Time evolution of two types of La Niña
We identify six and four multi-year and single-year La Niña, respectively, using the observed Niño 3.4 SST anomaly (hereafter N3.4) during 1961–2016 (Supplementary Fig. 1). We define the period when the first La Niña develops as Year (0) in the composite analysis. By taking composites for these events of N3.4 and the ocean heat content (OHC) integrated over the equatorial Pacific (OHCeq: 120° E–60° W, 5.5° S–5.5° N, surface-500 m), the latter measuring the equatorial Pacific warm water volume, trajectories associated with the two types of La Niña are obtained in the phase space (Fig. 1a). The composite-mean trajectories are akin to the limit cycle4,7, showing that La Niña in Year (0) follows El Niño in Year (-1), both of which reach their peak in boreal winter (November–December–January: NDJ, circles in Fig. 1a). Four out of six multi-year La Niña events accompany extreme El Niños (the NDJ-mean N3.4 exceeding the 1.5 standard deviation) in the preceding year, whereas all El Niño before a single-year La Niña has a moderate amplitude (Supplementary Fig. 1). Consistent with the recharge theory, the OHCeq anomaly lead N3.4 by 2–3 months and peaks in September–October–November (SON) before the mature phase of La Niña. While the positive OHCeq anomaly during SON(-1) is comparable in magnitude between the two composites, the negative OHCeq anomaly in SON(0) preceding multi-year La Niña is four times as large as that of single-year La Niña. Despite the large difference in the OHCeq anomaly, the negative N3.4 in NDJ(0/1) in the multi-year composite is only 1.3 times larger than that in the single-year composite due to a strong asymmetry in the thermocline feedback and nonlinear dynamical heating, which suppresses La Niña but enhances El Niño7,27,28. This contrast in magnitude between the SST and OHCeq anomalies is also an important feature of multi-year La Niña and may contribute to the recurrence of La Niña.
After NDJ(0/1), the negative OHCeq anomaly eventually turns positive in the single-year composite, leading to the termination of La Niña. In contrast, the OHCeq anomaly in the multi-year composite decays but remains negative until the following year, resulting in an intensified subsequent La Niña in NDJ(1/2). The time evolution shown in Fig. 1a indicates that the recurrence of La Niña is consistent with the linear recharge oscillator theory. An exceedingly negative OHCeq anomaly in NDJ(0/1) that is not restored within a year is crucial in understanding multi-year La Niña22. The spatial distribution of composite OHC anomalies in its peak season, SON(0), is shown in Fig. 1b,c. The multi-year composite is characterized by a contrast between large negative OHC anomalies in the equatorial Pacific and positive anomalies in the western-central Pacific at approximately 5°–15° N, suggesting that the former was induced by a mass exchange between the equatorial strip and northern off-equator. Such an equatorial asymmetry is not observed in the single-year composite, which indicates weak negative OHC anomalies in the central-eastern equatorial Pacific and positive anomalies in the tropical western Pacific.
Physical link between multi-year La Niña and preceding extreme El Niño
A significant difference between multi-year and single-year La Niña is clearly observed in the composite time series of N3.4 and OHCeq anomalies (Fig. 2a,b). To clarify the processes responsible for the strong discharge of warm water during the growth phase of multi-year La Niña, heat budget analysis was performed on OHCeq using ocean reanalysis datasets (Methods). We present the result based on ORAS4 in Fig. 2b-d because the budget terms reveal the smallest error among the four reanalysis data; however, our conclusion depends little on the dataset (Supplementary Fig. 2).
A large negative OHCeq anomaly in SON(0) for the multi-year La Niña composite occurs because of a large negative OHCeq tendency during the first half of Year (0), i.e., from February to June, denoted as FMAMJ(0) (black solid curve in Fig. 2c). For both multi-year and single-year La Niña composites, the OHCeq tendency is reproduced well by the aggregated OHCeq budgets (shading in Supplementary Fig. 2a,e), which can then be decomposed into individual terms (zonal and meridional advection terms due to geostrophic and Ekman currents, heat exchange at the bottom of the subsurface, and net heat flux at the surface). The sum of the geostrophic and Ekman terms (i.e., Sverdrup heat transport) is called the recharge rate, which explains most of the OHCeq tendency (green curves in Fig. 2c). Unlike the linear recharge oscillator theory, the composited recharge rate indicates a persistent large negative anomaly during FMAMJ(0) when the N3.4 signal is weak.
