In the isotope hydrogeology the critical depth of soil is reached if the isotope variability in the recharge waters is below the analytical precision (2 sigma). Is there any fixed value assigned to the anylytical precision (e.g. 2 per mille or 0.5 per mille)?
No, there is not a fixed value assigned for the analytical precision, at least this is our experience from several isotope hydrological case studies. It depends usually on the type and the precision of the gauge. We used data produces in different isotope labs (UFZ, Hydrosisotop, and a lab from Hungary) and the data precision can differ a bit.
As the approach of Clark and Fritz originated as a solution to practical interpretations of field profiles (under particular conditions), the determination of "critical depth" depends on the particular application. Factors in determining this heuristic parameter include variations in input concentrations and water velocities, soil parameters, vegetation effects, limitations of sampling and measurement systems etc., and the inherent time scales of the processes of interest, for example. The method cannot safely be used without a good process understanding of the system gleaned from other, independent data.
As previous researchers stated, there is no assigned fixed value for this, but in many fields of science there are rules of thumb. I recommend the following article about isotope measurement precisions as a starting point: Wassenaar, L.I., Ahmad, M., Aggarwal, P., van Duren, M., Pöltenstein, L., Araguas, L., Kurttas, T., 2012. Worldwide proficiency test for routine analysis of δ2H and δ18O in water by isotope-ratio mass spectrometry and laser absorption spectroscopy. Rapid Commun. Mass Spectrom. 26, 1641-1648 (doi: 10.1002/rcm.6270).
http://onlinelibrary.wiley.com/doi/10.1002/rcm.6270/abstract
