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The relevance of parametric U-uptake models in ESR age

Rainer Grün

Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia

Figure 1. Compilation of p-values from cave sites
A: p-values from dentine
B: p-values from enamel
C: Relationship between p(EN), p(CE) and p(DE).

Ever since the inception of ESR dating of tooth enamel, it was clear that the unknown uranium uptake history has to be addressed in dose rate calculations. Various parametric models have been proposed for the reconstruction of U-uptake in dental tissues, notably early (EU), linear (LU) and very recent (RU) uptake. The EU model has some physical meaning, it presents the closed system and provides the minimum age. The RU model is physically less meaningful, but provides the maximum age. The main virtue of these parametric models lies mainly in their reasonable simple computability. Nevertheless, many publications have either favoured a particular U-uptake model, for the convenience of being able to explain a dating result, or claimed that the correct age of the sample lied somewhere between the EU and LU results. However, without any knowledge of the U-uptake history, it is only safe to assume that the correct age of a sample lies somewhere between the EU and RU calculations. Depending on the contribution of the U in the dental tissues to the total dose rate, this difference ranges between negligible and utterly enormous.

U uptake can be modelled by combining ESR and U-series data. Although the explicit U-uptake in nature may occur in multiple phases, two models can bracket virtually all possible scenarios, as long as no U-leaching occurs. Grün et al. (1988) used a smooth diffusion function:  U(t) = Um (t/T)p+1, where U(t) is the uranium concentration at the time t, Um the measured, present day U-concentration, T the age of the sample and p the uptake parameter. This system provides minimum age estimates for given ESR/U-series data sets. A delta function, where Um is accumulated instantly at the apparent closed system U-series age of the dental tissue, provides the maximum age. For younger samples, the differences between these two models are relatively small, which means that the explicit U-uptake history has little effect on the age calculation. For older samples (> 700 ka), with larger differences between the closed system U-series and ESR age estimates, the differences may be large (by more than a factor of 2).

To get more general insights into the general behaviour of U-uptake, published p-values were compiled and separated into two groups, from cave sites (and rock shelters) and open air sites. For the cave sites, most of the p-values of the dentine fall between about -1 and 1, but still a significant number give higher values (Figure 1A). All enamel values fall within -1 and 0.5 (Figure 1B). Note, however, that many of the teeth with high p-values in the dentine had not their enamel analysed (partly because of low U-concentrations). Most of the measured p-values in cement, p(CE), indicate a more rapid accumulation in cement than dentine (Figure 1C). This is expected, as the cement is located on the outside of the tooth. The relationship between p(EN) and p(DE) is random, most values lying in a band of 0.5 around the 1:1 line. The results on the open air sites are markedly different (Figure 2). Most p(DE) and p(EN) lie outside the -1 to 0 range (Figures 2A and B). A large number of results show p-values of > 2. There is no trend whether enamel or dentine experienced a faster uptake (Figure 2C). The p(CE) values are reasonably close to p(DE). For open air sites it is impossible to define a range of p-values that could be used for general approximations. It is even not possible to claim that the correct uptake is somewhere between  EU and RU, because there is a significant number of sites where model violations have been observed (the closed system U-series age is older than the corresponding ESR age) or U-leaching (with 230Th/234U ratios lying outside the isotope evolution diagram).

In the former case it is not unequivocally clear whether U-leaching has occurred of whether the ESR results underestimate the correct age because of problems with the distributions of the orientated and non-orientated CO2- radicals (Grün et al. 2008a), thermal transfer processes (Joannes-Boyau and Grün, submitted), reworking of samples, or the usual vagrancies in dose rate estimation. Leaching has been observed in a range of sites (Grün et al. 2008b, Grün, unpublished data).

Figure 2.Compilation of p-values from open air sites
A: p-values from dentine
B: p-values from enamel
C:Relationship between p(EN), p(CE) and p(DE).

The differences between cave and open air sites can probably be explained through the different sedimentological histories of the sites. Caves are systematically excavated because archaeologists know that ancient humans preferred to live in rock shelters and caves. Until excavated, the sedimentary stack is usually undisturbed. In contrast, many open air sites are discovered because erosion, starting at some time in the past, had provided an indication that a site was present. Erosion causes changes in the hydrological environment, e.g., by re-activation of drainage and changing the ground water table. This is accompanied with renewed U-mobilisation. Not surprisingly, many U-series age estimates of open air sites seem to reflect this change in the hydrology rather than the age of the sample.

To conclude, the statement that the correct ESR age of a sample probably lies somewhere between the EU and LU uptake age calculations is incorrect. It is not even true that the correct age lies always somewhere between the EU and RU model calculations, because there have been occasions of model violations and U-leaching. Any ESR dating study on teeth with substantial U concentrations in the tissues requires U-series age estimates. Anything else is simply a tenesmic approach to dating.


Grün, R.,  Aubert, M., Joannes-Boyau, R., Moncel, M.H. (2008a)  High resolution analysis of uranium and thorium concentrations as well as U-series isotope distributions in a Neanderthal tooth from Payre using laser ablation ICP-MS. Geochimica Cosmochimica Acta 72: 5278-5290.

Grün, R., Joannes-Boyau, R., Stringer, C. (2008b) Two types of CO2- radicals threaten the fundamentals of ESR dating of tooth enamel. Quaternary Geochronology 3: 150-172.

GrĂ¼n, R., Schwarcz, H.P. and Chadam, J.M.  (1988) ESR dating of tooth enamel: Coupled correction for U-uptake and U-series disequilibrium. Nuclear Tracks and Radiation Measurements 14: 237-241.

Joannes-Boyau, R., Grün, R. (submitted). Thermal behaviour of orientated and non-orientated CO2- radicals in tooth enamel. Radiation Measurements.