  The ensemble Kalman filter (EnKF) is an efficient algorithm for many data
assimilation problems. In certain circumstances, however, divergence of the
EnKF might be spotted. In previous studies, the authors proposed an
observation-space-based strategy, called residual nudging, to improve the
stability of the EnKF when dealing with linear observation operators. The main
idea behind residual nudging is to monitor and, if necessary, adjust the
distances (misfits) between the real observations and the simulated ones of the
state estimates, in the hope that by doing so one may be able to obtain better
estimation accuracy.
  In the present study, residual nudging is extended and modified in order to
handle nonlinear observation operators. Such extension and modification result
in an iterative filtering framework that, under suitable conditions, is able to
achieve the objective of residual nudging for data assimilation problems with
nonlinear observation operators. The 40 dimensional Lorenz 96 model is used to
illustrate the performance of the iterative filter. Numerical results show
that, while a normal EnKF may diverge with nonlinear observation operators, the
proposed iterative filter remains stable and leads to reasonable estimation
accuracy under various experimental settings.
