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I tried smoothing the temperature data with running means for 3, 5, and 10 years (see issue #8). The results files are all virtually identical, with the only differences being very slight changes in beta and the objective function values being 0.1 less than in the initial experiment.
To determine if the lack of change is because of a bug, I decided to do an optim run on temperature data that was smoothed for a running mean of 50 years, but I still got similar results.
As far as I can tell, there isn't a bug in my code, but I definitely could have missed something. My best guess is that the lack of change in results is because the smoothed temperature MSEs are still much lower magnitude than the CO2 MSEs. These results could also have something to do with beta and Q10 being on the boundaries of the "box" of valid values.