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Discussions of climate sensitivity tend to talk about "climate response to a doubling of greenhouse gases". More generally, the additional forcing is expressed in terms of a logarithm $$ \Delta F = \alpha \ln (C/C_0) $$ where $\Delta F$ is forcing, $\alpha$ is a constant (the climate sensitivity), $C$ is the current GHG concentration and $C_0$ is a reference value.
What is the reason for the logarithm? Does it arise from some fundamental physical principle, or is it an empirical fit to modeling output? Any references to a derivation? The only one that I found is "Logarithmic Response and Climate Sensitivity of Atmospheric CO2", S.H. Lam, 2007 (see here), but there must be others.