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, that is, the Langmuir, Freundlich, Temkin, and linear models, constitute our set of alternative (competing) mathematical formulations. Experimental results reveal that the soil samples characterized by the finest grain sizes are 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 Akaike information criteria [AIC and AIC C ] and the Bayesian and Kashyap information criteria). 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 subregions of the parameter space. In this context, the modelling strategy resulting from coupling the Langmuir isotherm with a two-layer solute transfer model is then evaluated as the most skilful 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) 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.
We provide qualitative and quantitative assessment of the results of a grid convergence study in terms of (a) the rate/order of convergence and (b) the Grid Convergence Index, GCI, associated with the numerical solutions of Moment Equations (MEs) of steady-state groundwater flow. The latter are approximated at second order (in terms of the standard deviation of the natural logarithm, Y, of hydraulic conductivity). We consider (i) the analytical solutions of Riva et al. (2001) for steady-state radial flow in a randomly heterogeneous conductivity field, which we take as references; and (ii) the numerical solutions of the MEs satisfied by the (ensemble) mean and (co)variance of hydraulic head and fluxes. Based on 45 numerical grids associated with differing degrees of discretization, we find a supra-linear rate of convergence for the mean and (co)variance of hydraulic head and for the variance of the transverse component of fluxes, the variance of radial fluxes being characterized by a sub-linear convergence rate. Our estimated values of GCI suggest that an accurate computation of mean and (co)variance of head and fluxes requires a space discretization comprising at least 8 grid elements per correlation length of Y, an even finer discretization being required for an accurate representation of the second-order component of mean heads.
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