Abstract by Svetlana Dubinkina:
Data assimilation of high-dimensional nonlinear models is subject to curse of dimensionality. It is when an ensemble of small size is unable to reduce an error of the estimate. A typical remedy to the curse of dimensionality is distance-based localization. Distance-based localization reduces the model state dimension by taking into account only a few numerical cells of the model state near each observation. Even though distance-based localization reduces the error substantially for both linear data-assimilation methods such as ensemble Kalman filter and nonlinear data-assimilation methods such as particle filtering, linear data-assimilation methods still considerably outperform nonlinear data-assimilation methods in linear and quasi-linear regimes. We propose a further dimension reduction based on projection. We analyze the proposed projected ensemble Kalman filter and the projected particle filter in terms of error propagation. The numerical results show considerable error decrease when used with small ensemble sizes.
- in collaboration with Jana de Wiljes (UP)
Abstract by Femke C. Vossepoel:
Ground motion estimates can be obtained by assimilating geodetic observations into geomechanical models. In this study, we investigate how correlations in the observed deformation affects the data assimilation performance. To do this, we use a particle method in two experiments with models of increasing complexity. The first model, which calculates subsidence for a single observation point due to a single source, considers independent and uncorrelated parameters and observations. The second model calculates the observed subsidence as a summation of subsidence contributions from multiple sources. In the latter model, a single subsidence source causes deformation over a region and the observations within this region will be correlated. The correlation in the resulting observations may trigger weight collapse in the particle method.
The information loss related to the spatial correlation can be quantified with mutual information. Using the quantification of information loss confirms we illustrate how this loss of information is reflected in the log likelihood, and how this depends on the number of parameters of the model. Based on the results of these experiments, we propose criteria to evaluate the required ensemble size for assimilation of spatially correlated subsidence observations.
- in collaboration with Samantha S.R. Kim, TU Delft