Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting...

Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting

Initialization and Ensemble generation for Seasonal Forecasting

Magdalena A. Balmaseda


• The importance of the ocean initial conditions in seasonal forecasts A well established case: ENSO in the Equatorial Pacific

A tantalizing case: NAO forecasts

• 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

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 memoryo Higher heat capacity (Thermodynamic argument)o Predictable dynamics

•Oceanic point of view: Initial value problem Prediction of tropical SST: need to initialize the ocean subsurface. Examples:

o A well established case is ENSOo A more tantalizing case is the importance subsurface temperature in the

North Subtropical Atlantic for seasonal forecasts of NAO and European Winters.


Need to Initialize the subsurface of the ocean


A tantalizing case: SF of NAO and European Winters

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

Longitude

20OS

0O

20ON

40ON

60ON

80ON

Latit

ude

20OS

0O

20ON

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

-3

-2.5

-2

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-1

-0.5

0.25

0.75

1.25

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

SST anomaly Autumn 2005

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

Longitude

20OS

0O

20ON

40ON

60ON

80ON

Latit

ude

20OS

0O

20ON

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

20060115

-3

-2.5

-2

-1.5

-1

-0.5

0.25

0.75

1.25

1.75

2.25

2.75

MAGICS 6.10 hyrokkin - neh Fri Apr 21 17:36:24 2006

SST anomaly Winter 2005/6

T anomaly@ 90m: Autumn 2005

Anomalies below the mixed layer re-emerge and

Do they force the Atmosphere?


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


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 in 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


Real Time Ocean Observations

ARGO floatsXBT (eXpandable BathiThermograph)

Moorings

Satellite

SST

Sea Level


Time evolution of the Ocean Observing System

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

1982 1993 2001

1998-1999 PIRATA

TRITON


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

120°W

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°

0°

▲Moorings: SubsurfaceTemperature

◊ ARGO floats: Subsurface Temperature and Salinity

+ XBT : Subsurface Temperature

Data coverage for June 1982

Ocean Observing System


Impact of data assimilation on the mean

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


ORA-S3• Main Objective: Initialization of seasonal forecasts

Historical reanalysis brought up-to-date (11 days behind real time) Source of climate variability

Main Features

•ERA-40 daily fluxes (1959-2002) and NWP thereafter

•Retrospective Ocean Reanalysis back to 1959

•Multivariate on-line Bias Correction (pressure gradient)

•Assimilation of temperature, salinity, altimeter sea level anomalies an global sea level trends.

•3D OI, Salinity along isotherms

•Balance constrains (T/S and geostrophy)

•Sequential, 10 days analysis cycle, IAUBalmaseda etal 2007/2008


The Assimilation corrects the ocean mean state

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

Longitude

500

400

300

200

100

0

Depth

(m

etr

es)

500

400

300

200

100

0Plot resolution is 1.4063 in x and 10 in yZonal section at 0.00 deg NICODE=178 contoured every 0.0002 XXXHOPE gcm:: 0001

Interpolated in y 0 ( 31 day mean)

difference from20020101 ( 31 day mean)

-0.0008

-0.0006-0.0

00

4

0.0002

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-0.0024

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-0.0012

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0.0002

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MAGICS 6.9.1 hyrokkin - neh Tue Jul 25 19:19:38 2006

Mean Assimation Temperature Increment

Free model

Data Assimilation

z

(x)Equatorial Pacific

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


The Assimilation corrects the ocean mean state

-1.5 -1.2 -0.9 -0.6 -0.3 0temperature

-400

-200

De

pth

(m

) S3-a S3-c

Mean(199301-200201) of Model minus Observationseq3-All in situ data

-0.4 -0.2 0 0.2 0.4 0.6temperature

-400

-200

De

pth

(m

)

S3-a S3-cMean(199301-200201) of Model minus Observations

eqind-All in situ dataWestern Pacific Equatorial Indian

Analysis minus Observations

DATA ASSIM

NO DATA ASSIM


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

Longitude

40OS

30OS

20OS

10O

S

0O

10O

N

20O

N

30O

N

40ON

Latit

ude

40OS

30OS

20OS

10O

S

0O

10O

N

20O

N

30O

N

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

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

40OS

30OS

20OS

10O

S

0O

10O

N

20O

N

30O

N

40ON

Latit

ude

40OS

30OS

20OS

10O

S

0O

10O

N

20O

N

30O

N

40ON

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

0.5

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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


•Progress is not monotonic: Need good coupled models to gauge the quality of initial conditions

Skill can be limited by the quality of the coupled model

So far so good, but:

0 1 2 3 4 5 6Forecast time (months)

0.4

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0.6

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0.8

0.9

1

An

om

aly

co

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wrt NCEP adjusted OIv2 1971-2000 climatology

NINO3 SST anomaly correlation

0 1 2 3 4 5 6Forecast time (months)

0

0.2

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0.6

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1

1.2

Rm

s e

rro

r (d

eg

C)

