Conditional nonlinear optimal perturbation (CNOP) is the initial perturbation that has the largest nonlinear evolution at prediction time for initial perturba-tions satisfying certain physical constraint condition. It does not only represent the optimal precursor of certain weather or climate event, but also stand for the initial error which has largest effect on the prediction uncertainties at the prediction time. In sensitivity and stability analyses of fluid motion, CNOP also describes the most unstable (or most sensitive) mode. CNOP has been used to estimate the upper bound of the prediction error. These physical characteristics of CNOP are examined by applying respectively them to ENSO pre-dictability studies and ocean’s thermohaline circulation (THC) sensitivity analysis. In ENSO predictability studies, CNOP, rather than linear singular vector (LSV), represents the initial patterns that evolve into ENSO events most poten-tially, i.e. the optimal precursors for ENSO events. When initial perturbation is considered to be the initial error of ENSO, CNOP plays the role of the initial error that has larg-est effect on the prediction of ENSO. CNOP also derives the upper bound of prediction error of ENSO events. In the THC sensitivity and stability studies, by calculating the CNOP (most unstable perturbation) of THC, it is found that there is an asymmetric nonlinear response of ocean’s THC to the finite amplitude perturbations. Finally, attention is paid to the feasibility of CNOP in more complicated model. It is shown that in a model with higher dimensions, CNOP can be computed successfully. The corresponding optimization algo-rithm is also shown to be efficient.
A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter＇s atmosphere. Conditional nonlinear optimal perturbations （CNOPs） and linear singular vectors （LSVs） are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter＇s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter＇s atmosphere and to compare the stability of motions in Jupiter＇s atmosphere and Earth＇s atmosphere further.
