I simply gave you my understanding.
Here, I just found this
http://rankexploits.com/musings/2011/berne-first-order-co2-absorbtion/ for you. It will save me a great deal of time and frustration if you will just study the article at the link which explains the Bern Model in a manner consistent with my own interpretation of the formula; thus saving me endless frustration and a great deal of time if I were to attempt to explain it in more detail, and as I mentioned I have no scientific software here that would allow me to properly input the Model's equations. I have access to such, but am not inclined to bother. If you have a different interpretation then mine, I'd be happy to consider it.
The basic problem is that the model provides results that differ from experimental observation. Therefore the model is at best only very approximately right. But my opinion is that it is so flawed as to be no longer useful at all other than as a means of comparing what would occur were the assumptions and the values of the parameters underlying the Bern Model correct.
I am in no way putting down those who developed the model, it was a best effort at the time, 1992 I think. Now it is time to move on.
There are no scientists whose work I have respect for saying that anthro CO2 contributions are unimportant, what they are saying is we don't know how important they are, but it looks more and more like they are less important to climate change then we had previously thought. Those who are jumping to conclusions that this is a settled matter, and the layman can not be faulted for that, are making what for trained scientists is a classic mistake.
I heard Mayor Bloomberg expounding on climate change in an interview of the bloomberg website. He is a very smart guy, but he is a businessman, not a scientist, and he can't evaluate the state of the our understanding directly. He has to rely on the conclusions of various panels as filtered through the news media. When you look at the unfiltered results you get different picture. One in which our understanding is very much in flux. It's unfortunate that this issue has been so politicized because it should have nothing to do with left/right politics (and I wish Jem and FC, for all their good contributions to the discussion here, would stop characterizing it that way).