Data-driven discovery of dimensionless numbers for extreme flow

Extreme climate events (e.g., extreme rainfall and glacier melting) in alpine areas can result in significant runoff or mass movements (e.g., flash floods and debris flows) that pose substantial threats to human life and infrastructure downstream. However, due to sparse measurements, understanding the sediment transport mechanisms that control these processes still needs to be completed. Scaling laws and dimensionless numbers provide valuable insights into complex physical systems and processes. Several dimensionless numbers (e.g., Einstein number and Savage number) have been proposed to investigate the relative importance of different sediment transport-related stresses for different systems or processes. In this study, we propose a new data-driven approach that embeds the principle of dimensional analysis in an unsupervised machine learning scheme to discover the best combination of dimensionless numbers that can describe sediment transport mechanisms in torrent processes. We reduce high-dimensional parameter spaces (12 dimensions) to descriptions involving only a few (about 3-4) physically interpretable dimensionless numbers. Using a unique field dataset, we demonstrate this idea to investigate the transition in different transport mechanisms. The result is generally applicable criteria that can improve existing classification models and aid in developing appropriate hazard assessments in mountainous regions based on scarce hydrologic measurements.