SUPPLEMENTARY MATERIAL
Background on the Superposed Epoch Analysis
The Superposed Epoch Analysis (SEA) technique is a statistical method used to resolve
significant signal to noise problems. This is especially desired in cases where the responses to
particular events (in our case large radiative forcing from explosive volcanic eruptions) may be
obfuscated by noise from other competing influences that operate at similar time scales (internal
El Nino variation). Through simple compositing, the SEA method involves sorting data into
categories dependent on a ‘key-date’ for synchronization and then comparing the means of those
categories. Given sufficient data, a common underlying (causal) response to a forcing event
should theoretically emerge in the average (composite) while other noise in the data should
cancel. Examples of applications of the SEA method are widespread in various scientific fields
of study. For example, the SEA has been employed in studies on the relationship between
climate and fire histories (Swetnam and Betancourt, 1990), magnetospheric physics (Lühr et al.,
1998), the lunar cycle and rainfall (Brier and Bradley, 1964), and the relationship between
volcanic activity and climate variations (Mass and Portman, 1989). Compositing can also lend
insight into periodic responses that, because of the relative magnitude of the signal and
associated noise, are not detected by spectral analysis.
The SEA method is simple and involves basic arithmetic calculations (averaging). However, the
randomization procedure used to determine statistical significance, depending on the number of
iterations performed, can be computationally demanding. The method requires a random number
generator for the Monte Carlo randomization procedure. We used the commercially available
Matlab™ statistical software package to perform our SEA.
As with any statistical method, care must be taken in the application and interpretation of SEA
results. For instance, the SEA can be vulnerable to leveraging resulting from the influence of a
single large anomaly. This problem typically arises when the ‘key date’ sample size is small. To
deal with this explicitly, our approach embraces proxy data to considerably increase the number
of climatically-relevant eruptions incorporated into the SEA. We also include a normalization
step in our SEA in order to provide a methodological safeguard to leveraging.
Applying the SEA to the ‘Volcano-ENSO Hypothesis’
We employ the SEA method to determine the response (if any) of the El Niño-Southern
Oscillation ocean-atmospheric system to negative radiative forcing resulting from volcanic dust
veils following large explosive eruptions in the tropics. Such a response to explosive volcanism
was proposed from observations by Handler (see references in main text) and was discussed in
early model simulations (Hirono, see main text; and MacCrackan and Luther). Because the
details of the SEA method can be specifically tailored to each individual application, a detailed
description of the basic structure of our statistical approach is included below. This supplements
the information provided in the ‘Methods’ section.
First, SEA forcing events are selected based on physical criteria and typically referred to as ‘key
dates’. For our application, the forcing component determining the selection of ‘key dates’ are
years in which explosive eruptions took place in low-latitude (20 N to 20 S). Data sources
included both the Ice-core Volcanic Index (IVI) and/or the Volcanic Explosivity Index (see
‘Methods’ sections for selection criteria and references). Given an array of key dates, we then
sampled the time series that we analyze for a possible impact (NINO3 or SOI) using a window of
data points centered on each key date. For each key date, the typical window used in our
analysis is 21 years with 10 data points on either side of the key date. The extracted windows are
then stacked in what we refer to as the ‘eruption matrix’. This symmetrical matrix contains
before- and after-event information for all selected eruptions (key dates). Thus, for an 18eruption key date list, for example, the accompanying eruption matrix would contain 18 rows
and 21 columns of data.
Before analyzing the data, an adjustment intended to remove any disproportionate weight any
extreme case could have on the overall composite is applied. This involves normalizing the
individual data in each key date window by dividing each value in that row by the maximum
absolute value of all anomalies in that window. This scales the magnitudes in each row of the
eruption matrix so that the chance that a single anomaly may unduly influence the composite
analysis is restricted. The overall mean of the eruption matrix is then removed.
