Renyi Entropy and Random Walk Hypothesis to Study Suspended Sediment Concentration

Abstract

Sediment concentration in open channels is fundamental to modeling sediment and pollutant transport. This study employs Renyi entropy for deriving the vertical distribution of suspended sediment concentration in open-channel flow. The derivation maximizes entropy by invoking the principle of maximum entropy, which selects the least-biased probability distribution out of many probability distributions that satisfy a given set of constraints. By considering point source release of sediment particles along with the assumption that the movement of sediment particles follow a nonlinear differential equation, the concentration distribution of suspended sediment is also investigated using a random walk hypothesis. The distribution obtained here is found to be similar to that obtained using entropy. The distribution is evaluated with experimental and field observations and good agreement is observed between computed and measured data. An error analysis is carried out to support the results and the relative root-mean-square error varies from 0.125 to 0.872 for experimental and from 0.141 to 0.510 for field data. Comparison with another entropy-based distribution shows higher accuracy of the proposed distribution.