Abstract
Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, including the geosciences, but their application to high‐dimensional geoscience systems has been limited due to their inefficiency in high‐dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localization and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state‐of‐the‐art discussion of present efforts of developing particle filters for high‐dimensional nonlinear geoscience state‐estimation problems, with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations and unifications, highlighting hidden connections, including pseudo‐code, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present‐day methods for numerical weather prediction, suggesting that they will become mainstream soon.
Highlights
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An extra complication is localisation over time needed in ensemble smoothers like the Ensemble Kalman Smoother and 4DEnsVar when the fluid flow is strong: what is local at observation time is not necessary local at the start of the assimilation window because the observation influence is advected with the flow
This remarkable result shows that firstly the optimal proposal density, so p(xn|xni −1, yn), does lead to the lowest variance in the weights for the class of particle filters in which the transition density is of the form q(xn|i, xn1:−N1, yn)
Summary
To illustrate the idea of a proposal density we consider the following simple example. For the second term we use that varXn|I (W ) ≥ 0 with equality if This shows two things: First, in this special case, the simple and only if W is almost surely constant in Xn, that is if and only relaxation scheme of Section 2.1 is equal to the optimal proposal if p(xn|xni −1, yn) q(xn|i, xn1:−N1, yn) cst(i, xn1:−N1, yn). Snyder et al (2015) show that the optimal proposal is the proposal of this form with minimal variance in the weights in this case too, which can be seen by applying the above to This remarkable result shows that firstly the optimal proposal density, so p(xn|xni −1, yn), does lead to the lowest variance in the weights for the class of particle filters in which the transition density is of the form q(xn|i, xn1:−N1, yn). This was first explored in detail by Morzfeld et al (2017)
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Schedule a callMore From: Quarterly journal of the Royal Meteorological Society. Royal Meteorological Society (Great Britain)
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