RESEARCH ARTICLE
10.1029/2019MS002022
Special Section:
Community Earth System
Model Version 2 (CESM2)
Special Collection
Key Points:• El Niño–Southern Oscillation in themodel exhibits realistic timescale,precursors, temporal evolution, andteleconnections• The El Niño–Southern Oscillation
amplitude is about 30% larger
than observed, with anomalies
displaced too far west than observed• The model Paciﬁc Decadal
Variability has a realistic
spatial pattern

Correspondence to:
A. Capotondi,
antonietta.capotondi@noaa.gov

Citation:
Capotondi, A., Deser, C., Phillips, A. S.,
Okumura, Y., & Larson, S. M. (2020).
ENSO and Paciﬁc Decadal Variability
in the Community Earth System Model
Version 2. Journal of Advances inModeling Earth Systems, 12,e2019MS002022. https://doi.org/
10.1029/2019MS002022
Received 26 DEC 2019
Accepted 29 APR 2020
Accepted article online 29 OCT 2020

ENSO and Paciﬁc Decadal Variability in the Community
Earth System Model Version 2
A. Capotondi1,2, C. Deser3, A. S. Phillips3, Y. Okumura4, and S. M. Larson5

1

Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, CO, USA,
Physical Sciences Laboratory, NOAA, Boulder, CO, USA, 3Climate and Global Dynamics Division, NCAR, Boulder,
CO, USA, 4Institute for Geophysics, University of Texas at Austin, Austin, TX, USA, 5Department of Marine, Earth, andAtmospheric Sciences, North Carolina State University, Raleigh, NC, USA

2

Abstract This study presents a description of the El Niño–Southern Oscillation (ENSO) and Paciﬁc
Decadal Variability (PDV) in a multicentury preindustrial simulation of the Community Earth System
Model Version 2 (CESM2). The model simulates several aspects of ENSO relatively well, including dominanttimescale, tropical and extratropical precursors, composite evolution of El Niño and La Niña events, and
ENSO teleconnections. The good model representation of ENSO spectral characteristics is consistent
with the spatial pattern of the anomalous equatorial zonal wind stress in the model, which results in thecorrect adjustment timescale of the equatorial thermocline according to the delayed/recharge oscillator
paradigms, as also reﬂected in the realistic time evolution of the equatorial Warm Water Volume. PDV in themodel exhibits a pattern that is very similar to the observed, with realistic tropical and South Paciﬁcsignatures which were much weaker in some of the CESM2 predecessor models. The tropical component of
PDV also shows an association with ENSO decadal modulation which is similar to that found inobservations. However, the ENSO amplitude is about 30% larger than observed in the preindustrial CESM2
simulation, and even larger in the historical ensemble, perhaps as a result of anthropogenic inﬂuences.
In contrast to observations, the largest variability is found in the central Paciﬁc rather than in the eastern
Paciﬁc, a discrepancy that somewhat hinders the model's ability to represent a full diversity in El Niño
spatial patterns and appears to be associated with an unrealistic conﬁnement of the precipitation anomalies
to the western Paciﬁc.
Plain Language Summary The Community Earth System Model Version 2 (CESM2) is the latest
version of the Earth System models developed at the National Center for Atmospheric Research in
Boulder, CO. This study examines how well CESM2 simulates the El Niño–Southern Oscillation (ENSO), theleading mode of climate variability in the tropical Paciﬁc at interannual timescales, with a large
inﬂuence on the global climate and very important societal impacts. The modeled ENSO exhibits a larger
amplitude than observed, with anomalies displaced further west than in observations, but withdominant timescale, temporal evolution, precursors, and teleconnections in good agreement withobservations. This study also examines the model performance in simulating climate variability at decadal
timescales in the Paciﬁc sector. The spatial pattern of Paciﬁc Decadal Variability and the relationship between
decadal variations in the tropical Paciﬁc and decadal ENSO modulation are well simulated by CESM2.

1. Introduction©2020. The Authors.
This is an open access article under theterms of the Creative Commons
Attribution License, which permits use,
distribution and reproduction in any
medium, provided the original work is
properly cited.

CAPOTONDI ET AL.

The El Niño–Southern Oscillation (ENSO) is the dominant mode of variability in the tropical Paciﬁc at interannual timescales. This naturally occurring phenomenon is characterized by warm conditions in the central/eastern equatorial Paciﬁc, known as El Niño events, which occur every 2 to 7 years and alternatewith the cold La Niña phase. A sea level pressure seesaw, known as the “Southern Oscillation,” constitutes
the atmospheric component of this coupled phenomenon (McPhaden et al., 2006). The tropical Paciﬁc sea
surface temperature (SST) anomalies associated with ENSO alter tropical convection and trigger atmospheric teleconnections which are responsible for worldwide temperature and precipitation impacts of critical societal importance (Glantz, 2000; Ropelewski & Halpert, 1987; Tippett & Barnston, 2008).
The evolution of the equatorial Paciﬁc upper‐ocean heat content provides memory to the coupled equatorial
system, and is primarily responsible for the quasi‐cyclic nature of ENSO. However, stochastic atmospheric
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and oceanic variability within the tropical Paciﬁc, as well as inﬂuences from the extratropical Paciﬁc(Chiang & Vimont, 2004; Zhang et al., 2014) and from other ocean basins (Cai et al., 2019; Wang, 2019),
which themselves may be stochastic in nature, result in deviations of the ENSO evolution from a regularcycle, and may contribute to event‐to‐event differences in spatial pattern, amplitude and propagation characteristics. Slow variations of the tropical background conditions may also lead to a low‐frequency modulation of ENSO characteristics (Capotondi & Sardeshmukh, 2017; Fedorov & Philander, 2000).
A large body of literature has recently emphasized the diversity in ENSO amplitudes and spatial patterns(Cai et al., 2018; Capotondi, Wittenberg, et al., 2015; Okumura, 2019; Taschetto et al., 2014; Timmermann
et al., 2018, and references therein) which may result in different ENSO impacts both within the tropicalPaciﬁc (Dewitte et al., 2012; Gierach et al., 2012; Lee et al., 2014; Radenac et al., 2012; Turk et al., 2011)
and remotely (Ashok et al., 2007; Larkin & Harrison, 2005; Patricola et al., 2019, among others). El Niño
events with the largest anomalies in the far eastern Paciﬁc produce intense rainfall in that usually coldand dry region. These events also greatly reduce equatorial upwelling in the eastern Paciﬁc with dramaticconsequences for ocean productivity and marine life. Warm ENSO events with largest anomalies locatedin the central equatorial Paciﬁc, on the other hand, may be associated with neutral and cooler conditionsin the eastern Paciﬁc, but lead to a reduction of marine productivity in the area where the largest anomalies
occur (Gierach et al., 2012). The location of ENSO‐related SST anomalies appears to also affect atmosphericteleconnections. For instance, SST anomalies in the central‐western tropical Paciﬁc appear to be more effective in forcing the Paciﬁc North American pattern (PNA) than anomalies in the eastern Paciﬁc where “canonical” El Niño events typically have their largest signal (Barsugli & Sardeshmukh, 2002). The central‐westernequatorial Paciﬁc seems to also play a key role in forcing ocean warming along the U.S. West Coast(Capotondi et al., 2019; Shi et al., 2019), while precipitation in Southern California appears to respond morestrongly to SST anomalies in the eastern equatorial Paciﬁc (Shi et al., 2019). The presence of a large level ofatmospheric noise may, however, obscure the inﬂuence of ENSO diversity on atmospheric teleconnections
and associated temperature and precipitation impacts over North America (Deser et al., 2018).
The complexity of ocean‐atmosphere feedbacks underlying ENSO evolution and diverse expressions makes
the simulation of ENSO by climate models extremely challenging. A steady progress in the representation of
ENSO has been documented (Bellenger et al., 2014; Guilyardi et al., 2012) across the generations of models
participating in the Climate Model Intercomparison Projects Phases 3 and 5 (CMIP3 and CMIP5). For example, the large spread in ENSO amplitude exhibited by the CMIP3 models was largely reduced in the CMIP5
archive, and the ENSO seasonal phase locking was found modestly improved in the CMIP5 relatively to
CMIP3 multimodel ensembles (Bellenger et al., 2014). Important improvements were detected in the
National Center for Atmospheric Research Community Climate System Model Version 4 (NCAR‐CCSM4)
relative the previous model version CCSM3 (Deser et al., 2012). CCSM4 and CCSM3 are the predecessorsof the Community Earth System Models versions 1 and 2 (CESM1 and CESM2), and therefore are of interest
here. Unlike CCSM3, which exhibited a quasi‐regular biennial ENSO behavior, CCSM4 had a broader spectral peak with a dominant timescale closer to the observed, an improvement that was attributed to a more
realistic spatial pattern of the wind stress response to ENSO SST anomalies (Capotondi et al., 2006), and toa larger level of atmospheric noise (Neale et al., 2008). Relative to CCSM3, CCSM4 was also able to more realistically simulate observed asymmetries in spatial pattern and duration between El Niño and La Niña events(Deser et al., 2012).
In spite of these improvements, notable biases in the representation of ENSO in climate models persist. Oneof these biases is the excessive westward extension of the SST anomalies associated with ENSO, a bias that
could affect the models' ability to produce realistic teleconnections (Bellenger et al., 2014). A related issue isthe models' difﬁculty to simulate the observed broad range of El Niño spatial patterns (Capotondi, Ham,et al., 2015; Capotondi et al., 2020). This problem appears to arise from the intensity of the eastern Paciﬁc“Cold Tongue,” which in the models tends to be larger than in nature (Ham & Kug, 2012). Since anomalous
convective activity depends on the total SST relative to the tropical mean SST (He et al., 2018), an excessively
cold mean eastern tropical Paciﬁc will be unable to support local convection, even in the presence of positive
SST anomalies, resulting in an atmospheric response conﬁned to the western part of the basin, and a more
limited range of SST anomaly patterns (Ham & Kug, 2012; Kug et al., 2012).
Apart from the interannual variations associated with ENSO in the tropical Paciﬁc, the Paciﬁc sector also
exhibits variability at decadal and multidecadal timescales (Deser et al., 2004; Mantua et al., 1997;

