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The surface warming response to anthropogenic forcing is highly sensitive to the strength of feedbacks in both the physical climate and carbon cycle systems. However, the definitions of climate feedback, lambda(Climate) in W.m(-2).K-1, and climate sensitivity, S-Climate in K/(W/m(2)), explicitly exclude the impact of carbon cycle feedbacks. Here we provide a new framework to incorporate carbon feedback into the definitions of climate feedback and sensitivity. Applying our framework to the Global Carbon Budget reconstructions reveals a present- day terrestrial carbon feedback of lambda(Carbon) = 0.31 +/- 0.09 W.m(-2).K-1 and an ocean carbon feedback of - 0.06 to 0.015 W.m(-2).K-1 in Earth system models. Observational constraints reveal a combined climate and carbon feedback of lambda(Climate+Carbon) = 1.48 W.m(-2).K-1 with a 95% range of 0.76 to 2.32 W.m(-2).K-1 on centennial time scales, corresponding to a combined climate and carbon sensitivity of SClimate+Carbon = 0.67 K/(W/m(2)) with a 95% range of 0.43 to 1.32 K/(W/m(2)).

Plain Language Summary Feedback processes in the physical climate system and the carbon cycle affect the Earth's climate response to emissions of greenhouse gases, such as carbon dioxide. Physical climate feedbacks include the responses of clouds and atmospheric water vapor to rising surface temperatures, while carbon cycle feedbacks affect how much of the emitted carbon dioxide is removed from the atmosphere and stored in the ocean and on land. Conventionally, definitions of climate feedback and climate sensitivity include all the feedbacks in the physical climate system but do not include carbon cycle feedbacks. This study provides a new framework to incorporate carbon feedback into the definitions of climate feedback and sensitivity. Evaluating the historical strengths of physical climate system and carbon cycle feedbacks suggests emissions of carbon dioxide will cause equilibrium (century time scale) surface warming to increase between 0.6 and 2.0 degrees C for every 1,000 PgC emitted when an equilibrium is approached between the atmosphere and the ocean over many centuries.