Sampling, feasibility, and priors in data assimilation

Tu, Xuemin; Morzfeld, Matthias; Miller, Robert N.; Lu, Fei; Chorin, Alexandre J.

doi:10.3934/dcds.2016.36.4227

Title: Sampling, feasibility, and priors in data assimilation

Journal Article · Tue Mar 01 00:00:00 EST 2016 · Discrete and Continuous Dynamical Systems

DOI:https://doi.org/10.3934/dcds.2016.36.4227· OSTI ID:1439205

Tu, Xuemin ^[1]; Morzfeld, Matthias ^[2]; Miller, Robert N. ^[3]; Lu, Fei ^[4]; Chorin, Alexandre J. ^[4]

Univ. of Kansas, Lawrence, KS (United States)
Univ. of Arizona, Tucson, AZ (United States)
Oregon State Univ., Corvallis, OR (United States)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Importance sampling algorithms are discussed in detail, with an emphasis on implicit sampling, and applied to data assimilation via particle filters. Implicit sampling makes it possible to use the data to find high-probability samples at relatively low cost, making the assimilation more efficient. A new analysis of the feasibility of data assimilation is presented, showing in detail why feasibility depends on the Frobenius norm of the covariance matrix of the noise and not on the number of variables. A discussion of the convergence of particular particle filters follows. A major open problem in numerical data assimilation is the determination of appropriate priors, a progress report on recent work on this problem is given. The analysis highlights the need for a careful attention both to the data and to the physics in data assimilation problems.

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Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1439205

Alternate ID(s):: OSTI ID: 1379537

Journal Information:: Discrete and Continuous Dynamical Systems, Vol. 36, Issue 8; ISSN 1078-0947

Publisher:: American Institute of Mathematical SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data Lu, Fei; Weitzel, Nils; Monahan, Adam H. Nonlinear Processes in Geophysics, Vol. 26, Issue 3 https://doi.org/10.5194/npg-26-227-2019	journal	January 2019
Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy data Lu, Fei; Weitzel, Nils; Monahan, Adam H. arXiv https://doi.org/10.48550/arxiv.1904.05310	text	January 2019

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