We perform a Monte Carlo pattern recognition analysis of the coincidence between three regional volcanic histories from ice coring of Greenland and Antarctica over the period 2 to 45 ka, using SO4 anomalies in Greenland and East Antarctica determined by continuous core chemistry, together with West Antarctic volcanic ash layers determined by remote optical borehole logging and core assays. We find that the Antarctic record of volcanism correlates with Glacial abrupt climate change at a 95% to >99.8% (∼3σ) significance level and that volcanic depositions at the three locations match at levels exceeding 3σ, likely indicating that many common horizons represent single eruptive events which dispersed material world wide. These globally coincident volcanics were associated with abrupt cooling, often simultaneous with onsets or sudden intensifications of millennial cold periods. The striking agreement between sites implies that the consistency of current timescales obtained by isotopic and glaciological dating methods is better than estimated.
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 North Atlantic climate during the last glacial period appears to have been a distinct, qualitatively different regime than during the Holocene, having undergone state changes not seen for the last ten thousand years [Dansgaard et al., 1993]. The period before about 11 ka was an erratic sequence of cold snaps, many taking hold within one human generation, that lasted several hundred to a few thousand years before being punctuated by abrupt warmings (e.g., see trace in Figure 1). Syncopation observed in glacial cycles has inspired studies of threshold instability and stochastic resonance in systems subject to weak periodic driving forces which can be perturbed into metastable states, possibly by random events [Alley et al., 2001; Ganopolski and Rahmstorf, 2001; Broecker, 2003].
 Climate-driven reorganizations or intensity variations of atmospheric circulation could have altered the transport of volcanic tracers [Castellano et al., 2005] to simulate modulations of volcanic activity, especially in polar records. Determining the geographic extent [Langway et al., 1988; Palais et al., 1992; Langway et al., 1995] of specific eruptions and tracing events to specific volcanoes are vital to developing a clear picture. Early attempts to quantify volcano-climate interaction were hampered by poor coverage and large uncertainties in dating. Recent advances in the use of synchronous atmospheric methane and O2-isotopic anomalies in both Greenland and Antarctica have permitted cross-dating between hemispheres to within a few centuries [Bender et al., 1994; Blunier et al., 1998; White and Steig, 1998; Blunier and Brook, 2001; Brook et al., 2005]. Glaciological modeling [Schwander et al., 2001] now obtains remarkable linearity with respect to true age when used to interpolate between dating control points [Shackleton et al., 2004]. As more ice cores are collected and new measurement and analysis techniques develop, we are gaining quickly in our search for answers.
2. Global Volcanic Records From Ice Coring
 We compare three records of volcanic tracers over the period 2–54 ka, particularly 25–45 ka, obtained by ice coring in Antarctica and Greenland.
 Ash depositions below the firn layer were identified using an optical technique [Bay et al., 2001; Miočinovič et al., 2001] which has been verified by melting, filtration, and microscopic examination of the core [Dunbar et al., 2003; Bay et al., 2004]. The identification of thin, highly absorbing horizons with this method is expanded in Appendix A; note that many of the ash layers found were not visible to the naked eye in the core. Integer ash amplitudes were estimated from area under the curve in arbitrary units [Bay et al., 2001] and roughly track layer absorptivity (particle number density, blackness, and mass to the 2/3 power); however, there is likely large residual variation among events assigned unit weight. We determine ash layer ages for the present analysis with the more recent depth relationship (Table 2, Ed Brook and Michael Bender, private communication, 2003) of the two used to calculate correlation with stadials from Bay et al. . The newer dating incorporates more methane markers to tie Siple Dome chronology to the GISP2 timescale of Meese et al.  with relative errors estimated to be of order hundreds of years. In addition, we repeat the analysis using the timescale reported by Brook et al.  to evaluate robustness of coincidences and consistency of relative age scales.
