Localised instant climate sensitivity for 2xCO2

X-axis: surface temperature,
Y-axis temperature offset for 3.7 W/m2

Following the discussion with Lord Mockton on Wattupwiththat. I calculated the Stefan-Boltzmann temperature needed to adjust for a forcing of 3.7 W/m2.

It turns out that the hotter the surface, the less temperature increase is needed to offset the forcing.

Stefan-Boltzmann law: I = σT4

What the graph is saying is that a constant 3.7 W/m2 is inverse proportional to the first derivative of the Stefan-Boltzmann law

dI/dT = 4 σT3

Which gives dT = dI/(4 σT3),

or in approximation
ΔT = 3.7/(4 σT3)

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