A novel approach for longitudinal dispersion coefficient estimation via tri-variate archimedean copulas

Abstract

Longitudinal dispersion coefficient (LDC) is a crucial component in the modeling of pollutants and sediment transport in rivers. Several researches carried out to find an equation for LDC based on geometrical and hydrodynamic parameters. Also, different approaches including, analytical, empirical, and soft computing were utilized for this purpose. While several researches were carried out in this field, the implementation of the estimated LDC is restricted due to the accuracy of estimation and the small number of datasets. In this research to overcome these problems, a novel approach based on copula functions is considered to propose a range of LDC instead of a single value. For this purpose, an extended dataset including 164 worldwide of geometrical and hydrodynamic parameters was utilized. These data were classified into six dimensionless classes. Also, tri-variate copula functions were used to the calculate conditional probability of LDC. Results indicated that Frank copula is the best fit in bi-variate and tri-variate modeling. Based on Frank copula, the conditional probability of different classes was calculated. Among all classes, the lowest conditional probability assigned to the KxHU*>5000 and in the next rank to KxHU*<30. 60–70% of conditional probability was calculated for 120<KxHU*<1400. Physical interpretation of the dispersion process justifies the results which strengthen the methodology. So, the results have the capability to use worldwide in pollutant and sediment transport modeling.