Separating Signal from Noise in the Global Warming Data

  I stumbled upon an interesting way of doing a curve fit a few days ago that is a variant of the idea behind Chebyshev polynomials. Instead of using fixed polynomials though one finds a series of best fitting polynomials of increasing degree to the successive remainders of the data fits. One also needs to re-scale the time about a mean value to keep the powers involved in the polynomials manageable. In the case of the global land anomaly the fit soon reaches the point of diminishing returns.

I found that an 8-degree polynomial gives a reasonably good fit for the anomaly with an approximately linear start and finish. To limit the sensitivity of the fit to the ends I used 5 year buffers with a lower statistical weight (0.25 vs 1) in the sums involved. 

The quick approach to a limiting value for the rms error as one increases the degree of the polynomial seems to indicate that most of the data is "noise." As one increases the degree of the polynomial a point is reached where the any remaining global warming is masked by the fluctuations present present in the data. The 6-degree polynomial shows a sharp downturn in the fitted curve on the right side. The 10-degree polynomial shows a rapid change on the left side. The results are similar to the 20-year average used for the prediction made in October 2013 but much easier to do. But effects analogous to the Gibbs phenomenon and large fluctuations interfere with making an accurate prediction of what will happen.

  It's been reported in the news lately that the global warming anomaly will pass the 1°C mark this year. It appears the global land anomaly has already done so.