Estimating uncertainty in pooled stable isotope time-series from tree-rings

Abstract

Stable carbon isotope time-series (δ13C) from tree-rings are capable of providing valuable palaeoclimatic information, but analysis of individual tree-rings is time consuming and expensive. Pooling material from several tree-rings prior to isotopic analysis reduces costs, but does not allow the magnitude of uncertainty in the mean δ13C chronology to be calculated unless the pool is broken and each tree-ring measured individually at regular intervals. Here we use a comparison of pooled and mean individual (the arithmetic mean of isotopic data from tree series measured individually) δ13C records between AD 1650 and 2007, comprising cores from 21 Scots pine (Pinus sylvestris L.) trees growing in the western Highlands of Scotland. The aim is to determine whether the true error structure of the time series is better captured by using the overall mean error estimate for the entire time series or by linear interpolation between the equally spaced measurements. We conclude that where autocorrelation exists within the error structure of a chronology, annual estimates of 95% confidence intervals, developed through linear interpolation at 5-year or 10-year intervals, are preferable to using the overall mean uncertainty. The method outlined increases the viability of pooled δ13C records for palaeoclimatic research by retaining error structure whilst reducing analytical time and costs. The method is applied here using tree-ring data, but could theoretically be applied to any well-replicated time-series.