How smooth should curves be for calibrating radiocarbon ages?

We show that smoothed versions of the high-resolution calibration curves should be used when ¹⁴C ages are calibrated with large (>~30 ¹⁴C yr) measurement errors (represented by standard deviation σ_m) or are mixtures of elements of variable age (natural sample error with standard deviation σ_n). The degree of smoothing should agree with the standard deviation of total sample error, σ_t, the square root of the quadratic sum of σ_m and σ_n. However, in most cases, σ_t is not well known, especially due to difficulties in quantifying σ_n. We present an inverse method that gives a measure of mean σ_t 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 σ_t of such materials is generally much larger than previously assumed, mainly because of large values of σ_n. This means that particularly in organic deposits, strongly smoothed calibration curves should be used where medium-term ¹⁴C variations (wiggles) are completely straightened. -from Authors