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Type: Journal article
Title: Particle filters for data assimilation based on reduced-order data models
Author: Maclean, J.
Van Vleck, E.S.
Citation: Quarterly Journal of the Royal Meteorological Society, 2021; 147(736):1892-1907
Publisher: Wiley
Issue Date: 2021
ISSN: 0035-9009
Statement of
John Maclean, Erik S. Van Vleck
Abstract: We introduce a framework for data assimilation (DA) in which the data is split into multiple sets corresponding to low-rank projections of the state space. Algorithms are developed that assimilate some or all of the projected data, including an algorithm compatible with any generic DA method. The major application explored here is PROJ-PF, a projected particle filter. The PROJ-PF implementation assimilates highly informative but low-dimensional observations. The implementation considered here is based on using projections corresponding to assimilation in the unstable subspace (AUS). In the context of particle filtering, the projected approach mitigates the collapse of particle ensembles in high-dimensional DA problems, while preserving as much relevant information as possible, as the unstable and neutral modes correspond to the most uncertain model predictions. In particular, we formulate and implement numerically a projected optimal proposal particle filter (PROJ-OP-PF) and compare this with the standard optimal proposal and the ensemble transform Kalman filter.
Keywords: Data assimilation; dimension reduction; numerical analysis
Rights: © 2021 Royal Meteorological Society
DOI: 10.1002/qj.4001
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Mathematical Sciences publications

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