Samantha S.R. Kim, Femke C. Vossepoel

The particle method is an ensemble-based data assimilation method for state- and parameter estimation in a quasi-static problem. We apply the particle method in two different experiments with models of increasing complexity. The first model, which calculates subsidence for a single observation point due to a single source of strain, considers uncorrelated parameters and observations. In the second model subsidence can be seen as a summation of subsidence contributions from multiple sources. A single source in the second model causes deformation over a region and the observations within this region will be correlated. Assimilating these correlated observations may trigger weight collapse. With synthetic tests we show in a model of subsidence with 50 independent parameters and spatially correlated observations a minimum of 10¹³ particles is required to have information in the posterior distribution identical to that in a model with 50 independent and spatially uncorrelated observations.
Spatial correlations cause information loss which can be quantified with mutual information. With synthetic experiments we illustrate how stronger spatial correlation results in a lower information content in the posterior. This quantification underpins our finding that a larger ensemble size is required for the particle method to remain effective in the case of spatial correlation. We furthermore 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 data assimilation of spatially correlated fields.