Radiocarbon calibration

Radiocarbon dating is one of the most reliable and well-established methods for dating the Holocene and Late Pleistocene. Natural radiocarbon or ¹⁴C is produced in the atmosphere by the interaction of the secondary neutron flux from cosmic rays with atmospheric ¹⁴N. Following its production, ¹⁴C is oxidised to produce ¹⁴CO₂, which is then transferred to other carbon reservoirs, such as the biosphere and oceans, via photosynthesis and air-sea exchange of CO₂, respectively. Living organisms take up radiocarbon through the food chain and via metabolic processes. When an organism dies, the original ¹⁴C concentration of the organism starts to decrease by radioactive decay. Radiocarbon age of that organism is determined by measuring its residual ¹⁴C concentration and by assuming a constant level of atmospheric ¹⁴C through time. However, not long after the establishment of the radiocarbon dating method (in the late 1940s), it was recognised that the ¹⁴C concentration of the atmosphere in the past had not been constant.

Variations in atmospheric ¹⁴C concentrations are mainly due to variations in the rate of radiocarbon production in the atmosphere, caused by changes in the Earth's magnetic field and variability in solar activity, and changes in the carbon cycle. The result is that radiocarbon and calendar ages are not identical, and the radiocarbon ages have to be converted to calendar ages using a calibration curve, which describes the atmospheric ¹⁴C concentration in the past measured in precisely and independently dated materials. The current internationally-ratified calibration curve for terrestrial samples (e.g., woods, charcoals and macro-fossils) from the Northern Hemisphere is IntCal04, which covers the past 26,000 calendar years (cal yr) (Fig. 1). This curve is based on dendrochronologically-dated tree rings for the period 0-12,400 cal yr before present (BP, with 0 BP being AD 1950). For the remaining period 12,400-26,000 cal yr BP, the curve is derived from independently dated marine samples such as foraminifera and corals. A new internationally-ratified calibration curve (IntCal09) covering the whole radiocarbon timescale (~50,000 cal yr) is being prepared by the IntCal Working Group.

There is a small difference in the natural atmospheric ¹⁴C concentration between the Northern and Southern Hemispheres. This value, known as the inter-hemispheric ¹⁴C offset, is ~40 yr but varies with time. The Southern Hemisphere has a larger surface ocean area than the Northern Hemisphere (~60% compared to ~40%) with greater wind velocities. As a result, more ¹⁴C in the southern troposphere is transported to the oceans through air-sea exchange of CO₂ and more ¹⁴C-depleted CO₂ from the oceans (see discussion later) is transported to the southern troposphere. Natural ¹⁴C levels in the southern troposphere are therefore usually lower than those in the northern troposphere, and the radiocarbon ages of terrestrial materials in the Southern Hemisphere for a particular period of time are usually older than those in the Northern Hemisphere. The current internationally-ratified radiocarbon calibration curve for terrestrial samples from the Southern Hemisphere is SHCal04. This curve covers the past 11,000 cal yr, which is based on the dendrochronologically-dated tree rings for the last millennium and on model ages for the remaining period.

The deep ocean waters are isolated from the atmosphere for long periods of time (the residence time of carbon in the deep ocean is ~800 yr). During this time the ¹⁴C content of deep ocean waters is depleted by radioactive decay. The surface ocean exchanges with the atmosphere and the ¹⁴C-depleted deep ocean and has a ¹⁴C level intermediate between these two reservoirs. Marine samples living in the surface ocean (e.g., shells, corals and planktonic foraminifera), therefore appear older than contemporaneous terrestrial samples. An age offset between surface ocean and terrestrial samples is known as the marine reservoir age (R), which is ~400 yr on average (Fig. 1). To calibrate a radiocarbon date for a surface ocean sample, one can use IntCal04 curve with a known value of R. Alternatively, one can use the current internationally-ratified marine calibration curve Marine04 (Fig. 1) with a known value of regional offset from the global marine model age for that sample, defined as ΔR. The latter method is generally preferred. For age calibration, ΔR and R of a location are usually assumed constant through time. However, recent studies have reported variations of these values of several hundreds to a couple of thousands of years for several regions during Late Glacial and the Holocene. These variations are due to changes in ocean circulation and the carbon cycles associated with climatic change. Temporal variations in ΔR and R values may therefore need considering when calibrating ¹⁴C ages of marine samples.

