Nonlinear Least Squares Fits

  The angular frequency, ω, is one of the unknowns for the fit functions used and complicates finding the best least squares fit. However if ω is known we can do an ordinary linear least squares fit since the functions used are linear functions of the coefficients. One can compare the variance for different values of ω and look for the one with the lowest variance. I was doing the fits using trial and error and got an optimal fit for function with the second harmonic that had problems at both of the smoothed curve for the data. I tried again and got one at a lower value for ω. This spurred a rewrite of the program that I was using to allow a scan of the ω values. This is the result that the scan produced.

It may be possible that the same functional form has more than one good fit and this can contribute to the uncertainty about what is happening w.r.t. global warming. Another possibility is that the smoothed curve may be slightly off since the signal may not be absolutely perfect and that could throw off the fit off as well.