Potential applications of the Benford’s Law for the investigation of hydrological time series alteration

The Benford’s Law, outlined in 1938, estimates the expected frequency of the significant first or first two digits of a time series of a generic variable based on a logarithmic pattern. Lower digits (i.e., 1, 2…) are expected to occur with frequencies higher than those associated to numbers with higher first digits (i.e., 8, 9). According to this law digit 1 typically occurs about 30% of the time, while 9 appears as significant first digit in less than 5% of the cases. The validity of Benford’s Law has been proven for a wide variety of data sets and in different contexts (e.g., public elections, false accounting detection, street addresses, stock and house prices, population numbers), among which few of hydrological relevance: lengths of rivers, river flow series, lake and wetlands extents. Nonconformity of hydrologic data sets to Benford’s Law could be a consequence of time series alteration and thus a signal of the presence of biases or errors, data modification, as well as of the fact that the sample is not fully representative of the variable or the series is affected by external drivers (e.g. anthropic alteration of the natural dynamics).

In this work we referred to more than 1200 GRDC sites to test the Benford’s Law validity over stream flow series longer than 40 years, as well as on the longest stream flow series (more than 12 million of data). Streamflow records have been investigated in parallel to other hydrological relevant datasets that serve as proxy for quantifying the potential human impact (e.g., GRanD-Global Reservoir and Dam Database, FFRs-Free Flowing Rivers). Results of this study, together with those of previous investigations (Nigrini and Miller, 2007) advocate that large hydrological data set should conform the Benford’s Law. On the contrary, the nonconformity to it might highlight data integrity and authenticity issue, or reveal alterations of the natural variability due to human activities or other driving factors (perhaps climate change).