Methodology Thirteen glaciers were selected in a limited area SE Iceland to guarantee climatic homogeneity. Conversely, geomorphic and glaciological parameters differ between glacier tongues we investigated. Each moraine corresponding to the LIA maximal extent was dated following standard lichenometric procedures.

The original approach consisted in measuring several large lichens and selecting the largest for dating purposes. Based on the assumption that the largest lichens were among the first to colonize a surface, a lichen growth curve was built based on regression line plots. To reduce errors linked to the choice of PT only one lichen per moraine, the average of the 5 or 10 largest lichens diameters was computed for RI each moraine. However, this approach is limited NU by the small data set that is not statistically robust McKinzey et al.

Furthermore, Jomelli et al.

Consequently, averaging maxima is not robust from a statistical point of view, and estimates of confidence intervals based on this average are not reliable. ED More recently, an alternative method has been applied: More than lichens have to be sampled by dating surfaces. This method uses the population gradient calculated from the size- CE frequency distribution curve expressed in Log The best-fitted slope of the size-frequency distribution versus the age of each dated surface provides the age of several features using a linear AC regression Bradwell, a.

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## Lichenometry in Iceland, results and application

The main advantage of this method is that age estimations are based on a large number of measurements rather than depending on a few large lichens. But the method suffers from the need to link dated to undated surfaces in two distinct steps. Traditionally, lichens measured on dated surfaces and lichens measured on undated surfaces are separated into two distinct data sets for the analysis: Separating the lichens into two groups is statistically arbitrary because the distribution of lichen diameters comes from the same family of distribution.

Furthermore, these past two-step procedures increase the potential for error by propagating uncertainties from the first step to the second stage of the estimation of dates. This new approach has already been explained in detail in different papers Cooley et al. Here, we briefly summarize the main principles and statistical differences compared with the older methods.

A new statistical approach: It consists in using the theory dedicated to extreme values because the largest lichen diameters belong to this category. MA To apply the generalized extreme value method GEV , measurements are needed of the largest lichen per boulder in a given geomorphic surface area. To implement the data, the strategy is to describe the largest lichen diameters by modelling the entire distribution of lichen size.

Maximum lichen measurements can be modelled by varying the distribution of GEV parameters as a function of moraine location and age. This function can be identified with a growth curve. Thus, each sample surface is characterised over time by letting the GEV location and shape parameters vary as a function of the age of the moraine and in space by fixing the scale parameter.

Based on this procedure, a Bayesian model is built; i. MCMC methods are a class of algorithms for sampling from probability distributions in our case we use the prior distribution based PT on constructing a Markov Chain. At each iteration, all the parameters GEV parameters and the SC parameters of the growth curve , are updated one-at-a-time until the best combination of parameters is NU found. This allows us to compute an empirical distribution for each parameter. In particular, the subsequent age distribution of each undated surface is obtained. Confidence intervals for the age of the MA undated moraine are computed from the mean and from the variance of previous age distributions.

Finally, to reduce errors in estimates, measurements corresponding to dated and undated surfaces are combined in the same data set and analysed together. ED To apply these methods, lichens Rhizocarpon Geographicum were measured on eight well-known PT dated surfaces in an area of ca.

Surfaces were dated using historical descriptions, aerial photographs available since , and personal communications from AC the Skaftafell Park staff. On dated surfaces, 50 boulders were randomly chosen. Only the surfaces on the side of boulders opposite the glacier were examined to limit the discrepancy effect of microtopography on lichen growth effects of wind, sun in relation to aspect. On each boulder, the longest axis of the biggest lichen was measured with an accuracy of 1 mm.

### Pré-publication

On eight surfaces, lichens were measured, i. Lichens that were not circular or flat were rejected to reduce risk of coalescence. The same sampling method was applied on the terminal moraines of the 13 selected glaciers.

When the terminal moraine was disaggregate, several moraine ridges were investigated to reduce the risk of dating error. In this way, lichens located on 29 moraine ridges were measured. SC Then the best-fitted slope of the size-frequency distribution versus the age of each dated surface NU provided the age of different features. Correlation between LIA glacial maximum dating and geomorphic and glaciological parameters ED To determine whether variations in dating were correlated with the geomorphic and glaciological PT parameters of the glacier, rank correlation coefficients were calculated.

Parameters were derived from a digital elevation model DEM of the region with an accuracy of 20 CE m. The DEM enabled us to calculate the following parameters for each glacier Table 1: ELAs were calculated using the toe-to-headwall altitude ratio THAR method that gives good results on small, geometrically regular glaciers with a normal distribution of areas and altitudes Porter, ; Osipov, Meierding and Murray and Locke found that ratios of 0. In this study a ratio of 0. The raw scores were converted into ranks, and the difference di between the ranks of each observation on the two variables was calculated.

If tied ranks exist, classic Pearson's correlation coefficient between ranks has to be used instead of this MA formula Myers and Well, The rank is an average of their positions in the ascending order of the values. Moraines corresponding to the maximum glacial advances were dated between A. These results reveal a high variability of glacier response time in SE Iceland, even PT though four groups of glaciers can be identified.

The second group is composed of five glaciers, with the LIA maximum dated to the beginning of the MA nineteenth century. PT and A.

## A new lichenometric dating curve for southeast iceland

No apparent AC relationship exists between these two glaciers regarding their location. The fourth group of glaciers reached their LIA maximum extent at the end of the nineteenth century. These results can be compared with previous results obtained using different approaches. Dates obtained by Evans et al. Although the Bayesian approach is more complex and time intensive, its application on a large SC sample of glaciers in the same area enabled us to propose confidence intervals associated with dates. It is important to notice that some MA glaciers might have known period of readvance after the date of maximal extent but not reached their maxima.

