Comparison Of Higher Order Fits For The Monthly Global Land Anomaly

  The "residuals" for the second harmonic fit of the global land anomaly showed what look like a third harmonic so I did two higher order fits. The first assumed there was a third harmonic present in the data and the second was just a polynomial fit. The resulting residuals showed an improvement along the smoothed anomaly for the first fit but the second still showed what looked like the presence of a third harmonic.

The higher order fits seem to favor periodic terms over non-periodic terms. Both projections are roughly in agreement for a period of about 10 years. Each fit had 24 months outside the 3σ limits for a total of 1604 months which is 1.50%. The expected value for the fitted probability distribution is 1.15%.

Supplemental (Oct 14): The statistics above were based on deviations of the anomaly from the unsmoothed 20-year average. I checked the statistics for deviations from the smoothed 20-year average and the results were slightly different. The standard deviation was σ = 0.315. The fit for the 3 harmonics had 19/1604 months (1.185%) outside the 3σ limits. The polynomial fit had 23/1604 months (1.434%) outside the 3σ limits. For a normal distribution with σ = 0.315 one would expect the number of outliers to vary from 13.5 to 21.9 with the expected number being 17.7 (1.103%). The polynomial fit may already be encountering some problems. The terms with the higher powers have more influence away from the center and affect the long term projections more.