Extratropical Sensitivity to Tropical SST

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Extratropical Sensitivity to Tropical SST
Prashant Sardeshmukh, Joe Barsugli, and Sang-Ik
Shin Climate Diagnostics Center
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Math slide 1
What is the simplest way to think about this
problem ?
x tropical SST, y Extratropical Response
y G x O(x2) Sensitivity of individual
components yi ?yi/ ?xj Gij (x i
th row of G will maximize yi) Sensitivity of
weighted sum of components R wTy ?R/ ? xj
wTG gT ( x g will maximize
R) GENERAL SENSITIVITY What patterns of x will
produce the largest global r.m.s response ? GTG
V s2 VT GGT U s2 UT yTy
(Gx)TGx xT (GTG) x x first eigenvector of
GTG (v1) will produce largest response y Gv1
s1 u1 Thus v1 is optimal SST forcing pattern
u1 is optimal response pattern
G U s VT s1 u1 v1T s2 u2 v2T .
. . . (1)
QUESTION Can G be approximated by just a few
optimal forcing-response pairs in (1) ? This
would be an important simplification.
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Math slide 2
We estimate G through the ensemble-mean CCM3
responses to an array of localized 2C SST
patches (i.e. as a Fuzzy Greens Function)
43 patches (27 Indo-Pacific, 16 Atlantic) 16
1.5 yr runs for each patch for ve and -ve
Forcing
y G x O(x2)
e / N1/2 ensemble-mean linear
Noise response signal
N 32 for each patch We do an EOF
analysis of the ensemble-mean responses.
Cyy G Cxx GT Cee / N
a2 GGT ( Cxx a2 I ) This
approximation is justified if signal/noise gtgt
1 Signal variance / Noise variance ? N a2 N
( Tmax ?A )2 We make this ratio large by
choosing relatively large N, Tmax and ?A
gt EOF analysis of y is same as SVD analysis of G
Y y1 y2 y3 . . . y43 gt EOFs and PCs
can be interpreted as optimal forcing-response
pairs v , u
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Dominant Response EOFs and their statistical
Significance
Fraction of Response Variance explained by
each EOF
Signal Variance / Noise Variance for
each EOF
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DJF EOFs 1 and 2 of Responses
Top and Middle Panels Combined EOF of N.H. 500
mb z, land surface temperature, and land
precipitation
Bottom Panels PC Local values show the
projection of the N.H. response to SST
anomalies at that location on the EOF. The map
as a whole is the optimal SST anomaly pattern
for generating the EOF with the largest
amplitude
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MAM EOFs 1 and 2 of Responses
Note large precipitation response over North
America
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JJA EOFs 1 and 2 of Responses
The 500 mb height response is weak in JJA, but
there is still a large precipitation response
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SON EOFs 1 and 2 of Responses
Both the 500 mb height and precipitation responses
are weak in SON, although there is still an
appreciable precipitation response over the
central and southeast U.S.
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EOF1 and Sensitivity of North American
Precipitation
MAM 44
DJF 44
JJA 49
SON 32
Note! Warm SST RED and Wet Precip BLUE
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DJF EOF 1 of Tropical Precipitation Responses
(left) and Noise (right)
Why is EOF 1 so dominant ? Why does it explain
more than 57 of the responses in DJF ? What is
responsible for organizing the responses to such
an extent even for effectively random
SST forcing ( Cxx a2 I ) ? One possible
explanation Tropical Precipitation response is
highly organized (It tends to be
relatively stronger over the warm pool)
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Math slide 3
But the dominance of EOF1 of the DJF
extratropical responses (57) is only partly
explained by the dominance of EOF1 of the
tropical precipitation responses (20 )
SST x ---gt Tropical Precipitation
Response p ---gt Extratropical Response y
x p
G1x e1 EOF1 of p responses
explains 20. Some of the dominance of EOF 1 of y
is because of this. p
y G2p e2 G2G1x (G2e1 e2)
Gx e This explains the other 57
- 20 37 of the dominance of EOF1 of y.
Both the relative insensitivity of the Rossby
Wave Source associated with the precip
response AND the organization of the
response to that source by the stationary waves
are responsible for this.
This explains why 1. EOF 1 of response is more
dominant than is the EOF1 of noise 2. EOF 1 of
response always explains more than 20 of
responses 3. EOF 1 of responses is most dominant
in DJF (57)
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Sensitivity of Local Tropical Precipitation
Response (as a function of background SST)
What about Nonlinearity ? How Important is it ?
For 2 C anomalies For - 2 C
anomalies
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EOF 1 of DJF Responses to warm and cold
SST anomalies
The patterns of the optimal DJF SST forcing and
response fields are slightly different for warm
and cold SST forcing. There is also a slightly
weaker response to cold forcing.
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Dominant SST sensitivity patterns are VERY
DIFFERENT from the dominant pattern
of observed SST variability
DJF 57
EOF 1 of Observed SST 32
MAM 30
There is much greater sensitivity to SST changes
in the Central and West Pacific and Indian
oceans. The sensitivity is generally opposite
to SST changes in the Indian and West Pacific
oceans .
JJA 40
SON 41
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Summary

• Extratropical sensitivity to tropical SST changes
  can be characterized by just
• 2 or 3 optimal forcing-response pairs in each
  season.
• The dominance of these pairs results partly from
  the relatively large sensitivity of the local
  precipitation response in regions of warmer
  background SST such as the warm pool, and partly
  from a modal dynamical extratropical response
  to tropical diabatic forcing (Ting and
  Sardeshmukh 1993).
• The optimal SST forcing patterns are VERY
  DIFFERENT from the ENSO pattern. The only area of
  significant overlap is Nino-4.
• The extratropical climate generally shows
  opposite sensitivities to SST changes in the
  western and eastern halves of the warm pool.
• 5. These results have important implications for
  understanding and modeling global climate changes
  from monthly to millenial time scales.

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An Array of localized SST patches
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The SST seasonal cycle
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DJF Local Variance Explained by Response EOFs 1
and 2