[8] Mathematical aspect 2


[8-1] February 28, 13:40-14:10

[Invited]

Nonlinear data assimilation via hybrid particle-Kalman filters and optimal coupling

Walter Acevedo, Universität Potsdam, Germany, acevedo@uni-potsdam.de Sebastian Reich, Universität Potsdam, Germany, sereich@rz.uni-potsdam.de

 
Abstract

Particle filters (PFs) constitute a powerful data assimilation approach as they provide consistent estimates in the context of nonlinear evolution equations, however their susceptibility to the curse of dimensionality have considerably hindered their application to spatially extended systems. Two popular approaches to overcome this limitation are (i) localization, in order to reduce the local dimensionality of the estimation problem, and (ii) hybridization with ensemble Kalman filters, in order to have a robust baseline for moderate ensemble sizes while still taking into account the non-Gaussian features of the involved PDFs. A particularly suitable PF for these two strategies is the Ensemble Transform Particle Filter (ETPF), where the resampling step of standard PFs is replaced by the optimal coupling between forecast and analysis probability measures. Such an update is given by a deterministic linear transformation very compatible with Ensemble Transform Kalman filtering schemes, and which can be naturally localized. We performed numerical experiments for a hierarchy of toy models and found that our hybrid approach can outperform both Kalman and particle filters at moderate ensemble sizes.