As an aside, we additionally employed a ranked approach to account for potential leveraging
(results not shown). A ranked SEA is a version of SEA where the ENSO diagnostic anomalies
extracted for each eruption are first ranked prior to insertion into the eruption matrix. This is one
way of protecting against the undue influence of anomalously large-magnitude events. Results
from the ranked SEA method are in good agreement with both normalized and traditional SEA
analyses that we performed. Thus we have taken every step possible to protect against this
potential bias.
For those eruption matrices that exhibit statistically significant cooling in the post-eruption
decade compared to the pre-eruption decade due to large scale volcanic cooling, the mean
difference between pre- and post-eruption decades is removed (see ‘Methods’ for more
discussion on the removal of the surface cooling expected). The significance of post-eruption
cooling is determined using the non-parametric Mann-Whitney difference-of-mean test.
The composite (or averaged) results of the SEA are simply calculated by averaging down each
column in the eruption matrix (e.g. the ‘year –10’ column is averaged for all eruptions yielding
the composite value for ten years before explosive eruptions). This compositing of the eruption
matrix yields what we call the ‘composite matrix’. The composite matrix contains 21 years of
averaged NINO3 or SOI anomalies ranging from ten years before to ten years after the selected
explosive eruptions (key dates). It is this averaging procedure that allows us to compare the
average values of the NINO3 or SOI in any particular year before and after large eruptions. It is
the stated goal here to determine if a systematic post-key date response emerges.
In order to compare these composite years and to evaluate the significance of an average
anomaly determined in each composite year, several further statistical steps are required. First,
the probability of occurrence for each composite value based on chance alone must be
determined. To do this, we employ a Monte Carlo randomization procedure that reshuffles
blocks of values inside each row of the ‘eruption matrix’ with equal weight given to each
eruption. This block resampling procedure generates a randomly generated eruption matrix from
the actual eruption matrix that is subsequently averaged to create a new, random composite
matrix. Block resampling is based on the fact that serial correlation must be taken into account
in estimating null distributions with time series with autocorrelation, or else the resulting
confidence limits will be too liberal. The most straightforward way to do this is simply to
resample the series in effectively independent blocks, rather than individual values. For a first
order autoregressive process, the size of effectively independent blocks is given by the formula
we specified (see ‘Methods’).
This is repeated 10,000 times to create 10,000 randomly generated composite matrices. These
10,000 randomized composite values are then sorted and a random composite distribution is
created for each column (i.e. year relative to the key year 0). These 21 distributions are used to
statistically judge how anomalous the actual composites are. We use these distributions to test
the significance of the actual composites at the 90%, 95%, and 99% confidence levels.
Other Applications of the Superposed Epoch Analysis
Brier, G.W., and Donald A. Bradley, 1964: The lunar synodic period and precipitation in the US.
J. Atmos. Sci. 21, 386-395.
Lühr, H., M. Rother, T. Iyemori, T. L. Hansen, R. P. Lepping. 1998. Superposed epoch analysis
applied to large-amplitude travelling convection vortices. Annales Geophysicae 16(7):
743-753.
MacCracken, M.C. and Luther, F.M., 1984: Preliminary estimate of the radiative and climatic
effects of the El Cichon eruption. Geofisica Internacional 23(3), 385-401.
Mass, C. F. and D. A. Portman, 1989: Major volcanic eruptions and climate: A critical
evaluation. J. Climate 2, 566-593.
Swetnam, T.W. and J.L. Betancourt. 1990. Fire-Southern Oscillation relations in the
southwestern United States. Science 249:1017-1020.
