# Presentation: 531431

## The Nonlinear Patterns of North American Winter Climate associated with ENSO

Aiming Wu, William Hsieh
University of British Columbia

Amir Shabbar
Environment Canada

**Aiming Wu, William Hsieh**
**University of British Columbia**
**Amir Shabbar**
**Environment Canada**

## ENSO = El Niño + Southern Oscillation

**El Niño**

**La Niña**

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**Composite of Z500 and tropical precipitation during El Niño (A) and La Niña (B) **** **
**(from ****Hoerling et al 1997**** J. of Climate)**

**B**

**A**

**     ****La Niña           El Niño**
** ****Sign reversed**
** ****Shifted eastward by 30-40°(asymmetric)**
** **

## Nonlinear Temperature Response to ENSO 

**Hoerling et al 1997 J. of Climate**

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## Winter Precipitation Variability (Nov-Mar)

## The Three Leading EOFs of SAT and Prcp

**The Three Leading EOFs of SAT and Prcp**

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**If *****x***** is the ENSO index, how do we derive the atmos. response **** y = ƒ(*****x*****) ****? **
**linear regression (or projection)**
**                              ****y ****=**** ****a**** ****•**** *****x***
***   ***
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**Linear method cannot extract asymmetric patterns  between *****–x***** and *****+x***
**Need a nonlinear method**
***   ***
** **

***–******x***

***+x***

## Nonlinear projection via Neural Networks (NN projection)

** *****x,***** the ENSO index **
** ****h, hidden layer**
** ****y ́****, output, the atmos. response **

***Cost function  ******J***** = || ****y**** – y ́ || ****is minimized to get optimal W*****x*****, b*****x*****, W****h ****and b****h****  (****y**** is the observation)  **

**   **A schematic diagram

## Data

_**ENSO index**__** (**__***x***__**)**_
**1st principal component (PC)**** of the tropical Pacific SSTA **
**Nov.-Mar. **
**1950-2001,monthly**
**SST data from ERSST-v2 (NOAA) **
**Linear detrend**
**standardized**

_**Atmos. Fields**__** (**__***y***__**)**_
**surface air temp. (SAT) and precip.(PRCP)****  **
**From CRU-UEA (UK) **
**Monthly,1950–2001, 1********1******
**Nov.-Mar.; North America**
**Anomalies (1950-01 Clim)**
** ****Linear detrend**
**PRCP standardized**
**Condensed by PCA**
**    ****10 SAT PCs (~90%) retained**
**     ****12 PRCP PCs (~60%)**

## Significance by Bootstrap

**A single NN model may not be stable (or robust)**** **
**Bootstrap: randomly select one winter’s data 52 times from the ****52-yr data (with replacement) ******** one bootstrap sample**** **
**Repeat 400 times ******** train ****400 NN models ******** average of ****the 400 models as the final solution**

**400 ****NN models**

**Given an *****x***** ******** NN model ******** y ******** (combined with ****EOFs****) ******** atmosphere anomaly pattern associated with *****x***

## NN projecton in the SAT PC1-PC2-PC3 space

**Green****: 3-D**
**Blue****: projected on 2-D PC plane **
**“****C****” extreme cold state; “****W****” extreme warm state**
**Straight line: linear proj.**
**Dots: data points **

## as ENSO index takes on its 
 (a) min. 
 (d) max.  
 (b) 1/2 min. 
 (e) 1/2 max.
 (c) a-2b
 (f)  d-2e

Darker color  above 5% significance

** ****(a) min. **
** ****(d) max.  **
** ****(b) 1/2 min. **
** ****(e) 1/2 max.**
** ****(c) a-2********b**
** ****(f)  d-2********e**
**Darker color ******** above 5% significance**

**SAT anomalies**

## PCA on Lin. & Nonlin. Parts of NN projection

**73%**

**27%**

**NL = NN – LR**

**Linear regression**

## SAT and SLP Linear and Nonlinear Projections

## PC1 of Lin. part vs. ENSO index   a straight line

PC1 of Nonlin. part vs. ENSO index  a quadratic curve
     A quadratic response

**PC****1**** of Nonlin. part vs. ENSO index ******** a quadratic curve**
**     ********A quadratic response**

## A polynomial fit

**A polynomial fit**

******1**** ****, ********2****  are *****x*****, *****x******2***** normalized, *****x***** is the ENSO index**

**SAT**

## as ENSO index takes on its 
 (a) min. 
 (d) max.  
 (b) 1/2 min. 
 (e) 1/2 max.
 (c) a-2b
 (f)  d-2e

Darker color  above 5% significance

** ****(a) min. **
** ****(d) max.  **
** ****(b) 1/2 min. **
** ****(e) 1/2 max.**
** ****(c) a-2********b**
** ****(f)  d-2********e**
**Darker color ******** above 5% significance**

**PRCP anomalies**

## Lin. & nonlin. prcp. response to ENSO 

**78%**

**22%**

**LR + NL = NN**

## Prcp and SLP Linear and Nonlinear Projections

## Lin. & nonlin. prcp. PC1 vs. ENSO index 

**Lin. & nonlin. prcp. PC****1**** vs. ENSO index**** **

## Forecast Skill in Linear and Nonlinear Models

******1 ****, ********2  are *****x*****, *****x2***** normalized, **
***x***** is the ENSO index**** **

## Summary and Conclusion

N. American winter climate responds to ENSO in a nonlinear fashion (exhibited by asymmetric SAT and PRCP patterns during extreme El Niño and La Niña events).

The nonlinear response can be successfully extracted by the nonlinear projection via neural networks (NN).

NN projection consists of a linear part and a nonlinear part. The nonlinear part is mainly a quadratic response to the ENSO SSTA, accounting for 1/4~1/3 as much as the variance of the linear part.

**N. American winter climate responds to ENSO in a nonlinear fashion (exhibited by asymmetric SAT and PRCP patterns during extreme El Niño and La Niña events).**
**The nonlinear response can be successfully extracted by the nonlinear projection via neural networks (NN).**
**NN projection consists of a linear part and a nonlinear part. The nonlinear part is mainly a quadratic response to the ENSO SSTA, accounting for 1/4~1/3 as much as the variance of the linear part.**

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Merci a tout !

**Merci a tout !**