REVIEW National Science Review
5: 813–825, 2018
Advance access publication 10 October 2018
Special Topic: Advances in El Ni˜
A review of ENSO theories
State Key Laboratory
China Sea Institute of
Academy of Sciences,
Received 6 March
2018; Revised 5
e El Ni˜
no and the Southern Oscillation (ENSO) occurrence can be usually explained by two views of (i)
a self-sustained oscillatory mode and (ii) a stable mode interacting with high-frequency forcing such as
westerly wind bursts and Madden-Julian Oscillation events. e positive ocean–atmosphere feedback in the
tropical Pacic hypothesized by Bjerknes leads the ENSO event to a mature phase. Aer ENSO event
matures, negative feedbacks are needed to cease the ENSO anomaly growth. Four negative feedbacks have
been proposed: (i) reected Kelvin waves at the ocean western boundary, (ii) a discharge process due to
Sverdrup transport, (iii) western-Pacic wind-forced Kelvin waves and (iv) anomalous zonal advections
and wave reection at the ocean eastern boundary. ese four ENSO mechanisms are respectively called
the delayed oscillator, the recharge–discharge oscillator, the western-Pacic oscillator and the
advective–reective oscillator. e unied oscillator is developed by including all ENSO mechanisms, i.e.
all four ENSO oscillators are special cases of the unied oscillator. e tropical Pacic Ocean and
atmosphere interaction can also induce coupled slow westward- and eastward-propagating modes. An
advantage of the coupled slow modes is that they can be used to explain the propagating property of
interannual anomalies, whereas the oscillatory modes produce a standing oscillation. e research
community has recently paid aention to dierent types of ENSO events by focusing on the central-Pacic
no. All of the ENSO mechanisms may work for the central-Pacic El Ni˜
no events, with an addition
that the central-Pacic El Ni˜
no may be related to forcing or processes in the extra-tropical Pacic.
Keywords: ENSO, ocean–atmosphere interaction, climate variability
no represents oceanic warming in the tropical
Pacic Ocean and the Southern Oscillation is a see-
saw of sea-level pressure (SLP) between the trop-
ical western and eastern Pacic. Bjerknes rst
recognized that El Ni˜
no and the Southern Oscilla-
tion (ENSO) are linked together and are oceanic
and atmospheric aspects of the same interannual cli-
matephenomenon. Bjerknes  hypothesizedthat a
positive ocean–atmosphere feedback process causes
ENSO. Given an initial warm sea-surface temper-
ature (SST) anomaly in the equatorial eastern Pa-
cic, the warm SST anomaly reduces the east–west
SST gradient and hence weakens the Walker circu-
lation [2,3], producing the westerly wind anomaly
in the equatorial central Pacic. e westerly wind
anomaly in turn drives the ocean circulation change
that further enhances the SST anomaly. As a result
of the positive feedback, the tropical Pacic reaches
awarm state, i.e. El Ni˜
no.Aer El Ni˜
ative feedbacks are required to turn El Ni˜
a warm phase to a cold phase, which was called La
Bjerknes’s landmark paper in 1969 was not
paid aention to until the 1980s. e occurrence
of the intensive 1982–83 El Ni˜
no event was not
realized by the community. is motivated the
international research community to heavily study
ENSO during the past three decades by focusing
on interaction between the tropical Pacic Ocean
and atmosphere [4–10]. ENSO is one of the
natural climate phenomena whose understanding,
observations and prediction are relatively successful
and complete due to hard and excellent work by the
international research community during the past
e Author(s) 2018. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. All rights reserved. For permissions, please e-mail:
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814 Natl Sci Rev, 2018, Vol. 5, No. 6 REVIEW
e present paper summarizes and reviews
ENSO theories associated with physical processes.
e ‘Self-sustained ENSO oscillators’ section
summaries the view of ENSO as self-sustained
oscillators. e ‘A stable mode interacting with
high-frequency forcing’ and ‘Eastward- and
westward-propagating slow modes’ sections dis-
cuss ENSO as a stable mode interacting with
high-frequency forcing and as a coupled slow (or
SST) mode, respectively. e ‘Dynamics of the
central-Pacic El Ni˜
no’ section briey discusses the
dynamics of the central-Pacic El Ni˜
summary and future work are given in the ‘Summary
and future work’ section.
SELF-SUSTAINED ENSO OSCILLATORS
Bjerknes  rst hypothesized that El Ni˜
no is a
product of the tropical Pacic Ocean–atmosphere
no is caused by a positive ocean–
atmosphere feedback process. e positive ocean–
atmosphere feedback leads the tropical Pacic to a
never-ending warm state. For the coupled ocean–
atmosphere system to oscillate, negative feedbacks
are required. e previous studies have proposed
four negative feedbacks. ese negative feedbacks
can explain the oscillatory nature of ENSO and are
called the delayed oscillator [11,12], the recharge–
discharge oscillator [13,14], the western-Pacic os-
cillator [15,16] and the advective–reective oscil-
lator . e physics of these four oscillator
models are the negative feedbacks of (i) reected
Kelvin waves at the ocean western boundary, (ii)
a discharge process due to Sverdrup transport, (iii)
western-Pacic wind-forced Kelvin waves and (iv)
anomalous zonal advection and reected Rossby
waves at the ocean eastern boundary, respectively.
e unied oscillator suggested that all four ENSO
mechanisms may operate in nature, and they are spe-
cial cases of the unied oscillator .
