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Nichtlineare Empirical Mode-Analyse komplexer Systeme: Entwicklung eines allgemeinen Ansatzes und Anwendung in der Klimaforschung

Fachliche Zuordnung Statistische Physik, Nichtlineare Dynamik, Komplexe Systeme, Weiche und fluide Materie, Biologische Physik
Förderung Förderung von 2019 bis 2023
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 405856037
 
Erstellungsjahr 2023

Zusammenfassung der Projektergebnisse

The project was able to achieve the goals from WP 2, 3, 6, and 7, albeit with some exceptions and caveats. The development of the novel recurrence quantifiers recurrence lacunarity and recurrence flow substantially contributed to the aim of WP 2, i.e., finding approaches in multi-scale and multivariate recurrence analysis. Recurrence lacunarity provides a quantification of scale-dependent features in nonlinear time series beyond line-based recurrence patterns. Its successful application to thermoacoustic combustion instabilities demonstrated its potential in detecting regime transitions for complex real-world data, e.g., real-time detection of instabilities in gas turbines. The recurrence flow measure represents a novel approach for characterising nonlinear couplings in high-dimensional data and paves the way for a first recurrence-based state space reconstruction method. By providing sound open source software packages, we enable researchers and practitioners to use the developed methods for their own applications. Together with our project partners, we were able to effectively address the challenges from WP 3, i.e., complex network analysis of atmospheric circulation patterns. Here, a novel approach was put forward that combines RA (recurrence networks, recurrence quantification analysis) with mode-decomposition and machine learning techniques (kernel PCA, modularity maximization). This allowed to characterize scale-dependent variability exhibited during atmospheric blocking conditions in the mid-latitudes. The proposed method could be of considerable value for the characterization of hazardous extreme weather events entailed by atmospheric blocking states. It appears promising for further developments and applications to other complex spatial data. We carried out a broad range of applications in the study of palaeoclimate proxy records that respond to some of the challenges that were particularly expressed in WP 2 and WP 6. While no empirical modelling of the ASM could be implemented, a more profound technical understanding of how irregular sampling and uncertainties affect RA could be gained. Non-stationarity of a proxy record’s sampling was identified as a key challenge. This understanding was put into practise in the case studies on stalagmites from Belize, Niue Island, and the ASM region. The latter application contributed to a better understanding of the Holocene evolution of the Asian monsoon system. Furthermore, we were able to inform on effective method design for palaeoclimate studies through two review papers which will likely spark interesting discussions that bridge gaps between the palaeoclimate and time series analysis communities. We have to emphasize here that the goal of empirical modeling of the ASM (based on WP 5 and 6) could not be achieved due to the severe limitations in communicating progress with our project partners. The goals of WP 6 could have only been successfully pursued if we had obtained effective modifications of the empirical modelling approach for gappy palaeoclimate records of our collaborators from the IAP. In the light of the severe limitations experienced due to the COVID-19 pandemic and the Russian invasion of the Ukraine, results from our joint research efforts unfortunately remained limited. Nevertheless, the publications from this project on key methodologies in the analysis of complex spatiotemporal data will most likely provide great value to future applications in a broad range of areas, both scientifically and commercially.

Projektbezogene Publikationen (Auswahl)

 
 

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