Coupled inverse modeling of vadose zone water, heat, and solute transport: Calibration constraints, parameter nonuniqueness, and predictive uncertainty

Abstract

In this study, an inverse methodology is presented and used to evaluate the effect that calibration of a synthetic artificial recharge model, constrained by different combinations of measurements (pressure head, temperature, and concentration), has on estimated vadose zone model parameter-value nonuniqueness and predictive water, heat, and solute transport uncertainty. Several findings are arrived at following model calibration and predictive analysis. First, composite scaled sensitivities revealed that all calibration measurement combinations contributed to the estimation of 30 water, heat, and solute transport parameters by inverting a set of vadose zone transport equations that were coupled explicitly through dependent variables and implicitly through parameters and fluid properties. Second, despite excellent model quality and perfect match of simulated-to-measured dependent field variables, the limitations in information content of field measurements used to constrain the calibration process promoted correlation among parameters; correlation among parameters promoted parameter nonuniqueness; and parameter nonuniqueness promoted predictive uncertainty. Consequently, simulations by transport models calibrated against field information represent a single realization associated with some quantifiable range of predictive uncertainty. Third, a primary reduction in uncertainty was achieved by increasing the number of calibration-constraint measurements, but reductions in uncertainty appeared restricted implying a practical limit to parameterization detail. Fourth, for a fixed number of measurements, a less prominent reduction in the range of predictive uncertainty could be realized through selective use of measurement types to constrain the calibration process. Therefore, field measurement types used to constrain the calibration process should be matched to target predictions. Fifth, because correlation among parameters contributes to predictive uncertainty, it may be possible to further reduce predictive uncertainty by estimating parameters that also minimize the largest eigenvalue in the normalized eigenvector matrix.