A Note on the Differences between Linear Singular Vectors and Conditional Nonlinear Optimal Perturbation

Singular Vectors (SVs) and Conditional Nonlinear Optimal Perturbation (CNOP) have been widely adopted in studies of the instabilities of the atmospheric and oceanic systems, the related predictability, ensemble forecasting, and targeted observations. This paper firstly reviews the development of SVs and CNOP and gives a brief description of their fundamental principles. Then, the similarities and differences between the First Singular Vector (FSV) and CNOP are discussed with a two-dimensional nondimensional barotropic quasi-geostrophic model and different combinations of norms. The results show that the different norms used to evaluate the amplitudes of SVs and CNOP induce a large difference between the FSV and CNOP even if the optimization time is relatively short, while the difference between the FSV and CNOP is mainly due to nonlinear physical processes when using the same norms to evaluate the amplitudes of SVs and CNOP. So, appropriate norms should be taken into account for different physical problems, in order to investigate the similarities and differences between the FSV and CNOP, and the atmospheric or oceanic dynamics they cause, and further to reveal the mechanism of influence of nonlinear physical processes.