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Newman et al., 2016; Zhang et al., 1997). The dominant pattern of variability in the North Paciﬁc was
identiﬁed as the leading empirical orthogonal function (EOF) of monthly SST anomalies poleward of 20°
N, and termed the Paciﬁc Decadal Oscillation (PDO) by Mantua et al. (1997). The PDO is characterized byanomalies of one sign in the central North Paciﬁc, and anomalies of the opposite sign along the west coastof North America and the Gulf of Alaska. EOF analysis of low‐pass‐ﬁltered SST anomalies over the entire
Paciﬁc basin reveals a pattern that is quasi‐symmetric about the equator, known as the Interdecadal
Paciﬁc Oscillation (IPO, Power et al., 1999), and “ENSO like” in the tropical Paciﬁc (Zhang et al., 1997).
While both the PDO and IPO have been viewed as “modes” of variability, and related to important climaticand ecological impacts, recent research (Newman et al., 2016) has shown that the PDO should be seen,
instead, as the result of a combination of different processes, including ENSO teleconnections, ocean mixed
layer “re‐emergence” mechanisms (Alexander et al., 1999), and slow propagation of midlatitude Rossby
waves (Kwon & Deser, 2007). In addition, although the PDO and IPO patterns are associated with variability
at decadal‐interdecadal timescales, no statistically signiﬁcant peak is usually found in the spectra of theirassociated time series, suggesting that these low‐frequency variations may simply represent thelow‐frequency tail of a red‐noise process, rather than a real oscillatory behavior. For these reasons, we willrefer to these decadal variations as “Paciﬁc Decadal Variability” (PDV).
In this paper, we document ENSO and PDV in the latest version of the National Center for AtmosphericResearch (NCAR) Community Earth System Model Version 2.1 (CESM2.1). Given the key role played by
ENSO in the global climate system, the model's ability to realistically simulate ENSO is of paramount importance. We start by describing the model, the observational data sets used for its validation, and the Linear
Inverse Modeling (LIM) approach employed for model diagnostics in section 2. In section 3, we examine
ENSO in CESM2 relative to observations and to previous NCAR model versions. We will consider, in particular, ENSO temporal evolution and spectral characteristics, precursors, spatial diversity and teleconnections. PDV is brieﬂy described in section 4, and conclusions are drawn in section 5.

2. Model Descriptions, Observational Data Sets, and LIMs
2.1. CESM2
CESM2 is the latest version of the NCAR suite of climate and earth system models. It includes fullyinteractive ocean, atmosphere, ice, land, and ocean biogeochemical components, building on component
models used in previous versions, but with important improvements in each of them. Speciﬁcally, theatmospheric component, the Community Atmospheric Model version 6 (CAM6) has improved parameterizations of all physical processes, the most notable of which is a new representation of convection
through the uniﬁed turbulent scheme Cloud Layers Uniﬁed by Binormals (CLUBB, Golaz et al., 2002).
The ocean component is based on the Parallel Ocean Program Version 2 (POP2; Smith et al., 2010) withseveral physical and numerical improvements, including, among others, the use of prognostic chlorophyll
for short‐wave absorption, and the inclusion of a wave model and associated Langmuir mixing parameterization (Li et al., 2016). Additional details on all the component models can be found in Danabasoglu
et al. (2020).
CESM2 has contributed simulations to the Climate Model Intercomparison Project Phase 6 (CMIP6), including preindustrial, historical, and future scenario simulations. For this study we will focus primarily on thepreindustrial control simulation (piControl) under 1850 radiative forcing conditions, as its millennial duration allows a robust characterization of ENSO and PDV. A 11‐member ensemble of historical simulations(HIST) and a 10‐member ensemble of historical AMIP simulations with speciﬁed observed SSTs are also
used for a few analyses to provide a more direct comparison with the observational record. All simulations
are conducted at a nominal 1° horizontal resolution. The piControl is 1,200 years long, but due to the presence of trends during the ﬁrst 200 years, our analyses are restricted to model years 201–1,200. Details of
the spin‐up and initialization procedures for the piControl and HIST ensemble are given in Danabasoglu
et al. (2020).
For some of the diagnostics, we compare CESM2 with previous model versions, speciﬁcally Community
Climate Model Version 4 (CCSM4; Gent et al., 2011) and CESM Version 1 (CESM1; Hurrell et al., 2013).
Extensive documentation of ENSO and PDV in CCSM4 was provided in Deser et al. (2012). A dynamical
analysis of ENSO in CESM1 is given in DiNezio, Deser, Karspeck, et al. (2017) and DiNezio, Deser,
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Okumura, and Karspeck (2017). For consistency with the length of the CESM2 piControl record analyzed,
we used comparable durations for the preindustrial control runs of CCSM4 (model years 301–1,300) andCESM1 (model years 1,201–2,200).
2.2. Observational Data Sets
We use the following data sets for model validation.
1. SST from the NOAA Extended Reconstructed SST version 5 (ERSSTv5; Huang et al., 2017) over the period 1900–2018.
2. Sea level pressure (SLP) from the National Center for Environmental Prediction (NCEP)‐NCAR
Reanalysis (Kalnay et al., 1996), and from ERA20C (Poli et al., 2016) updated with ERA‐Interim (Deeet al., 2011).
3. Precipitation from the NOAA reconstructed precipitation data set (Chen et al., 2002) and from GPCP
(Adler et al., 2003).
4. Surface winds from ERA5 (Hersbach et al., 2019) and surface wind stress from the NCEP‐Department ofEnergy (DOE) atmospheric reanalysis (Kanamitsu et al., 2002).
5. Sea surface height (SSH) from the European Center for Medium‐Range Weather Forecasting (ECMWF)
Ocean Reanalysis System 4 (ORAS4; Balmaseda et al., 2013), covering the period 1958–2015.
6. Near‐surface air temperature from Berkeley Earth Surface Temperature (Rohde et al., 2013).
2.3. Linear Inverse Model
To aid with model diagnostics, we use a Linear Inverse Model (LIM). LIMs are empirical models that havebeen extensively used to understand and predict ENSO (Penland & Sardeshmukh, 1995). In the LIM framework, the tropical Paciﬁc is described in terms of an anomaly state vector x, which contains information
about the key system variables. The evolution of x is then modeled according todx ¼ L x dt þ S r

pﬃﬃﬃﬃﬃ
dt;(1)

where the matrix L describes the predictable dynamics of the system, the matrix S represents the spatiallyvarying amplitude of the stochastic forcing, and r is a vector of random numbers drawn from a normal
distribution with zero mean and unit standard deviation. The operators L and S can be estimated directlyfrom the instantaneous and lagged covariance matrices of x. The leading eigenvectors of the L operator,
known as Empirical Normal Modes (ENMs), are nonorthogonal and damped and may have an oscillatorycomponent. In such a system, temporary growth is possible through a constructive superposition of theENMs, a property that allows the identiﬁcation of the optimal initial conditions conducive to the mature
ENSO phase. Thus, the representation of ENSO implied by Equation 1 is that of a damped oscillatorymode of variability energized by stochastic forcing, one of the commonly accepted ENSO paradigms(Wang et al., 2016). The stochastic term in 1 incorporates some of the fast atmospheric nonlinear feedbacks, resulting in a methodology that has proven very useful for ENSO modeling and prediction(Newman & Sardeshmukh, 2017). In this study, we will use the LIM approach for two purposes:(1) Objectively determine the optimal ENSO precursors (the optimal initial LIM structures) and (2)Assess the possible range of observed spectral estimates from multimillennia synthetic time series of x,
determined through the integration of 1, which, by construction, are consistent with the statistics of thedata used to train the LIM (Capotondi & Sardeshmukh, 2017). We construct LIMs for both observations
and CESM2, using SST and SSH as state variables. The observational LIM is trained on SST from
ERSSTv5 and SSH from ORAS4 over the period 1958–2014, while the CESM2 LIM is based on model years
201–1,200. To reduce the number of degrees of freedom, the SST and SSH anomalies are projected onto
their leading EOFs. We retain 20 SST and 10 SSH EOFs for both observations and CESM2, accounting
for 94% (72%) of the SST (SSH) variance in observations, and 86% (77%) of the variance in CESM2.

