Submitted as: development and technical paper
07 Jun 2022
Submitted as: development and technical paper | 07 Jun 2022
Status: this preprint is currently under review for the journal GMD.

A Local Particle Filter and Its Gaussian Mixture Extension Implemented with Minor Modifications to the LETKF

Shunji Kotsuki1,2,3, Takemasa Miyoshi1,4,5,6,7, Keiichi Kondo8,1, and Roland Potthast9,10 Shunji Kotsuki et al.
  • 1RIKEN Center for Computational Science, Kobe, Japan
  • 2Center for Environmental Remote Sensing, Chiba University, Chiba, Japan
  • 3PRESTO, Japan Science and Technology Agency, Chiba, Japan
  • 4RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program, Kobe, Japan
  • 5RIKEN Cluster for Pioneering Research, Kobe, Japan
  • 6Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan
  • 7Department of Atmospheric and Oceanic Science, University of Maryland, College Park, Maryland, USA
  • 8Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan
  • 9Deutscher Wetterdienst, Offenbach, Germany
  • 10Applied Mathematics, University of Reading, UK

Abstract. A particle filter (PF) is an ensemble data assimilation method that does not assume Gaussian error distributions. Recent studies proposed local PFs (LPFs), which use localization as in the ensemble Kalman filter, to apply the PF for high-dimensional dynamics efficiently. Among others, Penny and Miyoshi developed an LPF in the form of the ensemble transform matrix of the Local Ensemble Transform Kalman Filter (LETKF). The LETKF has been widely accepted for various geophysical systems including numerical weather prediction (NWP) models. Therefore, implementing consistently with an existing LETKF code is useful.

This study developed a software platform for the LPF and its Gaussian mixture extension (LPFGM) by making slight modifications to the LETKF code with a simplified global climate model known as Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY). A series of idealized twin experiments were accomplished under the ideal model assumption. With large inflation by the relaxation to prior spread, the LPF showed stable filter performance with dense observations but became unstable with sparse observations. The LPFGM showed more accurate and stable performances than the LPF with both dense and sparse observations. In addition to the relaxation parameter, regulating the resampling frequency and the amplitude of Gaussian kernels was important for the LPFGM. With a spatially inhomogeneous observing network, the LPFGM was superior to the LETKF in sparsely observed regions where the background ensemble spread and non-Gaussianity are larger. The SPEEDY-based LETKF, LPF, and LPFGM systems were available as open-source software on Github ( and can be adapted to various models relatively easily like the LETKF.

Shunji Kotsuki et al.

Status: open (until 02 Aug 2022)

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Shunji Kotsuki et al.

Shunji Kotsuki et al.


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Short summary
Data assimilation plays an important role in numerical weather prediction (NWP) to combine forecasted states and millions of observations. While data assimilation methods in NWP usually assume the Gaussian error distribution, some variables in the atmosphere are known to have non-Gaussian error statistics such as precipitation. This study extended a widely used ensemble data assimilation algorithm for enabling to assimilate more observation with non-Gaussian error characteristics.