Paper# 2012GL053098
A late Pleistocene - Mid-Holocene noble gas and stable isotope climate and
subglacial record in southern Michigan
Auxiliary Text 3: Statistical Analysis of abrupt Climatic events
3.1 Introduction
As mentioned in Section 4 of the main text, Saginaw and Marshall aquifer
samples were combined to develop a detailed paleoclimatic record in southern Michigan
since the LGM. Groundwater age distribution within this combined dataset indicates that
most samples are not evenly distributed since the LGM (Figs. 3, 4). Instead, samples
appear to be clustered around abrupt climatic events including the onset and termination
of the Younger Dryas (YD) as well as the Mid-Holocene (MH) climatic events. In
particular, the onset and termination of the YD at ~12,9kyrs BP and ~11,6kyrs BP,
respectively, are each represented by five samples from the Saginaw and Marshall
aquifers (Figs. 3, 4). Similarly, warming at the onset of the MH climatic event between
~5.4 kyrs BP and ~4.1 kyrs BP followed by subsequent cooling between ~4.1kyrs and
2.9kyrs BP are indicated by four samples each (Figs. 3, 4). In addition, most remaining
samples used in the paleoclimatic reconstruction are modern in age with only a few
samples displaying ages ≥ ~15 kyrs BP (m14a, m14b, m15) and two samples that are not
representative of any particular climatic event described in this study (m2a, 2b).
Clustering of samples at these abrupt climatic shifts and, in particular, at the onset
and termination of the YD can either be due to (1) a sampling bias related to the
availability of wells to sample and authorization to go into the owner’s properties to
sample their groundwater; and/or (2) both the YD and MH climatic events were dry
periods and therefore, it is expected that reduced recharge might have occurred during
these periods which, in turn, drastically reduces the probability of finding groundwater
with ages corresponding to the mid period of these climatic events. While hypothesis (2)
seems more likely, it is not possible at present to determine why groundwater age
distribution of the combined Marshall and Saginaw aquifer datasets is clustered around
abrupt climatic shifts. However, such a clustered groundwater age distribution allows for
a detailed reconstruction of the timing and magnitude of abrupt climatic oscillations if
individual climatic events are statistically distinct. Statistical analyses of abrupt climatic
events identified in this study are presented in detail below.
Abrupt climatic oscillations identified in this study (onset and termination of
Younger Dryas and Mid-Holocene oscillations) are thought to have occurred on very
short time scales [50-3000yrs; Taylor et al., 1997, Viau et al., 2006]. Because
groundwater age dating through 14C yields coarse age resolution (i.e., large age errors, cf.
Supplementary Table 2) and because NGT results from multiple samples may overlap
within error for these temperature climatic perturbations, it is critical to: (1) identify
whether samples within a specific time period (climatic event) represent actual variations
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in temperature or are simply representative of a single average temperature and; (2)
whether 14C age resolution is sufficient to distinguish between rapid climatic events that
occur on short time scales such as the onset and termination of the Younger Dryas.
Below, we test both conditions through statistical analysis.
3.2 Do identified abrupt climatic events represent actual temperature (NGT) variations?
In order to test whether the abrupt cooling of the Younger Dryas (YD) identified
through NGTs represents an actual climatic variation, a chi square test was performed on
the samples falling within this time period (m12b, m12a, sg7, sg11, sg9, sg5a, sg5b,
sg12a, m13, cf. Supplementary Table 2, 4). The null hypothesis (H0) tested is that NGTs
from all samples within the YD represent one single temperature (weighted mean) while
the alternate hypothesis (Ha) is that all samples do not represent one single temperature
but instead, a range of temperatures representative of the climatic variations that took
place during the YD. The null hypothesis is rejected if chi squared probability (p) is less
than 0.05 or 5%. Chi square values were calculated as the sum of squared differences
between measurements and weighted mean normalized by weighted standard deviation.
A Chi square value of 18.7 is obtained for the tested group of YD samples. For eight
degrees of freedom, this chi square value corresponds to a probability of less than 0.017.