3. ENSO
3.1. Nino‐3.4 SST Variability
ENSO characteristics, such as amplitude and dominant timescale, are strongly dependent on the equatorial
Paciﬁc mean state (Fedorov & Philander, 2000). In particular, the mean zonal SST gradient, which is strongly
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Figure 1. Mean SST (white contours) and SST monthly standard deviation (color shading) for detrended ERSSTv5 over
1900–2018 (top left), and 1,000‐year segments of the preindustrial control simulations of CESM2 (top right), CESM1(bottom left), and CCSM4 (bottom right). Contour interval is 3°C and the thick white contour indicates the 27°C
isotherm.

affected by the strength of the eastern Paciﬁc “Cold Tongue,” was identiﬁed by Fedorov and Philander (2000)
as a key parameter for ENSO stability characteristics. The mean climatological SST conditions in CESM2 arecompared with ERSSTv5, CESM1 and CCSM4 in Figure 1. The intensity and zonal extent of the equatorial
Cold Tongue, as indicated by the westward penetration of the 27°C isotherm (thick white contour), appear to
be improved in CESM2 compared to CCSM4, and especially to CESM1, relative to the ERSSTv5 data set.
The standard deviation of monthly SST anomalies, where anomalies are computed as departures from thelong‐term monthly means, in the central/eastern tropical Paciﬁc are overestimated by about 30–40% in all
three models relative to ERSSTv5. Apart from the amplitude, the spatial pattern of the variability also shows
discrepancies with the observed. While ERSSTv5 exhibits the largest standard deviations in the far eastern
Paciﬁc, the largest standard deviations are achieved around 110°W in CCSM4, near 120°W and 180° in
CESM1, and near 180° in CESM2. SST variability is also overestimated by the models in the Kuroshio
Extension region and in the Bering Sea. CESM1 and CESM2 slightly underestimate the observed variability
in the Gulf of Alaska and along the northern part of the U.S. West Coast.
The Niño‐3.4 index, deﬁned as the area average of monthly SST anomalies in the region 5°S to 5°N, 170–120°
W, is a commonly used index to represent SST variability associated with ENSO (e.g., Trenberth et al., 2002).
The evolution of the Niño‐3.4 index over the piControl simulation of CESM2 is compared in Figure 2 withthe evolution of the Niño‐3.4 index from ERSSTv5 over the 1900–2018 period. Although the amplitude of
the Niño‐3.4 index in the model is overall larger than in ERSSTv5 (the Niño‐3.4 standard deviations are
0.87 for ERSSTv5 and 1.14 for CESM2 over the periods shown in Figure 2), with some extreme events as large
as 4°C in the model, its temporal evolution shows similar visual behavior to the observed in terms of dominant timescale and degree of irregularity. For example, prevailing La Niña conditions, similar to thoseobserved during 1942–1957, are also seen in CESM2 (e.g., during model years 352–368, light blue shading),
and periods dominated by warm events such as 1982–1998 in observations are also seen in CESM2 (e.g.,model years 565–578, yellow shading). The millennial‐long model time series also highlights the presenceof low‐frequency modulation of ENSO characteristics, with decadal periods characterized by a more regular,
quasi‐oscillatory ENSO behavior (e.g., during model years 240–260, and 1,080–1,092, pink shading) relative
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Figure 2. Time series of the monthly Niño‐3.4 index for ERSSTv5 over the 1900–2018 period (top panel) and for CESM2,
from model year 201 to 1,200 (Rows 2–6), with each row displaying a 200‐year segment of the Niño‐3.4 index.
Vertical axis ranges from −4°C to 4°C in all panels. Shading is used to highlight periods with different characteristicsof the Niño‐3.4 index as described in the text.

to other periods with a more irregular alternation of warm and cold events (e.g., years 440–485 and 940–980,
green shading). These decadal variations in the Niño‐3.4 characteristics, which were already noted by
Wittenberg (2009) for the GFDL_CM2.1 model and Deser et al. (2012) for CCSM4, open the question of
how robustly we can characterize ENSO from the relatively short instrumental records.
Observed ENSO events peak in boreal winter, with a minimum in late spring to early summer, as illustrated
by the monthly standard deviations of the ERSSTv5 Niño‐3.4 index in Figure 3 (left panels, red bars). Thisseasonal phase locking has been a difﬁcult aspect for climate models to simulate correctly (Bellenger
et al., 2014), with models often exhibiting a secondary peak in a different part of the year, or showing comparable standard deviations in boreal winter and spring–summer. CCSM4, CESM1, and CESM2 all achieve
their largest standard deviations in December and January, and a minimum in late spring–summer, consistent with ERSSTv5 (although the minimum in CESM1 and CESM2 is delayed by 1–2 months compared toobservations; Figure 3, left panels). The monthly standard deviations also highlight the larger ENSO amplitude in the models, especially CCSM4 and CESM2, relative to the observations. The observational values fall
well below the range of modeled values in CCSM4 and CESM2 in all months, while the monthly standard
deviations in CESM1 are more comparable with the observed.
The power spectrum of the Niño‐3.4 index from ERSSTv5 shows a broad maximum with timescales ranging
from approximately 2.5 to 8 years (Figure 3, right panels, red curve). The spectra of CESM2, CESM1, and
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Figure 3. Monthly standard deviations (left panels), autocorrelation functions (middle panels, x axis showing lags inmonths), and power spectra (right panels) of the detrended Niño‐3.4 index for the piControl simulations of CESM2(top row), CESM1 (middle row), CCSM4 (bottom row), and ERSST.v5 (red lines). The range of estimates for the models
were obtained by dividing their 1,000‐year Niño‐3.4 records in 18,119‐year partially overlapping segments. The
light blue shading in the middle (right) panels shows the minimum and maximum values of the autocorrelation (spectral
estimate) at each lag (frequency). The statistics of the monthly standard deviations in the left panels are
summarized through the use of boxplots and whiskers showing the minimum values (whiskers minima), ﬁrst quartiles(lower edge of the boxes), median (black lines), third quartiles (upper edge of the boxes), and maximum values(whiskers maxima) of the standard deviations for each month.

CCSM4 are dominated by a pronounced spectral peak which is well within the 2.5–8 years observational
range (Figure 3, right panels). The spectra conﬁrm that ENSO is stronger in the models than inobservations, especially in CCSM4 and CESM2, whose range of spectral estimates is above theobservational values at the dominant ENSO frequencies, while in CESM1 the observational spectrum falls
within the model range. Another way to characterize the ENSO temporal evolution is through the lag
autocorrelation function of the Niño‐3.4 index (Figure 3, middle panels). In all cases, the ﬁrst zerocrossing occurs at a lag of 11–12 months. The maximum negative correlation occurs at a lag of 18–
24 months for ERSSTv5, 23–24 months in CESM1 and CCSM4, and 18–21 months in CESM2. The
magnitude of the maximum negative correlation is larger in the models relative to observations, especiallyin CCSM4 and CESM1, perhaps an indication of a more consistent and larger amplitude transition to the
opposite phase of the ENSO cycle in the models.
For a more direct comparison of CESM2 and ERSSTv5 we repeat the calculation of the monthly standard
deviations, autocorrelation functions and spectra over the historical period 1958–2014 (Figure 4). We
establish the statistical signiﬁcance of the CESM2 historical estimates by using all 11 CESM2 historical
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Figure 4. Monthly standard deviation (left panels), autocorrelation function (middle panels), and power spectra(right panels) of the detrended Niño‐3.4 index during 1958–2014 for observations (ERSSTv5, top panels) and CESM2
historical simulations (bottom panels). The range of estimates for the CESM2 autocorrelation function and spectrum(light blue shading) are estimated using the 11‐member ensemble of the CESM2 historical simulations, while theobservational uncertainties are based on a 28,500‐year LIM integration, yielding ﬁve hundred 57‐year segments that areconsistent with the statistics of the 1958–2014 period used to train the LIM. The statistics of the monthly standard
deviations in the left panels are summarized through the use of boxplots and whiskers as in Figure 3. The blue curve inthe top‐right panel shows the average spectrum of the ﬁve hundred 57‐year segments of the LIM output. Note thedifferent vertical axes of the left and right panels between Figures 3 and 4.

