Derivation of Rouse equation for sediment concentration using Shannon entropy

Sediment concentration is fundamental for determining sediment transport in open channels. The Rouse equation, one of several methods for computing sediment concentration, has been derived using deterministic hydraulic principles. This study derives the Rouse equation using the Shannon entropy theory. The derivation requires a hypothesis on the cumulative probability distribution function of sediment concentration in terms of flow depth which is formulated in a general form and can specialize in several specific forms reported in the literature. The advantage of using the entropy theory is that it permits quantification of uncertainty associated with concentration and determination of parameters in terms of specified information, such as mean concentration.