Equilibrium-and transient-state dependenciesof … · 2019. 10. 21. · EBM 1 EBM 2 EBM 3....

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Equilibrium- and transient- state dependencies of climate feedbacks: are they important for climate projections ? Olivier Geoffroy and David Saint-Martin CNRM, Météo-France / CNRS CFMIP, 2019

Transcript of Equilibrium-and transient-state dependenciesof … · 2019. 10. 21. · EBM 1 EBM 2 EBM 3....

Page 1: Equilibrium-and transient-state dependenciesof … · 2019. 10. 21. · EBM 1 EBM 2 EBM 3. Effectscannot bedissociated Assume one single effectfullyexplainthe nonlinearbehaviour CO2-ERF

Equilibrium- and transient- state dependencies of climate feedbacks:

are they important for climate projections ?

Olivier Geoffroy and David Saint-Martin

CNRM, Météo-France / CNRS

CFMIP, 2019

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Δ�

Δ�

Abrupt2xCO2 in a Gregory plot :

Some motivations

Are changing feedbacks important for constraining climate projections ?

- Need to use same type of estimations when comparing models and obs

- (Any estimate of) ECS not necessary the best metric for warming in 2100

different ECS estimates

Linear regressionof 150 years

1/12

- They are other effects than the pattern effect : equilibrium-state dependencies

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- State dependencies of λ and CO2-forcing relationshipin CMIP5 (+ CNRM-CM6.1)

- Importance for constraining climate projections ?

Outlines2/12

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pattern effect

(Winton et al., 2010; Held et al., 2010, Geoffroy et al., 2013b)

Linear 2-layer energy balance model3/12

� ≠ �

Upper ocean+ atmo + land

Deep ocean

EBM (Gregory et al., 2000 ; Held et al., 2010)

���

��= � − �Δ� − � − 1 � − �

�����

��= � = γ (Δ� − Δ��)

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Overestimation of TCRCalibration with abrupt4xCO2

Large spread

Upper ocean+ atmo + land

Deep ocean

� � = �� ���� �(�) with c = [���]

[���]�

Linear 2-layer energy balance model3/12

EBM (Gregory et al., 2000 ; Held et al., 2010) Log CO2-ERF relationship (Myhre et al., 1998)

Multimodel mean Error for each AOGCM (%)

���

��= � − �Δ� − � − 1 � − �

�����

��= � = γ (Δ� − Δ��)

TCR TCR4x

TCR

TCR4x

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� � = �� [ 1 − � ���� �(�) + � (���� �(�))� ]

(Byrne and Goldblatt, 2014, Etminan et al., 2016, Gregory et al., 2015)

with c = [���]

[���]�

f ≈ 0.09

BG14

Linear 2-layer energy balance model3/12

Log CO2-ERF relationship :

Quadratic CO2-ERF relationship from line-by-line RT model (BG14) :

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Linear 2-layer energy balance model3/12

Log CO2-ERF relationship :

Quadratic CO2-ERF relationship from line-by-line RT model (BG14) :

Better agreement, large spread

In agreement withGregory et al. (2015)

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×��×

�(�)

Log forcing

ΔT (K)

Δ�= F(t)- λ Δ���×

�(�)Δ�= ��× - λ

��×

�(�)Δ�

Rescaled 1% CO2 yr-1 in order to match the abrupt4xCO24/12

Rescaled 1% CO2 yr-1

Abrupt 4xCO2

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Quadratic forcing from BG14

ΔT (K) ΔT (K)

Δ�= F(t)- λ Δ���×

�(�)Δ�= ��× - λ

��×

�(�)Δ�

Rescaled 1% CO2 yr-1 in order to match the abrupt4xCO24/12

In agreement withGregory et al. (2015)

Good representation

Rescaled 1% CO2 yr-1

Abrupt 4xCO2

Rescaled 1% CO2 yr-1

Abrupt 4xCO2

×��×

�(�)

Log forcing

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Rescaled 1% CO2 yr-1 in order to match the abrupt4xCO2

Log forcing

Quadratic from BG14

Difference due to CO2-ERF relationship and/or equilibrium state dependency of λ

Large spread :

4/12

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f from BG14(f ≈ 0.09)

f from BG14(f ≈ 0.09)

f model dependent

Constant

CO2-ERF relationship and equilibrium state dependency of λ in an EBM

� = �� [ 1 − �� + �� ���� � ]

� = ��� [ 1 − �� + ��

Δ�

���� ]

f([CO2]) f(ΔT)λ

(Colman et al., 1997; Jonko et al. 2012, Block and Mauritsen, 2013; Bloch-Johnson et al., 2015)

Equilibrium state dependencies of λ

Quadratic ERF

5/12

�� [ 1 − � ���� � + f (���� �)� ]

EBM 1 EBM 2 EBM 3

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Effects can not be dissociated Assume one single effect fully explain the nonlinear behaviour

CO2-ERF relationship and equilibrium state dependency of λ in an EBM5/12

f from BG14(f ≈ 0.09)

f from BG14(f ≈ 0.09)

f model dependent

Constant f([CO2]) f(ΔT)λ

Quadratic ERF

�� [ 1 − � ���� � + f (���� �)� ]

EBM 1 EBM 2 EBM 3

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- Quadratic ERF- λ = constant

- Quadratic ERF from BG14

- λ = f([CO2])

- Quadratic ERF from BG14

- λ = f(ΔT)

Representation of the 1% CO2 yr-1 by each EBM 6/12

Similar reductionof the spread

TCR TCR4x

Error for each AOGCM (%)Multimodel mean

TCR

TCR4x

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- State dependencies of λ and CO2-forcing relationship in CMIP5

- Importance of CO2-ERF relationship and state dependencies of λfor constraining climate projections ?

