Analysis of the non-linearity in the pattern and time evolution of El Niño Southern Oscillation

Abstract

In this study the observed non-linearity in the spatial pattern and time evolution of El Niño Southern Oscillation (ENSO) events is analyzed. It is shown that ENSO skewness is not only a characteristic of the amplitude of events (El Niños being stronger than La Niñas) but also of the spatial pattern and time evolution. It is demonstrated that these non-linearities can be related to the non-linear response of the zonal winds to sea surface temperature (SST) anomalies. It is shown in observations as well as in coupled model simulations that significant differences in the spatial pattern between positive (El Niño) versus negative (La Niña) and strong versus weak events exist, which is mostly describing the difference between central and east Pacific events. Central Pacific events tend to be weak El Niño or strong La Niña events. In turn east Pacific events tend to be strong El Niño or weak La Niña events. A rotation of the two leading empirical orthogonal function modes illustrates that for both El Niño and La Niña extreme events are more likely than expected from a normal distribution. The Bjerknes feedbacks and time evolution of strong ENSO events in observations as well as in coupled model simulations also show strong asymmetries, with strong El Niños being forced more strongly by zonal wind than by thermocline depth anomalies and are followed by La Niña events. In turn strong La Niña events are preceded by El Niño events and are more strongly forced by thermocline depth anomalies than by wind anomalies. Further, the zonal wind response to sea surface temperature anomalies during strong El Niño events is stronger and shifted to the east relative to strong La Niña events, supporting the eastward shifted El Niño pattern and the asymmetric time evolution. Based on the simplified hybrid coupled RECHOZ model of ENSO it can be shown that the non-linear zonal wind response to SST anomalies causes the asymmetric forcings of ENSO events. This also implies that strong El Niños are mostly wind driven and less predictable and strong La Niñas are mostly thermocline depth driven and better predictable, which is demonstrated by a set of 100 perfect model forecast ensembles.

Full text

Analysis of the Non-linearity in the !"
Pattern and Time Evolution of El Niño #"
Southern Oscillation !$"
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1. Introduction!;U"
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2. Data!and!Models!UR"
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8. Summary!and!Discussion!H##"
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!R$R"
Acknowledgements!R$U"
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:,+3>?9-."O')'&-3>?*@("N%K!S$Rr<Z!QG"R;<"
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"!R;H"

References!R;R"
"#$! %&! '&$! (&! )&! *+,$! -&! %&! ./0$! 1&! 1&! -2#$! +#3! '&! %&! .+#0$! 45567! 89! :2#;! <+! :2#+!R;U"
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29("@,+"(?'"LP7IKcZaF7K"3&)98*(&,-G"!S<H"

Figure 1
a) EOF-1 (44%) b) EOF-2 (10%)
c) PDF PC-1 d) PDF PC-2
−4−2 0 2 4
0
50
100
150
PC−1
probability density
γ1 = 0.2
γ2 = 0.1
−4−2 0 2 4
0
50
100
150
PC−2
probability density
γ1 = 0.5
γ2 = −0.1
Figure 1: (a) EOF-1 and (b) EOF-2 patterns of the HADISST linear detrended monthly
mean SST anomalies from 1950 to 2010 are shown in the upper panels. The associated PC
probability density distribution function of (c) PC-1 and (d) PC-2 with the distribution
shape parameters skewness (γ1)andkurtosis(γ2)areshowninthelowerpanels.

