Estimation of river current using reduced Kalman filter finite element method

The purpose of this paper is to investigate estimation of velocity, water elevation and contaminant concentration in a river current using the Kalman filter finite element method (KE-FEM), which is an improvement of the Kalman filter finite element method previously presented by the authors group. The state variables, velocity, water elevation and contaminant concentration, in the whole domain can be obtained by the finite element method. Combining the Kalman filter and the finite element method, a practically useful method can be obtained. The Kalman filter is an estimation method based on the system and observation equations. The non-liner shallow water equation is utilized for the state equation. The explicit Euler method is used for the temporal discretization. The finite element method based on the linear interpolation is employed for the spatial discretization. The long computational time is required for the computation by the previous method. To reduce the computational time, the computational domain is divided into two parts, the main and subsidiary domains. In the main domain, filtering procedures are carried out, whereas only a deterministic process is taken for the variables in the subsidiary domain. Eliminating the state variables in the subsidiary domain, the drastically efficient computation is carried out. The flow in the Teganuma river in Japan is computed as practical applications. Close agreement between observed and computed results was obtained.