Time Period
1649-1979
1649-1868
1706-1868
1706-1977
1649-1979
1706-1977
1649-1979
1869 - 1979
1649-1868
1706-1977
1706-1868
1649-1979
1869 - 1979
1869 - 1979
1649-1868
1706-1868
1706-1977
1649-1979
1706-1977
1706-1868
Eruption Criteria
IVI Moderate-Large
IVI Moderate-Large
IVI Moderate-Large
IVI Moderate-Large
IVI Large Only
IVI Large Only
VEI >= 4 *
VEI >= 4 *
VEI >= 4 *
VEI >= 4 *
VEI >= 4 *
VEI moderate-large
Handler List
VEI moderate-large
VEI moderate-large
VEI moderate-large
VEI moderate-large
VEI large
VEI large
VEI large
pre-event mean
(A)
0.032
0.031
0.030
0.030
0.031
0.042
0.018
0.006
0.021
0.028
0.055
0.005
-0.006
0.006
-0.001
0.004
0.006
0.029
0.055
0.055
post-event mean
(B)
-0.035
-0.034
-0.033
-0.033
-0.034
-0.046
-0.020
-0.001
-0.024
-0.030
-0.061
-0.006
0.006
-0.007
0.001
-0.004
-0.006
-0.032
-0.061
-0.061
B-A
-0.067
-0.065
-0.063
-0.063
-0.065
-0.088
-0.038
-0.007
-0.045
-0.058
-0.116
-0.011
0.012
-0.013
0.002
-0.008
-0.012
-0.061
-0.116
-0.116
P-value
0.03
0.09
0.09
0.03
0.09
0.03
0.20
0.47
0.18
0.17
0.03
0.42
0.61
0.47
0.5
0.36
0.47
0.09
0.03
0.03
Table S1. Results of the non-parametric Mann-Whitney difference-of-mean test for pre- and
post- eruption periods for composite NINO3 reconstruction data. Significance values (bold)
show composites that exhibit a pre-eruption mean (A) significantly greater than the post-eruption
mean (B) at the p<0 .10 level according to a one sided test. The * marks eruption lists whose
selection criteria require that no other eruptions of magnitude VEI>=4 occur in the 12 months
before or 12 months after the chosen eruption.
Eruption Criteria
IVI Moderate-Large
IVI Moderate-Large
IVI Moderate-Large
IVI Moderate-Large
IVI Large Only
IVI Large Only
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
VEI moderate-large
Handler List
VEI moderate-large
VEI moderate-large
VEI moderate-large
VEI moderate-large
VEI large
VEI large
VEI large
Time Period
# of events
1649-1979
25
1649-1868
18
1706-1868
13
1706-1977
19
1649-1979
12
1706-1977
8
1649-1979
20
1869 - 1979
9
1649-1868
10
1706-1977
16
1706-1868
7
1649-1979
31
1869 - 1979
10
1869 - 1979
9
1649-1868
22
1706-1868
18
1706-1977
26
1649-1979
13
1706-1977
10
1706-1868
7
Total > positive 95%
Total > positive 95%
Total < negative 95%
Total < negative 95%
Combined total significant @ 95%
Total > positive 99%
Total > positive 99%
Total < negative 99%
Total < negative 99%
Combined total significant @ 99%
-9 -8 -7 -6 -5 -4 -3 -2 -1 0
1
2 3
4
5
6
7
8
9
N
P
P
N N
N
P
P
P*
P
P
P
P
P
N
P
N*
P
N
N
N
N*
P*
N
P
P
N
N
P
P
N
P
N
P
N
P
P
P
P
P
N
N
N
P*
4
0 0
3
0
0
1
0
0
8
0
0 0
0
0
1
0
0
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 1 10 0
2
6
0
0
3
0 0
0
0
0
0
0
0
0
0 0
1
0
0
1
0
0
36
0
0
0
1 0
19
9
0 0
9
17
1
0
7
N
0
3
0
0
0
2
0
5
Table S2. Normalized, Mean-adjusted Annual NINO3 Reconstruction S.E.A Results. Years
with positive composite values at the 95 and 99% confidence level are marked by P and P*,
respectively; years with negative composite values at the 95 and 99% confidence level are
marked by N and N*, respectively.
Eruption Criteria
IVI Moderate-Large
IVI Moderate-Large
IVI Large Only
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
VEI >= 4, +/- 12m sep.
