Discrepancies Between the Modeled and Proxy-Reconstructed
Response to Volcanic Forcing over the Past Millennium:
Implications and Possible Mechanisms
Michael E. Mann1
Department of Meteorology and Earth & Environmental Systems Institute
The Pennsylvania State University,
University Park, PA 16802
Scott Rutherford
Department of Environmental Science, Roger Williams University,
Bristol, RI, USA
Andrew Schurer, Simon F.B. Tett
GeoSciences, University of Edinburgh, United Kingdom
Jose D. Fuentes
Department of Meteorology , The Pennsylvania State University,
University Park, PA 16802
SUPPLEMENTARY INFORMATION
1
Corresponding author address: Michael E. Mann, Department of Meteorology, Penn State University,
Walker Building, University Park, FA 16802
Email: [email protected]
1
Additional Methodological Details
1. Monte Carlo Significance Estimation Procedure
We find (Table S1) that the peak AD 1258 cooling from the Monte Carlo
surrogates (-1.9C) breaches the 4.1 sigma cooling limit derived from the null distribution,
corresponding to a <0.001%ile (i.e. 1 in 100,000) event, something highly unlikely to
occur by chance alone given a sample of N=8000 surrogates. Due to skewness of the null
distribution, the %ile values differ from expectations from a Gaussian distribution with
standard deviation of sigma (the observed cooling is more significant than would be
expected for an equivalent Gaussian distribution, where a 4.1 sigma cooling event would
have a one-sided likelihood of roughly 1 in 50,000 rather than 1 in 100,000). Another
measure of the significance of the AD 1258 cooling event is the number of surrogates
that breach the 99.5%ile and 99.9%ile. For N=8000 realizations, we would only expect
40 and 8 events respectively from chance alone. Yet the actual distribution of Monte
Carlo surrogates yields 336 and 126 exceedances respectively.
The peak AD 1816 cooling (-1.6C) breaches the 4.9 sigma cooling limit. Due to
the non-Gaussian nature of the distribution, this corresponds to a 0.036%ile event, 2 of
which might be expected from change along given N=8000 realizations. However, the
distribution of Monte Carlo surrogates yields 90 and 13 surrogates that exceed the
99.5%ile and 99.9%ile of the null distribution respectively, which is 2.25 and 1.6 times
greater than would be expected from chance alone respectively
2
2. Impact of number of chronologies retained in estimation of AD 1258 cooling
The small sample size (8 regional series) and projected large percentage (90%) of series
missing at 1258 given Mann et al [2012—i.e. “MFR12”] predictions results in a single
region contributing to hemispheric mean temperature at 1258. To avoid artifacts (e.g.
large sampling variance) of a unit sample size, we lowered the projected percentage
missing to 80%, which yields a sample size of two, for the purpose of the main analysis
(i.e. Figure 2 of article). We show that similar results are nonetheless obtained whether 1
(Figure S1), 2 (Figure 2 of main article), 3 (Figure S2), or 4 (Figure S3) of the eight
regions (amounting in that case to 50% of available series) are retained.
3. Limitations on signal recovery with Monte Carlo resampling procedure
To test how threshold growth responses might limit the extent to which the full volcanic
cooling signal can be recovered from the underlying tree-ring signal through the Monte
Carlo chronological resampling procedure used in section 2 of the main article, we
performed a test using the standard experiment from MFR12 (i.e. results from Figure 2d
therein). We performed the same procedure that was described in section 2.2 of the main
article for the D’Arrigo et al [2006—i.e., “DO6”] regional composites instead to the
synthetic regional tree-ring series produced in the MFR12 standard experiment. It is clear
(Figure S5) in this case that the procedure is able to partially recover the volcanic cooling
signal, but with a substantially lower amplitude.
Interestingly, the underestimation of signal amplitude for the synthetic case (Figure S5) is
substantially more severe than what is apparent for the actual tree-ring data (i.e. Figure 2
3
of the main article). This may indicate that the real-world reconstruction of D06 suffers
only partially from the threshold cooling limits posited in MFR12, e.g. because the treering series contain a mix of chronologies with varying proximity to the actual treeline and
thus vary to the extent they are subject to the ~1.5C cooling threshold estimated in
MFR12. Or alternatively, this could indicate that the true threshold cooling limit is
spatially variable (e.g. depends on tree species) or otherwise differs from the idealized
values used in MFR12.
4. Results using RCS in place of STD D06 tree-ring chronologies
We find that broadly similar results to those shown in the main article are obtained using
the D06 RCS regional series in place of the STD chronologies (Figures S6-S9 and Table
S2). The primary difference (compare e.g. Figure S6 with Figure 2 of main article) is a
relative suppression of high-frequency variability with the RCS surrogates relative to the
STD surrogates. This difference in behavior is evident in the raw series themselves (see
Figure S4) and is likely a consequence of the differing frequency-domain impacts of the
two different standardization procedures. Given the emphasis on high-frequency
responses--i.e. the short-term cooling response to volcanic forcing-- in the current paper,
we thus favored the STD series over the RCS series for the analyses featured in the main
article. We note that use of the RCS series leads to a greater statistical significance of the
AD 1258 cooling but a lesser statistical significance of the AD 1816 cooling (see Figure
S6 and Table S2).
