Comparison of models for transient storage of solutes in small streams

Biogeochemical mechanisms in rivers and streams give rise to a transient storage of solute substances in hyporheic zones and hence retard the solute transport. Analytical solutions to the temporal moments of the residence times are used as the basis to compare three different transient storage models with respect to deviation in higher-order moments, model bias, and relationships between the parameters of the different models. The transient storage was formulated using either first-order mass transfer equations or a one-dimensional diffusion process in which the storage capacity of the storage zone is limited by an impermeable surface or groundwater seepage into the stream. In all three cases the mean residence time due to a solute pulse (Dirac type) at the upstream boundary increases linearly with the size ratio of the storage zone and the stream. The three models provide an identical representation up to the first three temporal moments, which implies that at least four moments must be taken into account to distinguish between the physical biases of the models and to estimate the deviation in model characteristics. By evaluating the results from three tracer experiments, limits of acceptable model bias could be estimated. Evaluation of the tracer experiments also indicated that the temporal moments can function as indicators of underlying physics. Groundwater infiltration may significantly decrease the skewness of the residence times.