Implicit Particle Methods and Their Connection with Variational Data Assimilation

Ethan Atkins Department of Mathematics, University of California, Berkeley, Berkeley, California

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Matthias Morzfeld Lawrence Berkeley National Laboratory, Berkeley, California

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Alexandre J. Chorin Department of Mathematics, University of California, Berkeley, Berkeley, California

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Abstract

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. A new and more general derivation of this approach is presented and the method is extended to particle smoothing as well as to data assimilation for perfect models. Minimizations required by implicit particle methods are shown to be similar to those that one encounters in variational data assimilation, and the connection of implicit particle methods with variational data assimilation is explored. In particular, it is argued that existing variational codes can be converted into implicit particle methods at a low additional cost, often yielding better estimates that are also equipped with quantitative measures of the uncertainty. A detailed example is presented.

Corresponding author address: Matthias Morzfeld, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720. E-mail: mmo@math.lbl.gov

Abstract

The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. A new and more general derivation of this approach is presented and the method is extended to particle smoothing as well as to data assimilation for perfect models. Minimizations required by implicit particle methods are shown to be similar to those that one encounters in variational data assimilation, and the connection of implicit particle methods with variational data assimilation is explored. In particular, it is argued that existing variational codes can be converted into implicit particle methods at a low additional cost, often yielding better estimates that are also equipped with quantitative measures of the uncertainty. A detailed example is presented.

Corresponding author address: Matthias Morzfeld, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA 94720. E-mail: mmo@math.lbl.gov
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