Pushing nonlinear data assimilation towards high dimensional systems

Peter Jan van Leeuwen, Department  of Meteorology, University of Reading, United Kingdom

Abstract for Special Colloquium on  Wednesday, February 22, 2017 from 2-3pm - Location TBD

Abstract:

There is a growing demand for data-assimilation methods that can handle complex highly nonlinear models and nonlinear relations between models and observations when the system is high dimensional. Examples are convective scale weather prediction, eddy-resolving ocean systems, and space weather, to name a few. Fully nonlinear data-assimilation methods do exist, typically based on Markov-Chain Monte-Carlo methods, but they are inefficient in high dimensions. Recently, Particle filters have been developed that use smart proposal densities, like the Implicit Particle Filter, but even for those it can be proven that they will fail in the high-dimensional limit.

In this talk I will introduce a different class of particle filters that are efficient in high-dimensions by construction. This comes at the price of a bias in the filter, but experimentation shows that the bias is smaller than the Monte-Carlo noise when the number of particles is in a realistic range of 10-500. Results on high dimensional geophysical systems will be shown, as well as initial attempts to understand the bias better, and attempts to elevate it altogether exploring ideas from statistical physics.

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