Clim Dyn
DOI 10.1007/s00382-017-3575-3

Predictability of 2‑year La Niña events in a coupled generalcirculation model
Pedro N. DiNezio1,3 · Clara Deser2 · Yuko Okumura2 · Alicia Karspeck3

Received: 15 August 2016 / Accepted: 2 February 2017
© Springer-Verlag Berlin Heidelberg 2017

Abstract The predictability of the duration of La Niña
is assessed using the Community Earth System Model
Version 1 (CESM1), a coupled climate model capable ofsimulating key features of the El Niño/Southern Oscillation (ENSO) phenomenon, including the multi-year duration of La Niña. Statistical analysis of a 1800 year longcontrol simulation indicates that a strong thermocline discharge or a strong El Niño can lead to La Niña conditions
that last 2 years (henceforth termed 2-year LN). This relationship suggest that 2-year LN maybe predictable 18 to
24 months in advance. Perfect model forecasts performed
with CESM1 are used to further explore the link between
2-year LN and the “Discharge” and “Peak El Niño” predictors. Ensemble forecasts are initialized on January and Julycoinciding with ocean states characterized by peak El Niño
amplitudes and peak thermocline discharge respectively.
Three cases with different magnitudes of these predictors
are considered resulting in a total of six ensembles. Each
“Peak El Niño” and “Discharge” ensemble forecast consists of 30 or 20 members respectively, generated by adding a infinitesimally small perturbation to the atmosphericinitial conditions unique to each member. The forecasts
School of Ocean and Earth Science and Technology publication
number XXXX.
* Pedro N. DiNezio
pdn@hawaii.edu
1

Department of Oceanography, School of Ocean and Earth
Science and Technology, University of Hawaii at Manoa,
1000 Pope Road, Honolulu, HI 96822, USA

2

National Center for Atmospheric Research, Boulder, CO,USA

3

University of Texas Institute for Geophysics, Austin, TX,
USAshow that the predictability of 2-year LN, measured by
the potential prediction utility (PPU) of the Nĩno-3.4 SST
index during the second year, is related to the magnitude of
the initial conditions. Forecasts initialized with strong thermocline discharge or strong peak El Niño amplitude show
higher PPU than those with initial conditions of weakermagnitude. Forecasts initialized from states characterized
by weaker predictors are less predictable, mainly because
the ensemble-mean signal is smaller, and therefore PPU is
reduced due to the influence of forecast spread. The error
growth of the forecasts, measured by the spread of the Nĩno-3.4 SST index, is independent of the initial conditions andappears to be driven by wind variability over the southeastern tropical Pacific and the western equatorial Pacific.
Analysis of observational data supports the modeling
results, suggesting that the “thermocline discharge” and“Peak El Niño” predictors could also be used to diagnose
the likelihood of multi-year La Niña events in nature. These
results suggest that CESM1 could provide skillful longrange operational forecasts under specific initial conditions.
Keywords ENSO · El Nino · La Nina · prediction ·discharge

1 Introduction
Year to year fluctuations in the sea-surface temperature(SST) of the tropical Pacific Ocean have dramatic impacts
on weather and climate throughout the world. These variations are mainly driven by the El Niño/Southern Oscillation (ENSO) phenomenon, which is characterized by aninitial warming of the central and eastern Pacific that peaks
in boreal winter, known as El Niño, typically followed byanomalous cooling on the subsequent year, known as La

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P. N. DiNezio et al.

Niña. After this sequence of warm and cold SST anomalies
the tropical Pacific returns to near normal conditions. Muchof the research on prediction and predictability of ENSO
has focused on the onset of El Niño (Latif et al. 1998; Kirtman et al. 2001), mainly because predicting the onset of La
Niña events is comparatively trivial since they generally
follow El Niño.
According to linear ENSO theory, the onset and decayof El Niño and La Niña events are governed by winddriven changes in the depth of the equatorial thermocline,
the boundary separating the warm surface waters fromdeep and colder waters (Cane and Zebiak 1985; Neelin
et al. 1998). Weaker trade winds associated with an El
Niño event drive an initial relaxation of east-west tilt of theequatorial thermocline, resulting in a deeper thermocline
in the east and a shallower thermocline in the west. This
response is followed by a zonal-mean shoaling that peaks a
few seasons later once Sverdrup balance is stablished. Thisanomalously shallow thermocline initiates the demise of El
Niño because it increases the entrainment and upwellingof cold subsurface waters. During this transition phase theupper ocean is characterized by a reduction in heat content,
which is typically referred as “discharge” of equatorial heat
content. Conversely, stronger trade winds at the peak of La
Niña drive a delayed zonal-mean deepening of the thermocline characterized by increased upper ocean heat content.
During this “recharge” phase the anomalously deeper thermocline diminishes the cooling effect of upwelling initiating the demise of La Niña and transition into El Niño.
Observed El Niño and La Niña events show striking
departures from this linear oscillatory behavior. First, mostEl Niño events last a few seasons and then quickly transition into La Niña. In contrast, one out of two observed La
Niña events last 2 years or longer (Kessler 2002; McPhaden
and Zhang 2009; Ohba and Ueda 2009; Okumura andDeser 2010; Okumura et al. 2011; Deser et al. 2012).
Moreover, very few La Niña events transition directly into
El Niño as expected from oscillatory behavior. Instead,the great majority of La Niña events slowly decay, oftentimes taking several years of near-neutral conditions until
the next El Niño event is triggered (Kessler 2002). Theseobservational findings suggest a break down of the oscillatory coupling between SST and thermocline anomalies thatare at the heart of linear ENSO theory.
Several mechanisms have been proposed to explainthese asymmetries in the dynamics and duration of El
Niño and La Niña. These mechanisms emphasize different asymmetries in the coupling between SST, wind, andthermocline depth during El Niño vs. La Niña. One mechanism argues that positive SST anomalies lead to a muchstronger wind response and associated delayed thermocline
response than negative SST anomalies of the same magnitude. This asymmetric wind response arises from the13

non-linear response of atmospheric deep convection to SST
anomalies and explains the quick and effective termination of El Niño events, as well as their consistent transition
into La Niña. In contrast, negative SST anomalies drive a
weaker wind response, which leads to a weaker thermocline recharge and an ineffective termination of La Niña
events (e.g. Frauen and Dommenget 2010; Choi et al. 2013;
DiNezio and Deser 2014). Spatial asymmetries in the patterns of the wind anomalies of El Niño and La Niña havealso been linked to their asymmetric duration (e.g. Ohba
and Ueda 2009; Okumura et al. 2011).
Other studies have focused on the role of thermocline
depth anomalies on the dynamics of 2-year La Niña. Hu
et al. (2013) proposed the following conditions for a second year La Niña: (1) a strong La Niña, which would interrupt the recharge phase by causing the subsurface ocean
to remain cold, and (2) absence of downwelling equatorial Kelvin waves after the first year, which would otherwise lead to the demise of La Niña. Because thermocline
depth anomalies lead SST anomalies by a few seasons, thenthese mechanisms could be used to predict the return or thedemise of La Niña, and hence its duration. However, themechanisms proposed by Hu et al. (2013) may not provide
predictions with lead times longer than 1 year for the following reasons. The first condition, a strong La Niña during
the first year, could provide information up to 12 months inadvance, however is not supported by observations whichshow that some of the strongest events (e.g. the La Niña
event of 1988/1989) have lasted only 1 year. The second
condition would provide prediction lead times shorter than
1 year, which would be useful, but would not represent an
improvement from the predictions provided by current seasonal climate forecast systems.
Longer term predictions have received less attention
beyond the study of DiNezio and Deser 2014, (hereafterDD14). Based on analysis of climate model output andocean reanalysis data, DD14 showed that the state of ENSO
the year following the first peak of La Niña is related to themagnitude of the thermocline shoaling 6 months before theonset of La Niña that is, 18 months before the second year
peak of La Niña. This relationship indicates that a strong
thermocline shoaling or discharge prior to La Niña’s firstpeak will lead to La Niña conditions during the following year, i.e. a 2-year La Niña. DD14 propose that eventswith a larger discharge must persist longer because therecharge—the thermocline deepening following the peakof La Niña–is proportionally weaker and therefore ineffective at returning to thermocline to neutral conditions in just
1 year. As discussed above, this asymmetry occurs becauseof nonlinearities in both the wind response (Choi et al.
2013), but also because vertical thermocline displacements
are less effective at influencing SSTs during the recharge
phase relative to the discharge phase. During the recharge,

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

the thermocline deepens and becomes progressively decoupled from the ocean’s surface layer becoming less effectiveat influencing SSTs. As a result, La Niña events initiatedby a large discharge have to persist for an additional year
in order to drive the integrated recharge heating required toreturn to neutral conditions.
Although our mechanistic understanding of the dynamics of La Niña events has advanced considerably, it is not
yet clear whether skillful prediction of the duration of La
Niña is possible. This is a critical issue for the predictionof persistent drought conditions associated with La Niña inareas such as, the Southeastern United States, Texas, andCalifornia (Schubert et al. 2004; Seager et al. 2008; Hoerling et al. 2009; Cook et al. 2011; Trenberth et al. 1988;
Hoerling and Kumar 2003; Seager 2007; Hoerling et al.
2013. Some of the proposed mechanisms, particularly those
focusing on the role of the equatorial thermocline, suggest that there are precursor conditions that could be used
to anticipate the evolution of La Niña. One observational
study evaluating the evolution of SST anomalies and heat
content, a proxy for thermocline depth, found that the transition from La Niña to El Niño may take longer than 1 year
(Kessler 2002). The study of DD14 found that the depth of
the thermocline six months before the onset of La Niña, i.e.
at the peak of the discharge phase, is correlated (r = 0.47
) with SST anomalies a year and a half later. This relationship could provide an 18-month lead time for predicting
a 2-year La Niña event. However, the value of r suggeststhat there is a large fraction of variability that could be
explained by other predictors or be caused by unpredictable
atmospheric variability (Penland and Sardeshmukh 1995;
McPhaden and Yu 1999; Thompson and Battisti 2001;
Fedorov et al. 2003; Chiodi and Harrison 2015).
The aim of our study is to explore the predictability ofthe duration of La Niña using the Community Earth System Model Version 1 (CESM1), a climate model that simulates realistic ENSO characteristics, particularly in regards
to the asymmetric duration of El Niño and La Niña. Our
approach is idealized in the sense that we use CESM1 topredict its own simulated climate trajectories. The resulting “perfect model” forecasts allow us to explore the upper
limits of predictability, that is, the skill of the model underthe best possible conditions. Using this “perfect model”
approach we explore the link between initial conditions
and long-term prediction of the duration of La Niña. Particularly, we focus on identifying initial conditions that
could allow skillful prediction of 2-year La Niña more than
1 year in advance. First, we explore the predictors of La
Niña duration in a long control simulation performed with
CESM1. We then perform a series of “perfect model” forecasts from selected events simulated in the CESM1 control
simulation. We use these forecasts to explore how long theforecasts remain skillful, mainly by focusing on 24 and18-month lead time forecasts initialized at the peak of El
Niño and the peak discharge, respectively. Last, we explore
the effect of other modes of variability on error growth andassociated predictability loss.

