PRINCIPLES AND PRACTICE OF CALIBRATION AND VALIDATION OF MATHEMATICAL-MODELS FOR THE INTERPRETATION OF ENVIRONMENTAL TRACER DATA IN AQUIFERS

Calibration and validation processes of mathematical models applied to environmental tracer dating of groundwater are discussed and their importance exemplified by a number of case studies. The calibration procedures are shown to be often ambiguous due to the scarcity of data, approximate nature of models, and interplay of fitting parameters when their number is too large. A unique calibration is a necessary condition, though not sufficient, for validation. A satisfactory agreement of the values of parameters obtained by calibration with those known from independent methods may be regarded as an indirect validation. Direct or indirect validation is usually obtainable only with respect to some quantities or parameters and in such cases it should be regarded as a partial validation. Very often validation is unavailable, and, consequently, the model and the values of its parameters are questionable, but still can serve as starting points for further studies. Case studies discussed demonstrate that sometimes several properly calibrated and partly validated mathematical models, based on different conceptual models, can be used. In such cases the conceptual model of flow pattern and hydrochemistry remains unidentified.