 We found ash amplitude to be partly misleading, as the darkest layers are strong not because of intense eruptions but because of proximity to local volcanoes. This interpretation is supported by recent measurements of chemical composition [Dunbar et al., 2003]. We will show that the medium to weak layers, however, match eruption patterns detected over large spatial scales. Removing the heaviest layers from the data set on the newer age scale would increase the volcanic correlation with millennial climate changes from the 99.7% level reported by Bay et al.  to 3σ significance (99.87% or about 800:1 odds against accidental coincidence). In the comparisons to follow we retain all events in the data set to avoid statistical trial factors. The high correlation over the full interval 20–75 ka is partly due to a pileup of events in both records between approximately 18 and 28 ka, with a high density of volcanic tracers in Siple Dome having occurred contemporaneously with the sporadic and less pronounced climate variations in GISP2 dust during Glacial Maximum. A higher statistical association of ash layers with the onsets as opposed to the peaks or trailing edges of stadials was measurable and persistent, but could not be considered convincing because uncertainties in the relative timing between sites were estimated to be of order 1 kiloyear.
 Dome C sulfate anomalies were identified using a log-normal threshold cut on sulfate flux, and key event patterns found in common between Dome C and Vostok were matched back to 45 ka by Udisti et al. . In the present analysis we treat the data set as a single representative of SO4 deposition in the East Antarctic, shown in a local climatic context in Figure A2, Appendix A. The tentative chronology for Dome C is based on a simple ice-flow model with accumulation rates derived from δD measurements and calibrated with volcanic tie points back to 7.1 ka, the CH4 event at the terminations of the Antarctic Cold Reversal and the Greenland Younger Dryas, a sharp fluoride signal also seen in the Byrd BS68 core, and a 41 ka 10Be spike [Schwander et al., 2001]. We find that this preliminary timescale lags the West Antarctic by only 200–300 years over the interval 23 to 45 ka (section 4.1). Similar to the findings in West Antarctica [Bay et al., 2004], over the interval 28 to 45 ka the East Antarctic volcanic record also correlates with onsets of Greenlandic cold periods at the >95% level (Figure 1, row 3).
 We adjusted the GISP2 SO4 anomalies before 45 ka to be consistent with the most recent age scale [Meese et al., 1997]. Zielinski et al.  used a multivariate analysis to determine a volcanic eigenvector of sulfate outliers. For comparison of discrete events between records, we imposed an amplitude threshold on GISP2 SO4 anomalies of 93 ppb. The cut was determined prior to any significance calculations to give an event density comparable with the other two records. Zielinski et al.  reported events above a 75 ppb threshold in their catalog of significant outliers, and we examine the effect of a lower threshold in the comparisons to follow.
 We evaluate the intersection (symbol ∩) of volcanic sequences in order to isolate common events of high correlation significance. By comparing the West and East Antarctic records, we identify events detected at both sites as candidates for a continent-wide depositional record of volcanism. Similarly, we promote events to candidacy for a global history by coincidence analysis between Antarctic and Greenlandic records. After comparing sequences pair-wise we examine the three-way conjunction.
 Calculating the statistical significance of a set of matches while naturally accommodating leads or lags is accomplished with a point series correlation technique developed by Stothers . Correlation measure is based on distance between nearest neighbors in overlapping segments and makes use of many repeated Monte Carlo trials to determine the likelihood that a random sequence outperforms the observed series. We define a matched event as one with at least one partner in the other series falling within a particular coincidence window. Scrambling the partner series many thousands of times until convergence, we compare the number of matches that occur with the number obtained from the original series. We combine this outcome with that obtained while scrambling the alternate record, which naturally accounts for closely spaced multiples and cases in which one record contains significantly more events. The fraction p of random sequences which produced at least as many matches as the original series is an estimate of the probability that the observed records are not correlated.
 Initially setting the coincidence window to a large value, we recalculate as the window is narrowed. We quote the correlation significance as 1 − p together with a critical coincidence window size in years, since significance depends on the tightness of agreement. Statistically significant sets of matching events abruptly exceed and sustain levels above 99% likelihood as test matches are winnowed away by a sufficiently small coincidence window, typically <200 years (e.g., see Figure 2). In most instances a high level of agreement can be appreciated visually in the color-coded comparison plots. SDM ∩ DCV and major subintervals of SDM ∩ G2 exceed 3σ significance.
