[show abstract][hide abstract] ABSTRACT: Geomorphic process modeling allows us to evaluate different methods for estimating moraine ages from cosmogenic exposure dates, and may provide a means to identify the processes responsible for the excess scatter among exposure dates on individual moraines. Cosmogenic exposure dating is an elegant method for estimating the ages of moraines, but individual exposure dates are sometimes biased by geomorphic processes. Because exposure dates may be either "too young" or "too old," there are a variety of methods for estimating the ages of moraines from exposure dates. In this paper, we present Monte Carlo-based models of moraine degradation and inheritance of cosmogenic nuclides, and we use the models to examine the effectiveness of these methods. The models estimate the statistical distributions of exposure dates that we would expect to obtain from single moraines, given reasonable geomorphic assumptions. The model of moraine degradation is based on prior examples, but the inheritance model is novel. The statistical distributions of exposure dates from the moraine degradation model are skewed toward young values; in contrast, the statistical distributions of exposure dates from the inheritance model are skewed toward old values. Sensitivity analysis shows that this difference is robust for reasonable parameter choices. Thus, the skewness can help indicate whether a particular data set has problems with inheritance or moraine degradation. Given representative distributions from these two models, we can determine which methods of estimating moraine ages are most successful in recovering the correct age for test cases where this value is known. The mean is a poor estimator of moraine age for data sets drawn from skewed parent distributions, and excluding outliers before calculating the mean does not improve this mismatch. The extreme estimators (youngest date and oldest date) perform well under specific circumstances, but fail in other cases. We suggest a simple estimator that uses the skewnesses of individual data sets to determine whether the youngest date, mean, or oldest date will provide the best estimate of moraine age. Although this method is perhaps the most globally robust of the estimators we tested, it sometimes fails spectacularly. The failure of simple methods to provide accurate estimates of moraine age points toward a need for more sophisticated statistical treatments.
[show abstract][hide abstract] ABSTRACT: Cosmogenic exposure dating provides a means of determining the ages of glacial landforms in places where sampling opportunities for radiocarbon dating do not exist. However, cosmogenic exposure dates from individual moraines are often widely scattered, as a result of geomorphic processes. The list of geomorphic processes that may influence exposure dates is long, but it is generally believed that moraine degradation and inheritance are two of the most important. Building on previous modeling work in this area, we have constructed numerical models that describe the effects of these two processes on the statistical distributions of exposure dates from moraines. These models show that the statistical distributions of exposure dates from boulders resting on degrading moraines should be left-skewed, whereas the statistical distributions of exposure dates from boulders that contain inherited nuclides should be right-skewed. However, the numbers of samples that are typically collected from moraines for exposure dating (n < ~20) do not allow us to reliably determine whether the underlying parent distributions are left-skewed or right-skewed. Random sampling of a small number of synthetic exposure dates from the modeled distributions produces a wide range of skewnesses, often with the opposite sign from the underlying parent distributions. That is, a small number of exposure dates drawn from a positively skewed parent distribution will often have a negative skewness, and vice versa. This result suggests a need for a more rigorous method for comparing our models to observations. We have developed a method that involves comparing the distributions of exposure dates produced by our models to observed distributions. This procedure yields estimates of moraine age and other parameters of geomorphic interest, such as topographic diffusivity and the depth of glacial erosion. The method is able to recover these parameters for test cases in which the parameter values are known. Our work provides a quantitative basis for assessing different methods of estimating moraine ages from collections of exposure dates.
[show abstract][hide abstract] ABSTRACT: Cosmogenic exposure dating provides insight into the timing of glacial fluctuations at high latitudes, but collections of exposure dates from isochronous surfaces often show unexpectedly large scatter. Here, we show that the structure of a recently published set of cosmogenic exposure dates from eastern Greenland (Kelly et al., 2008, Quaternary Science Reviews, v. 27, p. 2273) is distinctly different from the structures of selected data sets from the midlatitudes. Specifically, histograms of the eastern Greenland dates are right-skewed, whereas histograms of exposure dates from the mid-latitude sites are left-skewed. We infer that this difference in structure reflects a difference in the geomorphic processes active in eastern Greenland, as compared to the mid-latitude sites. Further, we fit the eastern Greenland data with a process model that relates moraine age, landscape age, and depth of glacial erosion to the observed distributions of cosmogenic exposure dates. Our model treats inherited nuclides in moraine boulders in a Monte Carlo framework. The unknown parameters for each boulder are 1) the amount of time it was exposed to cosmic rays before being incorporated into the moraine, and 2) the depth to which the sampled point on the boulder was buried during this predepositional exposure time. Neither of these parameters is known, so we assume that all values from zero up to some maximum are equally likely. We draw random values from these uniform distributions for a large number of synthetic boulders, calculate an apparent exposure time for each synthetic boulder, and histogram the apparent exposure times. The histograms produced by the inheritance model are right-skewed, consistent with the eastern Greenland data set. In contrast, the left-skewed structure of the other data sets is well reproduced by a model of moraine degradation. We present fits of the inheritance model to the eastern Greenland exposure dates, and discuss the implications of the resulting moraine age, landscape age, and glacial erosion depth estimates.
[show abstract][hide abstract] ABSTRACT: Cosmogenic exposure dating provides a method for estimating the ages of glacial moraines deposited in the last ~105 years. Cosmic rays break atoms in surface rocks at predictable rates. Thus, the ages of moraines are directly related to the concentrations of cosmic ray-produced nuclides in rocks on the moraine surfaces, under ideal circumstances. However, many geomorphic processes may interfere with cosmogenic exposure dating. Because of these processes, boulders sometimes arrive at the moraines with preexisting concentrations of cosmogenic nuclides, or else the boulders are partly shielded from cosmic rays following deposition. Many methods for estimating moraine ages from cosmogenic exposure dates exist in the literature, but we cannot assess the appropriateness of these methods without knowing the parent distribution from which the dates were drawn on each moraine. Here, we make two contributions. First, we describe numerical models of two geomorphic processes, moraine degradation and inheritance, and their effects on cosmogenic exposure dating. Second, we assess the robustness of various simple methods for estimating the ages of moraines from collections of cosmogenic exposure dates. Our models estimate the probability distributions of cosmogenic exposure dates that we would obtain from moraine boulders with specified geomorphic histories, using Monte Carlo methods. We expand on pioneering modeling efforts to address this problem by placing these models into a common framework. We also evaluate the sensitivity of the models to changes in their input parameters. The sensitivity tests show that moraine degradation consistently produces left-skewed distributions of exposure dates; that is, the distributions have long tails toward the young end of the distribution. In contrast, inheritance produces right-skewed distributions that have long tails toward the old side of the distribution. Given representative distributions from these two models, we can determine which methods of estimating moraine ages are most successful in recovering the correct age for test cases where this value is known. The mean is a poor estimator of moraine age for data sets drawn from skewed parent distributions, and excluding outliers before calculating the mean does not improve this mismatch. The extreme estimators (youngest date and oldest date) perform well under specific circumstances, but fail in other cases. We suggest a simple estimator that uses the skewnesses of individual data sets to determine whether the youngest date, mean, or oldest date will provide the best estimate of moraine age. Although this method is perhaps the most globally robust of the estimators we tested, it sometimes fails spectacularly. The failure of simple methods to provide accurate estimates of moraine age points toward a need for more sophisticated statistical treatments. We present improved methods for estimating moraine ages in a companion paper.
Geoscientific Model Development Discussions. 01/2009;