Why don't climate scientists use Feynman diagrams?

This paper, purporting to prove that the atmospheric greenhouse effect violates the second law of thermodynamics and therefore cannot exist, was apparently published in the International Journal of Modern Physics -- not the world's leading journal in the field, but hardly a crackpot publication.

Among the gems in the paper (spotted here) is this (pp 59-60 of the arXiv version): Climatological radiation balance diagrams...

1. cannot represent radiation intensities, the most natural interpretation of the arrows depicted in Figure 23, as already explained in Section 2.1.2 and Section 2.1.5;
2. cannot represent sourceless fluxes, i.e. a divergence free vector fields in three dimensions, since a vanishing three-dimensional divergence still allows that a portion of the field goes sidewards;
3. do not fit in the framework of Feynman diagrams, which represent mathematical expressions clearly defined in quantum field theory [159].
4. do not fit in the standard language of system theory or system engineering [160].

I kid you not. So radiation balance diagrams should fit in the framework of Feynman diagrams or system engineering diagrams?

In case you're wondering: section 2.1.2 supplies some basic definitions of radiation intensity and flux. Section 2.1.5 says "In classical radiation theory radiation is not described by a vector field assigning to every space point a corresponding vector..." but in fact mentions that the "modern" (not so modern, actually) description uses the Poynting vector, and also talks of black body radiation and its variation from real spectra. Nowhere do I see any relevance to point 1 here. As for point 2, so what?

Also, in case you are wondering, reference 159 is to the standard text on quantum field theory by Itzykson and Zuber, and reference 160 is to the SysML site. Apparently climate scientists should be specifying their Feynman diagrams in SysML.

More here (that blog takes the credit for spotting the Feynman Diagram thing: I didn't wade through the first 60 pages of it myself!)

The authors apparently submitted this paper in 2007 and it got accepted in 2009. It reads like a prank (after Sokal, I suppose one sees prankery everywhere). But apparently they are serious, and apparently the journal editors didn't care to take a second look at it, despite its bombastic title.