GEOPHYSICAL RESEARCH LETTERS

Supporting Information for: A two-year forecast for a60-80% chance of La Niña in 2017-18
1

2

2

2

Pedro N. DiNezio , Clara Deser , Alicia Karspeck , Stephen Yeager , Yuko
1

2

2

2

Okumura , Gokhan Danabasoglu , Nan Rosenbloom , Julie Caron , Gerald
A. Meehl

2

Submitted July 7, 2017
Revised September 20, 2017
Revised November 1, 2017

Corresponding author: Pedro N. Di Nezio, Institute for Geophysics, Jackson School of Geosciences, University of Texas at Austin, Austin, TX, USA. (pdn@ig.utexas.edu)
1Institute for Geophysics, Jackson Schoolof Geosciences, University of Texas atAustin, Austin, TX, USA.
2

Climate and Global Dynamics Division,

National Center for Atmospheric Research,
Boulder, CO, USA.

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Contents of this file
1. Text S1
2. Figures S1 to S9
3. Table S1
Text S1

1. ENSO simulation in CESM1
CESM1 simulates very realistic ENSO events in terms of their spatial patterns, amplitude, teleconnections, and particularly, the asymmetries in amplitude and duration between El Niño and La Niña. Sea-surface temperature anomalies (SSTA) computed fromthe CESM-CTL exhibit warming of central and eastern equatorial Pacific at the peak of El
Niño events (Fig. S2a), albeit extending slightly westward relative to observed events (Fig.
S2c). Simulated La Niña events show cooling of the central and eastern equatorial Pacific(Fig. S2b) also displaced slightly westward relative to observations (Fig. S2d). CESM1
simulates ENSO indices with amplitude consistent with the observed values. Niño-3.4
SST variability is slightly overestimated, as seen in the larger standard deviation (⇠10%
larger) of the Niño-3.4 SST index relative to observations (Table S1). The strong SST
variability does not translate into increased subsurface variability, since the simulated
Z̄ 0 T C indices show about the same standard deviation as the reanalysis-derived variability(Table S1).

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2. Decadal Prediction Large Ensemble
2.1. Drift correction
Each ensemble member evolves following a unique climate trajectory dictated by the
influence of the initial conditions, variations in the external forcings, and each member’s
weather and internal climate variability. Over time, each ensemble member slowly drifts
towards the climatology of the model, which will exhibit biases relative to the observed initial climate. We corrected this slowly evolving drift following the technique recommended
by CLIVAR [International CLIVAR Project Office, 2011]. This is done computing mean
climate fields from all ensembles at each lead time (months 1 to 122). The resulting timeevolving climatology captures the model’s drifting climate. The 51 ensembles initialized
over the 1964–2014 period were used because they allow the computation of a climatology for which the same-size ensemble (51⇥40 = 2040) exists for each lead time. This
time-evolving climatology is removed from each of the 2480 (62⇥40) members to obtaindrift-corrected climate anomalies.
This approach removes the drift that is common to all ensembles, isolating theinternally-generated and externally-forced climate anomalies. This methodology has been
extensively used in seasonal and decadal climate forecasts [Yeager et al., 2012; Meehl andTeng, 2012; Hazeleger et al., 2013]. SST and rainfall anomalies are computed following
this approach. For thermocline depth, we first compute the depth of the maximum thetemperature gradient from the uncorrected subsurface temperature fields, and then apply
the drift-removal technique to the full Ztc fields to compute anomalies. This drift removal
technique will be most e↵ective when the model errors are independent of the forecast
state (i.e., the system is linear in its error statistics), and if the error distribution is nor-

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mal [Stockdale, 1997]. These are reasonable assumptions for ENSO, although interactions
between forecast state and error are to be expected, diminishing forecast skill. In section
3 we show that the CESM-DP-LE is capable of predicting 2-year La Niña when initialized
at the peak of strong El Niño events. This gives us confidence that the drift-removal technique does not cause a large reduction in forecast skill relative the skill shown in “perfectmodel” experiments [DiNezio et al., 2017].
2.2. Forecast plumes
We computed the mean Niño-3.4g and Z̄ 0 T C indeces among all members of each ensemble
to quantify the predictable component of each forecast. We define a 2nd year La Niña when
the Niño-3.4g SST index is less than

