Improved El Niño forecasting by cooperativity detection

Abstract

The authors note that: "Due to a minor technical error in the calculation of the climatological average of the considered atmospheric temperatures for each calendar day, Figs. 2 and 3 appeared incorrectly. The amended figures and their legends are provided below. The main message and the interpretation of our paper remain unaffected by this correction." "The figures in the Supporting Information have been exchanged accordingly. We'd like to add that for the calculation of the climatological average, the leap days have been removed, and in the prediction phase, only the data from the past up to the prediction date have been considered. In addition, we note that for calculating the link strengths S ij (t), not the cross-covariance function C ij (t) (τ) has been considered but the absolute values of the corresponding cross-correlation functions c ij (t) (τ). When averaging over all link strengths, we obtain the time dependent average link strength S(t). In the learning phase, we compare S(t) with decision thresholds above its mean to obtain the optimal threshold used in the prediction phase." Fig. 2. The forecasting algorithm. We compare the average link strength S(t) in the climate network (red curve) with a decision threshold Θ (horizontal line, here Θ = 2.82) (left scale) with the standard NINO3.4 index (right scale), between January 1, 1950 and December 31, 2011. Only thresholds above the average of S(t) in the learning phase are considered. When the link strength crosses the threshold from below outside an El Niño episode, we give an alarm and predict that an El Niño episode will start in the following calendar year. The El Niño episodes (when the NINO3.4 index is above 0.5°C for at least 5 mo) are shown by the filled blue areas. The first half of the record (A) is the learning phase where we optimize the decision threshold. In the second half (B), we use the threshold obtained in (A) to predict El Niño episodes. Correct predictions are marked by green arrows and false alarms by dashed arrows. The index n marks a nonpredicted El Niño episode. To resolve by eye the accurate positions of the alarms, we show in SI Appendix, Fig. S5, magnifications of those parts of Fig. 2 where the crossings or non-crossings are difficult to see clearly without magnification. We also show the alarms for the slightly larger threshold Θ = 2.83 (SI Appendix, Fig. S6), which yields the same performance in the learning phase and one more false alarm in the prediction phase. The lead time between the prediction and the beginning of the El Nino episodes is 1.01 ± 0.28 y, while the lead time to the maximal NINO3.4 value is 1.35 ± 0.47 y.

Very early warning of next El Niño

“…31 high-quality atmospheric temperature data for the 1950-2011 period. The optimized algorithm (Data and Methods) involves an empirical decision threshold Θ.…”

“…In the first part , which represents the learning phase, all thresholds above the temporal mean of SðtÞ are considered, and the optimal ones, i.e., those ones that lead to the best predictions in the learning phase, are determined. We found that Θ-values between 2.815 and 2.834 lead to the best performance (31). In the second part of the data set (1981-2011), which represents the prediction (hindcasting) phase, the performance of these thresholds was tested.…”

Network analysis reveals strongly localized impacts of El Niño

“…35. The climate network approach has been found to be useful in improving our understanding of El Niño (8,(23)(24)(25) and in forecasting it (15,16). However, that approach has not been developed and applied to study systematically the global impact of El Niño, and that is what we try to achieve in quantitative terms here.…”

“…These networks have been used successfully to analyze, model, understand, and even predict climate phenomena (6-16). Specific examples of climate network studies include the investigation of the interaction structure of coupled climate subnetworks (17), the multiscale dependence within and among climate variables (18), the temporal evolution and teleconnections of the North Atlantic Oscillation (19,20), the finding of the dominant imprint of Rossby waves (21), the optimal paths of teleconnection (22), the influence of El Niño on remote regions (8,23,24), the distinction of different types of El Niño events (25), and the prediction of these events (15,16). A network is composed of nodes and links; in a climate network, the nodes are the geographical locations, and the links are the correlations between them.…”

Unified functional network and nonlinear time series analysis for complex systems science: Thepyunicornpackage

“…20 It has been already successfully used in a wide variety of applications, ranging from the complex structure of teleconnections in the climate system, 15,18,49 including backbones and bottlenecks, 19,89 to dynamics and predictability of the El Niño-Southern Oscillation (ENSO). 66,92,93 Climate networks (class climate.ClimateNetwork) represent strong statistical interrelationships between time series and are typically reconstructed by thresholding the matrix of a statistical similarity measure S (Fig. 8) …”