Optimal precursor perturbations of El Nino in the Zebiak-Cane model were explored for three different cost functions. For the different characteristics of the eastern-Pacific （EP） El Nino and the central-Pacific （C...Optimal precursor perturbations of El Nino in the Zebiak-Cane model were explored for three different cost functions. For the different characteristics of the eastern-Pacific （EP） El Nino and the central-Pacific （CP） El Nino, three cost functions were defined as the sea surface temperature anomaly （SSTA） evolutions at prediction time in the whole tropical Pacific, the Nino3 area, and the Nino4 area. For all three cost functions, there were two optimal precursors that developed into El Nino events, called Precursor Ⅰ and Precursor Ⅱ. For Precursor Ⅰ, the SSTA component consisted of an east-west （positive-negative） dipole spanning the entire tropical Pacific basin and the thermocline depth anomaly pattern exhibited a tendency of deepening for the whole of the equatorial Pacific. Precursor Ⅰ can develop into an EP-El Nino event, with the warmest SSTA occurring in the eastern tropical Pacific or into a mixed El Nino event that has features between EP-El Nino and CP-El Nino events. For Precursor Ⅱ, the thermocline deepened anomalously in the eastern equatorial Pacific and the amplitude of deepening was obviously larger than that of shoaling in the central and western equatorial Pacific. Precursor Ⅱ developed into a mixed El Nino event. Both the thermocline depth and wind anomaly played important roles in the development of Precursor Ⅰ and Precursor Ⅱ.展开更多
In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solutio...In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41006007)the National Basic Research Program of China (Grant No. 2012CB417404)
文摘Optimal precursor perturbations of El Nino in the Zebiak-Cane model were explored for three different cost functions. For the different characteristics of the eastern-Pacific （EP） El Nino and the central-Pacific （CP） El Nino, three cost functions were defined as the sea surface temperature anomaly （SSTA） evolutions at prediction time in the whole tropical Pacific, the Nino3 area, and the Nino4 area. For all three cost functions, there were two optimal precursors that developed into El Nino events, called Precursor Ⅰ and Precursor Ⅱ. For Precursor Ⅰ, the SSTA component consisted of an east-west （positive-negative） dipole spanning the entire tropical Pacific basin and the thermocline depth anomaly pattern exhibited a tendency of deepening for the whole of the equatorial Pacific. Precursor Ⅰ can develop into an EP-El Nino event, with the warmest SSTA occurring in the eastern tropical Pacific or into a mixed El Nino event that has features between EP-El Nino and CP-El Nino events. For Precursor Ⅱ, the thermocline deepened anomalously in the eastern equatorial Pacific and the amplitude of deepening was obviously larger than that of shoaling in the central and western equatorial Pacific. Precursor Ⅱ developed into a mixed El Nino event. Both the thermocline depth and wind anomaly played important roles in the development of Precursor Ⅰ and Precursor Ⅱ.
基金Acknowledgments The authors would like to thank the anonymous referees and the editor for their very helpful comments and suggestions. J. Wang and G. Li are supported by the Science and Technology Research Project of Department of Education of Heilongjiang Province （No. 12531495）. J. Wang is supported by Natural Science Foundation of China （TianYuan, No. 11226255）.
文摘In this paper, we present a differential infectivity SIR epidemic model with modified saturation incidences and stochastic perturbations. We show that the stochastic epidemic model has a unique global positive solution, and we utilize stochastic Lyapunov functions to show the asymptotic behavior of the solution.
