In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system...In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.展开更多
We use conditional nonlinear optimal perturbation （CNOP） to investigate the optimal precursory disturbances in the Zebiak- Cane El Nino-Southern Oscillation （ENSO） model. The conditions of the CNOP-type precursors...We use conditional nonlinear optimal perturbation （CNOP） to investigate the optimal precursory disturbances in the Zebiak- Cane El Nino-Southern Oscillation （ENSO） model. The conditions of the CNOP-type precursors are highly likely to evolve into El Nino events in the Zebiak-Cane model. By exploring the dynamic behaviors of these nonlinear El Nino events caused by the CNOP-type precursors, we find that they, as expected, tend to phase-lock to the annual cycles in the Zebiak-Cane model with the SSTA peak at the end of a calendar year. However, E1 Nino events with CNOPs as initial anomalies in the linearized Zebiak-Cane model are inclined to phase-lock earlier than nonlinear E1 Nino events despite the existence of annual cycles in the model. It is clear that nonlinearities play an important role in El Nino＇s phase-locking. In particular, nonlinear temperature advection increases anomalous zonal SST differences and anomalous westerlies, which weakens anomalous upwelling and acts on the increasing anomalous vertical temperature difference and, as a result, enhances E1 Nino and then delays the peak SSTA. Finally, we demonstrate that nonlinear temperature advection, together with the effect of the annual cycle, causes El Nino events to peak at the end of the calendar year.展开更多
基金Foundation item： Supported by the Science Foundation of Liuzhou Vocational Institute of Technology（2007C03）
文摘In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.
基金sponsored by the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.KZCX2-YW-QN203)the National Basic Research Program of China(Grant Nos.2010CB950400&2012CB955202)the National Natural Science Foundation of China(Grant No.41176013)
文摘We use conditional nonlinear optimal perturbation （CNOP） to investigate the optimal precursory disturbances in the Zebiak- Cane El Nino-Southern Oscillation （ENSO） model. The conditions of the CNOP-type precursors are highly likely to evolve into El Nino events in the Zebiak-Cane model. By exploring the dynamic behaviors of these nonlinear El Nino events caused by the CNOP-type precursors, we find that they, as expected, tend to phase-lock to the annual cycles in the Zebiak-Cane model with the SSTA peak at the end of a calendar year. However, E1 Nino events with CNOPs as initial anomalies in the linearized Zebiak-Cane model are inclined to phase-lock earlier than nonlinear E1 Nino events despite the existence of annual cycles in the model. It is clear that nonlinearities play an important role in El Nino＇s phase-locking. In particular, nonlinear temperature advection increases anomalous zonal SST differences and anomalous westerlies, which weakens anomalous upwelling and acts on the increasing anomalous vertical temperature difference and, as a result, enhances E1 Nino and then delays the peak SSTA. Finally, we demonstrate that nonlinear temperature advection, together with the effect of the annual cycle, causes El Nino events to peak at the end of the calendar year.
