Cool visualization. It's worth keeping in mind that the modeled data lines up with reality because it's supposed to. That's how you calibrate your model, by making sure it fits reality. The real trick is to see how well your model extrapolates from the data you have out into the future. As in, if you feed it data up to, say, 1990, will it correctly spit out 2015 temperatures that fit the reality of 2015, or will it s…
"The real trick is to see how well your model extrapolates from the data you have out into the future." That is the most common way to show the modeller is not shamelessly overfitting.:-| Another way, though, is less common but not vanishingly uncommon: the model may be so much simpler than the data it fits that overfitting is not a plausible explanation. (Roughly there are too many bits of entropy in the match to th…
Occam's razor is a rule of thumb and an aesthetic boon, but nothing more.
The real test is that you have a theory that is meaningful and has explanatory power. If it grants insight on the mechanisms that are driving the relationships or generating the data and these make sense - you are pretty golden.
Another one is that the theory makes unexpected predictions that you can then test. This is a real winner, and why complex physics is so well regarded.