Four ENSO oscillators
The delayed oscillator
e early oscillatory mechanism of ENSO, built
on Rossby wave reection at the ocean western
boundary, was originally hypothesized by McCreary
. McCreary demonstrated that reection of
oceanic Rossby waves might help to generate the
low-frequency interannual oscillations of ENSO by
using shallow-water ocean dynamics. By emphasiz-
ing the delayed eects of oceanic wave reection
at the ocean western boundary, Suarez and Schopf
introduced and presented thedelayed oscillator
explaining the oscillatory feature of ENSO. Zebiak
and Cane’s  coupled model—a coupled ocean–
130 E 80 W
Figure 1. Schematic diagram of the delayed oscillator. Red
shading represents positive SST anomalies and green ar-
rows represent wind anomalies. Kdown and Kup stand for
downwelling and upwelling Kelvin waves that propagate
eastward. Rup and Rdown represent upwelling and down-
welling Rossby waves that propagate westward.
atmosphere model of intermediate complexity with
the specied mean states—was the rst model to
successfully predict ENSO. Baisti and Hirst 
used this intermediate complexity model to develop
the Suarez and Schopf’s delayed oscillator model:
dt =AT −BT(t−η)−εT3,(1)
where Trepresents the SST anomaly in the equato-
rial eastern Pacic and the model parameters A,B,η
and εare constant. e rst term on the right-hand
side (RHS) of Equation (1) stands for the Bjerk-
nes positive feedback between the ocean and atmo-
sphere. e second term on the RHS of Equation (1)
represents the delayed negative feedback of wave re-
ection at the ocean western boundary. e warm
SST anomalies in the equatorial eastern Pacic ac-
cording to Gill’s  physics produce the equatorial
westerly wind anomalies in the central Pacic that
force westward-propagating Rossby waves. Aer the
Rossby waves reach the ocean western boundary,
they are reected into Kelvin waves and the reected
Kelvin waves propagate eastward to the eastern Pa-
cic, switching the sign of the anomalies in the east-
ern Pacic (Fig. 1). e cubic term in Equation (1) is
a damping term that is to limit SST anomaly growth,
but does not change the oscillation feature of Equa-
tion (1) [12,18].
e delayed oscillator overlooks the role of the
ocean–atmosphere interaction in the western Pacic
and also assumes that wave reection at the ocean
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REVIEW Wang 815
eastern boundary is not important. e delayed os-
cillator only considers the physics of wave reection
at the ocean western boundary. With a broad range
of model parameters, Equation (1) is able to oscillate
on interannual time scales . It was shown by Bat-
tisti and Hirst  that the delayed oscillator model
of Equation (1) was able to account for major oscil-
latory features of Zebiak and Cane’s coupled model.
The recharge–discharge oscillator
Wyrtki [22,23] indicated that the growth and de-
crease in sea level over the western Pacic Ocean
are related to ENSO. With these ideas and Zebiak
and Cane’s coupled model, Jin [13,14] developed a
recharge–discharge oscillator model for ENSO that
is represented by:
dt =CT +Dh −εT3,(2)
dt =−ET −Rhh,(3)
where Tis the SST anomaly in the equatorial east-
ern Pacic and his the thermocline-depth anomaly
in the equatorial western Pacic. e model param-
eters C,D,ε,Eand Rhare constant.
As explained by Jin, Equations (2) and (3) rep-
resent the discharge and recharge of tropical Pacic
Ocean heat content. e warm phase of ENSO is as-
sociated with the equatorial westerly wind anoma-
lies in the central Pacic and the equatorial warm
SST anomalies in the eastern Pacic, which result
in and produce the divergence of Sverdrup trans-
port and thus the discharge of tropical Pacic Ocean
heat content (Fig. 2). e discharge of tropical Pa-
cic Ocean heat content leads the tropical Pacic
to a transition phase in which the entire thermo-
cline depth is anomalously shallow due to the dis-
charge of tropical ocean heat content. is anoma-
lous shallow thermocline in the transition phase in
the tropical Pacic permits anomalous cold waters
to be pumped into the surface layer by climatological
mean upwelling (green arrows in Fig. 2). e whole
process then leads the warm phase of ENSO to the
cold phase. e same process but with the opposite
sign can lead the cold phase to the warm phase. us,
the recharge–discharge process makes the coupled
system oscillate on interannual time scales.
~ 0 SST ~ 0
SST ~ 0
Figure 2. Schematic diagram of the recharge–discharge oscillator. Shown are (a) the warm phase, (b) the warm-to-cold
transition phase, (c) the cold phase and (d) the cold-to-warm transition phase. Red (blue) SST represents warm (cold) SST
anomalies and thin black arrows stand for wind anomalies. Dashed lines represent zero of the thermocline-depth anomalies
and black lines are the thermocline-depth anomalies. Heavy black arrows mean the divergence and convergence of Sverdrup
transport. Green arrows represent climatological mean upwelling.
