Conditional nonlinear optimal perturbation(CNOP) is an extension of the linear singular vector technique in the nonlinear regime.It represents the initial perturbation that is subjected to a given physical constraint,and results in the largest nonlinear evolution at the prediction time.CNOP-type errors play an important role in the predictability of weather and climate.Generally,when calculating CNOP in a complicated numerical model,we need the gradient of the objective function with respect to the initial perturbations to provide the descent direction for searching the phase space.The adjoint technique is widely used to calculate the gradient of the objective function.However,it is difficult and cumbersome to construct the adjoint model of a complicated numerical model,which imposes a limitation on the application of CNOP.Based on previous research,this study proposes a new ensemble projection algorithm based on singular vector decomposition(SVD).The new algorithm avoids the localization procedure of previous ensemble projection algorithms,and overcomes the uncertainty caused by choosing the localization radius empirically.The new algorithm is applied to calculate the CNOP in an intermediate forecasting model.The results show that the CNOP obtained by the new ensemble-based algorithm can effectively approximate that calculated by the adjoint algorithm,and retains the general spatial characteristics of the latter.Hence,the new SVD-based ensemble projection algorithm proposed in this study is an effective method of approximating the CNOP.
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.
