Commensurate comparisons of models with energy budget observations - - PowerPoint PPT Presentation

Kyle C Armour

University of Washington School of Oceanography and Dept of Atmospheric Sciences

Cristian Proistosescu (UW) Tim Andrews (UK Met Office) Malte Stuecker (UW) Kelly McCusker (UW) Yue Dong (UW) Levi Silvers (GFDL) David Paynter (GFDL) Thorsten Mauritsen (MPI) Jonathan Gregory (Reading)

AGU Fall Meeting 2017

Courtesy of NASA’s Earth Observatory

Commensurate comparisons of models with energy budget

• bservations reveal consistent climate sensitivities

Standard Model of global climate response to forcing

§ Linearization of global top-of-atmosphere (TOA) energy budget

Q = λT + F

global TOA radiative response to warming [Wm-2K-1][K] global TOA radiative forcing [Wm-2] global TOA radiation flux anomaly [Wm-2]

§

Equilibrium warming (Q=0) in response to a doubling of atmospheric CO2 (forcing ≈ 3.7

Wm-2):

Standard Model of global climate response to forcing

§ Linearization of global top-of-atmosphere (TOA) energy budget Equilibrium climate sensitivity (ECS)

ECS = −F2⇥ λ −F2⇥

Q = λT + F

global TOA radiative forcing [Wm-2] global TOA radiation flux anomaly [Wm-2] global TOA radiative response to warming [Wm-2K-1][K]

Estimates of climate sensitivity

correspondence

Energy budget constraints on climate response

• e

s y

Alexander Otto1*, Friederike E. L. Otto1, Olivier Boucher2, John Church3, Gabi Hegerl4, Piers M. Forster5, Nathan P. Gillett6, Jonathan Gregory7, Gregory C. Johnson8, Reto Knutti9, Nicholas Lewis10, Ulrike Lohmann9, Jochem Marotzke11, Gunnar Myhre12, Drew Shindell13, Bjorn Stevens11 and Myles R. Allen1,14

ECS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

= 0.75 ± 0.2 °C = 0.65 ± 0.27 Wm-2 = 2.3 ± 1 Wm-2

(years 2000-2009 relative to 1860-1879)

⇥Tobs

− Qobs =

⇥

Fobs

Q = λT + F

1 2 3 4 5 6 0.2 0.4 0.6 0.8

Estimates of climate sensitivity

ECS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

correspondence

Energy budget constraints on climate response

• e

s y

Alexander Otto1*, Friederike E. L. Otto1, Olivier Boucher2, John Church3, Gabi Hegerl4, Piers M. Forster5, Nathan P. Gillett6, Jonathan Gregory7, Gregory C. Johnson8, Reto Knutti9, Nicholas Lewis10, Ulrike Lohmann9, Jochem Marotzke11, Gunnar Myhre12, Drew Shindell13, Bjorn Stevens11 and Myles R. Allen1,14

Equilibrium climate sensitivity [°C] Probability density [1/°C]

Otto et al. ECS

1 2 3 4 5 6 0.2 0.4 0.6 0.8

Estimates of climate sensitivity

ECS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

correspondence

Energy budget constraints on climate response

• e

s y

Alexander Otto1*, Friederike E. L. Otto1, Olivier Boucher2, John Church3, Gabi Hegerl4, Piers M. Forster5, Nathan P. Gillett6, Jonathan Gregory7, Gregory C. Johnson8, Reto Knutti9, Nicholas Lewis10, Ulrike Lohmann9, Jochem Marotzke11, Gunnar Myhre12, Drew Shindell13, Bjorn Stevens11 and Myles R. Allen1,14

Equilibrium climate sensitivity [°C] Probability density [1/°C]

median ECS: 2.0 °C 5-95% range: 1.2-3.9 °C

Otto et al. ECS

Estimates of climate sensitivity

correspondence

Energy budget constraints on climate response

• e

s y

Alexander Otto1*, Friederike E. L. Otto1, Olivier Boucher2, John Church3, Gabi Hegerl4, Piers M. Forster5, Nathan P. Gillett6, Jonathan Gregory7, Gregory C. Johnson8, Reto Knutti9, Nicholas Lewis10, Ulrike Lohmann9, Jochem Marotzke11, Gunnar Myhre12, Drew Shindell13, Bjorn Stevens11 and Myles R. Allen1,14

ECS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Estimates of climate sensitivity

§ Global energy budget constraints produce estimates of ECS that are quite a bit lower than ECS simulated by CMIP5 models § Are the models overly sensitive? § Or is something else going on…?

