# American Institute of Mathematical Sciences

August  2016, 36(8): 4227-4246. doi: 10.3934/dcds.2016.36.4227

## Sampling, feasibility, and priors in data assimilation

 1 Department of Mathematics, University of California, Berkeley, and Lawrence Berkeley National Laboratory, Berkeley, CA 94720, United States 2 College of Earth, Ocean and Atmospheric Science, Oregon State University, Corvallis, OR 97331, United States 3 Department of Mathematics, University of Arizona, Tucson, AZ 85721, United States 4 Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States

Received  May 2015 Revised  August 2015 Published  March 2016

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.
Citation: Alexandre J. Chorin, Fei Lu, Robert N. Miller, Matthias Morzfeld, Xuemin Tu. Sampling, feasibility, and priors in data assimilation. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4227-4246. doi: 10.3934/dcds.2016.36.4227
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