Effective water resources management typically relies on numerical models to analyze groundwater flow and solute transport processes. Groundwater models are often subject to input data uncertainty, as some inputs (such as recharge and well pumping rates) are estimated and subject to uncertainty. Current practices of groundwater model calibration often overlook uncertainties in input data; this can lead to biased parameter estimates and compromised predictions. Through a synthetic case study of surface‐ground water interaction under changing pumping conditions and land use, we investigate the impacts of uncertain pumping and recharge rates on model calibration and uncertainty analysis. We then present a Bayesian framework of model calibration to handle uncertain input of groundwater models. The framework implements a marginalizing step to account for input data uncertainty when evaluating likelihood. It was found that not accounting for input uncertainty may lead to biased, overconfident parameter estimates because parameters could be over‐adjusted to compensate for possible input data errors. Parameter compensation can have deleterious impacts when the calibrated model is used to make forecast under a scenario that is different from calibration conditions. By marginalizing input data uncertainty, the Bayesian calibration approach effectively alleviates parameter compensation and gives more accurate predictions in the synthetic case study. The marginalizing Bayesian method also decomposes prediction uncertainty into uncertainties contributed by parameters, input data, and measurements. The results underscore the need to account for input uncertainty to better inform postmodeling decision making.

Ground-water remediation optimization models were formulated using a statistical optimization methodology, chance-constrained programming (CCP), to account for uncertainty in the coefficients of the models. Several models were formulated that depended on which set of coefficients were considered uncertain. Such models were either mixed-integer linear programming models or mixed-integer nonlinear programming models. The CCP method transformed the probabilistic models to deterministic models. The deterministic models are easier to solve and use less computer memory and less storage space than probabilistic models. Results are presented that demonstrate the models formulated. The results showed that incorporating uncertainty into a ground-water optimization model using CCP could be a practical method for making decisions on well locations and pumping rates in ground-water remediation.