On calibration and validation of mathematical models for the interpretation of environmental tracer data in aquifers

Calibration and validation of mathematical models for the interpretation of environmental tracer data in acquifers are reviewed. Definitions of basic terms are recalled and the importance of calibration and validation processes for obtaining satisfactory results is discussed. The ages of ideal tracers are understood as those corresponding to the ages of water molecules, whereas the water ages are understood as those defined by the water flux in Darcy's law. In fissured rocks, flow and tracer velocities (or exit ages) differ by retardation factor caused by matrix diffusion (Rp) which is equal to the ratio of total to fissure porosity, and in a good approximation to the ratio of matrix to fissure porosity. Thus tracer ages must not be interpreted in terms of water ages. In consequence, though the environmental tritium as well as the stable isotopes of oxygen and hydrogen can be regarded as ideal groundwater tracers, their ages in fractured rocks may exceed by orders of magnitudes the water ages. In the case of 14C, additional retardation is caused by interactions between dissolved carbonate species and solid carbonates in the matrix. Which makes quantitative age determinations by the 14C method unreliable. Therefore, model validation should be attempted whenever possible. 62 refs