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816 Natl Sci Rev, 2018, Vol. 5, No. 6 REVIEW
The western-Pacic oscillator
When an ENSO event occurs, both the tropical east-
ern and western Pacic show interannual anomaly
paerns [24,16,25]. For example, during the warm
phase of ENSO, the warm SST and low SLP anoma-
lies in the equatorial eastern Pacic and the low
outgoing longwave radiation (OLR) anomalies in
the equatorial central Pacic are accompanied by
the cold SST and high SLP anomalies in the o-
equatorial western Pacic and the high OLR anoma-
lies in the o-equatorial far western Pacic. Addi-
tionally, the westerly wind anomalies over the equa-
torial central Pacic are associated with the easterly
wind anomalies in the equatorial western Pacic.
During the cold phase of ENSO, the relationship is
also held, but with anomalies of opposite signs.
e delayed oscillator only considers the ENSO
eastern-Pacic anomaly paern and overlooks or
does not consider the western-Pacic anomaly
paern. Consistently with and supported by ob-
servational and modeling results [15,16,25,26,27],
Weisberg and Wang  developed and formulated
a western-Pacic oscillator model for ENSO. is
oscillator model stresses the role of the ocean–
atmosphere coupling over the western Pacic.
Particularly, the equatorial wind anomalies in the
far western Pacic play an important role in the
evolution of ENSO. e western-Pacic oscillator
model is represented by the following equations:
dt =dT −Rτ1τ1,(6)
dt =eh −Rτ2τ2,(7)
where Tis the SST anomaly in the equatorial eastern
Pacic, his the thermocline-depth anomaly in the
o-equatorial western Pacic, and τ1and τ2are the
equatorial zonal wind-stress anomalies in the cen-
tral Pacic and the western Pacic, respectively. All
model parameters are constant.
According to Gill’s  atmosphere, heating in
the equatorial central Pacic [28,29] produces a
pair of cyclones in the o-equatorial region, which
results in the equatorial westerly wind anomalies
(Fig. 3). e wind anomalies in the Nino4 region
increase the Nino3 SST anomalies, and this process
is represented by the rst term on the RHS of
Equation (4). At the same time, a pair of cyclones in
the o-equatorial region raises the thermocline via
Ekman pumping. As a result, a shallow thermocline
anomaly in the o-equatorial region expands over
the Nino6 region of the western Pacic. e process
is represented by Equation (5) with a delay time of
λ. e shallow o-equatorial thermocline results in
the cold SST anomalies and the high SLP anomalies
in the Nino6 region . ese o-equatorial high
SLP anomalies initiate and induce the equatorial
easterly wind anomalies in the Nino5 region.
The Western Pacific Oscillator
Figure 3. Schematic diagram of the western-Pacic oscillator. The ENSO index regions of Nino3, Nino4, Nino5 and Nino6
are dened in Wang et al. . L, C and H represent low SLP, cold SST and high SLP, respectively. τ1and τ2stand for zonal
wind-stress anomalies in the Nino4 and Nino5 regions, respectively. T is the SST anomaly in the Nino3 region and h is the
thermocline-depth anomaly in the Nino6 region.
REVIEW Wang 817
e equatorial easterly wind anomalies force an
upwelling Kelvin wave that propagates eastward
and serves as a negative feedback for the coupled
system to oscillate on interannual time scales. is
delayed negative feedback is represented by the
second term on the RHS of Equation (4). Equation
(6) relates the Nino4 zonal wind-stress anomalies to
the Nino3 SST anomalies. Equation (7) states that
the initiation of the Nino5 easterly wind anomalies
is related to the Nino6 thermocline anomalies.
e western-Pacic oscillator emphasizes the
oceanic processes that relate to the westerly wind
anomalies in the central Pacic, the anomalous an-
ticyclone in the o-equatorial western Pacic and
the equatorial easterly wind anomalies in the west-
ern Pacic during ENSO. e thermocline in the
western Pacic shows a large variation around 10◦
north of the equator, although the mean thermocline
in the western Pacic is generally deep. Wang et al.
 showed that the o-equatorial shallow thermo-
cline anomalies could increase the SLP anomalies,
which in turn initiate the equatorial easterly wind
anomalies in the western Pacic. Subsequently, sev-
eral studies emphasized the atmospheric processes
and mechanisms for maintaining and developing the
anomalous anticyclone and the equatorial easterly
wind anomalies in the western Pacic: local wind–
evaporation–SST feedback , seasonal modula-
tions of atmospheric response to El Ni˜
and the Indian Ocean’s eect [33,34].
