Introduction
The calculation of the radiocarbon age of the sample assumes that the specific
activity of the 14C in the atmospheric CO2 has been
constant. However, early in the history of radiocarbon dating it was
recognized atmospheric 14C was not constant (de Vries, 1958).
A calibration dataset is necessary to convert conventional radiocarbon ages
into calibrated years (cal yr). By measuring the radiocarbon age of tree rings
of known or other independently dated samples it is possible to construct
calibration datasets. The need for a consensus radiocarbon calibration
dataset led to the first internaltionally agreed upon calibration in 1982
(Klein et al., 1982). Since that time the calibration datasets have continued
to be extended and improved. The IntCal working group established a set of
criteria for calibration datasets (Reimer et al. 2002). The current
calibration datasets including IntCal04, Marine04, and SHCal04 have been
presented for ratification at the 18th International Radiocarbon Conference
and are recommended for general use until further notice (Reimer et al., 2004).
These datasets are described in Reimer et al. 2004, Hughen et al. 2004, and
McCormac et al. 2004 and summarized in Section 2. The single year dataset
UWSY98 (Stuiver et al 1998) is also still in use for short-lived samples
350 14C BP.
For most non-marine radiocarbon samples from the Northern Hemisphere, the
IntCal04 curve is the preferred choice.
For short-lived (< 10 year), high precision samples (σ< 30 yr)
younger than 350 14C yr BP, the single year calibration
curve may be used for higher time resolution comparisons
although a moving average of 2 to 3 years is recommended to reduce
the noise and hence the number of cal ranges. For Southern Hemisphere
samples SHCal04 is available back to 11,000 cal BP (McCormac et al., 2004).
For marine samples such as shells, corals, fish etc. the Marine04 curve should
be used. Since this dataset represents the "global" ocean, no marine reservoir
correction should be made to the sample radiocarbon age prior to calibration,
however a regional difference ΔR should be input as discussed in
Section 2D. Age calibration of samples composed of both marine and terrestrial
carbon is discussed in Section 2E. Post-AD 1950 samples cannot be calibrated
with CALIB. A calibration program for post-nuclear testing samples is
available at http://www.calib.org
Ideally, before calibrating a radiocarbon age, the age should be adjusted
for the laboratory systematic offset if any. Although international
calibration efforts point towards the possibility of laboratory
offsets (for summary, see Scott et al., 1998), specific laboratories
have not been identified. The adjustment for any systematic offset
is not incorporated in this program.
The standard deviation reported with a radiocarbon age may be
based on count rate statistics only. The user must decide whether
to use the quoted laboratory error, or increase the quoted error
to account for other sources of variance by either applying a
lab error multiplier k or adding variance f² (yr²).
Thus the sample standard deviation σ becomes
either k·σ or (σ² + f²)½.
The calibration curve sigma σc is automatically added in
both cases to give the total sigma of the radiocarbon age prior
to its cal age transformation.
A lab error multiplier is based on the overall reproducibility
and should be supplied by the individual laboratory. The added
variance option can be used by calculating the f value from:
σt = (σs² + f²)½
where σs is the quoted standard error and σt
is the total error. Of course, &sigmat/σs equals
the error multiplier, which can be entered directly.
Organisms from marine (and lacustrine environments) have been
exposed to different levels of 14C than their counterparts
in the atmosphere. The marine calibration incorporates a time-dependent
global ocean reservoir correction of about 400 years. To accommodate
local effects, the difference ΔR in reservoir age of the local region of
interest and the model ocean should be determined. Guidelines for the
determination of ΔR values are given in Stuiver and Braziunas, 1993.
A global database of values is kept at
http://www.calib.qub.ac.uk/marine. The marine calibration dataset must
be selected for calibrating these samples.
Reservoir deficiences R for lacustrine samples are typically determined
from the age of the topmost sediments (e.g. Stuiver, 1970),
or comparisons between lacustrine and terrestrial samples (e.g.
Hutchinson et al., 2004).
Sample ages are calibrated with the atmospheric dataset due to
comparably rapid exchange rates. The user must subtract the reservoir
deficiency R from the sample radiocarbon age in this case.
For samples derived from a mixture of marine and terrestrial carbon, such as
bones of humans or animals with a mixed marine (fish, mollusk, plankton etc.)
and terrestrial (grain, grass, other terrestrial animals etc.) diet, the
percent of marine carbon should first be determined from other means, such as
ethnohistorical accounts, dental pathology, archaeological evidence, or stable
isotope composition (e.g. DeNiro and Epstein, 1978; Ambrose and Norr, 1993;
Molto et al., 1997). The ΔR value must be determined as for marine samples
above. The "mixed" marine and Northern or Southern atmospheric calibration curve
should be selected for calibrating these samples.
