San José State University
Thayer Watkins
Silicon Valley
& Tornado Alley

Statistical Characteristics of
the Record of Global Average Temperatures

The accepted record of average global temperatures is given below:

The temperature plotted on the vertical axis is the deviation of each year's temperature in degrees Celsius from the average temperature for the period. This is called the temperature anomaly. The average temperature for the period is 14°C.








Since there is the concern that matters have changed over time it is of interest to look the frequency distribution over different intervals. First the interval from 1856 to 1997 is split into two.



There is seemingly a sharp difference between the distributions. The average change for 1856 to 1926 is only 0.22°C per century where as for 1927 to 1997 the average change is 0.93°C per century. However in both cases the t-ratios indicate that the averages are not significantly different from zero at the 95 percent level of confidence. In both cases the distributions could be considered to be based upon normal distributions although the case for 1927 to 1997 looks as though it might represent a bimodal distribution; i.e., one that has to two peaks. It is notable that although the standard deviation of the temperature changes increased from 0.116°C/century to 0.129°C/century between the first seventy years and the second seventy years this is only an 11 percent change and not significantly different from no change.

To keep things in perspective a frequency distribution for a middle interval from 1880 to 1910 was created, as shown below, and it shows an average temperature change of −0.84°C per century.


Again the distribution is roughly that of a normal distribution. If this trend had been extrapolated the Earth's temperature would have been expected to decline by about 8°C by 2007 compared to 1910. This would be equivalent to another ice age. This points up the danger of making projections from limited ranges of variables. This is particularly true for variables which display autocorrelation. Such variables appear to follow trends even if there are no real trends in the system. In other words such variables display spurious trends. The autocorrelation structure of the global temperature changes is shown below.

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