# Contributions of El Niño Southern Oscillation (ENSO) Diversity to Low-
Frequency Changes in ENSO Variance

Jakob Schlör
Machine Learning in Climate Science
University of Tübingen, Germany
<EMAIL_ADDRESS>
&Felix Strnad
Machine Learning in Climate Science
University of Tübingen, Germany
&Antonietta Capotondi
Cooperative Institute for Research in Environmental Sciences
University of Colorado, Boulder, CO
NOAA/Physical Sciences Laboratory, Boulder, CO
&Bedartha Goswami
Machine Learning in Climate Science
University of Tübingen, Germany

###### Abstract

El Niño Southern Oscillation (ENSO) diversity is characterized based on the
longitudinal location of maximum sea surface temperature anomalies (SSTA) and
amplitude in the tropical Pacific, as Central Pacific (CP) events are
typically weaker than Eastern Pacific (EP) events. SSTA pattern and intensity
undergo low-frequency modulations, affecting ENSO prediction skill and remote
impacts. Yet, how different ENSO types contribute to these decadal variations
and long-term variance trends remain uncertain. Here, we decompose the low-
frequency changes of ENSO variance into contributions from ENSO diversity
categories. We propose a fuzzy clustering of monthly SSTA to allow for non-
binary event category memberships. Our approach identifies two La Niña and
three El Niño categories and shows that the shift of ENSO variance in the
mid-1970s is associated with an increasing likelihood of strong La Niña and
extreme El Niño events.

_Keywords_ El Nino Southern Oscillation Diversity $\cdot$ Unsupervised fuzzy
clustering $\cdot$ Decadal variability

##  1 Introduction

The El Niño-Southern Oscillation (ENSO), characterized by anomalous sea
surface temperatures (SSTs) in the tropical Pacific, exhibits notable
diversity in its amplitude, temporal evolution, and spatial pattern. The El
Niño events of 1982-83 and 1997-98, for instance, recorded exceptionally high
SST anomaly (SSTA) values in the eastern equatorial Pacific, whereas the El
Niño of 2002-03 was less extreme and exhibited the largest anomalies in the
central equatorial Pacific (McPhaden, 2004). In order to describe these event-
to-event differences, El Niño events have been generally categorized as
Eastern Pacific (EP), and Central Pacific (CP) types (Capotondi et al., 2015).
EP El Niño events typically have their peak SSTA in the eastern Pacific, may
exhibit stronger intensities, and a largely reduced zonal thermocline slope,
resulting in the pronounced discharge of warm water from the equatorial
thermocline. In contrast, CP events show peak SSTA in the central Pacific and
are comparatively weaker with smaller changes in zonal thermocline slope and
warm water discharge (Kug et al., 2009; Capotondi, 2013).

These different types of ENSO events have substantially different downstream
impacts on the global climate (Strnad et al., 2022; Beniche, 2023). For
example, extreme drought conditions were recorded in eastern Australia in
2002, while a minor impact on precipitation was detected during the extreme
1997 event (Wang and Hendon, 2007). Weaker and shorter-lived CP events are
associated with warm conditions in the equatorial Atlantic during boreal
winter, while stronger and persistent EP events lead to cold anomalies in that
area, with different impacts on precipitation over northeastern Brazil (Kao
and Yu, 2009; Rodrigues et al., 2011). Thus, a deeper understanding of ENSO
diversity is critical to support predictions of ENSO impacts.

ENSO characteristics, including amplitude and spatial pattern, exhibit decadal
variations, which are mediated by changes in the background state of the
tropical Pacific (Capotondi et al., 2023). Notable decadal phase transitions
were observed in the late 1970s (Miller et al., 1994) and around the year 2000
(McPhaden, 2012). Paleoclimate data also indicate an increase in ENSO
amplitude over recent decades (Grothe et al., 2020), consistent with modeling
results showing a significant increase in ENSO amplitude after 1960, which was
attributed to anthropogenic forcing (Cai et al., 2023). Analysis of a large
number of observationally-based datasets revealed that the longitudinal
location of the maximum SST anomalies, as well as the intensity of both El
Niño and La Nina events, undergo decadal fluctuations (Dieppois et al., 2021),
which can, in turn, modulate ENSO predictions (Lou et al., 2023). However,
event location and intensity were considered separately by Dieppois et al.
(2021), so that the contribution of different ENSO types to these decadal
changes and long-term trends in ENSO variance remains unclear. Paleoclimate
data (Lawman et al., 2022) indicate that extreme ENSO events may contribute to
increases in ENSO variance. Similarly, climate models that capture relevant
aspects of ENSO nonlinearities project an increase in ENSO variance that is
linked to an increase in the frequency of extreme ENSO events (Cai et al.,
2021). However, a more comprehensive understanding of these changes from an
ENSO diversity perspective is still missing.

One main reason hindering the estimation of the contribution of different ENSO
categories to its decadal modulation is that ENSO classifications often depend
on the chosen definitions (Pascolini-Campbell et al., 2015; Yu and Kim, 2013;
Capotondi et al., 2020a; Abdelkader Di Carlo et al., 2023). The disagreement
between different ENSO classification methods is likely due to the assumption
that ENSO events can be classified into binary types, based on indices
capturing the location of the highest SSTA in the Tropical Pacific (like the
Niño3 and Niño4 regions), or using Empirical Orthogonal Functions (EOFs)
(Ashok et al., 2007; Kug et al., 2009; Kao and Yu, 2009; Takahashi et al.,
2011). However, ENSO events are continuously distributed in the space spanned
by the two leading principal components (PCs) (Takahashi and Dewitte, 2016;
Cai et al., 2018; Capotondi et al., 2020a). Approaches that use a more
continuous distribution of SSTAs to identify diversity show that events occur
over multiple locations but with enhanced probabilities over the central and
eastern tropical Pacific (Dieppois et al., 2021; Shin et al., 2021). In
addition, both EP- and CP-type events appear to share common underlying
dynamical processes, albeit with varying relevance depending on the longitude
(Capotondi, 2013).

A notable example of an El Niño that eludes a binary classification is the
2015/16 events. While its SSTA and several of its impacts were typical of
extreme EP events (Santoso et al., 2017), this event was not associated with a
significant impact on California precipitation and was not followed by a
strong La Niña, as other events of this type (i.e., 1982-83 and 1997-98).
Indeed, this event was considered a mixture of EP and CP types (Paek et al.,
2017; Capotondi et al., 2020a).

