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"), and 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 equation to address both of these issues. This "double-Manning" approach employs Manning's equation for flow in and above the channel and a Manning-inspired power-law relationship for flows across the floodplain. When applied to data from established stream gauges, we can solve for Manning's n, channel-bank height, and two floodplain-flow parameters. When applied to limited data from a field campaign, constraints from Manning's equation and the surveyed cross section permit a robust fit that matches ground truth. Using these double-Manning fits, we can dynamically adjust the rating curve to account for channel width, depth, and/or slope evolution. Such rating-curve flexibility, combined with a formulation based in flow mechanics, enables predictions amidst coupled hydrologic – geomorphic change, which increasingly occurs as climate warms and humans modify the land surface and subsurface. Open-source software with example implementations is available via GitHub, Zenodo, and PyPI.