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Estimates of radiative feedbacks obtained by regressing fluctuations in top-of-atmosphere (TOA) energy imbalance and surface temperature depend critically on the sampling interval and on assumptions about the nature of the stochastic forcing driving internal variability. Here we develop an energy balance framework that allows us to model the different impacts of stochastic atmospheric and oceanic forcing on feedback estimates. The contribution of different forcing components is parsed based on their impacts on the covariance structure of near-surface air temperature and TOA energy fluxes, and the framework is validated in a hierarchy of climate model simulations that span a range of oceanic configurations and reproduce the key features seen in observations. We find that at least three distinct forcing sources, feedbacks, and time scales are needed to explain the full covariance structure. Atmospheric and oceanic forcings drive modes of variability with distinct relationships between temperature and TOA radiation, leading to an effect akin to regression dilution. The net regression-based feedback estimate is found to be a weighted average of the distinct feedbacks associated with each mode. Moreover, the estimated feedback depends on whether surface temperature and TOA energy fluxes are sampled at monthly or annual time scales. The results suggest that regression-based feedback estimates reflect contributions from a combination of stochastic forcings and should not be interpreted as providing an estimate of the radiative feedback governing the climate response to greenhouse gas forcing.

Plain Language Summary Climate sensitivity quantifies the long-term warming the Earth will experience in response to the additional energy trapped in the system due to greenhouse gases. The physical processes that ultimately determine climate sensitivitytermed climate feedbackshave been extensively investigated using information from natural variability in Earth's temperature and net energy imbalance. However, a complete physical model for what controls this natural variability has been lacking. We derive such a physical model and calibrate it to a hierarchy of numerical climate simulations of increasing complexity. We are able to answer several outstanding questions about previous estimates of climate feedbacks and sensitivity drawn from natural variability, such as what is the source of this variability, and how the estimates depend on the how the data is analyzed. We find that at least three different mechanisms for natural variability are needed to explain the relationship between temperature and energy imbalance and that none provide direct estimates of climate sensitivity.