Using our notation, the EnKF algorithm can be formulated as follows.
However, EnKF has various problems and numerous variants have been developed to overcome these issues; see, e.
In VEnKF, we calculate the sample covariance using the state estimate evolved from the previous time as the expectation instead of the sample mean used in EnKF.
Romine, 2014: An investigation of the Goshen County, Wyoming, tornadic supercell of 5 June 2009 using EnKF
assimilation of mobile mesonet and radar observations collected during VORTEX2.
The second regional-scale OSSE employing an EnKF
assimilation system (Anderson et al.
A practical implementation of a coupled DA system is most direct when starting from separate EnKF
systems because the EnKF
needs only the observation innovations.
The deterministic forecast in each case is initialized by the EnKF analysis (time-shifted to the closest 0000, 0600, 1200, or 1800 UTC) that assimilates the airborne Doppler radar observations in D1-D3, and then integrated forward for 126 h.
With the late-model treatment, the WRF EnKF forecast is still comparable to the NHC official forecasts in track (with noticeable degradation from day 3 to day 5; Fig.
Initialized at the end of the EnKF assimilation window--around four days before final landfall--the ensemble forecasts are from the individual members, whereas each deterministic forecast uses the ensemble mean.
The application of EnKF to real observations also showed progress in recent years.
One challenge for the application of EnKF to the convective scale is to properly account for model errors because the nonlinear error grows rapidly in a convective system and the EnKF technique relies on the model to produce flow-dependent error covariance.
EnKF has been shown to have a particular strength in handling complex physical processes.