Speaker: Nazanin Abedini (Vrije Universiteit Amsterdam)

Title: Convergence properties of a data assimilation method based on a Gauss-Newton iteration

Abstract: Data assimilation is widely used in many practical situations, such as weather forecasting, oceanography, and subsurface modeling. The study of these physical systems presents certain challenges. For example, their state cannot be observed directly and accurately, or the underlying weather-dependent system is chaotic, meaning that small changes in initial conditions can lead to large changes in forecast accuracy. The purpose of data assimilation is to correct the error in the state estimate by incorporating the information from the measurements into the mathematical model. The widely used data assimilation methods are variational methods. They aim to find an optimal initial condition of the dynamic model such that the distance to the observations is minimized (under the constraint that the estimate is a solution of the dynamic system). The problem is formulated as a minimization of a nonlinear least-squares problem with respect to the initial condition, and it is usually solved using a Gauss-Newton
method.

We propose a variational data assimilation method that also minimizes a nonlinear least squares problem but with respect to a trajectory over one time window at a time. The goal is to get a more accurate estimate. We prove the convergence of the method in the case of noiseless observations and provide an error bound in the case of noisy observations. We confirm our theoretical results by numerical experiments using Lorenz models.

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