“…However, it soon turned out that it was only possible to calculate the several trajectories of particles, which was insufficient for calculation of the bedload rate, so the goal was transformed into improving the models, such that they might be used further when the development of computers allowed for their employment. The focus was on better description of the shape of a single trajectory through more accurate assessment of the impact of individual processes such as: collisions between particles (Sørensen and McEwan 1996;Schmeeckle et al 2001;Lee et al 2002;Yeganeh-Bakhtiary et al 2009;Bialik 2010Bialik , 2011aMoreno and Bombardelli 2012), particles' collisions with the channel bottom (Sekine and Kikkawa 1992;Niño and Garcia 1994;Lukerchenko et al 2006;Bialik 2011b, Kharlamova andVlasak 2015), taking into account the three-dimensional nature of the particles' motion (Lee et al 2006;Lukerchenko et al 2009a;Bialik et al 2012) or a better approximation of the different forces acting on the flowing particles, such as: Basset force (Bombardelli et al 2008;Lukerchenko et al 2012), lift force (Lee and Hsu 1996;Zou et al 2007;Lukerchenko et al 2008) and drifting force (Lee 1987;Lee and Wiesler 1987;Czernuszenko 1998) due to turbulent diffusion, which, with some exceptions (Rowiński and Lee 1993;Rowiński 1995), has usually been neglected in the Lagrangian models of sediment transport. It should be noted that all of these models mostly skip the idea of their creation, namely their use for the evaluation of the phenomena associated with the movement of particles near the bed region.…”