State Estimation and Modeling Error Approach for 2-D Shallow Water Equations and Lagrangian Measurements

A state estimation method for two-dimensional shallow water equations (SWE) in rivers using Lagrangian drifter positions as measurements is proposed. Lagrangian drifters are sensors moving with the flow and reporting their location. The aim of this method is to compensate for the lack of accurate information about boundary conditions. The drifters move with the local flow and report their positions. Thus, they provide additional information about the state of the river compared to a case in which, for example, only a computational model is used to describe the river flow. In this work, the measurement information is incorporated into shallow water equations using ensemble Kalman filtering. Special attention is paid to the handling of modeling errors that arise from the use of simple and computationally lightweight models as evolution models for the flow. The proposed approach is tested with simulated and experimental data collected for this study in the Sacramento–San Joaquin Delta in California. It is shown that when modeling errors are taken into account, better estimates for the state of the river are obtained.