2 Data and methods
2.1 Coupled general circulation model
The CESM1 is a numerical model of the global coupledclimate system consisting of coupled atmosphere and ocean
global general circulation models (GCMs) and comprehensive land, cryosphere, and biogeochemistry models.
Our forecasts were performed with all components of themodel (ocean, atmosphere, cryosphere and land) were configured at nominal 1◦ latitude–longitude resolution. Landand ocean biogeochemistry modules were active, but configured so that their associated carbon fluxes do not affectatmospheric CO2 and hence climate. A brief overview of
CESM1 and salient improvements to the atmospheric andoceanic model components is given below. Further details
about CESM1 maybe found in Hurrell et al. (2013), Kay
et al. (2015), and in a special collection of the Journal of
Climate (see http://journals.ametsoc.org/page/CCSM4/
CESM1).
2.2 Long pre‑industrial control simulation
We use a multi-century control simulation performed
with CESM1 forced by constant external forcings set at
pre-industrial levels. The control simulation is 2200 years
in length, of which years 400–2200 are used in our study.
The first 400 years exhibit climate drift due to initialization
and are not considered in the analysis. The remaining 1800
years used in our analysis exhibit negligible climate drift.
More details on the initialization and equilibration of thecontrol simulation may be found in Kay et al. (2015).
2.3 Observational datasets
The following observational datasets are used to evaluate the realism of CESM1’s ENSO simulation: SST fromthe Hadley Centre Sea Ice and SST (HadISST) dataset(Rayner et al. 2003) during 1880–2013 on a 1◦× 1◦ longitude–latitude grid; and (2) upper-ocean temperature fromthe European Centre for Medium-Range Weather Forecasts (ECMWF) ORA-S4 ocean reanalysis for the period
1958–2013 (Balmaseda et al. 2013). ORA-S4 assimilates
temperature and salinity profiles, and along-track altimeterderived sea-level anomalies on a 1◦× 1◦ longitude–latitude
grid with progressively finer latitude resolution (0.3◦) in thetropics, and 42 levels in the vertical (18 of which are in the13

P. N. DiNezio et al.

The Nĩno-3.4 SST index is computed by averaging the SST
anomalies over the central Pacific (120◦W–170◦W, 5◦S–5◦
N) for both the CESM1 and HadISST V1.1. Thermocline
depth, ZTC, is computed as the depth of the maximum vertical temperature gradient in the upper 500 m using the threedimensional output from CESM1 and the ORA-S4 reanaly′
sis. The zonal-mean thermocline index, Z̄ TC, is defined as
the ZTC anomalies averaged across the equatorial Pacific(140◦W–80◦W, 5◦S–5◦N). SST and ZTC anomalies are computed relative to the 1958-2013 climatology, the common
period between the ORAS-4 and HadISST datasets.
2.5 Simulated ENSO
CESM1 simulates many features of ENSO observed innature, particularly the asymmetries in amplitude andduration between El Niño and La Niña. The Nĩno-3.4 SST
index, an index commonly used to capture SST variability
associated with ENSO, shows frequent multi-year La Niña
events, which generally follow strong El Niño events bothin observations (Fig 1a) and the CESM1 control (Fig 1b).
We define 2-year La Niña (2-year LN) events as those witha Nĩno-3.4 SST index less than −0.5 standard deviations
for two consecutive DJF seasons. Such persistent La Niña
events in the model occur with a 45% frequency similar
to observed events according the HadISST dataset whichshows 14 out of 29 (44%) 2-year LN during the 1870–2015
period. Note the more recent 1958–2013 period had a totalof 8 2-year LN out of 11 events (75%). The frequency ofoccurrence of simulated 2-year LN also exhibits remarkable multi-decadal variations, with values ranging from 6
to 73% over 50-year periods.
The spectrum of the simulated Nĩno-3.4 index shows abroad peak in the 2–7 years band similar to observations
and previous versions of the model (Fig. 1c). On average, the maximum power is approximately 50% larger
in CESM1 compared to HadISST, albeit it appears to be
more realistic than in CCSM4, which simulated a spectral peak twice as large as observed. The stronger ENSO
variability in CESM1 results is also reflected in a standard deviation of the Nĩno-3.4 SST index of 0.91 K compared to 0.76 K for the detrended HadISST1.1 data during the 1870–2015 period. Observations show centennialchanges in ENSO amplitude, with values of 0.70 K for

13

Nino−3.4 SST index (K)Observed

3
2
1
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(b)

s.d. = 0.88

1970

1980

1990

2000

2010

CESM1

3
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s.d. = 0.99

1440

1450

(c)
spectral power (K2 year−1)

2.4 ENSO indices(a)Nino−3.4 SST index (K)upper 200 m). The ORA-S4 reanalysis is driven by winds
from the 40-year ECMWF Re-Analysis Project (ERA-40)
until 1989, ERA-Interim from 1989–2010, and ECMWFNWP analysis thereafter. ORA-S4 also uses observed SST,
sea-surface salinity, sea-ice, and global mean sea-level tocorrect biases in the heat and fresh-water budgets.

1460

1470

frequency (year−1)
1
0.1

1480

0.01

Obs (HadISST1)
CESM1 control
CCSM4 control

1.5

1

0.5

0

0

10

1

10
period (year)

2

10

Fig. 1  a Observed and b simulated Nĩno-3.4 SST index corresponding to 50 year periods (1964–2015 for observations and 1436–1485
for CESM1). c Power spectrum [ K 2 year−1] of the Nĩno-3.4 SST
index from detrended observations (HadISST1.1, dashed red curvefor 1870–1969 and solid red curve for 1916–2015), CESM1 (modelyears 400–2200, blue curve), and CCSM4 (model years 1–1300;
green curve). CESM1 and CCSM4 data are from control simulations
performed with constant pre-industrial forcings. The light-blue shading depicts the 95% confidence intervals for the CESM1 power spectrum based on the individual spectra of 100-year segments. Dashedblue line shows the power spectra of CESM1’s simulated 100-year
period with the smallest spectral peak. Note that to quantitatively
compare the variance between the model and observations, the curves
must be integrated over the frequency

the 1870–1969 period and of 0.77 K for the 1916–2015
period. CESM1 simulates centennial variations in amplitude ranging from 0.81 to 1.02 K (computed from overlapping 100 year periods, not shown). Although the model’s ENSO amplitude is larger than observed, it represents
an improvement relative to CCSM4, which had a mean
ENSO amplitude of 1.07 K (Deser et al. 2012). Last,
CESM1 has a tendency to simulate El Niño events thatstart with weak Nĩno-3.4 SST warming (about 1 K) fora first year, attaining full amplitude 1 year later (Fig. 1b,e.g. El Niño events in 1540s and 1550s decades). Whilesimilar 2-year El Niño events have been observed (e.g.
during 1931 and 2015), these events are more frequent in
the CESM1 control, in which 1 in 3 strong El Niño eventsare preceded by warming the previous year.

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

2.6 Simulated 2‑year La Niña
We evaluate the dynamics of the simulated 2-year LN bycomparing the composite evolution SST and ZTC anomalies against observations. The observed composite is basedon 8 2-year events during the 1958–2013 period for which
there is available sub-surface temperature data from ORAS4 reanalysis. The simulated composite is based on 156
events. The observed composite agrees with the analysisof (Okumura and Deser 2010) which showed that 2-year
La Niña are common throughout the historical record. We
identify key times during the evolution of 2-year LN eventsby their calendar month together with a superscript indicating the lag in months relative to January of the second year
peak (Jan0), which is our target forecast date. Observed
and simulated La Niña have their first peak during boreal
winter, denoted Jan−12, 1 year after the preceding El Niño,
denoted Jan−24 (Fig 2, shading).
Both observations and CESM1 show that the thermocline shoals across the equatorial Pacific after the peak of
El Niño with peak shoaling occurring around July (Jul−18 )(Fig 2, contours). This zonal mean shoaling of the thermocline (Fig 2, purple contours), is a delayed response to(a) HadISST/ORAS4
1958−2013
10

Jan

8/11

156/343
5

15

0
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15

0

(b) CESM1 control

5

10

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10

0 20 20

0

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15

−12

10

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Jul

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0

−15

15

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−25
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Jul

−18

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10

Jan−240−5−6

Jan−24 −25−30

−15

−20

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15

5

5
o

o

o

o

o

o

150 E 180 150 W120 W 90 W
−1.5

−1

−0.5

o

o

o

o

150 E 180 150 W120 W 90 W
00.5

SST anomaly (K)1

1.5

Fig. 2  Spatiotemporal evolution of simulated sea-surface temperature (SST) anomalies (shading) and thermocline depth anomalies′(ZTC, contours) for a observed and b simulated La Niña (LN) events
lasting 2 years (2-year LN). Observational data are HadISST1.1(Rayner et al. 2003) and ORAS4 (Balmaseda et al. 2013) respectively. Simulated data are from the control simulation performed with
CESM1 under constant pre-industrial forcings. Orange (purple) contours show positive (negative) thermocline depth anomalies on 5 m′
intervals. Equatorial SST and ZTC
anomalies are averaged over the 5◦◦
S-5 N band. The observation-based composites are computed using
8 observed 2-year LN out of a total of 11 events from the 1958–2013
period. The model-based composite is computed using 156 simulated
2-year LN out of a total of 343 events from the CESM1 control. Refer
to Sect. 2.6 for details on the methodology used to select 2-year LN
eventswind anomalies during El Niño, and is typically characterized by a reduction in upper ocean heat content over theequatorial Pacific, hence the moniker “discharge” of equatorial heat content. La Niña onsets after the discharge (Fig2, blue sharing around Jan−12), as the shallower thermocline enhances the cooling effect of equatorial upwelling.
The termination of La Niña occurs 2 years later (Jul+6 )during the “recharge” phase characterized by an anomalously deeper thermocline across the equatorial Pacific (Fig′2). The simulated ZTC
anomalies are strikingly realistic interms of magnitude and timing suggesting that the simulated 2-year LN are governed by similar dynamics than innature.
2.7 Perfect model forecasts
We selected three events from the control simulation andran a series of forecasts for each case study. The forecasts
are not affected by ocean initial condition uncertainty, initialization shocks, or model drift because the model is use
to predict itself. Therefore the resulting “perfect model”
forecasts can be used to assess the potential predictabilityof the duration of La Niña in CESM1.
All three selected events exhibit 2-year LN of similar
magnitude, but are preceded by El Niño events of different amplitudes, both in terms of SST and thermocline depth
anomalies (Fig. 3). The first case is characterized by astrong El Niño leading to a large shoaling of the thermocline (Fig. 3a). This event shows the largest SST anomalies,
with peak values averaging more than 3 K over the Nĩno-3.4 region. This event also shows the largest thermocline
shoaling (discharge) among the three cases. Averaged
over the equatorial waveguide (5◦S–5◦N), the discharge isabout −40 m at its peak in May of year 1455. The secondcase shows weaker positive SST anomalies at the peak of
El Niño, as well as less pronounced thermocline shoaling,with peak Nĩno-3.4 SST anomalies of 2.5 K and dischargeof about −30 m (Fig. 3b). The third event shows a much
weaker El Niño and thermocline shoaling, with peak Nĩno-3.4 SST anomalies of less than 1 K and discharge of about−20 m (Fig. 3c). A lagged correlation analysis of subsurface ocean temperatures throughout the tropics shows that
there are no significant off-equatorial signals correlated tothe evolution of La Nina, other than the surface signature of
meridional modes.
The three selected cases will be referred to as “strong”,“moderate” and “weak”, corresponding to the magnitude of
the preceding El Niño and thermocline discharge anomalies. Ensemble forecasts were initialized for each case on
January 1st of years 1455, 1182, 1125 respectively. We
refer to these as “Peak El Niño” forecasts because the initial conditions coincide roughly with the time of maximum
positive SST anomalies over the central Pacific. Additional

