Physics

Geology

Meteorology

Nonlinear system

Inefficiency

Algorithm

Oceanography

Resampling

Artificial intelligence

Kalman filter

Economics

Microeconomics

Extended Kalman filter

Data assimilation

Particle (ecology)

Computer science

Quantum mechanics

Ensemble Kalman filter

Particle filter

Quarterly Journal of the Royal Meteorological Society

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.

Particle filters for high‐dimensional geoscience applications: A review