Estimating reach-averaged discharge for the River Severn from measurements of river water surface elevation and slope

•An inverse method is used to estimate river bathymetry and roughness coefficient.•The Bayesian method uses measurements of river height and slope.•Testing was done using in situ and remote sensing data for the River Severn, UK.•Estimation of discharge is shown to be possible if lateral inflows are known.

SummaryAn algorithm is presented that calculates a best estimate of river bathymetry, roughness coefficient, and discharge based on input measurements of river water surface elevation (h) and slope (S) using the Metropolis algorithm in a Bayesian Markov Chain Monte Carlo scheme, providing an inverse solution to the diffusive approximation to the shallow water equations. This algorithm has potential application to river h and S measurements from the forthcoming Surface Water and Ocean Topography (SWOT) satellite mission. The algorithm was tested using in situ data as a proxy for satellite measurements along a 22.4 km reach of the River Severn, UK. First, the algorithm was run with gage measurements of h and S during a small, in-bank event in June 2007. Second, the algorithm was run with measurements of h and S estimated from four remote sensing images during a major out-of-bank flood event in July 2007. River width was assumed to be known for both events. Algorithm-derived estimates of river bathymetry were validated using in situ measurements, and estimates of roughness coefficient were compared to those used in an operational hydraulic model. Algorithm-derived estimates of river discharge were evaluated using gaged discharge. For the in-bank event, when lateral inflows from smaller tributaries were assumed to be known, the method provided an accurate discharge estimate (10% RMSE). When lateral inflows were assumed unknown, discharge RMSE increased to 36%. Finally, if just one of the three river reaches was assumed to be have known bathymetry, solutions for bathymetry, roughness and discharge for all three reaches were accurately retrieved, with a corresponding discharge RMSE of 15.6%. For the out-of-bank flood event, the lateral inflows were unknown, and the final discharge RMSE was 19%. These results suggest that it should be possible to estimate river discharge via SWOT observations of river water surface elevation, slope and width.