Here, we propose a new approach for characterizing ENSO diversity to better
understand its relationship with decadal changes in ENSO variance. To that
end, we develop a fuzzy clustering of the low-dimensional representation of
monthly SSTA in the PC1-PC2 space to achieve a non-binary event categorization
(i.e., events belonging to one cluster or not). Instead, in this fuzzy
clustering approach, individual events are assigned a probability of belonging
to a given cluster. Such membership probabilities are then used to determine
their relative contributions to the low-frequency ENSO variance.

##  2 Methodology and data

###  2.1 Data

Our analysis is conducted on monthly SSTA in the tropical Pacific (130°E-70°W,
30°S-30°N) from eight reanalysis datasets merged together (Tab. S1 and SI Sec.
S1). To ensure the same number of data points per month, we randomly select
four data points per month from the eight datasets covering 1901–2022. While
the dimensionality reduction encompasses all months, we select El Niño and La
Niña winter months for the fuzzy clustering. Boreal winters (December-January-
February (DJF)) are selected as El Niño (La Niña) when the average SSTA in the
Niño3.4 region is larger than 0.5 K (smaller than -0.5 K).

###  2.2 Fuzzy clustering

Clustering algorithms are typically based on a distance measure between data
points which becomes ill-posed in high-dimensional spaces (Parsons et al.,
2004). To mitigate this issue, we first reduce the dimensionality of the
geospatial fields before applying fuzzy clustering using EOF analysis.

Our input data, $X=\left(x(t_{1}),\ldots,x(t_{N})\right)$, which consists of
tropical Pacific SSTA fields $x(t)\in\cal{R}^{N_{\rm{lon}}\cdot
N_{\rm{lat}}}$, are projected onto the first two EOF patterns to obtain the
two PCs $z(t)\in\cal{R}^{2}$, referred to as a latent vector. Besides EOFs, we
also use a nonlinear dimensionality reduction method, specifically a
convolutional autoencoder neural network (SI Sec. S2, Fig. S1).

We apply the Gaussian Mixture Model (GMM), a probabilistic unsupervised
clustering approach to identify different types of ENSO events. GMMs describe
each cluster via a multivariate Gaussian distribution, accommodating
overlapping probabilities. Mathematically, GMMs assume that the probability
distribution of latent states, $p(z)$, comprises a mixture of Gaussians:

$p(z)=\sum_{k=1}^{K}\pi_{k}\mathcal{N}\left(z\mid\mu_{k},\Sigma_{k}\right),$
(1)

with $K$ representing the number of Gaussians,
$\mathcal{N}\left(z\mid\mu_{k},\Sigma_{k}\right)$, each characterized by a
mean $\mu_{k}$ and covariance $\Sigma_{k}$. The probability of each Gaussian
is denoted as $p\left(c_{k}\right)=\pi_{k}$ with $\sum_{k=1}^{K}\pi_{k}=1$.
The optimal number of clusters $K$ is obtained, by minimizing the Bayesian
Information Criterion (BIC). The BIC balances model complexity and fit
quality, as described by Schwarz (1978) and in SI Sec. S3.

Figure 1: El Niño and La Niña categories in PC1-PC2 space. Monthly boreal
winter (DJF) SSTAs of El Niño and La Niña events of all reanalysis products
(see SI Tab. S1) projected onto the PC1-PC2 space and fitted by a Gaussian
Mixture Model (GMM). Each event (DJF averages are shown as black dots in A)
has a probability of belonging to each of the five categories (colored
Gaussians in A). Pacific SSTA composites for each category are obtained by
using the category membership as weights for the averages, depicted in panels
(B-F). We obtain three El Niño-like patterns: _Extreme EN_ (B), _Strong EN_
(C), and _Weak EN_ (D), while La Niña events form two categories: _Weak LN_
(E) and _Strong LN_ (F).

###  2.3 Variability estimation

The GMM allows assigning a probability, $p\left(c_{k}|z(t)\right)$, to each
data point, $z(t)$, that quantifies its likelihood of belonging to category
$c_{k}$. These are the category memberships of the data point (Sec. S4), which
are inherently fuzzy and non-binary (i.e. they are probabilities between 0 and
1), and allow us to model ENSO events in terms of their likelihood of
occurrence. As a consequence, we can decompose a variable $y(t)$, for
instance, SSHA, into the contributions of each category, by

$y(t)=\sum_{k}p\left(c_{k}|z(t)\right)\cdot y(t):=\sum_{k}y_{k}(t)$ (2)

where $y_{k}(t)$ is defined as the contribution of category $c_{k}$. Averaging
$y_{k}(t)$ over time corresponds to a weighted average, with the weights being
the categorical memberships (Sec. S5). Similarly, we can write the variance
$\langle y^{2}\rangle$, as

$\langle
y^{2}\rangle=\langle\left(\sum_{k}y_{k}\right)^{2}\rangle=\sum_{k}\langle
y_{k}^{2}\rangle+\sum_{l\neq m}\langle y_{l},y_{m}\rangle,$ (3)

where $\langle y_{k}^{2}\rangle$ is the variance contribution of category
$c_{k}$ and $\langle y_{l},y_{m}\rangle$ is the co-variability of categories
$l$ and $m$.

##  3 Results

###  3.1 ENSO diversity is well explained by five categories

The two most dominant EOFs of all eight SSTA datasets combined (Tab. S1)
present the well-known spatial patterns associated with ENSO, i.e. EOF1
depicts the typical ENSO pattern with anomalies in the Central-Eastern
Pacific, while EOF2 exhibits an east-west dipole structure (Fig. S2).
Projection of the monthly SSTA of all boreal winter (December-January-
February) El Niño and La Niña events onto EOF1 and EOF2, produces a
distribution in the corresponding PC1–PC2 space that exhibits a wide,
boomerang-like shape (Fig. 1A, Fig. S3). This nonlinear relationship between
PC1 and PC2 has been considered an expression of key ENSO dynamics (Cai et
al., 2018; Takahashi and Dewitte, 2016; Ham and Kug, 2012; Karamperidou et
al., 2017), and used in the selection of models to consider for examining
future projections (Cai et al., 2018, 2021). The nonlinear relationship itself
can be accounted for by using a nonlinear transformation in place of the
linear EOF-based transform, e.g., an autoencoder, and in that case, the
boomerang-like shape is replaced by a simple linear relation between the two
latent dimensions (SI Fig. S4 and SI Sec. S2).

