Investigate the Effect of Stagnant Zone Behavior in One-Dimensional Hydrodynamic Models and Solute Transport in Rivers

Showing the rivers as a one-dimensional problem has simplified or eliminated many processes affecting salinity transfer in the river. Storage processes are one of the factors affecting water quality in rivers. Generally, as a substantial factor, the limitation of observational data confines the use of two-dimensional and three-dimensional models, leading to the use of more widely employed one-dimensional models. Most existing computer models are developed based on the Advection-Dispersion Equation (ADE) and do not consider the storage zone. For this purpose, Modified Advection-Dispersion Equation (MADE) is proposed to consider the stagnant area by defining effective velocity and dispersion coefficient. In this study, a solution has been proposed to apply the effect of the Stagnant zone in water quality simulation in one-dimensional models. The river simulation is closer to the natural conditions. In this model, to prove the improvement of the proposed method, the average stagnant zone fraction expressed as the fraction of the average cross-sectional area of the river (η) and employed in a one-dimensional model through the definition of the effective velocity and the dispersion coefficient. This model is considered representative of the one-dimensional models developed only by the Advection /Dispersion relation, and the proposed method was investigated for the Arvand River. Observational data along the river were used to calibrate and validate the model.
Since the available and well-known one-dimensional computer programs are generally developed based on the 1D Advection-Dispersion model, they do not consider factors affecting salinity transport such as topography and river morphology heterogeneities known as storage areas. In such a way, these processes are not expressed by presenting the problem as a one-dimensional equation. In this research, in order to increase the accuracy of the simulation with well-known and available one-dimensional models a corrective solution is proposed. To compare the proposed modified method and the base ADE, at the first, the tidal and transboundary arvand river is modeled as a study area, which is a well-mixed river. The river's upstream and downstream boundary conditions were defined according to the available data in 2014. Manning's roughness parameters ranged from 0.017 to 0.033, and the dispersion coefficient was 285 m3/s according to previous studies. In order to apply the effect of stagnant areas in the modified equations, it is essential to determine the value of η for the river. This study uses three parameters of dispersion factor (a), dispersion exponent (b), and η by ant colony algorithm with the definition of 5 initial ants and 100 repetitions in Sehan station in the study area, Arvand river was optimized. The values of the estimated parameters are respectively η = 0.168, a = 273.4, b = 0.94. Therefore, in the modified model, corrections were made using the speed and effective dispersion coefficient as the modified Advection - Dispersion (MADE) method and considering variable dispersion coefficient depending on the flow's speed in the one-dimensional model. These changes were validated in the other two stations (Faw and Dweeb).
Based on this study results, increasing the parameter η caused the peak of the time series to rise and the river's travel time to decrease. The shortening of the water travel time in the river, although increases the dispersion coefficient due to the influence of the stagnant zone, the effect of this parameter on the time series of the simulated concentration is reduced. Like the observational data, the slope of falling and rising limbs is increased. By comparing the one-dimensional model in the two cases of using the effective dispersion coefficient and velocity and without it, the increase in accuracy in the simulation was determined at Sehan station - 123 km from the river formation site - after optimizing the coefficients with three statistical errors parameters. In addition, these changes at two other stations along the river with distances of 180 and 150 km from the river's source confirm this accuracy. For instance, the simulated and measured concentration in 12 months of the year by applying the optimized coefficients reaches the correlation coefficient (r) of 0.86 to 0.97 at a distance of 150 km from the upstream, and the root means square error (RMSE) improves 1.27 ppt. The remaining difference in the concentration estimation may be caused by the effect of other parameters or even the entry of agricultural runoff from the lands along the river.
Accurate estimation and simulation of concentration in river engineering have always been one of the environmental challenges. This research aimed to improve water quality simulation using one-dimensional model in well-mixed rivers. In order to increase the accuracy of the modeling and become closer to the actual conditions, correction factors such as considering the dead zones along the river have been suggested. Analysis showed that, on average, 16% of the surface of the Arvand River's cross-sections are stagnant areas, and the dispersion coefficient depends on the river's speed. These areas include bed dunes and meanderings of the river. The point that attracts attention is the tidal irrigation channels on the sides of the river. The results showed that in Sehan, Dweeb, and Faw stations, the root means square error decreases to 1.78, 1.27, and 0.84, respectively. Therefore, the modified 1D model estimated the concentration (in this study salinity) closer to the measurement data. In Dweeb and Sehan stations, the effect of dead zones such as river meandering is evident. Still, in Faw station, no significant improvement in the impact of stagnant zones was observed due to its proximity to the river mouth. The results of this research can be used for higher accuracy in one-dimensional water quality simulations and bringing the models closer to the natural conditions in rivers.