Statistical age determination of tree rings

Abstract

Dendrochronology, the study of annual rings formed by trees and woody plants, has important applications in research of climate and environmental phenomena of the past. Since its inception in the late 19 th century, dendrochronology has not had a way to quantify uncertainty about the years assigned to each ring (dating). There are, however, many woody species and sites where it is difficult or impossible to delimit annual ring boundaries and verify them with crossdating, especially in the lowland tropics. Rather than ignoring dating uncertainty or discarding such samples as useless, we present for the first time a probabilistic approach to assign expected ages with a confidence interval. It is proven that the cumulative age in a tree-ring time series advances by an amount equal to the probability that a putative growth boundary is truly annual. Confidence curves for the tree stem radius as a function of uncertain ages are determined. A sensitivity analysis shows the effect of uncertainty of the probability that a recognizable boundary is annual, as well as of the number of expected missing boundaries. Furthermore, we derive a probabilistic version of the mean sensitivity of a dendrochronological time series, which quantifies a tree's sensitivity to environmental variation over time, as well as probabilistic versions of the autocorrelation and process standard deviation. A computer code in Mathematica is provided, with sample input files, as supporting information. Further research is necessary to analyze frequency patterns of false and missing boundaries for different species and sites.

Adding Tree Rings to North America's National Forest Inventories: An Essential Tool to Guide Drawdown of Atmospheric CO2

“…The strength of correlations among tree-ring time series from forest inventory trees tends to be lower than the correlations among time series from trees at the more climate-limited locations usually selected by dendrochronologists (Girardin et al 2021a ), leaving potential uncertainty about year assignments. Strict adherence to traditional criteria for precise year assignments could lead to the rejection of many samples, limiting (and biasing) inference from NFI-based tree-ring data (Ricker et al 2020 ). A mitigating influence is that missing rings are uncommon in trees with the modest interannual ring-width variability that gives rise to low interseries correlation and therefore higher growth ring dating uncertainty (St. George et al 2013 ), because these trees are less climate limited.…”

Relationships Among Biomass, Carbon, and Microfibril Angle in Young <i>Shorea</i> spp. (Dipterocarpaceae) in Indonesia

“…After the cores were collected wood densities were calculated in the laboratory using ASTM standard. The cylindrical core samples were cut from the pith to the outer xylem rings into segments of approximately 1 cm, and these were weighted again until a constant value was achieved (Ricker et al 2020). This procedure was used to obtain an estimate of average wood density, which was calculated using the following formula: where: X is the sample density obtained from core measurements, a is the balance obtained when the weighing basket was empty, b is the balance obtained when the weighing basket contained the sample, c is the mass of the dry cores, and ρ is the density of water equal to 1000 kg per cubic meter (Scandinavian Pulp, Paper and Board Testing Committee 1995).…”