simulations, while for the observations we use a “synthetic observational ensemble” obtained from amultimillennia LIM integration trained over the 1958–2014 period. The LIM is run for 28,500 years
yielding 500 57‐year segments that are used to estimate the observational uncertainty. The resulting
ensemble spread, a measure of the internal system noise, is shown by the light blue shading in the middle
and right panels of Figure 4. For the monthly standard deviations (Figure 4, left panels) boxplots are used
to deﬁne minimum and maximum values, as well as the ﬁrst, second (median) and third quartile of theprobability density function of the standard deviations. The ENSO amplitude in the CESM2 historicalensemble is larger than in the piControl (note that the vertical axes in Figure 4 are different than in
Figure 3), perhaps reﬂecting the inﬂuence of anthropogenic forcing on ENSO (Cai et al., 2018). As in
piControl, the monthly standard deviations achieve their largest values in December and January, with asummer minimum that is delayed by about 2 months in CESM2 relative to observations. The availabilityof several ensemble members allows the detection of a negative skewness in the CESM monthly standard
deviations. This asymmetry is not present in the distributions of monthly standard deviations obtained
from the LIM, likely due to the assumption of a Gaussian noise distribution of the LIM methodology. The
ensemble mean autocorrelation function of CESM2 over 1958–2014 is in very good agreement with theobserved, with the ﬁrst zero crossing at a lag of about 12 months, the negative minimum at a lag of 18–
24 months, and the second zero crossing at a lag of about 30 months. As for piControl, the CESM2
spectrum in the historical period displays a peak between 2.8–8 years in agreement with the observed, butwith an approximately 40% larger amplitude. This amplitude discrepancy is put in a broader perspectiveby the large range of spectral estimates that can arise purely from sampling variability, as assessed throughthe use of an ensemble of simulations that differ only by small changes in initial conditions. This large
level of uncertainty highlights how the availability of only one observational realization may hinder ourability to meaningfully compare models and observations, unless the simulation is long enough (e.g., thepiControl) to provide several samples for comparison, as in Figure 3.
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Figure 5. Regression of zonal wind stress upon the normalized Nino‐3.4 index for observations (zonal wind stress fromthe NCEP/DOE reanalysis over 1979–2018, and Niño‐3.4 index from detrended ERSSTv5 over the same time period,
top‐left) and CESM2 (years 201–1,200, bottom left) as a function of longitude and latitude, and their zonal average(right panels). Dashed line in the left panels shows the “center of mass” of the positive zonal wind stress anomalies
computed as the equatorial (2°S to 2°N) zonal wind stress anomaly weighted longitude between 140°E and 120°W. Rightpanels show the zonal average of the zonal wind stress, from 20°S to 20°N, with red used for the observations andblue used for CESM2. The latitudes of zero crossing in the right panels are used to deﬁne the meridional scale Ly of theanomalous zonal wind stress for both observations and model. Ly is 18.8° of latitude for the observations and 20°
for CESM2.

Previous studies (An & Wang, 2000; Capotondi et al., 2006; Kirtman, 1997) have related the dominant ENSO
timescale to the spatial structure of the zonal wind stress response to the ENSO SST anomalies. Wind stressanomalies that are located further to the east, and have a broader meridional scale Ly are associated withlonger ENSO timescales. These zonal wind stress anomalies are associated with Ekman pumping anomalies
that can excite off‐equatorial Rossby waves further away from the western boundary and from the equator.
The decrease of the Rossby wave phase speed with latitude and the longer propagation distance from thegeneration longitude to the western ocean boundary lead to a longer adjustment timescale of the equatorial
thermocline, and a longer ENSO timescale. The spatial patterns of the zonal wind stress associated with
ENSO in observations and CESM2 are compared in Figure 5. The patterns are obtained by regressing thezonal wind stress at each grid point on the normalized Niño‐3.4 index. The zonal wind stress from the
NCEP/DOE reanalysis, available over the period 1979–2018 is used as the observational estimate. The spatial
pattern of the zonal wind stress in CESM2 has a somewhat excessive longitudinal elongation near the equator with a sharp transition to anomalies of the opposite sign along 4°N, from about 150°E to 120°W.
However, it is centered at a similar longitude as observations (177°E vs. 174°E), and its meridional width
Ly is very comparable with the observed (20° vs. 18.8° degrees of latitude), consistent with the similar
ENSO timescale in the model and observations. A similar analysis reported by Deser et al. (2012) for
CCSM4 and CCSM3 indicated a large improvement of the spatial pattern of the zonal wind stress in
CCSM4 relative to CCSM3, which was viewed as an important contributing factor to the more realistic spectral characteristics of ENSO in CCSM4 relative to its predecessor CCSM3. These improved characteristics are
retained in CESM2 (and CESM1). Our linear analysis of the wind stress response to the Niño‐3.4 variations
does not capture the asymmetry of the wind stress anomalies during warm and cold events, with anomalies
being larger during El Niño events than during La Niña events (Capotondi et al., 2018, and references
therein). This asymmetry in the ENSO wind stress feedback will be examined in detail in a future study.
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Figure 6. Longitude time sections of composite SST anomalies along the equator (3°S to 3°N) for (top) El Niño and (bottom) La Niña based on observations(ERSSTv5 over 1900–2018, left panels), CESM2 (model years 201–1,200, second column), CESM1 (model years 1,201–2,200, third column), and CCSM4(model years 301–1,300, right panels). See text for details of the compositing methodology.

3.2. Composite Evolution of El Niño and La Niña Events
To compare the spatiotemporal evolution of El Niño and La Niña events between the models and observations, we conduct composite analysis following the methodology of Okumura and Deser (2010). For eachmodel and observational SST data set, El Niño (La Niña) events are selected when the December Niño‐3.4
index exceeds 1 (is less than −1) standard deviation. Before selecting the events, the monthly Niño‐3.4 index
is smoothed with a 3‐month binomial ﬁlter to suppress subseasonal variability. When the El Niño or La Niña
criterion is satisﬁed for consecutive years, it is counted as a single event. For each event, the year containing
the December when the Niño‐3.4 index ﬁrst meets the criterion is denoted as year 0 and the subsequent years
as year + 1, year + 2, …. Following this methodology, El Niño (La Niña) composites contain 20 (15) events forobservations between 1900 and 2018, 142 (153) events for the CESM2 piControl, 130 (119) events for the
CESM1 piControl, and 146 (139) events for the CCSM4 piControl.
Longitude time sections of SST anomalies along the equator for composite El Niño and La Niña events arepresented in Figure 6. CESM2 reproduces observed asymmetry in the duration of El Niño and La Niña
events (e.g., Dommenget et al., 2013; Larkin & Harrison, 2002; McPhaden & Zhang, 2009; Ohba &Ueda, 2009; Okumura & Deser, 2010), similar to CCSM4 (Deser et al., 2012) and CESM1 (DiNezio, Deser,
Okumura, & Karspeck, 2017; Wu et al., 2019). In both models and observations, composite El Niño terminates and transitions to a weak La Niña state in year + 1, whereas composite La Niña persists and reintensiﬁes toward the end of year + 1. Compared to the earlier versions of the model, CESM2 shows a stronger
tendency for El Niño to transition to La Niña and a weaker tendency for La Niña to persist into year + 1.
Previous studies suggest that nonlinearities in both atmospheric and oceanic processes contribute to theasymmetric duration of El Niño and La Niña [see recent review by Okumura, 2019 and An et al., 2020].
Besides the event duration, all versions of the model simulate a zonal displacement of equatorial SST
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Figure 7. Frequency distribution (%) of (top row) El Niño and (bottom row) La Niña duration (in months) for(left column) observations (detrended ERSSTv5 1900–2018) and (right column) CESM2 control simulation (model years
201–1,200). The El Niño (La Niña) duration is deﬁned as the number of months for which the Niño‐3.4 index remains
above 0.25 standard deviations (below −0.25 standard deviations) after December of year 0. The number of El Niño
(La Niña) events in each 3‐month bin is divided by the total number of El Niño (La Niña) events. The numbers near the
top of each panel indicate the fraction of events that terminate in year + 1 (left numeral) and persist through year + 1(right numeral).

anomalies between El Niño and La Niña during year 0, with La Niña cooling shifted to the west by 10–20° of
longitude relative to El Niño. These equatorial SST anomalies during year 0 exhibit westward propagation.
The reintensiﬁcation of La Niña near the end of year + 1, on the other hand, occurs simultaneously acrossthe basin in both models and observations.
Composite El Niño and La Niña events last one and 2 years, respectively, but individual events show diverse
temporal evolution (Figure 7). As in Deser et al. (2012), we deﬁne the duration of an El Niño (La Niña) eventas the number of months for which the Niño‐3.4 index remains above 0.25 standard deviations (below −0.25
standard deviations) of the monthly index after December of year 0. Frequency distributions of the event
durations compare well between CESM2 and observations. In CESM2 (observations), 83% (80%) of El
Niño events terminate in year + 1, whereas 44% (50%) of La Niña events persist through year + 1. The larger
fraction of multiyear events for La Niña than El Niño is consistent with the overall asymmetry in their duration. Recent studies suggest that the duration of individual El Niño and La Niña events is controlled by multiple factors, including the magnitude of initial equatorial oceanic heat content anomalies, onset timing, andremote inﬂuences from the extratropical Paciﬁc and the tropical Indian and Atlantic Oceans (DiNezio,
Deser, Okumura, & Karspeck, 2017; Wu et al., 2019). It is noted that the fraction of multiyear events
decreases for both El Niño and La Niña in CESM2 compared to CESM1 and CCSM4 (not shown), consistent
with the differences shown in Figure 6.
3.3. ENSO Precursors
Variations in equatorial upper‐ocean warm water volume (WWV), usually described in terms of thermocline
depth or sea surface height (SSH), are a fundamental component of ENSO evolution, as theoretically
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Figure 8. Leading EOFs of SSH for ORAS4 (1958–2014, left panels) and CESM2 (model years 201–1,200, right panels).
Top panels show EOF1 for the two data sets, middle panels show EOF2, and bottom panel displays the lagcorrelation between the associated PCs, with PC1 leading PC2 for positive lags. In both ORAS4 (red line) and CESM2(blue line), the lag correlations indicate that EOF1, associated with the peak of the positive ENSO phase, leads
the negative phase of EOF2, that is, a discharged equatorial Paciﬁc thermocline. Conversely, a recharged state (positive
EOF2) leads to the positive phase of EOF1, that is, the development of an El Niño event.

