Application of genetic programming in presenting novel equations for longitudinal dispersion coefficient in natural...

Precise estimation of the longitudinal dispersion coefficient (LDC) is crucial for the accurate simulation of water quality management tools such as assimilation capacity. Previous research analyzed the LDC of natural streams in two general categories: ignoring or considering the river sinuosity (σ). Genetic programming (GP) is used in this study to investigate both mentioned categories by applying two experimental datasets from 56 to 24 different rivers worldwide. The first proposed LDC equation of this research (without σ) improves the amounts of statistical measures R² (Determination Coefficient), OI (Overall Index), NSE (Nash-Sutcliffe Efficiency), WI (Willmott's Index of Agreement), RMSE (Root Mean Square Error), and MAE (Mean Absolute Error) by 3.75%, 4.71%, 7.81%, 0.85%, 13.72%, and 0.68%, respectively, compared to the best values of these indicators in the previous investigations. Regarding the second category, relative and absolute sensitivity analyses are conducted, which reveal that σ is the most influential parameter in the accurate prediction of the LDC among all hydraulics and geometric parameters of the river. This part of the investigation presents four unique LDC equations that closely match the experimental results. Significant improvement of the most accurate presented LDC for statistical indices R², OI, NSE, WI, RMSE, MAE, and accuracy percentage are obtained equal to 3.27%, 2.41%, 3.16%, 0.81%, 35.1%, 24.47%, 3.8%, respectively, in comparison with the best previous relations. Also, a new indicator for measuring the efficiency of mathematical equations called Mean Normalized Statistical Index (MNSI) is introduced and applied in different parts of this research. Finally, the assimilation capacity of the Kashafrud River is determined based on the analytical method of pollution propagation for three types of water demands utilizing the accurately presented LDC in 1993-2020. The average amount of river assimilation capacity using accurate LDC is simulated at 91.93 tons/day, much lower than the currently reported pollution entrance, which equals 540 tons/day.