Figure 2
a) strong El Ni˜no b) strong La Ni˜na c) difference (a)-(b) (0.8)
d) weak El Ni˜no e) weak La Ni˜na f) difference (e)-(d) (0.8)
g) difference (a)-(d) (0.8) h) difference (e)-(b) (0.7) i) EOF-2
Figure 2: Composites of HADISST linear detrended monthly mean SST anomalies from
1950 to 2010 based on NINO3.4 SST anomalies. (a) for all data with NINO3.4 SST
anomalies >1oK, (b) with NINO3.4 SST anomalies <−1oK, (d) with NINO3.4 SST
anomalies >0.5oKand <1oKand (e) with NINO3.4 SST anomalies <−0.5oKand
>−1oK. All Composites are normalized by their mean NINO3.4 SST anomalies. Thus (b)
and (e) are shown with the reversed sign of the mean SSTs, as the mean NINO3.4 SST
anomalies of these composites is negative. (c) is the difference between (a) (b), (f) the
difference between (e) (d), (g) the difference between (a) (d) and (h) is difference between
(e) (b). Panel (i) shows the EOF-2 pattern of Fig.1b for comparison. The headings in
(c), (f), (g) and (h) show the difference pattern correlation values with the EOF-2 pattern.
Units are in K/K(in NINO3.4 region) for (a)-(h) and non-dimensional for (i).

Figure 3
a) PCs time series
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010
−4
−2
0
2
4
time
PC values
PC−1
PC−2
b) composite strong El Ni˜nos c) composite strong La Ni˜nas
−20 −10 0 10 20
−2
−1
0
1
2
3
time relative to Dec. [mon]
PCs values
PC−1
PC−2
−20 −10 0 10 20
−2
−1
0
1
2
time relative to Dec. [mon]
PCs values
Figure 3: (a) time series of PC-1 (blue) and PC-2 (red). The shaded areas mark the ±1
intervals, which roughly matches the composites selection criteria for Fig. 2. The mean
lag/lead time evolution of the PC-1 and PC-2 time series for (b) composite mean time
evolution for the 6 strongest El Ni˜no events (1966, 1973, 1983, 1988, 1992 and 1998) and
(c) the same for the 6 strongest La Ni˜na events (1955, 1971, 1974, 1989, 1999 and 2008) are
shown. The shaded areas around the PCs mark the 90% confidence interval. The x-axis
values refer to the month relative to December of each ENSO event.

Figure 4
a) PC-1 vs. PC-2 b) rotated PC
LaNina vs. PC
ElNino
−3−2−1 0 1 2 3 4
−4
−3
−2
−1
0
1
2
3
4
PC−1
PC−2
PC−2(PC−1)
mean PC−2(PC−1 intervals)
quadratic fit
−3−2−1 0 1 2 3
−3
−2
−1
0
1
2
3
4
5
PCLa Nina
PCEl Nino
c) El Ni˜no Pattern d) (-) La Ni˜na Pattern
e) PDF PC
ElNino f) PDF PC
LaNina
−4−2 0 2 4
0
50
100
150
PCEl Nino
probability density
γ1 = 1.3
γ2 = 2.7
−4−2 0 2 4
0
50
100
150
PCLa Nina
probability density
γ1 = −0.6
γ2 = −0.2
Figure 4:(a) scatter plot of tropical Pacific SST PC-1 and PC-2datapairs(blackdots)for
each linear detrended monthly mean SST anomaly from 1950 to 2010 corresponding to the
EOFs of Fig.1. In addition the mean PC-2 values for 0.2 intervals of PC-1 are shown (blue
open circles). The non-linear model of PC-2 as function of PC-1 (eq.[1]) is marked by a red
line. (b) is a counter clockwise 45o rotation of (a), defining the new rotated axes PC
ElNino
and PC
LaNina. (c) shows the pattern corresponding to the rotated PC
ElNino and (d) the
pattern corresponding to the rotated PC
LaNina.(e)and(f)areasinFig.1candd,butfor
(e) PC
ElNino and (f) PC
LaNina.

Figure 5
a) strong El Ni˜no b) strong La Ni˜na c) difference (a)-(b) (0.3)
d) weak El Ni˜no e) weak La Ni˜na f) difference (e)-(c) (0.0)
g) difference (a)-(d) (0.2) h) difference (e)-(b) (-0.5) i) EOF-2
Figure 5:Composites of HADISST SST anomalies as Fig.2, but for the data reconstructed
with the 20 leading EOF-modes and using PC −2residual (see eq.[2]) instead of PC-2, thus
excluding the non-linear interaction between the EOF-1 and EOF-2 modes.

