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

An 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.