13

P. N. DiNezio et al.
strongEl Nino/discharge

moderate
El Nino/discharge

weak
El Nino/discharge

1458

1185

1128

1457

1184

1127

1456

1183

1126

1455

1182

1125

time

Fig. 3  As in Fig. 2 but for the
events selected for the perfectmodel forecasts. Dashed orange
and magenta lines show theinitial January and July dates forthe 24- and 18-month lead forecasts. Dashed blue line shows
January peak of the second year
La Niña, the target forecast time

150°E

180° 150°W 120°W 90°W
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150°E
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180° 150°W 120°W 90°W
−1

0

1

150°E
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180° 150°W 120°W 90°W

3

SST anomaly (K)ensemble forecasts were initialized on July 1st of the same
years, which roughly coincides with the peak thermocline
shoaling; we refer to these as “discharge” forecasts. We
also refer to the “Peak El Niño” and “Discharge” ensemble forecasts as “24-month lead” and “18-month lead” forecasts respectively, corresponding the number of months
prior to the second La Niña January peak. Note that thenaming convention of both types of forecasts is based on
the initialized state and not the predictand.
For each of the “strong”, “moderate” and “weak” events
we generated an ensemble of 20 and 30 forecasts for the 18
and 24-month lead cases respectively. The 24-month forecasts consist of 30 members in order to estimate the spreadand ensemble-mean with higher accuracy. The size of theensembles allow us to minimally resolve the extremes ofthe forecast probability density function, such that, at least
one member will fall outside the 95% confidence interval(e.g., for an ensemble of 20 members, 1 member will falloutside the 95% confidence interval). Each member of theforecast ensembles was initialized with the same July 1st or
January 1st ocean, sea-ice, and land initial conditions. The
forecasts were initialized with a perturbed atmosphere andperfect knowledge of the ocean, sea ice, and land. However, we expect that the ocean initial conditions will be thedominant source of ENSO predictability. To simulate irreducible atmospheric uncertainty in the initial conditions,a unique roundoff level perturbation was made to the fullatmospheric temperature, velocity, and moisture fields foreach member. Each ensemble member was then integrated
forward in time for 4 years.
The spread of the Nĩno-3.4 SST index grows rapidly
from the infinitesimal perturbation, approaching 0.2 K
after the first two months. Note that both January- and Julyinitialized forecasts show similar spread over the first two

13months. Thus for the purpose of assessing multi-year predictability in this model, there is apparently no long-term
difference between perturbing with errors at the level ofrounding, versus at the level of real-world observations.
Any differences between these approaches would be effectively overcome after a few months of integration. The
month of initialization influences the spread after the second month, showing evidence of seasonal modulation andstate dependence. We discuss these features in great detailin Sect. 3.3.
2.8 Forecast plumes
For each forecast member, we computed SST anomalies
by removing the monthly mean climatology of the control
integration. We then computed each member’s Nĩno-3.4
SST index as described in Sect. 2.4. We follow the same′procedure to compute the forecasted Z̄ TC
index. We inter′
pret the ensemble mean Nĩno-3.4 and Z̄ TC
indices as thepredictable component of each forecast. The standard deviation of these indices within a given ensemble was used toquantify the spread among the different members, a measure of error growth of the predicted signals.
2.9 Measuring predictability
A number of metrics have been used in the literature toquantify predictability. Most of them are related in some
way to the magnitude of the ensemble spread relative to thevariance of the system, in other words, the signal-to-noise
ratio. However, other metrics can be useful for quantifying
the utility of ensemble forecasts (e.g. Kleeman 2002). In
this study we use the following two measures to examine
predictability: (1) the forecast ensemble spread, a simple

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

indicator of our confidence in a given forecast, and (2) the“potential prediction utility” (Kleeman and Moore 1999), a
measure of the usefulness of the forecast.
The potential prediction utility (PPU) can be expressedas:

PPU(t) =1,
1 + s2 (t)∕⟨x⟩2 (t)(1)

where s and ⟨x⟩ are the standard deviation and ensemble
mean Nĩno-3.4 SST indices, respectively. Like the commonly used correlation coefficient, the PPU also varies
from zero to one, with a value of one indicating a perfect forecast. The PPU naturally tends toward unity as theensemble spread tends to zero. According to this measure, the condition for a useful prediction is not simply low
ensemble spread; predictions can be equally useful whenthe ensemble mean signal is large.

3 Results
3.1 Precursors of 2‑year La Niña
We used the long control simulation to explore precursorsof 2-year LN. In this section we solely focus on predictors
based on equatorial dynamics and thus explore lead-lag
relationships between the Nĩno-3.4 SST index and the zonal′
mean thermocline depth index, Z̄ TC, which tracks the thermocline discharge and recharge. We selected a total of 536
El Niño events simulated by CESM1 regardless of whether
they transition into La Niña or not. In other words, we did
not consider “a priori” information, such as, whether: (1)El Niño evolves into La Niña, or (2) La Niña lasts 2 years.
The only criterion to select the events is that the Nĩno-3.4
SST index exceeds 0.5 standard deviations at the peak of El
Niño during the December-January-February (DJF) season.
The analysis thus includes a subset of El Niño events thatstart as a weak warming peaking to full amplitude 1 year
later as discussed in Sect. 2.5. We discuss the implicationsof these events below.
The predictand in this analysis is the magnitude of theNĩno-3.4 SST index two years after the peak of the selected
El Niño events. Nĩno-3.40 can be positive or negative
depending on whether El Niño or La Niña conditions occur
2 years later. 2-year LN events are identified when Nĩno3.40 is negative and less than −0.5 standard deviations. We
perform a lag-correlation analysis between Nĩno-3.40 andthe magnitude of the zonally averaged ZTC anomalies andthe Nĩno-3.4 SST index through the evolution of the simulated ENSO events for lead times from 24 to 6 months. All
correlation coefficients presented in this section are statistically significant with 99% confidence.

We begin the analysis with a “recharge” predictor,′
defined as Z̄ TC
6 months after the first peak of La Niña
�−6
̄
(ZTC , where the numeral superscript denotes the time
lag in months between the predictor and the predictand).
This predictor is based on the notion that La Niña events
are terminated by a deepening of the thermocline which
reduces the entrainment and upwelling of cold subsurface waters (Neelin et al. 1998). This deepening of thethermocline typically occurs 6 months after the peak of
La Niña and is sometimes described as a “recharge” ofheat content of the equatorial Pacific. We find that thisprecursor is significantly correlated (r = 0.48) with Nĩno-3.40 (Fig. 4a). Note that Nĩno-3.40 can either be positive(El Niño), neutral, or negative (La Niña) as shown by thered, gray, and blue shading in (Fig. 4a). This correlation
indicates that La Niña is more likely to end (Nĩno-3.40
�−6> −0.45 K) when the recharge is high (Z̄ TC> 0 m), andconversely, more likely to persist (Nĩno-3.40 < −0.45 K)
�−6when the recharge is low or absent (Z̄ TC< 0 m).
The “recharge” predictor provides information 6months in advance. However, other predictors earlier
in the evolution of ENSO events could provide longer
lead time information on the duration of La Niña. For
instance, the magnitude of the recharge is related to thepreceding La Niña and therefore could provide a 12month lead-time predictor. This “La Niña” predictor, themagnitude of La Niña during the first year (Nĩno-3.4−12 ),exhibits a relatively weak correlation (r = 0.12) with
Nĩno-3.40 (Fig. 4b). The fact that this correlation is positive is consistent with the idea that a stronger La Niña
will tend to persist longer than a weaker one (Hu et al.
2013); however this correlation is lower than that for the“recharge” predictor: thus longer-lead time forecasts may
�−6
not be more skillful. Note that in this and the Z̄ TC
predictor, we consider a subset of 320 events in which La Niña
already peaked for a first year following El Niño.
Predictors could be found earlier in the evolution of
ENSO events. For example, DD14 proposed that the magnitude of the thermocline anomalies 6 months prior to theonset of La Niña could be related to its magnitude on thesecond year (i.e. Nĩno-3.40). This predictor would provide
information on the return of La Niña with 18 month leadtimes. Our analysis of the CESM1 control shows a signifi�−18cant correlation (r = 0.46) between a Z̄ TC“discharge” pre0
dictor and Nĩno-3.4 (Fig. 4c). For this predictor we focus
the analysis on a subset of El Niño events with neutral or
negative Nĩno-3.4 SST index during July after the peak.
This additional condition rules out El Niño events that
return for a second year. Note that these events happen bothin nature and in CESM1 as discussed in Sect. 2.5. Our find�−18
ing of a significant correlation between Z̄ TC
and Nĩno-3.40
suggests that the return of La Niña could be predicted 18
months in advance.

13

P. N. DiNezio et al.

Recharge predictor: 6 month lead time(b)

La Nina predictor: 12 month lead time2

r = 0.48

2

r = 0.12

1

El Nino1

El Nino0

Neutral0

Neutral−1

La Nina−1

La NinaNino−3.40 (K)Nino−3.40 (K)

(a)

−2

−2
−10

0

10

20

−3

−2

−6
zonal mean Z′TC(m)

Nino−3.4(c) Discharge predictor: 18 month lead time

(d)
2

1

El Nino1

El Nino0

Neutral0

Neutral−1

La Nina−1

La NinaNino−3.40 (K)r = 0.46

−2

0

(K)

El Nino predictor: 24 month lead time20Nino−3.4 (K)−1−12

r = −0.35

−2
−50

−40

−30

−20

−10

0

−18
zonal mean Z′TC (m)

0

1

2

3

Nino−3.4−24 (K)Fig. 4  Scatterplots showing correlations between the Nĩno-3.4 index
on the year following the first peak of La Niña (Nĩno-3.4 0 , y-axis) andthe following predictors (x-axis): a heat content recharge 6 months
�−6
after the first year peak of La Niña (Z̄ TC), bNĩno-3.4 index during
the first year peak of La Niña (Nĩno-3.4−12), c the heat content dis�−18
charge during the transition between El Niño to La Niña (Z̄ TC),
and d the Nĩno-3.4 index at the peak of the El Niño event preceding
La Niña (Nĩno-3.4−24). The heat content discharge and recharge aremeasured as the negative and positive zonally averaged thermocline′
depth anomalies (Z̄ TC) respectively. Nĩno-3.4 0 values (y-axis) less than
−0.45 K indicate return of La Niña conditions on the second year
(blue shading), whereas values larger than 0.45 K indicate El Niño
conditions during the second year (red shading). Correlation coefficient r between the predictor and the predictand are indicated in eachpanel. Orange dots correspond to the events selected for the “perfectmodel” forecast experiments

