Evaluation of Nonparametric Shape Measures for Solute Breakthrough Curves

A better understanding of the relationships among preferential solute transport, hydrologic boundary conditions, and site properties will help to improve predictions of the fate of contaminants in the vadose zone. The diversity of mechanisms underlying preferential transport, together with problems of nonuniqueness in fitting models to experimental data, suggests that model-independent (nonparametric) indicators of solute transport may help to establish such relationships. We therefore investigated 17 distinct nonparametric measures of solute breakthrough curve (BTC) shape using a data set of 115 tracer BTCs sampled from the literature. We tested the shape measures for sensitivity to deconvolution approaches based on Gaussian, lognormal, and gamma probability density functions and the mobile-immobile model. Furthermore, we evaluated collinearities among the 17 shape measures. Most deconvolution approaches gave very good fits to the data, with coefficients of determination larger than 0.98. Dual-domain transfer functions were superior to single-domain ones, even after accounting for measures of parsimony. The least sensitive shape measures were the normalized first temporal moment, the mean transport velocity, the apparent dispersion coefficient, and the relative arrival time of the first 5 and 85% of the tracer mass. In contrast, the skewness and kurtosis were most sensitive to the choice of deconvolution approach, even for BTC experiments with very long data series of more than eight water-filled pore volumes. The relative arrival time of the first 5% of the tracer mass was identified as the most robust shape parameter that could serve as an indicator of preferential flow and transport.