A random map implementation of implicit filters

Authors:
Matthias Morzfeld;Xuemin Tu;Ethan Atkins;Alexandre J. Chorin
Affiliations:
Lawrence Berkeley National Laboratory, Berkeley, CA, United States;Department of Mathematics, University of Kansas, Lawrence, KS, United States;Lawrence Berkeley National Laboratory, Berkeley, CA, United States and Department of Mathematics, University of California, Berkeley, CA, United States;Lawrence Berkeley National Laboratory, Berkeley, CA, United States and Department of Mathematics, University of California, Berkeley, CA, United States
Venue:
Journal of Computational Physics
Year:
2012

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Abstract

Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined equation be solved for each particle and at each time an observation becomes available. We present a new implementation of implicit filters in which we find the solution of the equation via a random map. As examples, we assimilate data for a stochastically driven Lorenz system with sparse observations and for a stochastic Kuramoto-Sivashinsky equation with observations that are sparse in both space and time.