Thermocline anomalies associated with the discharge
are driven by the preceding El Niño. Thus we also exploredcorrelations between Nĩno-3.40 and the magnitude of
the preceding El Niño given by a Nĩno-3.4−24 predictor(Fig. 4d). The correlation between these quantities is lower(r = −0.35) than for the discharge predictor. However, thescatter plot shows that the strongest El Niño events (Nĩno-3.4−24 > 3 K ) are virtually always followed by 2-year
LN events (Nĩno-3.40 < −0.45 K ). These results suggestthat strong El Niño events could lead to skillful 24-monthlead time forecasts of 2-year LN. Note that these 18- and24-month lead time predictions are performed before theinitial onset of La Niña. Therefore in these calculations we

considered all El Niño events regardless of whether they
are followed by La Niña or not.
The correlations shown by the “Peak El Niño” and “Discharge” predictors with the Nĩno-3.4 SST index during
the 2nd year may not be sufficiently high to warrant skillful predictions of 2-year LN. However, the scatter plotsshow very few events with neutral or El Niño conditions
on the second year when the predictors show large magnitude (Fig. 4c, d). This suggests that the likelihood of 2-year
LN increases with the magnitude of the predictors. For
instance, 94% of all simulated events with discharge valuesof −40 m ± 5 m become 2-year LN (Table 1). Similarly,
92% of all events with peak El Niño amplitude of 3 ± 0.5

13Predictability of 2‑year La Niña events in a coupled general circulation model﻿	
Table 1  Percentage of eventsin the control simulation
showing La Niña, neutral, andEl Niño conditions on Januaryof the second year for different
values of the El Niño peak anddischarge predictors

Control simulation
Predictor name

Predictor
amplitude% La Niña% neutral% El Niño

% of
total
eventsDischarge

−40 m
−30 m
−20 m
−10 m
3K
2K
1K

94
75
60
35
92
71
44

6
24
27
42
6
27
36

0
1
13
23
2
2
18

10
22
35
33
16
25
59

El Nino peak amplitude

ENSO events are binned according to their predictor values prior to computing the percentages. The central
value of each bin is given in the second column

K become 2-year LN. Events initiated by a strong El Niño
are not common (they happen less than 10% of the time inthe long control), however, when they happen, their longterm evolution will be highly predictable. The percentageof 2-year LN drops to 35 and 44% for the lowest values ofthe discharge (−10 ± 5 m) and peak El Niño amplitude (1K ± 0.5). For these values of the predictors the frequencyof occurrence of neutral, El Niño and La Niña conditions
on the second year are about the same magnitude, therefore
predictors of this magnitude would lack predictive skill for
2-year LN.
Lastly, we note that the peak amplitude of El Niño andthe associated discharge are highly correlated (r = −0.90).
The high correlation confirms that these predictors are notindependent, since ENSO dynamics predicts that stronger
El Niño events would drive a stronger discharge. This tight
relationship, however, may allow skillful predictions as
early in the evolution of an ENSO event as the peak of the
El Niño phase. In the next subsections we present ensemble
forecasts initialized at the peak of El Niño and at the discharge and discuss and compare their skill.
3.2 Role of initial conditions
3.2.1 Discharge
Next we turn our attention to the perfect model forecasts inorder to more quantitatively explore the role of the “Discharge” and “Peak El Niño” predictors. We begin with the
18-month lead forecasts for the three (strong, moderate andweak) discharge predictor cases. All three forecasts starton July with the Nĩno-3.4 SST index near neutral conditions characteristic of the discharge phase. In all cases, theensemble mean Nĩno-3.4 SST index shows La Niña’s firstpeak around January, 6 months after the forecast start date,as well as a second peak during the subsequent January, 18months after the forecast start date (Fig. 5, left; blue lines).

The “strong” case predicts the strongest La Niña on thesecond year, with ensemble mean Nĩno-3.4 SST index of−1.37 K on January of the second year (model year 1457)(Fig. 5a), while the other cases show similar values of−1.05 and −0.94 K respectively, suggesting weaker 2-year
LN relative to the “strong” case (Fig. 5c, e).
In all cases, the ensemble members track the control
very closely during the first 6 months and diverge much
faster during late summer and early fall of the second year
(Fig. 5, left; green lines). We more quantitatively discuss
the predictability and error growth of these forecasts bycomputing the spread (Fig. 7a) and PPU (Fig. 7c), which
we discuss in more detail in Sect. 3.3. Despite the increasing forecasts spread suggested by the diverging trajectoriesof the individual members, the strong case shows only one
member above the La Niña threshold during January of
the second year (Fig. 5a, green line above the blue background). In contrast, the moderate and weak cases show 4
and 5 members above the La Niña threshold, respectively(Fig. 5c, green lines above the −0.45 K dashed line). We
computed the probability of 2-year LN as the percentage ofmembers predicting Nĩno-3.4 SST index under the −0.5 K
threshold during January of the second year (Table 2). We
find that the probability of predicting 2-year LN increases
for forecasts with a larger initial discharge. This occurs
because the value of the predictable signal, captured by theensemble-mean, is sufficiently negative such as most members remain under the La Niña threshold. Conversely, theprobability of predicting neutral or El Niño i.e. an unreliable forecast, is larger when the initial discharge is weaker.
These forecasts start from conditions characterized′
by an anomalously shallow thermocline, shown by Z̄ TC
index values of −35, −24, and −12 m, respectively. Notethat these values (given by the starting point of the redlines in Fig. 5b, d, f) are slightly less negative than the′peak shoaling (given by the minima of Z̄ TC, gray lines
in the same figures). The different events of the control

13

P. N. DiNezio et al.

Strong discharge predictor
(a)

(b)

3

zonal mean Z′TC (m)Nino−3.4 SST index (K)Fig. 5  Evolution of the Nĩno-3.4 index (left) and the zonal
�mean thermocline index (Z̄ TC)(right) in forecasts initialized
from ocean conditions characterized by discharge conditions′(i.e. negative Z̄ TC) ranging fromstrong (top), moderate (middle),
and weak (bottom). The Nĩno′-3.4 SST and Z̄ TC
indices arecomputed as described in Fig. 4′
and Sect. 22.4. Positive Z̄ TC
indicate a deeper thermocline′(recharge) and negative Z̄ TC
indicate a shallower thermocline(discharge)

2
1
0
−1
−2

20

0

−20

−40

−3
1453 1454 1455 1456 1457 1458 1459

1453 1454 1455 1456 1457 1458 1459

Moderate discharge predictor
(d)

20

(m)

3

TC

2
1

zonal mean Z′

Nino−3.4 SST index (K)

(c)

0
−1
−2

0

−20

−40

−3
1180 1181 1182 1183 1184 1185 1186

1180 1181 1182 1183 1184 1185 1186

Weak discharge predictor
(f)

TC

2
1
0
−1
−2
−3
1123 1124 1125 1126 1127 1128 1129

year

Table 2  Percentage ofmembers in the perfect model
forecasts showing La Niña,
neutral, and El Niño conditions
on January of the second year

0

−20

−40
1123 1124 1125 1126 1127 1128 1129

year

Perfect model forecasts
Initial state

Forecast name

Predictor
amplitude% La Niña% neutral% El Niño

Discharge

StrongModerate
Weak
StrongModerate
Weak

−41 m
−33 m
−17 m
3.1 K
2.6 K
1K

90
77
57
97
63
57

10
23
33
3
37
33

0
0
10
0
0
10

El Nino peak

13

20

(m)

3

zonal mean Z′

Nino−3.4 SST index (K)(e)

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

simulation show discharge peaking from April to July(not shown). We selected initial conditions in July toensure that all cases are initialized after the peak dis′charge. The ensemble-mean Z̄ TC
shows the thermocline
slowly returning to neutral depth throughout the durationof La Niña in all three cases (Fig. 5, right; red lines). The
index shows that the thermocline hovers around neutral
depths during the first peak of La Niña deepening during the following summer, returning to neutral conditions
during the second year peak of La Niña. Note, that the′plumes track the control very closely until the firstZ̄ TC
peak of La Niña (Fig. 5, right; lilac lines) starting to
spread out afterwards.

We continue with the analysis of the 24-month lead forecasts for the three (strong, moderate and weak) “Peak El
Niño” cases. All three forecasts start in January when theNĩno-3.4 SST index reaches its maximum value at the peakof El Niño. In all three forecasts, the ensemble mean Nĩno-3.4 SST index shows negative values associated with thepeak of La Niña the following January, 12 months after theforecast start date, along with a second peak the following
January, 24 months after the forecast start date (Fig. 6, left;
blue lines). The “strong” case predicts the strongest second
year La Niña, with ensemble mean Nĩno-3.4 SST index ofStrong El Nino predictor(b)3

zonal mean Z′TC (m)Nino−3.4 SST index (K)

(a)

2
1
0
−1
−2

20

0

−20

−40

−3
1453 1454 1455 1456 1457 1458 1459

1453 1454 1455 1456 1457 1458 1459

Moderate El Nino predictor(d)3

zonal mean Z′TC (m)Nino−3.4 SST index (K)

(c)

2
1
0
−1
−2

20

0

−20

−40

−3
1180 1181 1182 1183 1184 1185 1186

1180 1181 1182 1183 1184 1185 1186

Weak El Nino predictor
(f)

20

(m)

3

TC

2
1

zonal mean Z′(e)Nino−3.4 SST index (K)Fig. 6  As in Fig. 5, but for“Peak El Niño” forecasts

3.2.2 El Niño peak

0
−1
−2
−3
1123 1124 1125 1126 1127 1128 1129

year

0

−20

−40
1123 1124 1125 1126 1127 1128 1129

year

13

P. N. DiNezio et al.

(a)

(b)

18−month lead forecasts

2.5
2

CESM1 control (r = 0.46)
CESM1 forecasts
observations (r = 0.44)2
1.5

1 El Nino

Nino−3.40 (K)0

CESM1 control (r = −0.35)
CESM1 forecasts
observations (r = −0.27)

2.5

1.5

Nino−3.4 (K)24−month lead forecasts

0.5
0 Neutral−0.5−1 La Nina
−1.5

1

El Nino0.5
0Neutral−0.5−1

La Nina

−1.5

−2

−2

−2.5

−2.5
−50

−40

−30

−20

−10

0

′ −18

zonal mean Z TC (m)