0.60 K, during the November-December-January(NDJ) season, 2 years after the forecast start date (NDJ+2). Probability of 2-year La
Niña are computed as the fraction of members showing Niño-3.4g SST index under the
0.60 K threshold during NDJ+2.
A composite of events starting from strong and moderate El Niño shows that on average
the CESM-DP-LE hindcasts capture the evolution of the subsequent La Niña events interms of timing and amplitude (Figs. S6a–b). These composites exclude members thatshow returning El Niño conditions during the NDJ season 1 year after the forecast startdate (NDJ+1) (e.g. Figs. S6c–k, red curves). We identified the members that simulatea realistic transition from El Niño to La Niña during the first year by requiring that
the Niño-3.4g SST index be less than 0.6 K (i.e. ENSO neutral or La Niña) during the
May-June-July (MJJ) season during the first year of the hindcasts (MMJ+1). By therequiring neutral conditions during summer, this criterion imposes the condition that the

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initial El Niño transitions to La Niña, however, it does not impose the 2-year persistenceof La Niña. The fact that the composites for strong and moderate events agree withobservations (Fig. S6a and Fig. S6b) indicates that this correction is e↵ective at removing
forecast bias. Note, that the CESM-DP-LE predicts a consistent transition to La Niñain three out of four of the strongest El Niño events on record. Consistent for 1972 (Fig.
S6e), 1997 (Fig. S6i) and 2015 (now shown), with inconsistent transition for 1982 (Fig.
S6f). The causes for the inconsistent transition in the 1982-initialized hindcast will be
explored in a follow-up study. This approach is analogous to other techniques for bias
correction, such as amplitude corrections, which are commonly applied to correct biases
in climate forecasts. We emphasize that this correction is applied systematically to all
ensembles, without seeking to increase the skill of individual ensembles. This correctionis less needed for most forecasts initialized from strong El Niño events. For instance, weremoved only one member from the 2015-initialized forecasts used to predict the current
La Niña.

3. Retrospective verification of 2-year La Niña forecasts
Retrospective verification is required to demonstrate the skill of a forecast system prior
to its use for actual predictions [Kirtman et al., 2001; Tang et al., 2005; Barnston et al.,2009; Wang et al., 2010; Tippett et al., 2011; Ham et al., 2014]. This section presents
an assessment of the quality of the ENSO forecasts produced by the CESM-DP-LE. We
assessed quality in terms of bias and RMS error of the Niño-3.4g SST index relative toobservations focusing on the first 27 months (9 seasons) of the hindcasts.

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3.1. Verifying data
We evaluate the CESM-DP-LE against the observed evolution of ENSO events basedon the Niño-3.4g SST index. ERSST3b [Smith et al., 2008] data are used to computethe observed Niño-3.4g SST index. Observed SSTA are computed relative to the 1964–
2014 monthly-mean climatology, as in the CESM1-DP-LE. Neither the observed nor the
CESM-DP-LE Niño-3.4g SST indices are detrended since we expect that forced signals
will have a minimal e↵ect on our gradient-based definition.
3.2. Retrospective verification
We assess the quality of the CESM1-DP-LE predictions for di↵erent initial ENSO
states. We cluster the 61 ensembles according to whether they were initialized froman El Niño or a La Niña year. We use the definition of El Niño and La Niña years given
by NOAA’s CPC (http://www.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ensoyears.shtml). Each cluster contains 20 and 19 ensembles initialized
from El Niño and La Niña respectively. We evaluate the quality of the CESM1-DP-LE
forecasts in both cases to assess the skill at 2 and 1 year lead times. The 2015-initialized
forecast is excluded from the verification.
3.3. Hindcast bias
We explore biases in the CESM-DP-LE retrospective predictions by comparing composites of the hindcast and observed Niño-3.4g SST indices for each cluster. The temporal
evolution of the hindcast and observed composites suggest substantial di↵erences, particularly for hindcasts initialized from El Niño conditions (Fig. S7) These di↵erences reveal
pronounced biases during the first year of the El Niño-initialized hindcasts. On average,

