Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Liubov Tupikina; Nora Molkenthin; Cristóbal López; Emilio Hernández-García; Norbert Marwan; Jürgen Kurths

doi:10.1371/journal.pone.0153703

Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Liubov Tupikina, Nora Molkenthin, Cristóbal López, Emilio Hernández-García, Norbert Marwan, Jürgen Kurths

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Abstract

Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.

Original language	English
Article number	e0153703
Pages (from-to)	1-12
Number of pages	12
Journal	PloS ONE
Volume	11
Issue number	4
DOIs	https://doi.org/10.1371/journal.pone.0153703
Publication status	Published - 29 Apr 2016

Bibliographical note

Acknowledgments

We would like to thank Henk Dijkstra, Frank Hellman, Alexis Tantet for helpful and interesting discussions. Also we would like to acknowledge EC-funding through the Marie-Curie ITN LINC project (P7-PEOPLE-2011-ITN, grant No.289447), and FEDER and MINECO (Spain) through project ESCOLA (TM2012-39025-C02-01)

Funding: The authors would like to acknowledge EC-funding through the Marie-Curie ITN LINC project (P7-PEOPLE-2011-ITN, grant No.289447, http://climatelinc.eu/home/), and FEDER and MINECO (Spain) through project ESCOLA (TM2012-39025-C02-01, http://ifisc.uib-csic.es/). Thanks to LINC and ESCOLA projects, the interaction between groups was possible; as the result, the collaborators developed methods together and analyzed the methods applications.

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10.1371/journal.pone.0153703Licence: CC BY

Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics
© 2016 Tupikina et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://creativecommons.org/licenses/by/4.0/
Final published version, 1.25 MBLicence: CC BY

Cite this

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abstract = "Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate network's structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.",

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Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics

Abstract

Bibliographical note

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