0

1

2

3

4

Nino−3.4−24 (K)Fig. 7  Scatterplots showing correlations between the Nĩno-3.4 index
on the year following the first peak of La Niña (Nĩno-3.4 0 , y-axis)
and: a the heat content discharge and b the magnitude of the preceding El Niño (y-axis). Data are from the CESM1 control simulation(gray dots), perfect model forecasts (light blue dots), and ocean reanalysis data (magenta). The heat content discharge is measured as the′zonally averaged thermocline depth anomalies (Z̄ TC) during the tran�−18̄sition between El Niñoto La Niña(ZTC ). Nino-3.4 0 values (y-axis)

less than −0.45 K indicate return of La Niña conditions on the second
year (blue shading), whereas values larger than 0.45 K indicate El
Niño conditions during the second year (red shading). Orange dots
indicate the forecasted events selected from the control simulation.
Dark blue dots indicate the ensemble-mean forecasts. Correlation
coefficient r between the predictor and the predict and are indicatedfor both the CESM1 control simulation (gray) and the ocean reanalysis data (magenta)−1.44 K in January of the second year (model year 1457)(Fig. 6a), while the other cases show values of −0.87 and−0.63 K respectively, suggesting weaker 2-year LN relative to the “strong” case (Fig. 6c, e). During the first yearof the forecasts, the Nĩno-3.4 SST plumes do not track thecontrol as closely as in the “Discharge” forecasts (Fig. 6,
left; green lines). Despite this larger initial error growth, 29
out 30 members of the “strong” case and 26 out of 30 of
the “moderate” case predict the return of La Niña with a 24month lead time.
We find that the probability of predicting 2-year LN
increases for forecasts initialized from strong El Niño,
which is explained by the larger predictable signals givenby the ensemble mean. However, we also find that the likelihood of a 2-year LN forecasts are comparable to the corresponding “Discharge” cases despite the longer lead time
(Table 2). The temporal evolution of the spread explains
why these forecasts remain as skillful. We find that the
spread of these forecasts increases rapidly during the first
6 months, but then decreases reaching values similar to
the “Discharge” forecasts by January of the second year
(Fig. 7b) and PPU (Fig. 7d). This, explains why these forecasts appear to be as reliable as the corresponding “Discharge” cases.
All three cases of the 24-month lead forecasts exhibit′(Fig. 6,a similar evolution for the ensemble-mean Z̄ TC
right; red lines), with the initial thermocline discharge
rebounding to slight positive values after the onset of
La Niña. After then, the “moderate” and “weak” cases′
plumes with positive values consistent with theshow Z̄ TC
recharge phase (Fig. 6, right; lilac lines). The “strong”′
case shows Z̄ TC
plumes close to zero for the second year.
′
Lastly, the Z̄ TC plumes show little error grow during thefirst year for all cases. This suggest that the initial error
growth of SST anomalies may be decoupled from theerror growth of the thermocline anomalies, thus allowing
for long lead predictability.
We conclude the analysis of the role of initial conditions by comparing the 18- and 24-month lead forecastswith the statistical predictors from the control simulation and from observational data. We find that the three“Discharge” cases exhibit ensemble-mean Nĩno-3.40 values that are linearly related to the magnitude of the ini�−18; Fig. 8a, dark blue dots), consistent
tial discharge (Z̄ TC
with the correlation between these predictors seen in the
CESM1 control (Fig. 8a, gray dots). Observational dataalso show significant correlations between Nĩno-3.40 and�−18(r = 0.44 with 95% confidence; Fig. 8a, magentaZ̄ TCdots). The three “Peak El Niño” cases are also consistent with the CESM1 control, both regarding the relationship of the ensemble-mean Nĩno-3.40 with the magnitude of the preceding El Niño, Nĩno-3.4−24, and thescatter (Fig. 8, blue and light blue dots respectively). The
observed data, shows a similar correlation (r = −0.27)
and scatter (Fig. 8, magenta dots). The scatter of the
CESM control, the perfect model forecasts, and observations, agree in suggesting that strong El Niño events

13

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

0.8

18-month lead forecasts
StrongModerate
Weak

0.6
0.4
0.2
0
Jul −18 Jan−12(b) 1Nino−3.4 ensemble spread (K)(a) 1
Nino−3.4 ensemble spread (K)Fig. 8  Temporal evolution of
the spread (top) and potential
prediction utility (PPU) (bottom) of the Nĩno-3.4 index inforecasts initialized a during
the discharge phase and b at thepeak of the preceding El Niño
event. The dashed black line
indicates January of the second
year (Jan 0 ). The initial 6 monthsof the El Niño forecasts are notshown (shaded gray) because
the PPU becomes zero when theensemble-mean Nĩno-3.4 index
goes to zero during the transition from El Niño to La Niña

Jul−6

Jan0

0.8

0.4
0.2
0
Jan−24 Jul −18 Jan−12

Jul+618-month lead forecasts

(d)

Jan0

24-month lead forecasts
1
0.8

Nino−3.4 PPU

0.8

Nino−3.4 PPU

Jul−6

forecast lead time

1

0.6
0.4
0.2

StrongModerate
Weak

0.6

forecast lead time(c)24-month lead forecasts

0.4
0.2

StrongModerate
Weak

0
−18
−12
Jul
Jan

0.6

−6

Jul

0

Jan

forecast lead time

are likely to be followed by 2-year LN. In contrast, theselines of evidence suggest that weak El Niño events lead
to less predictable 2-year LN.
The “moderate” and “weak” cases show a range of outcomes (Fig. 8, light blue dots) that is distributed within
the scatter of the control run (Fig. 8, light blue dots). The“strong” cases, in contrast, do not map onto the distribution of the control, possibly because strong El Niño andtheir associated discharge are not sampled with sufficientfrequency in the control. In other words, the “strong” forecasts show that the control run does not provide complete
information of the outcomes associated with these extreme
events. In these cases the perfect model forecasts provide
more complete information on the amplitude of 2-year LN
events. For instance, both strong cases have members predicting extreme Nĩno-3.40 values < −2.5 K, suggesting thatvery strong 2-year LN events are possible, but extremely
unlikely.

+6

Jul

StrongModerate
Weak

0
−24
−18
−12
Jan
Jul
Jan

−6

0

Jul

Jan

forecast lead time

3.3 Predictability and error growth
The 18-month lead time forecasts show fast error growth,measured by the ensemble spread, from July to September,remaining constant afterward until July of the following
year (Jul−6), when the error resumes the growth at about thesame rate as the previous year (Fig. 7a). The seasonality ofthe spread suggests that error growth is governed by a mechanism active during late summer and early fall. The spreadof the “Peak El Niño” forecasts evolves differently. All three
El Niño forecasts show fast error growth during the first six
months, followed by a decline in error growth (Fig. 7b). The“strong” and “moderate” cases show constant spread for an
additional year that remains lower than the corresponding
discharge forecasts (Fig. 7a, red and blue lines). The “weak”
El Niño case, in contrast, resumes the error growth, which
exceeds the spread of the corresponding discharge caseby January of the second year (Jan0; Fig. 7a, green). This

13

P. N. DiNezio et al.

is consistent with the results from the weak El Niño forecast, which show largest scatter for the amplitude of the 2ndyear La Niña (Fig. 8b). It remains unclear why all El Niño
forecasts show decreasing spread from Jul−18 to Jul−6. The
reduction in spread could be indicative of the following two
processes. First, initial error growth may not be driven bycoupled process, therefore the coupled system may not beaffected by the initial spread. Second, that the thermocline
anomalies are not affected by this uncoupled variability, andonce the system goes into La Niña, the spread decreases
because the uncoupled variability decreases.
We computed the PPU of the Nĩno-3.4 SST indices asa measure of the usefulness of each ensemble forecast.
PPU values near one are indicative of useful predictions,while values near zero indicate that the ensemble predictions lack skill. All forecasts start with PPU close to 1,
which decays slowly until about Jan0, when all cases show
values higher than 0.7 (Fig. 7c) indicative of useful forecasts. PPU quickly decays after the target forecast dateof Jan0, indicating that the forecasts lose their usefulness
beyond 18-month lead times. Each case, however, decays
at a different rate. The strong discharge case shows the largest PPU values, which stays at about 0.85 by Jan0, whereas
the weak discharge case shows lower values of about 0.75,
consistent with a link between PPU and the magnitude of
the initial discharge.
In contrast, not all “Peak El Niño” forecasts remain useful at 24 month lead times. The “strong” and “moderate”
cases show values of PPU larger than 0.7 by Jan0 (Fig. 7d,
red and blue lines), indicative of useful forecasts. The“weak” case, in contrast, shows much smaller PPU values throughout the forecasts reaching values under 0.4 by
Jan0 (Fig. 7d, green line). The strong El Niño case shows
the largest PPU values, whereas the weak case shows thelowest values, suggesting a link between PPU and the magnitude of the preceding El Niño. Note that by normalizing
the spread by the square of the ensemble-mean, as is donein the PPU measure (Eq. 1), there is no longer a seasonal
modulation of the error growth. This simply suggests thatboth the spread and the ensemble-mean have a similar seasonality, possibly because they are both controlled by theseasonality of the equatorial Pacific climate.
We further explored the processes causing error growthby analyzing the spatio-temporal evolution of predicted
SST anomalies over the equatorial Pacific and Indianbasins. Here we discuss results only from the moderate discharge and El Niño cases because they are representative of
all other cases, particularly since the spread of the Nĩno-3.4
SST index evolves similarly in each type of forecast (Fig. 7,
top). The ensemble-mean SST anomalies evolve similarly,
with slightly larger amplitudes in the “Discharge” casecompared to the “Peak El Niño” case (Fig. 9a, c). In particular, negative SST anomalies begin in the eastern Pacific13

around Jun−19 and subsequently propagate westward overthe following year, peaking around Jan−12 (Fig. 9, left). The
negative SST anomalies persist in the central and western
Pacific over the following year, and then re-emerge in theeastern Pacific around December (Dec−1).
Both cases also show a similar evolution of the ensemble-mean SST anomalies in the Indian Ocean (IO), withweak negative (positive) SST anomalies over the eastern(western) basin around September of the first year (Sep−16 ).
This pattern reverses during the second year, when theeastern (western) IO shows stronger positive (negative)
SST anomalies. These SST anomalies show the same pattern and September–October–November (SON) seasonality
as Indian Ocean Dipole (IOD) events observed in nature(Webster et al. 1999; Saji et al. 1999). However, the simulated evolution of IO SST anomalies, with a negligible
warming over the eastern IO during the first La Niña year
and a strong warming on the second year, is not supported
by observations, which show strong negative IOD events
during both years (not shown).
Despite the similarity of their ensemble-mean SST
anomalies, the two cases exhibit pronounced differences inthe spatial evolution of the SST spread (Fig. 9, right). Bothcases show the largest initial error growth in the easternequatorial Pacific with values up to 0.4 K during Januaryof the first year for the discharge case (Fig. 9b, Jan−12 ) andover 0.6 K during July for the El Niño case (Fig. 9d, Jul−18 ).
Additional differences between the two cases arise as theforecasts evolve. The spread of the discharge forecasts
increases during the second year reaching values over 0.6
K at the peak of the second year La Niña (Fig. 9b, Jan0 ).
In contrast, the spread of the El Niño forecasts decreases
after the second year with values remaining below 0.5 K
at the peak of the second year La Niña (Fig. 9d, Jan0). An
additional similarity between the cases is the large forecast
spread over the eastern Indian Ocean during September ofthe first and second years. The seasonality and spatial pattern of these maxima in the SST spread suggest a role forclimate variability associated with the IOD. The eastern IO
exhibits the largest spread at the beginning of the forecasts;
however, we explore whether this error growth has an influence on the ENSO forecasts in the next subsection.
3.4 Role of Indian Ocean variability
Several studies suggest that IO variability associated with
dipole events could influence the evolution of ENSO
events (Saji and Yamagata 2003; Kug and Kang 2006;
Kug et al. 2006; Ohba and Ueda 2007; Yamanaka et al.
2009; Annamalai et al. 2010; Izumo et al. 2010). Therefore the large forecasts spread seen over the eastern IO
could be playing a role in the spread over the PacificPredictability of 2‑year La Niña events in a coupled general circulation model﻿	Fig. 9  Spatiotemporal evolution of equatorial sea-surface
temperature (SST) anomalies
predicted by CESM1 in themoderate discharge (top) and El
Niño (bottom) cases. Ensemble
mean (left) and spread (right)of the predicted SST anomalies.
The forecast start date is marked
by the solid horizontal lines.
SST anomalies before thesedates are from the control simulation. In this and subsequent
figures, Jan−12 and Jan 0 indicate
the peaks of the first and second
years of La Niña. Jan−24 indicates the peak of the preceding
El Niño. SST anomalies areaveraged over the 5◦S-5◦Nequatorial band over the Pacific
Ocean and over 10◦S-0◦over the
Indian Ocean

