Inverse modeling of lichen growth curves and implications for lichenometric dating

Abstract

Lichenometric dating represents a quick and affordable surface exposure dating method that has been widely used to provide a minimum age constraint on tectonic and geomorphic landscape changes as well as buildings and anthropogenic landscape changes in various settings during the late Holocene. Despite its widespread usage, this method has several limitations. Major problems relate to the sampling of lichen population on any given rock surface and the modeling of growth curves. In order to overcome these issues, it has been suggested to subdivide the rock surface into some areas and measure the largest lichen thallus on each one. However, how to express the data in terms of a probability distribution function and link it to an age of last exposure of the rock surface are still a matter of debate. Here, we propose a novel approach to the modeling of lichen growth curves by treating lichen growth as a continuous-time Markov process with a time-varying rate and additive Brownian noise. Given the growth rates, the probability distribution of the lichen population at any time can then be obtained by solving the Fokker–Planck equation. This method is illustrated using a dataset from the Huashan area of eastern China, which consists of measurements of the largest thalli on 12 rock surfaces of known age. We first build up the probability distribution of the lichen population for each rock surface based on extreme value theory and then use these to optimize the growth curve by minimizing the Jensen–Shannon divergence. A new method is also proposed to use the growth curve to map a sample of size data from an undated rock surface to the calendar age domain so as to yield a fully probabilistic estimate of the exposure age of the undated rock surface rather than a point estimate. • We propose a novel approach to lichenometric dating. • Lichen growth is modeled using a continuous-time Markov process. • Extreme-value theory is used to model the size distribution. • A MATLAB package for implementing the model is provided.