# Presentation: 421485

## On the origin of the observed ENSO variability

**Javier Zavala-Garay**
**(IMCS, Rutgers)**
**and**
**Chidong Zhang**
**(RSMAS, UM)**

## Motivation

- ENSO models show large dispersion in forecasted values and not always verify.
- Forecast skill is often times taken as a measure of how realistic the model is.
- These models exhibit different dynamical regimes.
- We need how the observed variability originates in order to (i) better evaluate ENSO models, (ii) design adequate prediction schemes, and (iii) wisely interpret such predictions.

## Motivation

- ENSO models show large dispersion in forecasted values and not always verify.
- Forecast skill is often times taken as a measure of how realistic the model is.
- These models exhibit different dynamical regimes.
- We need how the observed variability originates in order to (i) better evaluate ENSO models, (ii) design adequate prediction schemes, and (iii) wisely interpret such predictions.

## Motivation

- ENSO models show large dispersion in forecasted values and not always verify.
- Forecast skill is often times taken as a measure of how realistic the model is.
- These models exhibit different dynamical regimes.
- We need how the observed variability originates in order to (i) better evaluate ENSO models, (ii) design adequate prediction schemes, and (iii) wisely interpret such predictions.

## Motivation

- ENSO models show large dispersion in forecasted values and not always verify.
- Forecast skill is often times taken as a measure of how realistic the model is.
- These models exhibit different dynamical regimes.
- We need to understand how the observed variability originates in order to (i) better evaluate ENSO models, (ii) design adequate prediction schemes, and (iii) wisely interpret such predictions.

## All published models exhibit an ENSO mode and interannual variability.
Still some work to be done in order to get the correct spatial structure.
In this talk we concentrate mainly on the temporal evolution as characterized by the Nino-3 index

**Still some work to be done in order to get the correct spatial structure.**
**In this talk we concentrate mainly on the temporal evolution as characterized by the Nino-3 index**

- EOF1 off SST for different ENSO models
- (from van Oldenborgh et al., 2005)

## ...so the rest of this talk is organized as follows....

- Main characteristics of the observed ENSO Variability (EV)
- Hypotheses proposed to explain EV
- Intermediate model design
- Statistical evaluation of the ENSO models
- Hybrid model experiments
- Fully coupled GCM (in progress)
- Conclusion and implications for ENSO prediction and climate modeling

## Main characteristics of observed ENSO variability

-  **EV exhibits some unique characteristics that define some sort of “regularity” or structure characterizing some aspects of its underlying manifold. It is in this “regularity” that the potential for predictability resides and therefore it is desirable that ENSO models reproduce such variations **

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## EV checklist!!!!

- 136 years (1871-2006)
- Broad band spectrum
-  with no significant peaks
- Seasonal state-dependent
-  variance (larger for El Nino
-  and towards NH winter)
- Seasonal lag-correlation
-  with faster decorrelations
-  towards spring time
- PDF with small but significant
- Deviations from Gaussianity

## Hypotheses proposed to explain EV

## Several hypotheses have been proposed to explain EV, but they can be categorized in three groups

- H1: EV originates from deterministic low-order chaos (Tziperman et al., 1994; Jin et al., 1994)
- Special cases of an scenario proposed by Lau, 1985 and Lau and Chan 1986:
- H2: EV originates from the effect of subseasonal variability (the MJO, WWBs, etc.) or Stochastic Forcing (SF) acting on a self-sustained oscillation (Eckert and Latif, 1997; Blanke et al., 1997; Latif 1998; Kirtman and Schopf, 1998)
- H3: EV originates from the effect of SF acting on an otherwise stable system (Penland and Sardeshmukh, 1995; Chang et al., 1996; Moore and Kleeman 1999; Roulston and Neelin 2000, Zavala-Garay 2005,2006,2007).

## Several hypotheses have been proposed to explain EV, but they can be categorized in three groups

- H1: EV originates from deterministic low-order chaos (Tziperman et al., 1994; Jin et al., 1994)
- Special cases of an scenario proposed by Lau, 1985 and Lau and Chan 1986:
- H2: EV originates from the effect of subseasonal variability (the MJO, WWBs, etc.) or Stochastic Forcing (SF) acting on a self-sustained oscillation (Eckert and Latif, 1997; Blanke et al., 1997; Latif 1998; Kirtman and Schopf, 1998)
- H3: EV originates from the effect of SF acting on an otherwise stable system (Penland and Sardeshmukh, 1995; Chang et al., 1996; Moore and Kleeman 1999; Roulston and Neelin 2000, Zavala-Garay 2005,2006,2007).

## Several hypotheses have been proposed to explain EV, but they can be categorized in three groups

- H1: EV originates from deterministic low-order chaos (Tziperman et al., 1994; Jin et al., 1994)
- Special cases of an scenario proposed by Lau, 1985 and Lau and Chan 1986:
- H2: EV originates from the effect of subseasonal variability (the MJO, WWBs, etc.) or Stochastic Forcing (SF) acting on a self-sustained oscillation (Eckert and Latif, 1997; Blanke et al., 1997; Latif 1998; Kirtman and Schopf, 1998)
- H3: EV originates from the effect of SF acting on an otherwise stable system (Penland and Sardeshmukh, 1995; Chang et al., 1996; Moore and Kleeman 1999; Roulston and Neelin 2000, Zavala-Garay 2005,2006,2007).

