The nonlinear patterns of North American winter temperature and precipitation associated with ENSO
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The nonlinear patterns of North American winter temperature and
precipitation associated with ENSO
Aiming Wu, William W. HsiehDept. of Earth & Ocean Sciences,
University of British Columbia
and
Amir ShabbarMeteorological Services of Canada
Downsview, Ontario
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ENSO = El Niño + Southern Oscillation
El Niño La Niña
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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)
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Question
If x is the ENSO index, how to 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
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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
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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, 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%)
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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
Give a x NN model y (combined with EOFs) atmosphere anomaly pattern associated with x
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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
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• 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
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PCA on Lin. & Nonlin. Parts of NN projection
73% 27%
NL = NN – LRLinear regression
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• PC1 of Lin. part vs. ENSO index a straight line
• PC1 of Nonlin. part vs. ENSO index a quadratic curve
A quadraticresponse
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22110 iiii aaay
A polynomial fit
1 , 2 are x, x2 normalized, x is the ENSO index
SAT
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• 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
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Lin. & nonlin. prcp. response to ENSO
78% 22%
LR + NL = NN
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Lin. & nonlin. prcp. PC1 vs. ENSO
index
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Summary and ConclusionSummary and Conclusion
• N. Amer. 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), while linear method can not.
• 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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Thank you !