Data assimilation using particle filters in reduced-order model subspaces

Particle filters are a class of data assimilation techniques that can estimate the state and uncertainty of dynamical models by combining nonlinear evolution models with non-gaussian uncertainty distributions. However, estimating high dimensional states, such as those associated with spatially-discretized models, requires an exponentially-large size of estimation ensemble to avoid the so-called filter collapse, which dramatically decreases efficiency of the estimation. By combining particle filters with projection-based data-driven model reduction techniques, such as Proper Orthogonal Decomposition and Dynamic Mode Decomposition, we demonstrate that it is possible to reduce the effective dimension of the models and stave-off the filter collapse for a class of dynamical models relevant to forecasting of geophysical fluid flows. This technique can be adapted to account for models with transient change in parameters, by windowed building of the projection matrices. We demonstrate several variants of the technique on Lorenz’96-type models and on a simulation of shallow-water equations.