 We emphasize that it is a set of events forming a distinct and precise pattern in common between series, a matching code which is unlikely to have occurred by chance. The statistical significance of a set can depend sensitively on the relative timescale, and while the addition of a comparatively small number of (unmatched) events does not substantially reduce significance of the agreement between codes, the addition or removal of matches from a set can have a more considerable impact on confidence levels. Individual matches may be ambiguous or spurious and a specific match is not guaranteed to have been products of the same volcanic eruption. A match can be considered unambiguous if the age mismatch is considerably smaller than both the dating uncertainty and age difference of neighboring events. Matches may be sufficiently misdated that they do not register as significant, and there are no doubt additional events that were missed in the individual records.
4.1. Intra-Antarctic Matches
 The West and East Antarctic volcanic records agree at 99.8% to 99.95% (∼3.3σ or 2000:1) over the interval 2 to 22 ka, with 11 matches occurring within 185 years of each other. Figure 1 shows series SDM ∩ DCV overlaid with high-resolution, effectively continuous measurements [Bay et al., 2003; Bramall et al., 2005] of millennial climate trends reflected in the logarithm of Greenland mineral dust [Mayewski et al., 1997], with the positive y direction signifying more dust and colder conditions. Unmatched events are shown in blue-gray and candidate matches falling within 71 years are shown in red, within 206 years in orange, and within 311 years in green, with significances found to be of order >99.9%, >99%, and ∼90%, respectively. While agreement over the more recent half is convincing, in the older half prior to 23 ka, a number of DCV events are consistently young by about 200–300 years. A shift of the DCV record over the interval 23–45 ka by a uniform 270 years increases significance of the subinterval from 11 matches at ∼90% to 11 matches in a range 99.5% (200:1) to 3σ. As Figure 2 illustrates, significance over the entire interval 2 to 45 ka then also increases from 23 matches within 311 years at ∼95% (20:1), to 23 matches within 185 years at 99.7% and 15 matches within 82 years at 99.97% (3.44σ or 3300:1). This slight shift is the only timescale manipulation in the analysis and we consider the modified DCV record in addition to the original in what follows. Though probably too simplistic, the shift improves correlations while interchanging few if any match events (alternatives are retained throughout). The high significance and close agreement of the entire set of 23 matches implies that many, particularly those isolated by many hundreds or thousands of years, are likely to have been products of the same eruption.
4.2. Interpole Matches
SDM ∩ G2 over the interval 16–54 ka yields 20 matches within 163 years which exceed 99%, and 18 within 127 years at 99.4% (Figure 3). The subset of 10 matches between 31–54 ka are within 106 years of each other and exceed 99.97% (3.44σ or about 3400:1). Lowering the GISP2 SO4 threshold to 70 ppb over this subinterval results in two additional matches within 160 years, while maintaining significance >99%.
 The interpole DCV ∩ G2 (sulfate-to-sulfate intersection) appears to corroborate the DCV lag found in the Antarctic analysis. Intersection over the interval 25–45 ka yields only 3 out of a possible 14 matches prior to the DCV shift. The series shifted 270 years yields 5 matches, though both correlations were confined to a range 70%–95%. An ad hoc DCV series, in which only the subset of 8 events which could be unambiguously identified in the Antarctic analysis as lagging are shifted 270 years older, gives a set of 10 matches within 200 years in a 94%–99% range.
