Non-linear and Non-stationary Influences of Geomagnetic
Activity on the Winter North Atlantic Oscillation
Yun Li, Hua Lu, Martin Jarvis, Mark Clilverd and Bryson Bates
British Antarctic Survey, UK
CSIRO Climate Adaptation Flagship
SORCE Meeting, 13-16 Sep. 2011
North Atlantic Oscillation (NAO)
Positive phase
Positive NAO pro-dominate in 1980s
and 1990s  warmer & wetter winter
in North Europe and mild weather in
east coast of the US
Negative phase
Last 3 winter: Deep nagetive NAO
brought severe winter conditions
to North Europe and snow to east
coast of the US
Geomagnetic Disturbances by
Solar Wind
•
•
•
•
•
disturbance of the Earth's magnetosphere
energetic particles precipitate into the Earth’s atmosphere
produce ionization from 150km down to ~40 km
generate odd nitric oxide which may destroy ozone
cause changes in atmospheric wave propogation
Solar wind and
particles
Protective
magnetic
field
Rzaa
0 5 15
100 3
IDV aa
6 5 101514 30
IDV
Rz
IHV
14
20 60 10
40100
aaIHV
40
5 20
15 30
Geomagnetic aa-Index vs Sunspot Number
1750
1800
1850
1900
1950
2000
year
• a measure of the disturbance in the Earth’s magnetic field
• based on magnetometer observations at two nearly antipodal stations
IHV
20
40
1750
1950
2000
• the overall
level of1800
magnetic 1850
disturbance1900
has increased
substantially
from
a low around 1900, has then decreased from a high around 2003
Geomagnetic Signal in Surface Temperature Based
on Recent Data
High Geomagnetic
activity
Low Geomagnetic
activity
High – Low
(Seppälä et al., 2009, JGR)
• A positive NAO-like pattern is associated with high
geomagnetic activity
• Is the pattern stable when extended data are used?
Motivations & Aims
The relationship between the geomagnetic aa index and the
winter NAO has previously been found to be non-stationary,
being weakly negative during the early 20th century and
significantly positive since the 1970s.
Questions:
• Why the aa-NAO relationship is non-stationary?
• Can we model the aa-NAO relationship statistically
based on longer station-based data?
Aims:
• to draw together the apperently odd (even conflicting)
observations on the topic
• to elucidate the underlying physical reasons for the
observed aa-NAO relationship
3
The Time Series of the NAO and Its Long-term Trend
1
0
-2
-1
DJFM NAO
2
time evolution of NAODJFM
for the period of 1800-2009
(UEA, Jones et al. (2003)).
1800
1850
1900
1950
2000
Year
1907
1
0
-1
-2
U(t) & V(t)
2
1970 1995
1800
1850
1900
Year
1950
2000
the progressive (U(t), solid)
or retrograde (V(t), dashed)
scores of NAODJFM and
aaDJFM calculated by using
Sequential Mann-Kendall
test. significant turning points
of the NAODJFM trend
identified are shown as reddashed vertical lines
4
2
Year
1750
(e)
1800
1850
1900
1950
2000
Year
1750
1800
1850
1900
1950
2000
00.5 5001.00
Year
1750
1800
1850
1900
1950
2000
Year
(g)
1800
1850
1900
1950
2000
Year
1750
1800
1850
1900
1950
2000
Year
1750
1800
1850
1900
1950
2000
Year
1750
1800
1850
1900
1950
2000
0 -4 02 -2 2
4 -2
2000
0-4 4
2-2
1900
(d)
1800
1850
1900
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
1950
2000
Year
1750
1800
1850
1750
1800
1850
2 -2
-4
1950
Year
04 -4
1850
2000
4 -22
1800
1950
2 0
1750
1900
1750
1900
Modulated by
Long-term
Variation of Solar
Activity?
