts, needed to estimate climatological PDF, require a historical ocean reanalysis

Consistency between historical and real-time initial conditions is required.

Hindcasts are also needed for skill estimation

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 decade of progress on ENSO prediction

Half of the gain on forecast skill is due to improved ocean initialization

S1 S2 S3

Initialization into Context

- Steady progress: ~1 month/decade skill gain
- How much is due to the initialization, how much to model development?

Balmaseda et al 2010, OceanObs

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)

Usually forecast of SST indices, lead time 1-6 months

In complex non linear systems there is no “objective searching algorithm” for optimality. The problem is solved by subjective choices and physical insight.

- 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. Atmospheric initial conditions play a secondary role.

1982

1993

2001

XBT’s 60’s Satellite SST Moorings/Altimeter ARGO

Information to initialize the ocean- Ocean model Plus:

SST

Atmospheric fluxes from atmospheric reanalysis

Subsurface ocean information

Time evolution of the Ocean Observing System

How do we initialize the ocean?

To a large extent, the large scale ocean variability is forced by the atmospheric surface fluxes.

Different ocean models forced by the same surface fluxes will produce similar tropical variability.

Daily fluxes of heat (short and long wave, latent, sensible heat), momentum and fresh water fluxes. Wind stress is essential for the circulation.

Constrained by SST: Fluxes from atmospheric models

have large systematic errors and a large unconstrained chaotic component

Constrained by SST+ Atmos Observations: Surface fluxes from atmospheric reanalysis

Reduced chaotic component. But still large errors/uncertainty

Constrained by SST+AtmosObservations+Ocean Observations: Ocean reanalisys

Uncertainty in Surface Fluxes:Need for Data Assimilation

Equatorial Atlantic: Taux anomalies

Equatorial Atlantic upper heat content anomalies. No assimilation

Equatorial Atlantic upper heat content anomalies. 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? YES
- Does the assimilation of ocean data improve the ocean estimate? YES
- Does the assimilation of ocean data improve the seasonal forecasts. YES

Challenges on Ocean Initialization using data assimilation

In the production of the reanalysis

- Ocean model and surface forcing error
- Changing observing system

Need to take into account model bias. Balance Multivariate Relationships

In the production of the forecast

- Coupled model error can cause initialization shock and drift, even with perfect initial conditions

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

PIRATA

Impact of data assimilation on the mean

Assim of mooring data

CTL=No data

Large impact of data in the mean state leading to spurious variability

This is largely solved by the introduction of bias correction

The Assimilation corrects the ocean mean state

Equatorial Pacific

(x)

Mean Assimation Temperature Increment

z

Data assimilation corrects the slope and mean depth of the equatorial thermocline

Free model

Data Assimilation

Improves the Interannual Variability

ASSIM TS

T+S+Alti

CONTROL (no ASSIM)

Correlation with altimeter-derive sea level data.

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)

This was with S1. It has been subsequently repeated with S2, S3, S4. But it is not trivial

Ocean Initialization at the ECMWF

Ocean Reanalysis System 4 (ORAS4)

Main Objective: Initialization of seasonal forecasts

Historical reanalysis brought up-to-date => Useful to study and monitor climate variability

- Operational ORA-S4 NEMO-NEMOVAR
- ERA-40 daily fluxes (1958-1989) and ERA-Interim thereafter
- Retrospective Ocean Reanalysis back to 1958, 5 ensemble members
- Multivariate offline+on-line Bias Correction (pressure gradient, Temp,Sal, offline from recent period )
- Assimilation of SST, temperature and salinity profiles, altimeter sea level anomalies an global sea level trends
- Balance constrains (T/S and geostrophy)
- Sequential, 10 days analysis cycle, Incremental Analysis Update

