Particle filters and stochastic transport models for geophysical data assimilation: localization and scalability*

Data assimilation (DA) is an essential Bayesian inference methodology used in weather forecasting and ocean prediction. In recent years, higher model resolution and complex observation sensors make it a priority to develop DA techniques that can handle highly non-linear models. Particle filters, compared to other existing methodologies, are well-suited to deal with non-linear, non-Gaussian models. Their use in geophysical data assimilation, however, is not yet widespread due to the so-called "curse of dimensionality". In this talk we propose a new strategy for assimilation of high-resolution geophysical fluids data, combining particle filters with ocean models with stochastic transport. The particle trajectories are modelled by runs of stochastic partial differential equations, simulated at a coarser resolution than the data. The stochasticity is introduced in the models in a physical way, to capture subgrid-scale processes. To overcame the problem of weight degeneracy in the particle filter, we introduce a localization method based on the use of the Gaspari–Cohn localization function, which tapers off the importance of the observations the further away they are from each region of interest. In each region, we run a smaller, independent, particle filter, which, together with resulting in a parallelizable implementation, also reduces the number of resampling, tempering and jittering steps required to avoid degeneracy of the ensemble. We present some initial results by testing our particle filter in a "twin experiment" for the 2D (stochastic) rotating shallow water equations, where the signal is taken to be an SPDE path, run on the same grid as the particle ensemble. In later experiments we will first generate high-resolution data synthetically using fine grid PDE runs, and, if successful, we will then test our methodology on SWOT satellite data. This is joint work with Dan Crisan.