Before you go too far down the path of CO2-climate sensitivity, please
consider the work of Ed Lorenz who was interested in models that
emulate sudden jumps from one equilibrium state to another, in
patterns similar to the paleo-climatic record.

In his paper "Climate is what you expect," Lorenz wrote:
A climatologist encountering [fluctuations in real data] could not, on
the basis of the data alone, say whether the dominant cause of the
changes was external or internal.

Elsewhere (climate of the model), for climate variations over a 100-
year interval, as given by a simple one equation model designed to
support internally produced climatic changes:

"Two or more distinct climates may well be compatible with the same
external conditions."

 Finally:
"If the climate system is treated as a dynamical system--a system
whose evolution is governed by precise laws, or, more frequently, by
equations that represent such laws, the climate then becomes
identifiable with the attractor of the dynamical system—but the
dynamical system may have more than one attractor!"

Can we rely on single variable linear or logarithmic (non-chaotic)
forcing to predict the future state of the climate system?

Jim

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