Analytical evaluation of temporal and spatial sensitivity of longitudinal dispersion coefficient in rivers for unsteady and nonuniform flows

Longitudinal dispersion coefficient (LDC) is a key element in pollutant transport modeling in streams. The most important factor affecting dispersion coefficient is the hydrodynamic flow. Due to the variability of hydraulic and geometrical parameters of rivers, the dispersion coefficient is a function of time and place, therefore precise calculation in such conditions is difficult and almost impossible. Many researchers over the years have provided numerous relationships to estimate dispersion coefficients, which all of them are based on average hydraulic and geometric parameters, but none of them have acceptable accuracy. Therefore, according to the uncertainty in estimating the dispersion coefficient, this question is proposed, “can we -in some cases- neglect the accurate estimation of the longitudinal dispersion coefficient? “The aim of the present study is to investigate the importance of dispersion coefficient at different places and times in rivers in non-uniform and unsteady flow. To validate the proposed method, it is performed for a hypothetical river with two different input pollution time patterns as well as for a real river (Karun River) with a hypothetical and real input pollution intensity function. The results of this study show that accurate estimation of dispersion coefficient is necessary only in some time and place ranges of the river and in most cases precise calculation is not necessary throughout the river and under these conditions if the dispersion coefficient is estimated with high error, it will have little effect on concentration distribution calculations and cause little error.