Paul, you wrote in your CSALT model comment

>Regarding the thermodynamic analysis WRT global warming.

>I had the same idea and wrote about it here in the context of the CSALT model that I am working on

>http://contextearth.com/2013/10/26/csalt-model/

>I guess that’s what happens if one reads John’s forum and you get ideas. I provided a link to John’s post where he discusses variational principles.


The "thermodynamic analysis of global warming" is a sort of ongoing theme here in the Azimuth discussions and in global warming, which it should, as it is rather essential.
For example in this post on the wiki Frederic wrote about radiation balances. I was however not really up for a fully fledged analysis, but made just some comments, because amongst others I could imagine that the thermodynamic balance for forests is different than for a sheet of black metall. Like Planck's law (which is used for the Albedo argumentation) makes rather special assumptions and I could imagine that plants with their conversion into electrochemical energy could display a rather different behaviour, but I don't know.

And frankly I have problems with your CSALT model. That is the modelling of the temperature curve looks impressing, however I didn't see
at another place that mathematical problems
(with the software) were aliviated, moreover I have trouble to understand your derivation of the CSALT model.

That is I can somewhat see that a variational approach may in principle give a model, however I can't relate to what's written in your post Variational principles.

For the derivation you refer to a paper by W. Muschik, P. Van and C. Papenfuss.
I should point out that I personally know two of the authors, namely W. Muschik and C. Papenfuss. I had taken part in the one-semester thermodynamics lecture by W. Muschik, which
was a requirement for the physics diploma at TU Berlin. Chistina Papenfuss was about in the same year as me and I occasionally chit-chatted with her, while I was still at TU (which I left 14 years ago) It is interesting to see that she has been like me recently a lecturer for HTW. I have though been in media informatics at HTW and she has been in car construction. You can't live on this lecturing though, so I hope she has some other income sources or someone who supports her. The job market theoretical physicists/physical mathematicians in Berlin is tight....

Anyways I know two of the authors, but I don't know much about their work. The paper seems to be an overview article for insiders, that is quite some notation and quantities are introduced without much or no explanation and definition. Like e.g. the quantity q isn't even introduced and you can only guess that it is probably some kind of heat density flux. Their approach seems only somewhat similar to John's variational approach. In particular it seems they arrive at the free energy condition from an entropy principle not via Lagrange parameters, but via making some assumptions on the involved quantities and dynamics (which may eventually be similar, as assuming a Lagrange constraint).

However their assumptions are rather strict and I can't at all relate how your assignments:
>rho T S rightarrow Temperature and Heat Capacity

>rho epsilon rightarrow LOD as internal energy

go together with their definitions. Like why is the length of day an internal energy? It's a time.
Frankly it looks to me as that there are too many problems with your CSALT approach, that
it can't be saved.