The advective–reective oscillator
Picaut et al.  found an in-phase relationship be-
tween the eastern edge of the western-Pacic warm
pool (WPWP) and the Southern Oscillation index,
and Picaut and Delcroix  studied the wave
reections in both the ocean western and eastern
boundaries. Based on the results in these two studies,
Picaut et al.  proposed a conceptual model of the
advective–reective oscillator for ENSO (Fig. 4). In
this oscillator, they argued that the positive feedback
results from ocean zonal currents that advect the
WPWP toward the east. e three negative feed-
backs, all of which tend to push the WPWP back to
the western Pacic, include: (i) anomalous zonal
current associated with wave reection at the ocean
western boundary, (ii) anomalous zonal current
associated with wave reection at the ocean eastern
boundary and (iii) mean zonal current converging at
the WPWP’s eastern edge. When an El Ni˜
occurs, the equatorial westerly wind anomalies are
located in the central Pacic and the westerly wind
anomalies force westward-propagating upwelling
Rossby and eastward-propagating downwelling
Kelvin waves. e westward-propagating upwelling
130 E 80 W
Figure 4. Schematic diagram of the advective–reective
oscillator. Yellow arrows represent zonal wind anomalies
and gray arrows represent oceanic currents. The black thick
solid line indicates the eastern edge of the western-Pacic
warm pool. Kdand Kup stand for downwelling and upwelling
Kelvin waves that propagate eastward. Rup and Rdrepresent
upwelling and downwelling Rossby waves that propagate
Rossby waves are reected to upwelling Kelvin
waves aer they reach the ocean western boundary,
whereas the eastward-propagating downwelling
Kelvin waves are reected to downwelling Rossby
waves at the ocean eastern boundary. Because
both the upwelling Kelvin and downwelling
Rossby waves have westward zonal currents,
their eects are to push the WPWP back to the
western Pacic. ese negative feedbacks along
with the one associated with the mean zonal
current make the coupled system to oscillate
on interannual time scales.
Picaut et al.  did not give a set of heuristic
equations for the advective–reective oscillator,
unlike the other three oscillator models. However,
Picaut et al. demonstrated an interannual model
oscillation by using a linear ocean numerical model
forced by wind anomalies, which was associated
with the zonal current of the rst baroclinic Kelvin
and rst meridional Rossby waves. e physics for
the model to oscillate is due to the anomalous zonal
currents due to wave reections at both the ocean
western and eastern boundaries and the mean zonal
currents. As will be shown later in the section on
‘Special Case: e Advective–Reective Oscillator’,
the advective–reective oscillator can have a set
of heuristic equations and is a special case of the
818 Natl Sci Rev, 2018, Vol. 5, No. 6 REVIEW
The unied ENSO oscillator
As shown in the ‘Four ENSO oscillators’ section,
four ENSO oscillators have been proposed and they
are all capable of oscillating on interannual time
scales. Given these four oscillators, Wang  devel-
oped the unied ENSO oscillator based on the dy-
namics and thermodynamics of Zebiak and Cane’s
coupled ocean–atmosphere model. e motivation
is to include the physics of all previous ENSO os-
cillator models, with a hypothesis that ENSO may
be a multi-mechanism phenomenon and their rel-
ative importance may depend on time. Consider-
ing ENSO interannual anomalies in both the eastern
and western Pacic, Wang  formulated and de-
rived the unied oscillator:
dt =dT −Rτ1τ1,(10)
dt =eh −Rτ2τ2,(11)
where T,h,τ1and τ2are four variables that rep-
resent the SST anomalies in the equatorial east-
ern Pacic, the thermocline-depth anomalies in the
o-equatorial western Pacic, the zonal wind-stress
anomalies in the equatorial central Pacic and the
zonal wind-stress anomalies in the equatorial west-
ern Pacic, respectively. All of the model parame-
ters are constants. For a given set of parameters,
Equations (8)–(11) can oscillate on interannual
e rst term on the RHS of Equation (8) repre-
sents Bjerknes’s positive feedback. e second and
third terms represent the negative feedbacks as a
result of ocean western boundary wave reection
and the western Pacic wind-forced wave eect, re-
spectively (Fig. 5). e fourth term is the wave re-
ection contribution at the ocean eastern bound-
ary. Equation (9) shows that the o-equatorial ther-
mocline anomalies in the western Pacic are related
to the zonal wind-stress anomalies in the equatorial
central Pacic. Equation (10) states that the zonal
wind-stress anomalies in the equatorial central Pa-
cic are controlled by the SST anomalies in the
eastern Pacic and Equation (11) indicates that the
zonal wind-stress anomalies in the equatorial west-
ern Pacic are controlled by the o-equatorial ther-
mocline anomalies in the western Pacic. As shown
next, the unied oscillator of Equations (8)–(11)
can reduce to the four previous ENSO oscillators
by making further simplications and assumptions.
In other words, the four ENSO oscillators—the
delayed oscillator, the recharge–discharge oscilla-
tor, the western-Pacic oscillator and the advective–
reective oscillator—are special cases of the unied
Special case: the delayed oscillator
e delayed oscillator assumes that ocean–
atmosphere interaction in the western Pacic and
wave reection at the ocean eastern boundary
Forced K wave
Reflected K wave
(u<0, h<0) Reflected K wave
The unified oscillator for ENSO
Figure 5. Schematic diagram of the unied oscillator. The unied oscillator includes all negative feedbacks of the previous
four ENSO oscillators, which include the reected Kelvin wave at the ocean western boundary, the discharge process due
to Sverdrup transport, the western-Pacic wind-forced Kelvin wave and the reected Rossby wave at the ocean eastern
REVIEW Wang 819
are not important. By seing b2=0 and b3=0
in Equation (8), two variables of τ2and hin the
western Pacic are decoupled from the coupled
system. If the time derivative in Equation (10) is
further dropped, the unied oscillator reduces to:
Equation (12) is the delayed oscillator of Equa-
tion (1) with A≡ad/Rτ1and B≡b1d/Rτ1.
