Modeling Uncertainties in Lichenometry Studies

• Published in: Arctic, antarctic, and alpine research Vol. 39; no. 2; pp. 277 - 285
• Main Authors: Naveau, Philippe, Jomelli, Vincent, Cooley, Daniel, Delphine, Grancher, Rabatel, Antoine
• Format: Journal Article
• Language: English
• Published: UCB 450, University of Colorado, Boulder, Colorado 80309-0450, U.S.A The Institute of Arctic and Alpine Research 01.05.2007; Taylor & Francis; Institute of Arctic and Alpine Research; University of Colorado at Boulder, Institute of Arctic and Alpine Research
• Subjects: Confidence interval; Earth Sciences; Glacial landforms; Glaciers; Glaciology; Lichenometry; Lichens; Mathematical independent variables; Moraines; Parametric models; Research s; Sciences of the Universe; Statistical models; Statistics
• ISSN: 1523-0430; 1938-4246
• DOI: 10.1657/1523-0430(2007)39[277:MUILS]2.0.CO;2

To date glacial and periglacial landforms, lichenometry is a valuable method but, to improve efficiency, the estimated surface dates derived from traditional methods need to be more accurate. In other words, the statistical uncertainty associated with inferred dates has to be reduced. How to perform such a reduction is the main question that we will address in this paper. An interdisciplinary approach (lichenometry and statistics) allows reduction in the main sources of uncertainty: lichen diameters and their associated ages. Around 2600 lichen measurements collected on moraines from the Charquini glacier in Bolivia (Cordillera Real) are used to illustrate the advantages of our approach over past studies. As for any statistical estimation procedure, the error analysis in lichenometry is directly linked to the type of observations and the statistical model used to represent accurately these data. The attribute of lichenometry studies is that the measurements are not averages but maxima; only the largest lichen diameters provide information about the surface ages. To take this characteristic into account, we propose a novel statistical way to model maximum lichen diameters. Our model, based on the extreme value theory, allows us to compute small confidence intervals for the inferred surface ages. In addition, it offers three other advantages: (1) a global statistical model, as all our data (dated surfaces and all lichen maximum diameters) are represented with a unique function; (2) a mathematical framework within which the maximum lichen distribution is derived from a statistical theory; and (3) flexibility, as different types of growing curves can be investigated.