4.3. Triple Conjunctions and Global Candidates
Figure 4 shows the triple conjunction G2 ∩ SDM ∩ DCV. As in the pair-wise case, we compute likelihoods of triple-match sets over the interval 25–45 ka using many comparisons between real data and three random sequences of the same respective numbers of events, as the coincidence window is narrowed. Using both 93 ppb and 70 ppb thresholds for the G2 series, we find stable positive correlation between the three series with significance fluctuating around 90%. Applying the 270-year shift to the DCV series markedly strengthens the significance to 99.5% for 4 triple-matches at 93 ppb and 5 triple-matches for 70 ppb, all occurring within 106-year windows. In dating candidate global events, ages of matched GISP2 events supersede Antarctic ages, and matched ash layer ages in West Antarctica are preferred over East Antarctic sulfate anomalies. The bottom panel shows the four candidate global events over this interval, those which were both highly significant and could be unambiguously matched at all three locations. Global volcanic coincidences are compiled in Table 1.
Table 1. Candidate Large-Scale Volcanic Events by Locationa
DC ∩ Vostok SO4
Dates are given in years. Events in boldface are highly significant and unambiguous. Single alternative matches separated by at least 20 years and ambiguous cases are noted. TBD denotes an event to be determined.
 A first attempt to match the East and West Antarctic records using the preliminary Siple Dome timescale employed by Bay et al.  produced high-significance matches back to about ∼17 ka, yielding only the most recent 8 of the ultimately 23 candidate matches reported above. With this exception, the chronologies used in this analysis were the first and only timescales employed in Monte Carlo calculations of match significance. A reviewer pointed out that the Siple Dome age scale had evolved from the one available (Table 2) when we began this investigation, and here we examine the effects of employing the timescale ultimately agreed upon by Brook et al. .
Table 2. Siple Dome Age Scale Tie Points Used in This Analysisa
Estimated Uncertainty, ka
From Ed Brook and Michael Bender, private communication, 2003. All points were determined using atmospheric methane except for the last, which was based on isotopic composition of O2.
4.4.1. Intra-Antarctic Matching
Figure 5 shows SDM ∩ DCV after applying the latest age conversion for SDM. High match significance is preserved by slightly decreasing the 270-year shift of the earlier half of the East record to 185 years. However, the three common match candidates in the interval 34 to 39.5 ka are now already in close agreement without shifting. The best solution is a 185-year shift of the 23.5 to 45 ka record, excluding the interval 34 to 39.5 ka, as indicated by the arrows. This slight modification to the previous shift reproduces strong match significance with some informative differences. We find significance 99.7% for 19 matches within a shorter 141-year window; note that matches between 12 and 20 ka no longer register as significant. This is a bit surprising, particularly for the match near 16.2 ka which was an unambiguous close match in the first analysis. These changes could be pure coincidence, but more likely imply that the tie points in Table 2 are actually more consistent with the Schwander et al.  dating than the Brook et al.  reported timescale.
4.4.2. Interpole Matching
 Reanalysis of SDM intersected with GISP2 yields 7 matches within 193 years, and 6 matches within 136 years at 99.9% and 99.8%, respectively, between 34.5 and 54 ka. For the 5 matches over the interval 39 to 54 ka the confidence level is 99.97%. Using the lower 70 ppb threshold for GISP2 we find confidence levels of 99.6% and 99.9% for 8 matches and 6 matches within 136 years between 34.5 to 54 ka and 39 to 54 ka, respectively.
 Applying the modified shift of the DCV series as indicated by the Antarctic comparison, the interpole DCV ∩ G2 also matches at high confidence. Over the interval 34.5 to 45 ka, 6 matches within 244 years agree at the >99% level, considerably higher than for the shift applied in the first analysis.
4.4.3. Triple Conjunctions
Figure 6 shows the recalculated three-way conjunction G2 ∩ SDM ∩ DCV. Using the 93 ppb and 70 ppb thresholds for the G2 series, correlation between the three series over the (shorter) interval 34.5 to 45 ka is ∼99.9% for 5 triple-matches and 6 triple-matches within 232-year windows, respectively, after applying the new DCV series shift.
