Identifying weekly cycles in meteorological variables: The importance of an appropriate statistical analysis

Weekly cycles in several meteorological parameters have been previously reported. Yet the extent to which these cycles are caused by anthropogenic activity remains unclear. Some of the complications associated with establishing this link are discussed here. Specifically, we highlight and quantify some common errors that have been made in the application of statistical techniques to this problem. Some errors, including the inappropriate use of the Student t test, have been significant enough to affect the conclusions of previous studies. A resampling technique that can properly account for both temporal and spatial correlation is evaluated and is shown to be accurate for determining the statistical significance of weekly cycles at the station level and for evaluating total field significance. We demonstrate that this resampling approach performs comparably to a Fourier analysis that evaluates the significance of the power at a seven-day period. Regardless of the analysis technique used, an understanding of the behavior of and uncertainties associated with the statistical analysis is critical to arriving at a justifiable conclusion regarding a human influence on weekly cycles and for putting results in context with other studies. We also discuss some general errors that can be made in weekly cycle analysis. These include selection of an analysis region after identifying where weekly cycles are significant, acceptance of a physical explanation for the hypothesized link that has not been properly tested given its large number of degrees of freedom, and ignoring the correlation among meteorological parameters.