<figure><img src="image_1.png" /></figure>

# Extreme coastal El Niño events are tightly linked to the development of the Pacific Meridional Modes

<figure><img src="image_2.png" /></figure>

Check for updates

Cristian Martinez-Villalobos Ⓔ<fnref n="1" />,²✉, Boris Dewitte Ⓔ³,⁴,⁵, René D. Garreaud⁶,⁷ & Leandra Loyola<fnref n="1" />

Coastal El Niño events—marine heatwaves instances in the far eastern Tropical Pacific during otherwise basin-scale neutral or cold conditions—can have severe societal impacts for countries along the west coast of South America, as exemplified by the 2017 and 2023 Peru-Ecuador floods. Due to the brevity of the observational record, it is not well understood whether these events are driven by local or large-scale processes. Here, to overcome this limitation we use a data-driven modeling approach to address their return period and forcing mechanisms. It is shown that extreme coastal El Niño events are a local manifestation in the eastern tropical Pacific of the constructive interactions of the Pacific Meridional Modes (PMM). Specifically, the North PMM yields a dipole-like anomaly SST pattern along the equator that favors its development, while the positive phase of the South PMM reinforces it. A smaller group of more moderate coastal events are remotely driven by zonal wind anomalies in the western tropical Pacific without the PMMs' influence. The role of PMMs in the development of extreme coastal El Niño suggests that they may be more predictable than previously thought.

Coastal El Niño events are instances of long-lasting marine heatwaves in the easternmost Tropical Pacific not associated with typical basin-wide El Niño events. This type of event came into prominence with the large event of early 2017¹⁻⁶. This event was largely unexpected and unpredicted²,⁵, as it did not fit any of the known basin-wide ENSO types⁷⁻¹². Figure 1 shows the sea surface temperature and precipitation anomalies at the peak of the event. These showcase warming in excess of 1 °C in the Niño 1 + 2 region (OS-10; 270E-280E) which extended all the way down to Central Chile, with a Central Pacific—the region often used to define basin-wide El Niño events in the literature¹³—remaining neutral (Fig. 1a). The precipitation anomalies showcase a familiar north-south dipole pattern with large anomalies in Peru, Ecuador and Colombia (Fig. 1c). During Feb-Apr, precipitation averaged over the Niño 1 + 2 region area reached approximately 120 mm/month (Fig. 2c) compared with an average of approximately 60 mm/month in this season (Fig. 2a), an increase of 100%. In some continental regions of Ecuador and Peru, however, the effects were even larger. In parts of Northern Peru “rainfall exceeded 700 mm, about 15 times the long-term mean, and landslides and flooding were widespread, with a large cost in lives and infrastructure”². Other impacts include increases in exposure to pathogens and a dramatic increase in dengue cases in Peru⁶. Comparing this

pattern with the extreme 1997–1998 basin-wide event during the same season (Fig. 1b, d) highlights the singular nature of this event.

There are two main triggers, both with an important role for evaporative cooling, that have been proposed to explain the 2017 event. In the first case, a weakening of the southeast trade winds, triggered either by an extratropical Rossby wave train in the southern Pacific²,⁶ or through a teleconnection from the Amazon region³, weakened coastal upwelling and also reduced evaporative cooling. The second mechanism underscores the influence of remote forcing from the western/central Pacific¹⁴. In this case, westerly wind bursts¹⁵,¹⁶ excited an oceanic Kelvin wave response that depressed the thermocline in the eastern Pacific one or two months later⁵. As a result, anomalously warm water was upwelled in the eastern Pacific, increasing sea surface temperatures (SSTs) in the area. The warmer SSTs triggered a locally coupled wind response that further increased SSTs by a reduction in coastal upwelling and wind-induced evaporation⁵.

Due to their perceived rareness compared with basin-wide El Niño events—besides the 2017 event, a similarly large event occurred in 1891, 1925¹⁷, and 2023 (see discussion of this event below)—these coastal marine heatwaves have until recently been largely overlooked in the literature

<footnote n="1">¹Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile. ²Data Observatory Foundation, ANID Technology Center No. DO210001, Santiago, Chile. ³Centro de Estudios Avanzados en Zonas Áridas, La Serena, Chile. ⁴Departamento de Biología, Facultad de Ciencias del Mar, Universidad Católica del Norte, Coquimbo, Chile. ⁵CECI, Université de Toulouse III, CERFACS/CNRS, Toulouse, France. ⁶Departamento de Geofísica, Universidad de Chile, Santiago, Chile. ⁷Center for Climate and Resilience Research (CR2), Santiago, Chile. ✉e-mail: cristian.martinez.v@uai.cl</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1** | Spatial pattern associated with the coastal El Niño event of 2017.
a 3-month (Feb–Mar–Apr) running mean SST anomalies during the coastal El Niño event of 2017. b 3-month (Feb–Mar–Apr) running mean SST anomalies during the extreme basin-wide El Niño event of 1998. c 3-month (Feb–Mar–Apr) running mean precipitation anomalies during the coastal El Niño event of 2017. d 3-month (Feb–Mar–Apr) running mean precipitation anomalies during the extreme basin-wide El Niño event of 1998. Note different colorbar ranges for the 1998 and 2017 events. The black box shows the location of the Niño 1 + 2 region.</figcaption></figure>

despite their large societal implications. Here we show that a majority of Coastal El Niño events are associated with the development of the Pacific Meridional Modes (PMMs). These modes of variability contrast with the usual ENSO dynamics in that they are primarily driven by changes in wind-induced evaporation. Additionally, we constrain these events expected frequency, return periods, intensity, and associated precipitation. Moreover, we identify the cold counterparts of these events, here referred to as Coastal La Niñas, and show that they can also have substantial impacts.

# Results

## Coastal El Niño and La Niña events during the satellite era

Given the substantial social and environmental impacts of rainfall, we begin this section considering the precipitation climatology in the Niño 1 + 2 region (black boxes in Fig. 1). We focus on the period 1980–2020, where data for more relevant variables are available (see “Methods”). We also extend, when possible, most of the analysis back to 1948, showing qualitative agreement (see “Methods” and Supplementary Information). Figure 2a shows the 3-month climatological precipitation running-mean. We observe a strong seasonal cycle, with most of the precipitation falling in the earlier part of the year—coinciding with the highest sea surface temperature (SST; compare Fig. 2b, c) and southernmost position of the Intertropical Convergence Zone (ITCZ)¹⁸. The peak occurs in Feb–Mar–Apr where on average falls nearly 60 mm/month (2 mm/day) over the Niño 1 + 2 region. Over most of the year the absolute value of SSTs are too cold for any SST anomaly (SSTA) to produce a significant convective response (Fig. 2b). The situation is different during Feb–Mar–Apr, where an increase of 1 degree Celsius above 23.1 °C is associated with an increase in precipitation of 1.5 mm/day on average (Fig. 2c). While we acknowledge that ecological impacts can be present year-round, in this paper we focus on coastal events occurring during Feb–Mar–Apr, as societal impacts are maximized in this

season through the threat of flooding, and also, as we will see, droughts during Coastal La Niña events.

We identify coastal El Niño events as instances of warming in the far eastern Tropical Pacific (Feb–Mar–Apr 3-months running mean of Niño 1 + 2 index > 0.5 °C) not associated with warming in the eastern-central Pacific (Feb–Mar–Apr 3-months running mean of Niño 3 index < 0.5 °C). The last condition ensures that the coastal warming is not occurring in association with a basin-wide ENSO event, as it is sometimes the case with other coastal events definitions (cf.¹⁹, see also refs. 20,21; see Supplementary Note 1). Coastal La Niña events are identified oppositely. We note that using these indices calculated over broad areas as a basis for classification may miss some hyper-local events, such as the one that occurred in Feb–Mar 1975²². From 1980 to 2020 we identify 7 Coastal La Niña Events: 1982, 1984, 1988, 1994, 1995, 2005, 2013; and 3 Coastal El Niño events: 2002, 2012, 2017 (Fig. 3f). On average, it rained 106 mm/month (3.53 mm/day) over the Niño 1 + 2 region during Coastal El Niño events—an increase of approximately 77% compared with a normal year—and 33.4 mm/month during Coastal La Niña events—only 56% the normal amount. This implies that the often overlooked Coastal La Niña events are also of concern, as they can be associated with droughts.

Typically, El Niño events are classified within the “ENSO diversity” by the peak location of their SST anomalies⁷,¹⁰⁻¹²,²⁰. We follow ref. 8 and classify coastal events by their location in the phase-space of the first two principal components (PC1 and PC2) of tropical Pacific SST anomalies (Fig. 3e). The associated spatial patterns (denoted here as empirical orthogonal functions or EOFs) associated with these principal components are shown in Fig. 3a, b. The first EOF is associated with a canonical basin-wide ENSO event. The second EOF showcase an east-west and also north-south SST dipole that resembles the spatial pattern of the North Pacific Meridional Mode (NPMM)²³.
<figure><img src="image_4.png" /><figcaption>b. Precip vs SST in Niño 1+2 region</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>c. Precip vs SST in Niño 1+2 region (FMA)</figcaption></figure>

<figure><img src="image_6.png" /></figure>

Given the focus on the impacts of basin-wide El Niño events on the eastern Pacific one might think that there is strong connection between ENSO events and precipitation in the Niño 1 + 2 region (e.g., ref. 24). However, we find little relation between PC1 during Feb–Mar–Apr and precipitation anomalies in the Niño 1 + 2 region during the same season. Removing the “Super El Niños” of 1983 and 1998, the correlation coefficient

**Fig. 2 |** *Precipitation climatology in the Niño 1 + 2 region.* a Monthly mean precipitation in the Niño 1 + 2 region as a function of 3-month running season. b Scatter between 3-month running mean precipitation and 3-month running mean SST (absolute Niño 1 + 2 index) in the Niño 1 + 2 area. A rapid pickup in precipitation is observed with absolute Niño 1 + 2 index ≳23 °C. c Same as (b) but only for the Feb–Mar–Apr seasonal average. Black dots indicate conditions associated with the extreme basin-wide events of 1983, 1998, and 2016. Red dots indicate conditions associated with coastal El Niño events, and blue dots indicate conditions associated with coastal La Niña events (open: type-1, filled: type-2). The regression line (correlation coefficient 0.84) is given approximately by $Prec_{1+2} = -34.6 + 1.5Nino_{1-2}^{abs}$, and indicates an increase of approximately 1.5 mm/day (45 mm/month) for every 1 °C increase in SST in the Niño 1 + 2 area above 23.1 °C.

between PC1 and precipitation anomalies over the Niño 1 + 2 region (*Prec*<sub>1+2</sub>) is only 0.08 (Fig. 3c). On the other hand, there is a perhaps surprisingly stronger association between the second principal component and precipitation in the region (Fig. 3d; *r* = 0.63 if we do not take 1983, 1998 into consideration). This suggests that the second EOF, and by extension the North Pacific Meridional Mode, are key drivers to understand variability and associated precipitation in the Niño 1+2 region in this season.

