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

Abstract

AbstractMissing 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.