The Music of Rivers: The Mathematics of Waves Reveals Global Structure and Drivers of Streamflow Regime

River flows change on timescales ranging from minutes to millennia. These vibrations in flow are tuned by diverse factors globally, for example, by dams suppressing multi-day variability or vegetation attenuating flood peaks in some ecosystems. The relative importance of the physical, biological, and human factors influencing flow is an active area of research, as is the related question of finding a common language for describing overall flow regime. Here, we addressed both topics using a daily river discharge data set for over 3,000 stations across the globe from 1988 to 2016. We first studied similarities between common flow regime quantification methods, including traditional flow metrics, wavelets, and Fourier analysis. Across all these methods, the flow data showed low-dimensional structure (i.e., simple and consistent patterns), suggesting that fundamental mechanisms are constraining flow regime. One such pattern was that day-to-day variability was negatively correlated with year-to-year variability. Additionally, the low-dimensional structure in river flow data correlated closely with only a small number of catchment characteristics, including catchment area, precipitation, and temperature-but notably not biome, dam surface area, or number of dams. We discuss these findings in a framework intended to be accessible to the many communities engaged in river research and management, while stressing the importance of letting structure in data guide both mechanistic inference and interdisciplinary discussion.