Andrew H., E. David, 2005: Nonlinear dynamical analysis of noisy time series. Nonlinear Dynamics, Psychology and Life Sciences, 9, 399- 433.
Brockwell P. J., R. A. Davis, 2001: Time Series: Theory and Methods. Springer Press,596 pp.
Buizza R., P. L. Houtekamer, G. Pellerin, Z. Toth, Y. J. Zhu, and M. Z. Wei, 2005: A comparison of the ECMWF, MSC and NCEP global ensemble prediction systems. Mon. Wea. Rev., 133( 6), 1076- 1097.
Chou J. F., H. L. Ren, 2006: Numerical weather prediction-necessity and feasibility of an alternative methodology. Journal of Applied Meteorological Science, 17( 3), 240- 244. (in Chinese)
Chou J. F., Z. H. Zheng, and S. P. Sun, 2010: The think about——10-30 d extended-range numerical weather prediction strategy-facing the atmosphere chaos. Scientia Meteorologica Sinica, 30( 6), 569- 573. (in Chinese)
Ding R. Q., J. P. Li, 2007: Nonlinear finite-time Lyapunov exponent and predictability. Phys. Lett. A., 364, 396- 400.
Ding R. Q., J. P. Li, 2009a: Application of nonlinear error growth dynamics in studies of atmospheric predictability. Acta Meteorologica Sinica, 67( 3), 241- 249. (in Chinese)
Ding R. Q., J. P. Li, 2009b: The temporal spatial distributions of weather predictability of different variables. Acta Meterologica Sinica, 67( 3), 343- 354. (in Chinese)
Doswell C. A., H. E. Brooks, and R. A. Maddox, 1996: Flash flood forecasting: An ingredients-based methodology. Wea. Forecasting, 11, 560- 581.
Eckmann J. P., D. Ruelle, 1985: Ergodic theory of chaos and strange attractors. Rev. Mod. Phys., 57, 617- 656.
Epstein E. S., 1969: Stochastic dynamic prediction. Tellus, 21, 739- 759.
Farmer J. D., J. J. Sidorowieh, 1987: Predicting chaotic time series. Phys. Rev. Lett., 59( 8), 845- 848.
Feng J., R. Q. Ding, D. Q. Liu, and J. P. Li, 2014: The application of nonlinear local Lyapunov vectors to ensemble predictions in the Lorenz systems. J. Atmos. Sci., 71( 9), 3554- 3567.
Forrer J., M. W. Rotach, 1997: On the turbulence structure in the stable boundary layer over the Greenland ice sheet. Bound.-Layer Meteor., 85, 111- 136.
Gao S. T., J. Cao, 2007: Physical basis of generalized potential temperature and its application to cyclone tracks in nonuniformly saturated atmosphere. J. Geophys. Res., 112,D18101, doi: 10.1029/ 2007JD008701.
Gao S. T., L. K. Ran, 2009: Diagnosis of wave activity in a heavy-rainfall event. J. Geophys. Res., 114,D08119, doi: 10.1029/2008JD010172.
Gong J. D., W. J. Li, and J. F. Chou, 1999: Forming proper ensemble forecast initial members with four-dimensional variational data assimilation method. Chinese Science Bulletin, 44( 16), 1527- 1531.
He G. B., J. Chen, Y. H. Xiao, Q. Y. Gu, and C. Li, 2006: Precipitation prediction with AREM numerical model in Sichuan flood season in 2005. Meteorological Monthly, 32( 7), 64- 71. (in Chinese)
Houtekamer P. L., L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124, 1225- 1242.
Huang Y. Y., J. S. Xue, Q. L. Wan, Z. T. Chen, W. Y. Ding, and C. Z. Zhang, 2013: Improvement of the surface pressure operator in GRAPES and its application in precipitation forecasting in south China. Adv. Atmos. Sci.,30(3), 354-366, doi: 10.1007/s00376-012-1270-1.
Kantz H., T. Schreiber, 1997: Nonlinear Time Series Analysis. Cambridge University Press,388 pp.
Kennel M. B., 1997: Statistical test for dynamical nonstationarity in observed time-series data. Phys. Rev.E, 56( 2), 316- 321.
Kennel M. B., R. Brown, and H. D. I. Abarbanel, 1992: Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev.A, 45, 3403- 3411.
