Nonlinear Processes in Geophysics www.nonlin-processes-geophys.net 1023-5809 1607-7946 17 2 2010 10.5194/npg-17-211-2010 http://www.nonlin-processes-geophys.net/17/211/2010/ http://www.nonlin-processes-geophys.net/17/211/2010/npg-17-211-2010.html http://www.nonlin-processes-geophys.net/17/211/2010/npg-17-211-2010.pdf 211 220 2010-04-13 An extension of conditional nonlinear optimal perturbation approach and its applications M. Mu W. Duan duanws@lasg.iap.ac.cn Q. Wang R. Zhang Key Laboratory of Ocean Circulation and Wave, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China Graduate University of Chinese Academy of Sciences,Beijing100049, China The approach of conditional nonlinear optimal perturbation (CNOP) was previously proposed to find the optimal initial perturbation (CNOP-I) in a given constraint. In this paper, we extend the CNOP approach to search for the optimal combined mode of initial perturbations and model parameter perturbations. This optimal combined mode, also named CNOP, has two special cases: one is CNOP-I that only links with initial perturbations and has the largest nonlinear evolution at a prediction time; while the other is merely related to the parameter perturbations and is called CNOP-P, which causes the largest departure from a given reference state at a prediction time. The CNOP approach allows us to explore not only the first kind of predictability related to initial errors, but also the second kind of predictability associated with model parameter errors, moreover, the predictability problems of the coexistence of initial errors and parameter errors. With the CNOP approach, we study the ENSO predictability by a theoretical ENSO model. 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