Feedback temperature dependence determines the risk of high warming

The long-term warming from an anthropogenic increase in atmospheric CO2 is often assumed to be proportional to the forcing associated with that increase. This paper examines this linear approximation using a zero-dimensional energy balance model with a temperature-dependent feedback, with parameter values drawn from physical arguments and general circulation models. For a positive feedback temperature dependence, warming increases Earth's sensitivity, while greater sensitivity makes Earth warm more. These effects can feed on each other, greatly amplifying warming. As a result, for reasonable values of feedback temperature dependence and preindustrial feedback, Earth can jump to a warmer state under only one or two CO2 doublings. The linear approximation breaks down in the long tail of high climate sensitivity commonly seen in observational studies. Understanding feedback temperature dependence is therefore essential for inferring the risk of high warming from modern observations. Studies that assume linearity likely underestimate the risk of high warming.