A state-dependent quantification of climate sensitivity based in paleo data of the last 2.1 million years

The evidence from both data and models indicates that specific equilibrium climate sensitivity S[X] — the global annual mean surface temperature change (DTg) as a response to a change in radiative forcing X (DR[X]) — is state-dependent. Such a state dependency implies that the best fit in the scatter plot of (DTg versus DR[X] is not a linear regression, but can be some non-linear or even non-smooth function. While for the conventional linear case the slope (gradient) of the regression is correctly interpreted as the specific equilibrium climate sensitivity S[X], the interpretation is not straightforward in the non-linear case. We here explain how such a state-dependent scatter plot needs to be interpreted, and provide a theoretical understanding — or generalization — how to quantify S[X] in the non-linear case. Finally, from data covering the last 2.1 Myr we show that — due to state dependency — the specific equilibrium climate sensitivity which considers radiative forcing of CO2 and land ice sheet (LI) albedo, S[CO2;LI], is larger during interglacial states than during glacial conditions by more than a factor two.