The accepted half-life of 14C (Libby half-life) for
calculating a conventional radiocarbon age is 5568 years (Stuiver
and Polach, 1977). If the sample's age was calculated using the
half-life of 5730 years, it must be corrected by dividing the
5730 half-life radiocarbon age by 5730/5568 or 1.029. The user
must make this correction to the age, if necessary, before using
CALIB.
Samples with "negative" radiocarbon ages (i.e. samples formed
since the mid- 1950's with high initial 14C levels
due to nuclear testing 14C) cannot be calibrated with
this program. This also applies to marine samples when Radiocarbon
age minus ΔR is less than 460 14C yr BP.
A discussion of calbration of post-bomb atmospheric samples is given
in Reimer et al. 2004b and the program CALIBomb is available at
http://calib.org
There is a separate calibration curve for the Southern Hemisphere
atmosphere back to 11,000 cal BP.
Samples composed of material spanning more than 20 or 30 calendar years
are best calibrated with a moving average of the calibration
curve. This reduces the detail in the calibration curve, irrelevant
in this case, and minimizes the number of ranges and intercepts.
Enter a sample age span (i.e. the number of calendar years estimated
for sample growth or formation) to use a moving average of the selected
calibration curve.
The probability distribution P(R) of the radiocarbon ages R around
the radiocarbon age U is assumed normal with a standard deviation
equal to the square root of the total sigma (defined below).
Replacing R with the calibration curve g(T), P(R) is defined as
To obtain P(T), the probability distribution along the calendar
year axis, the P(R) function is transformed to calendar year
dependency by determining g(T) for each calendar year and transferring
the corresponding probability portion of the distribution to the
T axis.
Probabilities are ranked and summed to find the 68.3% (1 sigma)
and 95.4% (2 sigma) confidence intervals and the relative areas
under the probability curve for the two intervals calculated.
The total area under the probability curve is normalized to one.
For plotting purposes, the probabilities may be "renormalized"
so that the maximum probability equals one.
Intercepts with the calibration curve are no longer used because they do not
provide a robust indicator of sample calendar age, whereas either the weighted
average or the median probability of the probability distribution are more
stable estimates (Telford 2003). No single value completely describes the
probability distribution function and either the weighted average or median
probability may fall where the probability is low. CALIB provides the median
probability in the export file, but it is not recommended as a replacement for
the cal age ranges or the complete probability distribution.
Cal age sigma (one sigma range) represents the combined standard
deviation in the 14C age, where, depending on whether
one has chosen to use a lab error multiplier k or additional
lab variance f², the total sigma is given as:
one sigma = [(k·σs)² + σc²]½
or
one sigma = [σs² + σc² + f²]½
with σs = sample standard deviation and σc =
the curve standard deviation which is interpolated between data points for
each intercept with the radiocarbon age R. Marine samples are treated
similarly except the user must realize that ΔR, and the uncertainty in
ΔR, for each sample are based on its collection location (Stuiver and Braziunas, 1993).
The marine total sigma is taken as either:
one sigma = [(k·σs)² + σc² +
(ΔR uncertainty)²]½
For "mixed" marine and terrestrial samples of p% marine carbon
and (100-p)% terrestrial carbon the total sigma is:
one sigma = [(k·σs)²
+ ((1-p/100) · atmospheric σc)²
or
one sigma = [(σs)²
+ ((1-p/100) · atmospheric σs)² + f²
where the covariance between the atmospheric and marine curves
has been neglected.
This treatment of ΔR uncertainty assumes that ΔR is independent
for each sample. This may result in a slight overestimate of the uncertainty
(Jones and Nicholls, 2001).
However, given our limited knowledge of the changes in ΔR
over time, is not unreasonable.
Cal age results are rounded to the nearest year, which may be
too precise in many instances. Users are advised to round results
to the nearest 10 years for samples with standard deviations
greater than 50 years. Preliminary considerations
Choosing a calibration dataset
Adjustments for systematic offset
Lab error multipliers or additional lab variance
Reservoir correction for marine samples (e.g. shells,
corals, fish etc.)
Percent of marine carbon
Half-life correction
Post-atomic age
Southern Hemisphere correction
Sample calendar year span
Methods
Calibrated Probability Distribution Calculation
Total sigma
or
one sigma = [σs² + σc² +
(ΔR uncertainty)² + f²]½
+ (p/100 · marine σc)²
+ (ΔR uncertainty · p/100)²]½
+ (p/100 · marine σc)²
+ (ΔR uncertainty · p/100)²]½
Rounding