Flexible and physically based stage–discharge rating curves using a "double-Manning" approach

Abstract

Rating curves translate between river stage (i.e., water level) and water discharge. They are applied ubiquitously for stream monitoring, water-resource estimation, and flood forecasting. However, they are calculated using a basic empirical power-law fit that lacks flexibility to robustly represent channel–floodplain structure or to adapt to changing hydraulic geometry or roughness. Furthermore, such empirical fits require many measurements of stage and discharge. Gathering these measurements is expensive and might not be possible if the channel and/or floodplain evolve before a sufficient range of flows may be measured. To address this deficit with a similarly simple but physically grounded approach, we present a strategy based on Manning's equation. This "double-Manning" approach implements Manning's equation within and above the channel and a power-law relationship – analogous to a generalized Manning's equation – for flows crossing the floodplain. We demonstrate that the double-Manning equation can effectively fit field data and, in the process, accurately estimate bankfull width, bankfull depth, channel Manning's n, and Manning-style power-law parameters for floodplain-flow characteristics. For sites lacking exhaustive field data, the physical basis of the double-Manning approach enables rating-curve creation using a combination of stage–discharge data and common field measurements of the channel and floodplain. Such rating curves may be adjusted as the channel and floodplain evolve to predict how geomorphic change might affect flow depth and flood inundation. The double-Manning approach may be run as a forward (predictive) or inverse (fit to data) model. Documented, open-source code may be acquired from GitHub (https://github.com/MNiMORPH/doublemanning) and Zenodo.