Disentangling different types of El Niño episodes by evolving climate network analysis

Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network approach for characterizing the evolving correlation structure of the Earth's climate system based on reanalysis data for surface air temperatures. We provide a detailed study of the temporal variability of several global climate network characteristics. Based on a simple conceptual view of red climate networks (i.e., networks with a comparably low number of edges), we give a thorough interpretation of our evolving climate network characteristics, which allows a functional discrimination between recently recognized different types of El Niño episodes. Our analysis provides deep insights into the Earth's climate system, particularly its global response to strong volcanic eruptions and large-scale impacts of different phases of the El Niño Southern Oscillation.

Figure 1

Geographical neighborhoods of (a), (c) a high-latitude (North Atlantic between Svalbard and Northern Greenland) and (b), (d) a low-latitude (close to Singapore) grid point given on (a), (b) a standard (angularly regular) $2.5^{\circ }\times 2.5^{\circ }$ grid with $10226$ grid points and (c), (d) an icosahedral grid with $10242$ grid points (i.e., $n=5$ completed refinement steps), respectively. The chosen grid points (red) are connected to all other grid points that are closer than 500 km. For the standard grid, the high-latitude grid point has 56 geographical neighbors, whereas the one at low latitude has only 8. In contrast, for the icosahedral grid, both grid points have 16 neighbors each. Obviously the heterogeneous spatial distribution of grid points in the standard grid determines the huge difference between the two neighborhoods, whereas the homogeneous spatial distribution of grid points of the icosahedral grid enhances the comparability of vertex properties in different regions of the Earth.

Figure 2

Spatial distribution of the degree $k_{•}$ for two typical time windows (a) without (May 1960 to April 1961) and (b) with (May 1982 to April 1983) marked localized structures for the surface air temperature anomalies network obtained using the setting described in Sec. 3a.

Figure 3

Kernel estimates of the probability density functions $p(·)$ (obtained using a Gaussian kernel function with a bandwidth following Scott's rule [95]) of (a), (b) vertex degree $k_{•}$, (c), (d) local clustering coefficient ${\mathcal{C}}_{•}$, and (e),(f) edge lengths $d_{••}|A_{••}=1$ for the same time intervals and setting as in Fig. 2. In all cases, the empirical distributions have been normalized by the distribution of edge lengths of a fully connected graph in order to eliminate purely geometric effects.

Figure 4

Joint probability distributions $p(·,·)$ of (a), (b) strength of statistical association $W_{••}$ and geographical distance $d_{••}$ between all pairs of vertices (i.e., without thresholding), and (c), (d) degree $k_{•}$ and maximum edge length $d_{•}^{\text{max}}$, (e), (f) average shortest path length per vertex ${\mathcal{L}}_{•}$ and maximum edge length $d_{•}^{\text{max}}$, and (g), (h) local clustering coefficient ${\mathcal{C}}_{•}$ and degree $k_{•}$ of all vertices (i.e., after thresholding), for the same time intervals and settings as in Fig. 2. All distributions are represented as histograms using 100 (90 for $W_{••}$) equidistant bins. The gray lines in (a) and (b) depict the thresholds above which edges are established (here, $0.5\%$ of all possible pairs of vertices). Wherever appropriate, the distance dependences of the distributions have been corrected as in Fig. 3.

Figure 5

Threshold $W^{*}$, average path length $\mathcal{L}$, transitivity $\mathcal{T}$, global clustering coefficient $\mathcal{C}$, and (standard) Hamming distance ${\mathcal{H}}_{t,t-1}$ between networks obtained for successive periods in time for the evolving SATA network (using the settings given in Sec. 3a). Note that due to the fixed $\rho$, we have ${\mathcal{H}}_{t,t-1}^{*}={\mathcal{H}}_{t,t-1}$. Vertical bars indicate fall and winter seasons (September to November and December to February, respectively) with maximal intensity of EN (red) and LN (blue; darker colors represent stronger episodes according to the Niño 3.4 index; cf. [99, 100]).

Figure 6

Evolution of (a) degree distribution $p\left(k_{•}\right)$ and (b) edge length distribution $p\left(d_{••}\right|A_{••}=1)$ with the settings given in Sec. 3a. In (b), the distributions obtained for all time windows have been corrected as in Fig. 3.

Figure 7

Linear cross-correlation functions $C\left(s\right)$ between the different evolving climate network characteristics from Fig. 5. Positive (negative) $s$ refers to the situation of the measure in the row leading (lagging) the measure in the column.

Figure 8

As in Fig. 5 for SATA networks based on the maximum cross correlation for time lags $s\in [0,30]$ days. Note that $W^{*}$ is larger than in Fig. 5 for $s=0$ as expected.

Figure 9

As in Fig. 5 for SATA networks with a fixed threshold $W^{*}\approx 0.4958$ chosen as the minimal threshold from the evolution for fixed edge density of $\rho =0.005$ (see topmost panel in Fig. 5) —a value which was also used in [19, 20, 21]. Thus, $\rho =0.005$ is a lower boundary for the evolving edge density, ensuring that the network does not tend towards disintegration. In addition to the standard Hamming distance ${\mathcal{H}}_{t,t-1}$ (bottom panel, black line), the corrected Hamming distance $H_{t,t-1}^{*}$ is shown (red line).

Figure 10

Global network measures (without Hamming distance) for denser climate networks. The displayed results correspond to a fixed edge density $\rho =0.15$ (left axes, gray lines) and a fixed threshold $W^{*}=0.2997$ (right axes, black lines), respectively.

Figure 11

Evolving SATA network transitivity $\mathcal{T}$ and Hamming distance ${\mathcal{H}}_{t,t-1}$ for the same setting as in Fig. 5. In addition, the global mean temperature anomalies $\overline{T}$, the Niño 3.4 index (base period 1948–2010; vertical lines represent thresholds of $\pm 0.4{}^{\circ }$C as an indication of EN and LN episodes [109], respectively), and the stratospheric aerosol optical depth (SOD) (i.e., the global monthly mean optical thickness at 550 nm wavelength; cf. [110]) are shown. Vertical bars indicate fall and winter seasons (SON-DJF) with maximal intensity of EN (red) and LN (blue), respectively. Symbols (bullets, shifted towards the top, cold tongue; asterisks, warm pool) indicate EN episodes unambiguously classified in the literature (e.g., [111, 112]). Note that there is no 1:1 correspondence between the shown definitions of EN and LN based on the Niño 3.4 index and other methods.

Figure 12

Linear cross-correlation functions $C\left(s\right)$ between the evolving SATA network characteristics transitivity $\mathcal{T}$ and Hamming distance ${\mathcal{H}}_{t,t-1}$ (obtained based on lag-zero cross correlation with fixed $\rho =0.005$), the global mean temperature anomaly $\overline{T}$, the absolute value of the Niño 3.4 index, and the SOD index.