Measuring Bedload Motion Time at Second Resolution Using Benford's Law on Acoustic Data

Bedload transport is a natural process that strongly affects the Earth's surface system. An important component of quantifying bedload transport flux and establishing early warning systems is the identification of the onset of bedload motion. Bedload transport can be monitored with high temporal resolution using passive acoustic methods, for example, hydrophones. Yet, an efficient method for identifying the onset of bedload transport from long-term continuous acoustic data is still lacking. Benford's Law defines a probability distribution of the first-digit of data sets and has been used to identify anomalies. Here, we apply Benford's law to continuous acoustic recordings from Baiyang hydrometric station, a tributary of Liwu River, Taroko National Park, Taiwan at the frequency of 32 kHz from stationary hydrophones deployed for 3 years since 2019. We construct a workflow to parse sound combinations of bedload transportation and analyze them in the context of hydrometric sensing constraining the onset, and recession of bedload transport. We identified three separate sound classes in the data related to the noise produced by the motion of pebbles, water flow, and air. We identify two bedload transport events that lasted 17 and 45 hr, respectively, covering about 0.35% of the total recorded time. The workflow could be transferred to other different catchments, events, or data sets. Due to the influence of instrument and background noise on the regularity of the residuals of the first-digit, we recommend identifying the first-digit distribution of the background noise and ruling it out before implementing this workflow. Long-term, high-frequency monitoring of Earth surface processes brings huge data sets that can be of high quality. Benford's Law defines the specific probability distribution of the first-digit of the data sets and has been used to identify anomalies and high-energy events. We provide a workflow for applying Benford's Law to identify the onset of the motion of coarse sediment along the river bed at a time resolution of seconds. Since Benford's Law has demonstrated usefulness in acoustic amplitude analysis in this study, it could serve as a tool for identifying anomalous events in any kind of real-time data series, which could be beneficial for generating event samples for machine learning applications. Long-term, high-frequency acoustic monitoring constitutes huge-volume data sets with a low signal-to-noise ratio The distinct first-digit distribution between signal and noise can used to filter out 99% of background noise from acoustic recordings We applied the method to a three-year-long acoustic data set in Baiyang, identifying two bedload transportation events