Special case: the recharge–discharge oscilla-
e recharge–discharge oscillator considers two
variables: the SST anomalies in the equatorial east-
ern Pacic and the thermocline anomalies in the
equatorial western Pacic. Jin arguedthat
equatorial-wave propagations do not explicitly ap-
pear in the recharge–discharge oscillator, although
the tropical Pacic Ocean is adjusted by equatorial-
wave dynamics. If we drop the time derivatives in
Equations (10) and (11), set all delayed parame-
ters to zero (i.e. η=0, δ=0 and λ=0) and ig-
nore wave reection at the ocean eastern boundary
(b3=0), the unied oscillator reduces to:
dt =ad −b1d
e mathematical form of Equations (13) and
(14) is the same as the recharge–discharge oscil-
lator of Equations (2) and (3), with C≡(ad −
However, in Jin’s recharge–discharge oscillator, his
the thermocline anomaly in the equatorial western
Pacic (instead of the o-equatorial western Pacic
Special case: the western-Pacic oscillator
e western-Pacic oscillator emphasizes the im-
portance of western-Pacic Ocean–atmosphere in-
teraction in ENSO. For the western-Pacic oscilla-
tor model to oscillate, wave reections at the ocean
western and eastern boundaries are not necessar-
ily required. If we neglect the negative feedbacks
from wave reections by seing b1=0 and b3=0,
Equations (8)–(11) reduce to:
dt =dT −Rτ1τ1,(17)
dt =eh −Rτ2τ2.(18)
Equations (15)–(18) are the western-Pacic os-
cillator of Equations (4)–(7).
Special case: the advective–reective oscilla-
When Picaut et al.  proposed the advective–
reective oscillator for ENSO, they did not provide a
set of heuristic equations for the advective–reective
oscillator. However, if we set b2=0 in Equation
(8), the unied oscillator model is reduced to:
dt =dT −Rτ1τ1.(20)
As shown by Wang  and Baisti and Hirst
, two advection terms u∂¯
appear in the rst term of aτ1in Equation (19).
erefore, the contributions of zonal current are
in the rst term on the RHS of Equation (19), i.e.
in aτ1. e negative feedback of the anomalous
zonal current corresponding to wave reection
at the ocean western boundary is in the term
−b1τ1(t−η) in Equation (19). e contribution
of wave reection at the ocean eastern boundary is
presented by the third term on the RHS of Equation
Non-linear oscillatory models
All ENSO oscillator models in the ‘Four ENSO os-
cillators’ and ‘e unied ENSO oscillator’ sections
above are linear, producing periodic oscillations.
However, when a noise or high-frequency forcing is
added to these linear models, irregular oscillations
appear. On the other hand, non-linear oscillatory
models for ENSO were also built and developed
[37–43]. One of advantages for these non-linear
simple models is that models themselves can pro-
duce irregular oscillations without the need for a
noise or high-frequency forcing. Additionally, these
non-linear models also address some important
features associated with ENSO. For example, Guck-
enheimer et al.  investigated the predictability
of strong El Ni˜
no events that seem to occur on
decadal time scales, such as the events in 1982–83,
820 Natl Sci Rev, 2018, Vol. 5, No. 6 REVIEW
1997–98 and 2015–16. Using a non-linear simple
model, they argued that ENSO can be in a regime
of irregular switching between an oscillatory state
that has strong El Ni˜
no events and a chaotic state
that lacks strong events, and that, in this regime,
the timing of strong El Ni˜
no events on decadal time
scales is unpredictable. Liang et al.  employed an
analytical but non-linear model to study the ENSO
asymmetry—the strongest El Ni˜
no is stronger than
the strongest La Ni˜
na. eir model showed that the
ENSO asymmetry occurs when the two adjacent
strongest warm events are spaced farther apart and
more small events occur in between, consistently
with the recent result of Guckenheimer et al. .
Kohayama and Hartmann  used a non-linear
recharge oscillator model to suggest that the non-
linear ENSO warming suppression causes extreme
nos to dissipate but La Ni˜
nas to remain almost
unchanged, causing a La Ni˜
na-like mean state
warming in the tropical Pacic, which is consistent
with observations and GFDLESM2M model.
A STABLE MODE INTERACTING WITH
ENSO is also viewed as a stable mode interacting
with high-frequency forcing or triggering by stochas-
tic atmospheric/oceanic forcing [44–48]. is view
and hypothesis suppose that high-frequency forcing
or random forcing external to the ENSO system is
a cause of ENSO. e beautiful and aractive part
of this view is that it provides a natural explanation
in terms of noise for the irregular feature of ENSO.
Since this view of ENSO requires the presence of
‘noise’, it can easily explain why no El Ni˜
no is ex-
actly same and El Ni˜
no events are so hard to predict
[47,49]. e external atmospheric variability or forc-
ing may include the Madden-Julian Oscillation and
westerly wind bursts [50–56], and the oceanic noise
may involve oceanic high-frequency variability such
as the tropical instability waves .
no can be considered to be either a self-
sustained oscillator mode or a stable mode interact-
ing with high-frequency forcing. In either case, when
an El Ni˜
no event occurs, the tropical central and
eastern Pacic Ocean is warmer than the normal.
