08 Jan 2024
 | 08 Jan 2024

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

Andrew D. Wickert, Jabari C. Jones, and Gene-Hua Crystal Ng

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.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this preprint. The responsibility to include appropriate place names lies with the authors.
Andrew D. Wickert, Jabari C. Jones, and Gene-Hua Crystal Ng

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on egusphere-2023-3118', Anonymous Referee #1, 21 Feb 2024
    • AC1: 'Reply on RC1', Andy Wickert, 11 Jun 2024
  • CC1: 'Comment on egusphere-2023-3118', Richard Koehler, 26 Mar 2024
    • AC2: 'Reply on CC1', Andy Wickert, 11 Jun 2024
  • RC2: 'Comment on egusphere-2023-3118', Anonymous Referee #2, 16 Apr 2024
    • AC3: 'Reply on RC2', Andy Wickert, 11 Jun 2024
Andrew D. Wickert, Jabari C. Jones, and Gene-Hua Crystal Ng

Data sets

Minnesota River near Jordan: stream-gauge data and double-Manning fit J. Jones and A. D. Wickert

Cannon River at Welch: stream-gauge data (stage, discharge, and sediment grain size) and double-Manning fit J. Jones et al.

Stream-gauging Data: La Dormida Captación G. C. Ng et al.

Model code and software

doublemanning A. D. Wickert

Andrew D. Wickert, Jabari C. Jones, and Gene-Hua Crystal Ng


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Short summary
For over a century, scientists have used a simple algebraic relationship to estimate the amount of water flowing through a river (its discharge) from the height of the flow (its stage). Here we add physical realism to this approach by explicitly representing both the channel and floodplain, thereby allowing channel and floodplain geometry and roughness to these estimates. Our proposed advance may improve predictions of floods and water resources, even when the river channel itself changes.