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signi
cant thicknesses of material from their crests over
time, and boulders erode once exhumed. Second, geomor-
phic processes likely impart an additional uncertainty of at
least several percent in our present estimates of reference
cosmogenic nuclide production rates. For moraines of late
glacial to early Holocene age, these effects bias exposure
dates by hundreds to thousands of years. Thus, these chal-
lenges limit our confidence in the ability of cosmogenic
exposure dating to identify moraines associated with abrupt
climate changes, which have time scales of a few years to a
few hundred years.
Moreover, our results con
Our results imply that our ability to invert our models
against collections of exposure dates depends on how the
samples were chosen. The inverse methods can account for
the heights of boulders from which samples were taken, as
long as these heights are reported with the exposure dates.
However, the inverse methods cannot account for use of the
surface pristinity criterion. Preferentially sampling fresh
boulders produces distributions of exposure dates that are all
younger than the true age of the moraine and emphasize the
tail of the modeled distribution at the expense of the mode
(Figure 3) if both moraine degradation and boulder erosion
are active on a particular moraine. Given a data set collected
in this way, our methods would likely be unable to determine
whether the excess scatter in the data was caused by inher-
itance or moraine degradation. It is also possible that such a
data set would have a deceptively small scatter. Any age
estimates made from such a data set would be far too young.
For future
rm prior suggestions that pref-
erentially sampling tall boulders is a good strategy [Phillips
et al., 1990; Gosse et al., 1995a, 1995b]. However, even
exposure dates from tall boulders may underestimate the age
of a moraine by thousands of years, depending on boulder
height and the thickness of material lost from the moraine
'
s
crest.
Our conclusions do not hold where geomorphic processes
other than moraine degradation and boulder erosion affect
exposure dates. In particular, inheritance might cause the
exposure dates from tall boulders to overestimate the ages of
moraines; boulders that fall onto the glacier from over-
steepened valley walls will not be eroded in transport and
thus may be larger than other clasts that have had most of their
inherited nuclides stripped away by subglacial transport.
Moreover, we assume that the erosion rate for exposed
boulders is the same for all the rocks on a moraine. However,
we expect that boulders on real moraines will weather at
different rates, depending on their lithology, position in the
landscape, and size. Our models also assume slow, grain-by-
grain erosion of moraine boulders, but the rapid loss of
several centimeters of rock is also possible [Zimmerman et
al., 1995]. In the future, we plan to update our models to
represent this style of erosion, perhaps following Muzikar
[2009].
Here we explain the lack of correlation between boulder
height and apparent exposure time on the inner Titcomb
Lakes moraine (Figure 4) with moraine degradation. Other
explanations are also possible. In cases where inheritance
dominates the scatter among exposure dates, there may be no
relationship between boulder size and apparent exposure
time. If all the boulders on a moraine are taller than the
thickness of snow cover or the thickness of sediment that
has been removed from the surface of a moraine, there will
also be no correlation between boulder height and apparent
exposure time. We believe that the geomorphic processes
responsible for the scatter among exposure dates vary be-
tween moraines, and so the degree and sign of the correlation
between boulder height and apparent exposure time probably
also vary.
field campaigns, and in evaluating data sets
from the literature, we recommend determining what overall
precision would be necessary to answer the paleoclimate
question at hand. For example, con
dent determination of
whether a moraine dates to the Younger Dryas probably
requires an overall 1
σ
uncertainty of about 100 years or
about 10% of the event
s length.
With that information, the minimum number of samples
required to answer the question can be estimated from the
expected measurement uncertainty of the exposure dates
and Figure 1. Figure 1 represents the uncertainty of the
weighted mean [Bevington and Robinson, 2003, equation
4-19]. This quantity is the uncertainty of repeated exposure
dating on a single moraine in the special case where
geomorphology has no effect on the exposure dates. In
practice, the uncertainty of exposure dating will be larger
than Figure 1 implies, so more samples will be required.
Note that repeated sampling will not reduce uncertainty
associated with external factors such as production rate
estimation errors [Balco et al., 2008].
The number of samples required to achieve a desired
precision will sometimes be unrealistically large. The curve
in Figure 1 reaches a point of diminishing returns around 10
'
-
15 samples, where the uncertainty of the weighted mean is
25%
30% of the uncertainty of one date. The number of
samples required to achieve a precision better than 25%
-
-
30% of the uncertainty of one date will often be larger than
can be produced with available resources. For example, if
our measurement uncertainty is 5%, rather than 3%, we will
need 36 samples to achieve a 100 year overall uncertainty for
a Younger Dryas moraine (Figure 1). We are unaware of any
moraine with 36 published exposure dates. Thus, some ques-
tions can be answered only approximately with cosmogenic
exposure dating.
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