Predictability Training Course, 24-28 April 2006 Initialization and Ensemble generation for Seasonal Forecasting Magdalena A. Balmaseda

Predictability Training Course, 24-28 April 2006

Initialization and Ensemble generation for Seasonal Forecasting

Magdalena A. Balmaseda


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


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


Need to Initialize the subsurface of the ocean


Seasonal Forecasts for European Winters

80OW 70OW 60OW 50OW 40OW 30OW 20OW 10OW 0O 10OE 20OE

Longitude

20OS

0O

20ON

40ON

60ON

80ON

Latit

ude

20OS

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40ON

60ON

80ON

Plot resolution is 1.5 in x and 1 in y

Horizontal section at 5.0 metres depthPotential temperature contoured every 0.25 deg CASSIM (S3)

Interpolated in x and y

20051016

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MAGICS 6.10 hyrokkin - neh Fri Apr 21 17:35:41 2006


Longitude

20OS

0O

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40ON

60ON

80ON

Latit

ude

20OS

0O

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Plot resolution is 1.5 in x and 1 in y

Horizontal section at 5.0 metres depthPotential temperature contoured every 0.25 deg CASSIM (S3)


20060115

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SST anomaly Autumn 2005

SST anomaly Winter 2005/6


Longitude

20OS

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40ON

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Latit

ude

20OS

0O

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Plot resolution is 1.5 in x and 1 in yHorizontal section at 90.0 metres depthPotential temperature contoured every 0.25 deg CASSIM (S3)


20051016

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Anomalies below the mixed layer. They can reemerge

T anomaly@ 90m: Autumn 2005


Pro

bab

ilist

ic

fore

cast

calib

ratio

n Rel

iab

le p

rob

abili

ty f

ore

cast

sT

ailo

red

pro

du

cts

End to End

Forecasting System

atmosDA

atmos obs

SST analysis

oceanDA

ocean obs

ocean reanalysis

atmos reanalysis

land,snow…?

sea-ice?

initialconditions

initialconditions

AGCM

OGCM

ensemble

generation


Initialization

Data Assimilation

Different Strategies


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


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.


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


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…?


Data coverage for Nov 200560°S 60°S

30°S30°S

0° 0°

30°N30°N

60°N 60°N

60°E

60°E

120°E

120°E

180°

180°

120°W

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60°W

60°W

0°

0°

X B T p r o b e s : 9 3 7 6 p r o f i l e sOBSERVATION MONITORING Changing observing

system is a challenge for consistent reanalysis

Today’s Observations will be used in years to

come

60°S 60°S

30°S30°S

0° 0°

30°N30°N

60°N 60°N

60°E

60°E

120°E

120°E

180°

180°

120°W

120°W

60°W

60°W

0°

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▲Moorings: SubsurfaceTemperature

◊ ARGO floats: Subsurface Temperature and Salinity

+ XBT : Subsurface Temperature

Data coverage for June 1982

Ocean Observing System


Real Time Ocean Observations

ARGO floatsXBT (eXpandable BathiThermograph)

Moorings

Satellite

SST

Sea Level


Sea Level Evolution during the 1997/1998 El Nino

Courtesy of NASA



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

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


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

OIOI ST ,

OIT OIS


Updating Salinity: S(T) SCHEME

S

A) Lifting of the profile

Tanal

Tmodel

B) Applying salinity Increments

Sanal

Smodel

Troccoli et al, MWR 2002


2

2

2

2 )(

'K R

oa

T

TT

R

r

ee

System 3: Assimilation of Temperature and Salinity

T/S

Changedinsituinsitu ST ,

aa ST ,

T/S

conserved

', aa ST

insituT

))(H)((K)()( 'abaoaaaa TSTSTSTS

Assimilation of S(T) not S(z)


System 3: Assimilation of Temperature and Salinity

1S 2S

1 2

0 ( ) ( )

( ) ( )

a b o bT

a b o o b oS S

T T T z T z

S S S T S T

K

K K

Contribution To ENACT: Assimilation of salinity along T surfaces

are orthogonaland

(TM #458, Haines et al MWR)

Nice property:


