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Main trend

 Upon examination of the data in Fig. 4 and other similar plots, it becomes apparent that radiocarbon years and calendar years are not necessarily equivalent. If such had been the case, all of the data points plotted on Fig. 4 would lie along the horizontal 0 line. In fact, some of the points lie above the line, indicating that 14C values in these periods are too old. Conversely, those below the 0 line are too young when compared to the tree-ring data. This plot indicates that there are two major components to the deviations. The first is a general main-trend secular variation phenomenon (the curved line) exhibiting during the Holocene, a sine-wave function with an apparent period of about 8500–9000 years, with a maximum deviation of about 800 years, approximately 8000 years ago.

 Fig. 4  Secular variation/major trend; relationship between radiocarbon and dendrochronological age of wood samples. (After J. Klein et al., Calibration of radiocarbon dates, Radiocarbon, 24(2):103–150, 1982)

  The characteristic of the secular variation anomalies in the period before about 10,000 years ago cannot, at present, be documented by tree-ring/14C data. It has been argued, however, that the major part of the effect may be estimated by examining the record of the Earth's dipole geomagnetic field over time. Variations in the intensity of the dipole field modulate the cosmic-ray flux in the vicinity of the Earth. An increase in the field strength, for example, diverts more of the cosmic-ray particles away from the Earth, resulting in a decrease in the production of 14C.

Geophysicists have collected data which document changes in the intensity of the Earth's dipole field for the last few hundred thousand years. Because of the apparent inverse relationship between the intensity of the field and the 14C production rate, it would, in theory, be possible to extrapolate the maximum and minimum secular variation deviations back to the limit of the 14C method. Unfortunately, such data are not yet as precise as might be wished. However, comparisons of 14C ages with uranium-thorium (U-Th) ages obtained on cores from coral deposits support conclusions based on the 14C/tree-ring data up to the limit of the current dendrochronological data. Uranium-thorium values can be used to continue to examine the 14C deviations over the last 30,000 years. Such data indicate that radiocarbon ages earlier than 10,000 years B.P. continue to be systematically younger than U-Th ages, with a maximum difference of about 3500 years approximately 20,000 years ago.  See also: Paleomagnetism; Rock magnetism

 De Vries effect

 In addition to the long-term secular variation phenomenon, the bristlecone pine data have revealed the presence of high-frequency components to the variation in 14C activity. These short-term oscillations or wiggles have sometimes been called the De Vries effect after the pioneering Dutch researcher, Hessel de Vries, who was one of the first to call attention to the existence of systematic anomalies in 14C values. Although almost all investigators concerned with the issue have agreed that the tree-ring/14C data definitely reveal the presence of a number of short-term perturbations, the frequency and magnitude of earlier episodes during the Pleistocene, (that is, > 10,000 years B.P.) have not been resolved. Likewise, there are uncertainties as to the causes of the De Vries effect, although variation in solar activity (heliomagnetic effects) has been seen as an important factor.

 Calibration of radiocarbon dates

 The existence of main trend and De Vries deviations has important implications in the interpretation of 14C determinations. The long-term variations result in the necessity to calibrate conventional 14C dates in terms of the known variation between radiocarbon time and real or calendar time as documented by the dendrochronological/14C values. The magnitude of the calibration varies depending on from what time period a sample is derived. For the period back to about 1000 B.C., corrections required by virtue of the secular-variation deviations do not exceed about 150 years. Prior to 1000 B.C., the magnitude of the correction steadily increases. By using data such as those presented in Fig. 4, various approaches have been developed to “calibrate” radiocarbon values. In this context, calibration involves taking a 14C age value expressed as a conventional radiocarbon date and adding or subtracting the number of years required to bring the conventional age into conformity with the 14C determinations on known-age tree-ring-dated samples.

The documentation of the presence of the De Vries or short-term anomalies has introduced a second problem in the calibration of 14C values. Periods of rapid change in the 14C content of the atmosphere result in situations where a single 14C value may reflect two or more points in real time. The characteristics of the short-term anomalies are illustrated in Fig. 5. During periods of particularly rapid change in 14C activity, it is usually not possible to use 14C data to document temporal intervals in units of less than a few hundred years. Thus the dendrochronologically based calibration data can be used to identify the general degree of deviation of 14C values from real time and also the degree of maximum precision which is possible for specific temporal intervals.

