The influence of observation method on local concentration statistics in the subsurface

By introducing the concept of a finest possible time resolution in concentration observations, we extend the probabilistic Lagrangian transport formulation to account for the statistics of locally measured concentration values and their dependence on observation method for short pulse solute inputs. The outlined methodology for quantifying the ensemble expected value and variance of locally measured concentration values is relevant for transport under either unsaturated or saturated flow conditions and for different types of observation methods. The methodology is exemplified here for direct pore water sampling in aquifers (perfectly stratified/near-field transport, or three-dimensional isotropic and far-field transport) and for solute that is non-reactive or undergoes linear (reversible equilibrium or nonequilibrium, and irreversible) sorption. For nonreactive solute and for solute that undergoes irreversible sorption or equilibrium sorption-desorption, the observation procedure greatly influences the variance of locally measured solute concentrations: both the concentration variance and the coefficient of variation decreases considerably as the sampled water volume/sampling time increases. For solute that undergoes nonequilibrium sorption-desorption, both the concentration variance and the observation effect on the variance are considerably smaller than for nonreactive solute or solute undergoing equilibrium or irreversible sorption. The reason is that the concentration variance is highly dependent on the sorption kinetics, which implies that simple rules, based on average solute behavior, for when the sorption-desorption process can be regarded as being in equilibrium may be irrelevant for describing the concentration variance in heterogeneous fields.