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    Original Research Papers

    A Bayesian approach to Lagrangian data assimilation

    Authors:

    A. Apte ,

    Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore, IN
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    C. K. R. T. Jones,

    Department of Mathematics, University of North Carolina, Chapel Hill, NC 27599, US
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    A. M. Stuart

    Mathematics Institute, University of Warwick, Coventry CV4 7AL, GB
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    Abstract

    Lagrangian data arise from instruments that are carried by the flow in a fluid field. Assimilation of such data into ocean models presents a challenge due to the potential complexity of Lagrangian trajectories in relatively simple flow fields.We adopt a Bayesian perspective on this problem and thereby take account of the fully non-linear features of the underlying model.

    In the perfect model scenario, the posterior distribution for the initial state of the system contains all the information that can be extracted from a given realization of observations and the model dynamics. We work in the smoothing context in which the posterior on the initial conditions is determined by future observations. This posterior distribution gives the optimal ensemble to be used in data assimilation. The issue then is sampling this distribution. We develop, implement, and test sampling methods, based on Markov-chain Monte Carlo (MCMC), which are particularly well suited to the low-dimensional, but highly non-linear, nature of Lagrangian data. We compare these methods to the well-established ensemble Kalman filter (EnKF) approach. It is seen that the MCMC based methods correctly sample the desired posterior distribution whereas the EnKF may fail due to infrequent observations or non-linear structures in the underlying flow.

    How to Cite: Apte, A., Jones, C.K.R.T. and Stuart, A.M., 2008. A Bayesian approach to Lagrangian data assimilation. Tellus A: Dynamic Meteorology and Oceanography, 60(2), pp.336–347. DOI: http://doi.org/10.1111/j.1600-0870.2007.00295.x
      Published on 01 Jan 2008
    Peer Reviewed
     CC BY 4.0
     Accepted on 13 Nov 2007            Submitted on 13 Jun 2007

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