Figure 6
Strong Events
a) El Ni˜no b) (-) La Ni˜na c) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Wea k Event s
d) El Ni˜no e) (-) La Ni˜na f) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−1.5
−1
−0.5
0
0.5
1
1.5
Figure 6: Composite Hoevmoeller diagrams of the equatorial (averaged between 5oSto
5oN)PacificSSTanomaliesfor(a)strong(PC
ElNino >1.0 in December) and (d) weak ((0.5
<PC-1 <1.0 in December) El Ni˜no events and (b) strong ((PC
LaNina <-1.0 in December)
and (d) weak -1.0 <PC-1 <-0.5 in December) La Ni˜na events are shown. All Composites
are normalized by their mean NINO3.4 SST anomalies in the Decembers that passed the
selection criteria. Thus (b) and (e) are shown with the reversed sign of the mean SST
anomalies, as the mean December NINO3.4 SST anomalies of these composites is negative.
(c) is the difference between (a) (b) and (f) the difference between (d) (e). The y-axis
values refer to the month relative to the Decembers that passed the selection criteria for
each ENSO composite. Units are in K/K (in NINO3.4 region).

Figure 7
SLP
a) El Ni˜no b) (-) La Ni˜na c) difference
longitude
time relative to dec. [mon]
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
[hPa/K]
180 240
−20
−15
−10
−5
0
5
10
15
20
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
Zonal Wind
d) El Ni˜no e) (-) La Ni˜na f) difference
longitude
time relative to dec. [mon]
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/s/K]
180 240
−20
−15
−10
−5
0
5
10
15
20
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Thermocline Depth
g) El Ni˜no h) (-) La Ni˜na i) difference
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/(m/s)]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−40
−30
−20
−10
0
10
20
30
40
Figure 7: As Fig.6 a-c, but for (a-c) SLP and (d-f) zonal wind stress from NCEP reanalysis
and for (g-i) thermocline depth from the MPI-OM reanalysis.

Figure 8
CMIP3 models selection criteria
−0.4 −0.2 0 0.2 0.4 0.6
−1.4
−1.2
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1
1: BCCR
2
2: CCCMA T63
3
3: CCCMA T47
4
4: CNRM
5
5: CSIRO MK3.0
6
6: CSIRO MK3.5
7
7: GFDL 2.0
8
8: GFDL 2.1
9
9: GISS CM2.0
10 10: GISS CM2.1
11
11: GISS AOM
12
12: IAP
13
13: INGV
14
14: INM
15
15: IPSL
16
16: MIROC hires
17
17: MIROC medres
18
18: MIUB
19
19: MPI
20
20: MRI
21
21: NCAR CCSM3
22
22: NCAR PCM
23
23: UK HadCM3
24
24: UK HadGEM1
normalized eq. east−west difference [K/KNINO3]
normalized lag−lead difference [K/KNINO3]
Figure 8: CMIP3 models selection criteria ∆eq and ∆time for two different observational
data sets (circle for HADISST and triangle for ERSST) and for the24CMIP3models. The
shaded regions are considered to be different from observations.

Figure 9
a) PC-1 vs. PC-2 b) rotated PC
LaNina vs. PC
ElNino
−3−2−1 0 1 2 3 4
−4
−3
−2
−1
0
1
2
3
4
PC−1
PC−2
PC−2(PC−1)
quadratic fit
−3−2−1 0 1 2 3 4
−4
−3
−2
−1
0
1
2
3
4
PCLa Nina
PCEl Nino
PC−2(PC−1)
quadratic fit
c) Pattern El Ni˜no d) (-) Pattern La Ni˜na
e) PDF PC
ElNino f) PDF PC
LaNina
−4−2 0 2 4
0
5
10
15
PCEl Nino
probability density
γ1 = 0.7
γ2 = 2.3
−4−2 0 2 4
0
5
10
15
PCLa Nina
probability density
γ1 = −0.7
γ2 = 1.1
Figure 9: Scatter plot of tropical Pacific SST PC -1 and PC-2 data pairs as in Fig.4, but
for the combined data set of the 4 CMIP3 models that passed the selection criteria ∆eq and
∆time.

