First-order based cumulative distribution function for solute concentration in heterogeneous aquifers: Theoretical analysis and implications for human health risk assessment

Quantifying the uncertainty of solute concentration in heterogeneous aquifers is an important step in both human health and ecological risk analysis. The need for a probabilistic representation of transport is justified by the incomplete characterization of the subsurface. We derive the one‐point concentration cumulative distribution function (CDF) while taking into account the spatial statistical structure of the hydraulic conductivity, space dimensionality, the injection source size, the Péclet number, and the sampling volume at the monitoring location. The CDF is application oriented and derived at first order in the log‐conductivity variance. We illustrate how several key parameters control the shape of the concentration CDF. The CDF shape is important since it reflects both uncertainty and the dilution state of the plume. The transition from a bimodal to a unimodal CDF is examined and results are further supported by analyzing the concentration coefficient of variation. Results indicate the significance of the statistical anisotropy ratio (i.e., the ratio between the hydraulic conductivity correlation scales) in determining the CDF shape. The importance of the sampling volume in the tails of the concentration CDF and a comparison between the proposed model with the β‐CDF approach (i.e., beta distribution) are also shown. Finally, we illustrate how the framework could be used in applications by evaluating the human health risk CDF. Our results are formally valid for low to moderate heterogeneous aquifers and source sizes small as compared to the hydraulic conductivity correlation length. The proposed approach can serve as a benchmark tool for other methods. Key Points Concentration CDF and human health risk CDF First‐order/2‐D/3‐D/sampling volume/statistical anisotropy in K Explore the impact of the parameters in controlling the CDF shape