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We compare six methods of estimating effective radiative forcing (ERF) using a set of atmosphere-ocean general circulation models. This is the first multiforcing agent, multimodel evaluation of ERF values calculated using different methods. We demonstrate that previously reported apparent consistency between the ERF values derived from fixed sea surface temperature simulations and linear regression holds for most climate forcings, excluding black carbon (BC). When land adjustment is accounted for, however, the fixed sea surface temperature ERF values are generally 10-30% larger than ERFs derived using linear regression across all forcing agents, with a much larger (similar to 70-100%) discrepancy for BC. Except for BC, this difference can be largely reduced by either using radiative kernel techniques or by exponential regression. Responses of clouds and their effects on shortwave radiation show the strongest variability in all experiments, limiting the application of regression-based ERF in small forcing simulations.

Plain Language Summary Climate drivers such as greenhouse gases and aerosols influence the Earth's climate by perturbing the Earth's energy budget at the top of the atmosphere, which is referred to as effective radiative forcing (ERF) when the atmospheric response is included in the calculation. ERF plays a crucial role in understanding the climate response to these drivers and predicting long-term climate change. Previously, ERFs have been estimated for greenhouse gases using two techniques that generally lead to similar values. Here we show that such consistency holds for most climate drivers. ERF values estimated from different methods may differ by 10-50%, and this difference may reach 70-100% for black carbon. Regression techniques do not work well in some models when imposed forcings are relatively small.