The Preliminary Analysis of the Procedures of Extracting Predicable Components in Numerical Model of Lorenz System

The authors have proposed to extract the predictable components to make prediction in the numerical model which has nonlinear chaos. The method of extracting predicable components was introduced in a simple numerical model, and the numerical experiments were done based on Lorenz system. In the experiment, the authors found that the velocity of initial error increase is different for different components in the phase space, and there are some particular directions with slow error increase. That is to say, there exist predictable components which are relatively stable and insensitive to initial perturbation. The numerical model of the predictable components was established by extracting predicable components based on the evolution of the eigenvalues of the tangent operator error, and projecting the model variables onto the substrates. On the basis of these, the impacts of chaotic states, the errors of model parameters, and the external random noise on extracting the predicable components were studied. And the authors found that the numerical model of the predicable components has a better forecasting skill.