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.
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.