The effective equilibrium climate sensitivity is generally assumed to be constant in climate change studies, whereas it may vary due to different mechanisms. This study assesses the importance of the different types of state dependencies of the radiative feedbacks for constraining climate projections from the historical record. In transition, the radiative feedbacks may vary with the changes in the warming pattern due to inhomogeneous ocean heat uptake. They may also vary in equilibrium due to their dependence on both temperature and CO2 concentration. A two-layer energy balance model (EBM) that accounts for these effects is shown to improve the representation of any CO2 pathway for the CMIP5 ensemble. Neglecting the nonlinear effects in constraint studies of climate projections from the historical record may induce errors in the estimated future warming. The EBM framework is used to study these errors for three characteristic CO2 pathways. The results show that the pattern effect of ocean heat uptake is not of major importance by inducing a median error of roughly −2% for a high-emission scenario. In contrast, assuming a log-linear CO2–ERF relationship and neglecting the equilibrium-state dependencies induce a larger median error of roughly −10%. This median error is likely due to the non-log-linear dependency of the instantaneous (nonadjusted) forcing, suggesting that the equilibrium-state dependencies do not induce any systematic error. However, they contribute to increasing uncertainties in future warming estimation.

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