Flow-dependent Empirical Singular Vectors for El Nino ensemble prediction with Ensemble Kalman Filter data assimilation

In this study, a new approach to extract Flow-dependent Empirical Singular Vectors (FESVs) for seasonal prediction using ensemble perturbations obtained from Ensemble Kalman Filter (EnKF) assimilation is developed. EnKF perturbations are not optimal perturbations for seasonal predictions, because it does not represent the slowly varying coupled instability due to short analysis interval. To overcome this deficiency, empirical linear operator for seasonal time-scale is formulated using hypothesis of causality, then ESVs from linear operator for longer time-scale is extracted. It is shown that flow-dependent operator better represents nonlinear integration results than conventional linear operator, which is static in time. Through the 20-yr of seasonal prediction, it is shown that forecast skills using Flow-dependent ESV (FESV) is significantly improved than that using Conventional ESVs (CESV) or EnKF perturbations. For example, the correlation skill of Nino3 index using FESV is higher about 0.1 than that of CESV, or EnKF perturbations at 9-month lead forecasts. In addition, the improvement of the forecast skill is significant where the correlation skill of conventional methods is relatively low, indicating that the FESV is effective when the initial uncertainty is large.