Multidecadal to centennial global climate variability
November 15-17, 2006
Interdecadal modulation of ENSO
nonlinearity and its rectification into
the climate state
Department of Atmospheric Sciences
Yonsei University
Soon-Il An
Acknowledgements: J.-S. Kug, F.-F. Jin, W. Hsieh ,A. Timmermann
1950-2003
PDF of
Nino-3 index
100
90
80
70
60
50
40
30
20
10
0
-4
-3
-2
-1
Number of event
1
2
3
40
40
Pre-1980s (1950-69)
35
4
Post-1908s (1980-99)
35
30
30
25
25
Symmetric to Asymmetric
20
20
15
15
10
10
5
5
0
0
0
-4
-3
-2
-1
0
1
2
3
4
-4
-3
-2
-1
0
1
2
3
4
Skewness of ENSO index
Pre-1980s
(1950-70)
skewness 
m3
(m 2 )
3/2
Post-1980s
1950-1999
(1980-99)
Nino-3
0.174
0.987
0.838
Nino-3.4
0.100
0.346
0.314
Nino-4
-0.243
-0.625
-0.379
Reynolds SST data
Q.1 What causes the El Nino-La Nina asymmetry?
(i) Nonlinear dynamical heating
(ii) Tropical instability waves
(iii) etc
Q.2 Where does the interdecadal modulation of ENSO
nonlinearity come from?
(i) Interdecadal change of tropical climate state
(ii) Propagation
(iii) etc
Q.3 Is there any rectification of ENSO?
Nonlinear Dynamical Heating (NDH):
Jin et al. (2003), An and Jin (2004)
SST EQUATION
T 
 T 
T
T 
T
T 
T





 Q  u
u
v
v
w
w
t

x

x

y

y

z
z

 T 
T 
T  
 u 
 v
 w

x
y
z 

Nonlinear
dynamical
advections terms



SST
NDH
SST
NDH
“NDH strengthens El Nino events and weakens subsequent
La Nina events, which lead to the warm-cold asymmetry”
(Jin et al. 2003; An and Jin 2004)
SST and Nonlinear dynamic heating
(1S~1N, 150W~90W)
SST
SODA
NCEP
Eastward
Large
NDH
 w
dT 
dz
  w


T s  T sub
z
Westward
Small
NDH
(An and Jin 2004)
(Contour for Temp; shading for w)
Interdecadal changes in characteristics
of ENSO during the past decades
Period
Amplitude
Propagation
Structure
Skewness
NDH
Predictability
Pre-1980s
Post-1980s
3 - 4 year
Small (rms=1.47)
Westward
Toward the west
0.17 (Nino-3)
small
less
4 - 5 year
Large (rms=1.67)
Eastward/stationary
Toward the east
0.99 (Nino-3)
large
more
(An and Wang 2000; An and Jin 2004)
Tropical instability waves
Seasonal variation of TIWV
(An 2006)
EOF of monthly
TIW variability
(An 2006)
Meridional heat flux due to TIW over
Nino-3 region
NINO3
 ( v 'T ' )
y

( v 'T ' ) y  5 N  ( v 'T ' ) y  5 S
y
(An 2006)
Meridional heat flux due to TIW
Scatter plot
(An 2006)
A simple ENSO model
d
dt
d
dt
hW   rh w   T E
T E   ( c   )T E   hW  eT E
 0 . 086 ,
 
 0 . 42 ,
3
TE  0
TE  0
hW
TE
Simple model experiment
correlation
<150-YR
SST data>
EOF of 21-yr
moving skewness of SSTA
1.Anomaly
2.Apr. to Mar. annual mean
3.Detrend
4.150-YR annual mean data
5.21-YR moving skewness
6.Apply EOF
Data: 150-yr improved-extended-reconstructed
SST (Smith and Reynolds 2004)
Predictability of
ENSO (Chen et al.
2004)
An (2004)
Space-time spectra of the equatorial SST anomalies
- Skewness + Skewness
An (2004)
Pre-1980s
Post-1980s
Zonal advective feedback:
Thermocline feedback:
w h  / H
 u d T / dx
Westward Propagation
Eastward Propagation
Late 1970s
Small positive nonlinear
dynamic heating
BIG positive nonlinear
dynamic heating
Symmetric
ENSO
Asymmetric ENSO
Nonlinear rectification: Can the
changes in the characteristics of
ENSO influence the climate state?
During the recent decades, the warm event
tends to be stronger but the cold event is not
changed much. In addition, the warming trend
concurs with this tendency. Why?
 xd 
Symmetric case
0
 xd 
Asymmetric case
 R
EOF of 20o isotherm depth anomaly
Mature Phase
Transition Phase
(An et al. 2005)
Nonlinear PCA
Total
Post-1980s
(An et al 2005)
Pre-1980s
El Nino
Transition
El Nino to La Nina
La Nina
Transition
La Nina to El Nino
Life cycle of thermocline associated with ENSO induced by the first
NLPCA (1980-1999)
Thermocline change for one cycle of ENSO

non
h
d

 1

1986
hdt
1982
h
(Fedrov and Philander)
“The eastern Pacific
SST increases about
0.5o due to the NDH
warming for the recent
decade”
(Jin et al. 2003)
Time series of the 10-YR running-mean variance, Skewn
ess, NDH over the equatorial eastern Pacific
(An et al. 2005)
MRI2 SVD of 15-YR Running-mean NDH & skewness
Cor : 0.84
NDH var : 52%
SKEW var : 78%
MRI2 SVD of 15-YR Running-mean NDH & MEAN SST
Cor : 0.64
NDH var : 49%
SST var : 46%
Conclusions
1. Both the nonlinear dynamical heating and asymmetric
thermal flux induced by the tropical instability waves
cause the El Nino-La Nina asymmetry (i.e.
skewness).
2. Decadal changes in the tropical climate state lead the
decadal modulation of the ENSO nonlinearity. In
particular, the increase of NDH is related to the
eastward propagation of the ENSO.
3. The asymmetric oscillation of ENSO (i.e. nonlinearity
of ENSO) is rectified into the climate state.