非线性动力学与混沌：在天气和气候预测中的应用
Nonlinear Dynamics and Chaos: Applications for Prediction of Weather and Climate
摘要：
湍流，即空间和时间上的不规则波动，一般表征流体流动，特别是大气流动。各种尺度的非线性时空涨落都是短期天气和长期气候不可预测的重要原因，量化时空涨落的总体模式对于可预测性研究具有重要意义。时间涨落的功率谱是宽带的，在不同的尺度范围内呈现不同斜率的逆幂律形式。功率谱的逆幂律形式意味着斜率恒定的尺度范围的缩放（自相似性）。因此，大气流动具有多重标度或多重分形结构，标准气象学理论不能满意地解释观测到的大气流动多重分形结构，自相似空间格局意味着长期的空间相关性。因此，大气流动表现出长距离的时空相关性，即自组织临界性，表示秩序下明显的混乱。最近发展的一个大气流动的非确定性细胞动力学系统模型预测了观测到的自组织临界性，这是控制流动动力学的类量子力学所固有的，模型预测与气象数据集的连续周期谱分析一致。
英文摘要：
Turbulence, namely, irregular fluctuations in space and time characterize fluid flows in general and atmospheric flows in particular.The irregular,i.e., nonlinear space-time fluctuations on all scales contribute to the unpredictable nature of both short-term weather and long-term climate.It is of importance to quantify the total pattern of fluctuations for predictability studies. The power spectra of temporal fluctuations are broadband and exhibit inverse power law form with different slopes for different scale ranges. Inverse power-law form for power spectra implies scaling (self similarity) for the scale range over which the slope is constant. Atmospheric flows therefore exhibit multiple scaling or multifractal structure.Standard meteorological theory cannot explain satisfactorily the observed multifractal structure of atmospheric flows.Selfsimilar spatial pattern implies long-range spatial correlations. Atmospheric flows therefore exhibit long-range spatiotemporal correlations, namely,self-organized criticality,signifying order underlying apparent chaos. A recently developed non-deterministic cell dynamical system model for atmospheric flows predicts the observed self-organized criticality as intrinsic to quantumlike mechanics governing flow dynamics.The model predictions are in agreement with continuous periodogram spectral analysis of meteorological data sets.
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