Krishnamurti T. N., C. M. Kishtawal, Z. Zhang, T. LaRow, D. Bachiochi, E. Williford, S. Gadgil, and S. Surendran, 2000: Multimodel ensemble forecasts for weather and seasonal climate. J.Climate, 13, 4196- 4216.
Ledrappier F., 1981: Some relations between dimension and Lyapounov exponents. Commun. Math. Phys., 81, 229- 238.
Li J. P., J. F. Chou, 1996: Some problems exited in estimating fractal dimension of attractor with one dimensional time series. Acta Meteorologica Sinica, 54( 3), 312- 323. (in Chinese)
Li J. P., R. Q. Ding, 2009: Studies of predictability of single variable from multi-dimensional chaotic dynamical system. Chinese J. Atmos. Sci., 33( 3), 551- 556. (in Chinese)
Li J. P., R. Q. Ding, 2011: Temporal-spatial distribution of atmospheric predictability limit by local dynamical analogs. Mon. Wea. Rev., 139, 3265- 3283.
Li K. Y., X. D. Li, 2007: Nonlinear prediction of ENSO. Acta Scientiarum Naturalium Universitatis Pekinensis, 43( 2), 30- 34. (in Chinese)
Liu Z., 2010: Chaotic time series analysis. Mathematical Problems in Engineering,Vol. 2010, Article ID 720190, 31 pp.
Lorenz E. N., 1963a: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 130- 148.
Lorenz E. N., 1963b: Section of planetary sciences: The predictability of hydrodynamic flow. Transactions of the New York Academy of Sciences, 25, 409- 432.
Madden R. A., P. R. Julian, 1971: Detection of a 40-50 day oscillation in the zonal wind in the tropical Pacific. J. Atmos. Sci., 28( 6), 702- 708.
Molteni F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF ensemble prediction system: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122, 73- 119.
Mu M., Z. N. Jiang, 2008: A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation. Chinese Science Bulletin, 53( 13), 2062- 2068.
Mu M., W. Duan, Q. Wang, and R. Zhang.2010: An extension of conditional nonlinear optimal perturbation approach and its applications. Nonlin. Processes Geophys., 17, 211- 220.
Nichols J. M., M. D. Todd, M. Seaver, and L. N. Virgin, 2003: Use of chaotic excitation and attractor property analysis in structural health monitoring. Phys. Rev.E, 67, 016209.
Pecora L. M., T. L. Carroll, 1996: Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data, Chaos, 6, 432- 439.
Simmons A. J., R. Mureau, and T. Petroliagis, 1995: Error growth and estimates of predictability from the ECMWF forecasting system. Quart. J. Roy. Meteor. Soc., 121, 1739- 1771.
Sun G. W., F. Xin, C. Y. Kong, B. M. Chen, and J. H. He, 2010: Atmospheric low-frequency oscillation and extended range forecast. Plateau Meteorology, 29( 6), 1142- 1147. (in Chinese)
Takens F.1981: Detecting strange attractors in turbulence. Dynamical Systems and Turbulence. Lecture Notes in Mathematics, D. Rand and L. S. Young, Eds., Springer, 366- 381.
Toth Z., E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125, 3297- 3319.
Wei M., Z. Toth, R. Wobus, Y. J. Zhu, C. H. Bishop, and X. G. Wang, 2006: Ensemble transform kalman filter-based ensemble perturbations in an operational global prediction system at NCEP. Tellus A, 58, 28- 44.
Wolf A., J. B. Swift, H. L. Swinney, and J. A. Vastano, 1985: Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16, 285- 317.
Xia Z. Y., L. S. Xu, 2010: Research on optimal interpolation times of nonlinear time-series using metric entropy and fractal interpolation. International Workshop on IWCFTA,Kunming, Yunnan, 411- 415.
Yang P. C., X. J. Zhou, 2005: On nonstationary behaviors and prediction theory of climate systems. Acta Meterologica Sinica, 63( 6), 556- 570. (in Chinese)
Zhang X. L., S. Y. Tao, and J. H. Sun, 2010: Ingredients-based heavy rainfall forecasting. Chinese J. Atmos. Sci., 34( 5), 754- 766. (in Chinese)