Implications of the Form of the Ensemble Transformation in the Ensemble Square Root Filters
Year: 2008
Type: article
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.
Source: Monthly Weather Review
Authors: Pavel Sakov, Peter R. Oke
Institution: CSIRO Oceans and Atmosphere
Language: English
Subfield: Atmospheric Science
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W1970847893