Saturday, January 26, 2008

Symmetries in the Global Temperature Record - Hadley CRUT3 Time Series

This post continues a series on the global temperature record, climate cycles and natural and human-caused temperature changes. I noted in my previous post that an update to the NOAA NCDC global temperature anomaly time series in January of this year muddled the intricate symmetries observed in the December 2007 NCDC release. This post will note that the December release of the Hadley CRUT3 global temperature anomaly time series contains similar numerical patterns.

I begin by noting that a zero month-to-month change in the global temperature anomaly will be treated as a "0" for the purpose of this analysis. The Hadley CRUT3 time series calculates the anomaly to three decimal places (rather than four for the NOAA NCDC time series); as a result, there are 14 zero monthly anomaly change values. The reader may question why I am making this assumption. Although I will give a more detailed explanation later on, the short answer is the assumption compensates for a likely anthropogenic effect (MUCH more on that later!).

The reader may recall from the previous post that the essential underlying pattern was of symmetries between the first and fourth periods and second and third periods respectively throughout the global temperature anomaly time series. For convenience, we repeat Table 10 from the previous post which sums across the corresponding 95 month periods for each of the four 380 month periods in the transformed NOAA NCDC time series:

Performing the same transformation using the December 2007 release for the Hadley CRUT3 global temperature anomaly time series gives the following result:

Although the symmetries in Table 10C are not perfect (as they were in Table 10), the numerical patterns are essentially the same. That is, the first and fourth and second and third periods are, respectively, symmetrical.

We next look at the first and third quarter symmetries in the Hadley CRUT3 time series. The tables are combined to ease comparison:

Note how in both quarters the first and fourth periods are symmetric while the second and third periods are symmetric across quarters. That is, period Q1a is symmetric with Q1d and period Q3a is symmetric with period Q3d while period Q1c is symmetric with period Q3c and period Q1b is symmetric, to a lesser extent, with period Q3b. To clearly compare these Hadley CRUT3 results with the NOAA NCDC results, the below table combines Tables 4 and 5 from my previous post:

The second and fourth periods of the Hadley CRUT3 temperature series contain numerical patterns similar to those found in the NOAA NCDC time series. For comparison, I repeat the results from Table 6 in the previous post for the comparable NOAA NCDC time series:

While there are differences in the results across the two time series, the signs are the same. Finally, I show the results for the four quarter periods for the two time series beginning with Hadley CRUT:

The similarities between the two time series are more significant than their differences. And why the differences between the two time series? The Hadley CRUT3 first differences (that is, the month-to-month anomaly temperature changes) have more volatility, especially before about 1940, than do the NOAA NCDC first differences. Thus, it is not surprising that the Hadley CRUT3 results appear, from the standpoint of the NOAA NCDC results, less "sharp". From such a standpoint, one may view the NOAA NCDC results as "better". Whether this is true or not, I will choose to focus on the NOAA NCDC results since they are, afterall, more asthetically pleasing and, essentially, more improbable.

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