I've been working on separating the diffusion function from the drift function for the monthly global land anomaly for the years 1880 through 2012 and found a small steady seasonal change in the monthly anomalies that amounts to about 0.2 °C per 100 years. The change during the year is nearly sinusoidal producing relatively warmer winter months and cooler summer months.

To get a better estimate of the diffusion function for the anomaly I determined the yearly averages for use as the drift function and subtracted the anomaly values from these. Then I subtracted the seasonal change above. The differences were sorted by month to get the monthly means and the standard deviations for normal distributions in order to produce an equivalent probability function that was the weighted sum of the monthly normal distributions. The estimated probability distribution, p, gave a good fit for the diffusion data. The scale for the anomaly, x and ξ, between -2 and 2 was divided into 300 parts to obtain the frequencies for the diffusion histogram Φ. The calculated frequencies, F, were found by integrating the probability distribution, p(x), over the sub-intervals and multiplying this by the number of diffusion data points, N=1596.

The procedure above removed some of the "contaminants" present and consequently reduced the width of the peak of the diffusion function slightly. The result is a better measure of the short term random fluctuations in the anomaly.

Supplemental (Nov 11): The diffusion function by definition has a mean of zero and the seasonal change was measured relative to this average. The seasonal change tells us that the difference between summer and winter temperatures has been slowly decreasing over time but says nothing about their changes relative to the reference temperatures of the anomaly. Changes in the annual mean are associated with the drift function.

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