encapsulated by the recharge oscillator paradigm (Jin, 1997), and documented in observations (Meinen &McPhaden, 2000). The two leading EOFs of SSH effectively capture such variations as shown in Figure 8
for both observations and CESM2. In both data sets, the leading SSH EOF exhibits a dipole pattern withpositive anomalies (deeper thermocline) in the eastern equatorial Paciﬁc, and negative anomalies(shallower thermocline) in the western Paciﬁc. The reduced zonal thermocline slope produces ananomalous poleward ﬂow, which discharges the WWV and results in a shallower thermocline across theequatorial Paciﬁc, as described by EOF2 (with the opposite sign). Upwelling of colder water in the eastern
Paciﬁc can then lead to the opposite La Niña phase. The dynamical relationship between EOF1 and EOF2
is encapsulated by the lead‐lag relationship of the associated Principal Components (PCs, bottom panel of
Figure 8) showing that a recharged state (positive EOF2) tends to lead to a warm ENSO phaseapproximately a quarter of a cycle later, while positive EOF1 leads to the discharged state described by
EOF2 with the opposite sign. The magnitude and lags of the maximum correlations are very similar in themodel and observations, suggesting a realistic time evolution of WWV in the model.
While several studies have considered the WWV integrated across the entire equatorial Paciﬁc, recent
research has emphasized the key role of the western‐to‐central equatorial Paciﬁc as a more effective
ENSO predictor at lead times of about 1 year or longer (Izumo et al., 2019; McGregor et al., 2016; Neske& McGregor, 2018). The relationship between the WWV in the western‐central Paciﬁc (the “recharge”)
and the Niño‐3.4 index is illustrated in Figure 9 for several observational data sets and a subset of the
CESM2 output. The positive correlation at negative lags (recharge leading Niño‐3.4) indicates that therecharge‐discharge precedes Niño‐3.4 anomalies of the same sign. In other words, a recharge tends to occur
prior to an El Niño and a discharge tends to occur prior to a La Niña. The negative correlation at positive
lags (Niño‐3.4 leading recharge) indicates that a net discharge of heat content occurs at and following thepeak of an El Niño and a net recharge of heat content occurs at and following the peak of a La Niña. An
asymmetry is found in the relative amplitude of the discharge versus the recharge in both observations

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(c)

(a)

(b)

Figure 9. (a) Time evolution of the observed recharge‐discharge and Nino3.4 SST index over 1960–2010. The AVISO
and ORAS4 estimates for the recharge are deﬁned as the area‐averaged sea surface height anomalies over 5°S to 5°N, 120°
E to 155°W. AVISO coverage begins in 1993. (b) As in (a) but for CESM2 over years 1,120–1,200. The recharge isdeﬁned as the warm water volume integrated over 5°S to 5°N, 120°E to 155°W. All time series are standardized.
(c) Lead‐lag correlations of Niño‐3.4 and the recharge‐discharge in observations and CESM2 (model years
800–1,200). Positive (negative) lags indicates Niño3.4 leads (lags) the recharge.

and CESM2 (Figure 10). Whether this amplitude asymmetry in the recharge‐discharge translates into an
asymmetry in ENSO predictability is still debatable (Larson & Kirtman, 2019; Larson & Pegion, 2020;
Planton et al., 2018). That said, on average, in CESM2, La Niña events tend to follow a discharged state,
whereas El Niño events appear to follow a neutral state.
Apart from equatorial processes, the onset of ENSO events can also be affected by extratropical inﬂuences,including, for example, the Seasonal Footprinting Mechanism (SFM, Vimont et al., 2001) and the North andSouth Paciﬁc Meridional Modes (NPMM and SPMM; Chiang & Vimont, 2004; Zhang et al., 2014). The
NPMM and SPMM are meridional dipole patterns of SST anomalies that result from changes in evaporative
cooling associated with changes in the strength of the subtropical trade winds. They can inﬂuence equatorial
processes through either the propagation of the SST anomalies to the equator (Chiang & Vimont, 2004;
(a)

(b)

Figure 10. Scatterplot of the standardized March recharge‐discharge with the following December Niño‐3.4 SST
anomaly in (a) observations and (b) CESM2 years 800–1,200. Blue markers indicate La Niña events, black markers
indicate neutral, and red markers indicate El Niño events. The threshold for El Niño (La Niña) is exceedance of the + (−)
one standard deviation of the observed Niño‐3.4 SST anomaly over 1958–2010. Bold triangles indicate the averageover each of the three ENSO categories.

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Figure 11. Initial (a, b) and ﬁnal (c, d) optimal structures obtained with LIMs trained on observations (a, c, and e) andCESM2 (b, d, and f). Shading is for SST and contours are for SSH (contour interval is 0.5 cm for the initial and1 cm for the ﬁnal optimal structures, respectively). Bottom panels show the time series associated with the initial (blue)
and ﬁnal (red) optimal structures for the observations (left), and a 60‐year segment of CESM2 (right). The
observational (CESM2) LIM is trained over the period 1958–2014 (model years 201–1,200).

Larson et al., 2018) or through the dynamical adjustment of the equatorial thermocline induced by theirassociated wind anomalies (Alexander et al., 2010; Anderson et al., 2013). These extra‐equatorial precursors
are captured by the optimal initial conditions obtained with the LIM approach, as, by deﬁnition, these initialconditions provide the most effective forcing of the mature ENSO state (termed the “optimal ﬁnal”). The
optimal initial structure for the observational LIM (Figure 11a), computed for a lead time of 8 months, displays positive SST anomalies extending from the coast of California to the equator, consistent with the
NPMM (Chiang & Vimont, 2004), and positive anomalies extending to the equator along the southeastern
Paciﬁc coast, which are similar to the SPMM (Zhang et al., 2014). Positive SSH anomalies are present along
the equator, indicative of a recharged state, while negative SSH anomalies in the northern tropics are indicative of westward propagating upwelling Rossby waves. This initial optimal structure evolves, eight months
later, into a ﬁnal optimal structure (Figure 11c) that displays a “canonical” El Niño event, with the largest
SST anomalies in the Niño‐3.4 region, and SSH anomalies exhibiting the zonal dipole pattern associated witha reduced zonal slope of the thermocline seen in Figure 8 (top panels). The optimal initial and ﬁnal structures for CESM2 (Figures 11b and 11d) show patterns qualitatively similar to the observed, with two notabledifferences: (1) A much larger SSH signal along the equator, likely indicative of a more pronounced role ofrecharge‐discharge processes in the model and (2) The equatorial signature of the NPMM displaced 15–20°
further west than in the observations, consistent with the westward displacement of the ENSO SST anomalies discussed in Figure 1.
Time series associated with the initial and ﬁnal optimal structures are computed by projecting the SST and
SSH anomaly ﬁelds onto those structures. In both observations and CESM2, the initial and ﬁnal optimal
time series are highly correlated (0.75 and 0.73, respectively), with the initial leading the ﬁnal time series
by about 5 months. The large‐scale SST, SLP, and precipitation ﬁelds concurrent with the initial and ﬁnal
optimal structures are obtained by linearly regressing the SST, SLP, and precipitation ﬁelds at each locationon the initial and ﬁnal time series, respectively. The results (Figure 12) show that the optimal initial
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Figure 12. Regressions of SST (shading), SLP (black contours, negative values dashed), and precipitation(green contours, negative values dashed) anomalies upon the initial (left) and ﬁnal (right) optimal structure indicesfor (a, b) observations, and (c, d) CESM2. Observed SST (°C) is from ERSSTv5, SLP (hPa) is from the NCEP/NCAR
reanalysis, and precipitation (mm/day) is from the NOAA precipitation reconstruction for the period 1958–2014. Contour
intervals are 0.2 hPa for SLP and 0.5 mm/day for precipitation.

