OALib Journal期刊
误差非线性的增长理论及可预报性研究
DOI: 10.3878/j.issn.1006-9895.2007.04.02
Keywords: 非线性 ,Lyapunov指数 ,混沌 ,Logistic映射 ,Lorenz系统
Abstract:
对非线性系统的误差发展方程不作线性化近似，直接用原始的误差发展方程来研究初始误差的发展，提出了误差非线性的增长理论。首先，在相空间中定义一个非线性误差传播算子，初始误差在这个算子的作用下，可以非线性发展成任意时刻的误差；然后，在此基础上，引入了非线性局部Lyapunov指数的概念。由平均非线性局部Lyapunov指数可以得到误差平均相对增长随时间的演变情况；对于一个混沌系统，误差平均相对增长被证明将趋于一个饱和值，利用这个饱和值，混沌系统的可预报期限可以被定量地确定。误差非线性的增长理论可以应用于有限尺度大小初始扰动的可预报性研究，较误差的线性增长理论有明显的优越性。
References
[1] 段晚锁,穆穆.用非线性最优化方法研究El Nino可预报性的进展与前瞻.大气科学,2006,30 (5):759～766 Duan Wansuo,Mu Mu.Advance and prospect of the studies of El Nino predictability by nonlinear optimization method.Chinese J.Atmos.Sci (in Chinese),2006,30 (5):759～766 [2] Eckmann J P,Ruelle D.Ergodic theory of chaos and strange attractors.Rev.Mod.Phys.,1985,57:617～656 [3] Fraedrich K.Estimating weather and climate predictability on attractors.J.Atmos.Sci.,1987,44:722～728 [4] Fraedrich K.El Nino/Southern Oscillation predictability.Mon.Wea.Rev.,1988,116:1001～1012 [5] Lorenz E N.Predictability:A problem partly solved.Proceedings of a Seminar Held at ECMWF on Predictability (I),1995.1～18 [6] Nese J M.Quantifying local predictability in phase space.Physica D,1989,35:237～250 [7] Kazantsev E.Local Lyapunov exponents of the quasi-geostrophic ocean dynamics.Appl.Math.Comp.,1999,104:217～257 [8] Ziemann C,Smith L A,Kurths J.Localized Lyapunov exponents and the prediction of predictability.Phys.Lett.A,2000,4:237～251 [9] Lacarra J F,Talagrand O.Short-range evolution of small perturbations in a baratropic model.Tellus,1988,40A:81～95 [10] Mu M.Nonlinear singular vectors and nonlinear singular values.Science in China (D),2000,43:375～385 [11] Oseledec V I.A multiplicative ergodic theorem:Lyapunov characteristic numbers for dynamical systems.Trans.Moscow Math.Soc.,1968,19:197～231 [12] Dalcher A,Kalnay E.Error growth and predictability in operational ECMWF forecasts.Tellus A,1987,39:474～491 [13] Lorenz E N.Deterministic nonperiodic flow.J.Atmos.Sci.,1963,20:130～141 [14] Chen B H,Li J P,Ding R Q.Nonlinear local Lyapunov exponent and atmospheric predictability research.Science in China (D),2006,49:1111～1120 [15] May R M.Simple mathematical models with very complicated dynamics.Nature,1976,261:459～467 [16] Palmer T N.A nonlinear dynamical perspective on climate prediction.J.Climate,1999,12:575～591
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