The distribution of boreal winter El Niño and La Niña months in the PC1-PC2
space do not exhibit clear gaps visually, however, their density varies,
suggesting a categorical structure (Takahashi and Dewitte, 2016). We model
this distribution using a GMM with $k=5$ categories (Eq. 1), a number
determined using the BIC to ensure parsimony (see SI Sec. S3, Fig. S5A). The
five Gaussians are arranged in a row along the boomerang-shaped distribution
from the coldest events at the leftmost tip to the warmest events at the
rightmost end (Fig. 1A).

Figure 2: Probabilistic category membership. The GMM in Fig. 1 allows us to
estimate the likelihood, $p\left(c_{k}|z(t)\right)$, of each El Niño and La
Niña winter month, $z(t)$, to belong to each of the categories, $c_{k}$ (SI
Sec. S4). An event belongs only to one category when its probability is 1.
However, many events have shared probabilities across several categories. The
categories are sorted in the following order (top to bottom): _Extreme EN_
(A), _Strong EN_ (B), _Weak EN_ (C), _Weak LN_ (D), and _Strong LN_ (E). For
visual reasons, we average the monthly probabilities over each winter (DJF)
and over reanalysis products. The dashed lines indicate the reported shifts in
ENSO variability in 1976-77 and 2000.

We use the category memberships, $p\left(c_{k}|z(t)\right)$, as weights for
averaging the Pacific SSTAs of each category (SI Sec. S5) and find three El
Niño-like patterns (Fig. 1B-D), and two La Niña-like patterns (Fig. 1E-F).
Besides the different zonal locations of maximum warming/cooling, their
defining factor is the tropical Pacific SSTA intensity. Hence, we will refer
to the three El Niño categories as _Extreme EN_ (Fig. 1B), _Strong EN_ (Fig.
1C) and _Weak EN_ (Fig. 1D), and correspondingly to _Weak LN_ (Fig. 1E) and
_Strong LN_ (Fig. 1F) for the La Niña categories. We find that the overall
clustering of the SSTA patterns into the five categories is robust (SI Sec.
S6) upon changing the number of EOFs (SI Fig. S5B, Fig. S6, Fig. S7B),
incorporating SSHA data along with the SSTA (SI Fig. S8 K-O), or varying the
latitudinal range of the input (SI Fig. S8F-J). For comparison, we show the
Gaussians for k=4 (SI Fig. S9), and k=6 (SI Fig. S10) categories.

The mean category membership for each boreal winter averaged across the
datasets results in five time series of probabilities — one for each category
— which reflect the likelihood of their occurrences (Fig. 2). We find that the
indices are not sensitive to the dataset used for their estimation, as seen in
the relatively small spread of the membership probabilities over the datasets
at each time point (SI Fig. S11). As with the number of clusters, the category
membership is also robust to changes in the number of variables, spatial
domain, and the use of nonlinear encoding (SI Fig. S12).

Comparing the category membership series for _Strong_ and _Weak EN_ events
(Fig. 2B, C) to two conventional classifications – the Niño3-Niño4
classification by Kug et al. (2009) and the EOF-based E/C classification by
Takahashi et al. (2011) – we find that our classification mostly agrees with
them (SI Tab. S2, Sec. S7). Differences, when they do occur, correspond to
differences between the other classifications as well (Pascolini-Campbell et
al., 2015; Yu and Kim, 2013; Capotondi et al., 2015). The two El Niños of
1994-95 and 2006-07, however, are classified by both conventional
classifications as CP events, whereas we find them to be _Strong EN_ events
(Tab. S2). This is likely because the warm water anomalies span from the
Central to the Eastern Pacific during the duration of these events, leading to
possible ambiguities in the event definition (SI Fig. S13C, H). We also note
that unlike the 1982-83 and 1997-98 events, which unambiguously belonged to
the _Extreme EN_ category, the 2015-16 event also has a nonzero membership in
the _Strong EN_ category, confirming its mixed nature.

###  3.2 Extreme EN events are different from Strong EN events

Figure 3:  _Extreme EN_ and _Strong EN_ category. Hovmöller diagrams of SSTA
(A, B), SSHA (C, D), high-frequency (HF) zonal wind anomalies (E, F), and low-
frequency (LF) zonal wind (G, H) anomalies are obtained by meridional averages
(5°S - 5°N) of each month in the year preceding and succeeding El Niño events.
Each two-year period is weighted by the corresponding DJF average category
membership probability (Fig. 2). The black line in (A) and (B) indicates the
warm-pool edge, i.e., the 29°C SST isotherm (SI Sec. S8). Only values that are
statistically significant above the 95th percentile are displayed (SI Sec.
S9). SSTA and SSHA are taken from ORAS5 (1958–2022), while 10-meter zonal
winds, with their HF- and LF components (Sec. S1) are computed from ERA5.

A key distinction of our ENSO categorization from conventional methods is the
identification of the extreme El Niños as a separate class. While our _Weak
EN_ category corresponds to the conventional CP El Niño type, the conventional
EP El Niño type is split into _Extreme EN_ and _Strong EN_ categories (SI Sec.
S7, Tab. S2). SSTA composites of conventional EP El Niño events (SI Fig. S14A,
C, E, Fig. S15B) exhibit the maximum warming in the eastern Pacific. The
maximum warming is however strongly influenced by the few extreme EN events
(1982/83, 1997/98, 2015/16), with an eastward shift of the peak towards the
central Pacific when we exclude the extreme events (SI Fig. S14B, D, F).

The separation of _Extreme EN_ from _Strong EN_ events highlights differences
in their impacts. We find that during _Extreme EN_ events, statistically
significant (at 95 % confidence) warmer-than-average SSTs and negative OLR
anomalies occur in the Indian Oceans (SI Fig. S16A, K), which are not
significant for _Strong EN_ (SI Fig. S16B, L).

The two categories also differ in their evolution, analyzed using Hovmöller
diagrams for the year preceding and succeeding an event (Fig. 3, SI Fig. S17).
_Extreme EN_ events show significant warm water volume anomalies, as described
by SSHA, around the dateline already in the spring before an event,
corresponding with a shift of the warm pool edge near the dateline (black line
Fig. 3A, C). The _Extreme EN_ onset phase also shows strong positive HF and LF
zonal wind components to the west of the dateline, during the preceding
spring, extending further east as the event develops to its mature phase (Fig.
3E, G). _Strong EN_ events, on the other hand, do not demonstrate a consistent
onset pattern in the preceding spring (Fig. 3D, F, H).

