Whitaker J. S., and T. M. Hamill, 2002: Ensemble data
assimilation without perturbed observations. Mon. Wea. Rev.,
130, 1913-1924. The ensemble Kalman filter (EnKF) is a data
assimilation scheme based on the traditional Kalman-filter
update equation. An ensemble of forecasts are to estimate the
background-error covariances needed to compute the Kalman gain.
It has been shown that if the same observations and the same
gain are used to update each member of the ensemble, the
ensemble will systematically underestimate analysis-error
covariances. This will cause a degradation of subsequent
analyses and may lead to filter divergence. For large ensembles,
it has been shown that this problem can be alleviated by
treating the observations as random variables, adding random
perturbations to them with the correct statistics. Two important
consequences of sampling error in the estimate of analysis-error
covariances in the EnKF are discussed here. The first results
from the analysis-error covariance being a nonlinear fun