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the CESM-DP-LE predicts positive Niño-3.4g values peaking one year after initializationand negative values for the following year (Fig. S7a, gray line). In contrast, the observed
composite shows negative Niño-3.4g SST values from the first to the second year after
initialization consistent with the tendency of La Niña events to last 2 years (Fig. S7a,
black line). This di↵erence arises because some CESM-DP-LE hindcasts show an excessive tendency for predicting returning El Niño conditions for the first year, as discussed
in section 2.2.
The composite of El Niño-initialized members with neutral conditions during the first
MJJ season (MJJ+1) shows Niño-3.4 SST index with striking similarity to the observed
composite. This confirms that hindcasts that do not transition into 2-year El Niño havevery low bias (Fig. S7b). Therefore we can exclude the unrealistic hindcasts in ourevaluation of predictive skill. In real-time predictions, we would not know if year 1 turns
out to be El Niño or La Niña. However, the low bias found after this procedure suggeststhat excluding these members for moderate and strong El Niño will lead to higher quality
forecasts. Last, the La Niña-initialized ensembles show that, on average, the CESM-DPLE predicts negative Niño-3.4g SST index for the following boreal winter (Fig. S7c, greyline). This suggest that CESM-DP-LE could be skillful at predicting the return of La
Niña one year after the first peak.
3.4. RMS error
We use an autoregressive model of order 1 (AR1) derived from the observed Niño-3.4g
SST index to generate “forced persistence” hindcasts initialized in each November from1954 to 2014. For each initial November we generate an ensemble of 1000 AR1 hindcasts.

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We compare the RMS error of the Niño-3.4g SST index predicted by these AR1 ensembles
vs. the CESM-DP-LE. The RMS error is computed for each realization of the AR1and CESM-DP-LE member over the first 9 seasons (27 months). This procedure yields
distributions of RMS errors for the AR1 model and the CESM-DP-LE. Before comparing
these distributions, we separated the hindcasts into the same clusters discussed in theprevious section. The distribution of RMS error from the CESM-DP-LE is broader thanthe AR1 model (Fig. S8a). CESM-DP-LE appears to be more skillful than the AR1model under certain conditions, because of its ability to predict 2-year La Niña; but alsoless skillful, because of the excessive 2-year El Niño. The distribution of the RMS error
improves dramatically when we apply the neutral MJJ+1 condition (as in the composite
analysis) to the hindcasts initialized from strong and moderate El Niño (Fig. S8b). The
CESM-DP-LE shows less RMS error than the AR1 model. This supports the notion thata realistic transition to La Niña is critical for more skillful CESM-DP-LE forecasts. Lastly,
forecasts initialized from La Niña conditions are also more skillful than the AR1 model(Fig. S8c) supporting our previous point.

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SST anomaly (m)Observed Nino−3.4 SST indices3(a)Nino−3.4 SST index
Gradient index

2
1
0
−1
−2
1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

SST anomaly (m)Observed western Pacific SST index
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(b)

2
1
0
−1
−2
1960

1970

1980

1990

2000

Observed zonal−mean Z
ZTC anomaly (m)

TC

20

2010

index

(c)

10
0
−10

TAO/TRITONGODASORA−S4GECCO2

−20
−30
1955

Figure S1.

1960

1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

2015

Observed ENSO indices. (a) Niño-3.4 sea-surface temperature (SST) indicesand (b) zonally averaged thermocline depth index (Z̄ 0 T C ). The linear trend line corresponds to
the Niño-3.4 SST index. SST indices are computed using ERSST3b [Smith et al., 2008] data.
The Z̄ 0 T C index is computed using potential temperature data from di↵erent ocean reanalyses(ORAS-4 [Balmaseda et al., 2013], GECCO2 [Khl and Stammer , 2008], and GODAS [Huang
et al., 2010]) and from in-situ observations from the TAO/TRITON moored array.