Because the calculated probability is less than 0.05, we can reject the null hypothesis and
conclude that samples within the YD do indeed represent climatic variations 95% of the
time.
A similar chi square test was performed on a group of six samples (m4a, m4b,
sg6a, sg6b, sg4a, sg4b; cf. Supplementary Tables 2,4) within the Mid-Holocene assuming
a similar null hypothesis (H0) and similar rejection criterion (p<0.05). The sum of Chisquares for the Mid-Holocene group of samples yields a value of 19.5 with a p value of
0.0015 for five degrees of freedom. Because this p-value is less than the rejection
criterion (p<0.05), we can reject the null hypothesis and conclude that all Mid-Holocene
samples do not represent one single temperature but instead represent climatic variations
at least 95% of the time.
This statistical analysis to both set of samples within the YD and mid-Holocene
period allow us to state with confidence that NGT variations observed within these two
periods are indeed representative of the climatic perturbations that took place during
these two periods.
3.3 Is 14C age resolution sufficient to distinguish between abrupt climatic events?
Because 14C age resolution is relatively coarse, it is necessary to evaluate whether
two groups of samples that represent closely timed climatic events have sufficient age
resolution to distinguish between these events. For example, our climatic record shows a
group of five samples (m12a, m12b, sg7, sg9, sg11) that likely represents the onset of the
Younger Dryas (~12.9kyrs BP) while another group of four samples (sg12a, sg5a, sg5b,
m13) likely represents the termination of the Younger Dryas (~11,6kyrs BP). Because
these two events are closely timed (~1000yrs), it is important to distinguish whether ages
within these two groups are statistically different, thus representing two individual
climatic events or whether they represent climatic variations within a single climatic
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event. To address this issue we utilize a two-sample Z-statistical test to compare mean
ages from the two groups of samples at the beginning and end of the Younger Dryas. We
define the null hypothesis (H0) as the mean ages in the two groups of samples that are not
different while the alternate hypothesis (Ha) is that mean ages in the two groups are
indeed different and representative of individual climatic events. As indicated previously,
we reject the null hypothesis at the 95% confidence level. Samples from the beginning of
the Younger Dryas yield a mean age of 12949.8 yrs with a standard deviation of 84.55
yrs while samples at the end of the Younger Dryas yield a mean age of 11041yrs and
standard deviation of 56.07 yrs. The two-sample Z-statistic yields a probability of less
than 0.0001 that these two groups would have indistinguishable ages thus rejecting the
null hypothesis. It is thus concluded that the two groups of samples at the beginning and
end of the YD do indeed represent individual climatic events. Similarly, samples at the
onset (m4a, m4b) and termination (sg4a, sg4b) of the mid-Holocene climatic event are
also relatively closely timed (~2,400yrs). Similar to samples from the YD, we utilize a
two-sample Z-statistical test to compare mean ages from the two groups of samples
assuming a similar null hypothesis (H0) and rejection criterion (p<0.05). Samples from
the onset of the MH yield a mean age of 5339 yrs with a standard deviation of 844.5 yrs
while samples at the end of the MH yield a mean age of 2940yrs and standard deviation
of 1197 yrs. The two-sample Z-statistic yields a probability of 0.024 that these two
groups would have indistinguishable ages, thus rejecting the null hypothesis. In addition,
it was also concluded that samples from the beginning and end of the MH climatic event
represent actual climatic variations. Combining statistical test results from NGTs and
ages for MH samples, it can clearly be seen that observed rapid warming and cooling
during this period are indeed representative of climatic oscillations.
References
Taylor, K. C., et al. (1997), The Holocene-Younger Dryas Transition Recorded at
Summit, Greenland, Science, 278(5339), 825-827.
Viau, A. E., K. Gajewski, M. C. Sawada, and P. Fines (2006), Millennial-scale
temperature variations in North America during the Holocene, J. Geophys.
Res., 111(D9), D09102.
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