Ensemble Kalman Filter for State and Parameter Estimation of Low Dissipation Systems

Abstract: We conduct a fundamental study on how numerical diffusion and dispersion errors affect the performance of the ensemble Kalman filter (EnKF) for problems with low physical diffusion. We use the linear advection equation as our model problem. For a mesh that does not resolve all wavenumbers, it is shown that the EnKF can improve the predictions. EnKF can also be used to estimate the convection velocity, but the convergence of this estimate depends on the numerical diffusion and dispersion error. It is shown that the convection velocity estimated by EnKF is not necessarily the true physical convection velocity but the convection velocity that is needed by the numerical discretization scheme so that it is able to give the solution that best matches the observed data (the exact analytical solution in this study). Keywords: Numerical Method, Kalman Filters, Data Assimilation