Applying the Sinkhorn Algorithm for Resampling of Local Particle Filter

抄録

 The particle filter attracts interest from the data assimilation research community since it does not assume a Gaussian prior error distribution. Several local particle filters (LPFs) have been proposed to avoid weight collapse due to assimilation of observations in high dimensional systems. This study focuses on an LPF that uses the ensemble transform matrix as used in the local ensemble transform Kalman filter. Resampling of the transform-matrix-based LPF has been employed using Optimal Transport (OT) that minimizes analysis increments of particles. However, computations of OT increase by order of square, which limits its application for large-ensemble LPF problems.

 This study proposes using the fast Sinkhorn algorithm, an approximated solver of the OT method, for the resampling of LPFs. A series of perfect model experiments with a 40-variable toy model show that the Sinkhorn algorithm produces accurate analyses equivalent to that obtained with the OT method. In addition, the Sinkhorn algorithm accelerates total computational time more than two times compared to the OT-based LPF when the ensemble size is 64 or more. The Sinkhorn-based resampling would be a promising tool for applying the LPFs to account for non-Gaussian prior error distribution with many ensemble members.