Methods and codes for reservoir–atmosphere 14C age offset calculations

• Reservoir 14C age offsets are fundamental for carbon cycle and calibration purposes.
• The various ways to calculate reservoir 14C age offsets are detailed.
• The uncalibration process to properly calculate reservoir age offsets given pairs of 14C and calendar ages is described.
• R codes for reservoir 14C age offset calculations are provided to the community.
• A case study investigating dead carbon fraction in speleothem is presented.

Reservoir 14C age offsets are invaluable tracers for past changes in carbon cycle and oceanic circulation. Reconstruction of reservoir age offsets with time is also required for calibration purposes (reconstruction of atmospheric calibration curve, calibration of non-atmospheric radiocarbon ages). Thus, properly propagating the various uncertainties linked to reservoir age offset is important for proper interpretation. However, approaches for reservoir age offset calculation – especially when considering pairs of reservoir-derived 14C and calendar ages – are usually not detailed and inadequate for proper propagation of uncertainties. Here, the various ways to properly calculate reservoir age offsets are described with a focus on a new approach when considering pairs of 14C and calendar ages. This approach maps the calendar age distribution onto the 14C time scale prior to reservoir age offset calculation – the “uncalibration-convolution process”. R codes computing reservoir age offsets based on available data are presented. Finally, a case study focusing on the reconstruction of the speleothem-atmosphere 14C age offsets of speleothem 14C data used in the latest release of the atmospheric calibration curve is discussed.