The different styles of computer modelling used by "The Right Climate Stuff" (TRCS) group and the mainstream climate scientists reminds me of a conversation I once had with a manager when I was working in the UK nuclear industry back in about 1997. This manager had been the head of the department I had worked in for many years, but he then got moved sideways to make way for somebody else who was being 'fast-tracked', and he was given a job as something like a techical manager responsible for maintaining technical standards. The department did a lot of computer modelling, and this manager remarked to me that in all the candidates that were currently applying for jobs with the department, he was no longer seeing anybody in interviews who he would describe as being 'mathematical modellers' - they were all what he would describe as 'geometric modellers'. He thought that the traditional style of computer modelling, mathematical modelling, was on the way out, and did not regard that as being a desirable trend.
To provide some definitions of what I think this manager was talking about:
'Mathematical modellers' would be people who generally like to keep the computer model as simple as possible. Some of this desire to keep things simple originated from entering the world of computing at a time when computers were very slow, had little RAM (even though old mainframe computers filled a room, they had little RAM), and were tricky to use (input files might have to be entered using a deck of punched computer cards for example). These people tended to be good at maths, and did lots of background reading and checked up in the literature on how similar problems had been tackled in the past. They were also pretty keen on validation of computer models, partly to justify the use of simplified models.
'Geometric modellers' would be people who literally model the geometry, whatever the geometry is they chop it up into a detailed model of finite elements or grid cells. These people became more prevalent in the computer modelling field as computers got faster, had more RAM and became easier to use, though you did still get a few geometric modellers even back in the 1970s. These people tended to be quite mediocre at maths in comparison with the mathematical modellers, and were too busy sitting at a computer terminal to do any reading. They were less keen on validation, as they regarded that as being more the software developer's problem than theirs.
I can see some advantages in employing geometric modellers over mathematical modellers. One is that the geometric modellers tended to be more 'computer literate', they had often grown up with computers and liked playing around with them, whereas the mathematical modellers would tend to be less up-to-date with the computing world and a few even actively disliked computers. Another is that the geometric modellers' work would look a lot more professional, as they were able to produce all sorts of fancy countour-filled plots of results and animations of results. Project management type people also seemed to prefer the geometric modellers, because their style of computer modelling looked better from the point of view of reporting progress. Mathematical modellers might try out an idea and then throw it away if it didn't work, which looked terrible from a project management viewpoint.
Disadvantages of employing geometric modellers over mathematical modellers would be that computer modelling projects would generally tend to be more expensive, and there might be a greater probability of there being some overlooked 'howler' sitting somewhere in the analysis.
In terms of applying this terminology to climate modelling, the mainstream climate modellers would be geometric modellers. Even the veterans in climate modelling, like the now retired James Hansen, are geometric modellers. The ex-NASA people making up the TRCS group, are by contrast mathematical modellers.