This paper describes a mathematical model which solves the 1D unsteady flow over a mobile bed. The model is based on the Richtmyer second-order explicit scheme. Comparison of the model results with the experimental flume data for alluvial steady flow (aggradation due to overloading) and unsteady flow shows that, by using the two-step method of Richtmyer, one can solve the equations, governing the phenomenon, in a coupled method with the desired accuracy. Firstly, the Badalan reach located at the Aland River is considered. Variations of flow rate, water level and bed level profiles due to flood hydrographs are assessed. Secondly, bed load discharge data were collected from the Aland River and a variety of bed load discharge formulae were compared with measured data. Results show that, by using the grain size of the bed surface layer to predict the bed load discharge, a larger relative error will occur compared to the other two cases and a proper choice of grain size has the main role in reduction of the relative error of bed load discharge estimation in gravel bed rivers. The applicability of formulae varies depending on flow rate, and should be split into low and high flow transport formulae.