Basin-wide ENSO events are usually classified as either being Central Pacific (CP) or Eastern Pacific (EP), depending on where their peak anomalies are located (i.e., depending on the value of PC1 and PC2; see “Methods”)⁸. By construction, coastal events project only weakly onto the first EOF pattern (with index PC1) of Tropical SST anomalies, with most of their variation occurring along the PC2 axis (Fig. 3e). Here we identify two types of coastal events based on how strong their projection is onto the second Tropical Pacific SSTA EOF is:

(1) Type-1: (ENSO-like) $||PC2|| < 0.5σ$ (open circles in Figs. 1–3).

(2) Type-2: (dipole-like) $||PC2|| ≥ 0.5σ$ (solid circles in Figs. 1–3).

As it will be shown in the following subsections, this classification allows us to separate coastal events that substantially differ in their spatial patterns (ENSO-like and dipole-like) and associated mechanisms. Of the Coastal El Niños identified, 2002 is of Type1, and 2012 and 2017 are of Type-2. On the other hand, the 1984 and 2013 Coastal La Niñas are of Type-1, and the events of 1982, 1988, 1994, 1995, and 2005 are of Type-2 (Fig. 3f).

## Coastal events spatial patterns and asymmetry

There are only a few instances of these events during the satellite era. To calculate robust statistics of Coastal El Niño and La Niña events we analyze 40 realizations of the CESM Large Ensemble²⁵ over the same time period we mainly focus in observations (1980–2020), for a total of 1640 years. In addition, we generate 100,000 years long synthetic time series of our main fields of interest using a machine-learning technique known as nonlinear inverse modeling²⁶,²⁷. This type of modeling can serve as an emulator of a climate model or directly observations²⁸ and has been amply used to study different ENSO aspects⁹,²⁶,²⁷,²⁹⁻³², and here is used to study coastal events. Likewise, inverse models have also been used by several studies to understand the characteristics and predictability of marine heatwaves in different regions of the world³³⁻³⁵. Using this technique, we train a data model from observed tropical Pacific data (see “Methods”), which allow us to estimate deterministic and stochastic contributions to the tropical Pacific evolution. This in turn is used to generate many alternative “multiverse”³⁶,³⁷ realizations consistent with the physics that generated the observations. Details on the NLIM construction and validation are given in the “Methods” section and Supplementary Notes 2 and 3.

We first validate the CESM and NLIM simulations by comparing it with the limited observed record. The shape of the seasonal cycle of precipitation in CESM is well simulated, showing a peak in Feb–Mar–Apr (as in observations; Fig. 2a), and a dry second part of the year. However, biases in precipitation amount are large, with precipitation peaking at slightly more than 5 mm/day during Feb–Mar–Apr in CESM, compared with 2 mm/day
<figure><img src="image_7.png" /></figure>

**Fig. 3** | Coastal events characteristics in observations. **a,** **b** SST and wind anomalies regression pattern associated with the standardized first (second) principal component of Tropical SST anomalies. From east to west, green rectangles showcase the Niño 1 + 2 region, the Niño 3 region, Niño 4 region, and the region used to define westerly wind burst events (see "Methods"). We note that the sign of PC2 is opposite to previous uses in the literature. **c,** **d** Scatter plot between Feb–Mar–Apr precipitation anomalies in the Niño 1 + 2 region and the concurrent value of the standardized first (second) principal component index of Tropical SST anomalies. Black and green lines display regression lines with and without taking into account

the extreme 1983 and 1998 basin-wide El Niño events respectively. **e** Location of Feb–Mar–Apr Tropical Pacific SST anomalies in the PC1/PC2 chart. **f** Time series of the Feb–Mar–Apr 3-month running mean Niño 1 + 2 (solid black) and Niño 3 (dashed-gray) indices. In (c–f) black dots denote Feb–Mar–Apr (1980 to 2020; e also shows 2023) conditions associated with the extreme basin-wide El Niño events of 1983, 1998, and 2016. Red dots denote conditions associated with coastal El Niño events, blue dots conditions associated with Coastal La Niña events (open: type-1, filled: type-2), and open black dots denote remaining months.

in observations (a bias of 150%) (Supplementary Fig. 1). We also analyzed 25 CMIP6 historical simulations³⁸ showing biases of the same order or larger (Supplementary Fig. 2). In models, SST conditions remain warm enough to elicit a convective response over most of the year (e.g., Supplementary Fig. 1b), whereas in observations this is largely confined to Feb–Mar–Apr (Fig. 2b).

To assess spatiotemporal characteristics of NLIM and CESM models compared with observations, we calculated the probability distributions, correlation matrix, and standard deviation maps of our main variables of interest (see Methods). We find that the NLIM simulation generally

captures more accurately these aspects (probability distribution, correlation matrix and variability; see Supplementary Fig. 3 for a comparison of standard deviation maps for SSTs and winds) compared with the CESM Large Ensemble. Several of the key variables simulated by CESM have probability distributions that significantly differ (at the 90th confidence level) compared with observations (Supplementary Fig. 4) and the correlation matrix is less successfully simulated, especially the interaction between Pacific Meridional Modes, compared with the NLIM counterpart (Supplementary Fig. 7). Analysis of the coastal events in CESM shows that they are about 6 to 7 times rarer than in observations, an issue that is also common in other
<figure><img src="image_8.png" /><figcaption>**Fig. 4** | Composites of coastal events in the NLIM simulation. **a** Spatial pattern of the composite of the Feb–Mar–Apr wind and SST anomalies associated with type-1 Coastal El Niño events from a 100,000 year NLIM simulation (see “Methods”). Black cross-hatching denotes regions where at least 80% of the events agree on the sign of the SST anomaly. **b** Same as (a) but for type-2 Coastal El Niño events. **c** Same as (a) but for type-1 Coastal La Niña events. **d** Same as (a) but for type-2 Coastal La Niña events. **e** Antisymmetric part ($\frac{1}{2}$(Coastal El Niño + Coastal La Niña) of the composite of Coastal El Niño events of type-1. A perfectly symmetric pattern (i.e., the Coastal La Niña events composite pattern is the same as the Coastal El Niño events composite) should not have any signature in this plot. **f** Same as (e) but for type-2 coastal events.</figcaption></figure>

CMIP6 simulations (see Supplementary Table 2). These model biases would likely significantly impact our estimation of coastal events frequency, intensity, return periods, and associated precipitation (see next sub-section). The NLIM, on the other hand, is successful at emulating the observed SST and wind variability (Supplementary Fig. 3), and simulates well the observed statistical structure (Supplementary Fig. 7) and probability distributions of the main simulated variables (Supplementary Fig. 6; see “Methods”). For this reason, we mainly focus on the analysis of the NLIM output in what follows.

As it is shown in Fig. 4, the NLIM-derived composite of these different types both showcase warming or cooling in the easternmost Tropical Pacific, similarly as what it is seen in the limited observational composite (Supplementary Fig. 8), but with a roughly opposite wind and SST pattern in the rest of the Pacific basin. The spatial patterns and other derived statistics are robust to inverse modeling specification and to time-period used to train the models (see “Methods”; section “Linear and nonlinear inverse models”).

This spatial pattern is also relatively well captured by the CESM large ensemble (Supplementary Fig. 9). This warming (cooling) in the Niño 1+2 region is accompanied with a concomitant increase (decrease) in sea surface height (and ocean heat content$^{29}$) of events of both types, that start building up roughly 5 to 10 months earlier (Supplementary Fig. 10). We also note that the pattern of warming tends to extend south along the Chilean coast, which suggests there might be a connection between Coastal El Niños, and more localized warming patterns such as the recently identified Chile El Niños$^{40}$ and the prolonged 2017 marine heatwave along the Chilean coast$^{41}$.

