Verifying the prevalence, properties, and congruent hydraulics of at-many-stations hydraulic geometry (AMHG) for rivers in the continental United States

Hydraulic geometry (HG) has long enabled daily discharge estimates, flood risk monitoring, and water resource and habitat assessments, among other applications. At-many-stations HG (AMHG) is a newly discovered form of HG with an evolving understanding. AMHG holds that there are temporally and spatially invariant ('congruent') depth, width, velocity, and discharge values that are shared by all stations of a river. Furthermore, these river-wide congruent hydraulics have been shown to link at-a-station HG (AHG) in space, contrary to previous expectation of AHG as spatially unpredictable. To date, AMHG has only been thoroughly examined on six rivers, and its congruent hydraulics are not well understood. To address the limited understanding of AMHG, we calculated AMHG for 191 rivers in the United States using USGS field-measured data from over 1900 gauging stations. These rivers represent nearly all geologic and climatic settings found in the continental U.S. and allow for a robust assessment of AMHG across scales. Over 60% of rivers were found to have AMHG with strong explanatory power to predict AHG across space (defined as r2 > 0.6, 118/191 rivers). We also found that derived congruent hydraulics bear little relation to their observed time-varying counterparts, and the strength of AMHG did not correlate with any available observed or congruent hydraulic parameters. We also found that AMHG is expressed at all fluvial scales in this study. Some statistically significant spatial clusters of rivers with strong and weak AMHG were identified, but further research is needed to identify why these clusters exist. Thus, this first widespread empirical investigation of AMHG leads us to conclude that AMHG is indeed a widely prevalent natural fluvial phenomenon, and we have identified linkages between known fluvial parameters and AMHG. Our work should give confidence to future researchers seeking to perform the necessary detailed hydraulic analysis of AMHG.