ECS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Like-with-like comparisons of climate sensitivity

§ Emerging consensus: model-observational comparisons must be made in a like-with-like way

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Like-with-like comparisons of climate sensitivity

§ Emerging consensus: model-observational comparisons must be made in a like-with-like way, accounting for possibility that: 1) Feedbacks ( ) vary over time as the spatial pattern of warming evolves

(Armour 2017; Proistosescu & Huybers 2017)

⇥

λ

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Like-with-like comparisons of climate sensitivity

§ Emerging consensus: model-observational comparisons must be made in a like-with-like way, accounting for possibility that: 1) Feedbacks ( ) vary over time as the spatial pattern of warming evolves

(Armour 2017; Proistosescu & Huybers 2017)

2) Feedbacks affected by the “efficacy”

• f non-CO2 forcings (Shindell 2014;

Kummer & Dessler 2014; Marvel et al. 2015)

⇥

λ

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Like-with-like comparisons of climate sensitivity

§ Emerging consensus: model-observational comparisons must be made in a like-with-like way, accounting for possibility that: 1) Feedbacks ( ) vary over time as the spatial pattern of warming evolves

(Armour 2017; Proistosescu & Huybers 2017)

2) Feedbacks affected by the “efficacy”

• f non-CO2 forcings (Shindell 2014;

Kummer & Dessler 2014; Marvel et al. 2015)

3) Feedbacks depend on natural variability in the pattern of warming

⇥

λ

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

Like-with-like comparisons of climate sensitivity

§ Emerging consensus: model-observational comparisons must be made in a like-with-like way, accounting for possibility that: 1) Feedbacks ( ) vary over time as the spatial pattern of warming evolves

(Armour 2017; Proistosescu & Huybers 2017)

2) Feedbacks affected by the “efficacy”

• f non-CO2 forcings (Shindell 2014;

Kummer & Dessler 2014; Marvel et al. 2015)

3) Feedbacks depend on natural variability in the pattern of warming 4) Different definitions of global-mean temperature used in models vs

• bservations (Cowtan et al. 2015;

Richardson et al. 2016)

⇥

λ

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Equilibrium climate sensitivity [°C] Probability density [1/°C]

CMIP5 ECS Otto et al. ECS

(Armour 2017; see also Proistosescu & Huybers 2017)

CMIP5 response to 4×CO2 (Andrews et al. 2015)

1) Feedbacks vary as the pattern of warming evolves

CMIP5 response to 4×CO2 (Andrews et al. 2015)

1) Feedbacks vary as the pattern of warming evolves

CMIP5 response to 4×CO2 (Andrews et al. 2015)

1) Feedbacks vary as the pattern of warming evolves

Localized patches of warming

0.5 1 1.5

• 5
• 10

10 5 (°C) (Wm-2) Warming patch Radiative response Warming patch Radiative response Patches for Green’s Function simulations a b c d e

Global feedback response to localized patches of warming in NCAR’s CAM4 (Dong et al., in preparation)

see also Zhou et al. 2017

CMIP5 response to 4×CO2 (Andrews et al. 2015) Global feedback response to localized patches of warming in NCAR’s CAM4 (Dong et al., in preparation)

see also Zhou et al. 2017; Proistosescu & Huybers 2017; Andrews & Webb 2017; Ceppi & Gregory 2017; Silvers et al. 2017; Zhou et al. 2016; Gregory & Andrews 2016; Rugenstein et al. 2016; Rose et al. 2014; Armour et al. 2013; many others

1) Feedbacks vary as the pattern of warming evolves

• 15 -10
• 5

5 10 15 Global radiative feedback

[Wm-2K-1]

CMIP5 response to 4×CO2 (Andrews et al. 2015)

1) Feedbacks vary as the pattern of warming evolves

40 80 120 1 1.5 2 2.5

§ Feedbacks under transient warming ( ) are more negative than those at equilibrium ( ) § Inferred (or instantaneous) climate sensitivity (ICS) is generally smaller than equilibrium climate sensitivity (ECS)

− ICS = −F2⇥ λ

ECS = −F2⇥ λ2⇥

ECS/ICS = Year after CO2 quadrupling CMIP5 models

1) Feedbacks vary as the pattern of warming evolves

−

⇥

λ2⇥

⇥

λ

λ λ2⇥ CMIP5 response to CO2 forcing (Armour 2017)

see also Proistosescu & Huybers 2017

§ Feedbacks under transient warming ( ) are more negative than those at equilibrium ( ) § Inferred (or instantaneous) climate sensitivity (ICS) is generally smaller than equilibrium climate sensitivity (ECS) § Global energy budget constraints provide estimates of ICS only, so should be compared with model values of ICS (not ECS!)

