Estimation of observation error correlation within ensemble Kalman filter

The treatment of error-correlated observations is an important problem in practice, but usually the observation error covariance matrix is assumed to be diagonal for simplicity and computational reasons. The observation error variance can be estimated by innovation statistics (Hollingsworth and Lonnberg 1986), but it is generally difficult to estimate observation error correlations. Although most observations are made independently and those errors are assumed to be uncorrelated, some important observations including satellite-retrieved temperature profiles, atmospheric motion vectors (AMVs), and sea-surface winds by satellite scatterometers, are considered to have significantly correlated errors. The correlated errors are typically treated by increasing the observation error variance in data assimilation. Error-correlated observations have less information content than observations without error correlations, which is approximated by increasing observation error variance but still assuming no error correlation. This, which we call “method A”, is not equivalent to considering the error correlation explicitly in data assimilation, which we call “method B”.

One of the main purposes of this study is to see the difference between methods A and B. Another main issue addressed in this study is the capability of estimating the observation error correlations. For these investigations, we perform experiments using an ensemble Kalman filter (EnKF) applied to the Lorenz-96 model with 40 variables. Here, we simulate observations with correlated errors. First, we apply the method of adaptive estimation of the covariance inflation and observation error variance by Li et al. (2009) to see how the method works with error-correlated observations. Then, we generalize the method to estimate the observation error correlations explicitly. The comparison between the two experiments addresses how much impact the explicit consideration of correlated errors has in EnKF data assimilation.