Spurious correlations, localization, and inflation

The use of a finite ensemble size to approximate the error covariance matrix introduces sampling errors that are seen as spurious correlations over long spatial distances or between variables known to be uncorrelated. The spurios correlations imply that variables that are supposed to be uncorrelated with an observation, experience a small unphysical update. Over time and with many data, the spurious updates may cancel out and the drift in the mean may be negligible. However, with each spurious update there is an associated reduction of ensemble variance and over time the ensemble variance may significantly underestimate the true variance. This problem is present in all EnKF applications and can lead to filter divergence. On the other hand, the consistency of the updated variance improves when a larger ensemble is used.