Coastal El Niño events of type-1 are accompanied with lower intensity warming of the rest of the Tropical Pacific basin, that extends north along the coast of California and south along the coast of Peru and Chile (Fig. 4a). Coastal La Niña events behave roughly the opposite (Fig. 4c), with little spatial asymmetry compared with warm events of this type (Fig. 4e). In a sense, these are weak basin-wide ENSO events, with warming peaking in the east, but that nonetheless would be missed by most conventional ENSO events.
<figure><img src="image_9.png" /><figcaption>**Fig. 5 |** Coastal events' frequency distribution, return periods and associated precipitation. a Normalized histogram of the number of Feb–Mar–Apr coastal El Niño (red) and coastal La Niña (blue) type-1 events as a function of the Niño 1 + 2 index magnitude. The height of the bars shows the percentage of years with coastal events in the NLIM simulation with a Niño 1 + 2 index within a given range of 0.1 °C width. The numbers in the legend are the percentage of all Coastal El Niño and La Niña events occurring in the full NLIM simulation (regardless of magnitude). b Same as (a) but for type-2 events. c Average return period of the different types of events (y-axis) exceeding a given magnitude of the Niño 1 + 2 index (x-axis) in the NLIM simulation. Red denotes coastal El Niño events and blue coastal La Niña events. The dashed line denotes type-1 events, the dashed-dotted line type-2 events,</figcaption></figure>

and the solid lines both types combined. d Cumulative distribution function (y-axis) of precipitation in the Niño 1 + 2 region during Feb–Mar–Apr for the different types of events in the NLIM simulation as a function of precipitation. The precipitation values are obtained as a function of Niño 1 + 2 and Niño 4 indices through a separate statistical fit (see “Methods”). The dashed line showcase the median precipitation amount for each type of event (in increasing order: type-2 coastal La Niña: 25.4 mm/month, type-1 coastal La Niña: 35.1 mm/month, type-1 coastal El Niño: 69.0 mm/month, and type-2 coastal El Niño: 111.3 mm/month). The dots over each curve showcase the observed precipitation amount for the 10 coastal events within 1980–2020.

monitoring entities, as they would not display sufficiently large anomalies in the Central Pacific to be classified as basin-wide events.

On the other hand, coastal events of type-2 showcase a strong east-west SST anomaly dipole, similar to the pattern of stand-alone events identified by Lübbecke et al.³⁹, with warming (cooling) in the east for Coastal El Niños (Fig. 4b) (La Niñas; Fig. 4d) and cooling (warming) of the western Pacific. This is also seen in the contrasting evolution of the Niño 4 index during these events (see Supplementary Fig. 11). In addition, events of this type are also associated with a meridional dipole reminiscent of the North Pacific Meridional Mode pattern (as defined in Chiang and Vimont²³), where warm (cold) events tend to be associated with cold (warm) conditions along the coast of western North America. There is a much stronger spatial asymmetry between Coastal El Niño and La Niña events of this type, with a cooler Central North Pacific and stronger warming in the Eastern Tropical Pacific that also extends farther south along the coast of Chile compared with opposite conditions during Coastal La Niña events (Fig. 4f).

There is a good degree of correspondence between the observed patterns and the composites derived from nonlinear inverse model output (Fig. 4; see “Methods”). The average SST spatial correlation coefficient of the observed events at their peak and their corresponding mean ensemble pattern (Fig. 4) along the equatorial band (15S–15N) ranges from 0.45 to 0.87, with an average of 0.74 (Supplementary Fig. 8).

## Coastal events frequency, intensity, return period and associated precipitation

In this subsection we estimate the frequency, intensity, return periods and associated precipitation associated with coastal events. As with the previous analysis, we remind the reader that the observed period is too short to make inferences about these quantities using the historical record, even if this is extended back to the pre-satellite era (from 1948 to 2020 we have 7 events type-1 events and 11 type-2 events; Supplementary Fig. 8). In what follows any mention of quantities estimated using the historical record it is only with the purpose of providing context to what is inferred from the long NLIM simulation.

With the very long synthetic time series we can accurately calculate the probability distributions of these events (Fig. 5a, b). Both types of coastal events showcase skewed distributions, implying a larger frequency of Coastal La Niña events compared with Coastal El Niño events, the latter on average being more extreme. This is particularly the case for events of type-2 (skewness coefficient S of 1.63 vs. 0.52 in type-1 events). Taking into account both type-1 and type-2 events, the probability distribution of the Niño 1 + 2 index is similar to the probability distribution of the Niño 1 + 2 index over all years (S = 1.16 during coastal events, S = 1.18 for Feb–Mar–Apr in the NLIM simulation). An in-depth study of the mechanisms behind this asymmetry will be deferred for future study. However, we note that there are several
<figure><img src="image_10.png" /><figcaption>**Fig. 6** | Relationship between westerly wind bursts, Pacific Meridional Modes and coastal events. **a** Wind and SST anomalies spatial pattern associated with the North Pacific Meridional Mode. We note that the sign of the positive phase of the NPMM is the opposite to previous uses in the literature<sup>23</sup>. **b** Same but for the South Pacific Meridional Mode. **c** Evolution of the Niño 1 + 2 index (red) and westerly wind burst index (blue) 9 months before to 9 months after the peak of type-1 coastal El Niño</figcaption></figure>

events in the NLIM simulation. **d** Evolution of the Niño 1 + 2 index (red), North Pacific Meridional Mode SST index (blue), and South Pacific Meridional Mode SST index (green) 9 months before to 9 months after the peak of type-2 coastal El Niño events in the NLIM simulation. **e** Same as (c) but for Coastal La Niña events of type-1. **f** Same as (d) but for Coastal La Niña events of type-2. In (c–f) shading denotes estimates of the 25th–75th percentile of each index in the NLIM simulation.

nonlinearities in the underlying dynamics that can in principle account for this asymmetry, including an asymmetric thermocline feedback<sup>42</sup>, the existence of an SST threshold for strong convection<sup>24</sup>, state-dependent stochastic forcing<sup>32,43,44</sup>, and coastal current instabilities off Peru<sup>45</sup>.

The asymmetry also manifests itself in the expected return periods of these events. Return periods are calculated by measuring the years between consecutive events of a given magnitude. Figure 5c shows the average return period as a function of Niño 1 + 2 index anomaly. We tested the sensitivity
of the estimated return periods to time-period used to train the NLIM. Supplementary Fig. 12 shows general agreement when using an NLIM trained using 1948–2020 data. Testing the NLIM with a large-ensemble suggests that we can expect the NLIM-derived return periods to be accurate to a factor of two (Supplementary Note 3). While this level of precision can hopefully be improved in further NLIM iterations, it provides better estimates than using Global Climate Models directly, which overestimate return periods by a factor of 5 to 10 (see Supplementary Table 2). Overall, coastal events of any kind occur once every 6 years (16.3% of years) in the NLIM simulation on average, close to the 24% during the 1980–2020 period (10 out of 41 years). In the NLIM simulation, as well as in observations, coastal events of type 2 are more frequent than coastal events of type 1, with 10.0% of years showcasing a coastal event of type 2 and 6.3% of the years an event of type-1—in observations during 1980–2020 (1948–2020) there are three (seven) type-1 events and seven (11) type-2. Among events of type-1, about 39% of the events are coastal El Niños and 61% coastal La Niñas, close to the observed proportion (1 coastal El Niño and 2 Coastal La Niñas during 1980–2020; 3 coastal El Niño and 4 Coastal La Niñas if we extend the record back to 1948). Among events of type-2, only about 20% of all events are coastal El Niños (28% in observations during 1980–2020; 27% during 1948–2020) and the remaining 80% are coastal La Niñas. The average return periods increase steeply as a function of the Niño 1 + 2 index for all events, especially type-2 (Fig. 5c). Events with an anomaly comparable to the 2017 event (about 1 °C) are very rare, occurring on average approximately once every 90 years for Coastal El Niño events. We caution, however, that the aforementioned figures are averages and that the return periods probability distributions are broad, with many epochs in the NLIM simulation having frequent coastal events and other epochs being more quiescent (Supplementary Fig. 13).

Up to this point, the majority of research on coastal events had focused on Coastal El Niños. Figure 5d shows the cumulative density function of precipitation in the Niño 1 + 2 region occurring during these events as a function of precipitation amount above a threshold. As it might be expected, warm events are associated with positive precipitation anomalies and cold events with negative precipitation anomalies. On average, it rains about 60 mm/month during a normal season (180 mm for the three months). Coastal El Niño events can be associated with significant increases in precipitation, which can extend to inland areas as was the case of the 2017 event. The median precipitation during a type-1 Coastal El Niño event is 69mm/month, with a range that can go below-normal (42 mm/month, 5th percentile) to doubling the normal rain season (119 mm/month, 95th percentile across realizations). Effects can be even bigger for type-2 Coastal El Niños, with a median precipitation of 111 mm/month, and a range spanning from 57 mm/month (5th percentile) to more than quadrupling the amount of rain in the normal season (284 mm/month, 95th percentile).

Conversely, during a type-1 Coastal La Niña event, the median precipitation is approximately 35 mm/month, about half the usual amount, and 21 mm/month for the top 5% driest event (percentile 5th). Even more extreme, the median precipitation for a Coastal La Niña event of type-2 is 25 mmm/month, with rain during a top 5% dry event being less than 25% the usual amount (14mm/month, 5th percentile). This implies that the often overlooked Coastal La Niña events can also be of concern, as they could be associated with droughts over an already arid region.

## Possible physical mechanisms

The driving mechanisms behind these events are likely multifaceted, and a full analysis of them is outside the scope of this paper. Here we comment on the main processes/modes of variability that occur concurrently with the development of the majority of coastal events in the NLIM simulations and also in the limited observational record.

Events of type 1 seem to be driven by similar processes as basin-wide events, although with a lower intensity. A commonality of these events is the presence of sustained westerly (easterly) winds anomalies in the western Pacific before, during, and after the Coastal El Niño (La Niña) peak (Fig. 6c, e). This is also evident in the observational composite

(Supplementary Fig. 8a, c). The presence of these wind anomalies, which are often modulated by the state of the Madden-Julian Oscillation⁴⁶, generate downwelling Kelvin waves and have been argued by previous studies⁵,¹⁴,¹⁹,³⁹ to be key to the development of coastal El Niños in some cases. Some of these events can evolve onto full-fledged basin-wide events alike the “canonical” El Niño events of Rasmusson and Carpenter⁴⁷ that first peak in the far eastern Pacific. Others fail to fully develop¹⁵, with 43.3% (42.5%) of Coastal El Niños (La Niñas) evolving onto a basin-wide El Niño (La Niña) (Niño 3 index of at least 0.5 °C in magnitude) 6 months later. During 1980 to 2020, all three instances of coastal El Niño (2002) and coastal La Niña (1984, 2013) events of type1 evolved into basin-wide ENSO events (of the same sign) 6 months later.

