Technical Note: A double-Manning approach to compute robust rating curves and hydraulic geometries

Abstract. Rating curves describe river discharge as a function of water-surface elevation ("stage"). They are applied globally for stream monitoring, flood-hazard prediction, and water-resources assessment. Because most rating curves are empirical, they typically require years of data collection and are easily affected by changes in channel hydraulic geometry. Here we present a straightforward strategy based on Manning's classic equation to address both of these issues. This "double-Manning" approach employs Manning's equation for flow in and above the channel. Flow across the floodplain can follow either a Manning-inspired power-law relationship or, in the common case of a rectangular floodplain and valley-wall geometry, a second application of Manning's equation analogous to that applied within the channel. When applied to ample data from established stream gauges, we can solve for Manning's n for in-channel flow, channel-bank height, and two floodplain-flow variables. When applied to limited discharge data from a field campaign, additional constraints from the surveyed floodplain cross section permit a fit to the double-Manning formulation that matches ground truth. Using these double-Manning fits, we can dynamically adjust the rating curve to account for evolution in channel width, depth, and/or slope, as well as in channel and floodplain roughness. Such rating-curve flexibility, combined with a formulation based in flow mechanics, enables predictions during times of coupled hydrologic–geomorphic change. Open-source software with example implementations is available via GitHub, Zenodo, and PyPI.