El Ni ño, the Trend, and SST Variability or Isolating El Niño

1. El Niño, the Trend, and SST VariabilityorIsolating 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) = <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).

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 <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.

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 STA EA R = 0.44 R = 0.61 IND NTA Indices. Black: Unfiltered data. Red: El Niño signal.

14. 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.

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 won’t 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.