Using an approximation of the three-point Gauss–Hermite quadrature formula for model prediction and quantification of uncertainty

Abstract

Computer models are commonly used by regulators and managers to make predictions regarding groundwater flow and contaminant concentrations at various locations and times. However, the uncertainty associated with those predictions is often overlooked, despite the fact that an assessment of such uncertainty is critical in the formulation of policy decisions. One method of quantifying the uncertainty of model predictions, based on the collective uncertainties of the model parameter input values, is to use an approximation of the three-point Gauss–Hermite quadrature formula. The Gauss–Hermite approximation is a convenient substitute for simple Monte Carlo sampling, because it requires fewer model runs and provides an immediate sensitivity analysis of parameter main effects and two-way interactions. For example, a model with four parameters, each with its own associated uncertainty, needs to be run only 33 times to complete the Gauss–Hermite analysis. For an application to a contaminant-transport model, the Gauss–Hermite approximation compares well to the full method, with considerable savings in computing effort. By comparison, Latin hypercube sampling can be more flexible, but it is more complex to use in some circumstances and cannot as easily generate the detailed sensitivity analysis that the Gauss–Hermite approach offers.