Chief Hydrologist insists on writing this in multiple comments:
There is an energy equilibria of sorts at the top of th atmosphere -
dS/dt = Ein – Eout – where dS/dt is the change in planetary heat content (plus enthalpy if we are being pedantic).
Whereas in precise mathematical terms, the E terms are in defined in the dimensions of energy (and not power) so the correct formulation is:
dS/dt = d/dt(Ein – Eout)
What this says is that for changes in the energy balance over time (the right hand side) leads to a perturbation in the net energy flow (the left hand side). Over the long term, the net has to approach zero, otherwise we are not conserving energy
dS/dt = 0
This formulation allows us to apply Stefan-Boltzmann’s law where dEin/dt is the solar insolation (given in power per cross-sectional area) and dEout/dt is the statistical mechanical derivation of a black body radiator. This generates the first-order estimate of the planet’s temperature in the absence of GHG. Adding in the GHG’s gives us a gray-body modification that elevates the temperature beyond what the black-body SB law states.
For purposes of a more sophisticated analysis, we can leave it in the non-zero differential form, as this is useful for defining a forcing function perturbation. In this case we can estimate the transient response and the evolution to a steady state value. This is where terms such as the ocean’s heat capacity would fit into a spatio-temporal master equation.
Chief Hydrologist needs to go back over his arguments, as he is coming perilously close to joining the clown list I am compiling, where he can meet up with the other circus freaks, such as his brother Sideshow Bob.
I know that the Chief has the reputation of the smartest man in the room among climate skeptics on this blog, but I tend to think of his rants as Krugman describes Newt Gingrich, “A stupid person’s idea of what a smart person sounds like.”. I wouldn’t let Chief get near a classroom.