Modeling the statistical distributions of cosmogenic exposure dates from moraines

P. J. Applegate, N. M. Urban, B. J.C. Laabs, K. Keller, R. B. Alley

Research output: Contribution to journalArticle

67 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)293-307
Number of pages15
JournalGeoscientific Model Development
Volume3
Issue number1
DOIs
StatePublished - Jan 1 2010

Fingerprint

statistical distribution
Statistical Distribution
moraine
Date
Modeling
modeling
Degradation
Estimator
Model
exposure
skewness
Estimate
Sensitivity analysis
method
Isotopes
outlier
Skewed Distribution
sensitivity analysis
Skewness
Process Modeling

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Earth and Planetary Sciences(all)

Cite this

@article{be443eaa16584c04837e29ab2f6d6339,
title = "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.",
author = "Applegate, {P. J.} and Urban, {N. M.} and Laabs, {B. J.C.} and K. Keller and Alley, {R. B.}",
year = "2010",
month = "1",
day = "1",
doi = "10.5194/gmd-3-293-2010",
language = "English (US)",
volume = "3",
pages = "293--307",
journal = "Geoscientific Model Development",
issn = "1991-959X",
publisher = "Copernicus Gesellschaft mbH",
number = "1",

}

Modeling the statistical distributions of cosmogenic exposure dates from moraines. / Applegate, P. J.; Urban, N. M.; Laabs, B. J.C.; Keller, K.; Alley, R. B.

In: Geoscientific Model Development, Vol. 3, No. 1, 01.01.2010, p. 293-307.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Modeling the statistical distributions of cosmogenic exposure dates from moraines

AU - Applegate, P. J.

AU - Urban, N. M.

AU - Laabs, B. J.C.

AU - Keller, K.

AU - Alley, R. B.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=78650519529&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650519529&partnerID=8YFLogxK

U2 - 10.5194/gmd-3-293-2010

DO - 10.5194/gmd-3-293-2010

M3 - Article

AN - SCOPUS:78650519529

VL - 3

SP - 293

EP - 307

JO - Geoscientific Model Development

JF - Geoscientific Model Development

SN - 1991-959X

IS - 1

ER -