A numerical ensemble-mean approach was employed to solve a nonlinear barotropic model with chastic basic flows to analyze the nonlinear effects in the formation of the North Atlantic Oscillation （NAO）. The nonlinear response to external forcing was more similar to the NAO mode than the linear response was, indicating the importance of nonlinearity. With increasing external forcing and enhanced low-frequency anomalies, the effect of nonlinearity increased. Therefore, for strong NAO events, nonlinearity should be considered.
The persistence barrier of sea surface temperature anomalies （SSTAs） in the North Pacific was investigated and compared with the ENSO spring persistence barrier. The results show that SSTAs in the central western North Pacific （CWNP） have a persistence barrier in summer： the persistence of SSTAs in the CWNP shows a significant decline in summer regardless of the starting month. Mechanisms of the summer persistence barrier in the CWNP are different from those of the spring persistence barrier of SSTAs in the central and eastern equatorial Pacific. The phase locking of SSTAs to the annual cycle does not explain the CWNP summer persistence barrier. Remote ENSO forcing has little linear influence on the CWNP summer persistence barrier, compared with local upper-ocean process and atmospheric forcing in the North Pacific. Starting in wintertime, SSTAs extend down to the deep winter mixed layer then become sequestered beneath the shallow summer mixed layer, which is decoupled from the surface layer. Thus, wintertime SSTAs do not persist through the following summer. Starting in summertime, persistence of summer SSTAs until autumn can be explained by the atmospheric forcing through a positive SSTAs-cloud/radiation feedback mechanism because the shallow summertime mixed layer is decoupled from the temperature anomalies at depth, then the following autumnwinter-spring, SSTAs persist. Thus, summer SSTAs in the CWNP have a long persistence, showing a significant decline in the following summer. In this way, SSTAs in the CWNP show a persistence barrier in summer regardless of the starting month.
