Comparison between ensembles generated with atmospheric ... · Introduction oPro man's oceanic SVs...

Introduction Poor man's oceanic SVs Oceanic vs Atmospheric perturb Comparison with other methods Conclusion

Comparison between ensembles generated with atmospheric andwith oceanic perturbations, using the MPI-ESM model

C. Marini 1. A. Köhl 1. D. Stammer 1

Vanya Romanova 2. Jürgen Kröger3

1Institut für Meereskunde - Universität Hamburg

2Universität Bonn

3Max Plank Institut für Meteorologie

International workshop on seasonal to decadal prediction, May 2013

DecadalClimate Prediction

C. Marini. A. Köhl. D. Stammer Oceanic perturbations - decadal predictions


Ensemble generation for decadal predictions?

Our GOAL: representation of errors on OCEANIC initial conditions

WHY?Memory of the ocean = key hypothesis for predictability at decadal time scalesLarge errors on the oceanic state, especially at depth

? Zanna et al 2011, 2012 ?

Deep density perturbations in the Atlantic⇓

Faster (7.5 vs 18.5 yr) and larger AMOC ampli�cations than with upperoceanic perturbations

⇓Overestimation of oceanic predictability in decadal predictions exp where only

the atmospheric state is perturbed



Ensemble generation for decadal predictions?

Our GOAL: representation of errors on OCEANIC initial conditions

WHY?Memory of the ocean = key hypothesis for predictability at decadal time scalesLarge errors on the oceanic state, especially at depth

? Zanna et al 2011, 2012 ?

Deep density perturbations in the Atlantic⇓

Faster (7.5 vs 18.5 yr) and larger AMOC ampli�cations than with upperoceanic perturbations

⇓Overestimation of oceanic predictability in decadal predictions exp where only

the atmospheric state is perturbed



A need to create more relevant ensembles for decadal predictions?

For now, ensemble generation : rather pragmatic

Perturbing the atmospheric horizontal di�usion coe�cient(e.g. Matei et al Sci 2012)

Lagged initialization : shifting by a few days→ the atmospheric initial conditions→ the oceanic initial conditions(e.g Smith et al Sci 2007, Msadek et al GRL 2010, Müller et al GRL 2012)

Use of ensemble of ocean reanalyses/assimilation runsobtained by using di�erent initial conditial conditions of the historical run- obtained by perturbing the wind stress (+ SST perturbations at the hindcast's start) inWeisheimer et al GRL 2009, von Oldenborgh CD 2012

Get inspired from weather forecast and seasonal predictions :

Singular vectors (Hawkins and Sutton JCLI 2009)

Anomaly Transform

Breeding vectors



A need to create more relevant ensembles for decadal predictions?

Comparison between :

Perturbing the atmospheric horizontal di�usion coe�cient(e.g. Matei et al Sci 2012)

Lagged initialization : shifting by a few days→ the atmospheric initial conditions

→ the oceanic initial conditions(e.g Smith et al Sci 2007, Msadek et al GRL 2010, Müller et al GRL 2012)

Use of ensemble of ocean reanalyses/assimilation runsobtained by using di�erent initial conditial conditions of the historical run- obtained by perturbing the wind stress (+ SST perturbations at the hindcast's start) inWeisheimer et al GRL 2009, von Oldenborgh CD 2012

Get inspired from weather forecast and seasonal predictions :

Singular vectors ... A cheap version of oceanic singular vectors ...

Anomaly Transform

Breeding vectors



An attempt to generate climatic relevant perturbations

Goal : Finding perturbations

• growing the most rapidly with a time scale relevant for decadal predictions

• scaled to represent the uncertainties contained in the initial conditions

→ Singular vectors (SVs) of the tangent propagator of the dynamical systemrepresenting the evolution of the ocean(Molteni 1996 for the atmosphere, Palmer and Zanna submitted for a review about SVs)

TOO EXPENSIVE : requires the tangent propagator and its adjoint of the oceanic model ...

