Main

The El Niño–Southern Oscillation (ENSO) is the most prominent year-to-year variability in the climate system1. It is characterized by transitions between two phases: positive (El Niño) and negative (La Niña) sea surface temperature (SST) anomalies in the tropical Pacific. By disrupting the global weather patterns2, the hazards caused by ENSO range from droughts and forest fires to extreme rainfall and flooding in various parts of the world, damaging agriculture, ecosystems and human societies1,3,4.

ENSO events follow a distinct cycle with their mature phase in boreal winter and their decline in spring due to a persistence barrier (PB)5,6. However, ENSO is known to be highly variable in its evolution, and some ENSO events tend to persist for consecutive years7,8,9; notably, the recent triple-dip La Niña persisted for three succeeding years10. It is projected that multi-year La Niña and El Niño will probably increase in the future under anthropogenic forcings11,12. This trend has already been seen in the past decades where five out of six La Niña events turned into multi-year La Niña13. Since 1950 ce, five multi-year El Niño events have occurred, two of which developed in the past decade12. These multi-year ENSO variations come along with stronger, cumulative impacts compared with single-year ENSO events13,14. For instance, persistent wet conditions over Australia, Indonesia, tropical South America and South America, as well as dry conditions over the southern USA, equatorial Africa, India and southeast China are climate responses linked to multi-year La Niña events13. Multi-year El Niño events followed by La Niña events could cause a shift from one extreme to the other in some regions, increasing their severe damages due to their prolonged states15.

The possibility of more frequent multi-year ENSO has important societal implications. Climate models still have limitations in how they represent various physical processes vital to ENSO periodicity16. This brings uncertainties to the climate projections of future occurrence of multi-year ENSO. For instance, when investigating such projections, earlier studies usually selected a subset of models based on some aspects of ENSO dynamics, such as ENSO skewness11 and ENSO spatial pattern12, but those cannot guarantee a realistic simulation of ENSO duration and timing. The chaotic nature of ENSO on annual to centennial timescales17,18, combined with the relative scarcity of multi-year events and the modelling challenges, mean that the robustness of shifts in ENSO periodicity over the instrumental record12,13,19 is still under debate.

Reconstructions of ENSO in the geological past (palaeo-ENSO archives20,21) can greatly increase the sample size of multi-year events as well as explore their response to any external forcings (for example, seasonal insolation). Oxygen isotope records from central equatorial Pacific corals, which highly correlate with the local SST evolution, indicate the existence of multi-year ENSO in the past millennium15. Over the past decade, these monthly resolved central Pacific coral δ18O reconstructions22,23,24,25,26 have revealed a highly variable yet overall strengthening ENSO magnitude during the Holocene, but few studies have specifically examined variations in multi-year ENSO occurrence or ENSO duration. In this study, we use a synthesis of these reconstructions and the most recent climate model ensemble of transient Holocene simulations to investigate the changes in occurrence of multi-year ENSO over the much longer timespan of the past 7,000 years (7 ka; the Holocene) and relate these to the forcing mechanisms.

Multi-year ENSO in reconstructions and simulations

Multi-year ENSO events are evident in scattered coral δ18O anomalies from the equatorial central Pacific (Methods), with the development and decay of each event showing strong similarities with the Niño 3.4 (5° N to 5° S, 170° W to 120° W) SST reanalysis data of 1854–2023 ce (Fig. 1). The anomalies of multi-year ENSO events start to decline after the first-year’s peak, reaching a trough after ~6 months, but strengthen again and peak for a second year after ~12 months. Compared with single-year ENSO, multi-year events are preceded by stronger opposing anomalies; for instance, a stronger El Niño is followed by a multi-year La Niña (Fig. 1a,b, blue line versus Fig. 1c,d, blue line). Over the 1,265-years-worth of monthly records spanning the Holocene, we count 87 and 108 multi-year El Niño and La Niña events and 307 and 260 single-year El Niño and La Niña events, respectively.

Fig. 1: Single-year and multi-year ENSO in proxies and reanalysis.
figure 1

a–d, The temporal evolution of single-year (a and b) and multi-year (c and d) ENSO cases (red lines, El Niño; blue lines, La Niña), showing composites of selected proxy reconstruction of the coral oxygen isotope anomaly (a and c) and the Niño 3.4 SST anomaly (b and d). The solid lines and the shading show the mean and 1 s.d. of all cases in the corresponding composites. e, The locations of the fossil coral synthesis used in this study (magenta circles). The ERSST monthly SSTA variability (s.d.) during 1854–2023 ce is represented by the shaded colours. The black box is for the Niño 3.4 region.

