Hi Shi-Yong,

The reservoir age depends on how long the DIC remains in the water body before it is consumed by organisms, precipitated as carbonate, escapes back into the atmosphere, or is removed from the lake via river transport. In the ideal case that you outlined, where the DIC is exclusively sourced from the atmosphere, the reservoir age does not have to be zero, unless the aforementioned processes occur very quickly.

I am not sure what you mean by "conventional radiocarbon age". Are you talking about the Libby age? Or a calibrated age? In any case, care needs to be taken to take the reservoir effect of the lake into account.

In practice, the hard-water effect can be best taken into account by measuring the radiocarbon isotopic composition of the DIC directly. The gastropod calcite shell (I presume found on the surface sediment?) and the DIC should both have the same radiocarbon isotopic composition (if the source of the carbon for the gastropod shell is lake water DIC). The terrigenous leaves could have biases of their own with respect to how long they spent on land before being transported to the lake.

Best,

Thomas

Radiocarbon data is fractionation corrected. All radiocarbon data is normalized to -25 ‰ PDB. The effects of fractionation are thus canceled out.

See:

Stuiver, M., and Polach, H. A., 1977, Discussion; reporting of C-14 data: Radiocarbon, v. 19, no. 3, p. 355-363.

Thank you for your answer. I suppose you misunderstood my point. The correction for the fractionation effect is based on the mean of the delta13C of C3 plants, say -25 per mil. My point is that an ad hoc value should be used as a base, with respect to which different kind of samples can be corrected. For example, we may use -25 per mil for terrestrial samples of C3 plants, and -10 per mil for terrestrial samples of C4 plants. For marine or lacustrine shells, -6 per mil (the mean of pre-1950 atmospheric 13CO2) may be applied. Otherwise, it calls question: a millet and rice seed of the same age could have a different radiocarbon age.   

A millet and rice seed of the same age but with a different radiocarbon age; that is exactly why all measurements need to be normalized to one d13C value (consensus value of -25 permille PDB). C-4 plants, C-3 plants, shells, etc. fractionate not only the 13-C isotope, but also the 14-C isotope. It is assumed that the extent of fractionation for the 14-C is twice that of the 13-C isotope. If radiocarbon data is normalized with different 13-C values for different samples, the 14-C fractionation will not uniformly be corrected for and we will end up with different radiocarbon ages for samples of the same age.

For example, prior to applying the fractionation correction, samples of the same age and carbon source (atmosphere):

Shell with -6 permille PDB -> relatively rich in 14-C

C-3 plant with -25 permille PDB -> relatively poor in 14-C

If we do not normalize to one d13C value, the C-3 plant will appear older (radiocarbonwise).

Completely got it!  A C3 and C4  or shell sample of the same calendar age definitely would not have the same delta-14C value due to the differential fractionation, but normalizing with respect to a common d13C value (e.g. the average of those of C3 plants) would ensure them to have the same radiocarbon age. Thank you!