Characterizing spatio-temporal climate variability with complex network methods Reik V. Donner with Marc Wiedermann, Jonathan Donges, Alexander Radebach & others CITES 2017, Zvenigorod, 6 September 2017
How to infer information from climate data? Existing data cover various spatial and temporal scales: Station-based observations of meteorological conditions • Remote sensing (satellite-based) recordings • Assimilation of observations into globally homogeneous data sets (reanalyses) • Climate model simulations • Spatially distributed paleoclimate archives (plus climate field reconstructions) • Problem: Integration of different spatial sites into joint analysis Classical approach: (linear) multivariate statistics methods (principal component • analysis, canonical correlation analysis, and numerous variants thereof) Last 15 years: data mining/machine learning techniques and other computer • science methods to also address nonlinearity in climate system (climate knowledge discovery, climate informatics) Here: complex networks as a (statistical) physics-inspired third way • Reik V. Donner, reik.donner@pik-potsdam.de 2
EOF analysis Original motivation: extract dominating co-variability from spatio-temporal fields of climate observations records (dimensionality reduction) Linear PCA: Diagonalization of lag-zero covariance matrix C of multivariate time series (matrix X wth standardized components) = = T Σ Σ = σ σ T 2 2 with and C X X C U U diag ( ,..., ) 1 N Compute correlation matrix of all variables • Estimate eigenvalues and eigenvectors • Eigenvectors: additive decomposition into principal components (weighted • superpositions of original variables) with individual variances corresponding to associated eigenvalues ⇒ spatial EOF patterns + index/score time series describing magnitude and sign of individual EOF modes (characteristic for individual climate oscillations) Reik V. Donner, reik.donner@pik-potsdam.de 3
EOF analysis Example: leading EOF (EOF-1) of near-surface air pressure in Arctic => Dipole structure (Arctic Oscillation) Reik V. Donner, reik.donner@pik-potsdam.de 4
Limitations of EOF analysis Purpose: extract dominating spatio-temporal (co-)variability modes from fields of climate observations Linear decomposition/dimensionality reduction technique • Potential improvement: nonlinear extensions like kernel PCA, neural network PCA, • isometric feature mapping and other nonlinear dimensionality reduction methods Intrinsic tendency to exhibit dipole (or multipole) structures enforced by • orthogonality constraint between modes EOFs modes do not always coincide with specific climatic mechanisms • Relevance of EOF modes as dynamical modes (or even proper statistical modes) • questionable Multiple superimposed patterns need to be considered • Spatial patterns = strength of co-variability, unclear relevance of associated • temporal patterns in other regions not highlighted by the same EOF Integrated view on co-variability, pair-wise co-variability information is lost • Reik V. Donner, reik.donner@pik-potsdam.de 5
Climate networks: The starting point… (Bull. Amer. Meteor. Soc., 2006) Reik V. Donner, reik.donner@pik-potsdam.de 6
Mathematical background An unweighted network (graph) is described by • a set of nodes (vertices) V • a set of links (edges) E between pairs of vertices Basic mathematical structure: adjacency matrix A A ij =1 nodes i and j are connected by a link A ij =0 nodes i and j are not connected by a direct link ⇒ binary matrix containing connectivity information of the graph ⇒ undirected graph: A symmetric Degree (centrality): number of neighbors of a vertex Local clustering coefficient: relative fraction of neighbors of a vertex that are mutual neighbors of each other Reik V. Donner, reik.donner@pik-potsdam.de 7
Climate networks Starting point: Spatially distributed climate time series ⇒ Spatial locations (individual series) = “nodes” of a network ⇒ Statistical similarity (e.g., correlation) between time series = “weights” of links ⇒ Remove all links with “weak” similarity = unweighted network ⇒ Analysis of structural properties of the resulting climate network (spatially coarse- grained representation of climate variability) Different options for threshold selection: Global correlation threshold (% of strongest correlations) • Global edge density (implies global correlation threshold) • Global significance level of correlations (for removing artifacts due to different • serial correlation properties) Reik V. Donner, reik.donner@pik-potsdam.de 8
Climate networks: General workflow (Donner et al., 2017) Reik V. Donner, reik.donner@pik-potsdam.de 9
