Assessment of alternative adsorption models and global sensitivity analysis to characterize hexavalent chromium loss from soil to surface runoff

We investigate our ability to assess transfer of hexavalent chromium, Cr(VI), from the soil to surface runoff by considering the effect of coupling diverse adsorption models with a two-layer solute transfer model. Our analyses are grounded on a set of two experiments associated with soils characterized by diverse particle size distributions. Our study is motivated by the observation that Cr(VI) is receiving much attention for the assessment of environmental risks due to its high solubility, mobility, and toxicological significance. Adsorption of Cr(VI) is considered to be at equilibrium in the mixing layer under our experimental conditions. Four adsorption models, i.e., the Langmuir, Freundlich, Temkin, and the linear model, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes is associated with the highest release of Cr(VI) to runoff. We compare the relative abilities of the four models to interpret experimental results through Maximum Likelihood model calibration and four model identification criteria (i.e., the information criteria AIC and AICC, and the Bayesian criteria BIC and KIC). Our study results enable us to rank the tested models on the basis of a set of posterior weights assigned to each of them. A classical variance-based global sensitivity analysis is then performed to assess the relative importance of the uncertain parameters associated with each of the models considered, within sub-regions of the parameter space. In this context, the modeling strategy resulting from coupling the Langmuir isotherm with a two-layer solute transfer model is then evaluated as the most skillful for the overall interpretation of both sets of experiments. Our results document that (a) the depth of the mixing layer is the most influential factor for all models tested, with the exception of the Freundlich isotherm, and (b) that the total sensitivity of the adsorption parameters varies in time, with a trend to increase as time progresses for all of the models. These results suggest that adsorption has a significant effect on the uncertainty associated with the release of Cr(VI) from the soil to the surface runoff component