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El Ni ño, the Trend, and SST Variability or Isolating El Niño. C écile Penland and Ludmila Matrosova NOAA-CIRES/Climate Diagnostics Center. Review of Linear Inverse Modeling. Assume linear dynamics: d x /dt = B x + x Diagnose Green function from data: G ( t ) = exp( B t ) - PowerPoint PPT Presentation
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El Niño, the Trend, and SST Variability
orIsolating El Niño
Cécile Penland and Ludmila MatrosovaNOAA-CIRES/Climate Diagnostics Center
Review of Linear Inverse Modeling
Assume linear dynamics: dx/dt = Bx +
Diagnose Green function from data: G() = exp(B)
= <x(t+)xT>< x(t)xT>-1 .
Eigenvectors of G() are the normal modes {ui}.
Most probable prediction: x’(t+) = G() x(t)
Optimal initial structure for growth over lead time :
Right singular vector of G() (eigenvector of GTG() )
Growth factor over lead time : Eigenvalue of GTG().
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 <xxT>)
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.
This optimal initial pattern…
…evolves into this one 6 to 9 months later.
Cor. = 0.65
T3.
4(t)
Pat. Cor. (SST,O.S.)(t – 8mo)
Decay mode, = 31 months
0
0.5
1
1.5
0 5 10 15 20 25Mode number
momo
momo
momo
decay timeT = Period
Projection of adjoints onto O.S. and modal timescales.
-15
-10
-5
0
5
10
1950 1960 1970 1980 1990 2000 2010Date
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.
Location of indices: N3.4, IND, NTA, EA, and STA.
-3
-2
-1
0
1
2
3
1950 1960 1970 1980 1990 2000Date
-3
-2
-1
0
1
2
3
1950 1960 1970 1980 1990 2000Date
-2
-1
0
1
2
1950 1960 1970 1980 1990 2000Date
El Niño
El Niño + Trend
Background
Niño 3.4 Time Series
10-4
10-3
10-2
10-1
100
101
1 10 100 1000Period (months)
Red: Spectrum of unfiltered Niño 3.4 SSTA
Blue: Spectrum of residual Niño 3.4 SSTA
-5
0
5
10
15
20
25
1 10 100 1000Period (months)
66.4 mo39.9 mo18.1 mo
15.3 mo
Spectral difference: (Spectrum of unfiltered data – spectrum of residual) / Spectrum of residual.
-505
101520253035
100 101 102 103 104
43.9 mo
16.5 mo
5.2 mo
Period (weeks)
Weekly SST data with its own climatology removed, then projected onto COADS EOFs.
0
0.5
1
1.5
0 5 10 15 20 25Mode number
momo
momo
momo
decay timeT = Period
Projection of adjoints onto O.S. and modal timescales.
Trend mode = 31mo
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R(Unfiltered, El Nino) = 0.36
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000Date
R(Unfiltered, El Nino) = 0.44
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000Date
R(Unfiltered, El Nino) = 0.45
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000
R(Unfiltered, El Nino) = 0.61
EA
STA
IND
NTA
R = 0.36 R = 0.45
R = 0.44 R = 0.61
Indices. Black: Unfiltered data. Red: El Niño signal.
-0.8
-0.6
-0.4
-0.2
0
0.2
-100 -50 0 50 100Lead (months)
8 months
STA leads PC1 leads
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
-100 -50 0 50 100Lead (months)
IND leads PC1 leads
-0.6
-0.4
-0.2
0
0.2
0.4
-100 -50 0 50 100Lead (months)
EA leads PC1 leads
9 months
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
-100 -50 0 50 100Lead (months)
NTA leads PC1 leads
Lagged correlation between El Niño indices and PC 1.
STA leads PC1 leads PC1 leads
PC1 leads PC1 leads
EA leads
IND leads NTA leads
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000
R(Unfiltered, El Nino +Trend) = 0.75
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000Date
R(Unfiltered, El Nino+Trend) = 0.79
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000Date
R(Unfiltered, El Nino+Trend) = 0.77
-1.5
-1
-0.5
0
0.5
1
1.5
1950 1960 1970 1980 1990 2000
R(Unfiltered, El Nino + Trend) = 0.62
EA S
STA
(C)
STA
SST
A (C
)IN
D S
STA
(C)
NTA
SST
A (C
)
R = 0.75 R = 0.77
R = 0.79 R = 0.62
Indices. Black: Unfiltered data. Green: El Niño signal + Trend.
…evolves into this one 6 to 9 months later.
Cor. = 0.65
T3.
4 (t)
Pat. Cor. (SST,O.S.)(t-8mo)
This optimal initial condition…
0
0.5
1
1.5
2
2.5
3
3.5
4
0 5 10 15 20 25Lead (months)
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 5 10 15 20 25Lead (months)
Black: “Unfiltered”
Red: El Niño
Green: El Niño + Trend
Blue: El Niño + Parabolic Trend
MA Curve
Lagged correlation C(): O.S., Niño 3.4
Eige
nval
ue o
f G
T G(
) and
ex
pect
ed e
rror
.
Error variance normalized to climatology
Niñ
o 3.
4 (A
R1
Erro
r Var
ianc
e)N
iño3
.4 (E
xpec
ted
Erro
r Var
ianc
e)N
iño3
.4 (O
bser
ved
Erro
r Var
ianc
e)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
Error variance normalized to climatology
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
IND
(AR
1 Er
ror
Var
ianc
e)IN
D (E
xpec
ted
Erro
r Var
ianc
e)IN
D (O
bser
ved
Erro
r Var
ianc
e)
NTA
(AR
1 Error V
ariance)N
TA (Expected
Error Variance)
NTA
(Observed
Error Variance)
Error variance normalized to climatology
EA (E
xpec
ted
Erro
r Var
ianc
e)EA
(Obs
erve
d Er
ror V
aria
nce)
STA (A
R1
Error Variance)
STA (Expected
Error Variance)
STA (O
bserved Error V
ariance)0
0.5
1
1.5
0 5 10 15 20 25Lead (months)0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
0
0.5
1
1.5
0 5 10 15 20 25Lead (months)
EA (A
R1
Erro
r V
aria
nce)
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R=0.36
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R=0.30
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R=0.36
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R=0.48
Black: “Unfiltered” data. Blue: Background (No Niño, no Trend)
R = 0.36 R = 0.36
R = 0.30 R = 0.48
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R = -0.37; Trend = u1
-1
-0.5
0
0.5
1
1950 1960 1970 1980 1990 2000Date
R = -0.49; Trend = PC1 of residual
BLUE: NTA
No Niño, No Trend
RED: STA
No Niño, No Trend
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 won’t help the predictions, though.
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.
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