These findings corroborate ideas presented in prior research on the impact of
the Walker circulation’s zonal shift (Thual and Dewitte, 2023) and the
influence of stochastic high-frequency winds, called Westerly Wind Bursts
(WWBs), on ENSO Diversity (Fedorov et al., 2015; Capotondi et al., 2018; Puy
et al., 2019).

###  3.3 Interdecadal ENSO variability is driven by Strong and Extreme events

The membership probabilities of each category (Fig. 2A, B) encode a distinct
pattern of decadal-to-multidecadal ENSO variability. In particular, the
_Strong LN_ and the _Extreme EN_ categories show a markedly prominent low-
frequency variability, which is less evident in other categories. To quantify
the low-frequency variation of ENSO, we multiply the Niño3.4 index (from
HadISST) by the corresponding membership probabilities for each category (Eq.
2, Fig. 4A) and calculate their 20-year running variances every 10 years (Eq.
3). The variance of each category is normalized by the 20-year running
variance of the Niño3.4 index (Fig. 4C) to determine their relative
contributions.

The total variance of the Niño3.4 index shows a low-frequency modulation, with
a minimum around 1920-1960, followed by an increasing trend, which is
consistent with the shift in the mean and variance of ENSO after the so-called
“1976-77 climate shift” <e.g.>[]miller1994 (dashed line in Fig. 4C). A slight
decrease in variance is noticeable after the year 2000, in line with the other
reported climate shift <e.g.>[]mcphaden2012. While changes are noticeable in
the variance of all categories, only minor contributions to the total Niño3.4
variance are observed for the _Weak LN_ and _Weak EN_ categories (Fig. 4D).
The _Strong LN_ category exhibits a substantial contribution starting around
1970, and the _Strong EN_ category dominates the variance from 1890 to
$\sim$1930\. Meanwhile, the contribution of the _Extreme EN_ category is
particularly visible towards the end of the 19th century and after 1980. These
results are robust against variations in window size (SI Fig. S18) and using
different reanalysis products (SI Fig. S19).

Between 20-40% of the decadal variance is due to the covariance between the
different ENSO categories (denoted as _cov_ in Fig. 4D). The covariance
captures mainly the contribution of co-occurrences of different categories to
the overall variance in a decade. However, other factors such as events with
intermediate values of category memberships and statistical errors in
estimating the GMM categories also influence the covariance.

Figure 4:  Low-frequency changes of ENSO variance. For each category, the
Niño3.4 index is multiplied by their category membership probabilities (A).
The histogram of Niño3.4 intensities (B), highlights different SSTA amplitudes
between categories. The 20-year running variance of Niño3.4 every 10 years
(C), is used to normalize the 20-year running variance of each category (D).
_Extreme EN_ and _Strong EN_ categories dominate the Niño3.4 variance in the
early and late 20th century. The variance shift in 1976-77 and 2000 (dashed
lines) highlight reported changes in ENSO variability. The Niño3.4 index is
taken from HadISST (Rayner et al., 2003).

Our statistical approach does not allow us to assess the dynamics underpinning
these decadal changes in the contribution of the different ENSO categories.
ENSO decadal modulation is often associated with changes in the mean state,
but it is not clear whether mean state changes are induced by influences from
the extratropical Pacific or other ocean basins, or result as a residual of
random variations of ENSO itself (Capotondi et al., 2023). Some studies,
however, suggest that some ENSO events could induce decadal phase transitions
through either nonlinear dynamical heating (Liu et al., 2022) or by inducing a
discharge of upper ocean heat content in the off-equatorial Western Pacific
(Meehl et al., 2021).

Our results provide novel insights into low-frequency changes in ENSO
variance, which combines changes in frequency and intensity. We find that
although the magnitude of total variance contributed by Eastern Pacific
warming events (i.e. _Extreme EN_ and _Strong EN events_ combined) since the
turn of the 20th century is comparable to that seen during the period from the
1880s to 1940s, the variance in the recent decades has been dominated by the
_Extreme EN_ category, a result consistent with the statistically significant
change in ENSO properties in the late 1970s (Capotondi and Sardeshmukh, 2017).
This shift was associated with a weakening of the easterly trade winds and a
zonal reduction of the equatorial thermocline slope, conditions favoring
stronger El Niño events. Linked to the increased contributions from _Extreme
EN events_ is the concurrent increase in the contributions of _Strong LNs_
since the 1970s (dark blue in Fig. 4D), manifested in very strong, multi-year
events starting around 1970 (Fig. 4A). These results are consistent with a
higher likelihood of stronger CP La Niñas following the heat discharge of
strong El Niños, as exemplified by the 1998-99 La Niña event after the extreme
1997-98 El Niño (Cai et al., 2015; Geng et al., 2023). While the increasing
contribution of _Extreme EN_ and _Strong LN_ to ENSO variance starting around
1970 aligns with results from climate model simulations (Cai et al., 2021; Gan
et al., 2023), our findings more specifically highlight the key role played by
_Strong LN_ in the ENSO variance changes after 1970.

We also find that during the ‘quiescent’ period of ENSO, roughly from the
1930s to the 1960s, most of the ENSO variability originated from Central
Pacific warming and Eastern Pacific cooling events, i.e., from the weaker
event types, while the influence of Central Pacific warming on the ENSO
variance in recent decades has been almost negligible. This latter result is
in apparent disagreement with the reported increase in intensity and frequency
of CP events since 1980 (Lee and McPhaden, 2010), and especially after 2000
(dashed line in Fig. 4D; (McPhaden et al., 2011)). This discrepancy may be
related to the 20-year running variance we used to construct Fig. 4D, and our
inclusion of the 2015/16 El Nino, an event that was missing in the records
used by the earlier studies.

##  4 Discussion

We present a new approach for studying the influence of ENSO diversity on low-
frequency changes in ENSO variance. In particular, we use a Gaussian Mixture
Model (GMM) within the low-dimensional PC1-PC2 space of monthly SSTA, which
enables the assignment of non-binary event category memberships. We identify
two La Niña categories (_Weak LN_ , _Strong LN_) and three El Niño categories
(_Extreme EN, Strong EN, Weak EN_), which combine the two dimensions of ENSO
diversity — longitudinal location of maximum SSTA and its intensity. A key
contribution of our work involves utilizing the membership probabilities to
determine how each of the five categories individually affects the overall
decadal variability in the Niño3.4 region. We find that the increasing
frequency of both _Extreme EN_ and _Strong LN_ are the primary drivers of the
increased ENSO variance post-1970. While these findings are consistent with
previous studies that also detected an increase in extreme ENSO events in the
second half of the 20th century (Cai et al., 2018, 2023), our results further
highlight the key role played by the increasing frequency of _Strong LN_ in
these ENSO variance changes.

