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Spatio-temporal network analysis for studying climate patterns

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Abstract

A fast, robust and scalable methodology to examine, quantify, and visualize climate patterns and their relationships is proposed. It is based on a set of notions, algorithms and metrics used in the study of graphs, referred to as complex network analysis. The goals of this approach are to explain known climate phenomena in terms of an underlying network structure and to uncover regional and global linkages in the climate system, while comparing general circulation models outputs with observations. The proposed method is based on a two-layer network representation. At the first layer, gridded climate data are used to identify “areas”, i.e., geographical regions that are highly homogeneous in terms of the given climate variable. At the second layer, the identified areas are interconnected with links of varying strength, forming a global climate network. This paper describes the climate network inference and related network metrics, and compares network properties for different sea surface temperature reanalyses and precipitation data sets, and for a small sample of CMIP5 outputs.

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Notes

  1. Unless specified otherwise, the term “correlation" will be used to denote Pearson’s cross-correlation metric between two time series.

  2. When comparing data sets with different spatial resolution, the anomaly of a cell should be normalized by the size of the cell in that resolution.

  3. Imposing a threshold on the actual strength of the link (computed as the covariance between the cumulative anomalies of two areas) would be incorrect. For example, multiplying low correlations with large standard deviations can produce links of significant weight.

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Acknowledgments

This work was made possible by a grant from the Department of Energy, Climate and Environmental Sciences Division, SciDAC: Earth System Model Development. We thank the anonymous reviewers for the insightful comments that helped improve the paper.

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Authors and Affiliations

  1. College of Computing, Georgia Tech, Atlanta, GA, 30332-0280, USA

    Ilias Fountalis

  2. School of Earth and Atmospheric Sciences, Georgia Tech, Atlanta, GA, 30332-0340, USA

    Annalisa Bracco

  3. College of Computing, Georgia Tech, Atlanta, GA, 30332-0280, USA

    Constantine Dovrolis

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  1. Ilias Fountalis
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  2. Annalisa Bracco
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Corresponding author

Correspondence to Annalisa Bracco.

Appendices

Appendix 1: Selection of threshold τ

The threshold τ is the only parameter of the proposed network construction method. It represents the minimum average pair-wise correlation between cells of the same area, as shown in Eq. 1. Intuitively, τ controls the minimum degree of homogeneity that the climate field should have within each area. The higher the threshold, the higher the required homogeneity, and therefore the smaller the identified areas.

Throughout this paper, we select τ based on the following heuristic. First, we apply the one-sided t test for Pearson correlations at level α and with −2 degrees of freedom (recall that T is the length of the anomaly time series) to calculate the minimum correlation value r α that is significant at that level (Rogers 1969). For example, with α = 1 % and T = 81 (corresponding to 27 years of SST montly DJF averages), we get r α  = 0.34.

Instead of prunning any correlations r(x i , x j ) that are below r α , we estimate the expected value of only those correlations that are larger than r α ,

$$ \bar{r}_{\alpha }\, \triangleq \, E[r(x_{i} ,x_{j} ),r(x_{i} ,x_{j} )>r_{\alpha } ]$$
(7)

For a set of k randomly chosen cells that have statistical significant correlations (at level α) between them, \(\bar{r}_\alpha\) is approximately equal, for large k, to their average pair-wise correlation. A climate area, however, is not a set of randomly chosen cells, but a geographically connected region. So, we require that the average pair-wise correlation of cells that belong to the same area should be higher than \(\bar{r}_\alpha\), i.e.,

$$\tau = \bar{r}_\alpha $$
(8)

Note that τ is independent of the size of an area, but it depends on both α and on the distribution of pair-wise correlations r(x i , x j ).

Appendix 2: Pseudocode of area identification algorithm

Below we present the pseudocode for the area identification algorithm used in this paper.

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Fountalis, I., Bracco, A. & Dovrolis, C. Spatio-temporal network analysis for studying climate patterns. Clim Dyn 42, 879–899 (2014). https://doi.org/10.1007/s00382-013-1729-5

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