On variational data assimilation for 1D and 2D fluvial hydraulics

We address two problems related to variational data assimilation (VDA) as applied to river hydraulics (1D and 2D shallow water models). In real cases, available observations are very sparse (especially during flood events). Generally, they are very few measures of elevation at gauging stations. The first goal of the present study is to estimate accurately some parameters such as the inflow discharge, manning coefficients, the topography and/or the initial state. Since the elevations measures (eulerian observations) are very sparse, we develop a method which allow to assimilate extra lagrangian data (trajectory particles at the surface e.g. extracted from video images). The second goal aims to develop a joint data assimilation coupling method. We seek to couple accurately a 1D global net-model (rivers net) and a local 2D shallow water model (zoom into a flooded area), while we assimilate data. This ”weak” coupling procedure is based on the optimal control process used for the VDA. Numerical twin experiments demonstrate that the present two methods makes it possible to improve on one hand the identification of river model parameters (e.g. topography and inflow discharge), on the other hand an accurate 1D-2D coupling combined with the identification of inflow boundary conditions.