However, aer an El Ni˜
no event peaks in the winter,
negative feedbacks are needed to terminate the fur-
ther growth of the interannual anomalies. In other
words, the negative feedbacks associated with the
delayed oscillator, the recharge–discharge oscilla-
tor, the western-Pacic oscillator and the advective–
reective oscillator may be still valid for demise of an
no, even if El Ni˜
no is regarded as a stable mode
interacting with high-frequency forcing. Mantua and
Baisi  showed that independent warm events
still need the negative feedback due to wave reec-
tion at the ocean western boundary. In summary, the
physics of the previous ENSO oscillators are funda-
mental elements of ENSO, regardless of the views of
EASTWARD- AND WESTWARD-
PROPAGATING SLOW MODES
Tropical Pacic Ocean and atmosphere interac-
tion is able to produce coupled slow modes, which
can be a slow westward-propagating unstable mode
[59,60] or a slow eastward-propagating unstable
mode [60–67]. ese coupled slow modes were
further investigated numerically by Hirst  and
analytically by Wang and Weisberg , demon-
strating that they are related to ENSO anomaly
propagations on interannual time scales. e de-
layed oscillator physics are not relevant to these cou-
pled ocean–atmosphere slow modes. For example,
Wang and Weisberg  performed two groups of
model experiments with the closed and open ocean
western boundary conditions. eir model results
demonstrated that the evolutions of the eastward-
propagating slow modes in these two experiments
are nearly identical, indicating that wave reection at
the ocean western boundary does not play an impor-
tant role in the slow modes because the open ocean
western boundary does not allow waves to be re-
Neelin  introduced a concept of slow SST
modes that are similar to the coupled slow modes
due to air–sea coupling. ey argued that the SST
modes are largely distinct from the ocean dynamics
modes that are relevant to the delayed oscillator.
e existence of these modes in the coupled
ocean–atmosphere system depends on the ocean
adjustment processes. Two key adjustments on in-
terannual time scales are the dynamical adjustment
of the equatorial ocean and the thermodynamical
change in SST due to air–sea coupling. e relative
time length of these two adjustments determines
which modes appear in the coupled system. If
the thermodynamical change in SST is slow, the
coupled system favors the SST mode instead of the
ocean-wave dynamics. However, if the dynamical
adjustment of the ocean is slow, the equatorial-wave
dynamics plays an important role in the interannual
oscillation in the coupled ocean–atmosphere sys-
tem. Jin and Neelin  and Neelin and Jin 
further argued that, in most of the model parameter
space, the coupled modes are the mixed SST–ocean
dynamics modes. An advantage of the slow modes
is that they can explain the propagating property
REVIEW Wang 821
of interannual anomalies, whereas the delayed
oscillator mode produces a standing oscillation.
e direction of the mode’s eastward or west-
ward propagation is determined by physical pro-
cesses. We rst examine a case with a positive SST
anomaly in the equatorial eastern and central Pacic.
e atmospheric wind responses are westerly and
easterly wind anomalies in the west and east of the
positive SST anomaly, respectively . is wind
paern produces anomalous zonal currents that ad-
vect warm (cold) water to the west (east) of the re-
gion. At the same time, the westerly (easterly) wind
anomalies to the west (east) cause anomalous down-
welling (upwelling). Because both zonal advection
and downwelling increase the SST in its western
side, the SST anomaly then propagates westward.
On the other hand, the westerly wind anomalies
deepen the thermocline in the east, which increases
the SST in the east by mean upwelling. Furthermore,
the non-linear term of the anomalous vertical tem-
perature gradient by the anomalous upwelling can
also increase the SST in the east . us, both
these processes cause the SST anomaly to propagate
Next, we consider the interannual anomaly prop-
agation in the western Pacic Ocean [47,75]. We
rst discuss dynamical processes. e westerly wind
bursts or the Madden-Julian Oscillation events in
the western Pacic generate eastward current, which
advects the warm water eastward, thus reducing
the east–west temperature gradient. e reduction
of the east–west temperature gradient weakens the
easterly trade winds, which further increases the SST
in the east, resulting in an eastward propagation. Sec-
ond, we consider thermodynamical processes. e
mean zonal wind paern in the western Pacic dur-
ing the boreal winter and spring is a weak westerly
from 130◦E to 150◦E and an easterly from 150◦Eto
the Date Line. An equatorial westerly anomaly su-
perimposing the above mean zonal wind will cause
dierent SST changes. Because the region of 160E◦
to 170◦E is covered by the mean easterly wind,
the westerly wind anomalies reduce the total wind
speed and decrease evaporation, thus causing an
increase in SST. However, due to the mean west-
erly wind west of 150◦E, the westerly wind anoma-
lies enhance the total wind speed, resulting in a de-
crease in SST through increased evaporation. As a
result, an eastward SST zonal gradient is induced,
which in turn reinforces the equatorial westerly wind
anomalies in the western Pacic . e interac-
tion between the eastward SST gradient and west-
erly anomalies causes an eastward propagation of in-
terannual anomalies when an El Ni˜
no event occurs
in the tropical Pacic.
