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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/npg-2019-1
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2019-1
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 08 Feb 2019

Research article | 08 Feb 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Precision Annealing Monte Carlo Methods for Statistical Data Assimilation: Metropolis-Hastings Procedures

Adrian S. Wong1, Kangbo Hao1, Zheng Fang1, and Henry D. I. Abarbanel2,3 Adrian S. Wong et al.
  • 1Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093
  • 2Marine Physical Laboratory, Scripps Institution of Oceanography
  • 3Department of Physics, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093

Abstract. Statistical Data Assimilation (SDA) is the transfer of information from field or laboratory observations to a user selected model of the dynamical system producing those observations. The data is noisy and the model has errors; the information transfer addresses properties of the conditional probability distribution of the states of the model conditioned on the observations. The quantities of interest in SDA are the conditional expected values of functions of the model state, and these require the approximate evaluation of high dimensional integrals. We introduce a conditional probability distribution and use the Laplace method with annealing to identify the maxima of the conditional probability distribution. The annealing method slowly increases the precision term of the model as it enters the Laplace method. In this paper, we extend the idea of precision annealing (PA) to Monte Carlo calculations of conditional expected values using Metropolis-Hastings methods.

Adrian S. Wong et al.
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Adrian S. Wong et al.
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Latest update: 23 Mar 2019
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Short summary
Our paper deals with data assimilation methods for chaotic systems and how one can make predictions from incomplete data of such systems. The method that we chose to explore in detail is a Monte Carlo method with an annealing heuristic. Our results show that Monte Carlo methods are a viable alternatives to the standard set of derivative-based methods. We verify the method using the Lorenz 96 system due to the simplicity of that system.
Our paper deals with data assimilation methods for chaotic systems and how one can make...
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