The detection of weekly preferential occurrences and applications to rainfall

The detection of weekly preferential occurrences in atmospheric and hydrologic processes has recently attracted much attention as a way to identify the signature of anthropogenic climatic changes. The interpretation of previous analyses, however, is not unequivocal, in part as a result of a lack of widely accepted statistical criteria. Here, a general and exact method to detect the presence of weekly preferential occurrences is developed and applied to long rainfall observations in Marghera, Italy; Philadelphia, Pennsylvania; and Portland, Maine. The method makes use of the fact that, under the null hypothesis of stationarity, the process of event occurrence in the different days of the week is equivalent to the random distribution of a number of balls (the wet days) in a set of boxes (the days of the week). The departure from a homogeneous distribution is then characterized through the probability of the maximum number of balls in a box, which can be computed exactly with no ad hoc assumptions. The new method shows that (i) preferential rainfall weekly occurrences emerge in all cases in the most recent period analyzed (1990-2006), while they are absent-or are too weak to be detected-in previous years (before 1989); and (ii) the balls-in-boxes approach appears to be more sensitive than Pearson's test when deviations from homogeneity are associated with just one day of the week, a common occurrence in connection with day-of-the-week effects. The results presented help to reconcile previous contrasting studies and to contribute compelling evidence that anthropogenic changes in the local climate have occurred over the past century in urban and industrial areas.