River discharge estimation from synthetic SWOT-type observations using variational data assimilation and the full Saint-Venant hydraulic model

The upcoming Surface Water and Ocean Topography satellite mission, to be launched in 2021, will measure river water surface elevation, slope and width, with an unprecedented level of accuracy for a remote sensing tool. This work investigates the river discharge estimation from synthetic SWOT observations, in the presence of strong uncertainties in the model inputs, i.e. the river bathymetry and bed roughness. The estimation problem is solved by a novel variant of the standard variational data assimilation, the '4D-Var' method, involving the full Saint-Venant 1.5D-network hydraulic model SIC2. The assimilation scheme simultaneously estimates the discharge, bed elevation and bed roughness coefficient and is designed to assimilate both satellite and in situ measurements. The method is tested on a 50 km-long reach of the Garonne River during a five-month period of the year 2010, characterized by multiple flooding events. First, the impact of the sampling frequency on discharge estimation is investigated. Secondly, discharge as well as the spatially distributed bed elevation and bed roughness coefficient are determined simultaneously. Results demonstrate feasibility and efficiency of the chosen combination of the estimation method and of the hydraulic model. Assimilation of the SWOT data results into an accurate estimation of the discharge at observation times, and a local improvement in the bed level and bed roughness coefficient. However, the latter estimates are not generally usable for different independent experiments.