Recommendations on the 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 transformation of the ensemble is independent of the order of the ensemble members in the ensemble matrix in the ESTKF. 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. While the ESTKF provides these advantages it is computationally not more expensive than the SEIK filter.

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.

To use the global ESTKF with minimum transformation one has to specify (following the naming of variables used in the example in /testsuite/src/dummymodel_1D/):

parameter	value	comment
filtertype	6	Selecting ESTKF
type_sqrt	0	This specifies the SVD-based symmetric square root
type_trans	0	This specifies the deterministic ensemble transformation

For the global ESTKF with random transformation and cholesky decompostion one specifies:

parameter	value	comment
filtertype	6	Selecting ESTKF
type_sqrt	1	This specifies the Cholesky square root
type_trans	1	This specifies the random transformation