Integrative multi-model analysis of river pollutant transport: advancing predictive capabilities through transient storage dynamics and fractional calculus approaches

This paper discusses the detailed analysis of pollutant transport in river systems by considering multiple modeling approaches in an attempt to explain the complex dynamics governing contaminant fate and movement. Comparisons were made for the performance of the advection–dispersion equation, the transient storage model, the aggregated dead zone model, continuously stirred tank reactors in series, and the fractional advection–dispersion equation based on data from a conducted tracer experiment on Conococheague Creek. The best performance among models yielded a root mean square error of 1.56 ppm at the lowest and an R² of 0.982, based on six monitoring stations spanning a length of 33.86 km, from the transient storage model (TSM). The reach-specific analysis gave an exchange coefficient from 0.28 to 0.18 h⁻¹ along the river course, while the relative storage zone size increased from initially a value of 0.15 to an increase of 0.22 before dropping again to 0.17 in the last reach. It was found that the advective velocity was the most influential parameter, having a Sobol first-order index of 0.512, followed by the dispersion coefficient at 0.283. Moment analysis returned an average velocity of 0.69 km/h and a dispersion coefficient of 0.41 km²/h for the entire reach. Dimensional analysis involved developing empirical equations, in which the R² value ranged from 0.79 to 0.93 for the estimation of the parameters. These findings underline the role of transient storage processes and non-Fickian dispersion that is necessary for making an accurate prediction of pollutant transport.