Dangers of multiyear averaging in analyses of long-term climate trends

Multiyear averaging in studies seeking long-term trends can be risky and misleading. It is shown here that a change of 1 year in the starting point of the averaging done in generating a multiyear-average sequence can make a dramatic difference in the appearance of the sequence, even including whether the apparent trend is upward or downward. An example is given in which the same time series, when grouped to 3-year averages by starting in turn at the first, second, and third points of the series, yields one 3-year-average sequence that is monotonically increasing, a second 3-year-average sequence that is monotonically decreasing, and a third 3-year-average sequence that has constant values. Furthermore, it is proven in general that such series can be created for n-year averages for any integer n > 2, and can be extended to exceed any desired length. Finally, historical sea-ice data from Iceland are used to illustrate with a long-term climate data set the misrepresentation of climate statistics which can occur through selective multiyear averaging.