Birgin E. G. , J. E. Martinez , M. Raydan , 2000: Nonmonotone spectral projected gradient methods for convex sets. SIAM Journal on Optimization, 10, 1196- 1121.
Deb K. , 2000: An efficient constraint handing method for genetic algorithms. Comput. Methods Appl. Mech. Engrg., 186, 311- 338.
Deb K. , R. B. Agrawal , 1995: Simulated binary crossover for continuous search space. Complex System, 9, 115- 148.
Duan W. S. , M. Mu , 2006: Investigating decadal variability of El Niño -Southern Oscillation asymmetry by conditional nonlinear optimal perturbation. J. Geophys. Res., 111, C07015, doi: 10.1029/2005JC003458.
Duan W. , C. Wei , 2012: The spring predictability barrier for El Nino events and its possible mechanism results from a fully coupled model. Int. J. Climatol, doi: 10.1002/joc.3513.
Duan W. S. , M. Mu , B. Wang , 2004: Conditional nonlinear optimal perturbation as the optimal precursors for El Niño -Southern Oscillation events. J. Geophys. Res., 109, D23105, doi: 10.1029/2004JD004756.
Duan W. S. , H. Xu , M. Mu , 2008: Decisive role of nonlinear temperature advection in El Niño and La Niño amplitude asymmetry. J. Geophys. Res., 113, C01014, doi: 10.1029/2006JC003974.
Duan W. , X. C. Liu , K. Y. Zhu , M. Mu , 2009: Exploring the initial error that causes a significant spring predictability barrier for El Nino events, J. Geophys. Res., 114, C04022, doi: 10.1029/2008JC004925.
Duan W. , Y. Yu , H. Xu , P. Zhao , 2012: Behaviors of nonlinearities modulating El Niño events induced by optimal precursory disturbance. Climate Dyn., doi: 10.1007/s00382-012-1557-z.
Ding R. Q. , J. P. Li. , 2007: Nonlinear finite-time Lyapunov exponent and predictability. Physics Letters A, 364, 396- 400.
Ding R. Q. , J. P. Li , K.-H. Seo , 2010: Predictability of the Madden-Julian oscillation estimated using observational data. Mon. Wea. Rev., 138, 1004- 1013.
Fang C. L. , Q. Zheng , 2009: The effectiveness of genetic algorithm in capturing conditional nonlinear optimal perturbation with parameterization “on-off” switches included by a model. Journal of Tropical Meteorology, 13, 13- 19.
Fillion, L., Belair, S., 2004: Tangent linear aspects of the Kain-Fritsch moist convective parameterization scheme. Mon. Wea. Rev., 132, 2477- 2494.
Gregory J.? ? 1995 ? ? Nonlinear Programming FAQ, Usenet sci.answers. [Available online at ftp://rtfm.mit.edu/pub/usenet/sci.answers/nonlinear-programming-faq.]
Herrera F. , M. Lozano , J. L. Verdegay , 1998: Tackling real-coded genetic algorithms: Operators and tools for the behavioural analysis. Artificial Intelligence Review, 12, 265- 319.
Herrera F. , M. Lozano , A. M. Sánchez , 2005: Hybrid crossover operators for real-coded genetic algorithms: an experimental study. Soft Comput., 9, 280- 298.
Holland J. H. , 1975: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, And Artificial Intelligence. University of Michigan Press, Ann Arbor, MI, 183 pp.
Homaifar A. , S. Lai , X. Qi , 1994: Constrained optimization via genetic algorithms. Simulation, 62, 242- 254.
Jiang Z. N. , M. Mu , 2009: A comparison study of the methods of conditional nonlinear optimal perturbations and singular vectors in ensemble prediction. Adv. Atmos. Sci., 26, 465- 470, doi: 10.1007/s00376-009-0465-6.
Jiang Z. N. , D. H. Wang , 2010: A study on precursors to blocking anomalies in climatological flows by using conditional nonlinear optimal perturbations. Quart. J. Roy. Meteor. Soc., 136, 1170- 1180.
Joines J. , C. Houck , 1994: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with Gas. Proc. of the 1st IEEE Conf. on Evolutionary Computation, Orlando, IEEE Press, 569- 584.
