D&A at Météo France -CNRM

Aurélien Ribes

IDAG, 2 Feb 2016

D&A at CNRM

• Statistical methods for conventional D&A (long-termtrends), application to the analysis of temperature changes,

• Event attribution,

• Application of D&A to new/impact variables,• Recent examples: oceanic carbon fluxes, Leaf Area Index.

• Provide diagnoses at the national level,• e.g.: past observed warming, its anthropogenic component,

and the corresponding uncertainty.

D&A at CNRM

• Statistical methods for conventional D&A (long-termtrends), application to the analysis of temperature changes,

• Event attribution,• Relatively new activity,• Demand from Météo France,• attempt to perform event attribution based on existing

coupled simulations, see Soulivanh Thao’s poster,• also use the observed long-term trend in some events (ie

Gert Jan’s method), with application to extremeprecipitation near the Mediterranean.

• Application of D&A to new/impact variables,• Recent examples: oceanic carbon fluxes, Leaf Area Index.

• Provide diagnoses at the national level,• e.g.: past observed warming, its anthropogenic component,

and the corresponding uncertainty.

D&A at CNRM

• Statistical methods for conventional D&A (long-termtrends), application to the analysis of temperature changes,

• Event attribution,

• Application of D&A to new/impact variables,• Recent examples: oceanic carbon fluxes, Leaf Area Index.

• Provide diagnoses at the national level,• e.g.: past observed warming, its anthropogenic component,

and the corresponding uncertainty.

D&A at CNRM

• Statistical methods for conventional D&A (long-termtrends), application to the analysis of temperature changes,

• Event attribution,

• Application of D&A to new/impact variables,• Recent examples: oceanic carbon fluxes, Leaf Area Index.

• Provide diagnoses at the national level,• e.g.: past observed warming, its anthropogenic component,

and the corresponding uncertainty.

A new statistical approach to D&A

Towards the end of linear regression in D&A?

Towards the inclusion of climate modellinguncertainty in D&A?

Aurélien Ribes, Francis Zwiers, Jean-Marc Azaïs, PhilippeNaveau.

IDAG, 2 Feb 2016

A new statistical approach to D&A

Towards the end of linear regression in D&A?

Towards the inclusion of climate modellinguncertainty in D&A?

Aurélien Ribes, Francis Zwiers, Jean-Marc Azaïs, PhilippeNaveau.

IDAG, 2 Feb 2016

A new statistical approach to D&A

Towards the end of linear regression in D&A?

Towards the inclusion of climate modellinguncertainty in D&A?

Aurélien Ribes, Francis Zwiers, Jean-Marc Azaïs, PhilippeNaveau.

IDAG, 2 Feb 2016

Motivation: Is linear regression suitable?

Y =NX

i=1

�i

X

i

+ "

• Used from the deep past

• Assumes that• models are able to simulate response patterns,• response magnitudes are unknown.

• The reality is probably more balanced• Large uncertainty in the response magnitude (eg sensitivity), but

also in the spatial response pattern (eg land sea warming ratio,amplitude of the Artic amplification),

• Unknown feedbacks are likely to modify spatial response pattern.

Wish to include modelling uncertainty in D&A.Wish to treat uncertainty in the magnitude and the patternconsistently / symetrically.

Motivation: Is linear regression suitable?

Y =NX

i=1

�i

X

i

+ "

• Used from the deep past

• Assumes that• models are able to simulate response patterns,• response magnitudes are unknown.

• The reality is probably more balanced• Large uncertainty in the response magnitude (eg sensitivity), but

also in the spatial response pattern (eg land sea warming ratio,amplitude of the Artic amplification),

• Unknown feedbacks are likely to modify spatial response pattern.

Wish to include modelling uncertainty in D&A.Wish to treat uncertainty in the magnitude and the patternconsistently / symetrically.

Possibility to apply D&A to single scalar variables

IV−only

F1−only

F1+F2

• Detection: inconsistency with IV-only,• Attribution (1): consistency with F1+F2,• Attribution (2): incosistency with F1-only.

Possibility to apply D&A to single scalar variables

IV−only

F1−only

F1+F2

• Detection: inconsistency with IV-only,• Attribution (1): consistency with F1+F2,• Attribution (2): incosistency with F1-only.

Existing regression models

Y

⇤ =NX

i=1

�i

X

⇤i

,

(Y = Y

⇤ + "Y

, "Y

⇠ N(0,⌃Y

),

X

i

= X

⇤i

+ "X

i

, "X

i

⇠ N(0,⌃X

i

), i = 1, . . . , nf

,

• Inclusion of modelling uncertainty is possible (EIV;Huntingford et al., 2006; Hannart et al., 2014)

⇢⌃

Y

= ⌃iv

+ ⌃obs

,

⌃X

I

= ⌃iv

+ ⌃mod

.

• Most studies use TLS and neglect ⌃mod

and ⌃obs

.

The new approach

Y

⇤ =NX

i=1

X

⇤i

, (1)

(Y = Y

⇤ + "Y

, "Y

⇠ N(0,⌃Y

),

X

i

= X

⇤i

+ "X

i

, "X

i

⇠ N(0,⌃X

i

), i = 1, . . . , nf

,

(2)(3)

• Just remove the �s,

• Inference focuses on X

⇤i

(instead of �i

),

• Only additivity is assumed,

• Interpretation: models give information on each term X

⇤i

, then anadditional constraint on the sum comes from observations.

• All inference can be made with maximum likelihood

bX

⇤i

= X

i

+ ⌃X

i

(⌃Y

+ ⌃X

)�1(Y � X ) ⇠ N(Xi

,⌃bX

⇤i

).

Comparing EIV with this method

EIV This method

• knowledge on magnitude ig-nored

• magnitude and pattern treatedconsistently

• non explicit and difficult tocompute estimators

• explicit estimators

• approximated CI on �, • exact CI.no CI on �X

⇤ (attrib. trend),

How does this work (for scalars) ?

The method is efficient if all terms but one are well constrained

a) b) c)

• a) large uncertainty in both F1 and F2: little gain.

• b) large uncertainty in both F1 and obs: little gain.

• c) limited uncertainty in both obs and F2: substantial gain on F1.

How to estimate modelling uncertainty for D&A?

• Need to set a paradigm: how far are the models from the truth?• We assume “models are stat. indistinguishable from the truth”

(mi

� m

j

) ⇠ N(0, 2⌃m

), (mi

� m

⇤) ⇠ N(0, 2⌃m

).

• Magnitude and pattern uncertainty are estimated consistently.

1 1.5 2 2.5

TCR (°C)

• Should we assume a larger distribution?• Should we care about model dependences?• How can we estimate ⌃

m

from only ⇠ 10 models?

Analysis of the observed 1951-2010 GMT linear trend

Detection step Consistency with all forcings

Obs warming: +.65K,ALL-induced: +.67K [+.55K,+.79K],NAT-induced: -.01K [-.03K,+.02K],ANT-induced: +.67K [+.55K,+.80K],NATA (consistent with Fig 10.5)

Attribution to ANT / NAT

Conclusions

Our proposed statistical method:• only assumes additivity,• takes physical information on response amplitude into

account,• takes climate modelling uncertainty into account,• treats the pattern and the magnitude symmatrically,• involves simplified statistical treatment (inference).

Remaining challenge to properly estimate the climate modellinguncertainty from current CMIP ensembles.