## In this talk we evaluate hypothesis H1-H3 in a parallel way of thinking by...

**Developing two stochastic models (SM1 and SM2) from the most outstanding example of a chaotic ENSO model: The Cane and Zebiak model (Cane et al., 1986; Cane and Zebiak, 1987; Zebiak and Cane 1987).**
** ****The two models strongly differ from previous studies in that they can admit SF with fast decorrelation times**
**The SF used in SM1 and SM2 is estimated from observations**
** **
**The unstable regime of SM1 recreates the chaotic behaivor of the original CZ model**
**The unstable regime of SM2 recreates the limit cycle of other models**
**Both models can be tunned to neutral and stable regimes to recreate yet other studies/models.**

## Intermediate model design

## The Cane and Zebiak ENSO model

**It is a model of intermediate complexity: reduced gravity ocean dynamics coupled to a mixed layer model and a steady-state Gill-type atmospheric model slaved to SST  **
**It exhibits a forecast skill comparable to other ENSO models including fully coupled GCMs**
**“*****Our analysis suggests that the evolution of El Niño is controlled to a larger degree by self-sustaining internal dynamics than by stochastic forcing. Model-based prediction of El Niño therefore depends more on the initial conditions than on unpredictable atmospheric noise.”   (Chen et al., Nature 2004). ***

- Figure from
- Chen et al., 2004

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## SM1 stable

**CM = standard Cane **
** ****and Zebiak model**
**(dt = 10 days)**
**SM1 (dt = 1 day)**
**Unstable is chaotic**
**SM1 Neutral**
**SM1 stable**
**SM2 (dt = 1 day)**
**Unstable is limit cycle**
**SM2 neutral**
**SM2 stable**

## The last very important ingredient in the design of SM1 and SM2 is the stochastic forcing used:

**Determined from residual of SVD-based multivariate regression of Reynolds SST and NCEP2 surface zonal wind**
**25 years (1979-2003)**
**The original residual can be represented by the sequence (year,month) = (****1979****,1),(****1979****,2),...,(****2003****,11),(****2003****,12)**
**Synthetic timeseries were generated by bootstrapping the years, so a possible realization of SF is (****1985****,1),(****1983****,2),....,(****1994****,12),(****1979****,1)... **
**The of defining exactly the same sequence of noise is very low, and the probability having that noise acting on the same model state is even lower**
**The resulting SF preserves key characteristics of the noise as its seasonality, temporal and spatial decorrelation scales, and structure and eastward propagation of the MJO **

## Based on the KS test for Gaussianity,

- the SF used cannot be rejected to be Gaussian at the 5% CL

## Models’ validation: Estimate the PDF of selected metrics and compare with

**Models’ validation: Estimate the PDF of selected metrics and ****compare with**
**the corresponding metric derived from observations (shown in red)**
**Ran the model for each case for 500*136 years**
**Divide the timeseries in chunks of 136 years each**
**Standarize the timeseries**
**Summarize the associated PDF based on percentiles and ensemble mean**

## EV checklist aspect 1: spectrum

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## Comparison of spectral

**Comparison of spectral**
**Power from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## EV checklist aspect 2: seasonal state-dependent variance

## Comparison of seasonal

**Comparison of seasonal**
**state-dependent **
**variance observed (****red**
**For El Nino****, ****blue for**
**La Nina****)**** ****and ensemble **
**PDFs (approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## EV checklist aspect 2: seasonal lag correlations

## Long term seasonal 

**Long term seasonal **
**lag-correlation**
**maps for all models**

## Comparison of selected

**Comparison of selected**
**lag-correlations**
**from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **

## EV checklist aspect 2: Probability Density Functions

## Comparison of PDF

**Comparison of PDF**
**from ****observations**
**and ensemble PDFs**
**(approx. 500 totally**
**independent ensemble **
**members for each **
**case) **
**ENSO asymmetry**
**still present in the **
**stable versions of the**
**models!!!! **

## Two-sample KS test:

**Two-sample KS test:**
**how likely is that two**
**samples come from the**
**same PDF?**
**Consistent improvement**
**as one moves from **
**unstable (chaotic or limit**
**cycle), to neutral, to **
**stable....**

## Hybrid model (OPA + statistical atmosphere)

- “Western Pacific optimal perturbation”

**Influence of the MJO at the onset of the 97/98 El Nino**

- (Moore and Kleeman 1999)

-  “Western Pacific optimal perturbation”

**Influence of the MJO at the onset of the 97/98 El Nino**

## Slide 50

## BAM coupled GCM (realistic MJO, not so well seasonal variation)

## Conclusion: EV is likely to originate from a weakly damped nonlinear systemImplications: (i) ENSO prediction is a probabilistic problem.not deterministic. (ii) Future evolution of ENSO is an interplay the coupled dynamics implied by the initial conditions and the SF-induced dispersion(iii) ENSO models need to incorporate SF in their predictions   

## Conclusion: EV is likely to originate from a weakly damped nonlinear systemImplications: (i) ENSO prediction is a probabilistic problem.not deterministic. (ii) Future evolution of ENSO is an interplay the coupled dynamics implied by the initial conditions and the SF-induced dispersion(iii) ENSO models need to incorporate SF in their predictions   

## Fedorov et al., 2000

## Extra slides follow.....

## Slide 56

## Slide 57

## Slide 58

## Slide 59

## Slide 60

## Slide 61

## Slide 62

## Slide 63