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Individual fossil coral slices reveal that multi-year ENSO occurrence is common throughout the Holocene, with at least one multi-year event happening in almost every coral slice longer than 20 years (Fig. 2a and Extended Data Fig. 1a). Most records show a ratio of multi-year to single-year events below 1, suggesting that single-year events have dominated throughout the Holocene (Fig. 2a–c). Also, the multi-year La Niña events are generally more frequent than the multi-year El Niño events (Fig. 2b versus Fig. 2c). These features are consistent with the instrumental record (Fig. 2a–c, purple circles).

Fig. 2: Multi-year ENSO in proxies and simulations during the past 7 ka.
figure 2

a–h, The evolution of the ratio of multi-year to single-year El Niño + La Niña rENSO (a and e), El Niño rEN (b and f), La Niña rLN (c and g) and ENSO-dominant period (d and h) from proxy reconstructions (a–d) and model simulations (e–h). In a–d, each black circle represents a fossil coral slice, and the purple circles show the values for ERSST reanalysis of 1854–2023 ce. The blue circles in a provide reference diameters of the circles (proportional to data length). The dashed blue lines are weighted (by data length) linear fits. In e–h, the black curves show the selected model ensemble mean and the grey shading shows the model ensemble spread of 1 s.d.

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The multimodel ensemble of the Holocene transient simulations (Methods) reproduces considerable multi-year ENSO events during the Holocene (Fig. 2e–g). The multimodel ensemble usually provides a more reliable representation for long-term ENSO evolution, potentially cancelling out the intrinsic decadal or centennial variability of ENSO in individual simulations17,18. We set a criterion to select a subset of four simulations to exclude the models biased by too-regular ENSO cycles27 or those that show limited performance on critical ENSO metrics28 considered unsuitable for this study (Methods). However, the multimodel simulations still tend to underestimate the occurrence of consecutive ENSO, and the simulated ratio of multi-year to single-year ENSO is about half the level suggested by the proxy data and observation (see more details in the Methods).

The Holocene evolution of multi-year ENSO occurrence

Despite potential uncertainties due to data length or chronology (Supplementary Discussion), a robust linear increase in the ratio of multi-year to single-year ENSO events over the past 7,000 years emerges from the proxy reconstructions (Fig. 2a–c, dashed blue line), driven by an increasing (decreasing) occurrence of multi-year (single-year) ENSO (Extended Data Fig. 1). Modern ratios obtained from instrumental data (Fig. 2a–c, purple circles) are very close to those obtained in recent (long) fossil corals, which supports the reliability of the palaeoclimate reconstruction. However, in short coral records, the large internal variability in ENSO introduces noise (outliers in Fig. 2b,c and Extended Data Fig. 1b,c), which can be minimized by considering El Niño and La Niña together as this increases the total number of events (Fig. 2a). Nonetheless, we estimate an increasing trend in the ratio of combined multi-year events to single-year events (rENSO), and those of multi-year to single-year El Niño (rEN) and La Niña (rLN) are all statistically significant (P < 0.05; samples weighted by data length; Methods). The ratio rENSO increases from 0.09 during the earliest 1,000 years of the proxy compilation to 0.44 during the last millennium (compared with 0.42 in the instrumental period) by a factor of 5.

The four-model ensemble mean also shows an increasing proportion of multi-year events during the Holocene (Fig. 2e–g; P = 0.064, P = 0.827 and P < 0.05), which coincides qualitatively with the proxy reconstructions. The increase in the ratios is more modest, but the ratios themselves are also smaller. The uncertainties due to the sliding window size when analysing the simulations can be almost neglected when window size is larger than 50 years (Supplementary Discussion).

Notably, the proxies and model simulations consistently show that this increasing occurrence of consecutive ENSO events is contributed by more frequent multi-year La Niña as well as multi-year El Niño, with a greater contribution from the former (as seen in its larger slope of linear fit). The averaged rEN and rLN of all proxies are 0.28 and 0.42, respectively. These features are in agreement with the observation that multi-year La Niña cases are more common than multi-year El Niño7,19 (Fig. 2b,c, purple circle).