Forecast initialized during discharge phase:moderate case
(a)

(b)

Ensemble mean

Spread

0

Jan 0

Jan

−12

Jan

−24

Jan−24

−12

Jan

Jan

60oE
−2

o

o

120 E
−1

0

60oE

o

180

120 W
1

0

2

120oE
0.1

0.2

SSTA (K)180o
0.3

σSSTA (K)

120oW
0.4

0.5

0.6

Forecast initialized during El Niño peak:moderate case
(c)

(d)

Ensemble mean

0

Jan 0

Jan−12

Jan−12Jan−24Jan−24

Jan

o

120 E

−2

−1

60 E

o

o

0

(Fig. 9). Moreover, this SST spread over the IO shows amaximum around September, which could be related tothe seasonality of the spread of the Nĩno-3.4 SST index(Fig. 7a, b). We performed an additional set of forecasts
in order to test this link. In these forecasts we prescribedclimatological SSTs in the eastern Indian Ocean (75◦
E–105◦E 9◦S–1◦N). This effectively disables the variability associated with the eastern lobe of the IOD andtherefore the forecasts show negligible ensemble-mean

o

o

180

SSTA (K)

Spread

1

2

120oE

60 E

120 W
0

0.1

0.2

180o
σ

0.3

SSTA

(K)

120oW
0.4

0.5

0.6

and spread over the eastern equatorial IO. Beyond thisdifference, disabling the IOD does not lead to substantial
differences in the evolution of the forecasts in the equatorial Pacific (not shown). Disabling the IOD also does
not lead to obvious changes in the spread of the Nĩno-3.4
SST index (Fig. 10). These results suggests that the evolution of the La Niña forecasts is largely uncoupled fromthe strong IOD variability as suggested by the study of
Ohba and Watanabe (2011).

13

P. N. DiNezio et al.

Discharge forecasts
1

Active IOD
Inactive IOD

0.8
0.6
0.4
0.2
0
Jul −18 Jan−12

Jul−6

Jan0

forecast lead time

3.5 Role of other modes of variability
We explore additional mechanisms responsible for error
growth using output from the perfect model forecasts. We
identify additional predictors via lagged-correlation analysis of various anomaly fields [sea level pressure (SLP),
wind stress, thermocline depth and SST] with the departures of the Nĩno-3.4 SST index from the ensemble-meanat the Jan−12 and Jan0 peaks. Data from 60 “Discharge”
forecasts and 60 moderate and strong “Peak El Niño”
forecasts were combined in each calculation. These cases
show similar error growth (Fig. 7, top), thus we expectthat will be governed by similar processes, allowing us
to combine their data and thus increase the statistical significance of the analysis. We removed the ensemble mean
anomaly from each member’s predicted SLP, wind stress,
thermocline depth, and SST anomalies in order to focus
the analysis on the departures from the ensemble mean (i.e.
ensemble-spread).
We first analyze processes within the equatorial Pacificrelated to the spread of the 2-year LN forecasts in boththe “Discharge” and “Peak El Niño” cases. We focus ouranalysis on the correlations during months preceding thestrong error growth prior to the second year peak, as shownby the spread of the Nĩno-3.4 SST index (Fig. 7, top). The
correlation analysis shows that the spread of the Nĩno-3.4
SST index is positively correlated with the spread of zonal
wind stress, 𝜏x′, over the western equatorial Pacific during
the previous April (Apr−9, Figs. 11a, 12a, shading). Both′cases show concurrent correlations with the ZTC
spreadcharacterized by a pattern of positive correlations extending across the equatorial Pacific (Figs. 11e, 12e, contours).
′
The ZTC
correlation patterns evolve with time and by July
their magnitude becomes largest over the eastern equatorial
Pacific (Figs. 11f–h, 12f–h, shading). Positive SST correlations appear in the eastern equatorial Pacific around June13(b)Nino−3.4 ensemble spread (K)(a)
Nino−3.4 ensemble spread (K)Fig. 10  Temporal evolution of
the spread of the Nĩno-3.4 index
in forecasts initialized a during
the discharge phase and b at thepeak of the preceding El Niño
event. Dashed lines indicate thespread of forecasts where the
IOD is inactive

Jul+6

El Nino forecasts
1

Active IOD
Inactive IOD

0.8
0.6
0.4
0.2
0
Jan−24 Jul −18 Jan−12

Jul−6

Jan0

forecast lead timeand continue to increase and propagate westward by July(Figs. 11f–h, 12f–h, contours).
Overall, the evolution of these correlation patterns is
consistent with the dynamics of the equatorial Kelvinwaves triggered by wind fluctuations over the western′equatorial Pacific. The positive ZTC
and SST correlations inJune and July also suggest that these Kelvin waves influence SSTs over the eastern equatorial Pacific. Moreover,as the westward propagation of the SST anomalies appear
to reinforce the initial zonal wind anomalies over the western side of the basin, as shown by the positive 𝜏x′ correlations (Figs. 11d, 12d, shading). We extended this analysis
to months before Apr−9, however no significant correlations
where found. This suggests that variability prior to first La
Niña peak has little influence on the spread of the second
year forecasts.
′
The relationship between 𝜏x′, ZTC, and SSTA revealedby the correlation analysis strongly suggests that coupledinstabilities within the equatorial waveguide contribute to forecast spread. However, the analysis is unclear
regarding the drivers of the initial wind stress variability. We identify subtle differences in the location of theinitial zonal wind stress anomalies. The “Discharge”
forecasts show initial 𝜏x′ correlations centered around
10◦N (Fig. 11a, shading). This 𝜏x′ variability coincides
with SST variability over the subtropical north Pacific(Fig. 11e, shading) reminiscent of the “seasonal footprinting” mechanism (Chang et al. 2007; Vimont et al.
2001, 2003, 2009). We note that the 𝜏x′ correlations do
not fully project on the equatorial waveguide, thus may′
be unable to explain the ZTC
variability revealed by correlations (Fig. 11e, contours). However, off-equatorial
wind variability could trigger equatorial Kelvin waves via
the so-called “trade wind-induced charging” mechanism
proposed by Anderson et al. (2013), and thus generate
SST spread in the Nĩno-3.4 region (Fig. 11h, shading).

Predictability of 2‑year La Niña events in a coupled general circulation model﻿	Fig. 11  Correlation coefficientof zonal wind stress (leftshading), thermocline depth(contours) and sea-surface
temperature (right shading)with the peak Nĩno-3.4 SST
spread in the “Discharge”
forecasts. Correlation coefficients with 95% statisticalconfidence are shown. The
rectangle indicates the regionused to compute the 𝜏 x−9WeqPacindex used in the statisticalprediction model (Eq. 2)

In contrast, the “Peak El Niño” forecasts show correlated wind variability centered on the western equatorial
Pacific (Fig. 12a, shading), which could effectively trig′
ger Kelvin waves, as suggested by the ZTC
correlations(Fig. 12e, contours), generating SST variability over theNĩno-3.4 region (Fig. 12h, shading).
Additional predictors outside the equatorial waveguidewere explored focusing on the summer season prior to boththe first and second peaks. Note that in this analysis we also
focus on the mechanisms leading to spread of the first year
forecasts, as they could show similarities with the mechanisms generating spread at the second year peak. Prior toperforming the lag-correlation analysis, we regressed eachmember’s anomaly fields on the corresponding May−8′
value of the zonally averaged ZTC. This procedure allows
us remove the effect of the equatorial processes discussed
above and focus on additional processes. The resulting correlation maps for July prior to the first peak (Jul−18) show
few areas over the tropics correlated with the Nĩno-3.4 SST
spread 6 months later (Fig. 13a). The sole exception is thesoutheastern (SE) tropical Pacific, where SLP anomalies
show significant negative correlations. The negative correlation between SLP anomalies persists during August and
September when SSTs also start to be positively correlated,showing the largest values over the SE Pacific (Fig. 13b, c).

The negative correlations indicate that negative SLP
anomalies in the SE Pacific are related to positive departures of the Nĩno-3.4 SST index relative to the ensemble
mean. This suggests that low SLP anomalies are associated with Nĩno-3.4 SST forecasts that are warmer than theensemble mean, and conversely high SLP anomalies withcooler La Niña forecasts. The correlations between SST
and Nĩno-3.4 index are initially stronger off the equator(Fig. 13b) and then become stronger in the eastern equatorial Pacific (Fig. 13c). A similar evolution of SLP and SST
anomalies is found for the second year (Fig. 13, bottom),suggesting that a common mechanism influences the error
growth of the La Niña forecasts during the first and second
years. The second year exhibits negative SLP correlations
associated with positive SST correlations over the central
north Pacific from May to July (Fig 13d–f). In addition,
positive SLP correlations are found over the western equatorial Pacific during June and July (Fig 13e, f).
The El Niño forecasts show similar evolution of SLP and
SST correlations, with the only difference that the anomalies in the north Pacific are also present during the first year
(Fig. 14, left). The spatial pattern and temporal evolution ofthese negative and positive SLP and SST correlations suggests that circulation anomalies over the SE and NE Pacificcontribute to the spread of Nĩno-3.4 SSTs. These SST

13

P. N. DiNezio et al.
Fig. 12  As in Fig. 11, but for“Peak El Niño” forecasts

anomalies first emerge in the SE Pacific and then propagate equatorward. The negative SLP correlation suggeststhat a cyclonic anomaly in the SE Pacific is associated withwarming over the eastern equatorial Pacific, resulting in a
Nĩno-3.4 forecast that is warmer than the ensemble mean.
Conversely, an anticyclonic anomaly in the SE Pacific is
associated with cooling over the eastern equatorial Pacific,
resulting in a Nĩno-3.4 forecast that is colder than theensemble mean. In all cases the magnitude of the negative
correlation increases with time as the positive SST correlations emerge, indicating that SST anomalies are driven by
circulation anomalies. Moreover, the correlation maps do
not show evidence for large-scale wave train patterns prior
to the occurence of the SLP correlations, suggesting that
local internal atmospheric dynamics are more likely to contribute to variability in the southeast trade winds. A similar
mechanism could be invoked to explain the SLP and SST
correlation results over the NE Pacific.
The spatial pattern and temporal evolution of these correlations are consistent with the South Pacific Meridional
Mode (Zhang et al. 2014), according to which, fluctuationsin the strength of the SE trades associated with regionalscale cyclonic anomalies can have an influence on theequatorial Pacific. According to this mechanism, tradewind variability associated with monthly and sub-monthly

