The influence matrix reflects the regression fit of the analysis to the observation data. The diagonal value, which is the self-sensitivity, gives a measure of the sensitivity of the analysis to the changing observation value. These measures give the analysis sensitivity to the observations, and can further show the relative impact of the observation on the performance of the analysis system. The sum of the diagonal values for a particular set of observations defines its information content (Cardinali et al, 2004).

Based on Cardinali et al. (2004), we propose a method to calculate the influence matrix and the self-sensitivity along with the LETKF data assimilation scheme. Since the Kalman gain is computed within the LETKF, and the influence matrix is the transformation of the Kalman gain into the observation space, the computation of the sensitivity does not need much extra computation time. However, in the LETKF, each observation is used more than once in different local patches so that we propose an averaging scheme over different patches to calculate the self-sensitivity for each observation or set of observations. We validate the averaging scheme by comparing the self-sensitivity of ETKF and the LETKF on the Lorenz-40 variable model.

With a primitive equation model, we further compare the information content and the quantitative observation impact calculated from data denial sensitivity experiments. The results show that the information content qualitatively reflects the observation impact spatially. It implies that the spatial information content distribution can be utilized in the design of observation impact experiments, and may also be a good measure to compare the effectiveness of the instruments that measure the same type of observations.