Nonlinear Empirical Mode Analysis of Complex Systems: Development of General Approach and Applications in Climate

地球气候动力学的复杂性和多样性是由系统各组成部分在不同时间尺度上的非线性相互作用引起的。通过结合和使用统计物理学和动力系统理论的几种新方法，如复杂网络和经验建模，我们将提高我们分析，建模和预测复杂自然系统行为的能力，并将这种方法应用于气候科学中的重要问题，弥合物理学和地球科学之间的差距和交叉融合思想。我们研究的基础将是一种新的主经验模式搜索方法，它适当地描述了所观察到的动力学的演变。主流形方法将用于构建复杂气候网络和研究气候系统遥相关的全新方法。它提供了一个相空间重建随后的多维递归分析和预测经验随机模型。递归和复杂的网络分析将进一步发展，以允许在不同的空间和时间尺度上的相互作用的多变量检测使用这样的想法，如多层网络，网络的网络，递归的概率，或小波变换。在这一新概念的指导下，随机建模方法的最优预测因子（变量）将通过复杂网络和经验模式分析来确定。所开发的创新框架将在原型系统上进行测试，并应用于：（i）研究过去10-20 kyr期间古气候的时空模式和关键转变（例如，亚洲季风动力学、具有时空空白的古气候数据集）和（ii）与热浪和极端降水等极端事件发生率增加有关的中纬度大气条件的季节间和年际预测。该项目的成功依赖于俄罗斯和德国研究小组的合作，在数值方法和科学学科方面提供不同的专业知识。

A great number of feedbacks involving nonlinear interaction of many system’s components with various time scales is responsible for highly complex and diverse Earth’s climate dy­namics. By combining and using several new approaches from statistical physics and dy­namical systems theory such as complex networks and empirical modeling we will advance our ability to analyze, model and forecast the behaviour of complex natural systems and apply this approach to important problems in climate science, bridging the gap and cross-fer­tilizing ideas between physics and geosciences. The base of our research will be a novel principal empirical mode search method which properly describes the evolution of the ob­served dynamics. A principal manifold approach will be used for a completely new way of constructing complex climate networks and studying teleconnections in the climate system. It provides a phase space reconstruction for subsequent multidimensional recurrence analysis and for prognostic empirical stochastic models. Recurrence and complex network analysis will be further developed in order to allow multivariate detection of interactions on different spatial and temporal scales using such ideas like multi-layer networks, network of networks, probability of recurrence, or wavelet transforms. Following this novel concept, optimal pre­dictors (variables) for stochastic modeling methods will be determined by complex network and empirical mode analysis. The developed innovative framework will be tested on proto­typical systems and applied for: (i) studying spatio-temporal patterns and critical transitions in the palaeoclimate during the last 10-20 kyr (e.g., Asian monsoon dynamics, palaeoclimate data sets with spatio-temporal gaps) and (ii) interseasonal and interannual forecast of mid-latitude atmospheric conditions related to the increased occurrences of extreme events, such as heat waves and extreme precipitation. The success of this project relies on the col­laboration of the Russian and German research groups, providing different expertise in the numerical approaches and scientific disciplines.