The Nonlinear Patterns of North American Winter Climate associated
with ENSO
Aiming Wu, William HsiehUniversity of British Columbia
Amir ShabbarEnvironment Canada
ENSO = El Niño + Southern Oscillation
El Niño La Niña
Atmos. Response to ENSO is nonlinear
+-
+ +-+
-
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
Objective of the StudyIf x is the ENSO index, how do we derive the
atmos. response y = ƒ(x) ?
• linear regression (or projection) y = a • x
+ + -- + -•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
hh bhWy'
bWh
)tanh( xx x
Cost function J = || y – y´ || is minimized to get optimal Wx, bx, Wh and bh (y is the observation)
A schematic diagram
DataENSO 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, 11•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-2b (f) d-2e
•Darker color above 5% significance
SAT anomalies
PCA on Lin. & Nonlin. Parts of NN projection
73% 27%
NL = NN – LRLinear regression
•PC1 of Lin. part vs. ENSO index a straight line
•PC1 of Nonlin. part vs. ENSO index a quadratic curve
A quadratic response
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A polynomial fit
1 , 2 are x, x2 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-2b (f) d-2e
•Darker color above 5% significance
PRCP anomalies
Lin. & nonlin. prcp. response to ENSO
78% 22%
LR + NL = NN
Lin. & nonlin. prcp. PC1 vs. ENSO
index
Forecast Skill in Linear and Nonlinear Models
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1 , 2 are x, x2 normalized,
x is the ENSO index
Summary and ConclusionSummary 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.
Merci a tout !