Correlation networks from flows. The case of forced and time-dependent advection-diffusion dynamics

TL;DR

This paper develops a theoretical framework linking correlation matrices to climate network structures in non-stationary advection-diffusion systems, revealing how flow dynamics influence network topology.

Contribution

It generalizes previous methods to include forced, time-dependent flows, providing new insights into how flow decay rates affect climate network measures.

Findings

Correlation networks are insensitive to steady sources and sinks.

Signal decay rate significantly impacts network topology.

Application to a geophysical ocean jet model demonstrates the approach.

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.