ALBERT

Description: 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.

Description: Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables. Complex networks have recently attracted a rising interest for studying dynamical patterns in geophysical flows such as in the atmosphere and ocean. For this purpose, two distinct approaches have been proposed based on either (i) correlations between values of a certain variable measured at different parts of the flow domain (correlation-based flow networks) or (ii) transition probabilities of passively advected tracers between different parts of the fluid domain (Lagrangian flow networks). So far, the investigations on both types of flow networks have mostly addressed classical topological network characteristics, disregarding the fact that such networks are naturally embedded in some physical space and, hence, have intrinsic restrictions to their structural organization. In this paper, we introduce a novel concept to obtain a complementary geometric characterization of the local network patterns based on the anisotropy of edge orientations. For two prototypical model systems of different complexity, we demonstrate that the geometric characterization of correlation-based flow networks derived from scalar observables can actually provide additional and useful information contributing to the identification of the underlying flow patterns that are often not directly accessible. In this spirit, the proposed approach provides a prospective diagnostic tool for geophysical as well as technological flows

Description: During the last years, complex network approaches have demonstrated their great potentials as versatile tools for exploring the structural as well as dynamical properties of complex systems from a variety of different fields. Among others, recent successful examples include their application to studying flow systems in both, abstract mathematical and real-world geophysical contexts. In this context, two recent developments are particularly notable: on the one hand, correlation-based functional network approaches allow inferring statistical interrelationships, for example between macroscopic regions of the Earth’s climate system, which are hidden to more classical statistical analysis techniques. On the other hand, Lagrangian flow networks provide a new tool to identify dynamically relevant structures in atmosphere, ocean or, more generally, the phase space of complex systems. This chapter summarizes these recent developments and provides some illustrative examples highlighting the application of both concepts to selected paradigmatic low-dimensional model systems.