# Presentation: 398070

## El Niño, the Trend, and SST VariabilityorIsolating El Niño

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

## Review of Linear Inverse Modeling

- Assume linear dynamics: *d****x****/dt *= **B*****x*** + ******
- Diagnose Green function from data: **G**(**) = exp(**B****)
- 				  = <***x***(*t*+**)***x***T>< ***x***(*t*)***x***T>-1 .
- Eigenvectors of **G**(**) are the ***normal modes ***{**u***i*}.
- Most probable prediction: ***x***’(*t*+**) = **G**(**) ***x***(*t*)
- Optimal initial structure for growth over lead time **:
-  	Right singular vector of **G**(**) (eigenvector of **G**T**G**(**) )
- Growth factor over lead time **: Eigenvalue of **G**T**G**(**).

## 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 <***xx***T***>***)*** ***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)

**Notes:**
Penland and Sardeshmukh (1995) and Penland and Matrosova (1998) identified in SSTA an optimal initial structure for growth (top), which precedes a mature El Nino pattern (bottom) by 7 to 9 months.  The optimal structure occurs preferentially in the spring

## Projection of adjoints onto O.S. and modal timescales.

- EOF 1 of Residual

**u**1 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.

**Notes:**
Top:  EOF 1 of residual.  Middle: Decay mode of unfiltered data
Bottom: Time series of graphs.

## Location of indices: N3.4, IND, NTA, EA, and STA.

- Location of indices: N3.4, IND, NTA, EA, and STA.

## Niño 3.4 Time Series

- El Niño

- El Niño + Trend

- Background

- Niño 3.4 Time Series

## Red: Spectrum of unfiltered Niño 3.4 SSTA

- Red: Spectrum of unfiltered Niño 3.4 SSTA
- Blue: Spectrum of residual Niño 3.4 SSTA

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

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

## Weekly SST data with its own climatology removed, then projected onto COADS EOFs.

## Projection of adjoints onto O.S. and modal timescales.

- Trend mode  = 31mo

## EA

- STA

- IND

- NTA

- R = 0.36

- R = 0.45

- R = 0.44

- R = 0.61

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

**Notes:**
Red: El Nino TS.  Black: Unfiltered TS

##    Lagged correlation between El Niño indices and PC 1.

-    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

## EA SSTA (C)

- STA SSTA (C)

- IND SSTA (C)

- NTA SSTA (C)

- R = 0.75

- R = 0.77

- R = 0.79

- R = 0.62

- Indices.  Black: Unfiltered data. Green: El Niño signal + Trend.

**Notes:**
Black: Unfiltered.  Green: El Nino + Trend

## ...evolves into this one 6 to 9 months later.

- ...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...

## Black: “Unfiltered”

- Red: El Niño
- Green: El Niño + Trend
- Blue: El Niño + Parabolic Trend

- MA Curve

- Lagged correlation C(): O.S., Niño 3.4

- Eigenvalue of **G**T**G**(**) and expected error.

**Notes:**
Top: MA Curve.  Bottom: Correlation function between time series of pattern correlations and Nino 3.4 SSTA.

## Error variance normalized to climatology

- Niño 3.4  (AR1 Error Variance)

- Niño3.4 (Expected
- Error Variance)

- Niño3.4 (Observed
- Error Variance)

## Error variance normalized to climatology

- IND (AR1 Error Variance)

- IND (Expected
- Error Variance)

- IND (Observed
- Error Variance)

- NTA (AR1 Error Variance)

- NTA (Expected Error Variance)

- NTA (Observed Error Variance)

## Error variance normalized to climatology

- EA (Expected
- Error Variance)

- EA (Observed
- Error Variance)

- STA (AR1 Error Variance)

- STA (Expected Error Variance)

- STA  (Observed Error Variance)

- EA (AR1 Error Variance)

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

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

- R = 0.36

- R = 0.36

- R = 0.30

- R = 0.48

## BLUE: NTA

**BLUE: NTA**
**No Ni****ño, No Trend**

**RED: STA**
**No Ni****ño, 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.