 Fig. 5  Secular variation/De Vries effect. Example of short-term variations in 14C activity; detail of De Vries effects using high-precision measurements for period of approximately 4500–5100 14C years B.P. (After A. F. M. de Jong and W. G. Mook, Medium-term atmospheric 14C variations, Radiocarbon, 22(2):267–272, 1980)

 The impact of the De Vries effects on the precision of 14C values, as applied to archeological and historical problems, must be considered. The need to take into account these shorter-term variations have, for example, been demonstrated in the evaluation of 14C values on twelfth- and fourteenth-century European medieval archeological materials.  See also: Archeological chronology

 Lack of geographical and altitude variations

 Concern has been expressed as to whether variation in the 14C content of wood samples taken from a small number of localities in the Northern Hemisphere can be used to document worldwide secular variation effects. This question has been specifically answered as a result of studies of 14C concentrations in tree rings from Patagonia, Canada, and Europe. The maximum deviations noted in contemporaneous woods were between those grown in the Southern and Northern hemispheres. However, even in this case, the variation did not exceed 0.5% or about the equivalent of 40 years.

Studies have also shown the lack of any significant altitude effect on 14C concentrations in wood. A concern had been expressed that solar protons of appropriate energies would interact with nitrogen to form 14C directly in wood samples growing at high elevations. The projected effect would be to inflate the 14C content of a sample so that the 14C age would appear to be significantly younger than its true age. However, calculations indicate that the maximum effect that could be obtained, assuming the most advantageous parameters, would not exceed 40 years. Other evidence suggests the actual effect is much less. The bristlecone pine wood of the White Mountains grows at about the 3350-m (11,000-ft) level. That there is no measurable 14C produced as a function of altitude is indicated by the essential agreement in age between the high-altitude bristlecone and low-altitude European and American sequoia samples of the same dendrochronological age.

  Variability in radiocarbon distribution

 An important feature of the 14C method is its potential to provide directly comparable age determinations on a worldwide basis for a wide variety of organic samples. For this potential to be realized, 14C, following its production, has to be mixed rapidly and completely throughout all of the carbon-containing reservoirs on a time scale not exceeding a few tens of years. To the degree that such conditions prevail, the contemporary 14C content of all organic samples will be essentially identical. It was quickly determined that such is not the case. The initial 14C content of samples could be significantly affected as a result of environmental conditions. A classic illustration of the problem was the discovery of living organisms from a fresh-water lake exhibiting 14C ages of approximately 2000 years. In this case a large percentage of the carbon used by the organisms was derived from dissolved CO2 from the limestone bed of the lake. The fictional age of the modern samples had been produced as a result of the dilution of contemporary 14C activity by “dead” carbon (that is, containing no 14C) from the limestone. Another example is provided from trees growing in active volcanic areas. The CO2 emitted during volcanic discharges is characteristically depleted of its 14C. Living trees exhibiting apparent ages as much as 1000 years from such environments have been reported.

One effect of the recognition that the geochemical environment of a sample can affect its initial 14C concentration has been to cast doubt on the reliability of particular types of samples. The use of shells in 14C studies has been affected, since a tradition arose that their use should be discouraged. Terrestrial shells (gastropods) from most fresh-water environments generally merit this negative evaluation, since they typically take up carbonate which is not in equilibrium with atmospheric 14C. The reputation of marine shells was adversely affected primarily as a result of early experiences with shells taken from several archeological sites along the Peruvian coast. Marine shell samples were found to have 14C values that exhibited an apparent age as much as 900 years greater than that of charcoal samples assumed to have been deposited contemporaneously. It was therefore assumed that marine shells would consistently yield anomalous values.