− ICS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

ECS = −F2⇥ λ2⇥

40 80 120 1 1.5 2 2.5

Year after CO2 quadrupling CMIP5 models

1) Feedbacks vary as the pattern of warming evolves

−

⇥

λ2⇥

⇥

λ

ECS/ICS = λ λ2⇥ CMIP5 response to CO2 forcing (Armour 2017)

see also Proistosescu & Huybers 2017

§ Feedbacks under transient warming ( ) are more negative than those at equilibrium ( ) § Inferred (or instantaneous) climate sensitivity (ICS) is generally smaller than equilibrium climate sensitivity (ECS) § Global energy budget constraints provide estimates of ICS only, so should be compared with model values of ICS (not ECS!)

− ICS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

ECS = −F2⇥ λ2⇥

1) Feedbacks vary as the pattern of warming evolves

1 2 3 4 5 6 2 4 6 8

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

ICS or ECS [°C] Probability density [1/°C]

Otto et al. ICS CMIP5 ECS

−

⇥

λ2⇥

⇥

λ

CMIP5 response to CO2 forcing (Armour 2017)

see also Proistosescu & Huybers 2017

1 2 3 4 5 6 2 4 6 8

§ Feedbacks under transient warming ( ) are more negative than those at equilibrium ( ) § Inferred (or instantaneous) climate sensitivity (ICS) is generally smaller than equilibrium climate sensitivity (ECS) § Global energy budget constraints provide estimates of ICS only, so should be compared with model values of ICS (not ECS!)

− ICS = −F2⇥ λ = F2⇥Tobs Fobs − Qobs

ECS = −F2⇥ λ2⇥

1) Feedbacks vary as the pattern of warming evolves

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

ICS or ECS [°C] Probability density [1/°C]

Otto et al. ICS CMIP5 ICS

−

⇥

λ2⇥

⇥

λ

CMIP5 response to CO2 forcing (Armour 2017)

see also Proistosescu & Huybers 2017

§ Feedbacks under historical forcing may differ from those under CO2 forcing alone (Shindell 2014;

Marvel et al. 2015)

§ Radiative Forcing Model Intercomparison Project (RFMIP; Pincus et al. 2016) protocol produces coupled model estimates of forcing and feedbacks over historical period

2) Feedbacks depend on the type of radiative forcing

1 2 3 4 5 6 0.2 0.4 0.6 0.8

ICS or ECS [°C] Probability density [1/°C]

Otto et al. ICS

1 2 3 4 5 6 2 4 6 8

§ Feedbacks under historical forcing may differ from those under CO2 forcing alone (Shindell 2014;

Marvel et al. 2015)

§ Radiative Forcing Model Intercomparison Project (RFMIP; Pincus et al. 2016) protocol produces coupled model estimates of forcing and feedbacks over historical period

2) Feedbacks depend on the type of radiative forcing

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

GISS-E2-R ECS GISS-E2-R ICS

Historical simulations with GISS-E2-R

(Marvel et al. 2015)

1 2 3 4 5 6 2 4 6 8

§ Feedbacks under historical forcing may differ from those under CO2 forcing alone (Shindell 2014;

Marvel et al. 2015)

§ Radiative Forcing Model Intercomparison Project (RFMIP; Pincus et al. 2016) protocol produces coupled model estimates of forcing and feedbacks over historical period

2) Feedbacks depend on the type of radiative forcing

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Historical simulations of NCAR’s CESM1-CAM5 Large Ensemble (Cristi Proistosescu and Malte Stuecker)

Otto et al. ICS

CESM1 ECS CESM1 LE mean ICS

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

3) Feedbacks vary due to internal climate variability

Otto et al. ICS

CESM1 ECS CESM1 LE mean ICS

§ Feedbacks under historical forcing can vary due to only internal climate variability Historical simulations of NCAR’s CESM1-CAM5 Large Ensemble (Cristi Proistosescu and Malte Stuecker)

