“…Mean flow entrainment models derive a transport initiation threshold Shields number from a force balance, and/or torque balance, between mean fluid forces and resisting contact forces acting on a representative particle resting on the bed surface (Agudo et al, 2017;Ali & Dey, 2016;Bagnold, 1936Bagnold, , 1941Bravo et al, 2014Bravo et al, , 2017Claudin & Andreotti, 2006;Dey, 1999Dey, , 2003Dey & Papanicolaou, 2008;Duan et al, 2013;Durán et al, 2011;Edwards & Namikas, 2015;He & Ohara, 2017;Iversen et al, 1976Iversen et al, , 1987Iversen & White, 1982;Lee et al, 2012;Lehning et al, 2000;Ling, 1995;Lu et al, 2005;Luckner & Zanke, 2007;Recking, 2009;Rousar et al, 2016;Schmidt, 1980;Shao & Lu, 2000;Vollmer & Kleinhans, 2007;Ward, 1969;Wiberg & Smith, 1987;White, 1940;Wu & Chou, 2003). Many of these models have been proposed to reproduce the Shields diagram, which displays two kinds of fluvial thresholds: a threshold obtained from extrapolating measurements of the transport rate to (nearly) vanishing transport and visual measurements of the initiation threshold of individual transport (see section 4.3 for details).…”