Application of Data Assimilation to Three-Dimensional Hydrodynamics: the Case of the Odra Lagoon

Abstract

A data assimilation scheme enables to correct a model estimate, or rst-guess, of a physical state using measurements of the state variables. The best estimate is given by minimization of the estimation variance, as it is done in kriging. In sequential data assimilation, the spatial covariance of the rst-guess error is propagated forward in time using the physical model and requires only the knowledge of the model error (system noise). Since the data are often scarce in space, it is however a real scienti c challenge to assess its covariance structure. We present here an application to three-dimensional hydrodynamics, where a suboptimal lter is coupled with a numerical model solving the Navier-Stokes equations for shallow water. An original method for the construction of a spatial covariance from time series of water level measurements is introduced, making use of the physical properties of the system. The ltering has been applied to the simulation of water level in the Odra lagoon for the ood period of summer 1997. The method proves very e cient, despite a small number of assimilated measurements, and enables an improved reconstruction of the physical system.