Events of type 2 are not associated with the usual dynamics of basin-wide events. They are more closely connected to the development of the North and South Pacific Meridional Modes²³,⁴⁸,⁴⁹. These modes are thought to be primarily thermally driven by the wind-evaporation-SST (WES) feedback⁵⁰—a process in which SST-driven wind anomalies reduce evaporation, modifying SSTs which then feedback onto the wind response. Simple theoretical models of the WES feedback are successful in reproducing the spatial pattern of the North Pacific Meridional Mode⁵¹, which further reinforces the relevance of wind-driven changes in evaporation as an important driver of these events. A reduction of wind-driven evaporation is a common factor behind the development of most marine heatwaves⁵²,⁵³. Additionally, the wind anomalies associated with the Pacific Meridional Modes can suppress the total along-the-coast wind field, leading to further warming due to a reduction in upwelling⁵⁴, an effect that can be particularly important near to the coast.

As can be appreciated comparing Fig. 6a with Fig. 4b, d, there is a strong resemblance between the North Pacific Meridional Mode spatial pattern and Coastal El Niño and La Niña events of type 2. A possible interpretation is that this association between the North Pacific Meridional Mode and coastal events is purely statistical and rooted in how the NPMM is defined using maximum covariance analysis (MCA; see section “Calculation of indices” in “Methods”). This is because the first MCA mode is associated with a canonical El Niño event, while the second mode (the NPMM) represents the remaining variability in the western tropical Pacific and Niño 1 + 2 region unaccounted by the first mode. This would naturally lead to an association between the NPMM and Niño 1 + 2 indices. However, this association is relatively weak in general ($r = 0.37$ during all months, and $r = 0.3$ during Feb–Mar–Apr), and only becomes prominent during coastal events (see Table 1 and discussion below).

Although less apparent, the South Pacific Meridional Mode pattern (Fig. 6b) strongly resembles the spatial asymmetry between Coastal El Niño and La Niña patterns in the southern hemisphere (Fig. 4f), suggesting that it may also play a role in the evolution of these events, although in an asymmetric fashion comparing warm and cold phases.

Indeed, both Coastal El Niño (Fig. 6d) and Coastal La Niña (Fig. 6f) events of type 2 are tightly linked to the evolution of the North Pacific Meridional Mode, with the peak of Niño 1 + 2 anomalies roughly

<table><caption>**Table 1 | Statistics of NPMM/SPMM indices at the peak of type-2 events**</caption><thead><tr><td>NPMM/SPMM index</td><td>Type-2 Coastal El Niño</td><td>Type-2 Coastal La Niña</td></tr></thead><tbody><tr><td>NPMM 25th/75th perc</td><td>0.29/1.60 (σ)</td><td>-1.05/-0.32 (σ)</td></tr><tr><td>NPMM 5th/95th perc</td><td>-0.46/3.46 (σ)</td><td>-1.66/0.17 (σ)</td></tr><tr><td>SPMM 25th/75th perc</td><td>0.28/1.47 (σ)</td><td>-0.59/0.50 (σ)</td></tr><tr><td>SPMM 5th/95th perc</td><td>-0.57/2.51 (σ)</td><td>-1.42/1.29 (σ)</td></tr><tr><td>NPMM > 0 (<0)</td><td>86.3%</td><td>90.3%</td></tr><tr><td>SPMMM > 0 (<0)</td><td>84.0%</td><td>53.2%</td></tr><tr><td>NPMM and SPMMM > 0 (<0)</td><td>71.6%</td><td>48.5%</td></tr><tr><td>NPMM or SPMMM > 0 (<0)</td><td>98.6%</td><td>95.0%</td></tr></tbody></table>
<figure><img src="image_11.png" /><figcaption>**Fig. 7** | **The 2023 coastal El Niño event.** a Observed (red line) and simulated (histogram) precipitation amounts in the Niño 1 + 2 region during Feb–Mar–Apr 2023. The simulated values are the range of possible precipitation outcomes given</figcaption></figure>

the observed Niño 1 + 2 and Niño 4 indices (see “Methods”). b Pattern of sea surface temperature anomalies during Feb–Mar–Apr 2023.

coinciding with the peak of the NPMM. The SPMM, on the other hand, does not contribute on average to the evolution of Coastal La Niñas (Fig. 6f), but tends to reinforce Coastal El Niños of this type (Fig. 6d). This finding remains robust to NLIM training period (Supplementary Fig. 14). In the NLIM simulation, roughly 7 out 10 (71.6%) Coastal El Niño events of type-2 are associated with the joint evolution of the positive phases of both NPMM and SPMM, and 98.6% of events with a positive NPMM or SPMM event. Table 1 shows the interquartile and 5th–95th ranges of NPMM/SPMM indices at the peak of type-2 (dipole-like) events, as well as details on PMM phases at the peak of coastal events.

The relationship between the PMMs and coastal events is also apparent in observations, where most events coincide with active phases of these modes (Supplementary Fig. 15a). This is also the case in the CESM Large Ensemble (Supplementary Fig. 15b), although this is sensitive to details of the domain in which the NPMM index is calculated. Using the domain of ref. 23 (as it is standard) the relationship between coastal events and the NPMM is less clear than using the domain (5S–32N; 175E–95W). This distinction, important due to model biases in GCMs, is largely inconsequential in observations, where the NPMM pattern and index time series are insensitive to which one of the two domains is used ($r = 0.98$ between respective NPMM indices). In any case, the NPMM is less strongly associated with coastal events in CESM-LE, with the phase of the SPMM being more important in determining their sign and magnitude. Using the domain (5S–32N; 175E–95W) to calculate the NPMM index, all three coastal El Niño events of type 2 occurring in CESM-LE were associated with positive phases of the SPMM and NPMM, and 32 (24) out of 37 instances of coastal La Niña events of type 2 were associated with SPMM (NPMM) negative phases (Supplementary Fig. 15b). On the other hand, in observations NPMM and SPMM events are roughly independent<sup>55</sup> (correlation coefficient of their time series is 0.39 in Feb–Mar–Apr, and 0.19 over all month in observations and also in the NLIM), but they can combine and generate significant SST anomalies in the eastern tropical Pacific. This is precisely what happened during the strong 2017 event. Here, a moderate NPMM event (NPMM index of 0.33σ, percentile 65th of the observed index) combined with a strong SPMM event (SPMM index of 1.35σ, percentile 92th) to generate a coastal event with a Niño 1 + 2 anomaly in excess of 1 °C.

## The Coastal El Niño event of 2023

During early 2023 a strong Coastal El Niño event developed. With a magnitude surpassing the coastal event of 2017 (Niño 1 + 2 index of 1.62 °C during Feb–Mar–Apr), it created favorable conditions for the development of a rare unorganized tropical cyclone (Yaku cyclone)⁵⁶. The event brought widespread damage concentrated in Peru mainly, with the government declaring emergency in more than half of the country and spending more

than a 1 USD billion for response and recovery⁵⁷. The precipitation amount in the Niño 1 + 2 region during Feb–Mar–Apr was about 120mm/month, more than twice the average during the season. Although at the lower end, this precipitation amount was within the range of estimations given the contemporary values of the Niño 1 + 2 and Niño 4 indices (Fig. 7a) (see “Methods”).

The pattern of SST anomalies during the event fits neatly into a type-2 event (compare Fig. 7b with Fig. 4b), with a strong warming in the easternmost Tropical Pacific that also extended southward, cooling of the western Tropical Pacific (Niño 4 index of -0.6 °C), and cold conditions reminiscing the opposite of the horseshoe pattern typically associated with marine heatwaves off the North American coast³³,⁵⁸,⁵⁹. This can also be seen in the event location (Feb–Mar–Apr) in the Tropical Pacific PC1/PC2 chart (Fig. 3e), which showcases a negligible projection onto PC1 and a strong projection onto the second principal component. Similarly as the event of 2017, this event was driven by the simultaneous development of the North and South Pacific Meridional Modes, although with their orders reversed in terms of their importance. In this case a moderate SPMM event (SPMM index of 0.48σ, percentile 70th) combined with an extreme NPMM event (NPMM index of 2.20σ, percentile 98th) yielding an extreme coastal event surpassing even the one in 2017.

## Discussion

The easternmost tropical and subtropical Pacific is located within a productive eastern boundary upwelling system, supporting fisheries and marine activities⁶⁰. It is well recognized that instances of warming, most of them associated with typical basin-wide events, can significantly alter the functioning and productivity of this marine zone⁶¹,⁶². Here we have shown the existence of two types of warming/cooling events in this region—here termed Coastal El Niño/La Niña—not associated with basin-wide ENSO events. These often overlooked kinds of events have received increasingly more attention, as they can be associated with significant ecological damages, as well as flooding in neighboring areas²,⁴,⁶.

