Particle Filtering for Stochastic Navier-Stokes Signal Observed with Linear Additive Noise

TL;DR

This paper develops a particle filtering approach tailored for stochastic Navier-Stokes equations with linear noisy observations, enhancing data assimilation in weather and climate models.

Contribution

It introduces a novel particle filtering method combining likelihood-informed proposals, adaptive tempering, and MCMC steps for improved efficiency and accuracy.

Findings

Method achieves better performance in numerical experiments.

Incorporating MCMC steps improves filter accuracy.

Adaptive tempering enhances computational efficiency.

Abstract

We consider a non-linear filtering problem, whereby the signal obeys the stochastic Navier-Stokes equations and is observed through a linear mapping with additive noise. The setup is relevant to data assimilation for numerical weather prediction and climate modelling, where similar models are used for unknown ocean or wind velocities. We present a particle filtering methodology that uses likelihood informed importance proposals, adaptive tempering, and a small number of appropriate Markov Chain Monte Carlo steps. We provide a detailed design for each of these steps and show in our numerical examples that they are all crucial in terms of achieving good performance and efficiency.