Spatio-temporal Analysis of Extreme Values from Lichenometric Studies
and their Relationships to Climate

Daniel Cooley and Philippe Naveau
Dept of Applied Mathematics, University of Colorado,
Boulder, CO 80309-0526  USA
Daniel.Cooley@colorado.edu

Vincent Jomelli and Antoine Rabate
Laboratoire de Geogrphie Physique
CNRS-Meudon-Bellevue, France

Abstract.  Arctic and alpine regions are very important to understand the effects of climate change and other geophysical phenomena.  The lack of relevant time series in such environments gave rise to lichenometry, the study of lichen growth for the purpose of dating rock features such as glacial moraines.  Although lichenometry has been practiced for years, it has lacked a solid statistical basis.  The statistical challenge is to propose a spatio-temporal model for extreme lichen diameters and to investigate the spatial structure between different glaciers with different environmental factors.  We develop a spatio-temporal bivariate model (lichen sizes and their associated dates) based on extreme value theory.  The statistical framework is a random effect model for the Generalized Extreme Value (GEV) distribution whose parameters vary in function geographical location of the site and the temporal effects.

In addition to providing for the first time a probabilistic framework to the field of lichenometry, the flexibility of our statistical model allows us to integrate the error associated with the dating process (i.e. estimating the age of each moraine). To validate our statistical methodology, simulated examples were analyzed and tested. Finally, the proposed techniques are applied to 14 different glaciers in Bolivia.

Keywords:  Climate Change, Maximums, Extreme Value Theory