Prolonged ENSO cycles and their cause

The Holocene annual mean climate is relatively stable compared with the glacial period29. Nonetheless, changes in the distribution of incoming solar radiation across the year (caused by orbital precession) still drove important regional climate variations30,31. This seasonal insolation change caused a marked reduction in ENSO amplitude in the eastern and central Pacific23,24,32,33 that has been linked to systematic changes in the upper-ocean structure and climate background in the tropical Pacific21,34. They could further affect the ENSO periodicity.

The fact that multi-year El Niño and La Niña consistently became more frequent is associated with a prolonged ENSO period, as the anomalies remain in the warm or cold phase for longer. The ENSO-dominant period (Methods) is found to significantly (P < 0.05) increase in the proxy data by roughly 6 months (Fig. 2d). This is consistent with an increase in ENSO period in the model ensemble (although this is not statistically significant, P = 0.058). The correlation between the rENSO and the ENSO period is 0.58 as estimated from the reconstructions (Fig. 3a) and verifies the relationship between consecutive ENSO occurrence and ENSO period.

Fig. 3: Multi-year ENSO, ENSO period and amplitude relationship in proxies and selected simulations.
figure 3

a,b, The relationship between the ratio of multi-year to single-year ENSO rENSO on the x axis and the ENSO-dominant period (a) or ENSO amplitude (b) on the y axis. The dashed blue lines show the linear fit. The blue circles in a provide reference diameters of the circles (proportional to data length). The purple circle in a is for ERSST reanalysis of 1854–2023 ce, but it is not shown in b because it is not appropriate to compare the variability of SST and δ18O directly. In a and b, the P values in the Pearson correlation (corr) are shown in the figure legend. c, A comparison of corr(rENSO, ENSO period) (blue) and corr(rENSO, ENSO amplitude) (red) in proxies and four selected simulations.

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We propose that extended periods of ENSO provide a broad explanation for more frequent multi-year El Niño as well as multi-year La Niña cases, with its root cause in the changes of upper-ocean structure (detailed below). This is based on the classic linear oscillatory theories of ENSO, rather than mechanisms tied to surface and/or nonlinear processes such as the cross-equatorial wind35, North Pacific variability12,36, trade wind anomalies11 or teleconnections from other ocean basins37. These theories are used to explain recent trends in multi-year La Niña or El Niño alone and tend to focus on anthropogenic influence within the past few decades12,13 or the near future11. We next demonstrate how the linear framework that encompasses slowly varying insolation forcing links the mean climate changes and prolonged ENSO periods.

We adopt the conceptual recharge oscillator (RO) model38 (Methods) to investigate the relationship between the climate background, sensitivity in key ENSO feedbacks, and ENSO periods. By perturbing one parameter for a set of sensitivity experiments with RO, we elucidate the dependence of ENSO period on the thermocline depth (Methods and Extended Data Fig. 2). The RO sensitivity experiments show a series of steady-state ENSO conditions: when the zonal mean thermocline depth begins to decrease artificially in RO until 40% of it is removed (parameter λ changes from 0 to 0.4), the period of ENSO increases from 3.82 years to 4.63 years, or prolonged by 21% (Extended Data Table 1).

The thermocline depth–ENSO period relationship revealed by RO is in line with the transient Holocene simulations. Three models have monthly subsurface ocean data available, and they all show a decreased vertical temperature gradient in the central and eastern equatorial Pacific from January to August and, thus, on an annual mean basis (Fig. 4c), implying an overall deeper and/or warmer thermocline during the mid-Holocene, consistent with a shorter ENSO period and fewer multi-year ENSO events. Although cooler surface temperature has been recorded in the easternmost Pacific39,40, subsurface temperature estimates from the western equatorial Pacific41, and eastern Pacific42,43 suggest a warmer and/or deeper thermocline in the mid-Holocene, in agreement with the mid-Holocene (6 ka) multimodel time-slice ensemble44 and with our transient experiments.

