Modeling the statistical distributions of cosmogenic exposure dates from moraines

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.