Comparison of Ensemble-Based Data Assimilation Methods for Sparse Oceanographic Data

Abstract

Probabilistic forecasts in oceanographic applications, such as drift trajectory forecasts for search-and-rescue operations, face challenges due to high-dimensional complex models and sparse spatial observations. We discuss localisation strategies for assimilating sparse point observations and compare the implicit equal-weights particle filter and a localised version of the ensemble-transform Kalman filter. First, we verify these methods thoroughly against the analytic Kalman filter solution for a linear advection diffusion model. We then use a non-linear simplified ocean model to do state estimation and drift prediction. The methods are rigorously compared using a wide range of metrics and skill scores. Our findings indicate that both methods succeed in approximating the Kalman filter reference for linear models of moderate dimensions, even for small ensemble sizes. However, in high-dimensional settings with a non-linear model, we discover that the outcomes are significantly influenced by the dependence of the ensemble Kalman filter on relaxation and the particle filter's sensitivity to the chosen model error covariance structure. Upon proper relaxation and localisation parametrisation, the ensemble Kalman filter version outperforms the particle filter in our experiments.