Climate networks Basic assumptions: • Relevant processes in the (continuous) climate system can be approximated by an underlying spatial network structure (spatial coarse-graining is reasonable) • Statistical interdependences between climate variations at different locations reveal corresponding network topology - “functional” network (statistics reflect dynamics) – also used in other fields (e.g., functional brain networks, economics) Different possible types of climate networks based on climatological variable and employed similarity measure (e.g. Pearson correlation, different types of mutual information, event synchronization) Reik V. Donner, reik.donner@pik-potsdam.de 10
Correlation climate networks vs. EOF analysis Examples: Modulus of EOF-1 and degree field of correlation climate networks from monthly SLP (top) and SAT (bottom) anomalies (NCEP/NCAR reanalysis) (Donner et al., 2017) Reik V. Donner, reik.donner@pik-potsdam.de 11
Correlation climate networks vs. EOF analysis Correlation climate networks and EOF analysis based on the same correlation matrix EOF analysis: eigenvector decomposition – linear transformation • Climate network analysis: binarization by thresholding – nonlinear transformation • If EOF-1 dominates the data set (high fraction of explained variance): approximate relationship between degree field and modulus of EOF-1 (Donges et al., Climate Dynamics, 2015): Reik V. Donner, reik.donner@pik-potsdam.de 12
Correlation climate networks vs. EOF analysis Added value of climate network analysis: Commonly, more than just one EOF are statistically relevant – EOF-1 does not tell • the whole story Network allows investigating spatial structure of links (e.g., where are strong • correlations with a given location/region located?) EOF analysis just gives a single spatial pattern and time-dependent score per mode; • network analysis provides a multiplicity of characteristics that capture higher-order statistical properties of the spatial correlation structure Aspects of spatio-temporal organization of climate variability hidden to EOF • analysis may be revealed Reik V. Donner, reik.donner@pik-potsdam.de 13
Spatial range of correlations Surface air temperatures: correlations decay with spatial distance – implications for degree and edge length distributions Donges et al., EPL, 2009 Reik V. Donner, reik.donner@pik-potsdam.de 14
Evolving global surface air temperature network What can we learn from the temporal variation and spatial patterns of network properties? (Radebach et al., Phys. Rev. E, 2013) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 15 reik.donner@pik-potsdam.de
Evolving global surface air temperature network Climate network analysis for running windows in time: evolving climate networks Global network characteristics show distinct temporal variability profile strongly related to ENSO (Radebach et al., Phys. Rev. E, 2013) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 16 reik.donner@pik-potsdam.de
Evolving global surface air temperature network Climate network analysis for running windows in time: evolving climate networks Global network characteristics show distinct temporal variability profile strongly related to ENSO: El Nino and La Nina episodes can create hubs with long-range links (global impact) (Radebach et al., Phys. Rev. E, 2013) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 17 reik.donner@pik-potsdam.de
Evolving global surface air temperature network But: peaks in global network Transitivity, NINO3.4, strat. opt. depth characteristics do not coincide 1:1 with timing of known El Nino and La Nina episodes Reason: peaks indicate the formation of “localized structures” of high connectivity - Can also arise after strong volcanic eruptions (common regional cooling trend – increase of correlations) - Different types (“flavors”) of El Nino and La Nina episodes: functional discrimination based on global (Radebach et al., Phys. Rev. E, 2013) impacts? Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 18 reik.donner@pik-potsdam.de
Evolving global surface air temperature network Strong eruptive volcanism: Mt Pinatubo as example ⇒ Injection of large amounts of aerosols into stratosphere ⇒ Large-scale regional cooling (with spatial shift and lag of 12-18 months) ⇒ Elevation of correlations in confined region ⇒ Introduction of spatially confined correlations in affected region (Kittel et al., in prep.) Reik V. Donner, RD IV Transdisciplinary Concepts & Methods 19 reik.donner@pik-potsdam.de
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