Comparative statistical study of two local clustering coefficient formulations as tropical cyclone markers for climate networks

TL;DR

This paper introduces a new weighted local clustering coefficient for climate networks, using Kendall's rank correlations, which improves detection of tropical cyclone markers by reducing data requirements and enhancing association strength.

Contribution

The paper presents a novel formulation of local clustering coefficient based on Kendall's rank correlations, tailored for weighted climate networks, and demonstrates its superior association with tropical cyclones.

Findings

New formulation shows stronger association with tropical cyclones.

Reduces data requirements for correlation computation.

Enhances real-time climate network analysis capabilities.

Abstract

We introduce a new formulation of local clustering coefficient for weighted correlation networks. This new formulation is based upon a definition introduced previously in the neuroscience context and aimed at compensating for spurious correlations caused by indirect interactions. We modify this definition further by replacing Pearson's pairwise correlation coefficients and three-way partial correlation coefficients by the respective Kendall's rank correlations. This reduces statistical sample size requirements to compute the correlations, which translates into the possibility of using shorter time windows and hence into a shorter response time of the real-time climate network analysis. We construct evolving climate networks of mean sea level pressure fluctuations and analyze anomalies of local clustering coefficient in these networks. We develop a broadly applicable statistical methodology to study association between spatially inhomogeneous georeferenced multivariate time series and binary-valued spatiotemporal data (or other data reducible to this representation) and use it to compare the newly proposed formulation of local clustering coefficient (for weighted correlation networks) to the conventional one (for unweighted graphs) in terms of the association of these measures in climate networks to tropical cyclones. Thus we substantiate the previously made observation that tropical cyclones are associated with anomalously high values of local clustering coefficient, and confirm that the new formulation shows a stronger association.