Testing particle filters on simple convective-scale models. Part2: Amodified shallow-water model

摘要

The nonlinearities and stochastic features of atmospheric dynamics pose severe challenges for data assimilation. The particle filter is a method that can potentially address these challenges and has attracted significant interest for convective-scale applications. Unlike data assimilation techniques used in current numerical weather prediction (NWP), the particle filter does not presuppose Gaussian error statistics but estimates the full probability density function (PDF) with a small number of state vectors (particles). The nudging proposal particle filter operates as a hybrid combination of nudging and sequential importance resampling (SIR). In this article, we investigate a refined nudging proposal particle filter algorithm, the equivalent-weight particle filter, that combines the nudging proposal particle filter with weight equalization and thus permits an improved representation of the PDF. An idealized, nonlinear, one-dimensional shallow-water model is used as a testbed to show that the equivalent-weight particle filter outperforms both nudging and SIR filters under certain conditions. The selection mechanism of particles during resampling and the effect of nudging on the weights are analyzed. With the help of analytical and experimental results, we identify a numerical quantity that determines whether the equivalent-weight particle filter can outperform nudging alone and we derive a theoretical criterion for the equivalent-weight particle filter to outperform nudging. Further, we investigate the effect of equalizing weights on the resampling and the statistical behaviour of the ensemble.