Outlines

Use idealized scenarios Use the 2-layer EBM calibrated with CMIP5 models as a perfect model

7/12

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ΔT

t

Error in projected warming ?

Obs Projection

Assume we can measure but not λ and ε

Use the value at t 0

����������(�) = � +� − 1 �(�)

Δ�(�)

Reality : EBM with pattern effect

Projection with ���������� = ���� = �������� �����

����������

8/12Importance of pattern effect for constraining climate projections : method

1% CO2 yr-1

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Importance of pattern effect for constraining climate projections

Reality : EBM with pattern effect

Estimation : EBM with constant estimated at t 0 yr����������

����������(�) = � +� − 1 �(�)

Δ�(�)

Neglecting the pattern effect to constrain TCR4x median relative error of only 3 %

9/12

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Importance of CO2-ERF relationship and/or equilibrium state dependent λ

Effects can not be dissociated

Use one EBM with one single effectand assume it well represents all the 3 effects

10/12

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Reality : EBM with quadratic forcing with f model dependent

Estimation : EBM with Log forcing with F4 estimated at t 0

Importance of CO2-ERF relationship and/or equilibrium state dependent λ10/12

Median error = -10 % , large spread

�� [ 1 − � ���� �+ � (���� �)�]

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Median error = 0 % , large spread

Reality : EBM with quadratic forcing with f model dependent

Estimation : EBM with BG14 quadratic forcing with F4 estimated at t 0

Importance of CO2-ERF relationship and/or equilibrium state dependent λ11/12

�� [ 1 − � ���� �+ � (���� �)�]

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Same results : median error = 0 % , large spread

Reality : EBM with BG14 quadratic forcing and CO2-dependent λ

Estimation : EBM with BG14 quadratic forcing and constant λ estimated at t 0

Importance of CO2-ERF relationship and/or equilibrium state dependent λ11/12

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Similar results : median error = 0 % , large spread

Reality : EBM with BG14 quadratic forcing and T-dependent λ

Estimation : EBM with BG14 quadratic forcing and constant λ estimated at t 0

Importance of CO2-ERF relationship and/or equilibrium state dependent λ11/12

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Conclusion

• 2-layer EBM with pattern effect calibrated from abrupt4xCO2,

+ quadratic forcing from line-by-line RT models median TCR well represented

Large spread due to i) deviation from BG14 forcingii) equilibrium-state dependencies of λ (on CO2, T)

• Importance for constraining climate projections (use TCR4x, ΔTstabilization, ΔTramp-down)

The (forced) pattern effect is not important (3 % of error for TCR4x)

If AOGCMs correctly represent BG14 forcing, a log forcing lead to a error of -10 %

Equilibrium state dependencies and/or deviation from BG14 forcing do not induce any systematic error when a BG14 forcing is used, but contribute to increase uncertainties

12/12

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Importance of pattern effect for constraining climate projections

Reality : EBM with pattern effect

Estimation : EBM with constant with value « measured » at t 0 yr����������

����������(�) = � +� − 1 �(�)

Δ�(�)

Neglecting the pattern effect to constrain TCR4x median relative error of only 3 %

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Neglecting the pattern effect to constrain TCR4x median relative error of only 3 %

Reality : EBM with pattern effect

Importance of pattern effect for constraining climate projections

Estimation : EBM with constant with value « measured » at t = 40 yr����������

����������(�) = � +� − 1 �(�)

Δ�(�)

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t 0 yr

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t = 40 yr

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ΔT

t

Error in projected warming ?

Obs Projection

Assume we can measure but not ε

Use the limit of t=0 :

���������� = � +� − 1 �

Δ�

= � + (1 − �)γ

Reality : EBM with pattern effect

Projection with ���������� = ���� = �������� �����

����������

Importance of pattern effect for constraining climate projections

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Linear forcing feedback framework

Δ�= F(t)- λ Δ�rescaling ��×

�(�)Δ�= ��× - λ

��×

�(�)Δ�

Any deviation from the abrupt2xCO2 line shows a limitation of the linear F-λ framework

(Δ�, Δ�) ×��×

�(�)

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Explications possibles : - forçage pas en log(CO2), - lambda non constant (autre que pattern effect)- Param de H

Limitation de l’EBM (avec ou sans ε) : biais TCR

TCR (=ΔT à 2xCO2i.e. t=70 ans)

Time (yr)

Probablement en lien : ΔT(t=2100) dans un RCP8.5 mieux correlé à « ECS » qu’à TCR(Grose et al. 2018)

radiatif

OHU