时空序列预测误差的敏感性试验分析

Sensitivity Tests Analysis on Spatio-Temporal Series Prediction Error

利用 33模Lorenz系统得到的“理想”混沌时空序列 ,作为时空混沌序列“发生器”。通过状态空间重构 ,建立“场时间序列”局域近似预测模型 ,对资料空间分辨率 ,资料的长度、噪音 ,以及模型的参数选取等因素进行敏感性试验分析 ,了解时空混沌序列预测中误差产生和增长的一些影响因素。得到以下初步结论 :对于理想混沌时空序列 (33模Lorenz系统 )而言 ,与系统相适应的资料空间分辨率和较长的资料长度都将会提高预测精度 ;可预报时效与资料长度之间近似服从指数关系。另外 ,在建立预测模型时 ,适当的邻近点数目 ,以及采用二阶映射关系和迭代法都可以有效地改善预测精度。对于加入噪音的混沌时间序列 ,通过“场时间序列”的局域近似方法和 4阶自回归方法的预测试验的对比表明 ,前者显示了更强的抗“干扰”能力。以上结论可以有分析地应用于短期气候预测中。

The ideal spatio-temporal series from 33 modes Lorenz system as an series generator is used for testing sensitivity of data spatial resolution, data length and noise, parameters in prediction model established by means of spatio-temporal series local approximation prediction methods to understand some influencing factors for the prediction error growing. Followings are the preliminary results: the spatial resolution and relative longer series length can improve the predictability; and there may be the exponential relation between the predictability and series length. Furthermore, nearest points, 2nd order mapping and iteration chosen in establishing the prediction model oppropriate can also improve the predictable skill. To the noisy chaotic time series, comparative tests between the spatio-temporal series with local approximation method and 4th order auto-regressive method show that the former can better resist the noise influence, these results can be applied to the short term climate prediction analytically.