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CESM control

El Niño
(a)

60˚N
0.5

30˚N

2

−1

1

La Niña

(b)

−2

−1

−0.5

−0
.5

0.5

0.5

1

−1

−0.5

0˚

1

1

.
−0

5

0.5

−1

1

−1

0.
5

−0.5

−0.5

0.5

0.5

30˚S

−0.5

−0.5

−0.5
0.5

60˚S

Observed
0.5

1

(d)

−1

.5

30˚N

−0

0.5
.5

−0
.5

−0

(c)

60˚N

−0.5

1

1

0.5

−0

0.

5

−1

−0

−1

1

.5

30˚S
−0

60˚S

0.5

0.5

.5

0˚

.5

−0

−1

0.5

−0

.5

0.5
.5

0.5

−0.5

0.5

60˚E 120˚E 180˚ 120˚W 60˚W
−1.5

−1.0

−0.5

60˚E 120˚E 180˚ 120˚W 60˚W
0.0

0.5

1.0

1.5

surface temperature anomaly (K)Figure S2. Observed and simulated climate anomalies associated with El Niño and
La Niña. Composite anomalies of sea-surface temperature (SST, shading) and sea level pressure(SLP, contours) during December-January-February (DJF) for simulated (top) and observed(bottom) El Niño (left) and La Niña (right) events. The composite El Niño and La Niña events
are based on observations (years 1901–2012) and the CESM-CTL (years 401–2200). Observed
SST and SLP data are from ERSST3b [Smith et al., 2008] and the 20th Century Reanalysis[Compo et al., 2011]. Solid (dashed) contours show positive (negative) SLP anomalies at 0.5 hPa
intervals. The simulated composite anomalies are scaled so that the amplitude of the Niño-3.4
SST index matches observations.

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15

7/12

15
−5

2

Jan

15

Jan1

Jan

10
5

15

2

0

−10

−5

−5

15
−5

510
0

Jan1

−10
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5

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Jan

−20

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−15
−10
0
o 5

150 E

10

15

10

10
o

180

o

15
20
10
5
o

−1

0

5

−0.5

−5
0

10
05
−5 −10−15−20o

150 W 120 W 90 W

−1.5

−5
−5

−5

−10

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−20
−25
0
−20
−15 −10−25
Jan −15
−5
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0 5
−5
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5
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15
o

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15

−15
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2520
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7/12

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o

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−10
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−5
0

5
10
10
0
5

o

o

150 E

180

150 W 120 W 90 W

0.5

1

1.5

SSTA (K)

Figure S3. 2-year La Niña in observational data and the CESM-CORE simulation.
Composite sea-surface temperature anomalies (SSTA, shading) and thermocline depth anomalies(Ztc0 , contours) for 2-year La Niña events in (a) observational data and the (b) CESM-CORE
simulation used to initialize predictions. The SSTA and Ztc0 are averaged over the 5 S-5 N band.
Orange (purple) contours show positive (negative) Ztc0 on 5 m intervals. Observational anomalies(right) are computed from detrended ERSST3b [Smith et al., 2008] and ORAS4 [Balmaseda
et al., 2013] data. The CESM-CORE simulation is described in section ??. Both composite La
Niña events were formed using anomalies from seven 2-year events observed over the 1958-2014
period when the two datasets overlap.

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X - 15Predicted and observed 2−year La Nina (first peak)
CESM−DP−LE

Observed

NDJ 1973/74
30˚N

(a)

(b)

0˚
30˚S

NDJ 1983/84
30˚N

(c)

(d)

0˚
30˚S

NDJ 1998/99
30˚N

(e)

(f)

0˚
30˚S

NDJ 2010/11
30˚N

(g)

(h)

0˚
30˚S

NDJ 2016/17
30˚N

(i)

(j)

0˚
30˚S
60˚E 120˚E

180˚ 120˚W
−1.5

−1.0

60˚E 120˚E
−0.5

0.0

0.5

1.0

180˚ 120˚W
1.5

SSTA (K)

Figure S4.

