Functioning of the multilinear lag-cascade flood routing model as a means of transporting pollutants in the river

The purpose of this paper is to use the application of the multilinear lag cascade model as a contaminant transport model through river networks. Monocacy River and Antietam Creek data, which were collected by USGS with different reach lengths and discharge conditions, have been used in the current study. It was found that the multilinear discrete lag-cascade (MDLC) model is capable of reconstructing contaminant breakthrough curves. A complete study was performed to estimate the reach length for use in the accurate simulation, and it was concluded that by assuming a uniform flow through the reach, the length unit should be obtained by applying Pe = 12. Moreover, by using temporal moment matching, explicit relationships for MDLC model parameters (k, n, and τ) and based on conventional advection-dispersion equation (ADE) parameters (D, u, x) were extracted. MDLC parameters of the field breakthrough curves were extracted, and it was found that the increase of Pe number caused an increase in delay time and the number of cascades. However, the residence time was obtained to be fixed. Additionally, by assuming the dispersivity parameter (D/u) is constant, the changes in the MDLC parameters were investigated by velocity variation, and new relationships were proposed to estimate the parameters under different hydraulic conditions. Using presented equations provided in this study for residence time (k), cascade number (n), and delay time (τ), the sensitivity analysis was performed, and it was found that the parameters of velocity (u), dispersion coefficient (D), and velocity (u) have the most important effect in calculation of them, respectively.