Ensemble sizes are 5 (0001) and 1 (0001) 60 start dates from 19870501 to 20010201

NINO3 SST rms errors

Fc S2 /m1 Fc S2 /m0 Persistence

MAGICS 6.11 verhandi - neh Fri Jun 1 16:49:20 2007

a) ERA15/OPS fluxes S2 NO Asim S2 Assim

b) ERA40/OPS fluxes DEM NO Assim DEM Assim


Impact on ECMWF-S3 Seasonal Forecast Skill

0 1 2 3 4 5 6 7Forecast time (months)

0.4

0.5

0.6

0.7

0.8

0.9

1

An

om

aly

co

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wrt NCEP adjusted OIv2 1971-2000 climatology

NINO4 SST anomaly correlation

0 1 2 3 4 5 6 7Forecast time (months)

0

0.2

0.4

0.6

0.8

Rm

s e

rro

r (d

eg

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Ensemble sizes are 3 (esj6) and 3 (esj6) 76 start dates from 19870101 to 20051001

NINO4 SST rms errors

Fc esj6/m1 Fc esj6/m0 Persistence Ensemble sd


S3 Nodata S3 Assim


Initialization into context

Ocean Initial Conditions

Versus

Coupled Model

S2 S2ic_S3model S3


Some general considerations on initialization


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:o Initialization of SST and ocean subsurface. o Land/ice/snow potentially important. Not much effort so far …o Atmospheric initial conditions play a secondary role.

We choose a metric, forecasts of SST from 1-6 months.


Perceived Paradigm for initialization of coupled forecasts

Real world Model attractor

Medium rangeBeing 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 longerNeed to initialize the model attractor on the relevant time and spatial scales.

Model attractor different from real world.

•Experiments:

•Uncoupled SST + Wind Stress + Ocean Observations (ALL)

•Uncoupled SST + Wind Stress (NO-OCOBS)

•Coupled SST (SST-ONLY) (Keenlyside et al 2008, Luo et al 2005)

Seasonal?Somewhere in the middle?

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


Impact of “real world” information on skill:

NINO3.4 RMS ERROR

ALL NO-OCOBS SST-ONLY

Adding information about the real world improves ENSO forecasts

From Balmaseda and Anderson 2009


NINO-W

EQATL

EQ3

STIO

WTIO

Reduction (%) in SST forecast error Range 1-3 months In Central/Western

Pacific, up to 50% of forecast skill is due to atmos+ocean observations.

Sinergy: > Additive contribution

Ocean~20%

Atmos ~25%

OC+ATM~55%

Impact of “real world” information on skill:


•Relation between drift and Amplitude of Interannual variability.

•Upwelling area penetrating too far west leads to stronger IV than desired.

Western Pacific

•Relation between drift and Amplitude of Interannual variability.

•Possible non linearity: is the warm drift interacting with the amplitude of ENSO?

Impact of Initialization

•Drift and Variability depend on Initialization !!

•More information corrects for model error, and the information is retained during the fc.

•Need “more balanced” initialization methods to prevent initialization shock hitting non linearities

Eastern Pacific ALL

NO-OCOBS

SST-ONLY

DRIFT

VARIABILITY


Initialization Shock and non linearities

Forecast lead time

pha

se s

pace

Model Attractor (MA)

non-linear interactions important

Real World (RW)

Initialization shock

a

b

c


Initialization shock and non linearities

Forecast lead time

pha

se s

pace

Model Attractor (MA)

non-linear interactions important

Real World (RW)

Empirical Flux Corrections


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. Problem with different time scales

•Simplified coupled models? Initialization of slow time scales

only, limited number of modes.

•Weakly-coupled initialization? Atmosphere initialization with a

coupled model

Ocean initialization with a coupled model.

Ocean initialization in anomaly mode with a coupled model (DePreSyS)

Uncoupled: Most common Other Strategies


Delayed Ocean Analysis ~12 days

Real Time Ocean Analysis ~Real time

ECMWF:

Weather and Climate Dynamical Forecasts

ECMWF:

Weather and Climate Dynamical Forecasts

18-Day Medium-Range

Forecasts

18-Day Medium-Range

Forecasts

Seasonal Forecasts

Seasonal Forecasts

Monthly Forecasts

Monthly Forecasts

Ocean model

Atmospheric model

Wave model

Atmospheric model

Ocean 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):~ For Var-EPS/Monthly forecasts


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•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

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


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 perturbationsERA40-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 monthMainly 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 is a probabilistic parameterization, but it does not intend to sample 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

2.1) Sampling model error: The Real Time Multimodel


2.2) Sampling model error: The Real Time Multimodel

Persistence

ECMWF

ensemble spread

RMS error of Nino3 SST anomalies

Bayesian Calibration

EUROSIP

EUROSIP

ECMWF-UKMO-MeteoFrance

Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting...

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Transcript of Training Course 2009 – NWP-PR: Initialization and Ensemble Generation in Seasonal Forecasting...