Year
1900
Year
1750
(f)
1800
1850
1900
Year
1750
1800
1850
1900
Year
5 0 -2
1850
3 -2
4
1800
0 -2 1 -1 2 0 3 1 -2
4 2 -1
5 30 4 1 5 2
1750
-2 -1
2000
U(t) & V(t) U(t) & V(t) U(t) & V(t) U(t) & V(t)
1950
U(t) & V(t) U(t) & V(t)
1900
U(t) & V(t)
1850
U(t) & V(t) U(t) & V(t)
1800
Year
1750
-0.5-1.0 0.0-0.5 0.5-1.0
0.0 1.0-0.5
0.5
(b)
40
U(t) & V(t)
100
50
150
-0.5 0 0.0
0.5 10050
1.0 150100
1500
0
2500500 -1.0
2500
1500
2500
50 0
0
(c)
0.0
1.0
1500
500
1750
-1.0
As(N-S)/(N+S)
DJFM DJFM (N-S)/(N+S)
DJFM (N-S)/(N+S)
DJFM
Corr(aa, Rz)
NSSA
Cor aa & RzRz (Ann) Rz (Ann)
Area
DJFM NDJFM
DJFM N Area DJFM N Area
Rz
(Ann)
Rzann
150
(a)
1750
1800
1850
1900
Year
1750
(h)
1800
1850
1900
Year
1750
1800
1850
1900
Year
1750
1800
1850
1900
Year
1750
1800
1850
1900
red vertical lines:
change points of trendYearin the NAO
Year
black vertical lines: change points of trend in solar indices
Sunspot number-NAO
R2 = 0
black line:
the shaded region:
vs
Geomagnetic-NAO
R2 = 0.08, significant at 0.001
General Additive Model (GAM) fitting
95% confidence interval
GAMs for the aa-NAO relationship in
the four sub-periods
R2 = 0
R2 = 0.15
black line:
the shaded region:
R2 = 0.50
General Additive Model (GAM) fitting
95% confidence interval
R2 = 0
4
44
(b)
• The concave-shaped
aa-NAO relationship is
strengthened if data from
odd numbered solar cycle
are excluded
3
33
(a)
DJFM_NAO
DJFM_NAO
DJFM_NAO
NAODJFM
-3
-2
-1
0
1
2
-3
00
11
22
-3 -2
-2 -1
-1
0
00
1880
1880
1920
1920
1960
1960
2000
2000
• R2: 0.08  0.17
10
15
20
25
30
35
10
15
20
25
30
35
year
aa DJFM
DJFM.aa
DJFM.aa
NLM(0%
); LM(0%
) )
NLM(0%
); LM(0%
NLM(18% ); LM(1% )
NLM(18% ); LM(1% )
(d)
3
33
4
44
(c)
-2
-2
-2
DJFM_NAO
DJFM_NAO
DJFM_NAO
NAODJFM
-2
-1
0
1
2
-2
00
11
22
-2 -1
-1
DJFM_NAO
NAODJFM
DJFM_NAO
DJFM_NAO
-1
0
1
2
-1
-1
00
11
22
3
33
NLM(8% ); LM(0% )
NLM(8% ); LM(0% )
11 12 13 14 15 16 17 18 19 20 21 22 23
DJFM_Rz
RzDJFM
DJFM_Rz
DJFM_Rz
50
100
150
50
100
150
50
100
150
200
200
200
GAM built from odd/even numbered solar cycles
10 10 15 15 20 20 25 25 30 30 35 35
aa
DJFM.aa
DJFM
DJFM.aa
10 10 15 15 20 20 25 25 30 30 35 35
aa
DJFM.aa
DJFM
DJFM.aa
GAM Bulit Based on the Ascending/Declining
Phase of Even Numbered Solar Cycles
14
16
18
20
NLM(18%
); LM(1%
LM(1%
NLM(18%
);
)) ))
NLM(18%
NLM(18%
); LM(1%
LM(1%
);
22
44
44
(a)
• The concave-shaped aaNAO relationship is
further strengthened if
only the data from the
declining phase of even
numbered solar cycle are
used
(b)
00
00
-2-2
-2-2
50
50
50
50
DJFM_Rz
DJFM_Rz
Rz
DJFM
DJFM_Rz
DJFM_Rz
100
100
100
100
DJFM_NAO
DJFM_NAO
DJFM_NAO
DJFM_NAO
NAO
-1-1 00 DJFM
11 22
-1-1 00 11 22
33
33
150
150
150
150
12
1880
1880
1880
1880
1920
1920
1920
1920
1960
1960
1960
1960
2000
2000
2000
2000
10 15
15 20
20 25
25 30
30 35
35
10
10 10
15 15
20 20
25 25
30 30
35 35
year
aaDJFM.aa
DJFM
DJFM.aa
DJFM.aa
DJFM.aa
44
44
NLM(34%
); LM(6%
LM(6%
NLM(34%
);
)) ))
NLM(34%
NLM(34%
); LM(6%
LM(6%
);
(c)
(d)
-2-2
-2-2
-1-1
-1-1
DJFM_NAO
DJFM_NAO
NAODJFM
DJFM_NAO
DJFM_NAO
00
11
22
00
11
22
DJFM_NAO
DJFM_NAO
DJFM_NAO
DJFM_NAO
NAO1DJFM
-1-1 00
1
22
-1-1 00
11
22
33
33
33
33
44
44
NLM(40%
); LM(1%
LM(1%
NLM(40%
);
)) ))
NLM(40%
NLM(40%
); LM(1%
LM(1%
);
10
10
10 10
15
15
15 15
20
20
20 20
aa DJFM
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
25
25
25 25
10 15
15 20
20 25
25 30
30 35
35
10
10 10
15 15
20 20
25 25
30 30
35 35
aa
DJFM
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
• R2: 0.17  0.34
Bootstrap Assessment of the Winter
aa-NAO Relationship
The concave-shaped
aa NAO relationship is
statitically stable and
robust
black lines – 10,000 GAMs built by sampling with replacement of the aa and
the NAO from the declining phase of even-numbered SCs
Red line – mean of all fitted GAMs
Modulated by Long-term Variation of Solar Activity?
