Simplified entropic model for the evaluation of suspended load concentration

Suspended sediment concentration is a key aspect in the forecasting of river evolution dynamics, as well as in water quality assessment, evaluation of reservoir impacts, and management of water resources. The estimation of suspended load often relies on empirical models, of which efficiency is limited by their analytic structure or by the need for calibration parameters. The present work deals with a simplified fully-analytical formulation of the so-called entropic model in order to reproduce the vertical distribution of sediment concentration. The simplification consists in the leading order expansion of the generalized spatial coordinate of the entropic velocity profile that, strictly speaking, applies to the near-bed region, but that provides acceptable results also near the free surface. The proposed closed-form solution, which highlights the interplay among channel morphology, stream power, secondary flows, and suspended transport features, allows reducing the needed number of field measurements and, therefore, the time of field activities. Its accuracy and robustness were successfully tested based on the comparison with laboratory data reported in literature.