Predicted vs. observed sea-surface temperature anomalies for the firstpeak of 2-year La Niña. Ensemble-mean (left) and observed (right) sea-surface temperature
anomaly (SSTA) during the first November-December-January (NDJ) peak of selected 2-year La
Niña events. The ensemble-mean SSTA are from CESM-DP-LE forecasts initialized at the peakof the El Niño events of 1972, 1982, 1997, 2009, and 2015. Members that evolve into 2-year El
Niño are not included in the ensemble mean calculation as described in section 2.2. Observed
SSTA are from ERSST3b [Smith et al., 2008].
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Predicted and observed 2−year La Nina (second peak)
CESM−DP−LE

Observed

NDJ 1974/75
30˚N

(a)

(b)

0˚
30˚S

NDJ 1984/85
30˚N

(c)

(d)

0˚
30˚S

NDJ 1999/ 0
30˚N

(e)

(f)

0˚
30˚S

NDJ 2011/12
30˚N

(g)

(h)

0˚
30˚S
60˚E
NDJ 2017/18
30˚N

120˚E

180˚ 120˚W

(i)

0˚
30˚S
60˚E 120˚E

180˚ 120˚W
−1.5

−1.0

−0.5

0.0

0.5

1.0

1.5

SSTA (K)

Figure S5.

Predicted vs. observed sea-surface temperature anomalies for thesecond peak of 2-year La Niña. As Fig S4, but for the second NDJ peak of 2-year La Niña.

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Nino−3.4g SST index (K)Strong El Nino

Moderate El Nino
CESM1
OBS

(a)

2

1

1

0

0

−1

−1

+1

+1

+2

+3

+2

Nino−3.4g SST index (K)

(c)

3

J

ND

J

JJ

M

(d)

2

1

1

0

0

0

−1

−1

−1

−2

−2

−2

−3

−3

9

8

J

5
19

J
ND

ND

5
19

J
ND

3

J

66
19

J

67
19

ND

ND

2

J

(g)

2
1

0

0

0

−1

−1

−1

−2

−2

−2

−3

−3

J
ND

4

J

ND

J
ND

8
19

J
ND

J

88
19

J

89
19

ND

ND

4

J

2

2

1

1

0

0

0

−1

−1

−1

−2

−2

−2

−3

−3

J
ND

1

J

ND

1

J
ND

J

1

9
99

J
ND

95
19

J

96
19

ND

ND

(k)

3

1

8
99

74
19

2009

(j)

2

7
99

9
19

ND

2006
3

J

ND

−3

87
19

1997

(i)

3

73
19

(h)

3

1

3

J

ND

1994

1

8
19

7
19

ND

2

2

(e)

−3

65
19

2

8
19

JJ

M

1987

(f)

3

J

1972
3

2

5
19

+3

+2

ND

1965

1982
Nino−3.4g SST index (K)

+2

+1

ND

1

J
ND

Nino−3.4g SST index (K)

JJ

M

2

7

Figure S6.

+1

+0

J
JJ DJ
JJ DJ
JJ
M
M
ND M
N
N
1957
3

CESM1
OBS

(b)

2

+0

X - 17

−3

06
20

J

ND

7
00

2

J

ND

08
20

9

J

ND

0
20

J

ND

10
20

J

11
20

ND

Niño-3.4g SST index from CESM-DP-LE hindcasts initialized at thepeak of strong and moderate El Niño events. Observed and ensemble-mean predicted
Niño-3.4g SST index for a composite of historical La Niña events preceded by (a) strong and (b)moderate El Niño conditions. Shading indicates the standard deviation among the ensembles
in each composite. (c-k) Niño-3.4g SST plumes for the individual ensembles. Green curves
correspond to the observed Niño-3.4g SST index. Blue curves identify the members (thin curves)and ensemble-mean (solid curve) that show realistic initial transition from El Niño to La Niña.
Thin red curves identify the members that are excluded because of the their unrealistic evolution
into 2-year El Niño. Solid red curve shows the ensemble-mean of all members regardless of theirinitial transition into La Niña.

