How important is a 4-d approach in the LETKF framework?
We compare a 3d version of LETKF with the operational 4d version in our KENDA framework. KENDA (Kilometer scale Ensemble Data Assimilation) is the operational data assimilation system at DWD for the convective scale. It applies a LETKF implementation following Hunt et al. (2007) to the COSMO model and currently uses conventional data plus latent heat nudging.
In the 4d version, the observation increments are computed and collected during the model run started from previous analysis step. The observation operator is applied any time a new observation is available. As a consequence, the B matrix in observation space as used in the LETKF is 4d and contains spatial as well as temporal correlations. In the 3d version, the observation increments are applied after the model run, assuming that all observations since the previous analysis step are valid at analysis time. Though we find many advantages of 4d methods over 3d methods, there are also some technical issues and restrictions, e.g. when using IAU (Incremental Analysis Update) or applying additive covariance inflation.
Also, we are testing to expand KENDA by the EnVar method (Buehner 2005), which is currently running operationally at DWD for the global model in a 3-hourly cycle.
Dr. Hendrik Reich German Weather Service (DWD)