[mac01021]

I understand that from a variety of factors including greenhouse gas concentration, albedo, and solar intensity you can, in principal, compute the earth's atmosphere's equilibrium mean temperature.

I understand this function to be such that any doubling of the atmosphere's CO2 concentration (while holding the other factors constant) will increase the equilibrium temperature by the same fixed number of degrees.

One thing I know nothing about is how to expect the earth's actual temperature to change over time when there is a difference between actual and equilibrium temperatures.

Suppose A(t) is the earth's actual temp at time t and E(t) is the earth's equilibrium temp at time t.

   Presumably, dA/dt = F(A,E), for some function F.

Is anyone here physics-savvy enough to know what F looks like?

[itcrowd]

Well.. it is complicated. Depending on what exactly you want to know, you could look into the concept of "Transient Climate Response" (e.g. start at [1]).

[1] https://www.nature.com/articles/nature08047