Once is not enough

In the past I’ve explored simple energy balance models for the evolution of global average temperature. One of the important things to note is that a “1-box” energy balance model — in which the entire climate system is considered to have a single time constant — isn’t really sufficient. It can give a pretty good fit, but for a more realistic estimate you need at least two boxes. One represents rapid response to climate forcing — think of it as the “atmosphere” if you wish. The other is for slower response — think of it as “ocean” if you wish, or as “upper ocean,” or as “everything else.” One could be even more realistic with more than two boxes, after all the deep ocean certainly effects climate but with a longer time scale still, and there’s the cryosphere on top of it all, but rather than go the way of the full-blown computer simulation model, let’s see what happens if we just use a 2-box model with two time constants. We’ll think of box 1 as the atmosphere, so that it should correspond to the surface temperature we’re all familiar with.