Yuan Cheng
This thesis discusses various data assimilation methods, with a special focus on the applicability to spatio-temporal systems. With ensemble Kalman filters being the state-of-the-art way to perform data assimilation, particle filters are gaining more and more attention as people realize that the drawback of Kalman-based filters of not being consistent, when some simple assumptions are violated, is actually becoming an issue. However, particle filters were held back by the fact that the concept of localization has not been successfully established. Therefore, making the use of which in high dimensional models more than difficult.
The main contribution of this work is to at least partially solve the problem. By coupling the prior/forecast and the posterior/analysis and introducing an optimality criterion that we want to be fulfilled, we derive the ensemble transform particle filter (ETPF). The additional distance in the cost funtional of the optimal transport problem allows the successful application of R-localization in the ETPF. Thus, making possible the use of the particle filter in a high dimensional system when the ensemble size is limited to a small number.
