Variational assimilation of satellite data into a full Saint-Venant based hydraulic model in the context of ungauged basins

Overview & Synopsis

The present thesis investigates the potential of variational data assimilation (DA) in discharge estimation from the future Surface Water and Ocean Topography (SWOT) satellite mission, using a 1.5D full Saint-Venant hydraulic model in the context of fully ungauged basins. Two distinct approaches for treating the model error are being investigated; the extended control vector approach, and a novel approach based on a modified covariance matrix. Adjoint sensitivity analysis was first performed to assess the local influence of the hydraulic model inputs, on the model response, defined using an objective function of the model state. The latter is highly sensitive to the upstream boundary condition on discharge as well as the river bed elevation and roughness coefficient. Sensitivities indicate the control sections of the river that have major influence on the flow hydraulics, which emphasizes the need of accurate measurements and/or at these locations. Second, the estimation of river discharge from simulated SWOT observations using a variant of the conventional variational DA method '4D-Var' has been investigated. The variational DA scheme involves an extended control vector and is developed to apply the method to fully ungauged basins. The method was tested using two experimental set-ups: (i) Observing System Simulation Experiments over the Garonne River and a more realistic and general framework using (ii) the SWOT hydrology simulator, which simulates the radar system on-board the satellite, over the Po and Sacramento Rivers. Water surface elevation was assimilated leading to local improvements on bathymetry and roughness which allowed successful estimation of discharge. Nevertheless, the estimates of the space distributed variables are subjected to the equifinality issue which may prevent their use for subsequent applications. Moreover, results emphasize that successful estimation of discharge over the whole study period requires an observation frequency comparable to the characteristic time of the hydraulic system. Finally, a novel method for the treatment of the model error using the variational approach is proposed. Based on the 'nuisance parameter' idea, it allows implicit treatment of the model error by using a modified observation covariance matrix. The equivalency theorem substantiating the method has been proved. A case of the biased model error is also considered. Numerical experiments involving the 1D generalized Burger's equation and the 1.5D full Saint-Venant equations illustrate the presented theory.