The proposed fuzzy clustering approach could also be used to quantify how well
climate models represent ENSO diversity, akin to Dieppois et al. (2021) and
Ayar et al. (2023). A preliminary analysis of the Community Earth System Model
version 2 (CESM2) shows that this model only exhibits four ENSO categories
instead of five (SI Sec. S10, Fig. S20), a discrepancy which cannot be
explained by the different number of samples or other technical choices.
Specifically, the _Extreme EN_ category is missing in the model. While ENSO in
CESM2 has an amplitude larger than observed, modeled SSTAs tend to occur
preferentially in the central equatorial Pacific, with a more limited range of
ENSO spatial patterns (Capotondi et al., 2020b), a behavior that seems to
align with the model’s inability to simulate extreme events in the eastern
Pacific. In addition, the model appears to underestimate ENSO’s
nonlinearities, as quantified by the quadratic fit coefficient, $\alpha$, in
PC1-PC2 space (Dommenget et al., 2013; Karamperidou et al., 2017; Cai et al.,
2018), which is smaller in CESM2 compared to reanalysis (Fig. S21). An
extensive examination of several climate models using our methodology is
beyond the scope of this paper. However, our analysis of CESM2 demonstrates
the potential value of our approach for achieving a detailed assessment of
ENSO diversity in climate models. Such an investigation, as well as the
analysis of possible changes in ENSO types in future climate scenarios, will
be considered in subsequent studies.

## Open Research

The data on which this article is based are publicly available in Zhang et al.
(2019); Hersbach et al. (2020); COBE (2006); Rayner et al. (2003); ORAS5
(2021); Giese and Ray (2011); Behringer et al. (1998); Laloyaux et al. (2018),
with their details are listed in SI Tab. S1. Our code is publicly available
under Schlör (2023) and _https://github.com/jakob-schloer/LatentGMM.git_.

## Acknowledgments

The authors thank the International Max Planck Research School for Intelligent
Systems (IMPRS-IS) for supporting J. Schlör and F. Strnad. Furthermore, we
express our gratitude to the NOAA Physical Science Laboratory for making their
resources available for this study. Funded by the Deutsche
Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s
Excellence Strategy – EXC number 2064/1 – Project number 390727645. We
acknowledge support from the Open Access Publication Fund of the University of
Tübingen. A. Capotondi was supported by the NOAA Climate Program Office’s
Climate Variability and Predictability (CVP) and Modeling, Analysis,
Predictions and Projections (MAPP) programs and by DOE Award No. DE-SC0023228.

