A Robust Deterministic Model Describing the Bomb Radiocarbon Signal for Use in Fish Age Validation

Abstract

AbstractThe bomb radiocarbon chronometer has become a standard tool for assessing the accuracy of otolith‐based fish age estimates. Use of the chronometer depends upon the increase in 14C that occurred due to the atmospheric testing of nuclear weapons in the middle of the 20th century. In previous analyses, a variety of ad hoc methods have been used to compare test chronologies with reference chronologies. This paper proposes a deterministic coupled‐functions model that describes bomb radiocarbon chronologies and standardizes and facilitates comparisons within and across species. In this model, a Gaussian pulse of radiocarbon over time is assumed, and dispersion and dilution are described by continuous exponential decay. The model simplifies to the product of a cumulative normal function and an exponential function; despite its simplicity, the model approximates the observed changes in oceanic radiocarbon quite well. It also allows for statistical testing of the timing of increase between different time series and thus permits quantitative aging validation as well as analysis of geographical differences in the timing of the bomb radiocarbon signal. Estimated model parameters describe the timing of the onset and temporal midpoint of the bomb‐related increase in 14C and the rate of 14C dispersion or dilution, which corresponds to the observed rate of decline during the postbomb period. Nine published chronologies are used to demonstrate the model and compare it with other published methods of summarizing bomb radiocarbon data for age validation purposes.