Mathematical model of the radial cross section of tree rings

Abstract

A mathematical model of tree rings in the form of an interference pattern is presented. The model allows retrospective reconstruction of continuous radial growth of a tree during the entire vegetation season. The radial dependence of the wood density is considered as a certain oscillation whose phase is a strictly increasing function of radius. The radial growth is defined as a monotonic function of time, inverse with respect to the phase. Algorithms for model analysis are based on the condition of dispersion causality. Experimental results are discussed.