Shape analysis of cumulative probability density function of radiocarbon dates set in the study of climate change in the Late Glacial and Holocene

We report on a statistical analysis of a large set of radiocarbon dates for reconstruction of pateoclimate. Probability density functions were constructed by summing the probability distributions of individual ¹⁴C dates. Our analysis was based on 2 assumptions: 1) The amount of organic matter in sediments depends on paleogeographical conditions; 2) The number of ¹⁴C-dated samples is proportional to the amount of organic matter deposited in sediments in the examined time intervals. We quantified how many dates are required to give statistically reliable results. As an example, 785 peat dates from Poland were selected. The dates encompassed the Holocene and Late Glacial period. All dates came from the Gliwice Radiocarbon Laboratory. Results were compared with other paleoenvironmental records. Detailed analysis of the frequency distributions showed that preferential sampling plays an important part in the shape determination. The general rule to take samples from locations where visible changes of sedimentation are apparent (e.g. from the top and the bottom of the peat layer) results in narrow peaks in the probability density function near the limits of the Holocene subdivision.