“…(5) proposed by Greimann, et al, (2008) is used to estimate the approximate velocity ratio for weak sediment transport; for the severe sediment transport, we assume the sediment and flow velocity to be approximately equivalent. Furthermore, the non-equilibrium adaptation length L has been investigated by many researchers (Armanini and Di Silvio, 1988, Greimann, et al, 2008, Phillips and Sutherland, 1989, Wu, 2004, but still warrants further study. Here, following the previous research, L is calculated by Eq.…”