Abstract
The present manuscript analyzes monthly equatorial Pacific indices by using a specific neural algorithm, the so-called “Self-Organizing Maps” (SOMs). The main result is a change found in the nature of the transitions between cold to warm and warm to cold extreme events from 1950 to present, around the late 1970s. SOM is an unsupervised clustering technique which allows one to reduce high-dimensional data space (in this case, three indices over 636 months) in terms of a smaller set of three-dimensional reference vectors (100) characterizing pertinent situations. These reference vectors, which are displayed on a two-dimension map, are closely related by a topological relationship leading us to discriminate La Niña conditions from the opposite El Niño conditions. In a second step, a Hierarchical Agglomerative Clustering (HAC) method is used to further group the reference vectors into a small number of clusters (12) whose spatial and temporal characteristics can be analyzed and interpreted in terms of physical parameters. Schematically, these 12 clusters can be divided into two “warm” clusters, six “neutral” or “transition” clusters and four “cold” clusters. In each particular group (warm, neutral, cold), the clusters mainly differ from each other by the amplitude of the anomalies, their spatial patterns and their temporal variability. Some clusters are found to be strongly linked to the boreal spring period, while others have barely any records during that season. Other clusters are associated with records mainly observed either prior to or after 1980. This suggests that the method is able to identify changes in the variability of the tropical Pacific basin observed on decadal time scales (1976 climate shift in our case). Each monthly record can be summarized by the cluster to which it belongs. The temporal evolution of this value during extreme ENSO events shows similar patterns (persistence in specific clusters and transition between groups of clusters) associated with comparable El Niño or La Niña events. The methodology described in the present study (SOM plus HAC) is suggested to be useful both for seasonal ENSO predictability and for the detection of decadal changes in ENSO behavior.
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Acknowledgments
We wish to thank the Institut de Recherche pour le Développement (IRD), the Institut Pierre-Simon-Laplace (IPSL), the Centre National de la Recherche Scientifique (CNRS; Programme ATIP-2002) for their financial support crucial in the development of the author’s collaboration. We are grateful to the “Universidad de Buenos Aires” and the “Departamento de Ciencias de la Atmósfera y los Océanos” for welcoming Jean-Philippe Boulanger and Julie Leloup. We are also grateful to the Hadley Centre for providing the HadISST data set. We also want to thank Christophe Menkes, Sean Kennan, Matthieu Lengaigne and Pascal Terray for stimulating discussions. We are thankful to Michel Crépon for his advices and to Keith Rodgers for computed the D20 data in an easy form. We thank the three anonymous reviewers for their constructive comments.
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Appendix
Appendix
In this paper, the SOM algorithm is used and presented below.
The SOM is a two-layers neural networks, first described by Kohonen (1984), that allows one to project a high dimensional data space onto a reduced and ordered space. The input layer is the original data set, denoted D (the three indices Niño 3.4, Niño 1+2 and Longi28 in the present study). The output layer is a topological map, denoted M, composed of a set of neurons (a 10 × 10 grid here). The map is usually a regular lattice in which one node is a neuron. Each neuron c of M is defined by its position on the map and fully connected to the input layer through its weight vector w c , whose dimension is the dimension of the observation. From this lattice structure, one can first define a distance δ(c,r) for each pair of neurons (c,r). Second, using this distance, a neighborhood of order d for each neuron c is defined as follows:
The main property of the SOM is the conservation of a topological order on the map. This property ensures that two neighboring neurons c and r on the map, according to the δ-distance, will be associated to two close reference vectors w c and w r in D, according to the Euclidean distance. And conversely, two close observations x i and x j in D will be projected onto two close neurons w i and w j of M.
In practice, the SOM algorithm can be summarized as follows:
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1.
Initialization step (time step t = 0).
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(a)
Choice of the structure of the map and its size (a regular 10 × 10 grid in our case).
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Random initialization of the set W 0 of the p reference vectors (p = 10 × 10 in the present paper).
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(c)
Definition of the initial neighborhood order d 0.
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(d)
Definition of the initial learning rate ε(0).
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(e)
Choice of the maximum number of iterations N iter .
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(a)
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2.
Iterative phase (time step t + 1). The set of reference vectors W tof the previous time step is known.
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Affectation. The observation x i is affected to its best-matching neuron using an affectation function χ, from D to C, based on the minimum Euclidean distance criterion:
$$ \chi ({\mathbf {x}}_{i})= \arg\,{\mathop {{\text{min}}}\limits_j }\parallel{\mathbf {x}}_{i}-{\mathbf {w}}_{j}\parallel, $$j = 1:100 in this case (10 × 10 = 100 neurons on the map M).
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Update. The new set of reference vectors W t+1 is computed. The weight vector of the best matching neuron in the defined neighborhood is updated using:
$${{\mathbf {w}}_{j}}{\text{(}}t{\text{ + 1) = }}{{\mathbf {w}}_{j}}{\text{(}}t{\text{) + }}\epsilon {\text{(}}t{\text{) }}(x(t) - {{\mathbf{w}}_{j}}(t){\text{) }}\quad\forall j \in \it {{V}_{i}}{\it{(d}}_{t}), $$where ε(t) is the learning rate parameter.
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The neighborhood order d t+1 and the learning parameter ε(t + 1) are updated and decrease at each time step.
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3.
The iterative phase is repeated until convergence of the parameters or until N iter is reached.
During the iterative phase, the grid changes, moving according to the evolution of the parameters. The conservation of the topological order provides an adaptation of the grid to the studied data. At the end, each observation is associated to one neuron, and only one, via a weight vector. All this allows to consider the map M and the reference vectors W as a reduction of the initial data space D.
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Leloup, J.A., Lachkar, Z., Boulanger, JP. et al. Detecting decadal changes in ENSO using neural networks. Clim Dyn 28, 147–162 (2007). https://doi.org/10.1007/s00382-006-0173-1
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DOI: https://doi.org/10.1007/s00382-006-0173-1