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ENSO complexity controlled by zonal shifts in the Walker circulation


The El Niño/Southern Oscillation (ENSO) represents the most consequential fluctuation of the global climate system, with dramatic societal and environmental impacts. Its general dynamics are reasonably well understood in terms of ocean–atmosphere interactions that modify the Walker circulation in the equatorial Pacific. However, some of its space–time features remain stubbornly elusive, such as its event-to-event diversity and asymmetry. Here we show that zonal shifts in the Walker circulation control ENSO space–time complexity in a low-dimensional theoretical framework. We encapsulate these movements in a conventional recharge–discharge oscillator for ENSO by replacing the regionally fixed sea surface temperature index with a warm-pool edge index that displaces the Walker circulation structures. By doing so, we can model essential ingredients of ENSO diversity and nonlinear behaviour without increasing the complexity of the dynamical model. The simple framework is able to reproduce the continuum of ENSO flavours and the asymmetry in the amplitude of warm and cold events. The spatial shifting concept paves the way for a more unified understanding of ENSO and its associated climate teleconnections.

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Fig. 1: Observed and modelled ENSO variability.
Fig. 2: Idealized Walker circulation.
Fig. 3: Pattern continuum from spatial shifting.
Fig. 4: Principal component analysis of SST.

Data availability

GODAS47 data and OLR48 data are provided by the National Oceanic and Atmospheric Administration Physical Sciences Laboratory, Boulder, Colorado, USA, from the website CESM-LE49 data are provided by National Science Foundation/Computational and Information Systems Lab/Yellowstone from the website

Code availability

The code associated with this paper is available upon request from the corresponding author.


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The research of S.T. is supported by Agence Nationale de la Recherche (grant ANR-18-CE01-0012). B.D. acknowledges support from Agencia Nacional de Investigación y Desarrollo (Concurso de Fortalecimiento al Desarrollo Científico de Centros Regionales 2020-R20F0008-CEAZA, Anillo Eclipse ACT210071, Núcleo Milenio UPWELL NCN19-153, Centro de Investigación Oceanográfica en el Pacífico Sur-Oriental COASTAL FB210021) and Agence Nationale de la Recherche (grant ANR-18-CE01-0012). We thank G. Bellon and O. Thual for discussions.

Author information

Authors and Affiliations



S.T. designed and performed the research. S.T. and B.D. discussed the research and wrote the paper.

Corresponding author

Correspondence to Sulian Thual.

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Nature Geoscience thanks Fei-Fei Jin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Tom Richardson, in collaboration with the Nature Geoscience team.

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Extended data

Extended Data Table 1 Indices statistics
Extended Data Table 2 Model units and parameters

Extended Data Fig. 1 Idealized Walker circulation structure.

Zonal profiles of zonal wind stresses (ZWS, a), sea surface temperatures (SST, b) and thermocline depth (TD, c) in a longitudinal strip spanning the equatorial Pacific (black lines and fillings). The circulation can vary in terms of its warm pool extent χ, and thermocline depth can additionally vary in terms of its basin-wide average hM (blue dashed lines). We adjust these variables in the figure in order to match observed temporal averages of ZWS, SST and TD (purple dashed lines). Observed temporal average of outgoing longwave radiations (OLR) is displayed in (a) as an indicator of convective heating over the warm pool that drives the atmospheric part of the circulation.

Extended Data Fig. 2 Time-longitude hovmollers for totals.

a,b,c,d, Time-longitude hovmollers of outgoing longwave radiation (OLR), zonal wind stress (ZWS), sea surface temperature (SST) and thermocline depth (TD) in the equatorial Pacific, as computed from observations (averaged 5N-5S with seasonal variations removed). e,f,g, Analysis repeated for the outputs of the oscillator model (which excludes OLR), displayed over a hand-picked period. Solid lines in each panel indicate the longitudinal position of the warm pool edge (that is, 29C SST isotherm, see methods). The spatial shifting of the Walker circulation consists of a general and coherent longitudinal movement of the atmospheric and oceanic structures that follows the warm pool edge. The movement is less apparent on thermocline depth (panels d,g) that also varies substantially in terms of its basin-wide average.

Extended Data Fig. 3 Phase space evolution.

a,b, Timeseries of warm pool extent χ and basin-wide heat content hM obtained from a numerical integration of the oscillator model (Eq. (1)), and which represents ENSO variability. Warm pool extent χ within 0-1 corresponds to a warm pool edge position within 120E-80W. Shading indicates the hand-picked period used in other figures. c,d, Kernel density estimates (filled contours) and individual realizations (black lines) in phase space of warm pool extent χ and basin-wide heat content hM, compared between observations and model solutions. For clarity, density estimates are shown only above 0.04% where they hide individual realizations that are too dense to visualize. Phase space is divided into El Niño or La Niña states as well as recharged or discharged states as defined here with respect to average conditions (white dashed lines). El Niño events may reach larger amplitudes than La Niña events but are more short-lived.

