Ensemble Kalman Filter Based State Estimation in 2D Shallow Water Equations Using Lagrangian Sensing and State Augmentation

We present a state estimation method for two-dimensional shallow water equations in rivers using Lagrangian drifter positions as measurements. The aim of this method is to compensate for the lack of knowledge of upstream and downstream boundary conditions in rivers that causes inaccuracy in the velocity field estimation by releasing drifters equipped with GPS receivers. The drifters report their positions and thus provide additional information of the state of the river. This information is incorporated into shallow water equations by using Ensemble Kalman Filtering (EnKF). The proposed method is based on the discretization of the governing nonlinear equations using the finite element method in unstructured meshes. We incorporate the drifter positions into the unknown state, which directly exploits the Langrangian nature of the measurements. The performance of the method is assessed with twin experiments.