Modeling the statistical distributions of cosmogenic exposure dates from moraines

• Geomorphic process modeling allows us to evalu-   calculating the mean does not improve this mismatch. Theate different methods for estimating moraine ages from cos-   extreme estimators (youngest date and oldest date) performmogenic exposure dates, and may provide a means to iden-      well under specific circumstances, but fail in other cases. Wetify the processes responsible for the excess scatter among   suggest a simple estimator that uses the skewnesses of in-exposure dates on individual moraines. Cosmogenic expo-       dividual data sets to determine whether the youngest date,sure dating is an elegant method for estimating the ages of   mean, or oldest date will provide the best estimate of morainemoraines, but individual exposure dates are sometimes bi-     age. Although this method is perhaps the most globally ro-ased by geomorphic processes. Because exposure dates may      bust of the estimators we tested, it sometimes fails spectac-be either “too young” or “too old,” there are a variety of    ularly. The failure of simple methods to provide accuratemethods for estimating the ages of moraines from exposure     estimates of moraine age points toward a need for more so-dates. In this paper, we present Monte Carlo-based models     phisticated statistical treatments.of moraine degradation and inheritance of cosmogenic nu-clides, and we use the models to examine the effectivenessof these methods. The models estimate the statistical dis-tributions of exposure dates that we would expect to obtainfrom single moraines, given reasonable geomorphic assump-tions. The model of moraine degradation is based on priorexamples, but the inheritance model is novel. The statisticaldistributions of exposure dates from the moraine degradationmodel are skewed toward young values; in contrast, the sta-tistical distributions of exposure dates from the inheritancemodel are skewed toward old values. Sensitivity analysisshows that this difference is robust for reasonable parame-ter choices. Thus, the skewness can help indicate whether aparticular data set has problems with inheritance or morainedegradation. Given representative distributions from thesetwo models, we can determine which methods of estimatingmoraine ages are most successful in recovering the correctage for test cases where this value is known. The mean isa poor estimator of moraine age for data sets drawn fromskewed parent distributions, and excluding outliers before calculating the mean does not improve this mismatch. Theextreme estimators (youngest date and oldest date) performwell under specific circumstances, but fail in other cases. Wesuggest a simple estimator that uses the skewnesses of in-dividual data sets to determine whether the youngest date,mean, or oldest date will provide the best estimate of moraineage. Although this method is perhaps the most globally ro-bust of the estimators we tested, it sometimes fails spectac-ularly. The failure of simple methods to provide accurateestimates of moraine age points toward a need for more so-phisticated statistical treatments.

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