→ Simpli�cation of the evolution of the oceanic state based onLinear Inverse Modeling (LIM)

dx

dt= Bx+ F

- x : 3d EOFs of T and Sfrom the 156-yr long historical run of the MPI-ESM model68.4% of the total variance

- B : Deterministic matrix, F : White noise

? Tzipermann and Zanna JCLI 2008 : 3d EOFs of T and S annual anomalies in the Atlantic

? Hawkins and Sutton JCLI 2009 : idem but only from the upper 2km of the Atlantic










dx

dt= Bx+ F














dx

dt= Bx+ F







Linear Inverse Modeling (LIM)

Evolution of a perturbation of the system :

x(t + τ) = eτBx(t) = G(τ)x(t)

Ampli�cation over a time τ under the L2 norm :

µ(τ) =‖x(τ)‖2

‖x(0)‖2=

x(τ)T x(τ)

x(0)T x(0)=

x(0)TG(τ)TG(τ)x(0)

x(0)T x(0)

Singular vectors = eigenvectors of G(τ)TG(τ)

- τ = 5 yr- Selection of the �rst 4 SVs

+ Rotation and Scaling of the SVs similar to Molteni et al 1996

→ More uniform spatial distribution→ Match �on average� the estimates of the rms error1 of the oceanic reanalysisused to create the oceanic initial conditions (GECCO2)

1a posteriori errors



Linear Inverse Modeling (LIM)

Evolution of a perturbation of the system :

x(t + τ) = eτBx(t) = G(τ)x(t)

Ampli�cation over a time τ under the L2 norm :

µ(τ) =‖x(τ)‖2

‖x(0)‖2=

x(τ)T x(τ)

x(0)T x(0)=


x(0)T x(0)

Singular vectors = eigenvectors of G(τ)TG(τ)

- τ = 5 yr- Selection of the �rst 4 SVs

+ Rotation and Scaling of the SVs similar to Molteni et al 1996

→ More uniform spatial distribution→ Match �on average� the estimates of the rms error1 of the oceanic reanalysisused to create the oceanic initial conditions (GECCO2)

1a posteriori errors



Pattern of the rotated and scaled SVs. Temperature at 150m.

SV1 T at 150m SV2 T at 150m

SV3 T at 150m SV4 T at 150m



Pattern of the rotated and scaled SVs. Salinity at 150m.

SV1 S at 150m SV2 S at 150m

SV3 S at 150m SV4 S at 150m



Rms of the rotated and scaled SVs and rms error of GECCO2 at 150m.

rms of the SVs rms errors



Rms of the rotated and scaled SVs and rms error of GECCO2 at 1220m.

rms of the SVs rms errors



Hindcasts with the MPI-ESM model

Initial condition from an "assimilation run" :Nudging of T and S towards T and S anomalies from GECCO2 put onthe MPI-ESM climatology

10-yr long hindcasts starting every 1st January from 1991 to 2006

Two types of ensembles :

1 ensemble =

1 unperturbed member +

8 perturbed members

AtmosphericPerturbations

=Atm ICs shifted by 1 to 8 days

OceanicPerturbations

=Oce ICs

+SV1, +SV2, +SV3, +SV4,-SV1, -SV2, -SV3, -SV4

⇒ 16× 2 ensembles=

16× (2× 8+ 1)× 10yr = 2720 yr



A validation of the ensemble spread : Talagrand diagram

9 ensemble members sorted in ascending order⇓

10 bins for each time step : •| • | • | • | • | • | • | • | • |•At each time step the observation is located in one bin

⇓

Histogram :

Flat : relevant spreadL shape : bias

U shape : lack of spread

n shape : overestimated spread

Associated scores (Keller and Hense 2011) :• beta score (bS)bS=0 �at histogrambS>0 too large spreadbS<0 too narrow spread

• beta bias (bB)bB>0 bias towards higher values

bB<0 bias towards lower values

Mean bias removedfollowing the recommendation of the CMIP-WGCM-WGSIP Decadal Climate Prediction Panel



