Quantifying the Impact of Uncertainty within the Longitudinal Dispersion Coefficient on Concentration Dynamics and Regulatory Compliance in Rivers

Abstract

The one‐dimensional advection dispersion equation (1D ADE) is commonly used in practice to simulate pollutant transport processes for assessment and improvement of water quality conditions in rivers. Various studies have shown that the longitudinal dispersion coefficient used within the 1D ADE is influenced by a range of hydraulic and geomorphological conditions. This study aims to quantify the impact and importance of the parameter uncertainty associated with the longitudinal dispersion coefficient on modeled pollutant time‐concentration profiles and its implications for meeting compliance with water quality regulations. Six regression equations for estimating longitudinal dispersion coefficients are evaluated, and commonly used evaluation criteria were assessed for their suitability. A statistical evaluation of the regression equations based on their original calibration data sets resulted in percent bias (PBIAS) values between −47.01% and 20.78%. For a case study, uncertainty associated with the longitudinal dispersion coefficient was propagated to time‐concentration profiles using 1D ADE and Monte Carlo simulations, and 75% confidence interval bands of the pollutant concentration versus time profiles were derived. For two studied equations, the measured peak concentration values were above the simulated 87.5th percentile, and for the other four equations it was close to the 87.5th percentile. Subsequent uncertainty propagation analysis of four diverse rivers show the potential considerable impact on concentration‐duration‐frequency‐based water quality studies, with 1D ADE modeling producing predictions of quality standard compliance which varied over hundreds of kilometers.

Estimation of natural streams longitudinal dispersion coefficient using hybrid evolutionary machine learning model

“…Alizadeh, Ahmadyar, et al, 2017). Several models exist which rely on the advection-dispersion equation shown in Equation (1); however, the modeling results are highly affected by the nature of the K x (Camacho Suarez et al, 2019).…”

“…where K x is the longitudinal dispersion coefficient, t is the time, x and u are the longitudinal coordinate and mean cross-sectional velocity, respectively, and C is the averaged cross-sectional concentration (Noori et al, 2011). Regarding K x , it can be determined experimentally, empirically, and theoretically (Camacho Suarez et al, 2019;Data, 2019;Deng et al, 2002Deng et al, , 2001Disley et al, 2015;Milišić et al, 2019;Perucca et al, 2009;Seo & Baek, 2004;Seo & Cheong, 1998;Shin et al, 2019;Shucksmith et al, 2011;Swamee et al, 2000;Wang & Huai, 2016;Zeng & Huai, 2014). The direct experimental determination of the dispersion coefficient demands cost and time inefficient tracer studies and could be done only with rectangular flumes data (Etemad-Shahidi & Taghipour, 2012).…”