Figure 10
SST
a) El Ni˜no b) (-) La Ni˜na c) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Zonal Wind
d) El Ni˜no e) (-) La Ni˜na f) difference
longitude
time relative to dec. [mon]
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/s/K]
180 240
−20
−15
−10
−5
0
5
10
15
20
−1.5
−1
−0.5
0
0.5
1
1.5
Thermocline Depth
g) El Ni˜no h) (-) La Ni˜na i) difference
longitude
time relative to dec. [mon]
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
180 240
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/(m/s)]
180 240
−20
−15
−10
−5
0
5
10
15
20
−15
−10
−5
0
5
10
15
Figure 10: Composite Hoevmoeller diagrams of the equatorial Pacific as in Fig.6 a-c, but
for combined data set of the 4 CMIP3 models for (a-c) SST and (d-f) zonal wind stress
and for (g-i) thermocline depth. The thermocline depth composites are normalized by the
mean zonal wind stress anomalies in the central Pacific (160oEto 120oW)andnotbythe
NINO3.4 SST anomalies.

Figure 11
RECHOZ SST
a) El Ni˜no b) (-) La Ni˜na c) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Zonal Wind
d) El Ni˜no e) (-) La Ni˜na f) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/s/K]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−4
−3
−2
−1
0
1
2
3
4
Figure 11: Composite Hoevmoeller diagrams of the equatorial Pacific as in Fig.6 a-c but for
the RECHOZ model (a-c) SST anomalies and (d-f) zonal wind anomalies. As a selection
criteria the NINO3.4 SST is used instead of the PC
ElNino and PC
LaNina as no such
corresponding non-linear PCs exist in the RECHOZ model.

Figure 12
RECHOZ model
a) SST evolution b) Thermocline depth
−20 −10 0 10 20
−1
−0.5
0
0.5
1
lag lead [mon]
NINO3 SST [K/K]
elnino
lanina
−20 −10 0 10 20
−8
−6
−4
−2
0
2
4
6
8
lag lead [mon]
thermocline depth [m/K]
REOSC-MC model
c) SST evolution d) Thermocline depth
−20 −10 0 10 20
−1
−0.5
0
0.5
1
lag lead [mon]
NINO3 SST [K/K]
−20 −10 0 10 20
−10
−5
0
5
10
lag lead [mon]
thermocline depth [m/K]
Figure 12: Lag-lead composites of strong El Ni˜no and La Ni˜na events defined as in Fig. 11
for (a) NINO3 SST anomalies and (b) equatorial mean thermoclinedepthanomaliesofthe
RECHOZ simulation. (c) and (d) are as in (a) and (b), but for the linear (dotted lines) and
non-linear (solid lines) REOSC-MC model.

Figure 13
RECHOZ SST correlation skill
0 2 4 6 8 10 12
0
0.2
0.4
0.6
0.8
1
lead time [mon]
anomaly correlation skill
all
strong El Ninos
strong La Ninas
Figure 13: Anomaly correlation skills for RECHOZ perfect modelforecastensembles. The
strong El Ni˜no/La Ni˜na (red/blue) anomaly correlation skills are based on those forecasts
ensembles that have an NINO3 SST anomaly >1.0/<−1.0at12monthlead-timeinthe
RECHOZ control simulation. The blue shaded area marks the 90% confidence interval for
the La Ni˜na forecasts.

Figure 14
RECHOZ-PACO SST
a) El Ni˜no b) (-) La Ni˜na c) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
Zonal Wind
d) El Ni˜no e) (-) La Ni˜na f) difference
longitude
time relative to dec. [mon]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
150 200 250
−20
−15
−10
−5
0
5
10
15
20
longitude
[m/s/K]
150 200 250
−20
−15
−10
−5
0
5
10
15
20
−4
−3
−2
−1
0
1
2
3
4
Figure 14: Composite Hoevmoeller diagrams of the equatorial Pacific as in Fig.11 but for
the RECHOZ-PACO simulation.