The decomposition of the recharge rate into components of surface Ekman current heat transport (EHT) and geostrophic current heat transport (GHT) is shown in Fig. 2d. On the one hand, the GHT during the peak period of the preceding El Niño shows a large negative anomaly in the multi-year composite compared to the single-year composite; however, they are similar after scaling with N3.4 (Supplementary Table 1). This implies that the GHT-induced discharge is not a primary factor for generating the OHCeq difference between multi-year and single-year La Niña. On the other hand, EHT in the multi-year composite becomes negative in FMAMJ(0) and contributes to the large negative recharge rate (i.e., discharge); hence, a large negative OHCeq tendency is not observed in the single-year composite (Fig. 2c). The composite heat transport at the northern and southern boundaries indicates that the strong discharge for multi-year La Niña in FMAMJ(0) is attributed to EHT across the northern boundary, which is slightly weakened by the heat imported across the southern boundary (Supplementary Fig. 3). In general, GHT is inversely proportional to N3.4 throughout the year and primarily represents the recharge theory, while EHT has a similar magnitude to GHT but is proportional to N3.4 from the summer to late autumn, indicating that this process disturbs a theoretical recharge/discharge (Supplementary Fig. 4c–f). Consequently, the recharge rate is not correlated with N3.4 during the summer (Supplementary Fig. 4a,b).
During FMAMJ(0) corresponding to the transition period from El Niño to La Niña, composite anomalies of SST, precipitation, and surface wind stress show different patterns between multi-year and single-year La Niña (Fig. 3). The El Niño SST pattern persists in the multi-year La Niña composite but transforms to a weak La Niña pattern in the single-year composite (Fig. 3a,c) because strong El Niño tend to last several more months compared to weak El Niño22. In the multi-year composite map, anomalous positive precipitation is found to the south of the equator, while negative precipitation anomalies appear along the northern off-equator. This southward shift of the precipitation anomaly pattern has been identified during the decay phase of extreme El Niño and is because the climatological mean SST distribution shifted southward in this season16. Consistently, eastward wind stress anomalies are present over the south of the equator, whereas westward anomalies dominate over the northern off-equator, the latter being responsible for the strong EHT-induced discharge (Fig. 3b). The anomalous cross-equatorial wind stresses can form in response to diabatic heating anomalies associated with the southward-shifted precipitation anomaly pattern shown in Fig. 3a (Supplementary Fig. 5a,b). Overall, anomaly patterns in precipitation and wind stress in the multi-year composite are consistent with the equatorial asymmetric distribution of OHC anomalies during SON(0) (Fig. 1b). The atmospheric responses are similar to the C-mode, which acts to terminate extreme El Niño13,18, supporting links with a preceding extreme El Niño. The single-year composite maps lack anomalous zonal wind stresses over the off-equator, likely due to weak, symmetric precipitation anomalies around the equator (Fig. 3c, d).
Exceptional cases of coupling between extreme El Niño and multi-year La Niña exist. Yet, the importance of the easterly wind stress anomaly over the northern off-equator for multi-year La Niña is commonly identified. Two out of six multi-year La Niña events (1970–72 and 2007–09) are preceded by moderate but not extreme El Niño (Supplementary Fig. 6). Composite SST and precipitation anomalies for these two events are almost similar to those of the composites of single-year La Niña. However, the anomalous easterly wind stresses appear over the northern off-equator as a response to thermal forcing in the equatorial Pacific (Supplementary Fig. 5c,d; Supplementary Fig. 6c, d). In addition, two out of six extreme El Niño events (1965–66 and 1991–92) do not accompany a multi-year La Niña (Supplementary Fig. 7). The composite anomalies for these two El Niño events show that the negative OHCeq anomaly is weak in Year (0/1). Consistently, easterly wind stress anomalies are absent along the northern off-equator during FMAMJ(0). These results confirm that the anomalous easterly winds and associated EHT-induced discharge in the northern off-equatorial latitudes link multi-year La Niña with a preceding El Niño.
