Analysis sensitivity calculation in an ensemble Kalman filter

Analysis sensitivity indicates the sensitivity of an analysis to the observations, which is complementary to the sensitivity of the analysis to the background. In this paper, we discuss a method to calculate this quantity in an Ensemble Kalman Filter (EnKF). The calculation procedure and the geometrical interpretation, which shows that the analysis sensitivity is proportional to the analysis error and anti-correlated with the observation error, are experimentally verified with the Lorenz 40-variable model. With the analysis sensitivity, the cross-validation in its original formulation can be efficiently computed in EnKFs, and this property can be used in observational quality control. Idealized experiments based on a simplified-parametrization primitive equation global model show that the information content (the trace of the analysis sensitivity of any subset of observations) qualitatively agrees with the actual observation impact calculated from much more expensive data-denial experiments, not only for the same type of dynamical variable, but also for different types of dynamical variables. Copyright (C) 2009 Royal Meteorological Society