Both types of events can yield significant precipitation anomalies, especially events of type 2. While due to the threat of flooding most of the research community have focused on warm events, here we show that Coastal La Niñas are also of concern, as they can be associated with a significant decrease in precipitation. For example, Coastal La Niña event of type 2 are associated with a decrease in precipitation in the Niño 1 + 2 region of more than 50% (50th percentile). These events, while significant, are relatively rare (one every 6 years on average), with their rarity increasing with Niño 1+2 anomaly. Strong events (an anomaly > ± 1 °C in magnitude) are expected to occur on average every 70 years for Coastal La Niñas and 90 years for Coastal El Niños.
The two types of events seem to be driven by different dynamics. While both types are associated with an anomaly in sea surface height (and consequently ocean heat content) in the easternmost Tropical Pacific (Supplementary Fig. 10), events of type 1 (ENSO-like) are more similar to basin-wide events, although with a stronger imprint in the Niño 1 + 2 region and less overall magnitude. Our results suggest that they, in most cases, correspond to the early manifestation of the development of a basin-wide ENSO event, consistent with the fact that zonal wind anomalies in the western tropical Pacific seem key to their development. Coastal events of type 2 (dipole-like) are more common, and more asymmetric between their warm and cold phases, with Coastal La Niñas being 80% of their occurrences and Coastal El Niños being significantly more intense. These events are tightly linked with the development of the Pacific Meridional Modes. NPMMs events affect the development of both Coastal El Niño and La Niña events, depending on the polarity of the event. SPMM events, on the other hand, does not seem to play a role eliciting the development of Coastal La Niña events, but reinforces warm events. The combination of positive NPMM and SPMM events can yield a significant warming in the Niño 1 + 2 region, which is precisely what happened during the strong 2017 and 2023 events.

While the meridional modes set favorable conditions for coastal events to develop, their growth may require additional stochastic forcing. These can be in the form of ocean Kelvin waves associated with westerlies (easternlies) underneath the warmer (cooler) eastern equatorial waters when the NPMM-induced zonal SST dipole grows along the equator. Positive NPMM can also favor less stable atmospheric conditions favorable for the development of northerlies off Ecuador and Northern Peru, as was observed for the coastal event of 1925¹⁷. Noteworthy off Piura (5°S), a highly variable atmospheric coastal jet tied to local SST anomalies is present³³, which could favor excitation of local air-sea instability. Similarly the SPMM, through its link to the South Pacific anticyclone, has the potential to modulate upwelling conditions off Central Peru where the coastal jet is tied to extra-tropical storms activity⁶³. This would deserve further investigation based on regional coupled modeling to account realistically for upwelling dynamics, which is beyond the scope of our study.

Composites emphasize elements common in events of each type. However, much as for basin-wide ENSO events, there is a diversity of coastal events, even within each type (see confidence intervals in Figs. 4 and 6). While there are mechanistic processes or modes; namely, westerly and easterly wind events and Meridional Modes, yielding the main characteristics of these events, the stochastic forcing will necessarily imply that each event will have its own characteristics. Despite this, here we have shown that coastal events develop as part of large scale modes of variability (NPMM and SPMM) encompassing most of the Tropical and Subtropical Pacific. These modes have an important degree of associated memory coming from the ocean⁶⁴,⁶⁵, which may imply increasing prospects of coastal events predictability. For example, a recent study³³ shows that an optimal pattern preceding the development of Northeast Pacific marine heat waves along the Gulf of Alaska, also precedes the development of NPMM events, and consequently likely also of type 2 Coastal events. This suggests that coastal events could be more predictable than previously thought (cf. ref. 5).

Our results also have implications for the interpretation of climate simulations and long-term reconstructions of ENSO diversity (e.g. refs. 20,66). In particular, the link of extreme coastal El Niño events with PMMs established here calls to contrasting proxies of El Niño impacts in the far eastern Pacific (high temperatures, flooding, impacts on marine ecosystems) with proxies from the PMMs regions (e.g., off Southern California coast, where the NPMM has a strong loading) in order to reconcile information in a range of proxy records and for testing models of future El Niño behavior under climate change.

## Methods

### Data

We use monthly sea surface temperature from the NOAA Extended Reconstruction SST v5 reanalysis⁶⁷ with a 2° by 2° degrees resolution. We also use monthly precipitation from the Global Precipitation Climatology

Project dataset⁶⁸ on a 2.5° by 2.5° grid, monthly surface winds from the NCEP-NCAR reanalysis 1⁶⁹ on a 2.5° by 2.5° grid and monthly sea surface height from the NCEP Global Ocean Data Assimilation System⁷⁰ available from 1980 onwards on a regridded 2.5° by 2.5° resolution. We use data from all datasets covering 1980–2020. To show robustness of our conclusions to the time period selected, we repeat some of the analyses for 1948–2020, with qualitative agreement. We calculate anomalies by subtracting the first two harmonics of the climatological (1980–2020) seasonal cycle. All anomalies are detrended with a cubic polynomial.

In addition, we use monthly sea surface temperature, 925 mb (CESM-LENS) and surface winds, and precipitation data from one large-ensemble (CESM-LENS)²⁵, and 25 CMIP6 models (see Supplementary Table 2)³⁸. Anomalies are calculated similarly as with the reanalyses for the 25 CMIP6 simulations. In the case of the large ensemble, anomalies are calculated relative to the time-evolving ensemble mean.

## Calculation of indices

We keep track of the state of the Tropical Pacific during coastal events, by using several physically motivated indices. To capture the sea surface temperature variability across the deep Tropical Pacific we calculate the widely used Niño 1 + 2 index (Eastern Pacific), Niño 3 index (Central Pacific) and Niño 4 index (West-Central Pacific) as the monthly average of sea surface temperature anomalies in the Niño 1 + 2 region (0S–10S, 90W–80W), Niño 3 region (5N–5S, 150W–90W), and Niño 4 region (5N–5S, 160E–150W) respectively¹³. To capture the interaction between midlatitudes/subtropics and the tropics we use the North Pacific Meridional Mode²³ and South Pacific Meridional Mode⁴⁸ SST indices. Similarly to ref. 23, to calculate these indices we first remove the Niño influence by linearly regressing out the Niño 3.4 index from the SST and wind data, and then we perform an SST-wind maximum covariance analysis⁷¹ of the residual data. We identify the NPMM index as the first SST index from the maximum covariance analysis over region (21S–32N, 175E–95W). We note that here we define the NPMM index with the opposite sign of ref. 23. The NPMM index is robustly defined whether or not the Niño influence is first removed²³ (cf. 72). If the ENSO influence is not removed, the NPMM index is simply the second maximum covariance mode. Applying the same procedure in the region (40S–0S, 140W–90W; as in ref. 49) yields the SPMM index. The regression patterns of these indices are shown in Fig. 6a, b. To gauge the influence of easterly and westerly wind events¹⁶,⁷³ on these events, we calculate a westerly wind burst (WWB) index as the monthly zonal wind average in the region (10S–10N, 150E–150W; shown in Fig. 3a, b).

To classify events we also calculate the first two principal components (PC1 and PC2) of SST anomalies over the region (20S–20N; 120E–50W). We note that to emphasize warming in the eastern Pacific, the sign of PC2 and associated spatial pattern is flipped compared to previous uses in the literature⁸,⁹,¹¹. The spatial patterns associated with PC1 and PC2 (referred here as EOF1 and EOF2) explain 60.6% and 14.7% of SST variance over this region respectively. Coastal and basin-wide events are also categorized as either Central Pacific (CP) or Eastern Pacific (EP) based on where the peak of SST anomalies occur. Following ref. 8, EP and CP events are defined as:

$$ 
\begin{aligned}
\text{EP} &= \frac{1}{\sqrt{2}} \left( \frac{\text{PC1}}{\sigma_1} + \frac{\text{PC2}}{\sigma_2} \right) \\
\text{CP} &= \frac{1}{\sqrt{2}} \left( \frac{\text{PC1}}{\sigma_1} - \frac{\text{PC2}}{\sigma_2} \right),
\end{aligned} 
\quad (1) $$

where $σ_1$ and $σ_2$ are the standard deviations of PC1 and PC2 respectively. As seen in Fig. 3e, coastal events are neither EP nor CP events.

## Linear and nonlinear inverse models

In a nonlinear inverse model, the evolution of the vector x given by the indices x = (Niño 1 + 2, Niño 3, Niño 4, WWB, NPMM, SPMM) is
given by:

$$ \frac{dx_i}{dt} = M_{ij}x_j + C_{ikl}(x_kx_l - \langle x_kx_l \rangle) + B_{in}\eta_n. \quad (2) $$

Here, i, j, k, l, n are vector, or matrix indices, and they go from 1 to 6 (e.g., $x_1$ represents the Niño 1 + 2 index, $x_2$ the Niño 3 index,...). We follow Einstein convention, where there is a sum implied for repeated indices. We estimate the matrices in the model using data from 1980 to 2020. We repeat most of the analysis also for an NLIM estimated using 1948 to 2020 data, showing generally consistent results (see Supplementary Information). The matrix M represents the linear part of the deterministic dynamics, the 3-D matrix C a quadratic approximation to the nonlinear part of the deterministic dynamics, B is a stochastic forcing amplitude matrix, and η is a vector of centered Gaussian white noise processes. The combination Bη parameterizes the fast variability (e.g., wind-gusts, weather systems) influencing the evolution of these indices. Matrices M, C and B could be estimated seasonally. However, the data requirements to do so increase rapidly and fits may degrade (e.g. ref. 74). In addition, methods to incorporate seasonality in nonlinear inverse models are less developed than in the linear case, where several options exist$^{75-79}$. For this reason, as in most cases in inverse modeling, the matrices are estimated using all-season data. In principle, B can contain a state-dependent component$^{32,80,81}$, with potential consequences for the asymmetry in the probability distribution of the simulated indices$^{82,83}$. Here we neglect those terms as their accurate calculation needs substantially more data than available$^{83}$. Note that $C_{ikl}(x_kx_l - \langle x_kx_l \rangle)$ contains terms of the style $x_1^2$ and also cross-terms of the style $x_1x_2$. The bracket $\langle \cdot \rangle$ denotes an average, and it is in the formulation to ensure that the variables are centered (i.e., it prevents climate drift). Matrices M and C are calculated using multivariate linear regression, and B is calculated as $B = \sqrt{((RR^T dt)^8)}$, where R is a residual vector given by a discrete approximation of $R_i = \frac{dx_i}{dt} - M_{ij}x_j - C_{ikl}(x_kx_l - \langle x_kx_l \rangle)^{11,85}$.

