Friday, October 4, 2013
A Surprisingly Good Fit For The Anomaly Using A 20 Year Average
To reduce the effect of a damped random walk on the smoothed land northern hemisphere anomaly I increased the period for the average to p = 20 years and separated "signal" from "noise." When I smoothed the difference between the anomaly and the 20-year average with another 20-year average and compared it with smoothed anomaly it appeared to be present in the smoothed anomaly. Subtracting the smoothed difference from the smoothed anomaly improved the separation of signal and noise and resulted in a very smooth curve for this adjusted averaged anomaly.
Assuming a cubic curve plus a sinusoidal curve for the form of the function to be fitted produced a very accurate fit for the adjusted averaged anomaly. The value for t used in the fit was the difference between the time in years and the midpoint of the 20-year average data which was 1946.7917.
The values for the monthly standard deviations were similar to those found previously.
Using the weighted sum of the monthly probabilities for the yearly distribution of the variable part of the anomaly gave essentially the same distribution as before.