1 2 3 4 5 6 2 4 6 8

3) Feedbacks vary due to internal climate variability

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

CESM1 ECS CESM1 LE members ICS

§ Feedbacks under historical forcing can vary due to only internal climate variability Historical simulations of NCAR’s CESM1-CAM5 Large Ensemble (Cristi Proistosescu and Malte Stuecker)

1 2 3 4 5 6 2 4 6 8

3) Feedbacks vary due to internal climate variability

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

CESM1 ECS CESM1 LE members ICS

§ Feedbacks under historical forcing can vary due to only internal climate variability § Key question: what global feedback (and ICS) has the observed warming pattern engendered? Historical simulations of NCAR’s CESM1-CAM5 Large Ensemble (Cristi Proistosescu and Malte Stuecker)

AMIP II boundary conditions (Hurrell et al. 2008) Global feedback response to localized patches of warming in NCAR’s CAM4 (Dong et al., in preparation)

• 15 -10
• 5

5 10 15 Global radiative feedback

3) Feedbacks vary due to internal climate variability

• 2
• 1

1 2 Observed warming pattern

[Wm-2K-1]

1 2 3 4 5 6 2 4 6 8

3) Feedbacks vary due to internal climate variability

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

CESM1 ECS CESM1 LE members ICS

§ Prescribed sea-surface temperature (SST) simulations produce the same feedbacks as are induced by climate forcings (Haugstad et al. 2017) § Cloud Feedback Model Intercomparison Project (CFMIP; Webb et al. 2017) protocol produces estimates of feedbacks associated with observed warming pattern

1 2 3 4 5 6 2 4 6 8

3) Feedbacks vary due to internal climate variability

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

CESM1 ECS CESM1 LE members ICS CAM5 ICS w/

• bs warming

Prescribed observed SST simulation with CAM5

(Malte Stuecker and Cristi Proistosescu)

CAM5

§ Prescribed sea-surface temperature (SST) simulations produce the same feedbacks as are induced by climate forcings (Haugstad et al. 2017) § Cloud Feedback Model Intercomparison Project (CFMIP; Webb et al. 2017) protocol produces estimates of feedbacks associated with observed warming pattern

1 2 3 4 5 6 2 4 6 8

3) Feedbacks vary due to internal climate variability

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

Prescribed observed SST simulations with CAM4, CAM5, HadGEM2, HadAM3, ECHAM6, AM2.1, AM3, AM4 (Yue

Dong, Malte Stuecker, Cristi Proistosescu, Tim Andrews, Jonathan Gregory, Thorsten Mauritsen, Levi Silvers & David Paynter) CMIP5 ECS CMIP5 ICS w/

• bs warming

CAM4, AM2.1 CAM5, AM3 HadGEM2 CAM4 CAM5 HadGEM2, ECHAM6 HadAM3, AM3 HadAM3 ECHAM6

§ Prescribed sea-surface temperature (SST) simulations produce the same feedbacks as are induced by climate forcings (Haugstad et al. 2017) § Cloud Feedback Model Intercomparison Project (CFMIP; Webb et al. 2017) protocol produces estimates of feedbacks associated with observed warming pattern

AM4 AM2.1

1 2 3 4 5 6 2 4 6 8

4) Sensitivity estimates depend on global temperature definition

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS

§ Global temperature record is a blend of SST over

• cean, near-surface air temperature over land;

lacks full global coverage § Global temperature in models is calculated as a full global average of near-surface air temperature

CMIP5 ICS w/

• bs warming

Prescribed observed SST simulations with CAM4, CAM5, HadGEM2, HadAM3, ECHAM6, AM2.1, AM3, AM4 (Yue

Dong, Malte Stuecker, Cristi Proistosescu, Tim Andrews, Jonathan Gregory, Thorsten Mauritsen, Levi Silvers & David Paynter)

1 2 3 4 5 6 2 4 6 8

4) Sensitivity estimates depend on global temperature definition

ICS or ECS [°C] Probability density [1/°C]

0 1 2 3 4 5 6 0.2 0.4 0.6 0.8

Otto et al. ICS w/ Richardson correction

§ Global temperature record is a blend of SST over

• cean, near-surface air temperature over land;

lacks full global coverage § Global temperature in models is calculated as a full global average of near-surface air temperature § Blending/masking models consistently with

• bservations suggests an increase to Otto et al. ICS

estimate (Richardson et al. 2016)

