Lorenz系统的距平模式和标准化距平模式

The Anomaly Model and the Normalized Anomaly Model of the Lorenz System

本文对Lorenz系统作时间积分获得模式的一个现实,利用此现实求得模式变量A的均值和方差的估计值A,σ_A,分别作线性变换代和Lorenz系统中,则得关于A'和A''的方程称为距平模式和标准化距平模式,两个模式的数值试验结果表明:即使对于Lorenz系统这样一个高度理想化的非线性系统,它的距平和标准化距平模式的统计特征和原模型接近,且标准化距平模式的结果更接近于原模型,这为我们在长期数值天气预报中使用距平模式和标准化距平模式提供了一个例证。

By integrating the Lorenz equations, the real of the system evolutionis obtained. And with the real the means A and the variances σA of themodel variables are estimated. Through two reversible lineartransformation A' = A - A and A' = (A - A)/σA, the anomaly model andthe normalized anomaly model of the Lorenz system are developedrespectively. The results of the numerical simulation experiments indicatethat even though the Lorenz system is a very strong nonlinear system,its anomaly model and normalized anomaly model can simulate andpredict the statistical features fairly well. The results provide a case forus to use the anomaly model and the normalized anomaly model in long-range numerical weather prediction.