Fig. 4: Influence of orbital forcing on the upper ocean in the Eastern Pacific.
figure 4

a–c, The seasonal cycle of the difference between 6 to 5.5 ka and 1 to 0.5 ka of insolation (W m−2) (a), zonal mean SST of the Eastern Pacific (180–100° W) (b) and zonal mean subsurface ocean (at ~150 m depth) temperature of the Eastern Pacific (180–100° W) (c). b shows the ensemble mean of four selected simulations, and c shows the ensemble mean of three selected simulations (LOVECLIM data not included due to availability).

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The deepened tropical Pacific thermocline weakens the thermocline feedback, because the wind stress anomalies are less effective in reinforcing the thermocline anomalies that are linked by the mean upwelling5,45. Towards the late Holocene, increased thermocline feedback can contribute to more efficient ocean–atmosphere coupling and reduced ENSO PB5 (Extended Data Fig. 3). The PB for modern ENSO is present typically during the Northern Hemisphere spring when SST anomaly (SSTA) sharply weakens. When PB becomes weaker, ENSO anomalies after the first-year’s peak are more likely to persist and lead to prolonged ENSO, regardless of El Niño or La Niña. Similarly in principle, a deeper thermocline and enhanced thermocline feedback are found to be associated with a pronounced onset rate of multi-year La Niña events following super El Niño events in the past century13.

Alternatively, stronger ENSO activities may also contribute to more multi-year ENSO. Multiple earlier studies suggest reduced ENSO amplitude throughout most of the Holocene compared with the twentieth century21,46. In particular, ENSO activity in the tropical central Pacific appears to reach a minimum around 5 ka and gradually increases after that24 (Extended Data Fig. 4). In theory, a stronger ENSO case creates larger ocean heat content variation lagging the surface temperature anomalies, and subsequently it can take longer time for an opposite condition to neutralize the preceding strong anomalies through the slow recharge–discharge ocean heat content process47. This view is supported by the weak (P = 0.07) correlation of 0.39 between rENSO and ENSO amplitude in proxies (Fig. 3b and Methods) and selected simulations (Fig. 3c), which suggests that the precession-forced intensifying of ENSO across the Holocene also partly leads to a favourable condition for more persistent ENSO. Nevertheless, a consensus among proxies and simulations (Fig. 3c) indicates that rENSO is more closely linked to ENSO period rather than amplitude and underscores the primary role of ENSO period in driving multi-year ENSO variability.

Orbital forcing of the equatorial Pacific thermocline

Finally, we investigate how orbital forcing drove the tropical Pacific thermocline structure changes, and the resultant prolonged ENSO cycles towards the late Holocene. The forcing mechanism for deeper and warmer thermocline in the mid/early Holocene was first explored in earlier modelling studies21,33,48. By comparing the subsurface sea temperature, we can identify the warmer temperature anomalies throughout most of the year in the Tropical Eastern Pacific (Fig. 4c and Extended Data Fig. 5). This change is in contrast to the SST anomalies in the tropics which are colder during the first half year but warmer during the second half year (Fig. 4b and Extended Data Fig. 6). The SST largely follows the local insolation forcing, but with a phase-lagged response of 1–2 months (Fig. 4a,b) due to large heat capacity of sea water. Conversely, the subsurface ocean warming can be explained by the subduction process. Increased solar radiation in the Southern Hemisphere late winter/early spring warms the surface water in the subtropical South Pacific (Fig. 4b). This warm signal then propagates to the deeper Tropical Eastern Pacific thermocline through subduction when the local thermocline is the deepest and can be ventilated into the tropics49. Eventually, this warmer water reaches the equatorial thermocline, heating the subsurface and deepening the thermocline throughout most of the year (Fig. 4c and Extended Data Fig. 5). With the subsurface warming, the surface cooling39,40 further weakens the vertical gradient. In short, due to the ocean subduction, the precessional forcing in the subtropical South Pacific led to weaker ocean stratification and deeper thermocline depth in the tropical Pacific during the early/mid-Holocene epoch.

Using multiple approaches, we demonstrate an increasing occurrence of multi-year ENSO from the early/mid to late Holocene mainly under the orbital forcing. This increasing trend is robust in a synthesis of proxy reconstructions. It is also seen, albeit weaker, across the four climate models that adequately reproduce multi-year ENSO. This trend, caused by both increasingly frequent multi-year La Niña and multi-year El Niño events, is associated with a prolonged ENSO period. We attribute the lower frequency of multi-year events during the mid/early Holocene to a weaker vertical temperature gradient in the central and eastern equatorial Pacific, due to local surface cooling and subduction of warmer SST in the subtropical region of the Southern Hemisphere.

