# Reporting of Results

δ^{13}C correction

^{14}C units

Measurement uncertainty

The ^{14}C concentration of the sample is calculated by comparing the ^{14}C/^{12}C ratio of each sample, determined by AMS, with those of an international standard (NIST Oxalic Acid standard 2 - OxII). To calculate the conventional radiocarbon ages and/or calendar ages the measured data have to be corrected as described below:

### δ^{13}C correction

To account for mass-dependent isotopic fractionation arising from biochemical processes (e.g. photosynthesis), ^{14}C results are corrected (normalized) to a constant δ^{13}C value of -25 ‰ PDB as is the norm. – δ^{13}C, given in ‰ PDB, is the relative difference in the ^{13}C/^{12}C ratio of the sample and of an international standard. The reference material (PDB) is the carbonate fossil *Bellemnitella americana* from the Pee Dee formation in South Carolina. – This normalization allows the comparison of ^{14}C ages from different sample matrials regardless of the biogeochemical fractionation they have experienced (see details in Stuiver and Polach).

The δ^{13}C values we use to correct for isotopic fractionation are currently measured by the AMS system, comparing the ^{13}C/^{12}C ratio of the samples to that of the NIST OxII standard which are measured simultaneously to the ^{14}C/^{12}C ratios.

^{14}C units

Radiocarbon concentrations are reported in **percent Modern Carbon** (pMC) with +/- 1-σ measurement uncertainty. 100 pMC is defined as the radiocarbon concentration of the atmosphere in 1950 AD (details can be found in: Stuiver and Polach).

For geochemicals studies we additionally report **∆ ^{14}C values**, the

^{14}C deviation in parts per thousand (‰) of the sample from that of the absolute, decay corrected standard.

The **conventional radiocarbon** age is given in years Before Present (BP). This age is not comparable to a historical age since it comprises the (incorrect) 'Libby' half-life of 5568 years (instead of 5730 years), is corrected to 1950 AD as 0 years BP, and includes variations in the atmospheric ^{14}C concentration.

Conventional radiocarbon ages are converted into **calendar ages **(cal BP, cal AD/BC) by calibration, i.e. comparison of the conventional age with an international calibration data set. A calibration is necessary since the atmospheric ^{14}C concentration was not constant, a pre-requisit of the radiocarbon method, but varied due to natural and anthropogenic changes in ^{14}C production. The calibration data set for terrestrial material is based on tree rings (0-12,400 cal BP) and on ^{14}C data of foraminifera in varved sediments and uranium/thorium-dated corals (12,400-26,000 cal BP; INTCAL04, Reimer et al., 2004).

Probability distribution of the radiocarbon age (Y-axis) and |
These data are included in calibration programs such as CALIB 5.0 by Stuiver et al., 2005, which we use to calculate historical ages. Calendar ages can only be determined for the time previous to the release of ^{14}C from aboveground nuclear weapon testing (i.e. pre-1950). The calibration of post-1950 data is discussed by Reimer et al. 2004 (Radiocarbon 46, 1299-1304) and the program CALIBomb is available.
The report for our costumers includes a translation of the radiocarbon age into a calendar age with a graphic showing the probability distribution of the sample's true age (see figure). |

### Measurement uncertainty

For determination of the measurement uncertainty (standard deviation, s), both the counting statistics of the ^{14}C measurement and the variability of the 8–12 measuring interval results that, together make up one measurement are observed. The larger of the two is adopted as the ± 1 s measurement uncertainty, yielding the confidence interval in which the true value is to be expected with 68.3 % probability.

The precision of radiocarbon dates for recent samples (younger than 2000 years) of “normal” sample size (1-2 mg of carbon) is better than 0.5% (typically 0.3 - 0.4%) which equals +/-40 years (25 - 30 years) for the 1-σ statistical uncertainty of the measured age. The precision decreases with increasing sample age.

The accuracy of the results is tested with the frequent analysis of standard materials and laboratory intercalibrations.