Speaker: Nazanin Abedini (Vrije Universiteit Amsterdam)
Title: Convergence properties of a data-assimilation method based on a Gauss-Newton iteration
Abstract: Data assimilation is broadly used in many practical situations, such as weather forecasting, oceanography and subsurface modelling. There are some challenges in studying these physical systems. For example, their state cannot be directly and accurately observed or the underlying time-dependent system is chaotic which means that small changes in initial conditions can lead to large changes in prediction accuracy. The aim of data assimilation is to correct error in the state estimation by incorporating information from measurements into the mathematical model. The widely-used data-assimilation methods are variational methods. They aim at finding an optimal initial condition of the dynamical model such that the distance to observations is minimized (under a constraint of the estimate being a solution of the dynamical system). The problem is formulated as a minimization of a nonlinear least-square problem with respect to initial condition, and it is usually solved using a Gauss-Newton
We propose a variational data-assimilation method that minimizes a nonlinear least-square problem as well but with respect to a trajectory over a time window at once. The goal is to obtain a more accurate estimate. We prove method convergence in case of noise-free observations and provide error bound in case of noisy observations. We confirm our theoretical results with numerical experiments using Lorenz models.
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