Uncertainty Quantification for Delineation of Wellhead Protection Areas Using the Gauss‐Hermite Quadrature Approach

Missing from most wellhead protection area (WHPA) delineation studies is a measure of the uncertainty associated with model predictions. A quantitative representation of that uncertainty can be used by regulators to implement different degrees of protection for areas with different degrees of certainty. Uncertainty analysis was performed for one- and five-year WHPA delineation for two municipal wells within a buried-valley glacial-outwash aquifer in southwestern Ohio. An approximation of the three-point Gauss-Hermite quadrature formula was used. This method is an alternative to simple Monte Carlo random sampling, typically requiring fewer model runs. It results in model-prediction expected values and variances and quantifies parameter main and two-way interactive effects. This study explored the collective impact of the uncertainties associated with six model parameters. Parameter probability density functions (PDFs) were based on field data and modified using a ground water flow model to ensure that all combinations of parameter values, within their PDFs, yielded an acceptable model calibration. The one-year WHPA for the upgradient well had a high degree of associated uncertainty represented by the difference in size between the WHPA low and high 95% confidence interval limits. The large uncertainty was due to the uncertainties associated with model parameter values, especially effective porosity and horizontal hydraulic conductivity. River conductance also had a substantial impact on the WHPA predictions. The WHPAs for the downgradient well and the five-year WHPA for the upgradient well were limited by upgradient hydrogeologic boundaries; their prediction was, therefore, less sensitive to the uncertainties inherent in the model parameters.