奇异向量（singular vectors, SVs）和条件非线性最优扰动（conditional nonlinear optimal perturbation, CNOP）已广泛应用于研究大气—海洋系统的不稳定性以及与其相关的可预报性、集合预报和目标观测问题研究。本文首先回顾了SVs和CNOP的发展历史，并简单描述了它们的基本原理；然后针对二维正压准地转模式，使用不同的范数组合，分析了第一线性奇异向量（first singular vector, FSV）和CNOP之间的异同。结果表明，当优化时间较短时，度量SVs和CNOP大小的范数不同也将导致FSV和CNOP相差很大，而当度量SVs和CNOP大小的范数相同时，FSV和CNOP之间的差别则主要是由非线性物理过程作用的结果。因此，针对不同的物理问题，应该选取合适的度量范数研究FSV和CNOP以及其所引起的大气或海洋动力学的异同，从而揭示非线性物理过程的影响机理。%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.
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