Subsequent studies showed that marine shells can yield generally acceptable values if the conventional 14C values can be corrected for upwelling effects. By examining 14C concentrations in shells collected alive in the period before nuclear testing contributed bomb 14C, it was determined that many marine shells exhibited apparent ages ranging as high as 1200 years. Part of the reason has to do with the fact that ocean water depleted of 14C by long residence times in the deeper parts of the ocean is periodically upwelled or brought to the surface and mixed with surface ocean water. The effect is to dilute the contemporary 14C activity of the surface ocean near the westward-facing continental margins, resulting in a spurious apparent age for the organisms utilizing surface-ocean-water carbonates. Shells growing in locations adjacent to the outlets of major river systems whose water is depleted of 14C as a result of exchange with limestone or other carbonate-bearing rocks can also give spurious apparent ages. This is probably the explanation for the false ages exhibited by shells growing in the Gulf of California (Colorado River discharge) and the northern part of the Gulf of Mexico (Mississippi River discharge).  See also: Continental margin; Upwelling

Upwelling and other reservoir effects are highly variable depending on location and specific environmental conditions. For the western coasts of North and South America, for example, the magnitude of the upwelling effects can range from about 80 to 1000 years. It is most severe along the Peruvian coast, contributing to an explanation for the problematical 14C values on marine shells from that region. Unfortunately, it is possible for shells from highly localized regions to exhibit a sizable range in apparent ages. Samples from the Galápagos Islands show a variation of about 350 years. Such a fluctuation in such a relatively small area emphasizes the fact that the magnitude of upwelling effects for any region must be carefully established by multiple sampling of closely spaced areas.

Problems similar to those associated with marine shells arise for a number of sample types and geochemical environments where contemporary samples may not be in equilibrium with the atmosphere. In each case, empirically derived values for the contemporary standard must be obtained for each sample type or locality, or both. In practice, this is accomplished by determining the degree of deviation from whatever contemporary standard is used to define modern or “zero 14C age” samples. For example, specific values are required for marine shells from different oceanic regions, for fresh-water shells in specific terrestrial environments, and for Arctic and Antarctic specimens.

 Variability in carbon isotope ratios

 For the 14C method, the basic physical measurement used to index time is the 14C/12C ratio. However, carbon has three naturally occurring isotopes. Variation in this ratio can be effected by influences other than the decay of 14C. The most common problem occurs when carbon-containing compounds not indigenous to the original samples are physically or chemically introduced into the sample matrix resulting in the contamination of the sample. Usually less difficult to deal with are fractionation effects in which a variation in the stable carbon ratio translates into a change in the 14C/12C ratio.

 Contamination

 The sources and effects of the introduction of foreign organics into samples are complex; they depend on the nature and condition of the sample materials, the characteristics of the environment to which the samples were exposed, and the period of time over which the exposure occurred. Precautions exercised to avoid contamination effects are unique to each sample type and source locality. A series of procedures to remove potential contaminants in samples has been established by research laboratories. Most sample preparation techniques are concerned with completely removing what is assumed to have not been present when the original sample died or was removed from exchange with its carbon reservoir. Samples such as wood and charcoal, which can be subjected to treatment with strong acids and bases to facilitate the removal of absorbed carbonates and soil humic and fulvic acids and other soluble soil organic matter, are preferred. Less desirable are cases where it is difficult to distinguish between contamination and the original sample as with various types of carbonate samples, such as tufa and caliche.

It is usually possible to infer the effect of known contamination effects on a given sample in terms of the direction that the age change will take for a given type of contamination, but the magnitude of the errors can be calculated only if the true age of the original sample, the age of the contaminant, and the percentage contribution of the contaminant are all known. Usually this is difficult to determine. However, with few exceptions, problems of contamination for samples with ages of less than about 10,000 years can be solved, usually by applying standard pretreatment approaches developed by 14C laboratories. For materials with expected ages in excess of 10,000 years, sample contamination problems typically become more serious, and laboratories must exercise even more rigorous care in the pretreatment processes.

Fractionation effects

While all the isotopes of carbon follow the same chemical or physical pathway, the rate at which this occurs varies as a function of their difference in mass. The pioneering studies of Harmon Craig pointed to the need to consider variations in the stable isotope ratio (13C/12C) of samples to obtain precise 14C values. Variations equivalent to up to several hundred years can result if 14C values are not standardized in light of 13C/12C ratios. Fortunately, no significant fractionation effects are usually observed in standard sample materials such as charcoal or wood. Problems arise, however, when it is necessary to compare 14C values from a variety of sample types such as grasses, grains, seeds, succulents, and marine carbonates, as well as standard terrestrial organics. In such cases, it is necessary to use the stable isotope ratios to correct the 14C values onto a common scale