New Computer Fund

Wednesday, December 19, 2012

Interesting Comment

When I see the phrase “equilibrium climate sensitivity”, it’s clear to me the writer has no understanding of the meaning of either equilibrium or climate sensitivity. The latter is no more an equilibrium parameter than the conductivity of a 1M KCl solution. Were I to be generous, I might suppose a steady-state sensitivity was really meant, but steady-states are not equilibrium states and require a steady input of energy to prevent their relaxation towards equilibrium. It is the dissipation of this energy which goes to the heart of understanding climate sensitivity.
It has been increasingly apparent to many observers that something is wrong with the theory underlying computer simulations – and it’s not just a matter of parametric tunings for aerosols, etc. I can see two worthy questions for technical discussion and resolution wrt to the whole GHG fiasco.
1. Why is current AGW/CAGW theory wrong and how are its shortcomings manifest in its conclusions?
2. Is there a better analytical approach?
As to the first, mathematical descriptions of convection and feedback do not yet rise to the level of even being wrong.
As to the second, I believe there is. Current models are formulated in terms of the differential calculus – beloved of all programmers. For the analysis of complex problems, the integral calculus has some distinct advantages – e.g. thermodynamics. An elementary example: the Carnot equation for the maximum amount of useful work obtainable from a heat engine operating between two given temperatures. Within such an engine, convection is surely involved. Here we have a rigorous result for a process which has yet to be understood microscopically but can still be described in terms of a functional relation between surface fluxes and potentials.
Without spoiling your fun, I offer you three postulates:
Ju = Jf + TJs
div Ju = 0
div Js = Ju dot grad(1/T)
The first is a Helmholtz expression connecting local flux densities of energy, free energy, and entropy. The second, a definition for the steady state. The third, Onsager’s expression for the local creation of entropy.
From these postulates, one can derive a rigorous expression for the climate sensitivity of any system bounded by two isothermal surfaces through which only energy enters and departs.
Hint: define sensitivity as the change in free energy dissipation wrt the temperature of the warmer interface.
IMO: If you want to talk about climate sensitivity show the math, not the rhetoric.
Stolen from Dr. Curry's Climate Etc.
Close in my opinion.  The problem is still the Tale of Two Greenhouses.  

I am totally into the idea of isothermal boundary layers and the static model with moist air boundary allows estimation of dissipation through that "envelope", but the overlap of the ocean/atmosphere isothermal boundary layer complicates Quondam's elegant but not quite there model concept.  One hell of an improvement though.  
There is still the minor issue of time frames.  60 years appears too short for a reasonable estimate on the ocean energy flux, with a likely 1470 +/- 500 years pseudo cycle which could have a +/- 1C impact.  
Oh, there appears to be a new member of the SOC club :)

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