物理学报2017，Vol.66Issue(6)：34-42,9.DOI:10.7498/aps.66.060503
强迫Lorenz系统的可预报性研究
Predictability of forced Lorenz system
摘要
Abstract
In recent years, the actual atmospheric predictability has attracted widespread attention. Improving our under-standing of weather predictability is vital to developing numerical models and improving our forecast skill in weather and climate events. Given that the atmosphere is a complex and nonlinear system, taking the Lorenz system as an example is a better way to understand the actual atmosphere predictability. Up to now, some predictability problems of the Lorenz system have been investigated, such as the relative effects of the initial error and the model error. Previous advances in the research of predictability mainly focus on the relationship between the predictability limit and the initial error. As is well known, the external forcing can also result in the change of the predictability. Therefore, it is significant to investigate the predictability changing with the external forcing. The nonlinear local Lyapunov exponent (NLLE) is introduced to measure the average growth rate of the initial error of nonlinear dynamical model, which has been used for quantitatively determining the predictability limit of chaos system. Based on the NLLE approach, the influences of external forcing on the predictability are studied in the Lorenz system with constant forcing and Lorenz system with quasi-periodic forcing in this paper. The results indicate that for the Lorenz systems with constant and quasi-periodic forcings respectively, their predictability limits increase with forcing strength increasing. In the case of the same mag-nitude but different directions, the constant and quasi-periodic forcing both show different effects on the predictability limit in the Lorenz system, and these effects become significant with the increase of forcing strength. Generally speaking, the positive forcing leads to a higher predictability limit than the negative forcing. Therefore, when we consider the effects of positive and negative elements and phases in the atmosphere and ocean research, the predictability problems driven by different phases should be considered separately. In addition, the influences of constant and quasi-periodic forcings on the predictability are different in the Lorenz system. The effect of the constant forcing on the predictability is mainly reflected in the linear phase of error growth, while the nonlinear phase should also be considered additionally for the case of the quasi-periodic forcing. The predictability of the system under constant forcing is higher than that of the system under quasi-periodic forcing. These results based on simple chaotic model could provide an insight into the predictability studies of complex systems.关键词
非线性局部Lyapunov指数/可预报性/外强迫/Lorenz系统Key words
nonlinear local Lyapunov exponent/predictability/external forcing/Lorenz system引用本文复制引用
李保生,丁瑞强,李建平,钟权加..强迫Lorenz系统的可预报性研究[J].物理学报,2017,66(6):34-42,9.基金项目
国家自然科学基金优秀青年科学基金(批准号:41522502)、"全球变化与海气相互作用"专项(批准号:GASI-IPOVAI-06)和国家重点研发计划(批准号:2016YFA0601801)资助的课题. Project supported by the National Natural Science Foundation of China for Excellent Young Scholars (Grant No. 41522502), the National Programme on Global Change and Air-Sea Interaction, China (Grant No. GASI-IPOVAI-06), and the National Key Research and Development Plan of China (Grant No. 2016YFA0601801). （批准号:41522502）
