# Presentation: 097209

## El Niño and how to get rid of it

*C**écile Penland*

- With thanks to
- 	Prashant Sardeshmukh	Ludmila Matrosova
- 	Ping Chang			Moritz Flügel
- 	Brian Ewald			Roger Temam
- 	The Climate Diagnostics Center	OGP

## 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(*t*) >< ***x***(*t*)***x***T(*t*) >-1 .
- Eigenvectors of **G**(**) are the ***“normal” modes ***{**u***i*}.
- Most probable prediction: ***x***’(*t*+**) = **G**(**) ***x***(*t*)
- The neat thing: **G**(**) ={**G**(****) } ****

## SST Data used:

- COADS (1950-2000) SSTs in 30E-70W, 30N – 30S consolidated onto a 4x10-degree grid.
- 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.

## El Niño can be described this way.

- If LIM is successful, prediction error does not depend on the lag at which the covariance matrices are evaluated.  This is true for El Niño; it is *not* true for the chaotic Lorenz system.  Below, different colors correspond to different lags used to identify the parameters.

## But

*	**d****x****/dt *= **B*****x*** + ******(*t*)*********T ***(*t*)*** ************= ***Q**(*t*)************
- Given stationary **B** use (time-dependent) conservation of variance to diagnose **Q**(*t*).
- Result: The annual cycle of **Q**(*t*) looks *nothing *like the phase locking of either El Niño or the optimal structure to the annual cycle.
***But***
- A model generated with the stationary **B**** ***and *the stochastic forcing with cyclic statistics **Q**(*t*) *does *reproduce the correct phase-locking in both.

## What do models say?

- Hybrid coupled model (Chang 1994)
- Dynamical core of GFDL Ocean model, considerably simplified
- Statistical atmosphere based on EOFs of observed wind stress
- Interactive annual cycle
- Strength of coupling determines dynamical regime (Note: an artificial parameter **)

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## 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**(**).

## (a)	

- The transient growth possible in a multidimensional linear system occurs when an El Niño develops.  ***LIM*** predicts that an *optimal pattern *(*a*) precedes a mature El Niño pattern (*b*) by about 8 months.

- (*b*)

## Does it?  Judge for yourself! (c and d)

- 		*c*)									*d*)

- (*c*)

- (*d*)

- In (*c*), the red line is the time series of pattern correlations between pattern (*a*) and the sea surface temperature pattern 8 months earlier.  The blue line is a time series index of how strong pattern (*b*) is at the date shown; the blue line is an index of El Niño when it is positive and of La Niña when it is negative.
- In (*d*) we see a scatter plot of the El Niño index and pattern correlations shown in (*c*).
- Pattern (*a*) **really does **precede El Niño!  Pattern (*a*) with the signs reversed precedes La Niña!

## Slide 13

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

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

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

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## EA

- STA

- IND

- NTA

- R = 0.36

- R = 0.45

- R = 0.44

- R = 0.61

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

##    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

## 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.

## 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.

## All this results from SST dynamics being essentially linear.

- But linear dynamics implies symmetry between El Niño and La Niña events.
- SST anomalies appear to be positively skewed.
- Is the skew significant?

## Additive Noise Model 

- Additive Noise Model
*d****x****/dt *= **B*****x*** + ******

- Multiplicative Noise Model 1
*d****x****/dt*=(**B***+**A*********)***x*** + ******

- Multiplicative Noise Model 2
*d****x****/dt*=**B**’(**I**+**I********’)***x ***+ ******

## Conclusions

- El Niño appears to be a damped system forced by stochastic noise.
- There is evidence that the phase locking of El Niño to the annual cycle is due to the annually-varying statistics of the stochastic noise.
- An optimal initial structure for growth precedes a mature El Niño event by 6 to 9 months.
- The nonnormal dynamics are dominated by 3 nonorthogonal modes.
- The essential linearity of the system allows isolation of the El Niño signal.

## El Niño indices in the equatorial Indian Ocean and the North Tropical Atlantic Ocean are very similar.
El Niño and the (parabolic) trend dominate the SST variability in the Indian Ocean as well as in the Equatorial and S. Tropical Atlantic Ocean.
The observed skew in El Niño –La Niña events IS NOT significant compared with  realistic null hypothses.
The trend IS significant compared with realistic null hypotheses.

- El Niño and the (parabolic) trend dominate the SST variability in the Indian Ocean as well as in the Equatorial and S. Tropical Atlantic Ocean.
- The observed skew in El Niño –La Niña events ***IS NOT*** significant compared with  realistic null hypothses.
- The trend ***IS*** significant compared with realistic null hypotheses.

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