System 3: Assimilation of Temperature, Salinity and Sea Level

T/S

conserved

alt T/S

Changedinsituinsitu ST ,

aa ST ,

T/S

conservedinsituT

', aa ST

))(H)((K)()( ''obooaaaa TSTSTSTS

2

2

2

2 )(

'K R

oa

T

TT

R

r

ee

Assimilation of S(T) not S(z)


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

obs'

obsalt ' Observed SLA from T/P+ERS+GFORespect to 7 year mean of measurements

A Mean Sea Level


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

bckalt

insituinsitu ST ,

aTaS

11 , bckbck STbckTbckS

altalt ST ,


Impact of data assimilation

Assim of mooring data

CTL=No data

Large impact of data in the mean state: Shallower thermocline

PIRATA

EQATL Depth of the 20 degrees isotherm

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002Time

-95

-90

-85

-80

-75

-70ega8 omona.assim_an0edp1 omona.assim_an0


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)


50O E 100OE 150OE 160OW 110OW 60OW 10OW

Longitude

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40ON

Latit

ude

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30OS

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10O

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20O

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30O

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40ON

Plot resolution is 1 in x and 1 in ySurface fieldSea level contoured every 0.1 mCorrel: Control

Interpolated in y

20020101 ( 9 year mean)

0.5 0.5

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MAGICS 6.9 hyrokkin - neh Thu Sep 9 12:12:36 2004

CNTL:No data (1993-2001)

50OE 100OE 150OE 160OW 110OW 60OW 10OW

Longitude

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Latit

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Plot resolution is 1 in x and 1 in ySurface fieldSea level contoured every 0.1 mCorrel: Assim

Interpolated in y 0 ( 9 year mean)

difference from20020101 ( 9 year mean)

0.5

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MAGICS 6.9 hyrokkin - neh Thu Sep 9 12:12:37 2004

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)


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


Ocean data assimilation also improves the forecast skill

(Alves et al 2003)

Data Assimilation

Data Assimilation

No

Da

ta A

ss

imil

ati

on

No

Da

t a A

ss

imi l

at i

on

Impact of Data Assimilation

Forecast Skill


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


D1

Time (days)

11 1210987654321

BRT ocean analysis: D1-12 NRT 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


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…


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 common Other (potential) Strategies

Major challenge: initialization of different time scales


ENSEMBLE GENERATION

Representing Uncertainty without disrupting Predictability

Seasonal versus Medium Range

Source of Uncertainty

Different Strategies


0 0M M x t x t

Initial pdf

forecast pdf

0, ttM

x t

0x t

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)


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)


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 monthUncertainty 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 physicsMulti-model ensemble (EUROSIP)


-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


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-p20

+p1 +p2

1.2 Uncertainties in the ocean Subsurface

Wind perturbations +p1/-p1

EQ3 Depth of the 20 degrees isotherm

1986 1988 1990 1992 1994 1996 1998 2000Time

-20

-10

0

10

20

EQPAC Depth of the 20 degrees isotherm

1986 1988 1990 1992 1994 1996 1998 2000Time

-10

-5

0

5

10

Effect on Ocean Subsurface (D20)


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


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


) i X D P P ECMWF stochastic physics scheme:

is a stochastic variable, constant over time intervals of 6hrs and over 10x10 lat/long boxesBuizza, 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


•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?

SP

ST

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)


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?


Persistence

ECMWF

ensemble spread

RMS error of Nino3 SST anomalies

EUROSIP

EUROSIP

ECMWF-UKMO-MeteoFrance

2.2) Sampling model error: The Real Time Multimodel


Consider a stochastically forced linear ENSO oscillator:

( )ds dt As f t

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)


Example of Stochastic Optimals for and Intermediate Coupled Model for the Tropical Pacific

(Zabala-Garay et al,2003)


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)


NASA/NSIPP BV vs. NCEP/CFS BV

Z20 EOF2

Z20 EOF1

SST EOF1

NCEPNSIPP

Results by Yang et al 2005

Alternative methods: Breeding vectors


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”


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

Documents

Predictability Training Course, 24-28 April 2006 Initialization and Ensemble generation for Seasonal Forecasting Magdalena A. Balmaseda