## References

  * McPhaden (2004) Michael J. McPhaden.  Evolution of the 2002/03 El Niño.  _Bull. Am. Meteorol. Soc._ , 85(5):677–696, May 2004.  ISSN 0003-0007.  doi:10.1175/BAMS-85-5-677.
  * Capotondi et al. (2015) Antonietta Capotondi, Andrew T. Wittenberg, Matthew Newman, Emanuele Di Lorenzo, Jin Yi Yu, Pascale Braconnot, Julia Cole, Boris Dewitte, Benjamin Giese, Eric Guilyardi, Fei Fei Jin, Kristopher Karnauskas, Benjamin Kirtman, Tong Lee, Niklas Schneider, Yan Xue, and Sang Wook Yeh.  Understanding enso diversity.  _Bulletin of the American Meteorological Society_ , 96(6):921–938, June 2015.  ISSN 15200477.  doi:10.1175/BAMS-D-13-00117.1.
  * Kug et al. (2009) Jong Seong Kug, Fei Fei Jin, and Soon Il An.  Two types of El Niño events: Cold tongue El Niño and warm pool El Niño.  _Journal of Climate_ , 22(6):1499–1515, 2009\.  ISSN 08948755.  doi:10.1175/2008JCLI2624.1.
  * Capotondi (2013) Antonietta Capotondi.  ENSO diversity in the NCAR CCSM4 climate model: Enso Diversity in the NCAR CCSM4.  _Journal of Geophysical Research: Oceans_ , 118(10):4755–4770, October 2013.  ISSN 21699275.  doi:10.1002/jgrc.20335.
  * Strnad et al. (2022) Felix M. Strnad, Jakob Schlör, Christian Fröhlich, and Bedartha Goswami.  Teleconnection Patterns of Different El Niño Types Revealed by Climate Network Curvature.  _Geophysical Research Letters_ , 49(17):e2022GL098571, 2022.  ISSN 1944-8007.  doi:10.1029/2022GL098571.
  * Beniche (2023) Margot Beniche.  A distinct and reproducible teleconnection pattern over North America during extreme El Niño events.  https://www.researchsquare.com, October 2023.
  * Wang and Hendon (2007) Guomin Wang and Harry H. Hendon.  Sensitivity of Australian Rainfall to Inter–El Niño Variations.  _Journal of Climate_ , 20(16):4211–4226, August 2007.  ISSN 0894-8755, 1520-0442.  doi:10.1175/JCLI4228.1.
  * Kao and Yu (2009) Hsun Ying Kao and Jin Yi Yu.  Contrasting Eastern-Pacific and Central-Pacific types of ENSO.  _Journal of Climate_ , 22(3):615–632, February 2009.  ISSN 08948755.  doi:10.1175/2008JCLI2309.1.
  * Rodrigues et al. (2011) Regina R. Rodrigues, Reindert J. Haarsma, Edmo J. D. Campos, and Tércio Ambrizzi.  The Impacts of Inter–El Niño Variability on the Tropical Atlantic and Northeast Brazil Climate.  _Journal of Climate_ , 24(13):3402–3422, July 2011.  ISSN 0894-8755, 1520-0442.  doi:10.1175/2011JCLI3983.1.
  * Capotondi et al. (2023) Antonietta Capotondi, Shayne McGregor, Michael J. McPhaden, Sophie Cravatte, Neil J. Holbrook, Yukiko Imada, Sara C. Sanchez, Janet Sprintall, Malte F. Stuecker, Caroline C. Ummenhofer, Mathias Zeller, Riccardo Farneti, Giorgio Graffino, Shijian Hu, Kristopher B. Karnauskas, Yu Kosaka, Fred Kucharski, Michael Mayer, Bo Qiu, Agus Santoso, Andréa S. Taschetto, Fan Wang, Xuebin Zhang, Ryan M. Holmes, Jing-Jia Luo, Nicola Maher, Cristian Martinez-Villalobos, Gerald A. Meehl, Rajashree Naha, Niklas Schneider, Samantha Stevenson, Arnold Sullivan, Peter van Rensch, and Tongtong Xu.  Mechanisms of tropical Pacific decadal variability.  _Nature Reviews Earth & Environment_, 4(11):754–769, November 2023.  ISSN 2662-138X.  doi:10.1038/s43017-023-00486-x.
  * Miller et al. (1994) Arthur J. Miller, Daniel R. Cayan, Tim P. Barnett, Nicholas E. Graham, and Josef M. Oberhuber.  The 1976-77 Climate Shift of the Pacific Ocean.  _Oceanography_ , 7(1):21–26, 1994.  ISSN 1042-8275.
  * McPhaden (2012) Michael J. McPhaden.  A 21st century shift in the relationship between ENSO SST and warm water volume anomalies.  _Geophys. Res. Lett._ , 39(9), May 2012.  ISSN 0094-8276.  doi:10.1029/2012GL051826.
  * Grothe et al. (2020) Pamela R. Grothe, Kim M. Cobb, Giovanni Liguori, Emanuele Di Lorenzo, Antonietta Capotondi, Yanbin Lu, Hai Cheng, R. Lawrence Edwards, John R. Southon, Guaciara M. Santos, Daniel M. Deocampo, Jean Lynch-Stieglitz, Tianran Chen, Hussein R. Sayani, Diane M. Thompson, Jessica L. Conroy, Andrea L. Moore, Kayla Townsend, Melat Hagos, Gemma O’Connor, and Lauren T. Toth.  Enhanced El Niño–Southern Oscillation Variability in Recent Decades.  _Geophysical Research Letters_ , 47(7):e2019GL083906, 2020.  ISSN 1944-8007.  doi:10.1029/2019GL083906.
  * Cai et al. (2023) Wenju Cai, Benjamin Ng, Tao Geng, Fan Jia, Lixin Wu, Guojian Wang, Yu Liu, Bolan Gan, Kai Yang, Agus Santoso, Xiaopei Lin, Ziguang Li, Yi Liu, Yun Yang, Fei-Fei Jin, Mat Collins, and Michael J. McPhaden.  Anthropogenic impacts on twentieth-century ENSO variability changes.  _Nature Reviews Earth & Environment_, 4(6):407–418, June 2023.  ISSN 2662-138X.  doi:10.1038/s43017-023-00427-8.
  * Dieppois et al. (2021) Bastien Dieppois, Antonietta Capotondi, Benjamin Pohl, Kwok Pan Chun, Paul-Arthur Monerie, and Jonathan Eden.  ENSO diversity shows robust decadal variations that must be captured for accurate future projections.  _Communications Earth & Environment_, 2(1):212, October 2021.  ISSN 2662-4435.  doi:10.1038/s43247-021-00285-6.
  * Lou et al. (2023) Jiale Lou, Matthew Newman, and Andrew Hoell.  Multi-decadal variation of ENSO forecast skill since the late 1800s.  _npj Climate and Atmospheric Science_ , 6(1):1–14, July 2023.  ISSN 2397-3722.  doi:10.1038/s41612-023-00417-z.
  * Lawman et al. (2022) Allison E. Lawman, Pedro N. Di Nezio, Judson W. Partin, Sylvia G. Dee, Kaustubh Thirumalai, and Terrence M. Quinn.  Unraveling forced responses of extreme El Niño variability over the Holocene.  _Science Advances_ , 8(9):eabm4313, March 2022\.  doi:10.1126/sciadv.abm4313.