13

fluctuations of the atmospheric circulation in the mid-latitude South Pacific can initiate SST anomalies in the SE
Pacific which can then propagate westward and equatorward through the wind–evaporation–SST (WES) feedback
mechanism (Xie and Philander 1994). Moreover, the initial
SLP pattern, not only shows negative correlations over thetropical SE Pacific, but also a lobe of positive correlations
farther south. This SLP dipole resembles the Pacific-SouthAmerican (PSA) pattern, the leading mode of internal
atmospheric variability over the South Pacific. This mode
plays an important role in modulating the trade winds andsea surface temperature (SST) in the southeast tropical
Pacific (Okumura 2013). These fluctuations in the tradewinds, in the presence of ocean dynamics, can be amplified
by the positive Bjerknes feedback, altering the evolution of
the La Niña forecasts.
3.6 Multivariate statistical prediction models
We conclude the study with a systematic evaluation ofpredictors in the long control simulation. Here we combine our understanding on the subsurface ocean predictors
developed in Sect. 3.2 with the atmospheric predictors suggested from the results in Sect. 3.5. We formulated a seriesof multi-variate regression models of Nĩno-3.40 by linearlyPredictability of 2‑year La Niña events in a coupled general circulation model﻿	Fig. 13  Correlation coefficientof SLP (shading) and SST(contours) anomalies with thepeak Nĩno-3.4 SST spread in the“Discharge” forecasts. Months
prior to strong error growth
are shown. Correlations withthe spread of the Nĩno-3.4 SST
index during the first year peak(Nĩno-3.4−12, left) and second
year peak (Nĩno-3.4 0 , right).
Correlation coefficients with
95% statistical confidence areshown. The rectangles indicate
the regions used to computethe DMI−3, SLP−7, SLP−6
WeqPacSEPac−6and SLPNPac indices used in
the statistical prediction model(Eq. 2)

combining these predictors with the thermocline predictors
discussed in the first part of our study. The model showing the highest correlations (r = 0.85 ± 0.04; error given at
99% confidence level) with Nĩno-3.40 is:
−6
�−18
x
̄ �−6
Nĩno − 3.40 = a1 Z̄ TC+ a2 𝜏WeqPac−9 + a3 ZTC + a4 SLPSEPac + a5 ,

(2)
�−18
�−6
where Z̄ TC
and Z̄ TC
are the “discharge” and “recharge”
predictors discussed in Sect. 3.1, 𝜏 x−9 is an index of
WeqPaczonal wind variability in the western equatorial Pacific, andis an index of SLP variability in the SE Pacific.
SLP−6
SEPac
x
The 𝜏
−9 index is defined as the zonal wind stress
WeqPacanomalies averaged over the western equatorial Pacific(120◦E–160◦W 30◦N–10◦S) and shows peak correlation(r = 0.63) with Nĩno-3.40 at a lead time of 9 months. The
SLP−6
index is defined as the SLP anomalies averaged
SEPac
over the SE Pacific (120◦W–80◦W 30◦S–10◦S) and shows
peak correlation (r = −0.70) with Nĩno-3.40 at a lead timeof 6 months. The ai constants in (Eq. 2) are computed using
least-squares linear regression. Table 3 summarizes theresults from this analysis and provides more details on thedefinitions and lags of the different predictors.
Additional indices were considered, however thesepredictors did not increase the correlation significantly(Table 3). An index of SLP anomalies over the central
north Pacific (180◦–140◦W 10◦N–20◦N) is highly correlated with Nĩno-3.40 (r = −0.40) at a lead time of 6 months.
However, including this SLP−6
predictor in Eq. 2 does not
NPaclead to a statistically significant increase in the correlation
with Nĩno-3.40. We also considered the Dipole Mode Index(DMI) (Saji et al. 1999) during September of the first year
(DMI−3), which is highly correlated (r = −0.61) with Nĩno-3.40; however, including this predictor in Eq. 2 does not
improve the correlation.
We also explored the role of SSTs over the tropicalAtlantic. We found that SST anomalies averaged over theequatorial Atlantic (0◦–20◦E 5◦S–5◦N), the so-called ATL3
SST index (Zebiak 1993), is correlated (r = −0.36) with
Nĩno-3.40 with a lag of 12 months, suggesting that tropical Atlantic SSTs could have an influence on the evolution of La Niña. Including this ATL3−12 predictor in

13

P. N. DiNezio et al.
Fig. 14  As in Fig. 13, but forforecasts initialized at El Niño
peak

Table 3  Indices considered as predictors of the magnitude of the Nĩno-3.4 SST index on the second year (Nĩno-3.4 0 )Predictor

rmodelID

Name

Variable

Area

�−18
Z̄ TC

Discharge

Thermocline depth

𝜏xWeqPac−9

Coupled instabilities

�−6
Z̄ TC
−6
SLPSEPac

DMI−3
Nĩno-3.4−12−7
SLPWeqPac−6

SLPNPac
ATL3−12

Lead (months)

rNĩno−3.40

140 W–80 W 5 S–5 N

18

0.46

0.46

Zonal winds

140◦E–160◦W 5◦S–5◦N

9

0.63

0.65

Recharge

Thermocline depth

140◦W–80◦W 5◦S–5◦N

6

0.46

0.73

S. Pacific meridional mode

Sea level pressure◦

120 W–80 W 30 S–10 S

6

−0.70

0.85

Indian Ocean Dipole

Sea-surface temperature

3

−0.58

0.85

Sea-surface temperature

80 E–107 E 10 S–0

1st year La Niña

0.12

0.85

Western equatorial PacificSea level pressure

120 W–170 W 5 S–5 N

12120◦W–180◦ 10◦S–10◦N

6

0.20

0.85

N. Pacific meridional mode

Sea level pressure

180 –140 W 10 N–20 N

6

−0.40

0.83

Atlantic Nĩno

Sea-surface temperature

0 –20 E 5 S–5 N

12

−0.36

0.83

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦

◦
◦

◦

The first five columns provide information on each predictor. The sixth column shows the correlation coefficient (r) between each predictor with
�−18
Nĩno-3.4 0 . The seventh column shows r values of the linear multi-variate model combining all the predictors listed in the table from top (Z̄ TC)
to the given predictor. Bold r values indicate when the increase in r relative to the previous model is statistically significant with 99% confidence

13Predictability of 2‑year La Niña events in a coupled general circulation model﻿	

Eq. 2 does not lead to a substantial increase in correlation(r = 0.83 ± 0.08) mainly because ATL3−12 is also corre�−18
lated (r = −0.28) with Z̄ TC. In general, these predictors
�−18
are highly correlated with Z̄ TC, which is related to themagnitude of preceding El Niño: thus the bulk of the predictable information on the duration of La Niña is already�−18included in Z̄ TC.

4 Discussion
The purpose of this study was to assess the predictability of the duration of La Niña out to 2 year lead times ina perfect-model setting. In particular, we explored predictability as a function of ocean initial state during different
phases of ENSO. We performed ensembles of forecasts
starting from two different types of initial states. The firststate occurs during the transition from El Niño to La Niña,
during which the equatorial Pacific is characterized bynear-zero SST anomalies and a shallower than normal thermocline. In this state the thermocline has not fully adjusted
to prior wind anomalies and therefore provides a source ofpredictability for the evolution into La Niña state. The second state occurs at the peak of El Niño, when the source ofpredictability is the associated westerly wind anomaly, thedriver of the delayed thermocline shoaling responsible forthe onset of La Niña. The main objective of our study was
to explore how different magnitudes of these “discharge”
and “Peak El Niño” predictors control the reliability andskill of forecasts of 2-year La Niña.
Our results show that the forecasts initialized with thelargest discharge and peak El Niño amplitudes exhibit thelargest skill at predicting a 2-year La Niña event (according to the PPU metric). The higher skill in these cases
stems from the larger magnitude of the initial conditions,which leads to a larger predictable signal thoughout thefirst 2 years of the forecast. The forecast spread, in contrast,
appears to be independent of the magnitude of the initialconditions. Our results show that CESM1 can produce consistent forecasts of La Niña for the first and second years(up to 24 month lead time), mainly because the ensemblemean signal has sufficiently large amplitude to overcome
the forecast spread. The forecasts become significantly lessskillful and reliable beyond the second year peak, despiterobust ensemble-mean signals showing La Niña conditions for an additional (third) year. For instance, the El
Niño event selected for the “strong” cases was followed by
a 3-year La Niña (Figs. 5, 6, gray lines). However, only 13
in 30 members predicted a 3-year La Niña, rendering theforecast considerably less reliable. This occurs because thespread grows over time, dominating the decreasing ensemble-mean signal. Our conclusion that the ensemble-mean
component has a larger contribution to prediction utility

than the ensemble spread is consistent with previous studies showing that ensemble spread is not a good indicatorof skill (Kirtman et al. 1997). This is a well known difference with weather prediction, where ensemble spread is themain determinant of potential forecast skill. Because the
ENSO system could be viewed as a stochastically forced
damped linear system, the forecasts would also be controlled by the magnitude of the initial conditions. In otherwords, the ensemble-mean component of the PPU, in contrast to ensemble-spread, is related to the initial conditions,as shown by Kleeman (2002) using a simplified ENSO
model.
We used the perfect model forecasts to investigate how
early in the evolution of an ENSO event can the duration of
La Niña be skillfully predicted. The fact that the discharge
and the peak El Niño amplitude are highly correlated allows
the forecasts initialized at the peak of an El Niño eventto remain as skillful as those initialized at the discharge,
despite being initialized six months earlier. Particularly, we
find that the forecasts initialized at the peak of strong El
Niño events are more skillful, measured by the PPU value
at target date of Jan0, as forecasts initialized during theirdischarge phase. Because of the tight El Niño–discharge
relationship, particularly for strong El Niño events, the predictability (in a PPU sense) of the “Peak El Niño” and the“Discharge” forecasts will have the same contribution fromthe ensemble-mean signal and the differences in PPU willarise from differences in the spread. Note that the strong“Peak El Niño” ensemble forecast has a PPU of 0.90 by
the target date of Jan0, while the strong “Discharge” forecast has a lower PPU of 0.85 (Fig. 8, bottom, red curves),
indicating that the former forecast is more skillful despite
the longer lead time. The higher PPU of the “Peak El
Niño” forecasts relative to the “Discharge” occurs because
these forecasts have lower spread by Jan0 (Fig. 8, top, red
curves). The lower Jan0 spread in the “Peak El Niño” forecasts (relative to the “Discharge” forecasts) maybe related
to the seasonality and state of ENSO. Further investigationof the seasonality of the spread and dependence on ENSO
state is beyond the scope of this study and will be left for
future work.
In a linear ENSO system, strong events would drive acommensurate response of the delayed thermocline feedback, thus leading to events with the same duration. Our
results, in contrast, suggest that the predictability of La
Niña duration (in a PPU sense) is consistent with processes
governed by persistence, such that, events driven by large
initial perturbations will take longer to decay. However,
the enhanced persistence of La Niña should not be interpreted as the effect of thermodynamic damping; rather it
is caused by nonlinearities in dynamical feedbacks as proposed by DD14. The nonlinearity of the delayed thermocline feedback is caused by two processes. First, strong El

