Variational particle smoothers and their localization

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.Office of Naval Research [N00173-17-2-C003, PE-0601153N]; National Science Foundation [DMS-1619630]; Alfred P. Sloan Foundation; National Research Council Research Associateship Program fellowship12 month embargo; published online: 10 February 2018This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]