Variational data assimilation of lagrangian data for fluvial hydraulics simulations.

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A major difficulty in the simulation of river hydraulics flows is bound to model parameters definition. Solutions of the shallow water equations are determined by initial conditions, boundary conditions, bed elevation, physical and numerical parameters. Data assimilation methods make it possible to combine optimally physical information from the model and observation data of the physical system to identify the value of model inputs that correspond to a numerical simulation which is consistent with reality. Variational data assimilation consists in finding the control variables that minimize a cost function measuring the discrepancy between the model state variable and observation data of the physical system. An efficient minimization using a Quasi-Newton algorithm requires the computation of the gradient of the cost function. The latter is easily computed from the adjoint state which is solution of an adjoint model. However, in river hydraulics, observation data are available only in very small quantities. Local water level measurements are usually very sparse in space and velocity measurements are even rarer, especially in case of extreme events such as floods. Consequently, in practice these eulerian observations are usually not sufficient to take advantage of data assimilation. We present a method to use lagrangian data from remote sensing observation in the assimilation process, in addition to classical eulerian observations of the flow. The trajectory of particles advected by the flow can bring information on the surface velocity thanks to an appropriate transport model. Numerical twin experiments demonstrate that this additional information makes it possible to improve the identification of model parameters. In order to deal with real data, an observation operator based on a multi-scale filtering scheme is proposed.