Nonlinear data assimilation in geosciences: an extremely efficient particle filter

TLDR

Geoscience research combines numerical models and observations through data‑assimilation, but increasing model resolution and observation complexity make these systems highly nonlinear, causing standard linearized techniques like Kalman filters and 4D‑Var to fail and limiting existing nonlinear methods to low‑dimensional problems. The authors propose a fully nonlinear particle filter that exploits the flexibility of the proposal density to address higher‑dimensional data‑assimilation challenges. They demonstrate the filter on the Lorenz system, using three particles for the 3‑D model and twenty particles for the 40‑D model. Applying the same twenty‑particle filter to the 1000‑D Lorenz model shows strong scale‑invariance, suggesting the method could scale to realistic geophysical problems. © 2010 Royal Meteorological Society.

Abstract

Abstract Almost all research fields in geosciences use numerical models and observations and combine these using data‐assimilation techniques. With ever‐increasing resolution and complexity, the numerical models tend to be highly nonlinear and also observations become more complicated and their relation to the models more nonlinear. Standard data‐assimilation techniques like (ensemble) Kalman filters and variational methods like 4D‐Var rely on linearizations and are likely to fail in one way or another. Nonlinear data‐assimilation techniques are available, but are only efficient for small‐dimensional problems, hampered by the so‐called ‘curse of dimensionality’. Here we present a fully nonlinear particle filter that can be applied to higher dimensional problems by exploiting the freedom of the proposal density inherent in particle filtering. The method is illustrated for the three‐dimensional Lorenz model using three particles and the much more complex 40‐dimensional Lorenz model using 20 particles. By also applying the method to the 1000‐dimensional Lorenz model, again using only 20 particles, we demonstrate the strong scale‐invariance of the method, leading to the optimistic conjecture that the method is applicable to realistic geophysical problems. Copyright © 2010 Royal Meteorological Society