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Variational particle smoothers and their localization
Author(s) -
Morzfeld M.,
Hodyss D.,
Poterjoy J.
Publication year - 2018
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3256
Subject(s) - particle filter , gaussian , merge (version control) , ensemble kalman filter , smoothing , kalman filter , mathematics , numerical weather prediction , importance sampling , data assimilation , extended kalman filter , statistical physics , computer science , mathematical optimization , physics , statistics , meteorology , monte carlo method , quantum mechanics , information retrieval
Given the success of 4D‐variational methods (4D‐Var) in numerical weather prediction, and recent efforts to merge ensemble Kalman filters with 4D‐Var, we revisit how one can use importance sampling and particle filtering ideas within a 4D‐Var framework. This leads us to variational particle smoothers (varPS) and we study how weight‐localization can prevent the collapse of varPS in high‐dimensional problems. We also discuss the relevance of (localized) weights in near‐Gaussian problems. We test our ideas on the Lorenz'96 model of dimensions n = 40, n = 400, and n = 2,000. In our numerical experiments the localized varPS does not collapse and yields results comparable to ensemble formulations of 4D‐Var, while tuned EnKFs and the local particle filter lead to larger estimation errors. Additional numerical experiments suggest that using localized weights may not yield significant advantages over unweighted or linearized solutions in near‐Gaussian problems.