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A Lagrangian trajectory filter for constituent data assimilation
Author(s) -
Lyster Peter M.,
Cohn Stephen E.,
Zhang Banglin,
Chang LangPing,
Ménard Richard,
Olson Kevin,
Renka Robert
Publication year - 2004
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 - 10.1256/qj.02.234
Subject(s) - data assimilation , ensemble kalman filter , extended kalman filter , kalman filter , filter (signal processing) , covariance , invariant extended kalman filter , trajectory , eulerian path , mathematics , computer science , control theory (sociology) , meteorology , lagrangian , physics , statistics , artificial intelligence , control (management) , astronomy , computer vision
We have developed a new numerical algorithm, the Lagrangian filter, for solving the Kalman filter equations for assimilation of constituent observations directly on trajectories that propagate with the flow. This is a finite‐dimensional approximation of the solution of the state estimation problem by characteristics, and may be thought of as an extension of methods such as trajectory mapping. The Lagrangian filter provides a natural framework for the study and solution of the constituent data assimilation problem because of the conservative properties of the state and its estimation‐error variance and covariance along trajectories. Considerable insight into the behaviour of the filter is gained as a result of these properties. The Lagrangian filter also requires significantly fewer floating point operations than the Eulerian Kalman filter because of its simple error covariance propagation step. We implemented it for two‐dimensional flow on isentropes in the stratosphere and assimilated methane observations from the Upper Atmosphere Research Satellite. Results are validated against those of the Eulerian filter. Copyright © 2004 Royal Meteorological Society