Suspended Sediment Concentration and Discharge in Open Channels Using Rényi Entropy

Abstract

The vertical distribution of suspended sediment concentration in an open channel is modeled using Rényi entropy. The model, derived by invoking the principle of maximum entropy, is tested against field and laboratory observations by taking into account nonzero sediment concentration at the surface, and is also compared with other entropy-based and deterministic sediment concentration models. The proposed model is found to be in good agreement with observed data, and its prediction accuracy is superior to that of the other models. It is expressed in terms of a dimensionless entropy parameter that is constant along any vertical in a given river cross section. Errors, namely relative bias (RBIAS) and root-mean-square error (RMSE), are calculated for each of the data sets to validate the model and establish its superiority. It is observed that the RMSE of the present model varies from 0.045 to 4.197 g/L, and from 16.438 to 74.470 g/L, for experimental and field data, respectively, which lie within reasonable limits. In addition, the suspended sediment discharge per unit width is calculated using the Rényi entropy-based models of velocity and sediment concentration. The computed and observed values of sediment discharge are calculated from experimental observations, and it is found that the model can estimate observed values well.