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

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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.