NEMOVAR

- Variational data assimilation system for the NEMO ocean model (follow up of OPAVAR)
- Collaborative project with several institutions: CERFACS, MetOffice, INRIA, ECMWF
- Multiple loops. Adjoint and Tangent linear exist.
- NEMOVAR in ORAS4: Multivariate Incremental 3Dvar FGAT IAU
- Flow dependence background errors:
- T error depends on vertical gradients
- T/S relationship: linearized vertical profile displacement
- Sea Level and density: vertical profile displacement taking into account stratification
- Geostrophy
- It assimilates T/S profiles and along track altimeter.
- Automatic QC, thinning, supperobbing
- See Mogensen et al 2012. ECMWF techmemo 668
- http://www.ecmwf.int/publications/library/do/references/show?id=90389
- OUTSIDE NEMOVAR:
- SST is used to correct surface heat fluxes
- Global Sea Level corrects the fresh water flux
- Bias Correction

Bias Correction Algorithm

Slow varying term, estimated online from assimilation increments dk

Seasonal term, estimated offline from Argo Period

Bias online: Time evolution

- Need to determine:
- Offline bias correction
- Time evolution of on-line bias: a(memory) andb(updating factor)
- A(y): Partition of bias into T/S and pressure gradient.
- Function of latitude. At the equator the bias correction is mainly adiabatic (pressure gradient)
- Refinement of Balmaseda et al 2007, Dee 2005, Bell et al 2002

The offline bias correction is estimated from Argo period.

The correction is applied since 1957-00-01 to present.

It is a way of extrapolating Argo information into the past.

Time correlation with altimeter SL product

CNTL: NoObs

NEMOVAR T+S

ORAS4 T+S+Alti

CNTL

NEMOVAR TS

ORAS4 (TS+Alti)

Impact on Seasonal Forecast Skill

Consistent Improvement everywhere. Even in the Atlantic, traditionally challenging area

ORAS4

CNTL

Quantifying the value of observational information in seasonal forecasts

- The outcome may depend on the coupled system
- In a good system information may be redundant, but not detrimental.

If adding more information degrades the results, there is something wrong with the methodology (coupled/assim system)

- Experiments conducted with the ECMWF S3

Balmaseda and Anderson 2009, GRL

SST (SYNTEX System Luo et al 2005, Decadal Forecasting Keenlyside et al, 2008)

SST+ Atmos observations (fluxes from atmos reanalysis)

SST+ Atmos observations+ Ocean Observations (ocean reanalysis)

Impact of external “real world” information

ALL ATMOS+SST SST only

Central Western Pacific

Eastern Pacific

SST only produces a cold drift in both eastern and western Pacific. Large interannual variability (not shown)

ATMOS+SST does not have drift in the Eastern Pacific, but its bias cold in the Western-Central Pacific

ALL produces warm bias in the Eastern Pacific, no bias in the Western-Central Pacifi.

The warm bias in the eastern Pacific is a consequence of the unbalanced initialization:

Weak winds in coupled model -> downwelling Kelvin wave->warming in Eastern Pacific

What about the forecast skill?

Impact of “real world” information on skill:

Reduction in Error (MAE) in SST SF by adding observational information

WINDS = [(ATMOS+SST) – SSTonly ]/ SSTonly

OCDATA = [ALL - (ATMOS+SST)]/ (ATMOS+SST)

OC+WINDS = [ALL - SSTonly]/SSTonly

The additional information about the real world improved the forecast skill, except in the Equatorial Atlantic

Still, optimal use of the observations needs more sophisticated assimilation techniques and better models, to reduced initialization shock

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?

At first sight, this paradigm would not allow a seamless prediction system.

- Seasonal traditional approach:
- Full initialization + A aposteriori calibration of forecast
- Not clear how to achieve initialization in model attractor
- Anomaly Initialization (decadal forecasts, Smith et al)
- Coupled with observed SST interface (SST only): This means neglecting observational information. Keenlyside et al 2008. As shown before, this is not optimal
- Other more sophisticated (EnKF, coupled DA, weakly coupled DA)

Initialization Shock and Skill

e

Model Attractor (MA)

c

non-linear interactions important

b

phase space

Real World (RW)

Forecast lead time

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

Initialization Shock and non linearities

Model Attractor (MA)

non-linear interactions important

phase space

Empirical Flux Corrections

Real World (RW)

Forecast lead time

b

a

CLIVAR 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/

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 Data Assimilation: MEAN+ ANOMALYObservational 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.