Analysis of CMIP6 control simulations
To obtain a robust relationship between extreme El Niño and multi-year La Niña, we repeated our analyses in 500-year long preindustrial control simulations using 37 Earth system models (ESMs) participating in CMIP629 (Supplementary Table 2). First, we evaluated the ability of ESM to generate multi-year La Niña defined for each model (Methods). The ratio of the number of multi-year events against the total number of La Niña, 0.60 for 1961–2016 and 0.48 for 1901–2018 in observations, varies across models at 0.28 ± 0.13 (the range denotes the inter-model standard deviation). On average, multi-year La Niña occur less frequently in ESMs than in observations; however, some models capture the observed frequency of multi-year events. As expected, a significant positive correlation (\(r=0.62\)) is found between the frequencies of multi-year La Niña and extreme El Niño in CMIP6 models (Fig. 4a). This indicates that multi-year La Niña tend to occur more often in a model that generates many extreme El Niño, supporting a physical link between them.
We calculate the ratio of the number of multi-year La Niña events accompanying preceding extreme El Niño against the total number of multi-year La Niña events. This ratio, denoted as RE−L, measures the coupling between extreme El Niño and multi-year La Niña (Fig. 4b). The observed values of RE−L are 0.67 for 1961–2016 and 0.40 for 1901–2018, indicating an enhanced coupling between multi-year La Niña and extreme El Niño since the late 20th century. The multi-model ensemble (MME) mean estimate of RE−L is similar to the observed value for 1901–2018; however, RE−L in the ensemble varies considerably across models. Interestingly, RE−L is significantly correlated with the ENSO amplitude measured by the standard deviation of N3.4 (\(r=0.59\) for the entire ensemble). Indeed, the average ENSO amplitude in ten highest RE−L models is approximately 50% larger than the average amplitude in ten lowest RE−L models (\(1.13\pm 0.24\) K versus \(0.76\pm 0.25\) K). This relationship can be understood given that a frequent occurrence of extreme El Niño which increase both the overall ENSO amplitude and frequency of multi-year La Niña. Thus, the analysis of CMIP6 models supports the physical mechanism linking extreme El Niño with multi-year La Niña. An increase in observed RE−L in the late 20th century may also be related to an increase in ENSO amplitude.
Implications for ENSO dynamics
In this study, we examined the mechanisms of multi-year La Niña which occupies two third of La Niña events during the period 1961–2016. A physical link was determined between multi-year La Niña and extreme El Niño, of which the latter often accompanied in the preceding year. The essential mechanism for the transition from an extreme El Niño to multi-year La Niña is explained by a modification of the recharge/discharge cycle, which is schematically illustrated in Supplementary Fig. 8. Using composite analyses of observations and reanalysis data, we found that significant negative OHC anomalies form in the equatorial Pacific during the first La Niña and they persist after its peak. This strong mass discharge of the upper ocean cannot be restored by a single La Niña and, therefore, causes another La Niña to occur in the second year. The large negative OHC anomaly before the peak of the first La Niña is induced by intensified northward Ekman heat transport driven by surface easterly anomalies along the northern off-equator. The patterns of surface wind stress anomalies, easterly anomalies to the north, and westerly anomalies to the south of the equator have occurred when extreme El Niño decays. This plays a central role in linking extreme El Niño with subsequent multi-year La Niña.
Given that ENSO is positively skewed27,28,30, i.e., El Niño is stronger than La Niña, it is reasonable to doubt that multi-year La Niña is an apparent feature arising from the climatological mean shifted toward El Niño due to amplitude asymmetry. However, our results clearly show that multi-year La Niña is not a statistical artefact but a part of the intrinsic complex nature of ENSO. Previous studies have shown the contribution of anomalous wind stress curl causing GHT in the ENSO transition9,20,31−33, an active role of inter-basin interaction for the transition asymmetry34, and a meridional shift of westerly surface wind anomalies for the transition from extreme El Niño to La Niña12–14, 35. Although we do not exclude these processes during ENSO phase transition, we demonstrate that the anomalous Ekman heat transport is crucial to transition from extreme El Niño to multi-year La Niña. The link between extreme El Niño and multi-year La Niña as represented by RE−L is robust; therefore, the occurrence of multi-year La Niña may be predictable beyond the typical predictability of ENSO events36. If a coupled atmosphere-ocean model initialized with an extreme El Niño condition can reproduce the wind stress pattern responsible for the anomalous Ekman heat transport, the subsequent two years, when a multi-year La Niña will occur, maybe predicted owing to the large memory in the ocean heat content21,37. Regarding long-term changes in ENSO properties, we demonstrated that multi-year La Niña occurred frequently during 1961–2016 compared to previous decades. This is consistent with an increasing ENSO amplitude and, hence, frequent extreme El Niño since the late 20th century38. Since ENSO is suggested to be amplified in a warming climate, multi-year La Niña may be observed more frequently as global warming continues39.