Examining the Inherent Variability in ΔR: New Methods of Presenting ΔR Values and Implications for MRE Studies

Abstract

Currently, there is significant ongoing research into the temporal and spatial variability of marine radiocarbon reservoir effects (MREs) through quantification of ΔR values. In turn, MRE studies often use large changes in ΔR values as proxies for changes in ocean circulation. ΔR values are published in a variety of formats with variations in how the errors on these values are calculated, making it difficult to identify trends or to compare values, unless the method of calculating the ΔR is explicitly described or all of the data are made available in the publication. This paper demonstrates the large range in ΔR values (+34 to -122) that can be obtained from a single, secure archaeological context when using the multiple paired sample approach, despite the fact that the terrestrial entities were of statistically indistinguishable 14C ages, as were the marine samples. This demonstrates the inherent variability in the ΔR calculations themselves and we propose that, together with calculation of mean ΔR, the distribution of ΔR values should be displayed, e.g. as histograms in order to illustrate the full data range. This spread is only apparent when employing a multiple paired sample approach as the uncertainty derived on a single pair of samples, taking account only of the errors on the individual 14C ages, will never truly represent the overall variability in ΔR that results from the intrinsic variability in the population of 14C ages in samples that might have been used. Consequently, ΔR values and the associated uncertainty calculated from single pairs should be treated with some caution. We propose that, where possible, when using paired archaeological samples, that a multiple paired approach should be employed as it will test the context security of the material used in the ΔR calculations. When summarizing the values by the weighted average, we also propose that the standard error for predicted values should be employed as this will fully encompass the uncertainty of a future ΔR calculation, using different samples for a similar time and location. Finally, we encourage future publishing of ΔR values using the histogram format, making all of the data available. This will help ensure that ΔR values are comparable across the literature and should provide a framework for standardization of publication methods.