Utilising Benford's Law in the Validation of Precipitation Datasets

ABSTRACT The increasing magnitude and complexity of precipitation datasets necessitate robust and efficient data integrity assessment. This study systematically applies Benford's Law, a mathematical theorem describing leading digit frequencies, as a novel diagnostic tool for precipitation data in the environmental and hydroclimate sciences. We present a reproducible and robust methodology, demonstrating that global monthly precipitation consistently conforms to Benford's Law across diverse data types, including raw observations, gridded products, reanalysis and synthetic simulations. This key finding fundamentally challenges traditional assumptions regarding the influence of data origin on Benford's Law adherence, significantly broadening its applicability. Our findings underscore the importance of underlying quantitative characteristics for successful application: while regional analyses reveal that monthly precipitation data in the United Kingdom and Ireland do not conform to Benford's Law‐based principles, a shift to daily temporal granularity successfully restores conformance, highlighting how temporal resolution can introduce the necessary data properties. This research uniquely positions Benford's Law as a powerful, complementary diagnostic tool capable of detecting subtle data corruptions, as demonstrated through an artificial experiment. Ultimately, this work advances the utility of Benford's Law in climate research, providing a scalable method to enhance the reliability of foundational datasets critical for climate modelling, forecasting and a wide array of hydroclimatological applications.