Efficient Nonlinear Filtering of Multiscale Systems with Specific Structure

The purpose of this paper is to build on efficient nonlinear filtering techniques of multiscale dynamical systems by focusing on the case where the multiscale systems of interest have specific structure and properties, that can be exploited to reduce computational runtime while maintaining a fixed accuracy. We use ideas previously implemented in deterministic and stochastic parameterizations to shift computational work related to resolving transition densities and integrations against these densities to an offline calculation, as opposed to schemes like the heterogenous multiscale method, which is an inherently online computation. The technique is independent of the ensemble based filter chosen, as the contributions effect the predictor step of the filtering algorithm. We extended these techniques to a nudged particle filter that excels when the dynamical system is chaotic and compare against a standard particle filter and one using the heterogenous multiscale method on the Lorenz 1996 atmospheric test problem.