Least-Squares Fitting a Smooth Curve to Radiocarbon Calibration Data

F. B. Knox
900 Ohariu Valley Road, R.D., Johnsonville, New Zealand

and

B. G. McFadgen
Conservation Sciences Centre, Department of Conservation, P.O. Box 10420, Wellington New Zealand

ABSTRACT. We Fourier transformed and filtered calibration curve data to compensate for the averaging effect of radiocarbon-dating sets of adjacent tree rings. A Wiener Filter was also applied to minimize the effects of the counting errors of the dates on the resulting calibration curve and to produce a least-squares curve through the data. The method is illustrated using a short 14C-dated tree-ring sequence from New Zealand to produce a calibration curve at yearly intervals for New Zealand matai (Prumnopitys taxifolia). The resulting curve has a nominal standard error of 10 3 yr, which is ca. half the average standard error of the original raw data.

[Radiocarbon Volume 39, Number 2, 1997]