Dynamics Seminar by Nazanin Abedini (VU Amsterdam) on 13th of March

On Wednesday 13th of March at 4pm in the MathLab, Nazanin Abedini (VU Amsterdam) will give an Amsterdam Dynamics seminar.

The talk will take place in the Maryam seminar room (9A-46) and everyone is welcome to join for drinks at Bar Boele after the talk.

Title: Error analysis of variational and ensemble methods in data assimilation

Abstract: Data assimilation (DA) is broadly used in many practical situations, such as weather forecasting, oceanography, and subsurface modelling. DA is a way to combine models and observations allowing for obtaining more accurate representation of the current state of a system. This accurate estimate is important in dynamical systems where conditions are constantly changing such as the Earth’s atmosphere. Many real-world systems exhibit nonlinear behavior, and the distribution of model errors and observational errors may not be Gaussian. Some methods address these challenges in data assimilation. During my PhD, I have been working on two well-known approaches, the variational and the ensemble Kalman filtering (EnKF) methods.

Variational methods and Ensemble Kalman Filtering differ in their approaches to combining models and observations. Variational methods use optimization techniques to find the best approximation of the system state, while EnKF uses an ensemble approach to represent the probability distribution of the system state and evolves this ensemble over time through assimilation of observations.

In the variational method, I consider a cost function that takes into account discrepancy between the state and observations and is regularized by the dynamical model. I will show the method converges to the true state in the case of noise-free observations and provide error bound in the case of noisy observations.

In Kalman filtering method, I consider a general nonlinear dynamical system with partial observations. I will provide error bound and present stability and accuracy results under randomized observations.

The contents of the talk are based upon joint work with Svetlana Dubinkina (VU Amsterdam), Jana de Wiljes (Ilmenau University of Technology) and Jonas Latz (University of Manchester).