5. Impact of threshold responses on estimated ECS
4
Finally, we further assess the impact of threshold tree growth responses on the estimation
of ECS by investigating the sensitivity to using annual, rather than (as in main article—
i.e., Figure 8) decadally-smoothed, series in the assessment. Figure S10 shows the results
using annually-resolved data. The results are very similar to those obtained for the
decadally-smoothed data (Figure 8 of main article) with one key exception. The ECS
value for the AD 1300-1849 interval using the actual (D06) tree-ring series is now
considerably lower (T2xCO2~0.2oC, rather than ~1oC) consistent with the tendency of
decadal smoothing to reduce the impact of errors in the precise annual chronology.
References
1. D'Arrigo, R., Wilson, R. & Jacoby, G., J. Geophys. Res 111, D03103 (2006).
2. Mann, M.E., Fuentes, J.D., Rutherford, S., Nature Geoscience, 5, 202-205 (2012)
5
Figure S1. Response to the AD 1258/1259 eruption showing 10 coldest surrogates
(blue) along with GCM simulation from MFR12 (red) and the D06 tree-ring
reconstruction (green). Here, the surrogates were forced to retain one of the
available eight regional series corresponding to the actual MFR12 prediction.
6
Figure S2. Response to the AD 1258/1259 eruption showing 10 coldest surrogates
(blue) along with GCM simulation from MFR12 (red) and the D06 tree-ring
reconstruction (green). Here, the surrogates were forced to retain three of the
available eight regional series.
7
Figure S3. Response to the AD 1258/1259 eruption showing 10 coldest surrogates
(blue) along with GCM simulation from MFR12 (red) and the D06 tree-ring
reconstruction (green). Here, the surrogates were forced to retain four of the
available eight regional series.
8
Figure S4. Comparison between the D06 reconstructions (red) and our attempted
replication (blue). The top panel shows the RCS series while the bottom shows
the STD series.
9
Figure S5. As in Figure 2 of the main article, but using simulated tree ring series of
MFR12 showing the partial recovery of the 1258 and 1816 cooling signals.
10
Figure S6. As in Figure 2 of the main article but for RCS case.
11
Figure S7. RCS-case response to the AD 1258/1259 eruption showing 10 coldest
surrogates (blue) along with GCM simulation from MFR12 (red) and the D06
tree-ring reconstruction (green). Here, the surrogates were forced to retain one
of the available eight regional series.
12
Figure S8. RCS-case response to the AD 1258/1259 eruption showing 10 coldest
surrogates (blue) along with GCM simulation from MFR12 (red) and the D06
tree-ring reconstruction (green). Here, the surrogates were forced to retain three
of the available eight regional series.
13
Figure S9. RCS-case response to the AD 1258/1259 eruption showing 10 coldest
surrogates (blue) along with GCM simulation from MFR12 (red) and the D06
tree-ring reconstruction (green). Here, the surrogates were forced to retain four
of the available eight regional series.
14
a.
b.
Figure S10. PDFs of ECS as in Figure 8 of main article, but using annual rather than
decadally-smoothed data. (a) AD 1300-1849 and (b) AD 1200-1849 (red=simulated
actual temperature series; green=synthetic tree-ring temperature series). Shown by dashed
vertical lines are mean of ESC distribution for simulated temperature series (red), mean
of ECS distribution for synthetic tree-ring temperature series (green), ECS estimate using
MFR12 simulated tree-ring temperature series where chronological error accumulation
due to inferred missing rings is taken into account (cyan), and sensitivity estimate for
D06 tree-ring temperature reconstruction (blue). True value of ESC is 3.0 in both cases.
15
Table S1. Significance Estimates Based on “Random Volcanic Year” Monte Carlo
Simulations (using STD series). Results are provided for both AD 1258
(based on 80% retained = 2 regions) and AD 1816. Tabulated are: (i)
nominal cooling in raw (unperturbed chronology) series, (ii) maximum
cooling produced among 8000 Monte Carlo surrogates, (iii) difference
between (ii) and (i) in sigma units (sigma derived from null distribution
generated by random eruption surrogates) , (iv) 99.5%iles and 99.9%ile
values for cooling based on null distribution, (v) # of events out of the
N=8000 realizations that breach 99.5%ile and 99.9%ile null distribution
limits, and (vi) actual percentile represented by (iii) based on null
distribution. Also provided (below) are AD 1258 results using alternative
(1,3, and 4) numbers of retained regions.
2 series at 1258
Year
Raw
Temp.
-0.38
1258
Max
Cool
-1.90
Sigma
-0.85
-1.61
-4.94
1 series at 1258
-0.38
1258
-1.93
3 series at 1258
-0.38
1258
4 series at 1258
-0.38
1258
1816
99.5%
#exceeding
-1.30
336
-1.29
90
99.9%
#exceeding
-1.45
126
-1.44
13
Max %ile
Cool
<0.001%
-3.19
-1.68
535
-1.89
92
0.05%
-1.78
-4.40
-1.18
332
-1.34
120
<0.001%
-1.59
-4.34
-1.09
310
-1.25
106
0.003%
-4.13
0.026%
Table S2. Significance Estimates as Table S2 but with RCS tree-ring series
2 series at 1258
Year
Raw
Temp.
-0.62
1258
Max.
Cool
-1.89
Sigma
-0.81
-1.27
-3.74
1 series at 1258
-0.62
1258
-1.92
3 series at 1258
-0.62
1258
4 series at 1258
-0.362
1258
1816
99.5%
#exceeding
-1.34
278
-1.15
36
99.9%
#exceeding
-1.45
173
-1.25
3
Max %ile
Cool
<0.001%
-3.31
-1.67
547
-1.68
547
<0.001%
-1.77
-4.59
-1.25
372
-1.38
186
<0.001%
-1.69
-5.27
-1.15
332
-1.25
209
<0.001%
-4.59
16
0.075%