JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. B12, PAGES 24,637-24,649, DECEMBER 10, 1995 Precision of terrestrial exposure ages and erosion rates estimated from analysis of cosmogenic isotopes produced in situ Alan R. Gillespie and Paul R. Bierman • Department of GeologicalSciences, Universityof Washington, Seattle Abstract. The concentration of cosmogenic isotopes produced within mineral grains varies with both the exposure age and erosion rate of the rock surface. In principle therefore, exposure age and erosion rate may be determined by analyzing two cosmogenic isotopes from the same sample, provided the erosion rate is constant. It is alsopossible to find either age or erosion rate from one isotope if the other parametercan be determined independently. Simple mathematical modelspredict the precision and accuracy of the exposure ages and erosion rates.The results provideinsight into the use of cosmogenic isotopes and a framework to optimizedatingexperiments and predicttractable geologic questions. The precision and accuracy of the exposure ages and erosion ratesdepend on the precision of the measured isotope concentrations, the half-lives of the isotopes, and the age and erosion rate of the sampled rock surface. They alsovary with the analytic strategy. Exposure age estimates from someisotopepairs approach measurement precision for late-Pleistocene surfaces eroding at <1 cm kyr -•. Uncertainties in erosion ratefor the same surfaces may be better than_+0.2 cmkyr -•. For older surfaces the upperlimitsfor both age and erosion rate estimates become infinite.Pairingof isotopes with different half-livesmay give misleading results unless the erosionrate is constant because they record differenterosion histories. Analyzinga single isotope removes this source of error but is appropriate only if either the age or erosionrate can be well determined independently. If the erosionrate is poorly constrained, ages for somerealistic situations may be inaccurate by 50% or more eventhough their precision may approach the measurement precision. Although it is important to understand the limitations of cosmogenic dating,it is equally importantnot to lose sightof the potential of this powerfultool for quantitative geomorphologic studies. Introduction Determining the agesand erosionrates of landforms is im- portant to studiesof long-term geomorphicprocesses. These parametersof landscape evolution can be estimatedfrom the abundance of cosmogenic isotopes producedby cosmic raysin samples collected from Earth's surface. Cosmogenic analysis has stimulatedwidespreadinterest among Quaternary geolo- gists because landscape stabilityand age are typicallydifficult to determine by other means.In this paper, simplemathemat- ical models are used to calculate theoretical precisionsfor different strategiesdesigned to estimate exposure ages and erosion ratesfrom measurements of cosmogenic isotopeabun- dance.While straightforward, the calculations for the general case are more complicated than simple error propagation, mainly because two nonlinear equations must be solved simul- taneously. The results are important both for optimizing ex- perimental design (picking whichisotopes to use,for example) and for predicting or evaluating the significance of geologic conclusions drawn from cosmogenic isotopeanalysis. Cosmogenic isotopesare produced in terrestrial rocks by a variety of nuclear interactions occurring primarily within 1Now at Department of Geology, University of Vermont, Burling- ton. Copyright1995 by the American Geophysical Union. Paper number 95JB02911. 0148-0227/95/95 JB-02911 $05.00 metersof the exposed surface. Important reactions involvethe targetelements Si, O, C1, K, and Ca andproduce such isotopes as -•He, 21Ne, •øBe, 26A1, 36C1, and14C, the abundance of which can be measured by mass spectrometric techniques. Processes creatingcosmogenic isotopes include spallation of heavier nu- clei and thermal neutron capture, as well as muon capture (reviewed by Lal [1988] and Bierman [1994]). In particular, 36C1 is created by allthree processes (36Cls and 36Clt in this text refer to the first two processes, respectively). The abundance of cosmogenic isotopes in a rock surface increases with the time of exposure to cosmic rays, but erosion reducesthe rate at which they increase.Several studieshave measuredisotopic abundances to estimate either exposure ages [e.g.,Klein et al., 1986; Phillips et al., 1990]or erosion rates [Craig and Poreda, 1986; Nishiizumi, 1991; Brown et al., 1992] for rock surfaces in a varietyof landscapes, including volcanic fieldsand morainesequences. In principle, both exposure age and erosion rate may be estimated if two or more isotopes are measured from the same sample [Lal, 1991;Nishiizumi et al., 1991;Dep et al., 1994b].This approach has not yet been used widely but has clear theoretical advantages over the single- isotope methods. Accurate estimationof uncertainties of cosmogenic expo- sure agesand erosionrates involves compounding the uncer- tainties of all measuredparametersand propagatingthese throughthe pertinent equations; yet in someprevious studies the analyticprecisionalone has been used in place of these compounded uncertainties. This simplification results in un- 24,637