An Implementation of the Particle Flow Filter (PFF) in the Data Assimilation Research Testbed (DART)

Standard particle filter methods suffer from weight collapse when applied to high dimensional systems which makes them difficult to implement in geophysical models. Recently, the Particle Flow Filter (PFF), with matrix kernel, has been shown to work effectively in high dimensional models. The PFF is based on a particle flow, which transforms the particles iteratively in state space from samples of the prior to samples of the posterior, instead of resampling the particles. Therefore, the PFF avoids the problem of weight collapse as the particles have equal weight at every iteration by construction. The PFF is implemented in the Data Assimilation Research Testbed (DART) community data assimilation system, in order to test the performance of the PFF for atmospheric problems. To efficiently implement the PFF in DART, the localized prior background covariance matrix is used as the preconditioner, along with a special kind of matrix kernel for the PFF. With this choice of the preconditioner and kernel, we do not need to compute the full prior covariance matrix. This is especially important in the DART distributed computing framework since we can greatly reduce computation by exchanging messages between processors when computing in parallel. We will demonstrate the performance of the PFF in a simple atmospheric model to see how the PFF can correctly capture the relations between variables.