35
30
25
20
5
10
00
15
Annual aa
33
NAO
= 2.62-0.15aa
NAO
= 2.62-0.15aa
NAONAO
= 2.62-0.15aa
= 2.62-0.15aa
22
22
n = 6; R2 = 0.22; p = 0.29
11
-1-1
1969
-2-2
1996
-2-2
DJFM_NAO
DJFM_NAO
1995
33
(b)
DJFM_NAO
DJFM_NAO
-1-1
0NAO
11
0 DJFM
44
33
-2
DJFM_NAO
DJFM_NAO
NAODJFM
DJFM_NAO
DJFM_NAO
-1
00
11
22
-1
-2 -2 -1 -1 0 0 1 1 2 2 3 3 4 4
LM(6%)
NLM(34%);
LM(6%)
(a) n =NLM(34%);
42;NLM(34%);
R2 = 0.34 LM(6%)
(GAM);
1869-2009
NLM(34%);
LM(6%)
1850
1900
1950
2000
10 10 15 15 20 20 25 25 30 30
10 10 15 15 20 20 25 25 30 30
DJFM.aa
DJFM.aa
aa
DJFM
DJFM.aa
DJFM.aa
-2-2
-2-2
NAO
= 1.61-0.05aa
NAO
= 1.61-0.05aa
NAONAO
= 1.61-0.05aa
= 1.61-0.05aa
1.0
0.0
0.04
0.5
1869-2009
1869-1902
1903-1962
1963-1995
1996-2009
-1.0
-0.5
Density
Annual Cor(aa, Rz)
33
33
n = 15; R2 = 0.59; p = 0.0008
19951995
1995
1995
22
22
(d)
DJFM_NAO
DJFM_NAO
DJFM_NAO
DJFM_NAO
DJFM
-1-1
0NAO
11
0
-1-1
00
11
33
33
22
-2-2
-2-2
DJFM_NAO
DJFM_NAO
NAODJFM
DJFM_NAO
DJFM_NAO
-1-1
00
11
-1-1
00
11
22
n = 20; R2 = 0.15; p = 0.09
18 18
18 18
DJFM
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
DJFM.aa
(c)
aa
16 16
16 16
1850
1969
1996
1996 1969 1969
1969
20 20
20 20
NAO = -4.8+0.21aa
NAO
= -4.8+0.21aa
NAO
-4+0.18aa
NAO
= =-4+0.18aa
25 25
25 25
30 30
30 30
DJFM.aa
DJFM.aa
aa DJFM
DJFM.aa
DJFM.aa
35 35
35 35
1900
1950
2000
Year
0.00
aa DJFM
14 14
14 14
0.02
12 12
12 12
0.06
Year
10 10 15 15 20 20 25 25 30 30 35 35
10 10 15 15 20 20 25 25 30 30 35 35
0
20
40
60
aa
80
100
Summary
Our statitical analysis suggests that the winter aa-NAO relationship
is non-stationary; systematically modulated by the centurial scale variation of
solar activity
is non-linear concave-shaped  linear extropolation based on recent data
(e.g. satellite era) has no predictive power
may be linked to 27-day recurrent fast solar wind streams from high latitude
coronal holes; the significant positive aa-NAO relationship during the last 30
years of the 20th century coinciondes with a significnat increase of recurrent
solar wind streams during solar cycles 2022
Process-based studies are needed to understand:
territorial response to 27-day recurrent fast solar wind streams
the dynamic pathways in the ocean & atmosphere
Li, Y., H. Lu, M. J. Jarvis, M. A. Clilverd and B. Bates, (2011) Non-linear
and non-stationary influences of geomagnetic activity on the winter North
Atlantic Oscillation. Journal of Geophysical Research. 116, D16109,
doi:10.1029/2011JD015822.
