Discrimination among one‐dimensional models of solute transport in porous media: Implications for sampling design

A methodology is developed for discrimination among models of transient solute transport in porous media. The method utilizes nonlinear regression on observations of solute concentration. Discrimination requires comparisons of model predictions to observations, systematic error in residuals, stability in parameter estimates from regression on different observation sets, and other measures of model fit among hypothesized models of transport. The set of observations of solute concentration to which models are fitted strongly influences the assessment of these discrimination criteria. The most desirable observation set for discrimination amplifies the weaknesses of those models that appear to describe existing conditions but are in fact unsuitable for prediction. The inadequacies of various observation sets are illustrated in four examples of discrimination between one-dimensional models of solute transport. Our purpose in these examples is to understand the physical, deterministic basis of sampling design for model discrimination. In addition to physical attributes such as transport processes, boundary conditions, and flow geometry, the assumed distribution of random error in the regression model is also treated as a model attribute to be tested by the designed experiment. A common problem in field studies occurs when the set of available observations does not include sufficient information with which to discriminate among hypothesized models, hence supporting the need to design a second round of sampling specifically for discrimination. A proposed objective function in the sampling design problem favors design points at locations and times when two hypothesized transport models display the greatest differences in predicted concentration. Two hypothetical examples demonstrate the effectiveness of the objective function and the application of the discrimination criteria.

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