The age calibration program, CALIB (Stuiver & Reimer 1986), first made available in 1986 and subsequently modified in 1987 (revision 2.0 and 2.1), has been amended anew. The 1993 program (revision 3.0) incorporates further refinements and a new calibration data set covering nearly 22,000 cal yr (≈18,400 14C yr). The new data, and corrections to the previously used data set, derive from a 6-yr (1986–1992) time-scale calibration effort of several laboratories.

/pdf/extended-14c-data-base-and-revised-calib-3-0-14c-age-4x1nxe8awy.pdf

Extended 14C Data Base and Revised Calib 3.0 14C Age Calibration Program

http://quebec.hwr.arizona.edu/classes/hwr696t/gosse01-cosmogenic-nuclide-review.pdf

Terrestrial in situ cosmogenic nuclides: theory and application

Not less than 2% of the Earth's land surface is peat-covered, so it is important to try to understand the dynamics of peat accumulation. Peat-forming systems (mires) accumulate peat because conditions within them impede the decay of the plant material produced by their surface vegetation. This paper concerns the rate of peat production and some unexpected consequences of the processes of decay. These consequences are likely to be of interest to those concerned with mire ecology and with the history of vegetation during Flandrian times. Most peat-forming systems consist of two layers: an upper 10-50 cm deep aerobic layer of high hydraulic conductivity, the acrotelm, in which the rate of decay is relatively high; and a thicker, usually anaerobic, lower layer, the catotelm, of low conductivity and with a much lower rate of decay. Plant structure at the base of the acrotelm collapses as a consequence of aerobic decay, and the hydraulic conductivity consequently decreases. As long as precipitation continues the water table therefore rises to this level, thus engulfing material at the base of the acrotelm. The rate, p $\_c$ , of this input to the catotelm is exactly analogous to the rate, p $\_a$ , of input to the acrotelm i.e. of primary productivity of the vegetation. During passage through the acrotelm the peat becomes richer in the more slowly decaying components. The depth of, and the time for transit through, the acrotelm thus control p $\_c$ . The catotelm, however, usually forms much the largest part of the peat mass. Selective decay may continue in the catotelm. The specific composition of the peat thus becomes a progressively poorer indicator of the surface vegetation that formed it, and to a degree that is not generally realized: reconstructions of the past surface vegetation may become very inaccurate. If p $\_c$ were constant and there were no decay in the catotelm then for the centre of a peat bog the profile of age against depth (measured as cumulative mass below the surface) would be a straight line. But if either or both these conditions is untrue then the profile would probably be concave. Most of the cases for which data exist are consistent with a concave profile and a value (constant over several thousand years) of p $\_c$ of about 50 g m $^{-2}$ a $^{-1}$ and a decay rate coefficient, $\alpha\_c$ , proportional to the amount of mass remaining, of about 10 $^{-4}$ a $^{-1}$ . This rate of input to the catotelm is about 10% of the primary productivity i.e. about 90% of the matter is lost during passage through the acrotelm. The relation seems to hold in spite of short-term fluctuations such as those represented by recurrence surfaces. Although 10 $^{-4}$ a $^{-1}$ seems a very slow rate, it has important consequences. (i) The peat mass tends towards a steady state in which the rate of addition of matter at the surface, p $\_a$ , is balanced by losses at all depths: the rate of accumulation is zero. This depth is, for the cases examined, about 5-10 m. (ii) The very concept of \`peat accumulation rate' thus needs careful consideration. To calculate it as the difference between two $^{14}$ C dates divided by the depth between the samples from which they were measured, as is commonly done, may be seriously misleading. The error is likely to increase with age, depth and time span. (iii) Progress in such studies can be made only if the easily measured profile of bulk density is known. The position of the profile in the peat bog must also be known. There is some evidence that peat contains, or comes to contain, about 1% or less of the original mass in a highly refractory state, so that the concept of a steady state is unlikely to be correct if times much greater than about 50 000 years are involved. Three more consequences of the continued very slow decay in the catotelm may be of interest to mire ecologists. (iv) Most of the mass that leaves the catotelm probably does so as methane gas. The concentration of methane increases with depth and may be as high as 5 $\mu mol$ cm $^{-3}$ at 5 m depth (about 10% by volume). Diffusion alone is able to remove mass at the necessary rate and would create concentration profiles similar to those observed. The solubility of methane in water is exceeded, however, and much of the methane may in practice be lost by mass flow of bubbles to the surface. (v) The amplitude of temperature fluctuations, as well as the mean temperature, may have a significant effect on the rate of peat decay, particularly in a cold climate. (vi) If this analysis is correct then the maximum depth of peat which can accumulate in 50 000 years is determined largely by the value of the quotient p $\_c$ / $\alpha\_c$ . The usual view that the maximum depth is determined directly by climate operating through hydrology may be incorrect, though hydrology may have an indirect effect on the value of p $\_c$ , the rate of input to the catotelm at the bog centre. Away from the centre p $\_c$ is probably variable p $\_c$ and determined by hydrology. Its dependence on distance from the centre and on time is complicated: p $\_c$ /p $\_c$ may be more than, equal to, or less than 1.0. The age against depth profile away from the bog centre may be directly affected by hydrology, though the effect is not large except near the edge of the bog or near the base of the peat. There may, of course, be catastrophic failure - a bog-burst or \`flow' - before the p $\_c$ / $\alpha\_c$ limit is reached in the centre, or slower but equally destructive development of gullies and erosion.

The Limits to Peat Bog Growth

Archaeologists, along with other Quaternary researchers, seldom rely upon a single radiocarbon determination to provide an estimate of the age of the phenomenon which is the object of their study. There is an evident need for an explicitly formulated procedure for comparing sets of radiocarbon determinations from the same and from adjacent strata or sites, and for combining these where statistical and archaeological criteria indicate that this combination is warranted. The present contribution provides explicit modelling for a series of recommended procedures, a critique of previous methods, and paradigms for application of the recommended procedures.

Procedures for comparing and combining radiocarbon age determinations: a critique

This introduction to nonparametric regression emphasizes techniques that might be most accessible and useful to the applied economist. The paper begins with a brief overview of the class of models under study and central theoretical issues such as the curse of dimensionality, the bias-variance trade-off and rates of convergence. The paper then focuses on kernel and nonparametric least squares estimation of the nonparametric regression model, and optimal differencing estimation of the partial linear model. Constrained estimation and hypothesis testing is also discussed. Empirical examples include returns to scale in electricity distribution and hedonic pricing of housing attributes.

Nonparametric Regression Techniques in Economics

DY Malcolm Clark was a research student in the Department of Statistics in the University of Shefleld and when there worked in collaboration with Professor Renfrew. His Ph.D was on the statisticalproblems of C I ~ calibration, and he here presents us with an objectively derived calibration curve for radiocarbon dates which will be of great value to all archaeologists. He is now Lecturer in Statistics in the Department of Mathematics, Monash University, Clayton, Victoria, Australia.

R. M. Clark

Papers

A calibration curve for radiocarbon dates