A large amount of ¹⁴C was artificially produced when hundreds of nuclear test weapons were detonated in the atmosphere, mostly in the Northern Hemisphere, in the late 1950s and early 1960s. Nuclear bomb blasts produced intense fluxes of thermal neutrons, which in turn interacted with atmospheric ¹⁴N to form ¹⁴C. As a result, the atmospheric ¹⁴C level reached a maximum in the Northern Hemisphere in 1963-1964, at almost double its pre-bomb level. Since then, the atmospheric ¹⁴C concentration has been decreasing due to rapid exchange between the atmosphere and other carbon reservoirs (mainly the biosphere and oceans). The main feature of atmospheric bomb ¹⁴C is that there are significantly different atmospheric ¹⁴C levels between consecutive years during the bomb period, offering the possibility of dating terrestrial samples formed after 1950 by ¹⁴C with a resolution of one to a few years. This dating method is usually called bomb-pulse dating (for the interval from 1950 onwards) to differentiate from traditional radiocarbon dating (for the period from 1950 backwards). Four zonal data sets of tropospheric bomb ¹⁴C data at (mostly) monthly resolution (three in the Northern Hemisphere and one in the Southern Hemisphere) are available for use in bomb-pulse ¹⁴C dating (Figs. 2 and 3).

Calibration of ¹⁴C ages is usually undertaken using a computer program. Several calibration programs are available on-line. These include CALIB and CaliBomb (http://radiocarbon.pa.qub.ac.uk/), Oxcal (http://c14.arch.ox.ac.uk/embed.php?File=oxcal.html), and CalPal (http://www.calpal.de/). Additional calibration programs can be found on the Radiocarbon journal website at http://www.radiocarbon.org/Info/index.html. Examples of radiocarbon calibration for the traditional radiocarbon dating and the bomb-pulse dating are shown in Figs. 4 and 5, respectively.


Glossary

• The Holocene: the period covering the last 11,500 yr.
• Late Pleistocene: the period from ~126,000 to 11,500 yr ago.
• Dendrochronology: is the scientific method of dating based on the analysis of patterns of tree rings.

• Damon, P.E., Sonett, C.P., (1991). Solar and terrestrial components of the atmospheric ¹⁴C variation spectrum. In Sonett, C.P., Giampapa, M.S., Matthews, M.S., editors, The Sun in Time. University of Arizona Press, Tucson, p. 360-388.
• Hua, Q., (2009). Radiocarbon: A chronological tool for the recent past. Quaternary Geochronology, 4, 378-390, doi:10.1016/j.quageo.2009.03.006.
• Hua, Q., Barbetti, M., (2004). Review of tropospheric bomb radiocarbon data for carbon cycle modelling and age calibration purposes. Radiocarbon 46, 1273-1298.
• Hughen, K.A., Baillie, M.G.L., Bard, E., Bayliss, A., Beck, J.W., Bertrand, C., Blackwell, P.G., Buck, C.E., Burr, G., Cutler, K.B., Damon, P.E., Edwards, R.L., Fairbanks, R.G., Friedrich, M., Guilderson, T.P., Kromer, B., McCormac, F.G., Manning, S., Bronk Ramsey, C., Reimer, P.J., Reimer, R.W., Remmele, S., Southon, J.R., Stuiver, M., Talamo, S., Taylor, F.W., van der Plicht, J., Weyhenmeyer, C.E., (2004). Marine04 Marine radiocarbon age calibration, 0-26 cal kyr BP. Radiocarbon, 46, 1059-1086.
• McCormac, F.G., Hogg, A.G., Blackwell, P.G., Buck, C.E., Higham, T.F.G., Reimer, P.J., (2004). SHCal04 Southern Hemisphere calibration 0–11.0 cal kyr BP. Radiocarbon, 46, 1087-1092.
• Reimer, P.J., Baillie, M.G.L., Bard, E., Bayliss, A., Beck, J.W., Bertrand, C.J.H., Blackwell, P.G., Buck, C.E., Burr, G.S., Cutler, K.B., Damon, P.E., Edwards, R.L., Fairbanks, R.G., Friedrich, M., Guilderson, T.P., Hogg, A.G., Hughen, K.A., Kromer, B., McCormac, G., Manning, S., Bronk Ramsey, C., Reimer, R.W., Remmele, S., Southon, J.R., Stuiver, M., Talamo, S., Taylor, F.W., van der Plicht, J., Weyhenmeyer, C.E., (2004). IntCal04 Terrestrial radiocarbon age calibration, 0-26 cal kyr BP. Radiocarbon, 46, 1029–1058.