Technical Note: Calculating state dependent equilibrium climate sensitivity from palaeodata

Abstract

Abstract.The evidence from both data and models indicate that specific equilibrium climate sensitivity S [X] -the global annual mean surface temperature change (∆T g ) as a response to a change in radiative forcing X (∆R [X] ) -is state dependent. Such a state dependency implies that the best fit in the scatter plot of ∆T g versus ∆R [X] is not a linear regression, but for instance a higher order polynomial. While for the conventional linear case the slope (gradient) of the regression is correctly interpreted as the 5 specific equilibrium climate sensitivity S [X] , the interpretation is not straightforward in the non-linear case. We here elaborate how such a state dependent scatter plot needs to be interpreted, and provide a theoretical understanding how to calculate S [X] in the non-linear case.

Nonlinear climate sensitivity and its implications for future greenhouse warming

“…We referred to the detailed discussion by Köhler et al . ( 50 ). Here, we are mainly interested in deriving an average of S that is representative of warm climates and can be used for a global warming projection for the 21st century.…”

“…Here, we are mainly interested in deriving an average of S that is representative of warm climates and can be used for a global warming projection for the 21st century. Thus, we can use a slope average over a larger domain, avoiding uncertainties in the method of calculation ( 50 ) while still allowing for a state dependence. To distinguish cold and warm climates, we then used the SD of our SAT reconstruction.…”

“…11 of Köhler et al . ( 50 ). Taking into account the systematic errors in the SAT reconstruction and the estimate of radiative forcing described above, the specific equilibrium climate sensitivity for cold climate ( S cold ) amounts to 0.41 to 0.55 K W −1 m 2 (likely range, mean: 0.48 K W −1 m 2 ).…”

“…Interpreting the (local) slope of the fit in terms of a specific equilibrium climate sensitivity is not straightforward. We referred to the detailed discussion by Köhler et al (50). Here, we are mainly interested in deriving an average of S that is representative of warm climates and can be used for a global warming projection for the 21st century.…”

Atmospheric CO2 Concentration Based on Boron Isotopes Versus Simulations of the Global Carbon Cycle During the Plio‐Pleistocene

“…(2018a) are found in Köhler (2022). (b) Temperature forcing (Köhler et al., 2015a, 2015b). (c) Alternative temperature forcing (Stap et al., 2018a, 2018b).…”