Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model

An experiment has been performed, using a simple chaotic model, to compare different ensemble perturbation strategies. The model used is a 300 variable Lorenz 95 model which displays many of the characteristics of atmospheric numerical weather prediction models. Twenty member ensembles were generated using five perturbation strategies, error breeding, singular vectors, random perturbations (RPs), the Ensemble Kalman Filter (EnKF) and the Ensemble Transform Kalman Filter (ETKF). Based on normal verification methods, such as rank histograms and spread of the perturbations, the RPs method performs as well as any other method—this illustrates the limitations of using a simple model. Consideration of the quality of the background error information provided by the ensemble gives a better assessment of the ensemble skill. This measure indicates that the EnKF performs best, with the ETKF combined with RPs being the next most skillful. It was found that neither the ETKF, error breeding nor singular vectors provided useful background information on their own. Central to the success of the EnKF is the localization of the background error covariance which removes spurious long-range correlations within the ensemble. Computationally efficient versions of the EnKF (such as the ETKF) cannot accommodate covariance localization and their performance is seen to suffer. Applying the ETKF to a series of local domains has been tested, which allows covariance localization whilst remaining computational efficient, and this has been found to be nearly as effective as the EnKF with covariance localization.