Atlantic meridional overturning circulation around 26.5N

Monthly values, Veri�cation values : assimilation run

Total Overturning

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

1 2 3 4 5 6 7 8 9 100

100

200

300

400

1 2 3 4 5 6 7 8 9 100

100

200

300

400

1 2 3 4 5 6 7 8 9 100

100

200

300

400

Lag1

Lag2

Lag3

Lag4

Oceanic perturbations Atmospheric perturbationsbS=-0.16, bB=0.11 bS=-0.45, bB=0.09

bS=-0.23, bB=0.11 bS=-0.35, bB=0.08

bS=-0.07, bB=0.11 bS=-0.28, bB=0.10

bS=-0.22, bB=0.10 bS=-0.38, bB=0.08

The Ekman component has been removed

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 100

200

400

600

1 2 3 4 5 6 7 8 9 100

200

400

600

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

1 2 3 4 5 6 7 8 9 100

100

200

300

400

500

600

Oceanic perturbations Atmospheric perturbationsLag1 bS=-0.35, bB=0.15 bS=-0.95, bB=0.09

bS=-0.43, bB=0.13 bS=-0.98, bB=0.07

bS=-0.19, bB=0.11 bS=-0.63, bB=0.07

bS=-0.27, bB=0.11 bS=-0.81, bB=0.06

Lag2

Lag3

Lag4



Atlantic meridional overturning circulation around 47.5N

Monthly values, Veri�cation values : assimilation run

1 2 3 4 5 6 7 8 9 100

100

200

300

1 2 3 4 5 6 7 8 9 100

100

200

300

1 2 3 4 5 6 7 8 9 100

100

200

300

1 2 3 4 5 6 7 8 9 100

100

200

300

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

1 2 3 4 5 6 7 8 9 100

50

100

150

200

250

300

Oceanic perturbationsAtmospheric perturbationsLag1 bS=0.17, bB=0.17 bS=-0.59, bB=0.07

bS=-0.15, bB=0.10 bS=-0.60, bB=0.06

bS=-0.17, bB=0.10 bS=-0.51, bB=0.06

bS=-0.29, bB=0.12 bS=-0.35, bB=0.08

Lag2

Lag3

Lag4



Oceanic heat content upper 700m and SST in the Atlantic (yearly values)

Atlantic basin

Veri�cation values :NODC dataset (Levitus et al 2009)

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

1 2 3 4 5 6 7 8 9 100

5000

10000

15000

1 2 3 4 5 6 7 8 9 100

5000

10000

15000

1 2 3 4 5 6 7 8 9 100

5000

10000

15000

1 2 3 4 5 6 7 8 9 100

5000

10000

15000

Oceanic perturbations Atmospheric perturbations

Lag1

bS=0.14, bB=0.21 bS=-1.76, bB=0.05

bS=0.15, bB=0.21 bS=-0.91, bB=0.07

Lag2

Lag4

Lag3

bS=-0.57, bB=0.09bS=0.22, bB=0.22

bS=0.25, bB=0.23 bS=-0.43, bB=0.10

x 10⁴

x 10⁴

x 10⁴

x 10⁴

North Atlantic (80W-0, 0-60N)

Veri�cation values :HadISST dataset (Rayner et al 2003)

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

1 2 3 4 5 6 7 8 9 100

2000

4000

6000

8000

bS=0.39, bS=0.34 bS=0.23, bS=0.15

bS=0.43, bS=0.35 bS=0.02, bS=0.18

bS=0.38, bS=0.31 bS=0.09, bS=0.21

bS=0.38, bS=0.29 bS=0.17, bS=0.23

Oceanic perturbations Atmospheric perturbations

Lag1

Lag2

Lag3

Lag4



Ensemble spread of SST averaged in the North Atlantic

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

1 2 3 4 5 6 7 8 9 100

0.05

0.1

0.15

0.2

0.25

years

years

Ensemble spread from every starting date

oceanic perturbations

atmospheric perturbations

→ Ensemble spread of SST averaged in theNorth Atlantic decreases with time foroceanic perturbations

Idem for temperature averaged in the upper200m of the Atlantic basin.

Why?Perturbations averaged over these areas are larger than the std of the signal→ The model gets back to its climatology

Trade-o� between :? strong perturbations that actually represent the errors on initial conditions? when too strong perturbations, model gets back to its climatology



Does the ampli�cation predicted by the LIM occur in the hindcasts withoceanic perturbation?