13

P. N. DiNezio et al.

Niño events have much larger wind anomalies than La Niña
events and therefore drive much larger discharge (Frauen
and Dommenget 2010; Choi et al. 2013). The recharge, incontrast, is driven by the magnitude of the La Niña wind
anomalies, which are proportionally weaker. The second
process involves coupling between the thermocline and themixed layer. DD14 propose that shoaling of the thermocline
during the discharge has a much larger influence on SSTs
because the thermocline can continuously shoal, effectively entraining cold thermocline waters into the mixed
layer. This effect is not limited—in fact becomes more pronounced—as the thermocline becomes shallower (e.g. in
response to strong El Niño events). In contrast, deepeningof the thermocline decouples the thermocline waters fromthe mixed layer. In this case, strong recharge and associated positive thermocline depth anomalies become increasingly ineffective at detraining cold waters from the mixed
layer. This asymmetry appears to be more pronounced in
the central Pacific where the climatological mixed layer isshallower than the thermocline.
We speculate that this nonlinearity could also lead to
threshold behavior in the evolution of 2-year LN. Thisidea is motivated by the fact that the perfect model fore�−18
Nĩno-3.40 spacecasts do not completely map onto the Z̄ TC
defined by the events of the control. A sizable fraction of
La Niña events simulated in the control are preceded byweak discharge, last 1 year, and are followed by moderateand strong El Niño in the second year (Fig. 8a, gray dots
�−18over the region approximately defined by Z̄ TC> −20 m0
and Nĩno-3.4 > 0.45 K). In contrast, none of the ensemble
members initialized from weak discharge conditions lead to
El Niño on the second year as seen in many events from thecontrol. Instead, most of the perfect model forecasts predict
La Niña conditions for a second year (17 out of 20) and alesser fraction (3 out of 20) show neutral conditions in thesecond year (Fig. 8a, right blue dots). We cannot rule outthat our ensemble size is insufficient to fully describe therange of events simulated in the control simulation. However, it is also possible that the forecasts undergo a bifurcation depending on the magnitude of the discharge, resulting in forecasts with a more pronounced tendency to evolve
into 2-year LN, as in our case, or forecasts with a tendency
to evolve into neutral or El Niño. It is also possible that thisthreshold behavior is controlled by decadal variability, andour selected events coincided with periods more conducive
to 2-year LN. Both hypotheses deserve further exploration
since they could lead to additional sources of predictability.
The discharge-recharge asymmetry is reflected in the�−18correlation between the magnitude of the discharge (Z̄ TC)
0
and the value of the Nĩno-3.4 SST index (Nĩno-3.4 ) 18
months later. La Niña events preceded by strong discharge
must last 2 years in order for the recharge to drive SST
anomalies back to neutral. Our analyses of the CESM1

13control and perfect model forecasts show that the initial�−18conditions characterized by large-amplitude Z̄ TC
virtually
always lead to a 2-year LN. The large PPU of these cases
suggests that operational forecasts, which are generally lessskillful due to initial condition uncertainty and model drift,
could still provide reliable forecasts of 2-year La Niña.
Conversely, our analysis of observational data indicates that�−18
the Z̄ TC
and Nĩno-3.4−24 predictors could be used to determine the return of La Niña. For instance, the La Niña following the 1997/98 El Niño is one of three observed events
falling in the area of the Nĩno-3.4−24-Nĩno-3.40 space where
CESM1 would have predicted a 2 year duration. The first 2
years of this La Niña event could have been predicted using
the correlation between the peak El Niño amplitude andthe magnitude of the 2-year La Niña. Note, however, that
other events, such as the 2010–2012 La Niña, lie in a statistical regime where both the CESM1 control and the perfectmodel forecasts are less reliable. Last, the limited numberof events with subsurface reanalysis data precludes a morerobust assessment of this relationship in observations.
The evolution of the spread of the Nĩno-3.4 SST index
suggest that the processes causing error growth are modulated by both the state of ENSO and the seasonal cycle.
The forecasts initialized during the “discharge” phase show
error growth during late boreal summer and fall, and noerror growth during the rest of the calendar year. Similar
behaviour has been reported in July-initialized forecasts
of El Niño onset performed with CCSM4, a previous version of our model (Larson and Kirtman 2015). Our correlation analysis of the forecast spread shows that most of theforecast error is associated with (1) coupled instabilities inthe equatorial Pacific and (2) trade wind variability associated with the South Pacific meridional mode. Our analysis
shows that coupled instabilities are triggered by stochastic
wind variability in boreal spring (March/April), influencing
Nĩno-3.4 SSTs via Kelvin waves one or two seasons later(i.e. during boreal and fall summer). Variability in the tradewinds is caused with winter-time atmospheric variability
in the Southern Hemisphere, which is stronger during austral winter (boreal summer). This extratropical variability
influences Nĩno-3.4 SSTs via mixed-layer processes taking about a season to have an impact on the central equatorial Pacific SSTs and thus on forecasts error. These twoprocesses together could explain the large Nĩno-3.4 spread
during boreal summer and fall. The subsequent plateau offorecast spread occurs because coupled instabilities subside
during boreal fall when the equatorial Pacific is seasonallycolder, and also during austral summer because atmospheric variability in the SE Pacific is seasonally weaker.
The forecasts initialized at the peak of El Niño show thelargest spread in the first 3 months, which then stabilizes
at a lower level throughout the subsequent 2 years. Thisinitial forecast error does not appear to impact the skill ofPredictability of 2‑year La Niña events in a coupled general circulation model﻿	

the 2-year LN predictions, which overall exhibit less spreadthan the “discharge” forecasts, particularly during the target forecast season (DJF of the second year). The decreasein spread after spring may be caused by the emergence of
La Niña and the suppression of convective instability by
negative SST anomalies. This suggests that the more predictable thermocline anomalies are able to “pull through”
the predictability barrier, resulting in skillful forecasts.
While exploring these seasonal and state dependencies ofthe error growth would require a much larger number offorecasts, our results suggest that the spring predictability
barrier may be less influential when initializing at specific
ENSO phases. This results agree with a recent study suggesting that thermocline precursors during the onset of El
Niño can also overcome predictability loss during boreal
spring (Larson and Kirtman 2016).
We find two key processes causing error growth in thepredictions of 2-year LN. The first one involves coupledinstabilities within the equatorial Pacific. Our correlation
analysis of the perfect model forecasts shows that these
instabilities are initiated around April when stochastic windvariability over the western Pacific triggers ocean Kelvinwaves. These waves reach the eastern equatorial Pacific twomonths later initiating the spread of SST anomalies. This
result agrees with recent studies showing the importance ofhigh frequency wind variability over the western equatorial Pacific in the evolution of El Niño events (McPhaden
and Yu 1999; Thompson and Battisti 2001; Fedorov et al.
2003; Chiodi and Harrison 2015; Larson and Kirtman2015). According to these studies, Kelvin waves triggered
by westerly wind bursts over the western Pacific can influence SSTs over the eastern as seen in our La Niña forecasts. We find that April prior to peak 2-year La Nina is
an important window for coupled instabilities to impact the
final forecasts spread. This result agrees with the study of
Larson and Kirtman (2016), which using a previous versionof the model, showed that March is when stochastic zonal
wind stress is more effective at initiating coupled instabilities that have a lasting influence forecast error.
The second mechanism involves atmospheric variability over the SE Pacific in agreement with previous observational studies suggesting that the Southern Oscillation
could also be a trigger of ENSO events (van Loon and
Shea 1985; Trenberth and Shea 1987). The spatial pattern
and temporal evolution of these correlations are consistent with the South Pacific Meridional Mode (Zhang et al.
2014). According to this mechanism, trade wind variability associated with the monthly and sub monthly cyclonicvariability in the extra tropical SE Pacific can initiate SST
anomalies in the SE Pacific which can then propagate westward and equatorward through the wind–evaporation–SST(WES) feedback (Xie and Philander 1994). In our forecasts,
this mechanism is initiated around July by mid-latitude

atmospheric variability, which influences the spread ofequatorial SSTs by August.
Both mechanisms appear to be active during the evolution of 2-year LN, however with a less disruptive effectthan during the onset of El Niño, because of the more predictable influence of the thermocline dynamics discuss inthis study. Our statistical model derived from the control
simulation suggest that both processes could play a comparable role in altering the evolution of 2-year LN. The extent
to which forecasts of 2-year LN events might be improvedby considering these additional predictors is left for futurework.
Our correlation analysis also reveals SLP and SST patterns in the North Pacific reminiscent of the meridionalmode and seasonal “foot printing” mechanisms (Changet al. 2007; Vimont et al. 2001, 2003, 2009). However, itremains unclear whether these processes influence the evolution of the forecasts. Off-equatorial wind variability associated with these mechanisms could be initiating coupledinstabilities leading to spread in the “discharge” forecasts.
The “Peak El Niño” forecasts do not show evidence for thislink. Moreover, our predictor analysis of the long control
did not reveal statistically significant correlation between
indices of north Pacific SST or SLP variability and 2-year
LN. Further research is needed to elucidate whether thesemodes of variability play a key role on the evolution of
La Niña forecasts or not. Similarly, SST variability in the
Indian and tropical Atlantic show correlations with 2-year
LN; however these predictors are also correlated with thepeak magnitude of the preceding El Niño and thus do notprovide additional independent information. Our experiments with disabled IOD confirm that this mode does notplay a role in the error growth, in agreement with a previous study showing that IO variability accelerates the transition from El Niño to La Niña, but does not play a role in thetermination of La Niña (Ohba and Watanabe 2011).

5 Conclusions
We assessed the predictability of the duration of La Niña
using CESM1, a climate model that simulates realistic
ENSO characteristics, including the multi-year duration of
La Niña. CESM1 skillfully predicts the return of La Niña
for a second year in forecasts initialized from ocean states
characterized by a strong discharge of the equatorial thermocline or by a strong El Niño. The high model skill, as
measured by PPU, stems from larger ensemble-mean signals, particularly since the spread evolves independently ofthe magnitude of the initial conditions. Thus, initial conditions with weaker anomalies lead to less skillful forecasts, mainly because the ensemble-mean signal becomes
weaker and is more influenced by error growth. Our results

13

P. N. DiNezio et al.

show that the predictability of La Niña duration is consistent with a process governed by persistence of thermocline
depth anomalies, wherein large thermocline depth anomalies will decay over multiple years. The enhanced persistence of La Niña should not be interpreted as the effect ofthermodynamic damping; rather it is caused by nonlinearities in dynamical feedbacks as proposed by DD14.
The high skill demonstrated by the CESM1 perfectmodel forecasts suggests that useful operational forecastsof the duration of La Niña in nature may be feasible. The
magnitude of the thermocline discharge in the equatorial
Pacific could be used as an observational diagnostic of thelikelihood of a 2-year LN event. For instance, the La Niña
following the 1997/98 El Niño is among very few observed
�−18
events falling in the range of Z̄ TC
values where CESM1
would have consistently predicted a 2 year duration. The
first 2 years of this 3-year La Niña event could therefore
have been predicted using the statistical relationship put
forward in this study. Our results also suggest that the realism of ENSO simulations could be critical for achieving
these long-range predictions. Therefore improvements inthe simulated characteristics of ENSO may lead to further
improvements in predictability. Due to the disproportionate
impact of La Niña on drought throughout the world, such
further research could result in concrete and direct societal
benefits.
Acknowledgements This study was supported by NOAA’s Climate
Program Office’s Modeling, Analysis, Predictions, and Projections
program (Grant NA14OAR4310229). PDN received additional support from the Climate and Global Dynamics division during a longterm visit to NCAR. Computing resources were provided by the Climate Simulation Laboratory at NCAR’s Computational and Information Systems Laboratory (CISL), sponsored by the National Science
Foundation (NSF) and other agencies. NCAR is sponsored by the
NSF.

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