Data assimilation for large scale spatio-temporal systems using a location particle smoother

Abstract

Data assimilation estimates the time evolution of the probability density function (PDF) of state vectors characterising high-dimensional nonlinear spatiotemporal dynamic systems, making use of available observations. The current best-practice statistical data assimilation technique – the ensemble Kalman filter – relies on restrictive normality assumptions. The particle filter provides a methodology for estimating these PDFs without requiring these restrictive distributional assumptions using samples drawn from the conditional state PDF given available observations. Unfortunately, particle filter weight collapse is severe when the state and/or observation vectors are high dimensional, making them impractical for systems with a spatial component. We offer a solution to this problem by drawing the required sample from the conditional PDF at each time step using a particle smoother across the spatial locations. A further innovation is the use of meta-elliptical copulas to provide a general framework for defining the prediction PDFs – one flexible enough to accurately describe the numerical model errors and fast enough to sample to be applicable in practice. The proposed methods perform well compared with other candidate approaches in a 1000 dimensional spatiotemporal simulation study and a real 1750 dimensional marine ecosystem application based on partial differential equations and ocean monitoring data.