Handler List
VEI moderate-large
VEI moderate-large
VEI moderate-large
VEI large
VEI large
Time Period
# of events -8 -7 -6 -5 -4 -3
1706-1868
13
1706-1977
19
N
1706-1977
8
1869 - 1979
9
N
1706-1977
16
N
1706-1868
7
Handler List
10
P
1869 - 1979
9
N
1706-1868
18
P
P
1706-1977
26
N
1706-1977
10
1706-1868
7
Total > positive 95%
1 1 0 0 1 0
Total > positive 95%
5
Total < negative 95%
0 1 0 0 0 4
Total < negative 95%
5
Total > positive 99%
0 0 0 0 0 0
Total > positive 99%
0
Total < negative 99%
0 0 0 0 0 0
Total < negative 99%
0
-2 -1 0
1 2 3 4 5 6 7 8
N
N*
P
N*
P
N N*
P
N
N*
0
2 0
0 0 0 0 0 0 1 0
1
0
0 1
6 0 0 0 0 0 0 0
7
0
0 0
0
0 0
0 0 0 0 0 0 0 0
0
4 0 0 0 0 0 0 0
4
Table S3. Normalized, Annual Winter SOI Reconstruction S.E.A Results. Years with
positive composite values at the 95 and 99% confidence level are marked by P and P*,
respectively; years with negative composite values at the 95 and 99% confidence level are
marked by N and N*, respectively.
Time Period
1856-2001
1856-2001
1856-2001
1856-2001
Eruption Criteria
Largest IVI/VEI
VEI >= 4, +/- 12m sep.
VEI Moderate-Large
IVI Moderate-Large
Total > positive 90%
Total > positive 90%
Total < negative 90%
Total < negative 90%
Total > positive 95%
Total > positive 95%
Total < negative 95%
Total < negative 95%
# of events -7 -6 -5 -4 -3 -2 -1
6
10
N n
p
11
N N
9
0 0 0 0 0 1 0
1
2 2 0 0 0 0 0
4
0 0 0 0 0 0 0
0
2 1 0 0 0 0 0
3
0 1 2 3 4 5 6 7
p
p
n
P
n
0
3
0
2
0
1
0
0
3 0 0 0 0 0 0
0 0 0 0 0 2 0
1 0 0 0 0 0 0
0 0 0 0 0 0 0
Table S4. Normalized, 3-yr Instrumental (Kaplan) Boreal Cold-season NINO3 S.E.A
Results. Years with positive composite values at the 90 and 95% confidence level are marked
by p and P, respectively; years with negative composite values at the 90 and 95% confidence
level are marked by n and N, respectively.
Eruption Criteria
Time Period
# of events -6 -5 -4 -3 -2 -1 0
Largest IVI/VEI
1869-2001
6
N
VEI >= 4, +/- 12m sep.
1869-2001
9
N
n
VEI Moderate-Large
1869-2001
11
N
N
IVI Moderate-Large
1869-2001
9
p n
0 0 0 0 0 1 0
Total > positive 90%
Total > positive 90%
1 0
0 0 0 2 0 0 4
Total < negative 90%
Total < negative 90%
2 4
0 0 0 0 0 0 0
Total > positive 95%
Total > positive 95%
0 0
0 0 0 2 0 0 2
Total < negative 95%
Total < negative 95%
2 2
1 2 3 4 5 6 7
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
Table S5. Normalized, 3-yr Instrumental Winter SOI S.E.A Results. Years with positive
composite values at the 90 and 95% confidence level are marked by p and P, respectively; years
with negative composite values at the 90 and 95% confidence level are marked by n and N,
respectively.
