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...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.40233029,and 4022 1503)the Knowledge Innovation Program of Chinese Academy of Sciences(Grant No.KZCX3-SW-230).
文摘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.