structures are associated with SLP dipoles in both the North and South Paciﬁc, which are typical of the North
Paciﬁc Oscillation (Rogers, 1981), and the South Paciﬁc Oscillation (You & Furtado, 2017). The equatorwardlobes of these SLP patterns are associated with wind anomalies that weaken the climatological trade winds
and produce the positive phases of the NPMM and SPMM through reduced latent heat ﬂuxes. SLP anomalies
associated with the optimal ﬁnal structures are dominated by a deepened and southeastward displaced
Aleutian Low in the North Paciﬁc, due to the well‐known atmospheric teleconnections of mature El Niño
events, a topic further discussed in section 3.5. While the model ﬁdelity in reproducing the large‐scale
ENSO precursors is overall remarkable, important discrepancies can be seen between the modeled andobserved patterns, including, in particular, the excessive amplitude and westward extension of equatorial
Paciﬁc SST and precipitation anomalies in the model ﬁnal ﬁelds.
3.4. ENSO Diversity
Several different indices have been introduced to characterize diversity in the spatial pattern of ENSO
events. Special attention has been devoted to the warm phase of ENSO, since El Niño events exhibit larger
variations in their spatial patterns than La Niña events (Kug & Ham, 2011). Here, we adopt the approach
introduced by Takahashi et al. (2011) to distinguish events that have their largest SST anomalies in the far
eastern Paciﬁc (E‐type) from those with the largest anomalies in the central Paciﬁc (C‐type). Following
the procedure of Takahashi et al. (2011), we ﬁrst compute the two leading SST EOFs over the 10°S to 10°
N tropical Paciﬁc domain, which together explain close to 75% of the SST variance in both observations
and CESM2. The spatial pattern of the two leading EOFs over a broader meridional domain is obtainedby regressing SST anomalies at each grid point on the corresponding PC time series (Figures 13a–13d).
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Figure 13. Linear regression of the SST anomalies (°C, shading) and SSH anomalies (cm, contours) on PC1 (a, b), PC2(c, d), E‐index (e, f), and C‐index (g, and h). The observational PCs were obtained from EOF analysis of 1900–2018
ERSSTv5 SST anomalies in the 10°S to 10°N tropical Paciﬁc domain, while the CESM2 PCs were computed from EOF
analysis of the model SST anomalies over model years 201–1,200 and over the same 10°S to 10°N tropical Paciﬁc domain.
SSH observations are from the ORAS4 reanalysis, and the corresponding regressions are based on the 1958–2015 period.
Contour interval for SSH is 1 cm. The variance explained by the SST EOFs in the 10°S to 10°N domain is shown above thepanels displaying the EOF patterns.

The resulting patterns are similar for observations and model, except for an excessive westward
displacement of the SST anomalies in CESM2. Regression of SSH anomalies on the PCs shows a zonal
dipole pattern (indicative of a ﬂatter thermocline) for EOF1 in both model and observations, while the
SSH pattern associated with EOF2 displays an equatorially symmetric pattern that is reminiscent ofequatorial wave signals (Fedorov & Brown, 2009) in observations, but an equatorial asymmetric patternwith an enhanced northern Hemisphere component in CESM2.
We construct the E and C indices as a linear combination of PC1 and PC2, following Takahashi et al. (2011):
E ¼ ðPC1 − PC2Þ=√2;

C ¼ ðPC1 þ PC2Þ=√2;and determine the associated patterns through linear regression of the SST and SSH ﬁelds on the E and C
indices. In observations, the E mode achieves its largest amplitude in the far eastern equatorial Paciﬁc,with a very deep thermocline near the South American coast, while the C mode has the largest anomalies
just to the east of the dateline, and the largest thermocline depth anomalies between 120°W and 150°W.
The model displays qualitatively similar patterns, except for the westward displacement of the largest
anomalies. Also, while the largest SST anomalies are weaker for the C mode relative to the E mode inobservations, they are comparable in magnitude in the model.

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Figure 14. Patterns of anomalous zonal wind stress (a–d) and precipitation (e–h) associated with the E and C modes forobservations (left) and CESM2 (right). The patterns are obtained by linearly regressing the zonal wind stress and2
precipitation anomalies on the E and C indices. The zonal wind stress (N/m ) is from the NCEP/DOE reanalysis, andprecipitation (mm/day) is from the NOAA precipitation reconstruction data set.

Regression of the zonal wind stress and precipitation ﬁelds on the E and C indices (Figure 14) shows thatboth quantities are conﬁned to the western Paciﬁc for the C modes in both observations and model, as noted
in previous studies of ENSO diversity (Capotondi, 2013; Kug et al., 2009, 2010). This westward conﬁnement
is particularly pronounced in CESM2, where the largest precipitation anomalies are found between 150°E
and 160°E. The largest precipitation anomalies remain localized around the dateline also for the E modein CESM2, with only a narrow band just north of the equator extending further east.
3.5. ENSO Teleconnections
Here we provide a more systematic view of global ENSO teleconnections in the CESM2 piControl, along withcomparison to observations and the 10‐member CAM6 AMIP ensemble. El Niño and La Niña events aredeﬁned as in section 3.2, and ENSO composites are deﬁned as the composite difference between El Niño
and La Niña. The seasonal evolution of the observed and CESM2 ENSO composites from June–August ofyear 0 (JJA0) through March–May of year + 1 (MAM + 1) are shown in Figure 15 for ﬁve different variables:
SLP, 300‐hPa stream function, SST, near‐surface air temperature and precipitation. Similar ENSO composite
maps based on CCSM4 are provided in Deser et al. (2012). Overall, the global patterns of ENSO teleconnections are realistically simulated in CESM2, and are similar to those found in CCSM4 (see Figure 15 inDeser et al., 2012). In particular, the seasonality and spatial structure of atmospheric circulation anomalies
are well reproduced, beginning in JJA0 with a wave train emanating from the central equatorial Paciﬁc to
the South Paciﬁc and followed in DJF + 1 by a similar Rossby wave train to the North Paciﬁc. Like CCSM4(and other models), CESM2 overestimates atmospheric teleconnections in MAM + 1, especially those over
the North Paciﬁc. This may be associated with the tendency for ENSO SST and precipitation anomalies
over the western equatorial Paciﬁc to persist too strongly into boreal spring in the model compared to nature (compare simulated and observed MAM + 1 panels in Figure 15). However, the amplitudes of the
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Figure 15. ENSO composite (positive minus negative) seasonal evolution from (top) JJA (year 0) through (bottom) MAM (year + 1) based on observations (leftpair of columns) and CESM2 piControl (right pair of columns). The left column of each pair shows SST and terrestrial near‐surface air temperature−1(color shading) and SLP (contours, negative values dashed, and contour interval of 2 hPa), and the right column of each pair shows precipitation (mm day ; color
6 2 −1
shading) and 300 hPa stream function (contours, negative values dashed, and contour interval of 3 × 10 m s ) anomalies. The observed composite isbased on years 1958–2014 except for precipitation and 300‐hPa stream function which are for 1979–2014. The CESM2 composite is based on model years
201–1,200. See text for details.

extratropical atmospheric circulation anomalies in other seasons are generally realistic in CESM2 despite
the fact that ENSO itself is approximately 30% stronger than observed (recall section 3.1). We shall returnto this point below.
ENSO‐related atmospheric teleconnections produce surface climate anomalies through changes in heat andmoisture transports. For example, the well‐known impacts of ENSO on North American temperature andprecipitation in boreal winter are reproduced in CESM2, especially the anomalous warming over westernand central Canada and cooling over the southeastern United States, and the increased precipitation overparts of the western and southern United States (Figure 15, DJF + 1 panels).
A number of factors may hinder a direct comparison of ENSO teleconnections and associated climate
impacts between observations and CESM2 piControl, including disparities in the length of record (approximately 56 years for observations and 1,200 years for CESM2) and thus the number of ENSO events composited; shortcomings in the model's simulation of ENSO amplitude, pattern and duration; and the fact that themodel is run under constant 1850 radiative forcing conditions whereas the real world is subject to evolving
radiative forcings. To circumvent these issues, it is instructive to analyze ENSO composites from the
10‐member CAM6 (1°) “Tropical Ocean‐Global Atmosphere” (TOGA) AMIP ensemble, which is forced at
the lower boundary by the observed (ERSSTv5) evolution of SSTs in the tropics (30°N to 30°S) from 1920
to 2014, with SSTs elsewhere set to their long‐term mean seasonal cycle, and subject to the observed evolution of historical radiative forcings (see Deser et al., 2018 for details). The only difference among the

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Figure 16. DJF ENSO composites of SST and terrestrial near‐surface air temperature (color shading) and SLP (contours, negative values dashed, contour intervalof 2 hPa) based on the period 1920–2014 for (top left) observations and (remaining panels) 10 CAM6 TOGA AMIP simulations. See text for details.

individual ensemble members is a tiny (order 10−14 K) perturbation to the initial atmospheric temperatureson 1 January, 1920, which serves to create ensemble spread due to internal atmospheric variability. Here wecompare observed and simulated ENSO composites using the same (observed) set of ENSO events during theextended 1920–2014 period, with a focus on the peak season DJF + 1. For this period, we identify 18 El Niño
and 14 La Niña events using the procedure outlined in section 3.2.
Figure 16 shows the DJF + 1 ENSO composites of SST, terrestrial air temperature and SLP for observations(top left) and each of the 10 CAM6 TOGA AMIP simulations (remaining panels) based on detrended data.
Recall that outside the tropics (30°N to 30°S), the model generates its own air temperature anomalies(although SST anomalies are identically zero by design). Each simulated ENSO composite shows a centerof negative SLP anomalies over the North Paciﬁc with a NW‐SE orientation; however, the maximum amplitude of this center varies from approximately 6 hPa (ensemble member #4) to 12 hPa (ensemble member #2).
The observed ENSO composite has a similar primary center‐of‐action, with a peak magnitude of approximately 8 hPa, well within the TOGA ensemble spread. Simulated teleconnections in other parts of the world
vary from member to member. For example, the north‐south SLP dipole over the North Atlantic, which
resembles the North Atlantic Oscillation (NAO), is evident in some members (#2, #8, and #10) but not inothers (#1, #3, and #4). This diversity in teleconnection patterns and amplitudes attests to the fact that,CAPOTONDI ET AL.

