Season-dependent dynamics of nonlinear optimal error growth and El Nino-Southern Oscillation predictability in a theoretical model

[ 1] Most state-of-the-art climate models have difficulty in the prediction of El Nino-Southern Oscillation (ENSO) starting from preboreal spring seasons. The causes of this spring predictability barrier (SPB) remain elusive. With a theoretical ENSO system model, we investigate this controversial issue by tracing the evolution of conditional nonlinear optimal perturbation (CNOP) and by analyzing the behavior of initial error growth. The CNOPs are the errors in the initial states of ENSO events, which have the biggest impact on the uncertainties at the prediction time under proper physical constraints. We show that the evolution of CNOP-type errors associated with El Nino episodes depends remarkably on season with the fastest growth occurring during boreal spring in the onset phase. There also exist other kinds of initial errors, which have either somewhat smaller growth rates or neutral ones during spring. However, for La Nina events, even if initial errors are of CNOP-type, the errors grow without significant seasonal dependence. These findings suggest that the SPB in this model results from combined effects of three factors: the annual cycle of the mean state, the structure of El Nino, and the pattern of the initial errors. On the basis of the error tendency equations derived from the model, we addressed how the combination of the three factors causes the SPB and proposed a mechanism responsible for the error growth in the model ENSO events. Our results help in clarifying the role of the initial error pattern in SPB, which may provide a clue for explaining why SPB can be eliminated by improving initial conditions. The results also illustrate a theoretical basis for improving data assimilation in ENSO prediction.