We chose the indices contained in x to represent the state of the tropical Pacific motivated by previous uses in the literature and a preliminary analysis of the spatial pattern of coastal events in the limited observational record. As seen in Supplementary Fig. 8a, c westerly wind anomalies in the western tropical Pacific occur concurrently with type 1 coastal El Niño events. Previous research has shown these wind anomalies to be important in the growth and evolution of coastal events$^{14,19,39}$. The inclusion of the NPMM index is motivated by the strong resemblance of events of type 2 in observations (Supplementary Fig. 8b, d) with the NPMM pattern (Fig. 6a). The NPMM is known to be a conduit between the Northern Pacific midlatitudes and the Tropics$^{23,65,86-89}$, so its inclusion provides information on the influence of North Pacific midlatitude transients on equatorial dynamics. Similarly, the SPMM index is included to explicitly account for the influence of midlatitude variability$^{64}$, such as the atmospheric disturbances that contributed to triggering the 2017 event$^{2,6}$, on coastal events.

With all matrices calculated from the observed data, we integrate (2) for 100,000 years. On occasions, for large anomalies (2) can be linearly unstable, which results in a runaway solution. To limit this, anytime an anomaly reaches a magnitude of 3.5 the system is switched to linear evolution. There, C is taken a zero, and the analogous of M and B are calculated similarly as before. The resulting system is similar, but not the same as the widely used linear inverse models$^{29}$. As can be seen in Supplementary Figs. 6 and 7, the resulting output provides an excellent simulation of the observed statistical structure of x and their probability distribution, including their asymmetry (e.g., there are more instances of extreme positive than negative Niño 1 + 2 values in both observations and the nonlinear inverse model output).

Additionally, we tested the ability of the NLIM to emulate the underlying dynamics using a relatively short dataset (41 years; comparable to the length of satellite-based data) by training the NLIM in one 41 years realization of the CESM Large ensemble and comparing its output with the statistics of the remaining realizations. With the exception of return periods, which could be considered to be accurate to a factor of two, the NLIM simulates well the spatial pattern, correlation matrix, key probability

distributions including their tails, and associated precipitation (see Supplementary Note 3).

We also fitted other versions of linear and nonlinear inverse models, including the widely used linear inverse models in principal component space (e.g. refs. 9,29–32,90,91), which do not rely on the indices used to calculate the NLIM (Supplementary Note 2), with a remarkable consistency in terms of spatial patterns found and evolution. This consistency occurs regardless the time period used to train the inverse models: 1980–2020 as in the main text, 1948–2020 as in some results in the Supplementary Information or even using the period before the coastal events analyzed in the main text (1948–1979) (Supplementary Note 2). The main difference is that the linear inverse models, by construction, generates only symmetric statistics and patterns between coastal El Niño and La Niña events. This suggests robustness of the results derived from the nonlinear inverse model used in the main text (see Supplementary Note 2).

## Offline simulation of SSH$_{12}$, PC2 and spatial patterns from nonlinear inverse model output

The nonlinear inverse model used in (2) predicts the evolution of N variables using $\frac{1}{2}(N^2 + 3N)$ predictors (with N = 6 variables and 27 predictors in our case). Increasing the number of variables that enter into the model can rapidly increase the number of predictors, which can lead to overfitting of our training model (although see Supplementary Note 2 that shows the robustness of our results with N = 6). For this reason, PC2 (needed for the classification of events) and the average of sea surface height anomalies in the Niño 1 + 2 region (SSH$_{12}$; a predictor of ocean heat content in the area) are reconstructed offline from the N = 6 simulated variables ($x = (x_1, x_2, x_3, x_4, x_5, x_6)$) using a linear model$^{92}$ with a stochastic component:

$$ \text{PC2}^{\text{rec}} = \sum_{i=1}^{6} \alpha_i x_i + r_{\text{PC2}} \quad (3) $$

$$ \text{SSH}_{12}^{\text{rec}} = \sum_{i=1}^{6} \beta_i x_i + r_{\text{SSH}}. $$

(Note that the LIM constructed in PC space simulates PC2 directly). Here, coefficients $\alpha_i$ and $\beta_i$ are calculated using multilinear regression, and $r_{PC2}$ and $r_{SSH}$ are centered Gaussian random numbers (also referred here as “noise”) with standard deviation given by the standard deviation of the regression residuals. These additions ensure that there is no loss in variance in the reconstructions. Time series of PC2 and SSH$_{12}$ and their reconstructions PC2$^{rec}$ and SSH$^{rec}$ have correlation coefficients in observations of 0.98 and 0.88 respectively (see Supplementary Fig. 18).

SST and wind anomalies time series over the regions of interest are similarly reconstructed off-line as in (3) using output from the 6 variables simulated from the nonlinear inverse model. The analogous of $r_{PC2}$ in this case are calculated point-wise (i.e., the noise is white in space). Ideally, the random numbers should be spatially correlated; however, in a grid encompassing around 2500 grid-points (40S–40N;120E–50W) that is not computationally feasible. From these reconstructed time series we can calculate composites, as shown in Fig. 4.

We have made available to other researchers one-hundred 1000 years realizations of NLIM-simulated Tropical Pacific SST and wind anomalies (for a total of 100,000 years of data). Accessibility details are given in the “Availability of data and materials” section.

## Statistical simulation of precipitation over the Niño 1 + 2 region during coastal events

Similarly to refs. 17,93, we aim to model precipitation over the Niño 1 + 2 region using two large-scale indices, the Niño 1 + 2 and Niño 4 SST indices. The Niño 1 + 2 index provides local information of the amount of water vapor available for deep convection$^{94}$, a process which at monthly timescales is often phrased as a SST convective threshold$^{95,96}$ (see Fig. 2b,c). The Niño 4 index provides nonlocal information on the vertical stability$^{97-99}$—i.e., the
difference between the Niño 4 and Niño 1 + 2 provides a rough indication of the strength of the Walker circulation. We restrict our model to Feb–Mar–Apr as absolute SSTs are too cold in other seasons for any SST anomaly to elicit much of a precipitation response (Fig. 2b). We note that while we have removed a cubic trend to the Niño 1 + 2 and Niño 4 indices— thus, partially removing an anthropogenic external signal—we have not detrended the absolute precipitation data. This introduces a caveat on the fitting, as the relationship between precipitation and absolute SSTs in the Niño 1 + 2 region is nonlinear close to the SST critical threshold for convection²⁰. Unlike refs. 17,93 that fitted linear regression models, we fit an exponential model using the Niño 1 + 2 and Niño 4 indices, and we add a noise component to ensure that no variance is lost in the process. Using an exponential model instead of a linear model ensures that the precipitation simulated is always positive. The model is fitted by assuming a relationship of the form:

$$ \log(\text{Prec}_{1+2}) = \alpha \text{Niño}_{1+2} + \beta \text{Niño}_4 + r_{\text{prec}}. \quad (4) $$

Here Prec$_{1+2}$ represents the absolute precipitation in the Niño 1 + 2 region, α = 0.66 and β = −0.47 are calculated using ordinary multilinear regression, and r$_{prec}$ is a residual. This yields the model for Prec$_{1+2}$:

$$ \text{Prec}_{1+2} = e^{\eta_{pr}} e^{\alpha \text{Niño}_{1+2}} e^{\beta \text{Niño}_4}. \quad (5) $$

Here, η$_{pr}$ is a centered random number picked from a Gaussian distribution with the same standard deviation as r$_{prec}$. Supplementary Fig. 19 shows that the model, applied to nonlinear inverse model output, is successful at simulating the observed precipitation characteristics on this season.

## Data availability

NOAA Extended Reconstruction SST v5 reanalysis can be accessed at https://psl.noaa.gov/data/gridded/data.noaa.ersst.v5.html. The Global Precipitation Climatology Project dataset can be accessed at https://psl.noaa.gov/data/gridded/data.gpcp.html. The NCEP-NCAR reanalysis v1 can be accessed at https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html. Data from the NCEP Global Ocean Data Assimilation System can be accessed at https://psl.noaa.gov/data/gridded/data.godas.html. CMIP6 simulations can be accessed at https://esgf-node.llnl.gov/search/cmip6/. Data from the CESM Large Ensemble can be accessed at https://www.cesm.ucar.edu/community-projects/lens/data-sets. The NLIM generated data can be accessed at https://doi.org/10.5281/zenodo.10411023.

## Code availability

The code used to generate the nonlinear inverse model output is available from the corresponding author on reasonable request.

Received: 1 September 2023; Accepted: 29 May 2024; Published online: 10 June 2024

## References

1. Ramírez, I. J. & Briones, F. Understanding the El Niño Costero of 2017: the definition problem and challenges of climate forecasting and disaster responses. *Int. J. Disaster Risk Sci.* **8**, 489–492 (2017).

2. Garreaud, R. D. A plausible atmospheric trigger for the 2017 coastal El Niño. *Int. J. Climatol.* **38**, e1296–e1302 (2018).

3. Echevin, V. et al. Forcings and evolution of the 2017 Coastal El Niño Off Northern Peru and Ecuador. *Front. Mar. Sci.* **5**, 367 (2018).

4. Takahashi, K. et al. The 2017 coastal El Niño [in “State of the Climate in 2017”]. *Bull. Am. Meteorol. Soc.* **99**, 210–211 (2018).