DYNAMICS OF THE CENTRAL-PACIFIC
EL NI ˜
Two dierent types of ENSO events have re-
cently been paid aention to, although they were
not new phenomena in the tropical Pacic and
were mentioned in the literature a long time ago
[76,25,77–82]. e two types of ENSO events are
dened based on locations of their maximum SST
anomalies: the eastern-Pacic (EP) type over the
eastern tropical Pacic and the central-Pacic (CP)
type near the International Date Line [79,81]. e
CP El Ni˜
no is also referred to as Date Line El Ni˜
, El Ni˜
no Modoki  or Warm Pool El Ni˜
. Does the CP El Ni˜
no have dierent mecha-
nisms from the EP El Ni˜
In spite of the maximum anomaly location dif-
ference, the CP and EP El Ni˜
no all have a com-
mon paern that the equatorial westerly (easterly)
anomalies are always located to the west (east) of the
positive SST anomalies. erefore, all of the ENSO
mechanisms discussed previously may work on the
CP El Ni˜
no. Ashok et al.  stated that the wind-
anomaly paern induces the thermocline changes
that are responsible for generating the CP ENSO
event. e equatorial westerly and easterly wind
anomalies force downwelling Kelvin and Rossby
waves that propagate eastward and westward, re-
spectively. ese propagating waves work together
to deepen the thermocline in the central Pacic, thus
inducing the CP El Ni˜
no. Kug et al.  showed that
the equatorial easterly anomalies in the eastern Pa-
cic increase upwelling and surface evaporation and
then decrease the warming of the CP El Ni˜
Because the thermocline depth in the central Pa-
cic is relatively deep, the wind-induced thermocline
variations may not be ecient in inducing the CP
SST anomalies. Instead, they suggested that ocean
advections are responsible for the development of
the CP El Ni˜
Yu et al.  performed a mixed-layer heat-
budget analysis and also concluded that ocean-
advection processes are responsible for the rapid in-
crease in the SST anomalies during the CP ENSO
event. However, they suggested that the origin of
the warm SST anomalies is not local, but from at-
mospheric forcing in the extratropics and subse-
quent air–sea interactive processes in the subtrop-
ics. ey indicated that the warm SST anomalies rst
appear in the northeastern subtropical Pacic and
then expand toward the equatorial central Pacic.
e air–sea interactive processes in the subtropics,
which make the warm SST anomalies spread equa-
torward, are similar to those depicted by the sea-
sonal footprinting mechanism [84–86]. e foot-
printing mechanism provides an explanation for how
822 Natl Sci Rev, 2018, Vol. 5, No. 6 REVIEW
mid-latitude atmospheric variations in the winter
can produce subtropical SST anomalies, maintain
them from the winter to the next summer and at
the same time spread them toward the equatorial
Pacic. In fact, many studies showed that the CP
type of El Ni˜
no event is aributed to the North Pa-
cicmeridional mode (NPMM) variability[87–89].
e NPMM is generated in the subtropical north-
eastern Pacic through the wind–evaporation–SST
feedback of Xie . e associated NPMM vari-
ability expands toward the equatorial central Pacic
and then the Bjerknes feedback comes in for the fur-
ther development of the CP El Ni˜
By emphasizing the role of the zonal advective
feedback in the CP El Ni˜
no event, Fang and Mu
 recently extended the work of the recharge–
discharge oscillator. ey developed a three-region
conceptual model including the central Pacic in ad-
dition to the two-region (the eastern and western
Pacic) model of the recharge–discharge oscillator.
e three-region oscillatory model is able to depict
the dierent variations between the CP and EP El
no events. Fang and Zheng  further showed
that the main characteristics of the CP type of ENSO
can be reproduced if the thermocline feedback is
switched o and the zonal advective feedback is re-
tained as the only positive feedback, conrming the
dominant role played by zonal advective feedback in
the development of the CP type of ENSO event.
e study by Chen et al.  suggested that
no diversity largely depends on westerly wind
bursts in the equatorial western and central Pacic.
ey showed that the CP type of El Ni˜
no will occur if
westerly wind bursts are relatively weak and are con-
ned to the equatorial western Pacic. However, if
westerly wind bursts are strong and move across the
Date Line, the extreme EP type of El Ni˜
no will ap-
pear in the eastern Pacic. eir heat-budget anal-
ysis also revealed that, for the extreme EP El Ni˜
the vertical advection, i.e. thermocline feedback, is
the dominant factor; whereas the horizontal advec-
tions are important for the CP El Ni˜
no. is study
also concluded that ENSO is likely to be a combi-
nation of the self-sustaining oscillatory dynamics (as
described by various oscillators in the ‘Self-sustained
ENSO oscillators’ section) and the forcing of west-
erly wind bursts. Recently, Levine et al. empha-
sized that multiplicative (i.e. state-dependent) west-
erly wind burst forcing can cause extreme El Ni˜
events to occur in the eastern Pacic.
SUMMARY AND FUTURE WORK
e ENSO occurrence can usually be explained
by two views: (i) a self-sustained oscillatory mode
and (ii) a stable mode interacting with high-
frequency forcing such as westerly wind bursts and
Madden-Julian Oscillation events. e positive
ocean–atmosphere feedback hypothesized by
Bjerknes leads ENSO event to a mature phase.