 The close relative timing and consequently high significance we found in matching volcanic records was achievable because of the independent dating analyses by Brook et al.  and Schwander et al. . Except for volcanic signals employed by Schwander et al.  to define Dome C ages in the Holocene, the timescales we have used were calculated without regard to volcanic records and interrelations. The Greenlandic and Antarctic volcanic histories were determined prior to investigation of coincidences between data sets and before implementation of the Siple Dome timescales, meaning the comparison analysis we performed here was effectively blind. Our findings are consistent with others [Parrenin et al., 2004; Shackleton et al., 2004] showing that Antarctic methane and glaciological-modeling age estimates are particularly consistent with one another and with Greenlandic timescales over the last 50 ka, and that the glaciological-model ages are uniformly somewhat younger than the methane ages until ∼40 ka or later. Shackleton et al.  found that the Dome C age estimates of Schwander et al.  are quite linear in representing true age over the interval, and that simple interpolation was preferable to additional control points for obtaining intermediate ages in present glaciological models. Comparison of our two analyses using the preliminary versus final reported timescales for SDM argues that for the most part matches are not likely to be coincidence, since agreement and relative lapses in agreement occur coherently over sustained subintervals.
 Several of the more recent GISP2 events in Table 1, particularly those after ∼17 ka, may be suspect because of considerable background in the record. The Greenland volcanic record is known to be heavily influenced by volcanism in Iceland [Hammer et al., 1980]. Soluble ion concentrations in ice cores depend on accumulation rate and post-depositional processes [Barnes et al., 2003; Castellano et al., 2005]. Similar to what we have found for ash, the amplitudes of sulfate spikes could also be strongly affected by source distance and local variability of fallout [Cole-Dai et al., 1997]. For ash we found that order-of-magnitude amplitude differences were misleading, but that within the same logarithmic decade ash opacity may be useful, roughly speaking, as a metric of relative eruption strength. While the heaviest ash layers appear to be from local activity, deposits of the finest tephra not visible in the core appear to correspond to much more wide-spread events. A number of the global volcanic event candidates in Table 1, especially some of the more recent, may correspond to eruptions known in the historical record. As dating is further refined and more records are compiled, we can expect to fill in gaps with additional eruptions of global extent. Since the matches we report are the result of a conservative statistical treatment and depend on qualities of the individual volcanic records as well as the relative timescales, we cannot necessarily draw firm conclusions about the rate of large events [Pyle et al., 1996] from these findings. Events detected at all three locations are not necessarily comparable in magnitude or character.
 Candidate matches are based on statistical likelihood of common event patterns between records, and any particular event match could have a variety of explanations, including sheer coincidence. The agreement between volcanic histories is unlikely accidental or entirely a result of periodically favorable atmospheric transport of volcanic fallout. Although the coincidences could in principle reflect contemporaneous activity of distinct volcanic provinces in separate hemispheres erupting sympathetically, possibly tied to variations of a universal variable such as sea level, the high match significances and small age discrepancies make this explanation seem contrived, particularly since volcanic response to changing glacial load has been shown to lag by as long as a few to several kiloyears [Jellinek et al., 2004]. Analogous to East-West Antarctic volcanic coincidences, many of the candidate interpole matches likely represent single far-reaching events, such as stratospheric equatorial volcanic eruptions or bolide impacts which dispersed material planet-wide.
 Volcanic events matching over great distances appear to have coincided with abrupt global cooling. The four events in the last panel of Figure 4, where matching volcanics could be clearly identified at high significance at all three locations, were virtually simultaneous with the onsets or sudden intensifications of stadials indicated by the arrows. Other events matching at two out of three locations were also consistent with this phasing. Plausible interpretations including volcanic triggering of climate change, climatic forcing of volcanism, a combination of both scenarios (feedback), or the two phenomena having some common other cause, cannot be refuted solely on the evidence presented here. Still, these findings bolster the volcanic lead we found in West Antarctica and could substantiate a number of previous assertions that large eruptive events precipitated or enhanced glacial conditions, or that feedback within the volcano-climate system pushed burgeoning climate oscillations over some critical threshold. Modeling [Mann et al., 2005] and observation [Adams et al., 2003] indicate that strong volcanic eruptions consistently produce El Niño episodes, suggesting the possibility of a mechanism involving the tropical Pacific. Explanations for higher climate variability during colder conditions generally involve periodic collapses of thermohaline circulation, possibly associated with meltwater discharge [Birchfield and Broecker, 1990; Clark et al., 1999; Keeling and Stephens, 2001]. Large volcanic events, perhaps by slowing ocean circulation or stopping an already weakened circulation, may have played a key role in late Pleistocene climate variability.
