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The effect of time series distance functions on functional climate networks

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Abstract

Complex network theory provides an important tool for the analysis of complex systems such as the Earth’s climate. In this context, functional climate networks can be constructed using a spatiotemporal climate dataset and a suitable time series distance function. The resulting coarse-grained view on climate variability consists of representing distinct areas on the globe (i.e., grid cells) by nodes and connecting pairs of nodes that present similar time series. One fundamental concern when constructing such a functional climate network is the definition of a metric that captures the mutual similarity between time series. Here we study systematically the effect of 29 time series distance functions on functional climate network construction based on global temperature data. We observe that the distance functions previously used in the literature commonly generate very similar networks while alternative ones result in rather distinct network structures and reveal different long-distance connection patterns. These patterns are highly important for the study of climate dynamics since they generally represent pathways for the long-distance transportation of energy and can be used to forecast climate variability on subseasonal to interannual or even decadal scales. Therefore, we propose the measures studied here as alternatives for the analysis of climate variability and to further exploit their complementary capability of capturing different aspects of the underlying dynamics that may help gaining a more holistic empirical understanding of the global climate system.

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Acknowledgements

This research received financial support from the São Paulo Research Foundation (FAPESP) Grants 2017/05831-9 and 2015/50122-0. The authors also acknowledge the National Council for Scientific and Technological Development (CNPq) for its financial support. This research was developed using computational resources from the Center for Mathematical Sciences Applied to Industry (CeMEAI) funded by FAPESP (Grant 2013/07375-0). RVD has received funding by the German Federal Ministry for Education and Research (BMBF) via the BMBF Young Investigators Group CoSy-CC\(^2\) (Complex Systems Approaches to Understanding Causes and Consequences of Past, Present and Future Climate Change, Grant no. 01LN1306A), the Belmont Forum/JPI Climate project GOTHAM (Globally Observed Teleconnections and Their Representation in Hierarchies of Atmospheric Models, Grant no. 01LP16MA) and the JPI Climate/JPI Oceans project ROADMAP (The Role of Ocean Dynamics and Ocean-Atmosphere Interactions in Driving ClimAte Variations and Future Projections of Impact-Relevant Extreme Events, Grant no. 01LP2002B).

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Authors and Affiliations

  1. Associated Laboratory for Computing and Applied Mathematics, National Institute for Space Research, Av. dos Astronautas, 1758, Jardim da Granja, São José Dos Campos, SP, 12227-010, Brazil

    Leonardo N. Ferreira & Elbert E. N. Macau

  2. Department of Physics, Humboldt University, Newtonstraße 15, 12489, Berlin, Germany

    Leonardo N. Ferreira

  3. Research Department IV-Complexity Science, Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A56, 14473, Potsdam, Germany

    Leonardo N. Ferreira & Reik V. Donner

  4. Center for Weather Forecast and Climatic Studies, National Institute for Space Research, Rodovia Presidente Dutra, Km 40, Cachoeira Paulista, SP, 12630-000, Brazil

    Nicole C. R. Ferreira

  5. Institute of Science and Technology, Federal University of São Paulo, Av. Cesare Monsueto Giulio Lattes, 1201-Eugênio de Melo, São José dos Campos, SP, Brazil

    Elbert E. N. Macau

  6. Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, Breitscheidstr. 2, 39114, Magdeburg, Germany

    Reik V. Donner

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  1. Leonardo N. Ferreira
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  2. Nicole C. R. Ferreira
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  3. Elbert E. N. Macau
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Corresponding author

Correspondence to Leonardo N. Ferreira.

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Computer code availability

The method and the experiments in this paper were implemented using the R programming language [79] with the packages igraph [80], TSclust [81], and TSdist [82]. The R software, the packages, and our implementation are all open-source (GPL) and freely available for download. Our source codes can be obtained at https://lnferreira.github.io/climate_networks_R .

Appendices

Definitions of time series distance functions

See Tables 2, 3 and 4.

Table 4 Time series distance functions used in this work
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Table 5 Time series distance functions used in this work
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Table 6 Global measures from networks created with percentile \(p=0.001\)
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Table 7 Global measures from networks created with percentile \(p=0.01\)
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Table 8 Continued
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Table 9 Global measures from networks created with percentile \(p=0.05\)
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Climate network characteristics

We present in Tables 5, 6, 7 and 8 the values of all network measures obtained for the climate networks constructed for the four edge densities \(p=\) 0.001, 0.01, 0.05 and 0.1.

Table 10 Global measures from networks created with percentile \(p=0.1\)
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Network distance matrices

See Fig. 7.

Fig. 7
figure 7

Network clustering according to the similarity of the respective network topology. For every distance function, we constructed climate networks considering four edge densities: \(p=\) 0.001, 0.01, 0.05 and 0.1. Then, we calculated the Hamming distances between all pairs of networks and clustered them using hierarchical clustering (Ward’s method). The results show that PDF-based distance functions form a cluster and generate similar networks independent of p. For the other measures, when p increases, the networks were very different except in two small groups. The first group is formed by correlation, cross-correlation, MI and MIC. The other group is formed by Manhattan, Euclidean and Fourier distances

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Teleconnections

See Fig. 8.

Fig. 8
figure 8

Teleconnections for all the 29 distance functions. We considered only the 500 strongest teleconnections (nodes distance greater than \(5000\,{\text {km}}\))

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Ferreira, L.N., Ferreira, N.C.R., Macau, E.E.N. et al. The effect of time series distance functions on functional climate networks. Eur. Phys. J. Spec. Top. 230, 2973–2998 (2021). https://doi.org/10.1140/epjs/s11734-021-00274-y

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