  * Cai et al. (2021) Wenju Cai, Agus Santoso, Matthew Collins, Boris Dewitte, Christina Karamperidou, Jong-Seong Kug, Matthieu Lengaigne, Michael J. McPhaden, Malte F. Stuecker, Andréa S. Taschetto, Axel Timmermann, Lixin Wu, Sang-Wook Yeh, Guojian Wang, Benjamin Ng, Fan Jia, Yun Yang, Jun Ying, Xiao-Tong Zheng, Tobias Bayr, Josephine R. Brown, Antonietta Capotondi, Kim M. Cobb, Bolan Gan, Tao Geng, Yoo-Geun Ham, Fei-Fei Jin, Hyun-Su Jo, Xichen Li, Xiaopei Lin, Shayne McGregor, Jae-Heung Park, Karl Stein, Kai Yang, Li Zhang, and Wenxiu Zhong.  Changing El Niño–Southern Oscillation in a warming climate.  _Nature Reviews Earth & Environment_, 2(9):628–644, September 2021.  ISSN 2662-138X.  doi:10.1038/s43017-021-00199-z.
  * Pascolini-Campbell et al. (2015) M. Pascolini-Campbell, D. Zanchettin, O. Bothe, C. Timmreck, D. Matei, J. H. Jungclaus, and H. F. Graf.  Toward a record of Central Pacific El Niño events since 1880.  _Theoretical and Applied Climatology_ , 119(1-2):379–389, January 2015.  ISSN 14344483.  doi:10.1007/s00704-014-1114-2.
  * Yu and Kim (2013) Jin-Yi Yu and Seon Tae Kim.  Identifying the types of major El Niño events since 1870.  _International Journal of Climatology_ , 33(8):2105–2112, June 2013.  ISSN 08998418.  doi:10.1002/joc.3575.
  * Capotondi et al. (2020a) Antonietta Capotondi, Andrew T. Wittenberg, Jong-Seong Kug, Ken Takahashi, and Michael J. McPhaden.  ENSO Diversity.  In _El Niño Southern Oscillation in a Changing Climate_ , chapter 4, pages 65–86. American Geophysical Union (AGU), 2020a.  ISBN 978-1-119-54816-4.  doi:10.1002/9781119548164.ch4.
  * Abdelkader Di Carlo et al. (2023) Isma Abdelkader Di Carlo, Pascale Braconnot, Matthieu Carré, Mary Elliot, and Olivier Marti.  Different Methods in Assessing El Niño Flavors Lead to Opposite Results.  _Geophysical Research Letters_ , 50(15):e2023GL104558, 2023.  ISSN 1944-8007.  doi:10.1029/2023GL104558.
  * Ashok et al. (2007) Karumuri Ashok, Swadhin K. Behera, Suryachandra A. Rao, Hengyi Weng, and Toshio Yamagata.  El Niño Modoki and its possible teleconnection.  _Journal of Geophysical Research: Oceans_ , 112(11):C11007, November 2007.  ISSN 21699291.  doi:10.1029/2006JC003798.
  * Takahashi et al. (2011) K. Takahashi, A. Montecinos, K. Goubanova, and B. Dewitte.  ENSO regimes: Reinterpreting the canonical and Modoki El Niño.  _Geophysical Research Letters_ , 38(10):L10704, May 2011.  ISSN 00948276.  doi:10.1029/2011GL047364.
  * Takahashi and Dewitte (2016) Ken Takahashi and Boris Dewitte.  Strong and moderate nonlinear El Niño regimes.  _Climate Dynamics_ , 46(5-6):1627–1645, March 2016.  ISSN 14320894.  doi:10.1007/s00382-015-2665-3.
  * Cai et al. (2018) Wenju Cai, Guojian Wang, Boris Dewitte, Lixin Wu, Agus Santoso, Ken Takahashi, Yun Yang, Aude Carréric, and Michael J. McPhaden.  Increased variability of eastern Pacific El Niño under greenhouse warming.  _Nature_ , 564(7735):201–206, December 2018.  ISSN 14764687.  doi:10.1038/s41586-018-0776-9.
  * Shin et al. (2021) Na-Yeon Shin, Jong-Seong Kug, F. S. McCormack, and Neil J. Holbrook.  The Double-Peaked El Niño and Its Physical Processes.  _Journal of Climate_ , 34(4):1291–1303, February 2021.  ISSN 0894-8755, 1520-0442.  doi:10.1175/JCLI-D-20-0402.1.
  * Santoso et al. (2017) Agus Santoso, Michael J. Mcphaden, and Wenju Cai.  The Defining Characteristics of ENSO Extremes and the Strong 2015/2016 El Niño.  _Reviews of Geophysics_ , 55(4):1079–1129, 2017\.  ISSN 1944-9208.  doi:10.1002/2017RG000560.
  * Paek et al. (2017) Houk Paek, Jin-Yi Yu, and Chengcheng Qian.  Why were the 2015/2016 and 1997/1998 extreme El Niños different?  _Geophysical Research Letters_ , 44(4):1848–1856, 2017.  ISSN 1944-8007.  doi:10.1002/2016GL071515.
  * Parsons et al. (2004) Lance Parsons, Ehtesham Haque, and Huan Liu.  Subspace clustering for high dimensional data: A review.  _SIGKDD Explor. Newsl._ , 6(1):90–105, June 2004\.  ISSN 1931-0145.  doi:10.1145/1007730.1007731.
  * Schwarz (1978) Gideon Schwarz.  Estimating the Dimension of a Model.  _The Annals of Statistics_ , 6(2):461–464, March 1978.  ISSN 0090-5364, 2168-8966.  doi:10.1214/aos/1176344136.
  * Ham and Kug (2012) Yoo-Geun Ham and Jong-Seong Kug.  How well do current climate models simulate two types of El Nino?  _Climate Dynamics_ , 39(1-2):383–398, July 2012\.  ISSN 0930-7575, 1432-0894.  doi:10.1007/s00382-011-1157-3.
  * Karamperidou et al. (2017) Christina Karamperidou, Fei-Fei Jin, and Jessica L. Conroy.  The importance of ENSO nonlinearities in tropical pacific response to external forcing.  _Climate Dynamics_ , 49(7):2695–2704, October 2017.  ISSN 1432-0894.  doi:10.1007/s00382-016-3475-y.
  * Thual and Dewitte (2023) Sulian Thual and Boris Dewitte.  ENSO complexity controlled by zonal shifts in the Walker circulation.  _Nature Geoscience_ , 16(4):328–332, April 2023\.  ISSN 1752-0908.  doi:10.1038/s41561-023-01154-x.
  * Fedorov et al. (2015) Alexey V. Fedorov, Shineng Hu, Matthieu Lengaigne, and Eric Guilyardi.  The impact of westerly wind bursts and ocean initial state on the development, and diversity of El Niño events.  _Climate Dynamics_ , 44(5):1381–1401, March 2015\.  ISSN 1432-0894.  doi:10.1007/s00382-014-2126-4.
  * Capotondi et al. (2018) Antonietta Capotondi, Prashant D. Sardeshmukh, and Lucrezia Ricciardulli.  The Nature of the Stochastic Wind Forcing of ENSO.  _Journal of Climate_ , 31(19):8081–8099, October 2018.  ISSN 0894-8755, 1520-0442.  doi:10.1175/JCLI-D-17-0842.1.
  * Puy et al. (2019) Martin Puy, Jérôme Vialard, Matthieu Lengaigne, Eric Guilyardi, Pedro N. DiNezio, Aurore Voldoire, Magdalena Balmaseda, Gurvan Madec, Christophe Menkes, and Michael J. Mcphaden.  Influence of Westerly Wind Events stochasticity on El Niño amplitude: The case of 2014 vs. 2015.  _Climate Dynamics_ , 52(12):7435–7454, June 2019\.  ISSN 1432-0894.  doi:10.1007/s00382-017-3938-9.
