A hybrid grid/particle filter for Lagrangian data assimilation. I: Formulating the passive scalar approximation

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Abstract

In this two-part paper, we present a new nonlinear method for the assimilation of Lagrangian data. In part I, we formulate the method as a generalization of other particle filters. A particularly novel feature of the formulation is the use of a hybrid discretisation of the probability density function (PDF) in physical/phase space. Moreover, we show that, under the assumption that the drifters are uncorrelated, the projection of the Fokker–Planck equation onto the observation space associated with the drifter positions reduces to a set of passive scalar equations. This property allows us to efficiently compute the transitional PDF. To compute the analysis states, we present a grid/particle filter specifically formulated for use with the hybrid representation of our PDF. In common with other particle filters, our filter can suffer from sample impoverishment. To remedy this problem, we extend the Gaussian resampling procedure of Xiong et al. to produce a very efficient filter. This produces a fully functional scheme for Lagrangian data assimilation when combined with our forecasts of the prior.
Original languageEnglish
Pages (from-to)1539-1550
Number of pages12
JournalQuarterly Journal of the Royal Meteorological Society
Volume134
Issue number635
DOIs
Publication statusPublished - 2008

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