Title: 		A General Probability Model for Analyzing 
			Lichens Growth in the Alps

Authors: 		Philippe Naveau (1,3), Vincent Jomelli (2), 
			Dan Cooley (3), Kenji Osé (2) Etienne Cossart(4)

Affiliation:	(1) LSCE-IPSL, Gif-sur-Yvette, (2) CNRS UMR 85 91, Meudon, 
			(3) Colorado University, Boulder USA, (4) CNRS UMR 8586, Paris

Abstract:
Lichenometry, a dating method for periglacial and glacial landforms, is especially well suited for arctic and alpine regions. In classical lichenometry studies, the largest lichen diameters are measured in different glacial basins. But traditional averaging methods are used to analyze these maxima and to compute uncertainty measures like confidence intervals for the growth curve. Unfortunately, all averaging methods are closely related to the normal distribution but maxima do not follow such a distribution. To solve this important discrepancy, we propose a novel way to model the lichen diameters distribution. Our strategy is to implement the probabilistic theory of extreme values to the study of the largest lichen diameters from different moraines in the French Alps. The advantage of this approach over classical statistical lichenometry analyzes is that the uncertainties associated with studying the largest lichen diameters is fully taken into account through identification of the distribution of these largest diameters. In addition to providing a probabilistic framework, the flexibility of our statistical model allows to integrate the error associated with the dating process. To validate our statistical methodology, simulated examples were analyzed and tested. Finally, the proposed techniques are applied to different sites in the massif des Ecrins , which allow us to date the maximal glacial advance, and to estimate paleo ELA during the Little Ice Age. 

Keywords 1: Lichenometry 2: extreme value theory 3: Little Ice Age 4: Treatment of maxima