Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters

• Published in: Monthly weather review Vol. 136; no. 3; pp. 1042 - 1053
• Main Authors: SAKOV, Pavel, OKE, Peter R
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 01.03.2008
• Subjects: Data assimilation; Data collection; Earth, ocean, space; Exact sciences and technology; External geophysics; Filters; Kalman filters; Matrix; Meteorology; Methods; Nonlinear systems; Studies; Outlier; models; performances; Ensemble Kalman filter; Data assimilation
• ISSN: 0027-0644; 1520-0493
• DOI: 10.1175/2007mwr2021.1

Abstract This paper considers implications of different forms of the ensemble transformation in the ensemble square root filters (ESRFs) for the performance of ESRF-based data assimilation systems. It highlights the importance of using mean-preserving solutions for the ensemble transform matrix (ETM). The paper shows that an arbitrary mean-preserving ETM can be represented as a product of the symmetric solution and an orthonormal mean-preserving matrix. The paper also introduces a new flavor of ESRF, referred to as ESRF with mean-preserving random rotations. To investigate the performance of different solutions for the ETM in ESRFs, experiments with two small models are conducted. In these experiments, the performances of two mean-preserving solutions, two non-mean-preserving solutions, and a traditional ensemble Kalman filter with perturbed observations are compared. The experiments show a significantly better performance of the mean-preserving solutions for the ETM in ESRFs compared to non-mean-preserving solutions. They also show that applying the mean-preserving random rotations prevents the buildup of ensemble outliers in ESRF-based data assimilation systems.