Useful to compare different ocean reanalysis with the same model (Zhu et al 2012, GRL). Widely used in decadal forecasts

Special case when only SST anomalies are used. (Keenlyside et al 2008)

2) ANOMALY INITIALIZATIONComparison of Strategies for dealing with systematic errors in a coupled ocean-atmosphere forecasting systemas part of the EU FP7 COMBINE project

Nature climate

Flux correction

Normal initialisation

Anomaly initialisation

Model climate

Magnusson et al. 2011 ECMWF Techmemo 658

Magnusson et al. 2012 ECMWF Techmemo To appear

Coupled model error

10m winds: model - analysis

T2m bias: model - analysis

Part of the error comes from the atmospheric component (too strong easterlies at the equator)

The error amplifies in the couped model (positive Bjerkness feedback)

Possibility of flux correction

Coupled Ucor

Coupled UHcor

Ucor: surface wind is corrected when passed to the ocean

UHCor: surface wind and heat flux are corrected when passed to the ocean

Different mean statesAnalysis

Coupled Free

Comparison of Forecast Strategies: Method

A) Raw Forecasts

Example of decadal forecasts: Global SST

B) Bias Estimation

C) Corrected Forecasts

Analysis

Full Initialization

Anomaly Initialization

U Correction

U+H correction

Comparison of Forecast Strategies: Seasonal

Nino 3 SST Drift 1-14 month forecast

Analysis Full IniAnomaly IniU Correction U+H correction

Nino3.4 SST forecasts November 1995 – November 1998

Full Initialization

Anomaly Initialisation

U-flux correction

U- and H-flux correction

99

96

97

98

Linus Magnusson et al.

Impact on Forecast Skill (SST and Precip)

Persistence Full IniAnomaly IniU Correction U+H correction

Depending on the variable and region, the forecast skill is more or less affected by Initialization and forecast strategy.

Where the non linearities are strong, having a good mean state helps. In these situations, anomaly initialization underperfoms (Precip in Nino3.4, for instance)

Representing Uncertainty without disrupting Predictability

Seasonal versus Medium Range

In Seasonal, the main source of error/uncertainty is error formulation

It uses random (but realistic) perturbations as opposed to optimal perturbations to the initial conditions

There has been some research on optimal perturbations (breeding vectors, stochastic optimals, empirical singular vectors), but it will not be covered here (some information is given as hidden slides at the end)

Ensemble Generation In the ECMWF Seasonal Forecasting System

- Uncertainty in initial conditions:

Burst ensemble: (as opposed to lag-ensemble)

50-member ensemble forecast first of each month

Uncertainty in the ocean surface

50 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)

SST Perturbations

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 50 members

1-3 months decorrelation time in wind

Wind perturbations +p1/-p1

Effect on Ocean Subsurface (D20)

~6-12 months decorrelation time in the thermocline

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

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

How to improve the reliability of the ensemble:

a) Sampling model error: multi-model, physical parameterizations

b) Calibrating the forecast a-posteriori

RMS error of Nino3 SST anomalies

Persistence

ECMWF

ensemble spread

EUROSIP

2.1) Sampling model error: The Real Time Multimodel

EUROSIP

ECMWF-UKMO-MeteoFrance

2.2) Sampling model error: The Real Time Multimodel

RMS error of Nino3 SST anomalies

Bayesian Calibration

Persistence

ECMWF

ensemble spread

EUROSIP

EUROSIP

ECMWF-UKMO-MeteoFrance

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.
- Initialization and forecast strategy go together. The best strategy may depend on the model. The anomaly initialization used in decadal forecasts can have problems in seasonal

”

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:
- Stochastic Physics
- Multi-model
- Perturbed parameters

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

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
- But the level of spread is not sufficient. Need to sample model error

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