ENSO flavour change may interact with different processes of ENSO excitation and feedbacks12 and lead to changes in ENSO duration. Proxy records from both the central Pacific and the eastern Pacific suggest that the present-day mix of flavours has occurred since 5 ka (ref. 24). However, constraining the shifts in the most active region of ENSO between the central Pacific and the eastern Pacific is challenging because of the scarcity of reconstructions and model inconsistency (Extended Data Fig. 7). These uncertainties highlight the need for further research with high-temporal-resolution datasets covering the Pacific basin to solidify our findings. Nonetheless, the reconstructions within the Niño 3.4 region are adequate to effectively record the history of multi-year ENSO (Supplementary Discussion), even if they cannot distinguish that of its separate flavours.

Historical observations and simulations have already demonstrated that the probability of multi-year La Niña and El Niño events has increased in the past decades11,12,13. The research here shows that the frequency of multi-year ENSO events has been trending upwards for the past 7,000 years, hinting that the recent probability may be unprecedented since the early/mid Holocene, particularly as the slowly varying upper-ocean stratification background at orbital timescales has become more favourable for prolonged ENSO. This implies that climate models with more realistic CO2-induced ocean response50 can be key for robust projections of ENSO periodicity. The shallower tropical Pacific thermocline, in addition to other emerging nonlinear and/or surface processes under anthropogenic forcings11,12 (although not evident at the Holocene timescale; Extended Data Fig. 8), will probably drive increased prevalence of multi-year ENSO events in the twenty-first century and will combine with the stronger amplitude of ENSO24,46 to have consequences across the globe. More climate mitigation efforts are urgently needed to tackle these impacts.

Methods

Proxy reconstructions

We synthesize the monthly resolved fossil coral oxygen isotope data from Kiritimati and Fanning Atolls in the equatorial central Pacific from several previous studies24,25,26. The Atolls are located within or near the Niño 3.4 region (5° S to 5° N, 170° W to 120° W, an ENSO-active region) (Fig. 1e) and collectively have over 1,200 years of coral proxy data spanning the last ~7,000 years of the Holocene. We use only the coral slice records longer than 20 years (22 out 38 records selected; Supplementary Table 1), while the mean (median) length of them is 57.5 (38.5) years. The oxygen isotopic composition of a coral’s carbonate skeleton is a proxy that jointly reflects SST and the oxygen isotopic composition of seawater, which is linearly related to sea-surface salinity. On interannual timescales, El Niño (La Niña) events bring warmer and wetter (cooler and drier) conditions to Kiritimati and Fanning, which collectively yield negative (positive) coral δ18O anomalies. Previous work (for example, Cobb et al.22) demonstrates the high correlation between modern coral δ18O at these sites and the Niño 3.4 SST index (a practical ENSO index). Bivalve δ18O records from the equatorial eastern Pacific32, although monthly resolved, are not included in our synthesis owing to the short length of data.

Models and simulations

We analyse the Holocene ENSO evolution in the Holocene transient simulation intercomparison contributed by eight research groups worldwide (Supplementary Table 2), which provides an opportunity to examine the continuous climate variations to orbitally induced changes in multiple model realizations. These simulations (except TRACE; more information on TRACE is given in Supplementary Table 2) were spun up from an early/mid Holocene initial condition (range from 10 ka to 6 ka, equilibrium or transient) and continued to run till the present day, driven primarily by the forcing of seasonal and latitudinal distribution of insolation (for example, Fig. 4a). Basic monthly climate output from the simulations, such as surface air temperature, SST are regridded to 1° by 1° for analysis.

