El Ni

1
El Niño, the Trend, and SST VariabilityorIsolati
ng El Niño

• Cécile Penland and Ludmila Matrosova
• NOAA-CIRES/Climate Diagnostics Center

2
Review of Linear Inverse Modeling
Assume linear dynamics dx/dt Bx x Diagnose
Green function from data G(t) exp(Bt)
ltx(tt)xTgtlt x(t)xTgt-1 . Eigenvectors of G(t) are
the normal modes ui. Most probable prediction
x(tt) G(t) x(t) Optimal initial structure for
growth over lead time t Right singular vector
of G(t) (eigenvector of GTG(t) ) Growth factor
over lead time t Eigenvalue of GTG(t).
3
SST Data used

• COADS (1950-2000) SSTs in the tropical strip 30N
  30S.
• Subjected to 3-month running mean.
• Projected onto 20 EOFs (eigenvectors of ltxxTgt)
  containing 66 of the variance.
• x, then, represents the vector of SST anomalies,
  each component representing a location, or else
  it represents the vector of Principal Components.
  
• This is what we call unfiltered data.

4
This optimal initial pattern
evolves into this one 6 to 9 months later.
Cor. 0.65
dT3.4(t)
Pat. Cor. (SST,O.S.)(t 8mo)
5
Projection of adjoints onto O.S. and modal
timescales.
Decay mode, m 31 months
6
EOF 1 of Residual
u1 of un-filtered data
The pattern correlation between the longest-lived
mode of the unfiltered data and the leading EOF
of the residual data is 0.81.
7
Location of indices N3.4, IND, NTA, EA, and STA.
8
El Niño
Niño 3.4 Time Series
El Niño Trend
Background
9
Red Spectrum of unfiltered Niño 3.4 SSTA Blue
Spectrum of residual Niño 3.4 SSTA
10
Spectral difference (Spectrum of unfiltered data
spectrum of residual) / Spectrum of residual.
11
Weekly SST data with its own climatology removed,
then projected onto COADS EOFs.
12
Projection of adjoints onto O.S. and modal
timescales.
Trend mode m 31mo
13
R 0.36
R 0.45
EA
STA
R 0.44
R 0.61

IND
NTA
Indices. Black Unfiltered data. Red El Niño
signal.
14
STA leads
PC1 leads
PC1 leads
EA leads
PC1 leads
PC1 leads
IND leads
NTA leads
Lagged correlation between El Niño indices and
PC 1.
15
R 0.75
R 0.77
EA SSTA (C)
STA SSTA (C)
R 0.79
R 0.62
IND SSTA (C)
NTA SSTA (C)
Indices. Black Unfiltered data. Green El Niño
signal Trend.
16
This optimal initial condition
evolves into this one 6 to 9 months later.
Cor. 0.65
dT3.4 (t)
Pat. Cor. (SST,O.S.)(t-8mo)
17
MA Curve
Black Unfiltered Red El Niño Green El Niño
Trend Blue El Niño Parabolic Trend
Eigenvalue of GTG(t) and expected error.
Lagged correlation C(t) O.S., Niño 3.4
18

Niño 3.4 (AR1 Error Variance)
Niño3.4 (Expected Error Variance)
Niño3.4 (Observed Error Variance)
Error variance normalized to climatology
19

IND (AR1 Error Variance)
NTA (AR1 Error Variance)
IND (Expected Error Variance)
NTA (Expected Error Variance)
IND (Observed Error Variance)
NTA (Observed Error Variance)
Error variance normalized to climatology
20


EA (AR1 Error Variance)
STA (AR1 Error Variance)
EA (Expected Error Variance)
STA (Expected Error Variance)
EA (Observed Error Variance)
STA (Observed Error Variance)
Error variance normalized to climatology
21
R 0.36
R 0.36
R 0.30
R 0.48
Black Unfiltered data. Blue Background (No
Niño, no Trend)
22
BLUE NTA No Niño, No Trend
RED STA No Niño, No Trend
23
Conclusions

• Two different ways of identifying the trend lead
  to qualitatively similar results.
• The pattern-based filter can be applied to data
  of any temporal resolution.
• The El Niño signals in the tropical Indian and
  North tropical Atlantic are highly correlated (R
  0.84).
• El Niño signals in EA and STA precede that in
  Niño 3.4 by about 8 months. This wont help the
  predictions, though.

24
Conclusions (cont.)

• El Niño plus the trend appear to dominate SSTA
  variability in IND, EA and STA.
• The trend seems to cause overestimation of
  nonmodal growth of El Niño.
• Isolating the signals with this filter seems to
  be more valuable for diagnosis than prediction,
  except in IND.
• The tropical Atlantic dipole is significant in
  the background SSTA field.