Nonlinear fastest growing perturbation and the first kind of predictability

Nonlinear fastest growing perturbation, which is related to the nonlinear singular vector and nonlinear singular value proposed by the first author recently, is obtained by numerical approach for the two-dimensional quasigeostrophic model in this paper. The difference between the linear and nonlinear fastest growing perturbations is demonstrated. Moreover, local nonlinear fastest growing perturbations are also found numerically. This is one of the essential differences between linear and nonlinear theories, since in former case there is no local fastest growing perturbation. The results show that the nonlinear local fastest growing perturbations play a more important role in the study of the first kind of predictability than the nonlinear global fastest growing perturbation.