[M-GI26] Data assimilation: A fundamental approach in geosciences

[MGI26-P04] Improving Resampling Process of Local Particle Filter Using the Sinkhorn Algorithm

*小槻 峻司¹、大石 健² (1.千葉大学　国際高等研究基幹、2.千葉大学大学院　融合理工学府)

キーワード：局所粒子フィルタ、リサンプリング、最適輸送、Sinkhornアルゴリズム

The particle filter is an ensemble data assimilation method generally applicable to nonlinear and non-Gaussian problems. Penny and Miyoshi (2015) developed the local particle filter (LPF) in a form as the ensemble transform matrix of the Local Ensemble Transform Kalman Filter (LETKF). In this form, the resampling step of the LPF is formulated by multiplying the ensemble transform matrix to the prior perturbation matrix. Kotsuki et al. (2022) implemented the LPF and its Gaussian mixture extension with an intermediate global circulation model known as the Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY), and reported that the LPFGM outperformed the LETKF in sparsely observed regions. Through a series of experiments, we have noticed that the way of generating the transform matrix is very important for stabilizing the LPFs.
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 by the ensemble transform matrix. A series of perfect model experiments with toy models showed that the Sinkhorn algorithm produced accurate analyses equivalent to that obtained with the OT method. In addition, the Sinkhorn algorithm accelerated 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 that account for non-Gaussian prior error distribution with many ensemble members.