Unconditional and conditional solute concentrations as sampled in natural aquifers.

The aim of this paper is to analyze the statistical properties of non-reactive solute concentrations in natural aquifers, taking into account the hydraulic conductivity heterogeneity. Quantifying the uncertainty in the evaluation of solute concentrations in aquifers is an important issue for human health and in ecological risk analysis. In particular, the concentration Cumulative Distribution Function (CDF) is a key element, as it informs the decision makers of the probability that the concentration at an environmental target is below a maximum contaminant level. The analysis presented in this paper is performed in a Lagrangian framework. According to the "reverse formulation", the origin of the particle being sampled is sought instead of considering the destination of the injected particles. Based on this formulation, a closed form for the unconditioned concentration CDF is derived. The same procedure is applied to obtain a closed form for the concentration conditioned by measurements at sampling points in an aquifer. [ABSTRACT FROM AUTHOR]