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Geomorphology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / g e o m o r p h

A response to the commentary of M. Dąbski about the paper Asynchronous Little Ice Age glacial maximum extent in southeast Iceland’ (Geomorphology (2010), 114, 253–260) Marie Chenet a,⁎, Erwan Roussel b, Vincent Jomelli a, Delphine Grancher a, Daniel Cooley c a b c

CNRS Laboratory of Physical Geography, 1 place Aristide Briand, 92195 Meudon cedex, France CNRS GEOLAB, 4 rue Ledru, 63057 Clermont-Ferrand cedex, France Department of Applied Mathematics, University of Colorado at Boulder, CO, USA

a r t i c l e

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Article history: Received 15 July 2010 Received in revised form 21 December 2010 Accepted 24 December 2010 Available online 1 January 2011 Keywords: Lichenometry Bayesian approach GEV method Fláajökull Iceland

a b s t r a c t In a commentary about the paper Asynchronous Little Ice Age glacial maximum extent in southeast Iceland’ (Geomorphology 114 (2010) 253-260), M. Dąbski questioned the validity of the generalized extreme value method and the Bayesian approach in lichenometric dating of the outermost LIA Fláajökull moraines in SE Iceland. This paper responds to these criticisms by explaining the relevance of the method applied and the relevance of the dates obtained. © 2010 Elsevier B.V. All rights reserved.

1. Introduction We have recently published a paper called “Asynchronous Little Ice Age glacial maximum extent in southeast Iceland” (Chenet et al., 2010). This paper dealt with the application of different lichenometric approaches to date the Little Ice Age (LIA) maximum glacial extent of 13 glaciers located in SE Iceland in order to determine whether the asynchrony of the maximal extent was due to the application of different methods or rather due to differences between investigated glacier tongues. Our results showed that all lichenometric approaches lead to high variability between glaciers. Otherwise, dates using generalized extreme value (GEV) method were correlated with geomorphic characteristics of glacier tongues. Hypsometric and slope parameters appeared to be determining factors in the variability of glacier timing during the LIA. This paper has been the target of critical comments by M. Dąbski. The critics are followed : - in the case of Fláajökull moraines, the GEV method produced apparently wrong dates because they differ from those obtained with the ﬁve largest thalli (Dąbski et al., 1998; Dąbski, 2002; Evans et al., 1999) or using the size-frequency approach (Bradwell, 2004;

⁎ Corresponding author. E-mail address: [email protected] (M. Chenet). 0169-555X/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.geomorph.2010.12.024

Dąbski, 2007) and they don't correspond well with the historical data, particularly from Thorarinsson (1943). - Because we have demonstrated that high altitude and steeper glaciers reached their maxima earlier, Fláajökull LIA maximum should have occurred later, regarding the characteristics of the Kotárjökull, Kviárjökull, Hrútárjökull and Fjallsjökull. - Following the Bradwell's statement (2009), the advocating of highly complex statistics in lichenometry, e.g., the GEV method, was unjustiﬁed. We would like to respond to these criticisms. 2. Discussion 2.1. The relevance of the GEV approach compared to other lichen methods The main criticism is about the GEV method and its reliability. This criticism is not the ﬁrst, as Bradwell (2009) has already expressed doubts about this method. However, Jomelli et al. (2010) argue that Bradwell does not fully understand all the assumptions made in a “traditional” lichenometric analysis and that these assumptions are not justiﬁed when applied to data such as the ﬁve largest lichens. We will not describe again the method as it has already been explained in details in different papers (Cooley et al., 2006; Jomelli et al., 2007; Naveau et al., 2007). We just want to remind that the strategy is to describe the largest lichen diameters by modeling the

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entire distribution of lichen size and that this approach is based on a simple statistical reasoning: the theory dedicated to extreme values is used because the largest lichen diameters belong to this category. So the question is: why do we prefer to use the GEV methods instead of previous methods? We can give several reasons, already detailed in our paper: - The “ﬁve largest” approach is very easy to apply but suffer from a major concern. As mentioned in any introductive book of statistics the calculation of the mean makes sense only if the distribution of lichen data follows a normal distribution. Hovewer it is well known in statistics (Coles, 2001; Gnedenko, 1943; Leadbetter et al., 1983) that the distribution of maxima cannot be normal but instead must follow a speciﬁc distribution called the Generalized Extreme Value distribution (GEV). In other words the value of the mean of 5 large lichens does not have any signiﬁcance from a statistical point of view. - In comparison, the size-frequency distribution method has the advantage of being based on a large number of measurements and is statistically efﬁcient. But ages were obtained using a regression modeling with uncertainties based on two standard deviations (95% conﬁdence limits), which is here not valid to compute meaningful conﬁdence intervals. - Furthermore, the two methods suffer from another major problem: the links between dated and undated surfaces is based on a two-step procedure. Traditionally, lichens measured on dated surfaces and lichens measured on undated surfaces are separated in two distinct data sets for the analysis, the ﬁrst is used to build the growth curve, this transfer function is then applied to determine the age of the second set of data. Separating the lichens in two groups is statically arbitrary because the distribution of lichen diameters comes from the same family of distribution. These past two-step procedures increase the potentiality of error, propagating uncertainties of ﬁrst step into the second stage of the estimation of dates. The GEV method compensates these difﬁculties and appropriately handles the type of data collected. Furthermore, Jomelli et al. (2007), from test bed of tombstones, have demonstrated that this method provides reasonably good estimates of dates. For all these reasons, we have chosen this approach to highlight and to establish whether the LIA maximum depends on geomorphic characteristics. 2.2. The relevance of the dates obtained for Fláajökull The commentaries of M. Dąbski concerns more especially the dates found for the oldest LIA moraine of Fláajökull. Two critics are expressed: - the results are not correlated with previous lichenometric dating and documentary records of Thorarinsson (1943), - the timing of LIA maximum is not correlated to hypsometry and slope of the glacier tongue. M. Dąbski argued the fact that its “obtained dates corresponded relatively well with previous ﬁndings of Evans et al. (1999) who used average of the ﬁve largest thalli”. This correspondence did not prove that the dates were exact, as we suggested that “the ﬁve largest” method was not statistically valid. Moreover it is very surprising from a scientiﬁc point of view to pretend to be able to obtain concordant ages from lichens without giving any conﬁdence intervals as any other dating techniques do, and to construct an attack on this argumentation. Concerning the records of Thorarinsson, they are based on the accounts of Gudmundur of Hoffels who noticed that “Fláajökull was slightly more advanced in 1880 than about 1850” (Thorarinsson, 1943, p.21). These words do not give any accurate position of the front

