Exploring practical estimates of the ensemble size necessary for particle filters
MetadataShow full item record
KeywordMathematical and statistical techniques; Statistical techniques; Models and modeling; Data assimilation; Ensembles; Nonlinear models
Particle filtering methods for data assimilation may suffer from the “curse of dimensionality,” where the required ensemble size grows rapidly as the dimension increases. It would, therefore, be useful to know a priori whether a particle filter is feasible to implement in a given system. Previous work provides an asymptotic relation between the necessary ensemble size and an exponential function of , a statistic that depends on observation-space quantities and that is related to the system dimension when the number of observations is large; for linear, Gaussian systems, the statistic can be computed from eigenvalues of an appropriately normalized covariance matrix. Tests with a low-dimensional system show that these asymptotic results remain useful when the system is nonlinear, with either the standard or optimal proposal implementation of the particle filter. This study explores approximations to the covariance matrices that facilitate computation in high-dimensional systems, as well as different methods to estimate the accumulated system noise covariance for the optimal proposal. Since may be approximated using an ensemble from a simpler data assimilation scheme, such as the ensemble Kalman filter, the asymptotic relations thus allow an estimate of the ensemble size required for a particle filter before its implementation. Finally, the improved performance of particle filters with the optimal proposal, relative to those using the standard proposal, in the same low-dimensional system is demonstrated.
Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Monthly Weather Review 144 (2016): 861-875, doi:10.1175/MWR-D-14-00303.1.
Showing items related by title, author, creator and subject.
Slivinski, Laura; Spiller, Elaine; Apte, Amit; Sandstede, Bjorn (American Meteorological Society, 2015-01)Lagrangian measurements from passive ocean instruments provide a useful source of data for estimating and forecasting the ocean’s state (velocity field, salinity field, etc.). However, trajectories from these instruments ...
Badiey, Mohsen; Wan, Lin; Lynch, James F. (American Meteorological Society, 2016-04-18)During the Shallow Water Acoustic Experiment 2006 (SW06) conducted on the New Jersey continental shelf in the summer of 2006, detailed measurements of the ocean environment were made along a fixed reference track that was ...
Rodell, Matthew; Beaudoing, Hiroko K.; L’Ecuyer, Tristan S.; Olson, William S.; Famiglietti, James S.; Houser, Paul R.; Adler, Robert; Bosilovich, Michael G.; Clayson, Carol A.; Chambers, Don P.; Clark, Edward A.; Fetzer, Eric J.; Gao, X.; Gu, Guojun; Hilburn, K. A.; Huffman, George J.; Lettenmaier, Dennis P.; Liu, W. Timothy; Robertson, F. R.; Schlosser, C. A.; Sheffield, Justin; Wood, E. F. (American Meteorological Society, 2015-11-01)This study quantifies mean annual and monthly fluxes of Earth’s water cycle over continents and ocean basins during the first decade of the millennium. To the extent possible, the flux estimates are based on satellite ...