On some aspects of the definition of initial conditions for ensemble prediction

Four methods for initialization of ensemble forecasts are systematically compared, namely the methods of singular vectors (SV) and bred modes (BM), as well as the ensemble Kalman filter (EnKF) and the ensemble transform Kalman filter (ETKF). The comparison is done on synthetic data with two models of the flow, namely, a low-order model introduced by Lorenz and a three-level quasigeostrophic atmospheric model. For the latter, both cases of a perfect and an imperfect model are considered. The performance of the various initialization methods is assessed in terms of the statistical reliability and resolution of the ensuing predictions. The relative performance of the four methods, which is statistically significant to a range of about 6 days, is in the order EnKF > ETKF > BM > SV. The difference between the former two methods and the latter two is on the whole more significant than the differences between EnKF and ETKF, or between BM and SV separately. The general conclusion is that, if the quality of ensemble predictions is assessed by the degree to which the predicted ensembles statistically sample the uncertainty on the future state of the flow, the best initial ensembles are those that best statistically sample the uncertainty on the present state of the flow.