Comment on npg-2021-32

doi:10.5194/npg-2021-32-rc2

Abstract

Rejuvenation in particle filters is necessary to prevent the collapse of the weights when the number of particles is insufficient to sample the high probability regions of the state space. Rejuvenation is often implemented in a heuristic manner by the addition of stochastic samples that widen the support of the ensemble. This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage. The ensemble transport particle filter, and its second order variant, are extended with the proposed rejuvenation approach. Numerical experiments show that modified filters significantly improve the analyses for low dynamical ensemble sizes.

Highlights

Ensemble-based data assimilation (Asch et al, 2016; Law et al, 2015; Reich and Cotter, 2015) aims to estimate our uncertainty 10 about the state of some dynamical system through an ensemble of possible states
This work aims at improving canonical rejuvenation methodology by the introduction of additional prior information obtained from climatological samples; the dynamical 5 particles used for importance sampling are augmented with samples obtained from stochastic covariance shrinkage
Previous work (Popov et al, 2020) has focused on augmenting the information represented by the ensemble with information derived from covariance shrinkage through a surrogate ensemble in the ensemble transport Kalman filter. We extend this idea to the ensemble transport particle filter (ETPF) (Reich, 2013)

Summary

Introduction

Ensemble-based data assimilation (Asch et al, 2016; Law et al, 2015; Reich and Cotter, 2015) aims to estimate our uncertainty 10 about the state of some dynamical system through an ensemble of possible states. The ensemble Kalman filter (Burgers et al, 1998; Evensen, 1994, 2009), could be thought of as an abuse of the principle of maximum entropy: by discarding information about the underlying dynamical system, and assuming that the ensemble only gives information about a mean (that lives in Rn), and a covariance, the underlying distribution of our uncertainty is taken to be normal. In such a way, any application of Bayes’ rule has to transform our assumed prior normal distribution into our 20 assumed posterior normal distribution

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