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even with so many ENSO events, the composites are still subject to considerable sampling uncertainty as aresult of strong internally generated modes of atmospheric circulation variability (see also Deser et al., 2017).
This makes it challenging to assess the impact of ENSO diversity and asymmetries on atmospheric teleconnections in the single observational record (see Deser et al., 2017, 2018, for further discussion).
The range of ENSO teleconnections in the CAM6 TOGA ensemble has implications for the associated surface climate impacts, including air temperature (Figure 16). For example, positive temperature anomalies
over western Canada range from 3°C to over 6°C depending on the inﬂuence from residual atmospheric“noise”. Similarly, the magnitude of cooling over the southern United States varies from −0.5°C to nearly−4.0°C across the TOGA composites. In both cases, the model spread encompasses the observed ENSO composite values. Another striking difference across the CAM6 TOGA ensemble is the variation in the sign of thecomposite air temperature anomalies over northern Asia, which range from −3°C to + 2°C. Again, this variation occurs despite the fact that the ENSO composites are based on a large number of events (18 El Niño
and 14 La Niña).

4. PDV
Although the main focus of this study is on ENSO, here we brieﬂy describe the related phenomenon of PDV(recall section 1). One way to deﬁne PDV is to perform EOF analysis of monthly SST anomalies over the
North Paciﬁc (20–60°N) following Mantua et al. (1997). This “mode of variability” is traditionally termed
the PDO, although as mentioned in the Introduction, we opt for the more general PDV nomenclature.
Observed PDV, based on ERSSTv5 over the period 1920–2014, exhibits a large‐scale pattern of SST anomalies
over the North Paciﬁc, with opposing sign in the east and west, and is associated with a an ENSO‐like pattern
in in the tropics and South Paciﬁc albeit with weaker magnitudes along the equator (Figure 17, upper left).
Observed PDV also has an atmospheric signature, depicted here in terms of regressions of the surface windﬁeld upon the normalized PDV time series (Figure 17, upper left). In its positive phase, observed PDV is
associated with a deepened Aleutian Low pressure center and westerly (southerly) wind anomalies over
the western (eastern) North Paciﬁc, as well as westerly wind anomalies over the western tropical Paciﬁc.
The CESM2 piControl run simulates a realistic spatial pattern of PDV SST and surface wind anomalies
throughout the Paciﬁc, including the tropics. Indeed, the match with observations is remarkable, and considerably better than many models including CCSM3 and CCSM4 which lack a strong tropical connection(Deser et al., 2012; Newman et al., 2016; Wang & Miao, 2018).
The observed PDV record (Figure 17) exhibits a nominal time scale of approximately 50 years, but the limited length of the record precludes attaching any meaningful statistical signiﬁcance to this value (see related
discussion in Deser et al., 2010 and Fedorov et al., 2020). A weak bidecadal time scale is also evident in theobserved PDV record (Deser et al., 2004; Minobe, 1999). In the CESM2 piControl, PDV exhibits a variety of
temporal expressions (Figure 17). Extended periods of 10–20 years in which PDV is in a predominantly positive or negative state are evident at times (for example, model years 360–440 and 815–900), reminiscent of
the character of the short observational record. However, there are also long periods in which PDV ﬂuctuates more rapidly. The rich variety of temporal behavior of the simulated PDV is a cautionary tale for theinterpretation of the short observational PDV record.
The tropical component of PDV is particularly important, since analyses of observed SSTs for the past century suggest that decadal variability of tropical Paciﬁc climate is associated with a decadal modulation of
ENSO (Figures 18a–18e). Here we deﬁne the two leading modes of tropical PDV (TPDV) based on EOF analysis of 10‐year low‐pass‐ﬁltered SST variability in the tropical Paciﬁc (23.5°S to 23.5°N, 120°E to 80°W). The
leading mode of TPDV (TPDV1) explains 44% of the total decadal variance and exhibits an ENSO‐like anomaly pattern (Figure 18a). This mode represents the tropical component of the basin‐wide PDV discussed earlier (Figure 17). During the positive phase of TPDV1, El Niño events tend to occur more frequently than La
Niña events, and vice versa (Figure 18d), as also suggested by previous studies (Kiem et al., 2003; Trenberth& Hurrell, 1994; Verdon & Franks, 2006). The leading PC (PC1) is positively correlated (r = 0.39) with therelative frequency of El Niño and La Niña events deﬁned as the difference between the fractions of El
Niño and La Niña event counts in a moving 10‐year window. The second leading mode of TPDV (TPDV2)
explains 16% of the total decadal variance and exhibits a zonal dipole pattern in the tropical Paciﬁc, withthe western Paciﬁc pole extending into the central‐western North Paciﬁc (Figure 18b). This mode is
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Figure 17. (top) Spatial pattern and (bottom) temporal evolution of the Paciﬁc Decadal Oscillation (PDO; Mantua
et al., 1997) in observations (1920–2014) and the CESM2 piControl simulation (model years 201–1,200) based on−1monthly SST anomalies. Maps show global SST (color shading, °C) and surface wind vector (arrows, m s ) anomaly
regressions upon the normalized PDO time series. Time series show the normalized PDO record based on monthly
SST anomalies from (top row) observations (1920–2014) and (subsequent rows) sequential 200‐year segments of the
CESM2 piControl (model years 201–1,200). The vertical axis is the same in all time series panels.

associated with multidecadal modulations of the ENSO amplitude discussed in previous studies (e.g., Gu &Philander, 1995; Li et al., 2011; McGregor et al., 2010; Trenberth & Shea, 1987). The second leading PC (PC2)
is weakly correlated (r = 0.20) with the ENSO amplitude deﬁned as the standard deviation of the monthly
Niño‐3.4 index in a moving 10‐year window (Figure 18e). The correlations between the PCs and theindices of ENSO modulation increase if the Hadley Centre Sea Ice and SST data set (Rayner et al., 2003) isused instead of the ERSSTv5 data set (r = 0.43 and 0.41 for PC1 and PC2, respectively), likely reﬂecting
the difference between the two data sets prior to 1950 when observations were sparse (Santoso et al., 2017).

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Figure 18. TPDV and ENSO modulations in (a–e) observations (ERSSTv5 over 1900–2018) and (f–j) CESM2 (model years
201–1,200). (a) SST anomaly pattern associated with TPDV1 obtained by regressing SST anomalies onto thestandardized PC1 of 10‐year low‐pass‐ﬁltered SST variability in the tropical Paciﬁc (23.5°S to 23.5°N, 120°E to 80°W).
The fraction of total decadal variance explained by this mode is indicated in the top right. (b) As in (a) but for TPDV2.
(c) Time series of the monthly Niño‐3.4 index smoothed with a 3‐month binomial ﬁlter (°C). (d) Time series ofPC1 (standard deviation units; shaded curve) and the relative frequency of El Niño and La Niña events (%; black curve)deﬁned as (E − L)/(E + L) × 100, where E and L are the numbers of El Niño and La Niña events in a moving 10‐year
window, respectively. El Niño and La Niña events are deﬁned as in Figures 6 and 7, although consecutive El Niño
or La Niña years are counted separately. The correlation coefﬁcient of these time series is indicated in the upper
right. (e) as in (d) but for PC2 and the ENSO amplitude (°C) deﬁned as standard deviation of the Niño‐3.4 index ina moving 10‐year window. (f‐j) As in (a)–(e) but for CESM2. Both observed and CESM2 SST data are linearly detrended
prior to the analysis.

