How Smooth Should Curves Be for Calibrating Radiocarbon Ages?

Abstract

We show that smoothed versions of the high-resolution calibration curve should be used when 14C ages are calibrated with large (> ~30 14C yr) measurement errors (represented by standard deviation sigma-m) or are mixtures of elements of variable age (natural sample error with standard deviation sigma-n). The degree of smoothing should agree with the standard deviation of total sample error, sigma-1 the square root of the quadratic sum of sigma-m and sigma-n. However, in most cases, sigma-1 is not well known, especially due to difficulties in quantifying sigma-n. We present an inverse method that gives a measure of mean sigma-1 for different materials that are widely used in (conventional) 14C dating. Calculations with large (>100) data sets of wood, charcoal, ombrotrophic peat and minerotrophic peat/gyttja samples indicate that sigma-1 of such materials is generally much larger than previously assumed, mainly because of large values of sigma-n. This means that particularly in organic deposits, strongly smoothed calibration curves should be used where medium-term 14C variations (wiggles) are completely straightened. This has especially major consequences for calibrating 14C histograms for natural 14C variations. We conclude that 14C histograms consisting of samples of organic deposits do not require correction for medium-term 14C variations and that uncalibrated 14C histograms need not be as suspect as is usually believed.