CMIP5 ICS w/

• bs warming

Prescribed observed SST simulations with CAM4, CAM5, HadGEM2, HadAM3, ECHAM6, AM2.1, AM3, AM4 (Yue

Dong, Malte Stuecker, Cristi Proistosescu, Tim Andrews, Jonathan Gregory, Thorsten Mauritsen, Levi Silvers & David Paynter)

Parting thoughts

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C]

§ Apparent offset between global energy budget constraints and models stems from sloppy comparison between observation-based estimates of ICS and modeled estimates of ECS

Parting thoughts

1 2 3 4 5 6 2 4 6 8

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C] Probability density [1/°C]

§ Apparent offset between global energy budget constraints and models stems from sloppy comparison between observation-based estimates of ICS and modeled estimates of ECS § Accounting for feedback dependence on evolving pattern of CO2-forced warming (slow warming of E. Pacific and Southern Ocean) gives model values

• f ICS that are in agreement with observation-based values (though still high)

Parting thoughts

1 2 3 4 5 6 2 4 6 8

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C] Probability density [1/°C] Probability density [1/°C]

§ Apparent offset between global energy budget constraints and models stems from sloppy comparison between observation-based estimates of ICS and modeled estimates of ECS § Accounting for feedback dependence on evolving pattern of CO2-forced warming (slow warming of E. Pacific and Southern Ocean) gives model values

• f ICS that are in agreement with observation-based values (though still high)

§ Accounting for the observed pattern of warming being pretty odd gives model values of ICS that are in good agreement

1 2 3 4 5 6 2 4 6 8

Parting thoughts

1 2 3 4 5 6 2 4 6 8

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C] Probability density [1/°C] Probability density [1/°C] Probability density [1/°C]

§ Apparent offset between global energy budget constraints and models stems from sloppy comparison between observation-based estimates of ICS and modeled estimates of ECS § Accounting for feedback dependence on evolving pattern of CO2-forced warming (slow warming of E. Pacific and Southern Ocean) gives model values

• f ICS that are in agreement with observation-based values (though still high)

§ Accounting for the observed pattern of warming being pretty odd gives model values of ICS that are in good agreement § Accounting for consistent global temperature definitions brings model ICS values to low end of observation-based ICS values

1 2 3 4 5 6 2 4 6 8 1 2 3 4 5 6 2 4 6 8

Parting thoughts

§ Apparent offset between global energy budget constraints and models stems from sloppy comparison between observation-based estimates of ICS and modeled estimates of ECS § Accounting for feedback dependence on evolving pattern of CO2-forced warming (slow warming of E. Pacific and Southern Ocean) gives model values

• f ICS that are in agreement with observation-based values (though still high)

§ Accounting for the observed pattern of warming being pretty odd gives model values of ICS that are in good agreement § Accounting for consistent global temperature definitions brings model ICS values to low end of observation-based ICS values § A host of unanswered questions: What’s so special about observed warming pattern? Why don’t coupled models ever generate warming patterns that induce such low ICS values? Is future warming pattern (and higher ECS) predicted by models realistic? How can ECS be constrained from observations?

1 2 3 4 5 6 2 4 6 8

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C] Probability density [1/°C] Probability density [1/°C] Probability density [1/°C]

1 2 3 4 5 6 2 4 6 8 1 2 3 4 5 6 2 4 6 8

Our papers on this

§ Accounting for feedbacks changing with pattern of warming:

Armour (2017) Nature Climate Change Proistosescu & Huybers (2017) Science Advances

§ Feedback variability in large ensemble simulations:

Proistosescu, McCusker, Stuecker, Armour, Bitz (in prep)

§ Green’s Function approach to feedback dependence on warming patterns:

Dong, Armour, Battisti (in prep)

§ Comparison of Otto-style energy budget constraints on ICS with ICS in prescribed historical SST simulations:

Armour, Andrews, Proistosescu, Stuecker, Dong, Mauritsen, Gregory, Silvers, Paynter (in prep)

§ Several other recent papers by Andrews, Silvers, Paynter, Mauritsen, Gregory looking at historical feedback variability in CFMIP-style simulations

1 2 3 4 5 6 2 4 6 8

1 2 3 4 5 6 2 4 6 8

ICS or ECS [°C]

Probability density [1/°C] Probability density [1/°C] Probability density [1/°C] Probability density [1/°C]

1 2 3 4 5 6 2 4 6 8 1 2 3 4 5 6 2 4 6 8