LIA maxima based on other lichenometric approaches CE Little Ice Age glacial maxima were also dated using previous lichenometric approaches. Although dating showed less difference than that obtained with the Bayesian approach, clear variability of glacier chronology exists. The size-frequency approach was also tested and showed higher variability between glaciers with dating ranging between A. Two parameters maximum altitude and altitude standard deviation showed very high correlations with the LIA glacial maximum 0.

A last parameter, the mean slope, which is directly linked RI with slope standard deviation, can also be taken into account 0. The others parameters, i. These results indicated that i in the case of glaciers at higher altitudes, the LIA maximum apparently MA occurred earlier than at glaciers at lower altitudes; ii in the case of glaciers with a major difference in altitude, the LIA maximum apparently occurred earlier than at glaciers with a slight difference in altitude; iii in the case of steeper glaciers, the LIA maximum apparently occurred earlier than in the ED case of less steep glaciers; and iv the geometry and the localization of the glaciers had minor impacts PT on the timing of the LIA glacial maximum extent.

Little Ice Age advances in the region occurred in or around the following decades: Results are also correlated with documentary records reviewed by Thorarinsson However the data are processed, if variations in size-age relationship over an area are not accounted for, the results will not be robust. The inconsistency of results and methods has led some authors to ignore lichenometric dating in Iceland in the study of the Little Ice Age for instance Grove, While the age of two contiguous moraines is well constrained between and through the identification of an aeolian layer that i shows the absence of tephra K deposited after the Katla volcano eruption between May and August and ii shows the presence of tephra layer K idem, eruption active between October and February ; the lichenometric analysis of thalli on one moraine and thallus on the other indicates a date of in one case and in the other, using several methods largest lichen, five largest lichens, size-frequency.

Thus, lichenometric analysis proposes an age to years younger that the date imposed by tephrochronology. Such a disparity, unquestionable due to tephrochronological evidence, arises even though the lichenometric techniques are apparently robust: The reason for the disparity is probably that lichens measured on boulders constituting the moraine are not the first generation ones. The fallacy of the assumption that the largest lichens on a surface have been there since the surface was exposed was pointed out by Joachimsen and Osborn et al.

However, the lichenometrical analysis proposes that the moraine dates from Evans et al. Lichenometry is a relative dating technique as the technique does not provide the time brackets tephrochronology does. The main reason being that it is impossible to ensure that lichens observed on the surface of blocks on moraines correspond to the very first generation, more so in environments where surface processes such as frost-shattering are active.

All ages are expressed in AD modified from Kirkbride, Lichenometry can then complement historical data by providing ages for instance for debris-flow events that were not recorded at the time they occurred, probably because they were not threatening at that the time of their release fig. The method has a limitation though, especially if a new event of a bigger magnitude totally covers the previous deposits. That is the case for debris flow no. Over short term periods, the inherent limitations of lichenometry such as lichen misidentification, concurrence on surfaces and mortality are not eliminated, but the problems are less with the younger ages: Debris flow path ID; 2.

Historical record of debris-flow occurrrence in the given path; 4. Lichenometric dating of debris-flow occurrence in the given path. Considered snow-avalanche path; 2. Boulders deposited by snow avalanches since ; 3. Boulders covered with different lichen species and mosses, probably deposited previous to However, work in Iceland shows that the ecological and environmental aspects of lichens impede the quality of the results, with researchers seeking at gaining more accurate dates to understand and better explain the dynamic of different geomorphologic processes.

Most authors having worked in Iceland were aware of the rough Icelandic nature, and aimed at finding a proxy that could date landforms they observed, lacking all source of accurate dating. They all attempted to limit the potential source of lichen growth rate variations that led to dating errors, for example by forcing thresholds in size measurements Thompson and Jones, , or selecting the face of boulders they sample Evans et al.

The recent shift of the debate toward methods did not improve lichen use for dating landforms, and occulted the biology of lichens. Confronting the results from several studies conducted in common places SE Iceland for instance show that lichenometry is a relevant relative dating technique, but not that an efficient absolute dating tool.

This point is made especially important when the different developmental stages of lichen growth and the different growth rates are properly considered i. A further serious issue is the recognition and discrimination of certain lichen species in the field. Due to the overlap with more accurate historical data during these years, lichenometry loses interest for the most recent years. Arctic and Alpine Research, 20, American Antiquity, 74, publication en ligne.

Journal of Glaciology, 36, Geografiska Annaler, 83, PhD thesis, University of Edinburgh, p. Geografiska Annaler, 86, Arctic, Antarctic and Alpine Research, 36, Geografiska Annaler, 91, Journal of Quaternary Science, 22, The Geographical Journal, , Arctic and Alpine Research, 19, Environmental change in Iceland: Kluwer Academic Publishers, Dordrecht, The Holocene, 3, Arctic and Alpine Research, 30, Boreas , 33, PhD thesis, University of Paris 1, p. Debris-flow hazards and mitigation: Geografiska Annaler, 87, Geografiska Annaler, 92, Earth Surface Processes and Landforms, 2, Quaternary Science Reviews, 18, Geografiska Annaler, 92, — Bulletin of Volcanology, 46, Journal of Quaternary Science, 15, Atuagkat, Rhodos and Danish Polar Center.

Geografisk Tidsskrift-Danish Journal of Geography, , Transactions of the Royal Society of Edinburgh: Earth Sciences, 01, Arctic and Alpine Research 16, 2, Progress in Physical Geography, 9, Joachimsen M — Does the size of lichen thalli really constitute a valid measure for dating glacial deposits? Arctic and Alpine Research, 5, Climatic Change, 48, Quaternary Research, 70, Eds , Neige et glace de montagne, reconstitution, dynamique, pratiques.

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