Abstract
Working with a large temporal dataset spanning several decades often represents a challenging task, especially when the record is heterogeneous and incomplete. The use of statistical laws could potentially overcome these problems. Here we apply Benford’s Law (also called the “First-Digit Law”) to the traveled distances of tropical cyclones since 1842. The record of tropical cyclones has been extensively impacted by improvements in detection capabilities over the past decades. We have found that, while the first-digit distribution for the entire record follows Benford’s Law prediction, specific changes such as satellite detection have had serious impacts on the dataset. The least-square misfit measure is used as a proxy to observe temporal variations, allowing us to assess data quality and homogeneity over the entire record, and at the same time over specific periods. Such information is crucial when running climatic models and Benford’s Law could potentially be used to overcome and correct for data heterogeneity and/or to select the most appropriate part of the record for detailed studies.
Highlights
Benford’s Law (BL) is an empirically discovered property related to the frequency of first digits occurring in “real-world” datasets[1]
While we have shown that BL prediction over the complete dataset is verifiable, a large deviation within the temporal record can clearly be attributed to technological improvements
The quality of discrete timespans within the dataset can be evaluated using BL, as demonstrated by the fact that the clustering of tropical cyclones (TC) events resulting from measurement precision was clearly observable in the BL misfit
Summary
Benford’s Law (BL) is an empirically discovered property related to the frequency of first digits (sensu stricto numerals from 1 to 9 forming numbers and values) occurring in “real-world” datasets[1]. It states that in certain datasets the leading digit is distributed in a predictable but non-uniform manner. This property arises in many situations but is known to occur when the underlying measurements have a log-uniform distribution: Prob (first digit = d) = lo g10 (1 + d−1), d = 1, ..., 9 Such datasets are often associated with a power-law distribution with a “heavy tail,” making extreme events far more likely than they would be, for example, in a Gaussian distribution. ® direct influence of El Niño/La Niña; (Figure made with ArcGIS software and Corel Draw X5)
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