How accurately can the climate sensitivity to ${\text{CO}}_2$ be estimated from historical climate change?

The equilibrium climate sensitivity (ECS, in K) to ${\text{CO}}_2$ doubling is a large source of uncertainty in projections of future anthropogenic climate change. Estimates of ECS made from non-equilibrium states or in response to radiative forcings other than $\text{2}\times {\text{CO}}_2$ are called "effective climate sensitivity" (EffCS, in K). Taking a "perfect-model" approach, using coupled atmosphere–ocean general circulation model (AOGCM) experiments, we evaluate the accuracy with which ${\text{CO}}_2$ EffCS can be estimated from climate change in the "historical" period (since about 1860). We find that (1) for statistical reasons, unforced variability makes the estimate of historical EffCS both uncertain and biased; it is overestimated by about 10% if the energy balance is applied to the entire historical period, 20% for 30-year periods, and larger factors for interannual variability, (2) systematic uncertainty in historical radiative forcing translates into an uncertainty of $\pm 30to45\%$ (standard deviation) in historical EffCS, (3) the response to the changing relative importance of the forcing agents, principally ${\text{CO}}_2$ and volcanic aerosol, causes historical EffCS to vary over multidecadal timescales by a factor of two. In recent decades it reached its maximum in the AOGCM historical experiment (similar to the multimodel-mean ${\text{CO}}_2$ EffCS of 3.6 K from idealised experiments), but its minimum in the real world (1.6 K for an observational estimate for 1985–2011, similar to the multimodel-mean value for volcanic forcing). The real-world variations mean that historical EffCS underestimates ${\text{CO}}_2$ EffCS by 30% when considering the entire historical period. The difference for recent decades implies that either unforced variability or the response to volcanic forcing causes a much stronger regional pattern of sea surface temperature change in the real world than in AOGCMs. We speculate that this could be explained by a deficiency in simulated coupled atmosphere–ocean feedbacks which reinforce the pattern (resembling the Interdecadal Pacific Oscillation in some respects) that causes the low EffCS. We conclude that energy-balance estimates of ${\text{CO}}_2$ EffCS are most accurate from periods unaffected by volcanic forcing. Atmosphere GCMs provided with observed sea surface temperature for the 1920s to the 1950s, which was such a period, give a range of about 2.0–4.5 K, agreeing with idealised ${\text{CO}}_2$ AOGCM experiments; the consistency is a reason for confidence in this range as an estimate of ${\text{CO}}_2$ EffCS. Unless another explosive volcanic eruption occurs, the first 30 years of the present century may give a more accurate energy-balance historical estimate of this quantity.