of the glacier downstream and are not in contradiction with our results: Fláajökull could have known a maximal extent around AD 1821 (1807–1831), dates obtained with the GEV method, and periods of advance around AD 1839 and AD 1894. This conﬁrms the point that we wanted to highlight: the absence of a single LIA maximum in SE Iceland and the succession of periods of advances in or around the following decades: A.D. 1740–1760; A.D. 1810–1820; A.D. 1840–1880. Of course, errors in the localization of the oldest moraine or in the measurements are always possible. Concerning the second point, we agree that the Fláajökull LIA maximum is not well correlated with hypsometry and slope parameters. We would like to remind that correlation coefﬁcients were determined from parameters collected from 13 glaciers. Insofar as the coefﬁcients were signiﬁcant but not equal to 1, the correlation can be weak for a few of glaciers, Fláajökull is part of them.

3. Conclusion It seems that the GEV method is not accepted by all users of lichenometry. We agree that this approach is based on less common statistics and is more needing in terms of time and mathematical knowledge than other lichenometric approaches. But our goal is to obtain dating in the most accurate way possible with reliable conﬁdence intervals. Can we criticize the other dating methods (e.g. radiocarbon or isotope dating) for being expensive and complex even though they give good results? To compensate for this difﬁculty, we already mentioned that anyone who is interested in determining the age of a geomorphological landform is welcomed. In order to make the analysis simple, the researcher just needs to send to the GEV team (http://www.lgp.cnrsbellevue.fr/index.htm) a classical excel ﬁle.

References Bradwell, T., 2004. Lichenometric dating in southeast Iceland: the size-frequency approach. Geograﬁska Annaler 86 (A), 31–41. Bradwell, T., 2009. Lichenometric dating: a commentary, in the light of some recent statistical studies. Geograﬁska Annaler 91 A, 61–69. Coles, S.G., 2001. An Introduction to Statistical Modeling of Extreme Values. SpringerVerlag, New York-Heidelberg Berlin, 228 pp. Cooley, D., Naveau, P., Jomelli, V., Rabatel, A., Grancher, D., 2006. A bayesian hierarchical extreme value model for lichenometry. Environmetrics 17, 555–574. Chenet, M., Roussel, E., Jomelli, V., Grancher, D., 2010. Asynchronous Little Ice Age glacial maximum extent in southest Iceland. Geomorphology 114, 253–260. Dąbski, M., 2007. Testing the size-frequency-based lichenometric dating curve on Fláajökull moraines (SE Iceland) and quantifying lichen population dynamics with respect to stone surface aspect. Jökull 57, 21–35. Dąbski, M., 2002. Dating of the Fláajökull moraine ridges, SE-Iceland; comparison of the glaciological, cartographic and lichenometrical data. Jökull 51, 17–24. Dąbski, M., Fabiszewski, B., Pękalska, A., 1998. Marginal zone of Fláajökull (Iceland). Initial result of Research. Miscellanea Geographica 8, 47–54. Evans, D.J.A., Archer, S., Wilson, D.J.H., 1999. A comparison of the lichenometric and Schmidt hammer dating techniques based on data from the proglacial areas of some Icelandic glaciers. Quaternary Science Reviews 18, 13–41. Gnedenko, R., 1943. Sur la distribution limite du terme maximum d'une série aléatoire. Annales de Mathématiques 44, 423–453. Jomelli, V., Grancher, D., Naveau, P., Cooley, D., Brunstein, D., 2007. Assessment study of lichenometric methods for dating surface. Geomorphology 86 (1–2), 131–143. Jomelli, V., Naveau, P., Cooley, D., Grancher, D., Brunstein, D., Rabatel, A., 2010. A Response to Bradwell's Commentary on Recent Statistical Studies in Lichenometry. Under review. Leadbetter, M.R., Lindgren, G., Rootzen, H., 1983. Extremes and Related Properties of Random Sequences and Processes. Springer Verlag, pp. 1–211. Naveau, P., Jomelli, V., Cooley, D., Grancher, D., Rabatel, A., 2007. Modelling uncertainties in lichenometry studies with an application: the Tropical Andes (Charquini Glacier in Bolivia). Arctic, Antarctic, and Alpine Research 39, 277–285. Thorarinsson, S., 1943. Oscillations of the Icelandic glaciers in the last 250 years. Vatnajökull, scientiﬁc results of the Swedish-Icelandic investigation 1937–38–39. Geograﬁska Annaler 1–2, 1–54.

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