Attractor radius and global attractor radius and their application to the quantification of predictability limits
Attractor radius and global attractor radius and their application to the quantification of predictability limits
复制标题
吸引子半径和全局吸引子半径及其在可预测性极限量化中的应用
DOI：
10.1007/s00382-017-4017-y
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发表时间：
2018-09
期刊：
影响因子：
4.6
通讯作者：
Ruiqiang Ding
中科院分区：
文献类型：
--
作者：
Jianping Li;Jie Feng;Ruiqiang Ding
量化混沌系统及其预测模型的可预测界是一个具有重要理论意义和实际意义的问题。引入吸引子的三个不变统计性质，即吸引子半径、全局吸引子半径(GAR)和两个吸引子之间的全局平均距离，以定义混沌系统的几何特征、平均行为及其误差增长。GAR是吸引子半径的倍数。这些不变量分别被用来定量地衡量全球集合平均预报和单个初始状态的全局和局部可预测界(两者都有实际可预测界和潜在可预测界，分别对应于吸引子半径和GAR)。吸引子半径和GAR都是混沌系统的内在属性，与预测模型和模型误差无关，因此提供了比传统的误差饱和或渐近值(AV)更准确、更客观的指标来评估预测模型的全局和局部可预测界。Lorenz63模式和业务预报数据都被用来论证这些几何特征的理论方面，并评估它们应用于可预测性分析的可行性和有效性。
Quantifying the predictability limits of chaotic systems and their forecast models is an important issue with both theoretical and practical significance. This paper introduces three invariant statistical properties of attractors, namely the attractor radius, global attractor radius (GAR), and the global average distance between two attractors, to define the geometric characteristics and average behavior of a chaotic system and its error growth. The GAR istimes the attractor radius. These invariant quantities are applied to quantitatively measure the global and local predictability limits (both have practical and potential predictability limits, which correspond to the attractor radius and GAR, respectively) of both global ensemble average forecasts and one single initial state, respectively. Both the attractor radius and GAR are intrinsic properties of a chaotic system and independent of the forecast model and model errors, and thus provide more accurate, objective metrics to assess the global and local predictability limits of forecast models compared with the traditional error saturation or asymptotic value (AV). Both the Lorenz63 model and operational forecast data are used to demonstrate the theoretical aspects of these geometric characteristics and evaluate the feasibility and effectiveness of their application to predictability analysis.
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