Processes causing the same global-average radiative forcing might lead to different global temperature changes. We expand the theoretical framework by which we calculate paleoclimate sensitivity with an efficacy factor. Applying the revised approach to radiative forcing caused by CO₂ and land ice albedo perturbations, inferred from data of the past 800 000 years, gives a new paleo-based estimate of climate sensitivity.

We document our best available data compilation of published ice core records of the greenhouse gases CO₂, CH₄, and N₂O and recent measurements on firn air and atmospheric samples covering the time window from 156 000 years BP to the beginning of the year 2016 CE. A smoothing spline method is applied to translate the discrete and irregularly spaced data points into continuous time series. The radiative forcing for each greenhouse gas is computed using well-established, simple formulations.

Evidence indicate that specific equilibrium climate sensitivity, the global annual mean surface temperature change as a response to a change in radiative forcing, is state dependent. We here show that the interpretation of data in the state-dependent case is not straightforward. We analyse the differences of a point-wise approach and one based on a piece-wise linear analysis, combine both, compare with potential model results and apply the theoretical concepts to data of the last 800 kyr.

We find that the specific equilibrium climate sensitivity due to radiative forcing of CO2 and land ice albedo has been state-dependent for the last 2.1Myr (most of the Pleistocene). Its value is ~45% larger during intermediate glaciated climates and interglacial periods than during Pleistocene full glacial conditions. The state dependency is mainly caused by a latitudinal dependency in ice sheet area changes. Due to uncertainties in CO2, firm conclusions for the Pliocene are not yet possible.