Localization and sampling error correction in ensemble Kalman filter data assimilation

The sample covariance can be suboptimal as a result of small ensemble size, model error, model nonlinearity, and other factors. The most common algorithms for dealing with these deficiencies are inflation and covariance localization.

A statistical model of errors in ensemble Kalman filter sample covariances is described and leads to an algorithm that reduces ensemble filter root-mean-square error for some applications. This sampling error correction algorithm uses prior information about the distribution of the correlation between an observation and a state variable. Offline Monte Carlo simulation is used to build a lookup table that contains a correction factor between 0 and 1 depending on the ensemble size and the ensemble sample correlation.