How Smooth Should Curves Be for Calibrating Radiocarbon Ages

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

Calibration · Geometry · Histogram · Inverse · Mineralogy · Peat · Physics · Radiocarbon dating · Smoothing · Standard deviation · Statistics · Archaeology and ancient environmental studies · Geology and Paleoclimatology Research · Mathematics · Pacific and Southeast Asian Studies · Geology · Paleontology

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