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boulders with minimal surface weathering will yield too
young exposure dates on moraines that have lost material
from their crests over time. Moreover, geomorphic processes
likely introduce errors into the calibration of nuclide produc-
tion rates. These problems limit our ability to confidently
identify moraines associated with abrupt climate changes.
This work is a proof of concept, which we hope will
stimulate discussion within the exposure dating community.
Practitioners of the exposure dating method are undoubtedly
aware of these issues, but we have not seen them discussed in
print. Nonpractitioners incorporate the results of exposure
dating studies into paleoclimate syntheses (e.g., G. Schmidt,
Younger Dry-as dust?, available at http://www.realclimate.
org/index.php/archives/2007/10/younger-dry-as-dust/, 2007,
accessed 28 July 2010). Thus, an explicit discussion of these
uncertainties may be valuable.
different processes, one might choose which method to apply
to any given data set based on the skewness of the dates. This
method tends to yield results that are close to the correct
answer for the parent distributions we have tested, but it
sometimes fails spectacularly; the numbers of samples that
are typically collected from moraines (20 or fewer per mo-
raine) do not allow us to con
dently determine the skewness
of the parent distribution. Thus, we sometimes choose the
wrong method for estimating moraine ages, leading to errors
of thousands of years.
To address this problem, we developed methods for in-
verting our process models against observations [Applegate,
2009]. These methods match the modeled distributions of
exposure dates to the observed dates [Price et al., 2005; A.
Clauset et al., Power-law distributions in empirical data,
2007, available at http://arxiv.org/abs/0706.1062v1,
accessed 30 January 2009, hereinafter referred to as Clauset
et al., data set, 2007]. Besides yielding explicit estimates of
moraine age, our inverse methods also give estimates of the
rates and magnitudes of the geomorphic processes described
by the forward models. These inversions require a fairly
large number of observations per moraine (n
2. PRIOR WORK
Much past work indicates that the best simple method of
estimating moraine ages varies among moraines (step 5
above). Where measurement error produces all the scatter
among exposure dates, the mean is the best estimator of
moraine age. The maximum exposure date in a data set is
the best estimator of moraine age, where moraine degrada-
tion and/or boulder erosion are the dominant processes, and
the minimum exposure date provides the best estimate of
moraine age, where inheritance is responsible for most of the
scatter [Phillips et al., 1990; Briner et al., 2005; Benson
et al., 2005].
We have developed models of two processes, moraine
degradation and inheritance, that likely increase the scatter
among exposure dates from moraines and cause the statisti-
cal distributions of these dates to be nonnormal. Applegate et
al. [2010] provide detailed descriptions of the models, with
computer code [see also Applegate, 2009; Zreda et al., 1994;
Hallet and Putkonen, 1994; Putkonen and Swanson, 2003;
Benson et al., 2005].
This modeling work shows that the statistical distributions
of exposure dates provide clues to the geomorphic processes
acting at individual
10 or greater)
≈
to achieve a good fit.
The models are not appropriate for all
field situations
because they make certain assumptions that are not met
everywhere. We provide a detailed discussion of our models
'
assumptions elsewhere [Applegate et al., 2010]. In particular,
the degradation model assumes that moraines evolve diffu-
sively from initially triangular cross sections [Hallet and
Putkonen, 1994]. Boulders are distributed uniformly through
the removed soil column in the model. Further, the model
assumes that the boulders do not erode while buried and
erode at a constant rate after exhumation. The model does
not apply to moraines with very low surface slopes (e.g., the
terminal moraines of the Laurentide Ice Sheet in North
America), clast-supported moraines (e.g., the Ledyard mo-
raine in southeastern New England [Balco and Schaefer,
2006], or moraines where the boulders are concentrated on
the moraine
s upper surface (e.g., the outermost Pinedale
moraine at Fremont Lake, Wyoming [Gosse et al., 1995a;
E. Evenson, personal communication, 2009].
Despite these limitations, the models are useful because
their assumptions are transparent. Traditional methods of
interpreting exposure dates rely on expert judgment, in
which the assumptions underlying a particular interpretation
may not be explicitly stated.
'
field sites [Applegate et al., 2010]. In
ideal cases, where geomorphic processes do not affect expo-
sure dating, the exposure dates will be normally distributed.
The statistical distributions of exposure dates from moraines
should be left-skewed where moraine degradation is predom-
inantly responsible for the scatter among exposure dates and
should be right-skewed where inheritance is the dominant
process.
However, it is difficult to determine which simple method
to apply to a given data set [Applegate et al., 2010]. Given
the differences in the statistical distributions produced by
3. SELECTED DATA SETS
We have attempted to identify moraines that were depos-
ited at about the time of the Younger Dryas and have a
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