Extended Data Fig. 4 ENSO cycle in the oscillator model.

a-d, Sketch of the Walker circulation at the four consecutive stages of one ENSO cycle: contracted (La Niña), recharged, expanded (El Niño) and discharged. This is shown for sea surface temperatures (SST) and thermocline depth (TD) represented as in Extended Data Fig. 1. The circulation is entirely determined by the warm pool extent χ that shifts the structures and the basin-wide heat content hM that sets the zonal mean TD, as indicated at each stage of the cycle (blue dashed lines) and for the entire cycle (red lines, years 132 to 135 in Fig. 1)). e-h, Mean state of SST and TD (that is temporal averages computed over the entire simulation, green dashed lines) with total fields from a-d repeated (gray fillings). i-l, Sea surface temperature anomalies (SSTA) and thermocline depth anomalies (TDA) at each stage as computed with respect to the mean state.

Extended Data Fig. 5 Indices timeseries.

a-d, Timeseries from observations of warm pool edge position (WPE, a), SST spatial averages (b), thermocline depth spatial averages (c), and Niño SST indices (d). e-h, Analysis repeated for outputs of the oscillator model displayed over a hand-picked period. We also show ad-hoc stochastic forcing ζ in the oscillator model (e, green line). The indices TW, TE, TM average SST conditions respectively over the warm pool (120E-WPE), cold tongue (WPE-80W) and entire basin (120E-80W). The indices hW, hE, hM average thermocline depth in same fashion. The conventional indices Niño 4, 3.4 and 3 SST average SST conditions respectively over the central (160E-150W), central-eastern (170W-120W) and eastern (150W-90W) Pacific. All averages are within the equatorial band (5N-5S).

Extended Data Fig. 6 Indices scatterplots.

a-o, Scatterplots between spatial averages (or combinations of them) and warm pool edge position (WPE) as measured in either model outputs (red), observations (black) or outputs from CESM-LE (see methods). The indices TW, TE, TM average SST conditions over the warm pool (120E-WPE), cold tongue (WPE-80W) and entire basin (120E-80W). The indices hW, hE, hM average thermocline depth in same fashion. The conventional indices Niño 4, 3.4 and 3 SST average SST conditions over the central (160E-150W), central-eastern (170W-120W) and eastern (150W-90W) Pacific (shaded areas). All averages are within 5N-5S. The relationships predicted by the oscillator model are either constant (C), linear (L), oscillatory (O), nonlinear quadratic (Q) or nonlinear saturating (S). The thermocline nonlinearity from Fig. 3d is encapsulated by the relationship in panel b. The model predicts that the Niño SST indices in panels e,j,o saturate to around 29C when the warm pool region overlaps their domain.

Extended Data Fig. 7 Principal components reconstruction.

a-e, Scatter plots between sea surface temperatures (SST) at different longitudes of the equatorial Pacific and first principal component timeseries of SST (PC1), as computed from observations. f-j, Analysis repeated for SSTs generated by the model. The present representation helps determine how well data is aligned with (and thus captured by) the SST reconstruction R1 from the first PC (black lines, see methods). Individual SST realizations are discriminated in terms of their belonging to the warm pool region where they saturate around 29C (WP, red) or cold tongue region where they slope (CT, blue), with total occurrences indicated in %. Where WP and CT occurrences are more alike (that is mixed), the SST variability is no longer captured by R1 but by R1 + R2* (green lines) where R2* is a nonlinear imprint of the first PC on the second PC (see methods).

Supplementary information

Evolution of the idealized Walker circulation. a,e,f, Idealized Walker circulation (black lines) compared with observations (purple dashed lines) in terms of zonal wind stresses (ZWS), sea surface temperatures (SST) and thermocline depth (TD), where each animated frame corresponds to a given month of the record. The idealized Walker circulation is entirely determined by warm-pool edge position and zonal mean thermocline depth (blue dashed lines), which values here match the ones from observations. b,c,d, longitude-time Hovmöller diagrams of ZWS, SST and TD, with indication of warm-pool edge position (blue dashed lines) and time of current frame (purple dashed lines).

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Thual, S., Dewitte, B. ENSO complexity controlled by zonal shifts in the Walker circulation. Nat. Geosci. 16, 328–332 (2023).

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