Thank you!
Statistical method: Generalized Additive Model
• The Generalized Additive Model (GAM) is a nonparametric
modelling technique that objectively estimates the functional
relationship between the predictand and predictors in an additive
model.
• Univariate GAM
Yt  0  f ( X t )   t
Yt
Xt
f
variable to be predicted (e.g. NAO)
predictor (e.g. the aa index)
unspecified smooth function to be estimated from observed data
M
f  X t    bi  X t  i
i 1
Sequential Mann-Kendall test
Gerstengarbe and Werner [1999]
• Time series
X   X1,
, X n
t
• Mann-Kendall test statistic
Wt   Ri
i 1
• Ri
is the rank of the t-th subseries
• The progressive series
U (t ) 
 X1, X 2 ,
Wt  E (Wt )
Var (Wt )
, X t 1
N (0,1)
• The retrograde test statistic variable V (t ) ~ N (0,1) can be
defined based on X t 1, X t , , X1
• When either the progressive U (t ) or retrograde V (t ) series
exceeds certain confidence limits before and after the
crossing point, the null hypothesis (the sampled time series
has no change points must be rejected)
Statistical Measure of Linear and GAM Models
of aa-NAO relationship for 1869-2009
Period
Linear Model
intercept Slope
18692009
0.36
(0.29)
R2
GAM
AIC
0.005 0.00 424
(0.014)
intercept EDF of
f(aa)
0.47***
(0.09)
2.50*
R2
AIC
0.08 417
•Standard errors for the intercept and slope of linear and the intercept for GAM
models are in brackets
•significant coefficients at the 0.05, 0.01, and 0.001 levels are marked by, “*”,
“**”, and “***”.
•AIC: The associated Akaike information criterion
•EDF: effective degree of freedom for nonparametric smooth terms
Statistical Measure of Linear and GAM Models
for the four subperiods
Period
Linear Model
GAM
Statistical
Measures
ofR2theAIClinear
and EDF
GAM
of fitting
intercept
Slope
intercept
R2 for
AIC
the four sub-periods identified by the f(aa)
SMK test
18691902
0.27
(0.58)
0.005
(0.036)
19031962
1.70***
(0.40)
-0.06** 0.13 168 0.60***
(0.02)
(0.12)
19631995
-2.68*** 0.13*** 0.42 92
(0.68)
(0.03)
19962009
0.33
(1.30)
0.01
(0.06)
0.00 106 0.34
(0.19)
0.00 48
1
0.00
106
1.78**
0.17
166
0.43**
(0.23)
1.94***
0.50
89
0.28
(0.31)
1
0.00
48
Statistical Measures of even (odd)-numbered SCs, the declining
(ascending) phases of odd-numbered SCs, and the declining
(ascending) phases of even-numbered SCs
Solar cycle
Linear Model
intercept Slope
GAM
R2
AIC
intercept
R2
AIC
1
0.00
225
2.39*
0.17
196
EDF of
f(aa)
odd NO. SC
0.56
(0.40)
-0.01
(0.02)
0.00
225
0.33**
(0.11)
even No. SC
0.27
(0.41)
0.02
(0.02)
0.01
206
0.64***
(0.13)
ascending odd No. SC
1.06
(0.79)
-0.04
(0.04)
0.04
96
0.24
(0.19)
1
0.04
96
declining odd No. SC
0.43
(0.46)
-0.001 0.00
(0.02)
132
0.40*
(0.15)
1
0.00
132
ascending even No. SC 0.97
(0.71)
-0.02
(0.04)
0.01
77
0.63*
(0.22)
4.59
0.40
74
declining even No. SC
0.04
(0.02)
0.06
133
0.64***
(0.14)
2.43**
0.34
121
-0.17
(0.54)