A Particle Flow method for high-dimensional atmospheric applications

Abstract:

Although linear data assimilation methods, such as various versions of the Ensemble Kalman Filter and variational methods, are able to improve the analysis of the atmospheric or oceanic model in weakly nonlinear regime, the linear approximation can fail when the problem involves complex nonlinear observation operators or highly nonlinear evolution equations.

Particle filters hold the promise of the fully nonlinear data assimilation. They are not limited to the Gaussian assumption, as is used in Ensemble Kalman Filters and variational methods. However, the standard particle filter methods suffer from weight collapse in high dimensional system, which makes them difficult to implement in the geophysical models. Recently, a newly proposed method, the Mapping Particle Filter (MPF), has been shown to have potential in high dimensional geophysical models. The MPF is based on a particle flow, which transforms the particles iteratively in state space from samples in the prior to samples of the posterior, instead of resampling the particles. Therefore, the MPF avoids the problem of weight collapse as the particles have equal weight at every iteration by construction. To solve this optimal transportation problem the method explores kernel embedding of the flow.

We will present application of the MPF to a high dimensional Lorenz 96 system with highly nonlinear observation operators and a very small number of particles. Furthermore, the MPF is applied in a high-dimensional atmospheric model. This involved reformulating the prior exploring Gaussian mixtures in the methodology. Furthermore, although theory shows that the shape of the kernel doesn’t matter when the ensemble size is infinitely large, it does matter when small ensemble sizes are used. We explored several kernel choices and will discuss their pro’s and con’s. Details of these new developments, of efficient implementation, and results and remaining issues will be discussed.

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