Li J. P. , R. Q. Ding , 2011: Temporal-spatial distribution of atmospheric predictability limit by local dynamical analogues. Mon. Wea. Rev., 139, 3265- 3283.
Li J. P. , R. Q. Ding , 2012: Temporal-spatial distribution of the predictability limit of monthly sea surface temperature in the global oceans. Int. J. Climatol., 32, doi: 10.1002/joc.3562.
Michalewicz Z. , 1995: Genetic algorithms, numerical optimization, and constrains. Pro. of the Sixth International Conference on Genetic Algorithms, Morgan Kauffman, San Mateo, 151- 158.
Michalewicz Z. , 1996: Genetic Algorithm + Data Structure = Evolution Programs. 3rd ed., Springer-Verlag, New York, 387 pp.
Michalewicz Z. , M. Schoenauer , 1996: Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation, 4, 1- 32.
Mu M. , 2000: Nonlinear singular vectors and nonlinear singular values. Sci. China (D), 43, 375- 385.
Mu M. , J. F. Wang , 2003: An adjoint method for variational data assimilation with physical “on-off” processes. J. Atmos. Sci., 60, 2010- 2018.
Mu M. , Q. Zheng , 2005: Zigzag oscillations in variational data assimilation with physical “on-off” processes. Mon. Wea. Rev., 133, 2711- 2720.
Mu M. , Z. Y. Zhang , 2006: Conditional nonlinear optimal perturbations of a two dimensional quasigeostrophic model. J. Atmos. Sci., 63, 1587- 1604.
Mu M. , Z. N. Jiang , 2009: A method to find out the perturbations triggering the blocking onset: Conditional nonlinear optimal perturbations. J. Atmos. Sci., 65, 3935- 3946.
Mu M. , W. S. Duan , B. Wang , 2003: Conditional nonlinear optimal perturbation and its applications. Nonlin. Processes Geophys, 10, 493— 501.
Mu M. , L. Sun , H. A. Dijkstra , 2004: The sensitivity and stability of the ocean’s thermocline circulation to finite amplitude freshwater perturbations. J. Phys. Oceanogr., 34, 2305- 2315.
Mu M. , F. F. Zhou , H. L. Wang , 2009: A method for identifying the sensitive areas in targeted observations for tropical cyclone prediction: Conditional nonlinear optimal perturbations. Mon. Wea. Rev., 137, 1623- 1639.
Sun L. , M. Mu , D. J. Sun , X. Y. Yin , 2005: Passive mechanism decadal variation of thermohaline circulation. J. Geophys. Res., 110, C07025, doi: 10.1029/2005JC002897.
Xu Q. , 1996: Generalized adjoint for physical process with parameterized discontinuities. Part I: Basic issues and heuristic examples. J. Atmos. Sci., 53, 1123- 1142.
Xu Q. , 1997: Generalized adjoint for physical processes with parameterized discontinuities. Part IV: Problems in time discretization. J. Atmos. Sci., 54, 2722- 2728.
Xu Q. , J. D. Gao , W. Gu , 1998: Generalized adjoint for physical processes with parameterized discontinuities. Part V: Coarse-grain adjoint and problems in gradient check. J. Atmos. Sci., 55, 2130- 2135.
Zebiak, S. E. M. A. Cane , 1987: A model EI Niño-Southen oscillation. Mon. Wea. Rev., 115, 2262- 2278.
Zheng Q. , M. Mu , 2006: The effects of the model errors generated by discretization of “on-off” processes on VDA. Nonline Processes Geophys., 13, 309- 320.
Zheng Q. , J. X. Sha , C. L. Fang , 2012: An effective genetic algorithm to VDA with discontinuous “on-off” switches. Science China Earth Sciences, 55, 1345- 1357, doi: 10.1007/s11430-011-4300-4.
Zou X. , 1997: Tangent linear and adjoint of “on-off ” processes and their feasibility for use in 4-dimensional variational data assimilation. Tellus, 49A, 3- 31.
Zou X. , I. M. Navon , J. G. Sela , 1993: Variational data assimilation with moist threshold processes using the NMC spectral model. Tellus, 45A, 370- 387.