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Composite Nino−3.4g SST index
strong and moderate El Nino (9)(neutral MJJ+1 members)

(a)

1.5
1
0.5
0
−0.5
−1
+0

J
ND

+1

J
ND

+2

J
ND

+3

J
ND

2

Observed
CESM−DP−LE
AR1

(b)

1.5
1
0.5
0
−0.5
−1
+0

J
ND

+1

J
ND

+2

J
ND

La Nina (19)Nino−3.4g SST index (K)2Nino−3.4g SST index (K)Nino−3.4g SST index (K)El Nino (20)

+3

J
ND

2

(c)

1.5
1
0.5
0
−0.5
−1
+0

J
ND

+1

J
ND

+2

J
ND

+3

J
ND

Figure S7. Composite evolution of Niño-3.4 SST index from El Niño- and La Niñainitialized hindcasts. Composite ensemble-mean Niño-3.4g SST index in hindcasts initialized
from initial conditions characterized by (a) El Niño, (b) strong and moderate El Niño followedby neutral May-June-July (MJJ), and (c) La Niña. Composites include observed events shown inblack, CESM-DP-LE hindcasts shown in blue, and forced persistence hindcasts generated with anautoregressive process of order 1 (AR1), shown in red. Gray shading indicates the spread among
the ensemble-mean indices. Dash-dotted red curves indicate the spread among the ensemblemean AR1 hindcasts. Dashed horizontal lines indicate the 0.6 K and

0.6 K thresholds used todefine El Niño or La Niña conditions.

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RMS error of Nino−3.4g SSTA hindcasts
strong and moderate El Nino (9)(neutral MJJ+1 members)

El Nino (20)(a)

3

La Nina (19)

(b)

3

2.5

2.5

2

2

2

1.5

PDF

2.5
PDF

PDF

3

1.5
1

1

0.5

0.5

0.5

0.5

1
RMSE (K)

1.5

0
0

0.5

1
RMSE (K)

1.5

(c)

1.5

1

0
0

CESM−DP−LE
AR1

0
0

0.5

1
RMSE (K)

1.5

Figure S8. RMS error of Niño-3.4g SST index from El Niño- and La Niña-initialized
hindcasts. Probability density function (PDF) of the root-mean-square (RMS) error of theNiño-3.4g index in CESM-DP-LE hindcasts (blue) initialized from conditions characterized by(a) El Niño, (b) strong and moderate El Niño followed by neutral May-June-July (MJJ), and(c) La Niña. RMS error PDF from hindcasts performed with an autoregressive process of order
1 (AR1) are also shown (red). The RMS error of the Niño-3.4g SST index is computed relative
to the observed values over the first nine seasons (27 months) of the CESM-DP-LE and AR1
hindcasts.

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November 1, 2017, 10:17am

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X - 20(a)Figure S9.

DINEZIO ET AL.: TWO-YEAR FORECAST OF LA NIÑA

(b)

(c)

NMME ENSO plumes. ENSO predictions produced by models participatingin the NMME initialized on (a) April, (b) July, and (c) September of 2017. Obtained fromhttp://www.cpc.ncep.noaa.gov/products/NMME/.

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DINEZIO ET AL.: TWO-YEAR FORECAST OF LA NIÑA

X - 21

Table S1. Standard deviation of ENSO indices computed from di↵erent observational datasets
and from the CESM control (CESM-CTL).
DatasetStandard
deviation

Zonal-mean thermocline depth index
CESM-CTL
GODAS
TAO/TRITON
ORA-S4Niño-3.4 SST index
CESM1-CTL
ERSST3b
ERSST4
HadISST1.1
Niño-3.4g SST index
CESM-CTLERSST3b
ERSST4
HadISST1.1

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9.7 m
9.8 m
9.4 m
10.5 m
0.91 K
0.80 K
0.80 K
0.76 K
1.12 K
0.93 K
1.01 K
0.89 K

November 1, 2017, 10:17am

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