Assimilation of spatially distributed water levels into a shallow-water flood model. Part I: Mathematical method and test case

Recent applications of remote sensing techniques produce rich spatially distributed observations for flood monitoring. In order to improve numerical flood prediction, we have developed a variational data assimilation method (4D-var) that combines remote sensing data (spatially distributed water levels extracted from spatial images) and a 2D shallow water model. In the present paper (part I), we demonstrate the efficiency of the method with a test case. First, we assimilated a single fully observed water level image to identify time-independent parameters (e.g. Manning coefficients and initial conditions) and time-dependent parameters (e.g. inflow). Second, we combined incomplete observations (a time series of water elevations at certain points and one partial image). This last configuration was very similar to the real case we analyze in a forthcoming paper (part II). In addition, a temporal strategy with time overlapping is suggested to decrease the amount of memory required for long-duration simulation.