5. Peng, Q., Xie, S.-P., Wang, D., Zheng, X.-T. & Zhang, H. Coupled ocean-atmosphere dynamics of the 2017 extreme coastal El Niño. *Nat. Commun.* **10**, 298 (2019).

6. Rodríguez-Morata, C., Díaz, H. F., Ballesteros-Canovas, J. A., Rohrer, M. & Stoffel, M. The anomalous 2017 coastal El Niño event in Peru. *Clim. Dyn.* **52**, 5605–5622 (2019).

7. Ashok, K., Behera, S. K., Rao, S. A., Weng, H. & Yamagata, T. El Niño Modoki and its possible teleconnection. *J. Geophys. Res.* **112**, C11007 (2007).

8. Takahashi, K., Montecinos, A., Goubanova, K. & Dewitte, B. ENSO regimes: reinterpreting the canonical and Modoki El Niño. *Geophys. Res. Lett.* **38**, L10707 (2011).

9. Vimont, D. J., Alexander, M. A. & Newman, M. Optimal growth of Central and East Pacific ENSO events. *Geophys. Res. Lett.* **41**, 4027–4034 (2014).

10. Capotondi, A. et al. Understanding ENSO Diversity. *Bull. Am. Meteorol. Soc.* **96**, 921–938 (2015).

11. Thomas, E. E., Vimont, D. J., Newman, M., Penland, C. & Martínez-Villalobos, C. The role of stochastic forcing in generating ENSO diversity. *J. Clim.* **31**, 9125–9150 (2018).

12. Dewitte, B. & Takahashi, K. Diversity of moderate El Niño events evolution: role of air–sea interactions in the eastern tropical Pacific. *Clim. Dyn.* **52**, 7455–7476 (2019).

13. Trenberth, K. E. *The Definition of El Nino*. Tech. Rep. 12 (1997).

14. Zhao, S. & Karamperidou, C. Competing effects of Eastern and Central-Western Pacific winds in the evolution of the 2017 extreme coastal El Niño. *Geophys. Res. Lett.* **49**, e2022GL098859 (2022).

15. McPhaden, M. J. et al. The response of the equatorial Pacific Ocean to a westerly wind burst in May 1986. *J. Geophys. Res.* **93**, 10589 (1988).

16. Harrison, D. E. & Vecchi, G. A. Westerly wind events in the tropical Pacific, 1986–95*. *J. Clim.* **10**, 3131–3156 (1997).

17. Takahashi, K. & Martínez, A. G. The very strong coastal El Niño in 1925 in the far-eastern Pacific. *Clim. Dyn.* **52**, 7389–7415 (2019).

18. Schneider, T., Bischoff, T. & Haug, G. H. Migrations and dynamics of the intertropical convergence zone. *Nature* **513**, 45–53 (2014).

19. Hu, Z.-Z., Huang, B., Zhu, J., Kumar, A. & McPhaden, M. J. On the variety of coastal El Niño events. *Clim. Dyn.* **52**, 7537–7552 (2019).

20. Karamperidou, C. & DiNezio, P. N. Holocene hydroclimatic variability in the tropical Pacific explained by changing ENSO diversity. *Nat. Commun.* **13**, 1–8 (2022).

21. Chen, H. C. & Jin, F. F. The mechanism of boreal summer SSTA phase-locking in the far eastern Pacific. *npj Clim. Atmos. Sci.* **6**, 1–9 (2023).

22. McPhaden, M. J., Timmermann, A., Widlansky, M. J., Balmaseda, M. A. & Stockdale, T. N. The curious case of the EL Niño that never happened: a perspective from 40 years of progress in climate research and forecasting. *Bull. Am. Meteorol. Soc.* **96**, 1647–1665 (2015).

23. Chiang, J. C. H. & Vimont, D. J. Analogous Pacific and Atlantic meridional modes of tropical atmosphere-ocean variability. *J. Clim.* **17**, 4143–4158 (2004).

24. Takahashi, K. & Dewitte, B. Strong and moderate nonlinear El Niño regimes. *Clim. Dyn.* **46**, 1627–1645 (2016).

25. Kay, J. E. et al. The Community Earth System Model (CESM) Large Ensemble Project: a community resource for studying climate change in the presence of internal climate variability. *Bull. Am. Meteorol. Soc.* **96**, 1333–1349 (2015).

26. Kondrashov, D., Kravtsov, S., Robertson, A. W. & Ghil, M. A hierarchy of data-based ENSO models. *J. Clim.* **18**, 4425–4444 (2005).

27. Chen, C. et al. Diversity, nonlinearity, seasonality, and memory effect in ENSO simulation and prediction using empirical model reduction. *J. Clim.* **29**, 1809–1830 (2016).

28. Moore, A. M., Fiechter, J. & Edwards, C. A. A linear stochastic emulator of the California Current system using balanced truncation. *Ocean Model.* **174**, 102023 (2022).

29. Penland, C. & Sardeshmukh, P. D. The optimal growth of tropical sea surface temperature anomalies. *J. Clim.* **8**, 1999–2024 (1995).

30. Capotondi, A. & Sardeshmukh, P. D. Optimal precursors of different types of ENSO events. *Geophys. Res. Lett.* **42**, 9952–9960 (2015).

31. Newman, M. & Sardeshmukh, P. D. Are we near the predictability limit of tropical Indo-Pacific sea surface temperatures? *Geophys. Res. Lett.* **44**, 8520–8529 (2017).
32. Martinez-Villalobos, C., Newman, M., Vimont, D. J., Penland, C. & David Neelin, J. Observed El Niño-La Niña Asymmetry in a Linear Model. Geophys. Res. Lett. 46, 9909-9919 (2019).

33. Capotondi, A., Newman, M., Xu, T. & Di Lorenzo, E. An optimal precursor of Northeast Pacific Marine heatwaves and Central Pacific El Niño events. Geophys. Res. Lett. 49, e2021GL097350 (2022).

34. Xu, T. et al. An increase in marine heatwaves without significant changes in surface ocean temperature variability. Nat. Commun. 13, 1-12 (2022).

35. Wang, Y., Holbrook, N. J. & Kajtar, J. B. Predictability of marine heatwaves off western Australia using a Linear inverse model. J. Clim. 36, 6177-6193 (2023).

36. Herein, M., Drótos, G., Haszpra, T., Márfy, J. & Tél, T. The theory of parallel climate realizations as a new framework for teleconnection analysis. Sci. Rep. 7, 44529 (2017).

37. McKinnon, K. A. & Deser, C. Internal variability and regional climate trends in an observational large ensemble. J. Clim. 31, 6783-6802 (2018).

38. Eyring, V. et al. Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev. 9, 1937-1958 (2016).

39. Lübbecke, J. F., Rudloff, D. & Stramma, L. Stand-alone eastern Pacific coastal warming events. Geophys. Res. Lett. 46, 12360-12367 (2019).

40. Xue, J., Luo, J. J., Yuan, C. & Yamagata, T. Discovery of Chile Niño/ Niña. Geophys. Res. Lett. 47, e2019GL086468 (2020).

41. Carrasco, D., Pizarro, O., Jacques-Coper, M. & Narváez, D. A. Main drivers of marine heat waves in the eastern South Pacific. Front. Mar. Sci. 10, 1129276 (2023).

42. Im, S.-H., An, S.-I., Kim, S. T. & Jin, F.-F. Feedback processes responsible for El Niño-La Niña amplitude asymmetry. Geophys. Res. Lett. 42, 5556-5563 (2015).

43. Levine, A. F. Z. & Jin, F. F. A simple approach to quantifying the noise? ENSO interaction. Part I: deducing the state-dependency of the windstress forcing using monthly mean data. Clim. Dyn. 48, 1-18 (2017).

44. Newman, M., Wittenberg, A. T., Cheng, L., Compo, G. P. & Smith, C. A. The extreme 2015/16 El Niño, in the Context of historical climate variability and change. Bull. Am. Meteorol. Soc. 99, S16-S20 (2018).

45. Capet, X., Colas, F., McWilliams, J. C., Penven, P. & Marchesiello, P. Eddies in eastern boundary subtropical upwelling systems. In Ocean Modeling in an Eddying Regime (eds M.W. Hecht and H. Hasumi). Geophysical Monograph Series (American Geophysical Union, 2013).

46. Puy, M., Vialard, J., Lengaigne, M. & Guilyardi, E. Modulation of equatorial Pacific westerly/easterly wind events by the Madden-Julian oscillation and convectively-coupled Rossby waves. Clim. Dyn. 46, 2155-2178 (2016).

47. Rasmusson, E. M. & Carpenter, T. H. Variations in tropical sea surface temperature and surface wind fields associated with the southern oscillation/El Niño. Mon. Weather Rev. 110, 354-384 (1982).

48. Zhang, H., Clement, A. & Nezio, P. D. The south pacific meridional mode: a mechanism for ENSO-like variability. J. Clim. 27, 769-783 (2014).

49. Dewitte, B. et al. The ENSO-induced South Pacific Meridional Mode. Front. Clim. 4, 247 (2023).

50. Xie, S.-P. & Philander, S. G. H. A coupled ocean-atmosphere model of relevance to the ITCZ in the eastern Pacific. Tellus A 46, 340-350 (1994).

51. Martinez-Villalobos, C. & Vimont, D. J. An analytical framework for understanding tropical meridional modes. J. Clim. 30, 3303-3323 (2017).

52. Holbrook, N. J. et al. A global assessment of marine heatwaves and their drivers. Nat. Commun. 10, 1-13 (2019).

53. Sen Gupta, A. et al. Drivers and impacts of the most extreme marine heatwave events. Sci. Rep. 10, 1-15 (2020).

54. Renault, L. et al. Upwelling response to atmospheric coastal jets off central Chile: a modeling study of the October 2000 event. J. Geophys. Res. Oceans 117, 2030 (2012).

