A new approach to the generation of initial perturbations for ensemble prediction: Conditional nonlinear optimal perturbation

Conditional nonlinear optimal perturbation (CNOP), which is a natural extension of singular vector (SV) into the nonlinear regime, is applied to ensemble prediction study by using a quasi-geostrophic model under the perfect model assumption. SVs and CNOPs have been utilized to generate the initial perturbations for ensemble prediction experiments. The results are compared for forecast lengths of up to 14 d. It is found that the forecast skill of samples, in which the first SV is replaced by CNOP, is comparatively higher than that of samples composed of only SVs in the medium range (day 6-day 14). This conclusion is valid under the condition that analysis error is a kind of fast-growing ones regardless of its magnitude, whose nonlinear growth is faster than that of SV in the later part of the forecast. Furthermore, similarity index and empirical orthogonal function (EOF) analysis are performed to explain the above numerical results. Supported by the State Key Development Program for Basic Research of China (Grant No. 2006CB400503), the Chinese Academy of Sciences (Grant No. KZCX3-SW-230) and the National Natural Science Foundation of China (Grant Nos. 40221503 and 40675030)