An Explicit Solution for Characterizing Non-Fickian Solute Transport in Natural Streams

Abstract

One-dimensional solute transport modeling is fundamental to enhance understanding of river mixing mechanisms, and is useful in predicting solute concentration variation and fate in rivers. Motivated by the need of more adaptive and efficient model, an exact and efficient solution for simulating breakthrough curves that vary with non-Fickian transport in natural streams was presented, which was based on an existing implicit advection-dispersion equation that incorporates the storage effect. The solution for the Gaussian approximation with a shape-free boundary condition was derived using a routing procedure, and the storage effect was incorporated using a stochastic concept with a memory function. The proposed solution was validated by comparison with analytical and numerical solutions, and the results were efficient and exact. Its performance in simulating non-Fickian transport in streams was validated using field tracer data, and good agreement was achieved with 0.990 of R2. Despite the accurate reproduction of the overall breakthrough curves, considerable errors in their late-time behaviors were found depending upon the memory function formulae. One of the key results was that the proper formula for the memory function is inconsistent according to the data and optimal parameters. Therefore, to gain a deeper understanding of non-Fickian transport in natural streams, identifying the true memory function from the tracer data is required.

Estimating Net Retention Time of Solute in Storage Zones of a Stream

“…Although Equation 5is advantageous for a lower risk of error due to the deterministic calculation, its underlying premise of the uniform cross section and instantaneous injection is not feasible in actual streams. In this study, an analytical solution in which the shape-free breakthrough curve could be applied as an upstream boundary condition was developed using the concept of routing procedure (Baek, 2020;Baek & Seo, 2010;Fischer, 1966;Kim et al, 2023). The routing procedure was initially developed to estimate the dispersion coefficient from two breakthrough curves measured at upstream and downstream boundaries.…”