55. Liguori, G. & Di Lorenzo, E. Separating the North and South Pacific Meridional Modes contributions to ENSO and tropical decadal variability. Geophys. Res. Lett. 46, 906-915 (2019).

56. SENAMHI. Ciclón Yaku se presenta frente al mar peruano-Noticias - Servicio Nacional de Meteorología e Hidrología del Perú - Plataforma del Estado Peruano. https://www.gob.pe/Institucion/senamhi/ noticias/721545-ciclon-yaku-se-presenta-frente-al-mar- peruano (2023).

57. OCHA. Peru: Rains and Flooding Situation Report No. 01, Peru | ReliefWeb. https://reliefweb.int/report/peru/peru-rains-and-flooding- situation-report-no-01-27-march-2023 (2023).

58. Di Lorenzo, E. & Mantua, N. Multi-year persistence of the 2014/15 North Pacific marine heatwave. Nat. Clim. Change 6, 1042-1047 (2016).

59. Holbrook, N. J. et al. Keeping pace with marine heatwaves. Nat. Rev. Earth Environ. 1, 482-493 (2020).

60. Pauly, D. & Christensen, V. Primary production required to sustain global fisheries. Nature 374, 255-257 (1995).

61. Hoegh-Guldberg, O. & Bruno, J. F. The impact of climate change on the world's marine ecosystems. Science 328, 1523-1528 (2010).

62. Chavez, F. P., Messié, M. & Pennington, J. T. Marine primary production in relation to climate variability and change. Annu. Rev. Mar. Sci. 3, 227-260 (2010).

63. Dewitte, B. et al. Modes of covariability between sea surface temperature and wind stress intraseasonal anomalies along the coast of Peru from satellite observations (2000-2008). J. Geophys. Res. 116, C04028 (2011).

64. You, Y. & Furtado, J. C. The south Pacific meridional mode and its role in tropical pacific climate variability. J. Clim. 31, 10141-10163 (2018).

65. Amaya, D. J. The Pacific meridional mode and ENSO: a review. Curr. Clim. Change Rep. 5, 296-307 (2019).

66. Sandweiss, D. H. et al. Archaeological climate proxies and the complexities of reconstructing Holocene El Niño in coastal Peru. Proc. Natl Acad. Sci. USA 117, 8271-8279 (2020).

67. Huang, B. et al. Extended Reconstructed Sea Surface Temperature, Version 5 (ERSSTv5): upgrades, validations, and intercomparisons. J. Clim. 30, 8179-8205 (2017).

68. Adler, R. F. et al. The Version-2 Global Precipitation Climatology Project (GPCP) monthly precipitation analysis (1979-present). J. Hydrometeorol. 4, 1147-1167 (2003).

69. Kalnay, E. et al. The NCEP/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77, 437-471 (1996).

70. Behringer, D. W., Ji, M. & Leetmaa, A. An improved coupled model for ENSO prediction and implications for ocean initialization. Part I: the ocean data assimilation system. Mon. Weather Rev. 126, 1013-1021 (1998).

71. Bretherton, C. S., Smith, C. & Wallace, J. M. An intercomparison of methods for finding coupled patterns in climate data. J. Clim. 5, 541-560 (1992).

72. Richter, I., Stuecker, M. F., Takahashi, N. & Schneider, N. Disentangling the north Pacific meridional mode from tropical Pacific variability. npj Clim. Atmos. Sci. 5, 1-9 (2022).

73. Lengaigne, M. et al. Triggering of El Niño by westerly wind events in a coupled general circulation model. Clim. Dyn. 23, 601-620 (2004).

74. Newman, M., Alexander, M. A. & Scott, J. D. An empirical model of tropical ocean dynamics. Clim. Dyn. 37, 1823-1841 (2011).

75. Penland, C. A stochastic model of IndoPacific sea surface temperature anomalies. Phys. D Nonlinear Phenom. 98, 534-558 (1996).

76. Ortizbeviá, M. J. Estimation of the cyclostationary dependence in geophysical data fields. J. Geophys. Res. Atmos. 102, 13473-13486 (1997).

77. Shin, S. I., Sardeshmukh, P. D., Newman, M., Penland, C. & Alexander, M. A. Impact of annual cycle on ENSO variability and predictability. J. Clim. 34, 171-193 (2021).

78. Vimont, D. J., Newman, M., Battisti, D. S. & Shin, S.-I. The role of seasonality and the ENSO mode in central and east Pacific ENSO growth and evolution. J. Clim. 35, 3195-3209 (2022).

79. Stuecker, M. F. The climate variability trio: stochastic fluctuations, El Niño, and the seasonal cycle. Geosci. Lett. 10, 1-19 (2023).
80. Sura, P., Newman, M., Penland, C. & Sardeshmukh, P. Multiplicative noise and non-Gaussianity: a paradigm for atmospheric regimes? *J. Atmos. Sci.* **62**, 1391–1409 (2005).

81. Bianucci, M. & Mannella, R. On the determination of the optimal parameters in the CAM model. *Chaos* **31**, 33113 (2021).

82. Sardeshmukh, P. D. & Sura, P. Reconciling non-Gaussian climate statistics with linear dynamics. *J. Clim.* **22**, 1193–1207 (2009).

83. Martinez-Villalobos, C., Vimont, D. J., Penland, C., Newman, M. & Neelin, J. D. Calculating state-dependent noise in a linear inverse model framework. *J. Atmos. Sci.* **75**, 479–496 (2018).

84. Penland, C. Random forcing and forecasting using principal oscillation pattern analysis. *Mon. Weather Rev.* **117**, 2126–2165 (1989).

85. Penland, C. & Hartten, L. M. Stochastic forcing of north tropical Atlantic sea surface temperatures by the North Atlantic Oscillation. *Geophys. Res. Lett.* **41**, 2126–2132 (2014).

86. Vimont, D. J., Battisti, D. S. & Hirst, A. C. Footprinting: a seasonal connection between the tropics and mid-latitudes. *Geophys. Res. Lett.* **28**, 3923–3926 (2001).

87. Larson, S. & Kirtman, B. The Pacific Meridional Mode as a trigger for ENSO in a high-resolution coupled model. *Geophys. Res. Lett.* **40**, 3189–3194 (2013).

88. Thomas, E. E. & Vimont, D. J. Modeling the mechanisms of linear and nonlinear ENSO responses to the Pacific Meridional Mode. *J. Clim.* **29**, 8745–8761 (2016).

89. Stuecker, M. F. Revisiting the Pacific Meridional Mode. *Sci. Rep.* **8**, 1–9 (2018).

90. Penland, C. & Matrosova, L. A Balance condition for stochastic numerical models with application to the El Niño-Southern oscillation. *J. Clim.* **7**, 1352–1372 (1994).

91. Kido, S., Richter, I., Tozuka, T. & Chang, P. Understanding the interplay between ENSO and related tropical SST variability using linear inverse models. *Clim. Dyn.* **61**, 1029–1048 (2023).

92. Dobson, A. J. & Barnett, A. G. *An Introduction to Generalized Linear Models* 4th edn. (Chapman and Hall/CRC, 2018).

93. Sulca, J., Takahashi, K., Espinoza, J. C., Vuille, M. & Lavado-Casimiro, W. Impacts of different ENSO flavors and tropical Pacific convection variability (ITCZ, SPCZ) on austral summer rainfall in South America, with a focus on Peru. *Int. J. Climatol.* **38**, 420–435 (2018).

94. Neelin, J. D., Peters, O. & Hales, K. The transition to strong convection. *J. Atmos. Sci.* **66**, 2367–2384 (2009).

95. Graham, N. E. & Barnett, T. P. Sea surface temperature, surface wind divergence, and convection over tropical oceans. *Science* **238**, 657–659 (1987).

96. Johnson, N. C. & Xie, S.-P. Changes in the sea surface temperature threshold for tropical convection. *Nat. Geosci.* **3**, 842–845 (2010).

97. Back, L. E. & Bretherton, C. S. On the relationship between SST gradients, boundary layer winds, and convergence over the tropical oceans. *J. Clim.* **22**, 4182–4196 (2009).

98. Vecchi, G. A. & Soden, B. J. Effect of remote sea surface temperature change on tropical cyclone potential intensity. *Nature* **450**, 1066–1070 (2007).

99. Jauregui, Y. R. & Takahashi, K. Simple physical-empirical model of the precipitation distribution based on a tropical sea surface temperature threshold and the effects of climate change. *Clim. Dyn.* **50**, 2217–2237 (2018).

## Acknowledgements

C.M. acknowledges support from Proyecto ANID Fondecyt Postdoctorado código 3200621, Data Observatory Foundation ANID Technology Center No. DO210001, Fondecyt Regular No. 1231174 and Research Office, Universidad Adolfo Ibáñez. B.D. acknowledges support from ANID (Concurso de Fortalecimiento al Desarrollo Científico de Centros Regionales 2020-R20F0008-CEAZA, Anillo Eclipse ACT210071 and Centro de Investigación Oceanográfica en el Pacífico Sur-Oriental COPAS COASTAL FB210021, Fondecyt Regular No. 1231174) and from the EU H2020 FutureMares project (Theme LC-CLA-06-2019, Grant agreement No. 869300). Support from LEFE-GMMC through the SEPICAF project is also acknowledged. R.G. is partially supported by CR2, FONDAP/ANID 1523A000.

## Author contributions

C.M. and B.D. conceived the study. C.M. performed the analyses, with assistance by L.L., and wrote the paper with contributions from B.D. and R.G.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41612-024-00675-5.

**Correspondence** and requests for materials should be addressed to Cristian Martinez-Villalobos.

**Reprints and permissions information** is available at http://www.nature.com/reprints

**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

© The Author(s) 2024