The simulated multi-year versus single-year ENSO ratio (rENSO) using Niño 3.4 region SSTA (or surface air temperature anomalies used as SSTA owing to data availability) was calculated for each simulation to evaluate the model performance of multi-year ENSO events (Supplementary Fig. 1). We then use a criterion of rENSO averaged during the last 1 ka, given rENSO = 0.44 in the fossil coral data of the last 1 ka and 0.42 in Extended Reconstructed Sea Surface Temperature (ERSST) (1854–2023 ce)51. Four out of eight models were selected with the best match of rENSO for further analysis and calculating ensemble mean, namely EC-Earth3-LR52, IPSL53, MPI-ESM54,55 and LOVECLIM1.3 (ref. 56). Other models simulating too regular and short ENSO cycles and too few multi-year ENSO events were excluded from the main results. For instance, TRACE (CCSM3 model) simulation is characterized by notable quasi-biannual ENSO, almost unable to reproduce any consecutive ENSO (Supplementary Fig. 1a, TRACE). These selected models can realistically represent observed SSTA evolution of single-year and multi-year El Niño and La Niña events (Supplementary Fig. 2). They also demonstrate the highest capability in realistically capturing some key ENSO assessment metrics (ENSO period, ENSO skewness and SST zonal structure)28 (Supplementary Fig. 1).

Nevertheless, we notice an overall underestimation of multi-year ENSO occurrence, but the sources of model biases need further investigation. The common ENSO periodicity biases in climate models can be model dependent and come from biases in the background climatology16,57, from improper combined ENSO feedback processes16 or, partly, from coarse model resolution27.

Definition of multi-year ENSO

Due to different amplitudes of ENSO simulated by models, we do not use a fixed threshold of specific Niño 3.4 SSTA but 0.5 standard deviation (s.d.)11 which is calculated every 100 years (comparable to the length of a long coral data, and for more stable results; Supplementary Discussion). For every 100 years of monthly Niño 3.4 SSTA, after applying for a running mean filter to retrieve interannual variability of 1.5–7 years, and a 3-month smoothing11, we first identify the peak ENSO seasons. For instance, if the ENSO peak is in December (ENSO phase locking58), then the ENSO season is from −2 to +2 months (October (0) to February (1)). Then, if the SST is 0.5 s.d. above/below average for a whole ENSO season, it is categorized as an El Niño/La Niña event. Multi-year events are identified when the El Niño (or La Niña) criterion is met for 2 years in a row during the whole ENSO season, in contrast to neutral conditions or an opposite phase in the second year. Note that in this way 3-year events are simplified as two 2-year events. The calculation of multi-year ENSO occurrence for coral δ18O anomalies is similar but using the s.d. of each coral slice depending on its length (not a fixed 100-year window) (Fig. 1a,c). It should be pointed out that the ENSO peak month in coral data could be highly variable and did not always occur in December throughout the Holocene (Supplementary Fig. 3). We also tested different thresholds of ENSO (for example, 0.4× s.d. or 0.6× s.d.) for the coral data, and the results are not affected (figure not shown).

ENSO-dominant period (spectrum analysis) and amplitude

ENSO periods in proxy reconstructions and model simulations (Niño 3.4 SSTA) are estimated by spectrum analysis. We first apply a running mean filter to exclude the variability longer than 7 years or shorter than 1.5 years in the time series of δ18O anomalies and SSTA. The rest ENSO-band time series are then processed by power spectrum analysis and a calculation of its s.d. for ENSO amplitude. Due to the irregularity of ENSO, the power spectra show high values of variability at a broad interannual band with multiple peaks. Rather than the period associated with maximum power, we instead use the weighted-averaged (by power) period within the band of 1.5–7 years to determine the ENSO-dominant period (as a centroid).

Significance test for the linear trend

We apply the commonly used Mann–Kendall (MK) statistical test59,60 for the significance test of linear trends in time series of the occurrence of multi-year ENSO and ENSO periods (Fig. 2, dashed blue lines). The MK is rank-based and non-parametric and has the advantage that the input variable does not have to be normally distributed. The null hypothesis (H0) of the two-tailed MK suggests that there is no change of trend, while the alternative hypothesis (H1) implies a positive or negative trend over time. The H0 was rejected when the P value fell below 0.05. The weight of sample data (proportional to length) is considered when calculating the linear trend of coral slice data and its significance.

The conceptual RO

We use the classic conceptual RO model38 to verify the relationship between the depth of the mean thermocline in the tropical Pacific and the period of ENSO. It is based on coupling SST evolution to ocean adjustment processes to provide a simplified framework with which to understand the oceanic and atmospheric roles in driving variations in ENSO cycles. RO does not incorporate multi-year events, but it allows for changes in the period of ENSO. We modify the model to give us the ability to introduce changes in the zonal mean thermocline depth in the equatorial Pacific. Compared with complex GCMs, this approach allowed us to explicitly isolate and examine the specific impact of thermocline depth on ENSO periodicity.

