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The Behavior of Filters and Smoothers for Strongly Nonlinear DynamicsThe Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.
Document ID
Document Type
Reprint (Version printed in journal)
Zhu, Yanqiu (NASA Goddard Space Flight Center Greenbelt, MD United States)
Cohn, Stephen E. (NASA Goddard Space Flight Center Greenbelt, MD United States)
Todling, Ricardo (NASA Goddard Space Flight Center Greenbelt, MD United States)
Date Acquired
August 19, 2013
Publication Date
January 1, 1999
Subject Category
Statistics and Probability
Meeting Information
Data Assimilation
Distribution Limits
Work of the US Gov. Public Use Permitted.