Climate sensitivity ($\Delta T_{\mathrm{eq}}$)

Climate sensitivity quantifies the equilibrium temperature response to a specified change in forcing. Distinguish the response to doubled carbon dioxide from the gain per unit radiative forcing: for a linear net restoring coefficient $\lambda >0$ and constant forcing $F_0$, the gain is $1/\lambda$, whereas the equilibrium warming is $\Delta T_{\mathrm{eq}}=F_0/\lambda$. The forcing convention and the climate feedbacks permitted to adjust are part of the definition. A transient warming before the ocean heat content has adjusted is a different quantity.

A symmetric positive uncertainty interval for a stabilizing feedback coefficient produces asymmetric uncertainty in its reciprocal. With both cooling magnitude $x$ and forcing magnitude $f$ uncertain, constant-sensitivity lines are rays $x/f=\mathrm{constant}$; tangents from the origin to a Gaussian covariance ellipse give a one-parameter profile interval for the ratio. A unit-radius two-variable covariance ellipse is not itself a 68 percent joint confidence region.

The approximately proportional increase in global temperature per cumulative carbon-dioxide emission over a stated regime. Units must distinguish tonnes of carbon from tonnes of carbon dioxide.

Global mean surface warming near the time of carbon-dioxide doubling in an idealized experiment increasing concentration by one per cent per year. Ocean heat uptake generally keeps it below the equilibrium response.

The long-term global surface warming after atmospheric carbon dioxide is doubled and the modeled system reaches equilibrium, with stated feedback conventions. A response to another forcing amplitude must be rescaled before being called the conventional ECS.