Parameter uncertainty in the mobile-immobile solute transport model

The four-parameter mobile-immobile model (MIM) is often used to describe solute transport processes in aggregated porous media by assuming no advective solute transport in the aggregates or immobile zone and a first-order kinetic diffusion transport process between the mobile and immobile zones. When the concentration in the immobile zone reaches an equilibrium with the concentration in the mobile zone (local equilibrium assumption, LEA), the MIM 'degenerates' to a two-parameter convective-dispersive model (CDE) and the MIM parameters cannot be accurately obtained using inverse optimization techniques. Two criteria to test the LEA applicability-the difference in skewness and a criterion derived from the SKIT (separation of kinetically influenced terms, Bahr and Rubin, 1987, Water Resourc. Res., 23: 438-452) method-are evaluated using statistical inference about model building applied to the MIM and CDE model. The results show that the criterion derived from the SKIT method evaluates the LEA applicability the best. To assess MIM parameter uncertainty as a function of the data uncertainty and the input boundary condition, asymptotic confidence intervals are obtained from sensitivity matrices. The parameter uncertainty as a function of the data uncertainty is well predicted by the criterion proposed by Bahr and Rubin, 23: 438-452) and depends on the type of input boundary condition and the type of optimization used, i.e. ordinary or weighted least squares. Using relationships between the MIM parameters and the size and shape of the aggregates, it is shown that for soils consisting of spherical aggregates, the MIM parameters are not identifiable from miscible displacement experiments using water fluxes prevailing under climatic boundary conditions. For soils with cylindrical macropores, the MIM parameters can be identified even for relatively low values of the pore velocity, nu.