A Lagrangian trajectory filter for constituent data assimilation

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

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