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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 )

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el ni o the trend and sst variability or isolating el ni o

El Niño, the Trend, and SST VariabilityorIsolating El Niño

Cécile Penland and Ludmila Matrosova

NOAA-CIRES/Climate Diagnostics Center

review of linear inverse modeling
Review of Linear Inverse Modeling

Assume linear dynamics: dx/dt = Bx + x

Diagnose Green function from data: G(t) = exp(Bt)

= <x(t+t)xT>< x(t)xT>-1 .

Eigenvectors of G(t) are the normal modes {ui}.

Most probable prediction: x’(t+t) = 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).

sst data used
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.
slide4

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)

slide6

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.

slide8

El Niño

Niño 3.4 Time Series

El Niño + Trend

Background

slide9

Red: Spectrum of unfiltered Niño 3.4 SSTA

Blue: Spectrum of residual Niño 3.4 SSTA

slide10

Spectral difference: (Spectrum of unfiltered data – spectrum of residual) / Spectrum of residual.

slide13

R = 0.36

R = 0.45

STA

EA

R = 0.44

R = 0.61

IND

NTA

Indices. Black: Unfiltered data. Red: El Niño signal.

slide14

STA leads

PC1 leads

EA leads

PC1 leads

IND leads

PC1 leads

NTA leads

PC1 leads

Lagged correlation between El Niño indices and PC 1.

slide15

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.

slide16

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)

slide17

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

slide18

Niño 3.4 (AR1 Error Variance)

Niño3.4 (Expected

Error Variance)

Niño3.4 (Observed

Error Variance)

Error variance normalized to climatology

slide19

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

slide20

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

slide21

R = 0.36

R = 0.36

R = 0.30

R = 0.48

Black: “Unfiltered” data. Blue: Background (No Niño, no Trend)

slide22

BLUE: NTA

No Niño, No Trend

RED: STA

No Niño, No Trend

conclusions
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
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.