Climate feedbacks vary strongly among climate models and continue to represent a major source of uncertainty in estimates of the response of climate to anthropogenic forcings. One method to evaluate feedbacks in global climate models is the radiative kernel technique, which is well suited for model intercomparison studies because of its computational efficiency. However, the usefulness of this technique is predicated on the assumption of linearity between top-of-atmosphere (TOA) radiative fluxes and feedback variables, limiting its application to simulations of small climate perturbations, where nonlinearities can be neglected. This paper presents an extension of the utility of this linear technique to large forcings, using global climate model simulations forced with CO2 concentrations ranging from 2 to 8 times present-day values. Radiative kernels depend on the model's radiative transfer algorithm and climate base state. For large warming, kernels based on the present-day climate significantly underestimate longwave TOA flux changes and somewhat overestimate shortwave TOA flux changes. These biases translate to inaccurate feedback estimates. It is shown that a combination of present-day kernels and kernels computed using a large forcing climate base state leads to significant improvement in the approximation of TOA flux changes and increased reliability of feedback estimates. While using present-day kernels results in a climate sensitivity that remains constant, using the new kernels shows that sensitivity increases significantly with each successive doubling of CO2 concentrations.
