Climate sensitivity

Builds on Radiative forcing Climate model

Definition

Let $\Delta T$ be the change of the global mean surface temperature from its preindustrial equilibrium. Let $N$ be the net downward radiative flux at the top of the atmosphere. In the linear forcing-feedback model, a radiative forcing $\Delta F$ gives $N = \Delta F - \lambda \, \Delta T,$ where $\lambda > 0$ is the climate feedback parameter, in $\mathrm{W\,m^{-2}\,K^{-1}}$ .

The equilibrium climate sensitivity (ECS) is the value of $\Delta T$ at equilibrium ( $N = 0$ ) after carbon dioxide is doubled and then held fixed. In the linear model, $\mathrm{ECS} = \Delta F_{2\times} / \lambda$ , with $\Delta F_{2\times}$ the forcing of the doubling.
The climate sensitivity parameter is $1/\lambda$ , the equilibrium warming per unit forcing.
Let carbon dioxide rise by $1\%$ per year. The transient climate response (TCR) is the value of $\Delta T$ at the time of doubling, averaged over 20 years.

Remarks

Example: in the zero-dimensional energy balance model with outgoing flux $\sigma T^4$ and no other feedback, $\lambda = 4 \sigma T_e^3$ at the emission temperature $T_e \approx 255$ K, so $\lambda \approx 3.8 \ \mathrm{W\,m^{-2}\,K^{-1}}$ . With $\Delta F_{2\times} \approx 3.7 \ \mathrm{W/m^2}$ this gives an ECS of about $1$ K, the no-feedback sensitivity. Positive feedbacks lower $\lambda$ and raise the ECS.

Non-example: the warming observed while the concentration is still rising is not the ECS, since the deep ocean is still taking up heat and $N > 0$ . It is closer to the TCR, which is smaller than the ECS.

The assessment of the IPCC in 2021 gives a likely range of $2.5$ to $4$ K for the ECS, with a best estimate of $3$ kelvin. In climate models the feedback parameter is often estimated after an abrupt quadrupling of carbon dioxide. One regresses $N$ against $\Delta T$ and reads $\lambda$ from the slope.

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Tag	`7AC9KYPCNY`
URI	`m2://7AC9KYPCNY`
Kind	definition
Writing	W0 stub
MSC	86A08
Defines	Climate sensitivity
Uses	Radiative forcing, Climate model
Changed	3 November 2026

Climate sensitivity

Definition

Remarks

Reading path

Further reading

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