Screening-level estimates of mass discharge uncertainty from point measurement methods

The uncertainty of mass discharge measurements associated with point-scale measurement techniques was investigated by deriving analytical solutions for the mass discharge coefficient of variation for two simplified, conceptual models. In the first case, a depth-averaged domain was assumed, consisting of one-dimensional groundwater flow perpendicular to a one-dimensional control plane of uniformly spaced sampling points. The contaminant flux along the control plane was assumed to be normally distributed. The second case consisted of one-dimensional groundwater flow perpendicular to a two-dimensional control plane of uniformly spaced sampling points. The contaminant flux in this case was assumed to be distributed according to a bivariate normal distribution. The center point for the flux distributions in both cases was allowed to vary in the domain of the control plane as a uniform random variable. Simplified equations for the uncertainty were investigated to facilitate screening-level evaluations of uncertainty as a function of sampling network design. Results were used to express uncertainty as a function of the length of the control plane and number of wells, or alternatively as a function of the sample spacing. Uncertainty was also expressed as a function of a new dimensionless parameter, Ω, defined as the ratio of the maximum local flux to the product of mass discharge and sample density. Expressing uncertainty as a function of Ω provided a convenient means to demonstrate the relationship between uncertainty, the magnitude of a local hot spot, magnitude of mass discharge, distribution of the contaminant across the control plane, and the sampling density.