A method based on the Tsallis entropy for characterizing threshold channel bank profiles

Abstract

As a stable channel forms, a point is reached when particles shift to motion threshold (threshold channel). As such, the most common challenges related to alluvial channels include the variation in the transverse bank slope (st) and channel geometric profile formation. The present study introduces a novel reliable method of estimating the transverse slope distribution of stable channel bank profiles in different hydraulic conditions by using the Tsallis entropy concept. Accordingly, an equation for calculating st and subsequently the vertical boundary level of bank profiles is presented based on the principle of maximum entropy. The threshold channel bank profile features are defined according to the probability density function and cumulative density function to adjust the general form of the Tsallis entropy for this specific engineering problem. An extensive, detailed study of Lagrange multipliers is carried out and a wide range of observational data are used to determine the Tsallis entropy model accuracy in measuring the st of stable channel banks. The results indicate that the Tsallis entropy model is capable of detecting the ascending trend governing the profiles of stable channel banks in different hydraulic conditions. This model exhibits excellent predictive performance with a mean absolute relative error (MARE) of 0.265 and a coefficient of determination (R2) of 0.975. The proposed Tsallis entropy-based equation can be used to predict river morphology changes for river management plans.