Ampli�cation over a time τ = 5 yr under the L2 norm :

µ(τ) =‖x(τ)‖2

‖x(0)‖2 =x(τ)Tx(τ)

x(0)Tx(0)=


x(0)Tx(0)with x =

(Tunpert − Tpert

Sunpert − Spert

)

0 1 2 3 4 51

1.5

2

2.5

0 1 2 3 4 50.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 1 2 3 4 50.8

1

1.2

1.4

1.6

1.8

2

2.2

0 1 2 3 4 50.8

1

1.2

1.4

1.6

1.8

2

2.2

SV3 SV4

SV1 SV2

year year

Ampli

Ampli

- Red : Ampli�cation predicted by the

LIM

- Mean of ampli�cation over the

hindcasts :

Black : +SVBlue : -SVSolid thin line : contribution of temperature

Dashed thin line : contribution of salinity

Ampli�cations of the perturbationsdo occur under the L2 norm

BUT the average over a given areaof the perturbations decreases



Comparison with other methods

Comparison between ensemble generated with:

Cheap Oceanic Singular vectors

Atmospheric laggged initialization

Atmospheric and Oceanic laggged initialization Jürgen Kröger

Ensemble of assimilation runsobtained by using di�erent initial conditions of the historical run Jürgen Kröger

Anomaly Transform Poster 31 of Vanya Romanova

Set up :

Initial condition from the "assimilation run" towards GECCO2 anomalies

10-yr long hindcasts starting the 1st January 1996



Atlantic Meridional Overturning Circulation at 26.5N

1996 1997 1998 1999 2000 2001 2002 2003 2004 200515

16

17

18

19

20

21

22

23

24

25

1996 1997 1998 1999 2000 2001 2002 2003 2004 200515

16

17

18

19

20

21

22

23

24

25

1996 1997 1998 1999 2000 2001 2002 2003 2004 200515

16

17

18

19

20

21

22

23

24

25

1996 1997 1998 1999 2000 2001 2002 2003 2004 200515

16

17

18

19

20

21

22

23

24

25

Atmospheric lagged initialization

Oceanic lagged initialization

Cheap oceanic Singular Vectors

Anomaly transform

1996 1997 1998 1999 2000 2001 2002 2003 2004 200515

16

17

18

19

20

21

22

23

24

25

From ensemble of assimilation run 1996 1997 1998 1999 2000 2001 2002 2003 2004 20051516171819202122232425

1996 1997 1998 1999 2000 2001 2002 2003 2004 20050

0.5

1

1.5

2

assimilation runatmospheric lagged initializationanomaly transformcheap oceanic singular vectorsfrom ensemble of assimilation run

Ensemble Mean (dashed), +/-ensemble std (solid), and reference run (red)

Ensemble std and std of the reference run



Temperature averaged in the upper 200m

North Atlantic basin

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005268.7

268.8

268.9

269

269.1

269.2

269.3

269.4

1996 1997 1998 1999 2000 2001 2002 2003 2004 20050

0.05

0.1

0.15

0.2

0.25

Ensemble Mean (dashed), +/-ensemble std (solid),

and reference run (red)

Ensemble std


Paci�c basin

1996 1997 1998 1999 2000 2001 2002 2003 2004 2005284

284.1

284.2

284.3

284.4

284.5

284.6

284.7

1996 1997 1998 1999 2000 2001 2002 2003 2004 20050

0.05

0.1

0.15

0.2


Ensemble Mean (dashed), +/-ensemble std (solid),

and reference run (red)

Ensemble std

WORK IN PROGRESS part of Miklip...Hard to evaluate the bene�ts of one method with only one starting date...



Conclusion

F Comparison between a cheap version of oceanic singular vectors andatmospheric lagged initialisation

Oceanic perturbationsglobally better spread, at least not worse

Too large perturbations ⇒ model gets back to its climatology?

F How to improve the cheap oceanic singular vectors?

Get rid of the linear approximation

Choice of a better norm to compute the singular vectors


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Comparison between ensembles generated with atmospheric ... · Introduction oPro man's oceanic SVs...

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