Aer an ENSO event matures, negative feedbacks
are needed to cease ENSO anomaly growth in the
tropical Pacic. e previous studies have proposed
four negative feedbacks: (i) reected Kelvin waves
at the ocean western boundary, (ii) a discharge pro-
cess due to Sverdrup transport, (iii) western-Pacic
wind-forced Kelvin waves and (iv) anomalous
zonal advections and wave reection at the ocean
eastern boundary. ese four ENSO mechanisms
are respectively called the delayed oscillator, the
recharge–discharge oscillator, the western-Pacic
oscillator and the advective–reective oscillator.
Given the existence of four ENSO oscillators, the
unied oscillator is developed by including all
ENSO mechanisms, i.e. all four ENSO oscillators
are special cases of the unied oscillator. e unied
oscillator suggested that all physics associated with
the four oscillators may work in nature, and their
relative importance is time-dependent. e issue of
ENSO as a self-sustained oscillatory mode or a stable
mode interacting with high-frequency forcing is not
seled yet. ENSO may be a self-sustained oscillatory
mode during some periods, a stable mode during
others or a mode that is intermediate or mixed
between the former and the laer. e predictability
of ENSO is more limited if ENSO is a stable mode
interacting with high-frequency forcing than if
ENSO is a self-sustained oscillatory mode because
the former depends on random disturbances.
On interannual time scales, oceanic and atmo-
spheric variables are also observed to propagate east-
ward or westward. e propagating property of in-
terannual anomalies can be explained by the coupled
slow or SST modes due to the ocean–atmosphere
coupling. A number of dynamical and thermody-
namical processes compete to determine the direc-
tion of modes’ eastward or westward propagation.
An advantage of the coupled slow modes is that they
can explain the propagating property of interannual
ENSO anomalies, whereas the oscillator modes pro-
duce a standing oscillation.
ENSO studies have been focused on two types of
ENSO events: the EP and CP ENSO events. ese
two types of ENSO events have dierent locations of
maximum SST anomalies and heating anomalies, re-
sulting in dierent climate- and weather-related im-
pacts on the globe. In spite of the location dierence
of maximum SST anomalies, both the EP and CP
no events show the westerly wind anomalies
in the west of maximum SST anomalies. us, it is
not surprising that the physical processes (e.g. wave
REVIEW Wang 823
reections at the ocean western and eastern bound-
aries and ocean zonal advections) associated with
the dierent oscillator mechanisms involve the
CP El Ni˜
no events. Unlike the EP El Ni˜
CP El Ni˜
no may more involve the ocean zonal
advection feedback than the thermocline feedback.
In additional to the processes in the tropical ocean–
atmosphere system, the CP El Ni˜
no events may
originate processes in the extra-tropical Pacic.
In other words, the CP El Ni˜
no events may be
initiated and related to forcing or processes in the
Compared with other climate variability, ENSO
is the most successful climate phenomenon in terms
of its complete understanding due to the ocean–
atmosphere interaction. However, there are at least
several issues regarding the ENSO understanding
that require the research community to focus on in
the future. First, inter-ocean interactions can mod-
ify or change Pacic ENSO events, and thus in-
teractions among the Pacic, Indian and Atlantic
Oceans should be paid aention to in future re-
search. Several studies have recently demonstrated
the inuences of the Indian Ocean and Atlantic
Ocean on Pacic variability. For example, tropical
Indian Ocean warming can prohibit the develop-
ment of Pacic El Ni˜
no  and can strengthen the
tropical Pacic trade winds observed during the last
two decades . e Atlantic multidecadal oscil-
lation can increase the occurrence of the CP type
of ENSO events  and can aect multidecadal
ENSO variability . e tropical Atlantic warm-
ing induces a cold tropical eastern Pacic and a
warm Indo-Pacic on longer time scales . Sec-
ond, interactions among intra-seasonal variability
(e.g. westerly wind bursts and Madden-Julian Os-
cillation events), interannual ENSO variability and
decadal–multidecadal variability need to be further
studied [100,101]. ird, the relationship between
ENSO and global warming is uncertain. We are not
even sure whether greenhouse warming will produce
an El Ni˜
no-like or La Ni˜
na-like paern in the tropical
Pacic due to climate model uncertainty. Zheng et al.
 concluded that the spatial paern of tropical
Pacic surface warming is the major source of inter-
model uncertainty in ENSO amplitude change. On
the other hand, Cai et al.  claimed that the ex-
treme El Ni˜
no occurrence in the future in response
to greenhouse warming would double. To advance
and improve our understanding of anthropogenic
and natural ENSO variability, global coupled climate
models must be greatly improved and be able to sim-
ulate both ENSO and the response to greenhouse
warming. Fourth, it is unknown whether the ENSO
mechanisms discussed in this paper still hold in fu-
ture global-warming scenarios. It is hoped that these
issues and problems will be understood, or at least
partially understood, in the near future.
I would like to thank Mu Mu, Renhe Zhang, Chongyin Li, Hui-
jun Wang, Xiu-Qun Yang, Dongxiao Wang, Xin Wang and Huaxia
Liao for their comments and/or for helping get some references.
Four reviewers’ comments and suggestions helped to improve the
is research is supported by the National Natural Science Foun-
dation of China (41731173), the Pioneer Hundred Talents Pro-
gram of the Chinese Academy of Sciences, the Leading Talents
of Guangdong Province Program, the Strategic Priority Research
Program of the Chinese Academy of Sciences (XDA20060502)
and the National Program on Global Change and Air-Sea Inter-
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