A comparison of the equivalent weights particle filter and the local ensemble transform Kalman filter in application to the barotropic vorticity equation

A B S T R A C T Data assimilation methods that work in high dimensional systems are crucial to many areas of the geosciences: meteorology, oceanography, climate science etc. The equivalent weights particle filter has been designed, and has recently been shown to, scale to problems that are of use to these communities. This article performs a systematic comparison of the equivalent weights particle filter with the established and widely used local ensemble transform Kalman filter. Both methods are applied to the barotropic vorticity equation for different networks of observations. In all cases it was found that the local ensemble transform Kalman filter produced lower root mean squared errors than the equivalent weights particle filter. The performance of the equivalent weights particle filter is shown to depend strongly on the form of nudging used, and a nudging term based on the local ensemble transform Kalman smoother is shown to improve the performance of the filter. This indicates that the equivalent weights particle filter must be considered as a truly 2-stage filter and not only by its final step which avoids weight collapse.