A1. Siple Dome Volcanic Horizon Identification
 Repeatable, thin and strongly absorbing layers were previously identified and located in depth space (Figure A1), primarily by the asymmetric double-cusp absorptive signature created by such horizons in transmission [Bay et al., 2001, 2004; Bramall et al., 2005]. The signal from a second instrument in another experiment, with lower resolution in a back-scattering geometry, was less reliable but also considered. Back-scattering can be strongly affected by other factors, including significant borehole wall roughness due to drill scarring which is accentuated by an imperfect refractive-index match between the drill fluid and the ice, and also anomalous changes in scattering known to exist at the site (Jeff Severinghaus, private communication, 2005). The event candidates used here in all calculations were finalized in September 2002 by authors Bay and Bramall, through a combination of visual inspection and use of an auto-picker.
 For the purpose of evaluating our event selection in the present study, we gave our raw signal traces to Robert Rohde (Physics Department, University of California, Berkeley) who has also studied simulation of ash layers in our transmission instrument under various conditions. Rohde examined the raw data independently and identified likely ash horizons. We tabulate the results of our examinations from 2 to 60 ka in Table A1. Four additional events over the interval, not part of the original set and not included in any significance calculations above, have been identified as marginal candidate signals and are included for completeness. Two marginal signals in the original data set at 742.8 m and 752.5 m were deemed possibly spurious and have been removed; note this alteration would only increase significance levels (slightly) as these events did not register as matches in the analysis. Three marginal signals in the original set have been retained, including the event at 847.0 m which was part of a candidate triple match. The addition of a relatively small number of (unmatched) events does not substantially reduce significance of matched sets, while the addition or removal of matches from a set can have a more considerable effect on confidence levels. Although the strongest ash layers produced absorption over several meters, layer locations could be determined with order-centimeter precision. Logger payout depths were tied only linearly to strong ash layers visible in the core at 503.64 m and 759.23 m, and logger depths in the data set have been found to be approximately one-half meter greater than core depths near the bottom (1004 m) and possibly more than 2 m shallower than core depths near the surface. This error had a negligible effect on horizon dates.
Table A1. Siple Dome Optical Dust Logger Volcanic Events From 2 to 60 kaa
Numerical amplitudes explained in the text. “D” refers to closely spaced doublets; events assigned a dash were considered weak or of marginal signal quality. The two ages quoted were calculated from Table 2 and the timescale reported by Brook et al. , respectively.
 This work was made possible by Reid Bryson, Annalisa Schilla, Ed Brook, Jakob Schwander, Nelia Dunbar, Robert Rohde, Kurt Woschnagg, Predrag Miočinović, Jeff Severinghaus, Richard Alley, Alan Robock, Kurt Cuffey, Michael Bender, J. P. Steffensen, Jim W. C. White, Jihong Cole-Dai, Michael Solarz, Tony Gow, Dallas Abbott, Julien Emile-Geay, John Davis, the AMANDA/IceCube collaboration, the EPICA collaboration, and the Siple Dome A team. Two exceptional anonymous reviewers made important contributions. The Berkeley effort is supported by NSF Office of Polar Programs grant NSF ANT-0440609. The European effort is supported as part of the European Project for Ice Coring in Antarctica (EPICA), a joint European Science Foundation/European Commission scientific program, funded by the EU and by national contributions from Belgium, Denmark, France, Germany, Italy, the Netherlands, Norway, Sweden, Switzerland and the United Kingdom. This is EPICA publication 144.