On the calibration and validation of mathematical models for the interpretation of tracer experiments in groundwater

Abstract

Calibration and validation processes of mathematical models applied to the interpretation of tracer experiments in groundwater are reviewed and exemplified by a number of case studies. Definitions of basic terms related to those processes are given and adapted to specific problems of groundwater tracing. The calibration procedures commonly used are often ambiguous, due to the interplay of parameters, and then a proper validation is unavailable. The number of fitting parameters may sometimes be reduced by using information available from independent observations, or by calibration of a multi-tracer experiment. Even if a unique calibration is achieved, an ideal validation process is usually impossible or uneconomical to perform. Therefore, indirect validation methods must be used. A satisfactory agreement of the values of parameters obtained by calibration with those known from independent observations may be regarded as an indirect validation. Direct or indirect validation is often obtained only with respect to some parameters and in such cases it should be regarded as a partial validation only.