In this study, previous empirical equations used to compute the dispersion coefficient are analyzed in order to evaluate their behavior in predicting dispersion characteristics in natural streams. A comparative analysis of previous theoretical and empirical equations is reported. A new simplified method for predicting dispersion coefficients using hydraulic and geometric data that are easily obtained in natural streams is also developed. The one-step Huber method, which is one of the nonlinear multiregression methods, is applied to derive a new dispersion coefficient equation. This equation is proven to be superior in explaining dispersion characteristics of natural streams more precisely, as compared to existing equations.

In this study, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams. Equations of the transverse velocity profile for irregular cross sections of the natural streams are analyzed. Among the velocity profile equations tested in this study, the beta distribution equation, which is a probability density function, is considered to be the most appropriate model for explaining the complex behavior of the transverse velocity structure of irregular natural streams. The new equation for the longitudinal dispersion coefficient that is based on the beta function for the transverse velocity profile is developed. A comparison of the proposed equation with existing equations and the observed longitudinal dispersion coefficient reveals that the proposed equation shows better agreement with the observed data compared to other existing equations.