While the brevity and uncertainty of observational records make it difﬁcult to assess the robustness of therelationships between TPDV and ENSO modulations, the observed relationships are surprisingly well reproduced in the 1,200‐year CESM2 piControl run (Figures 18f–18j). Compared to observations, TPDV1 simulated in CESM2 explains a much larger fraction of the total decadal variance (65%) and shows larger SST
anomalies in the equatorial and southeastern tropical Paciﬁc (Figure 18f), presumably related to the excessively strong ENSO in this model (Figure 1). SST anomalies associated with TPDV2, on the other hand, show
a more meridionally asymmetric pattern in the central‐eastern tropical Paciﬁc (Figure 18g). It is also interesting to note that the North Atlantic SST anomalies seen in the observed TPDV2 are absent in CESM2. The

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PC1 and PC2 are signiﬁcantly correlated with the relative frequency of El Niño and La Niña events (r = 0.48)
and the ENSO amplitude (r = 0.46), respectively. Similar patterns of the TPDV modes and their relationships
to ENSO modulations are found in CCSM4 (Okumura et al., 2017) and CESM1 (not shown). Compared to
CESM2 and CESM1, TPDV2 simulated in CCSM4 explains a larger fraction of the total decadal variance(22%) and PC2 is more highly correlated with the ENSO amplitude (r = 0.79).
The causality of TPDV and ENSO modulations remains unclear (see a recent review by Fedorov et al., 2020).
In one view, mean state changes associated with TPDV affect ENSO by modulating the oceanic and atmospheric feedbacks (Capotondi & Sardeshmukh, 2017; Fedorov & Philander, 2000; Hu & Fedorov, 2018;
Kang et al., 2014; Sun & Okumura, 2020; Wang & An, 2002). In another view, ENSO modulations are stochastically forced or internally generated, and the resultant nonzero residuals induce changes in the meanstate (Atwood et al., 2017; Flügel & Chang, 1999; Rodgers et al., 2004; Thompson & Battisti, 2001;
Wittenberg et al., 2014). For example, a random increase in the relative frequency of El Niño would resultin El Niño‐like changes in the mean state. A random increase in the amplitude of ENSO would, on the other
hand, induce a zonal dipole pattern of mean SST changes due to the asymmetry in the El Niño and La Niña
SST anomaly patterns. Further studies are needed to understand the origins of TPDV and the degree of interaction of TPDV with the ENSO dynamics.

5. Conclusions
In this paper we have provided an overview of ENSO and PDV in the NCAR Community Earth System
Model version 2 (CESM2), focusing primarily on the 1,200‐year preindustrial integration. ENSO is a coupled
ocean‐atmosphere phenomenon, and its evolution involves both predictable oceanic processes and stochastic inﬂuences from within and outside the tropical Paciﬁc. This complexity of inﬂuences and feedbacks
results in a large diversity of ENSO spatial patterns and temporal evolutions which are very challenging
for climate models to simulate realistically. ENSO variations in CESM2 exhibits a dominant timescale very
close to the observed, an aspect that appears to be related to the spatial structure of the wind stress responseto the ENSO SST anomalies. Indeed, the longitudinal location and meridional scale of the wind stressanomalies are very similar to those found in observations, and can be expected to lead to an adjustment timescale of the equatorial thermocline also similar to the observed. The evolution of the equatorial Warm Water
Volume, as described by the leading modes of sea surface height variability appears to be also similar to theobserved, and consistent with the Recharge Oscillator paradigm (Jin, 1997). In addition, in agreement withrecent observational ﬁndings, the heat content in the western‐to‐central Paciﬁc during spring exhibits anasymmetric relationship with ENSO conditions during the following winter, with La Niña events usually following a discharged state and El Niño events being mostly associated with neutral spring conditions. CESM2
also shows a realistic asymmetry in the evolution and duration of warm and cold events, with El Niño events
typically transitioning to a La Niña event after their peak, and La Niña events tending to re‐occur for a second year, although not as frequently as in the observations.
Extratropical ENSO precursors, including the North and South Paciﬁc Meridional Modes and their associated atmospheric circulation anomalies appear to be reasonably well captured by CESM2. The model simulates some degree of diversity in the spatial patterns of El Niño events, with some events exhibiting large
anomalies that extend to the eastern equatorial Paciﬁc, and another class of events characterized by anomalies that are more conﬁned to the central Paciﬁc. As in observations, these two classes of events are associatedwith different patterns of wind stress and precipitation anomalies, which are more conﬁned to the westernpart of the basin in the case of the Central Paciﬁc events.
One main limitation in the CESM2 ENSO simulation is its excessive amplitude, which in the Niño‐3.4 region
is about 30% larger than the observed in the preindustrial simulation and 40% larger in the historical runs, asestimated from the magnitude of the Niño‐3.4 spectral peak. Estimates of uncertainty associated with thehigh level of system noise help to partly reconcile the discrepancy in the spectral power of model and observations, highlighting the strong limitation of relying on the relatively short and uncertain instrumental
record to assess model performance.
A second important limitation of the ENSO representation in CESM2 is the excessive westward extension of
the ENSO‐related SST anomalies, whose maximum standard deviation occurs near the dateline. This also
limits the range of ENSO spatial patterns, which are all shifted further west than observed, and the ability
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of convection to shift as far eastward as observed. The intensity of the eastern Paciﬁc cold tongue is critical todetermine how readily deep convection can shift eastward. Since anomalous convective activity depends on
the local total SST relative to the tropical mean SST (He et al., 2018), an excessive cold tongue may impede
the eastward displacement of deep convection (and precipitation) even in the presence of large SST anomalies. While CESM2 appears to have a reduced cold tongue bias relative to previous model versions, its zonal
mean SST is higher than in CESM1 and CCSM4, establishing a higher convective threshold which may be
responsible for the westward conﬁnement of precipitation in the model. Previous studies have emphasized
the key role of the atmospheric component in the coupled models performance in simulating ENSO
(Guilyardi et al., 2004), and in particular the fundamental importance of a realistic representation of theatmospheric feedbacks (e.g., the wind and heat ﬂux feedbacks), which themselves may be related to convective activity and to the choice of the convective scheme (Bellenger et al., 2014; Watanabe et al., 2011). In spiteof the several changes to the model physics, CESM2 does not show an overall marked improvement in its
representation of ENSO relative to the previous versions of the model. Further work is thus needed to elucidate how the physical parameterizations inﬂuence the key ENSO feedbacks.
In spite of the above limitations, global ENSO teleconnections are reasonably well represented in CESM2
relative to observations, including pattern and seasonality, although a deﬁnitive assessment of the model
performance is limited by many factors, the most prominent of which is the large level of atmospheric noise.
CESM2 also has a pattern of PDV that compares extremely well with the observed. The tropical signature of
PDV shows a realistic association with ENSO decadal modulation, although the exact mechanisms underlying this relationship are still unclear and a subject of active research.

Acknowledgments
The CESM project is supported
primarily by the National Science
Foundation (NSF). This material isbased upon work supported by the
National Center for AtmosphericResearch, which is a major facility
sponsored by the NSF under
Cooperative Agreement No. 1852977.
Computing and data storage resources,
including the Cheyenne supercomputer(doi:10.5065/D6RX99HX), were
provided by the Computational andInformation Systems Laboratory (CISL)at NCAR. We thank all the scientists,
software engineers, and administrators
who contributed to the development of
CESM2. Output from the Climate
Variability Diagnostics Package(Phillips et al., 2014) was used to
produce some of the ﬁgures. A. C. was
supported by the NASA Physical
Oceanography Program (Award
NNX15AG46G) and by the NOAA/
CPO/MAPP and NOAA/CPO/CVP
Programs. Y.O. was supported by
NOAA/CPO/MAPP (Award
NA17OAR4310149) and by the NSF
Physical Oceanography Program(Award OCE‐1756883). The Authors
would like to thank Dr. Chunzai Wang
and an anonymous Reviewer for their
excellent comments and suggestions
which have greatly improved themanuscript.

CAPOTONDI ET AL.

Several aspects of ENSO remain to be investigated in the model. Apart from the “deterministic” wind stressresponse to eastern Paciﬁc SST anomalies, tropical wind stress anomalies also include a stochastic component which appears to play an important role in the onset and magnitude of ENSO events (Capotondi
et al., 2018; Puy et al., 2019). The model representation of the stochastic wind component should be examined in detail in future studies. Similarly, additional analyses are needed to understand the inﬂuence of subseasonal wind variations, for example, those associated with the Madden‐Julian Oscillation, on the onset of
El Niño events. The mechanisms underlying asymmetric ENSO behavior (e.g., duration of warm and cold
ENSO events, state dependence of stochastic wind forcing) also deserve further investigation. Finally, while
the large level of atmospheric noise greatly limits our ability to detect differences in the impact of different
ENSO ﬂavors, large ensembles and novel diagnostic approaches should be considered to maximize the valueof the model ENSO as a predictor of global impacts.

Conﬂict of Interest
The Authors declare no conﬂict of interest.

Data Availability Statement
Observational data sets for SST, SLP, surface wind stress, and precipitation are available from the NOAA/ESRL/PSD website (https://psl.noaa.gov). The output of the ORAS4 ocean reanalysis was obtained fromhttp://icdc.cen.uni‐hamburg.de/projekte/easy‐init/esy‐init‐ocean.html website. CESM2 output is available
from the Earth System Grid Federation (ESGF; at http://esgf‐node.llnl.gov/search/cmip6). The data fromthe AMIP simulations used in this study can be obtained online (http://www.cesm.ucar.edu/working_groups/CVC/simulations/cam6‐prescribed_sst.html).

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