Comparison of Conventional Deterministic and Entropy-Based Methods for Predicting Sediment Concentration in Debris Flow

Abstract

In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.