title: State estimation and prediction using clustered particle filters.
abstract: Particle filtering is an essential tool to improve uncertain model predictions by incorporating noisy observational data from complex systems including non-Gaussian features. A class of particle filters, clustered particle filters, is introduced for high-dimensional nonlinear systems, which uses relatively few particles compared with the standard particle filter. The clustered particle filter captures non-Gaussian features of the true signal, which are typical in complex nonlinear dynamical systems such as geophysical systems. The method is also robust in the difficult regime of high-quality sparse and infrequent observations. The key features of the clustered particle filtering are coarse-grained localization through the clustering of the state variables and particle adjustment to stabilize the method; each observation affects only neighbor state variables through clustering and particles are adjusted to prevent particle collapse due to high-quality observations. The clustered particle filter is tested for the 40-dimensional Lorenz 96 model with several dynamical regimes including strongly non-Gaussian statistics. The clustered particle filter shows robust skill in both achieving accurate filter results and capturing non-Gaussian statistics of the true signal. It is further extended to multiscale data assimilation, which provides the large-scale estimation by combining a cheap reduced-order forecast model and mixed observations of the large- and small-scale variables. This approach enables the use of a larger number of particles due to the computational savings in the forecast model. The multiscale clustered particle filter is tested for one-dimensional dispersive wave turbulence using a forecast model with model errors.
authors.affiliation: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012; ylee@cims.nyu.edu jonjon@cims.nyu.edu.|Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.
authors.forename: Yoonsang
authors.initials: Y
authors.lastname: Lee
authors.affiliation: Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012; ylee@cims.nyu.edu jonjon@cims.nyu.edu.|Center for Atmosphere and Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012.
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Majda
keywords: data assimilation; non-Gaussian; particle filter; uncertainty quantification