Eruption Criteria
Time Period
# of eruptions
Eruption Years
IVI M-L
IVI M-L
IVI M-L
IVI M-L IVI Large IVI Large
1650-1980 1650-1868 1706-1868 1706-1980 1650-1980 1706-1980
25
18
13
19
12
8
1660
1665
1674
1694
1712
1721
1728
1747
1753
1775
1789
1795
1808
1813
1815
1824
1831
1835
1862
1884
1890
1903
1929
1963
1969
1660
1665
1674
1694
1712
1721
1728
1747
1753
1775
1789
1795
1808
1813
1815
1824
1831
1835
1721
1728
1747
1753
1775
1789
1795
1808
1813
1815
1824
1831
1835
1721
1728
1747
1753
1775
1789
1795
1808
1813
1815
1824
1831
1835
1862
1884
1890
1903
1929
1963
1665
1674
1694
1712
1747
1808
1815
1831
1835
1884
1903
1963
1747
1808
1815
1831
1835
1884
1903
1963
Table S6. IVI-based Eruption Lists. M-L denotes lists containing moderate and large
explosive eruptions.
Eruption
Criteria
Largest IVI/VEI VEI >= 4* VEI M-L
IVI M-L
Time Period
1856-2001 1856-2001 1856-2001 1856-2001
# of eruptions
6
10
11
9
Eruption Years
1884
1903
1951
1963
1982
1991
1869
1884
1899
1902
1911
1917
1943
1951
1963
1968
1884
1899
1902
1911
1917
1943
1951
1963
1968
1982
1991
1884
1890
1903
1929
1963
1969
1975
1982
1991
Table S7. Full Instrumental Period Eruption Lists. M-L denotes lists containing moderate
and large explosive eruptions. The * marks lists that require eruptions to be separated from any
other VEI>=4 eruptions by at least 12 months.
Eruption
VEI M-L Handler VEI M-L VEI M-L VEI M-L VEI M-L VEI Large VEI Large VEI Large
Criteria
Time Period 1650-1980 1869 - 1980 1869 - 1980 1650-1868 1706-1868 1706-1980 1650-1980 1706-1980 1706-1868
31
10
9
22
18
26
13
10
7
# eruptions
Eruption
Years
1661
1665
1674
1680
1720
1745
1756
1760
1761
1764
1768
1791
1793
1803
1808
1812
1813
1814
1815
1818
1823
1835
1884
1899
1902
1911
1917
1943
1951
1963
1968
1869
1883
1899
1902
1911
1917
1937
1950
1952
1963
1869
1884
1899
1902
1911
1917
1943
1951
1963
1661
1665
1674
1680
1720
1745
1756
1760
1761
1764
1768
1791
1793
1803
1808
1812
1813
1814
1815
1818
1823
1835
1720
1745
1756
1760
1761
1764
1768
1791
1793
1803
1808
1812
1813
1814
1815
1818
1823
1835
1720
1745
1756
1760
1761
1764
1768
1791
1793
1803
1808
1812
1813
1814
1815
1818
1823
1835
1884
1899
1902
1911
1917
1943
1951
1963
1671
1673
1680
1745
1768
1772
1812
1814
1815
1835
1869
1884
1951
1745
1768
1772
1812
1814
1815
1835
1869
1884
1951
Table S8. VEI-based Eruption Lists. M-L denotes lists containing moderate and large
explosive eruptions.
1745
1768
1772
1812
1814
1815
1835
Eruption Criteria
Time Period
# of eruptions
Eruption Years Used
VEI >= 4 * VEI >= 4 * VEI >= 4 * VEI >= 4 * VEI >= 4 *
1650-1980 1869 - 1980 1650-1868 1706-1980 1706-1868
7
20
9
10
16
1671
1673
1680
1745
1768
1772
1812
1814
1815
1835
1869
1884
1899
1902
1911
1917
1943
1951
1963
1968
1869
1884
1899
1902
1911
1917
1943
1951
1963
1671
1673
1680
1745
1768
1772
1812
1814
1815
1835
1745
1768
1772
1812
1814
1815
1835
1869
1884
1899
1902
1911
1917
1943
1951
1963
1745
1768
1772
1812
1814
1815
1835
Table S9. VEI>=4 Eruption Lists. M-L denotes lists containing moderate and large explosive
eruptions. The * denotes that the selection criterion requires eruptions to be separated from any
other VEI>=4 eruptions by at least 12 months. The criterion for selection used in these lists is
the same as that used by Handler and colleagues.