Recommendation on Choice of Filter Algorithm

PDAF provides several filter algorithms. Here, we provide some guidance about which filter algorithm one should use.

The filter algorithms that are currently implemented in PDAF have been used in comparison studies giving insight in the performance of different filter formulations. In particular, the Ensemble Kalman Filter (EnKF, Evensen, 1994) was compared with the SEEK and SEIK filters (Pham et al., 1998) in Nerger et al. (1995) (the links refer to the page listing the full references of the publications). The SEIK filter was then related to the ETKF (Bishop, 2002) in Nerger et al. (2012). This study also introduced the ESTKF. Nerger et al. (2006) introduced the localized SEIK filter LSEIK. The local filters LETKF and LESTKF use the same localization method as the LSEIK filter.

Based on our studies, we generally recommend to use the ESTKF or its localized variant LESTKF. Nerger et al. (1995) already showed advantages of the SEIK filter over the SEEK filter and the EnKF. Nerger et al. (2012) showed that the ESTKF combines the advantages for the ETKF and the SEIK filter. In particular, the ESTKF can be used with a deterministic minimum transformation as the ETKF, but at a slightly lower computational cost. Unlike the SEIK filter, the analysis ensemble of the ESTKF is independent of the order of the ensemble members in the ensemble matrix. The ESTKF can also be used with a random transformation, which is often used in the SEIK filter. In this case, the matrix square root can be computed by a Cholesky decomposition, which is faster than the singular value decomposition used to compute the symmetric square root that is required for the minimum transformation.

The choice whether a global filter like ESTKF or a local formulation as LESTKF is used depends on the problem that is simulated. If the model represents large scale features, the global filter should be a good choice. If the model fields represent many small scale features, the local filter is required. Also the availability of observations influences that choice. If only a very small number of observations is available, it might be better to use the global filter. In contrast, spatially resolved observations, like surface temperature fields of the ocean detected by satellites, call for the local filter.