The RO model can be expressed as

$$\begin{array}{l}\displaystyle\frac{{\mathrm{d}}{h}_{{\mathrm{W}}}}{{{\mathrm{d}}t}}\,=\,-r{h}_{{\mathrm{W}}}-\alpha b{T}_{{\mathrm{E}}}\\\;\displaystyle\frac{{\mathrm{d}}{T}_{{\mathrm{E}}}}{{{\mathrm{d}}t}}\,=\,R{T}_{{\mathrm{E}}}+{\gamma h}_{{\mathrm{W}}}-{e}_{{\mathrm{n}}}{({h}_{{\mathrm{W}}}+b{T}_{{\mathrm{E}}})}^{3}.\end{array}$$
(1)

These two equations describe the subsurface ocean adjustment dynamics and the SST dynamics, respectively. In equation (1), hW denotes the thermocline depth anomaly in the tropical Western Pacific, and TE denotes the SST anomaly in the Tropical Central to Eastern Pacific; r describes the collective damping rate of the upper ocean through mixing and the equatorial energy loss to the west and east boundary layer currents; α and b are coupling coefficients of wind stress and Sverdrup transport, and wind stress and SST anomalies, respectively; R is a collective Bjerknes feedback strength, and γ is the thermocline feedback coefficient; the cubic term in the SST equation introduces nonlinear effects to the coupled system with \({e}_{{\mathrm{n}}}\) to quantify its strength.

To study the sensitivity of the oscillation system to zonal mean equatorial thermocline depth (denoted \(\hat{h}\,{\rm{and}}\,\hat{h}=({h}_{{\mathrm{W}}}+{h}_{{\mathrm{E}}})/2\)), we update the RO model with variable \(\hat{h}\) (anomaly)38. Due to the quasi-balance between the thermocline depth tilt (and, thus, the pressure gradient force) along the Equator and the wind stress over the equatorial band (\(\hat{\tau }\)), there is a relationship \({h}_{{\mathrm{E}}}-{h}_{{\mathrm{W}}}=\hat{\tau }=\mu {T}_{{\mathrm{E}}}\) (refs. 61,62), in which \(\mu\) is the wind stress coupling coefficient. Also, \({b=b}_{0}\mu\), where \(b\) is the high-end estimation of \({b}_{0}\). If we introduce a parameter \(\lambda\) for the change in the zonal mean thermocline anomaly and replace \({h}_{{\mathrm{W}}}\,{\rm{by}}\,{h}_{{\mathrm{W}}}-\lambda \hat{h}\) in the SST equation (the second) in equation (1), so the original nonlinear RO system is updated as

$$\begin{array}{l}\displaystyle\frac{{\mathrm{d}}{h}_{{\mathrm{W}}}}{{{\mathrm{d}}t}}\,=\,-r{h}_{{\mathrm{W}}}-\alpha b{T}_{{\mathrm{E}}}\\\;\displaystyle\frac{{\mathrm{d}}{T}_{{\mathrm{E}}}}{{{\mathrm{d}}t}}\,=\,(R-\gamma {b}_{0}\mu \lambda /2){T}_{{\mathrm{E}}}+{\gamma (1-\lambda )h}_{{\mathrm{W}}}-{e}_{{\mathrm{n}}}{({h}_{{\mathrm{W}}}+b{T}_{{\mathrm{E}}})}^{3}.\end{array}$$
(2)

Other coefficients and parameters in this RO with variable thermocline depth are given values according to the original study38 as r = 0.25, α = 0.125, b = 2.22, b0 = 2.5, R = 0.667, γ = 0.75, μ = 8/9 and en = 3. We then conduct a series of sensitivity experiments focusing on different levels of \(\lambda \,\) (Extended Data Fig. 2 and Supplementary Table 1). Note that, when \(\lambda\) equals 1, the \({h}_{{\mathrm{W}}}\) term is removed from the SST equation, which becomes decoupled from the ocean dynamics equation; when \(\lambda\) equals 0, the system is not changed. The relationship between the thermocline depth and ENSO period is still robust, although slightly weakened, if we introduce a seasonal cycle to λ (Supplementary Table 1).