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above the moraine
s crest, can yield exposure dates that are
several thousand years younger than the moraine ' s true age.
Small boulders do sometimes yield exposure dates that ap-
proximate the true age of the moraine, even where moraine
degradation is rapid; these boulders originated near the top of
the removed soil column.
Sampling boulders with minimal surface relief always
yields exposure dates that are younger than the moraine ' strue
age (Figure 3, bottom). Moreover, as the criterion is made
more stringent, the median exposure date moves away from
the true age. Thus, the more strictly one adheres to the fresh-
ness criterion, the worse the resulting exposure dates become.
This result seems intuitive because till erodes more easily
than rock in many settings. The changes in moraine heights
implied by our model
'
Recent efforts to determine a reference production rate
from the calibration database [Balco et al., 2008] average
the measured nuclide concentrations to determine a repre-
sentative nuclide concentration for each site. This procedure
is reasonable, but it ignores the effects of geomorphic pro-
cesses on the nuclide concentrations, as well as problems
with the independent age constraints. These potential pro-
blems were fully acknowledged by Balco et al. [2008].
The time-averaged production rate of beryllium-10 at the
Titcomb Lakes site may be about 7% larger than previously
believed. The measured beryllium-10 concentrations from
the inner Titcomb Lakes moraine are part of the global
nuclide production rate calibration database [Gosse and
Klein, 1996; Balco et al., 2008]. The degree of scatter in the
exposure dates from the inner Titcomb Lakes moraine is
probably larger than can be explained by measurement error,
and the skewness of the data set suggests that the maximum
exposure date is the best estimator of the moraine
fits (Figure 3, top) are much greater
than the thickness of material that can be removed by erosion
from boulder surfaces over an equivalent period. Even if we
allow a very rapid boulder erosion rate of 100 mm kyr 1 [cf.
Gosse et al., 1995a, 1995b], a boulder exposed to surface
weathering for 12 kyr would lose only 1.2 m of material from
its surface. This thickness is much smaller than the 2
sage
(Figure 2) [Applegate et al., 2010; Applegate, 2009]. Thus,
the representative nuclide concentration at the Titcomb
Lakes study site is probably the maximum measured con-
centration. Prior studies that used the Titcomb Lakes con-
centration measurements to estimate the production rate of
beryllium-10 took the average of the nine largest observed
concentrations as the representative nuclide concentration
for this site, treating the smallest concentration as a statistical
outlier [Gosse and Klein, 1996; Balco et al., 2008]. The
largest concentration is about 7% greater than the mean of
the nine largest concentrations.
A potential error of a few percent in estimating nuclide
production rates has serious implications for our ability to
identify moraines associated with abrupt, short-lived climate
changes such as the Younger Dryas. Even a 5% error in
estimating nuclide production rates translates into an error
in apparent exposure time of ~600 years (5% of 12 kyr),
about half the length of the Younger Dryas.
This example suggests that the calibration of beryllium-10
production rates should be reevaluated, taking the effects of
geomorphology on the calibration measurements into ac-
count. This recalibration might help reduce the extreme
mismatch between some of the calibration samples and the
best
'
-
4mof
moraine height change implied by our model
fits. Thus, till
cover has a greater influence on exposure dates than boulder
erosion on young, steep, matrix-supported moraines, even
allowing for the difference in density between boulders and
till [Hallet and Putkonen, 1994].
5. IMPLICATIONS FOR DETERMINING NUCLIDE
PRODUCTION RATES
Step 5 in determining the age of a moraine using cosmo-
genic exposure dating involves calculating the apparent ex-
posure time of each sample, using the estimated local
production rate of the nuclide [Balco et al., 2008]. Thus, any
error in determining the local production rate will translate
into errors in the apparent exposure times, reducing our
ability to identify moraines associated with short-lived cli-
mate events.
The production rates of cosmogenic nuclides are not
known a priori. Instead, the concentrations of cosmogenic
nuclides are measured in rock surfaces whose exposure ages
are known independently from other chronologic methods,
usually radiocarbon dating. Not all the calibration samples
come from moraine boulders, but some do [Balco et al.,
2008]. Ideally, the nuclide concentration in a single rock
surface, divided by the independently determined exposure
age, yields the local time-averaged production rate after
correcting for nuclear decay. In practice, the nuclide concen-
trations at the calibration sites are highly scattered [Balco et
al., 2008]. Consequently, there is uncertainty about the rep-
resentative nuclide concentration at each calibration site.
fit of the scaling models to the calibration data set [Balco
et al., 2008, Figure 5].
6. DISCUSSION
ed two challenges in the
use of cosmogenic exposure dating to date moraines associ-
ated with abrupt climate changes such as the Younger Dryas.
First, pristine boulders will tend to yield exposure dates that
are younger than the true age of the moraine, if moraines lose
In this chapter, we have identi
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