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A Bayesian approach to Lagrangian data assimilation

Apte, A. and Jones, C. K. R. T. and Stuart, A. M. (2008) A Bayesian approach to Lagrangian data assimilation. Tellus A, 60 (2). pp. 336-347. ISSN 0280-6495. doi:10.1111/j.1600-0870.2007.00295.x.

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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.

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Additional Information:© 2008 The Authors. This journal is published under the terms of the Creative Commons Attribution 4.0 International (CC-BY 4.0) License. Manuscript received 13 June 2007; in final form 13 November 2007. AA and CKRTJ would like to acknowledge the support of ONR (grant number N00014-04-1-0215) and SAMSI (grant number 03-SC-NSF-1009). AS would like to acknowledge the support of ONR. The authors also like to thank Jie Yu for various discussions about linear shallow water equations.
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Office of Naval Research (ONR)N00014-04-1-0215
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Andrew StuartJ72
Issue or Number:2
Record Number:CaltechAUTHORS:20161108-173409695
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71845
Deposited By: Linda Taddeo
Deposited On:10 Nov 2016 00:45
Last Modified:11 Nov 2021 04:52

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