  Covariance inflation and localization are two important techniques that are
used to improve the performance of the ensemble Kalman filter (EnKF) by (in
effect) adjusting the sample covariances of the estimates in the state space.
In this work an additional auxiliary technique, called residual nudging, is
proposed to monitor and, if necessary, adjust the residual norms of state
estimates in the observation space. In an EnKF with residual nudging, if the
residual norm of an analysis is larger than a pre-specified value, then the
analysis is replaced by a new one whose residual norm is no larger than a
pre-specified value. Otherwise the analysis is considered as a reasonable
estimate and no change is made. A rule for choosing the pre-specified value is
suggested. Based on this rule, the corresponding new state estimates are
explicitly derived in case of linear observations. Numerical experiments in the
40-dimensional Lorenz 96 model show that introducing residual nudging to an
EnKF may improve its accuracy and/or enhance its stability against filter
divergence, especially in the small ensemble scenario.
