Behaviors of nonlinearities modulating the El Nio events induced by optimal precursory disturbances

In the present paper, we explore the manner in which nonlinearities modulate El Nio events by investigating the optimal precursory disturbance for El Nio events in the Zebiak-Cane model. The initial anomalies of conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are investigated. The CNOPs evolve into stronger El Nio events than the LSVs and act as the optimal precursor for El Nio events. By examining the role of nonlinearities in El Nio events induced by CNOPs and LSVs, we determined that, when the initial anomalies of the CNOP and LSV structures are large, the nonlinearities enhance CNOP-El Nio events but suppress LSV-El Nio events. Nonlinearities in the Zebiak-Cane model arise from nonlinear temperature advection (NTA), sub-surface temperature parameterization (STP), and wind stress anomalies (WSA). Using these types of nonlinearities, we trace the approach of the nonlinearities modulating the CNOP- and LSV-El Nio events. The results demonstrate that nonlinearities that originate from NTA enhance both CNOP-El Nio events and LSV-El Nio events, while nonlinearities originating from STP and WSA suppress these events. For the CNOP-El Nio events, the enhancement effect of NTA is larger than the suppression effect of STP and WSA, resulting in the combined effect of the nonlinearities in the Zebiak-Cane model being an enhancement of the CNOP-El Nio events. However, for the LSV-El Nio events, the enhancement effect of NTA is smaller than the suppression effect of WSA and STP. Consequently, the combined effect of the nonlinearities in the Zebiak-Cane model suppresses the LSV-El Nio events.