  * Rayner et al. (2003) N. A. Rayner, D. E. Parker, E. B. Horton, C. K. Folland, L. V. Alexander, D. P. Rowell, E. C. Kent, and A. Kaplan.  Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late nineteenth century.  _J. Geophys. Res. Atmos._ , 108(D14):4407, July 2003.  ISSN 0148-0227.  doi:10.1029/2002JD002670.
  * Liu et al. (2022) Chao Liu, Wenjun Zhang, Fei-Fei Jin, Malte F. Stuecker, and Licheng Geng.  Equatorial Origin of the Observed Tropical Pacific Quasi-Decadal Variability From ENSO Nonlinearity.  _Geophysical Research Letters_ , 49(10):e2022GL097903, 2022.  ISSN 1944-8007.  doi:10.1029/2022GL097903.
  * Meehl et al. (2021) Gerald A. Meehl, Haiyan Teng, Antonietta Capotondi, and Aixue Hu.  The role of interannual ENSO events in decadal timescale transitions of the Interdecadal Pacific Oscillation.  _Climate Dynamics_ , 57(7):1933–1951, October 2021.  ISSN 1432-0894.  doi:10.1007/s00382-021-05784-y.
  * Capotondi and Sardeshmukh (2017) Antonietta Capotondi and Prashant D. Sardeshmukh.  Is El Niño really changing?  _Geophysical Research Letters_ , 44(16):8548–8556, August 2017.  ISSN 19448007.  doi:10.1002/2017GL074515.
  * Cai et al. (2015) Wenju Cai, Guojian Wang, Agus Santoso, Michael J. McPhaden, Lixin Wu, Fei-Fei Jin, Axel Timmermann, Mat Collins, Gabriel Vecchi, Matthieu Lengaigne, Matthew H. England, Dietmar Dommenget, Ken Takahashi, and Eric Guilyardi.  Increased frequency of extreme La Niña events under greenhouse warming.  _Nature Climate Change_ , 5(2):132–137, February 2015.  ISSN 1758-6798.  doi:10.1038/nclimate2492.
  * Geng et al. (2023) Tao Geng, Fan Jia, Wenju Cai, Lixin Wu, Bolan Gan, Zhao Jing, Shujun Li, and Michael J. McPhaden.  Increased occurrences of consecutive La Niña events under global warming.  _Nature_ , 619(7971):774–781, July 2023.  ISSN 1476-4687.  doi:10.1038/s41586-023-06236-9.
  * Gan et al. (2023) Ruyu Gan, Qi Liu, Gang Huang, Kaiming Hu, and Xichen Li.  Greenhouse warming and internal variability increase extreme and central Pacific El Niño frequency since 1980.  _Nature Communications_ , 14(1):394, December 2023\.  ISSN 20411723.  doi:10.1038/s41467-023-36053-7.
  * Lee and McPhaden (2010) Tong Lee and Michael J. McPhaden.  Increasing intensity of El Niño in the central-equatorial Pacific.  _Geophysical Research Letters_ , 37(14):L14603, July 2010.  ISSN 00948276.  doi:10.1029/2010GL044007.
  * McPhaden et al. (2011) M. J. McPhaden, T. Lee, and D. McClurg.  El Niño and its relationship to changing background conditions in the tropical Pacific Ocean.  _Geophysical Research Letters_ , 38(15), 2011.  ISSN 1944-8007.  doi:10.1029/2011GL048275.
  * Ayar et al. (2023) Pradeebane Vaittinada Ayar, David S. Battisti, Camille Li, Martin King, Mathieu Vrac, and Jerry Tjiputra.  A Regime View of ENSO Flavors Through Clustering in CMIP6 Models.  _Earth’s Future_ , 11(11):e2022EF003460, 2023\.  ISSN 2328-4277.  doi:10.1029/2022EF003460.
  * Capotondi et al. (2020b) A. Capotondi, C. Deser, A. S. Phillips, Y. Okumura, and S. M. Larson.  ENSO and Pacific Decadal Variability in the Community Earth System Model Version 2.  _Journal of Advances in Modeling Earth Systems_ , 12(12):e2019MS002022, 2020b.  ISSN 1942-2466.  doi:10.1029/2019MS002022.
  * Dommenget et al. (2013) Dietmar Dommenget, Tobias Bayr, and Claudia Frauen.  Analysis of the non-linearity in the pattern and time evolution of El Niño southern oscillation.  _Climate Dynamics_ , 40(11):2825–2847, June 2013\.  ISSN 1432-0894.  doi:10.1007/s00382-012-1475-0.
  * Zhang et al. (2019) H.-M. Zhang, B. Huang, J. H. Lawrimore, M. J. Menne, and T. M. Smith.  NOAA Global Surface Temperature Dataset (NOAAGlobalTemp), Version 5.0, 2019.
  * Hersbach et al. (2020) Hans Hersbach, Bill Bell, Paul Berrisford, Shoji Hirahara, Julien Nicolas, Carole Peubey, Raluca Radu, Dinand Schepers, Adrian Simmons, Cornel Soci, Saleh Abdalla, Xavier Abellan, Gianpaolo Balsamo, Peter Bechtold, Gionata Biavati, Jean Bidlot, Massimo Bonavita, Giovanna De Chiara, Per Dahlgren, Dick Dee, Michail Diamantakis, Rossana Dragani, Johannes Flemming, Richard Forbes, Manuel Fuentes, Alan Geer, Leo Haimberger, Sean Healy, Robin J. Hogan, Sarah Keeley, Patrick Laloyaux, Philippe Lopez, Cristina Lupu, Gabor Radnoti, Patricia de Rosnay, Iryna Rozum, Freja Vamborg, and Sebastien Villaume.  The ERA5 global reanalysis.  _Q. J. R. Meteorolog. Soc._ , 146(730):1999–2049, July 2020.  ISSN 0035-9009.  doi:10.1002/qj.3803.
  * COBE (2006) COBE.  COBE Sea Surface Temperature: NOAA Physical Sciences Laboratory COBE Sea Surface Temperature.  https://psl.noaa.gov/data/gridded/data.cobe.html, 2006.
  * ORAS5 (2021) ORAS5.  ORAS5 global ocean reanalysis monthly data from 1958 to present, 2021\.
  * Giese and Ray (2011) Benjamin S. Giese and Sulagna Ray.  El Niño variability in simple ocean data assimilation (SODA), 1871-2008.  _Journal of Geophysical Research: Oceans_ , 116(2):C02024, 2011.  ISSN 21699291.  doi:10.1029/2010JC006695.
  * Behringer et al. (1998) David W. Behringer, Ming Ji, and Ants Leetmaa.  An Improved Coupled Model for ENSO Prediction and Implications for Ocean Initialization. Part I: The Ocean Data Assimilation System.  _Mon. Weather Rev._ , 126(4):1013–1021, April 1998.  ISSN 1520-0493.  doi:10.1175/1520-0493(1998)126<1013:AICMFE>2.0.CO;2.
  * Laloyaux et al. (2018) Patrick Laloyaux, Eric de Boisseson, Magdalena Balmaseda, Jean-Raymond Bidlot, Stefan Broennimann, Roberto Buizza, Per Dalhgren, Dick Dee, Leopold Haimberger, Hans Hersbach, Yuki Kosaka, Matthew Martin, Paul Poli, Nick Rayner, Elke Rustemeier, and Dinand Schepers.  CERA-20C: A Coupled Reanalysis of the Twentieth Century.  _J. Adv. Model. Earth Syst._ , 10(5):1172–1195, May 2018.  ISSN 1942-2466.  doi:10.1029/2018MS001273.
  * Schlör (2023) Jakob Schlör.  LatentGMM: An unsupervised fuzzy clustering approach for ENSO.  Zenodo, November 2023.