Table 1.

List of selected existing optimality hypotheses. V is the mean flow velocity, S is the channel slope, ρ is the density of water, g is the gravitational acceleration constant, Q is the flow discharge, L is the reach length, ρ_s is the density of sediment, Q_s is the sediment transport rate, W is the channel width, H is the hydraulic depth, and η is a constant. Q_j and L_j are the discharge and the length of link j (channel between two confluences), respectively. In application of these hypotheses, Q and Q_s are treated as given constants, and channel or network geometry is adjusted to obtain the optimal combination of variables such as V, S, H, W and L to satisfy a given objective function.

hypotheses	mathematical form	references
MUSP	min VS	Brebner & Wilson (1967); Yang (1973, 1976)
MSP =MSTC	min ρgQS	Chang & Hill (1977); Chang (1979a); White et al. (1982)
MEDR	min (ρgQ + ρsgQs)LS	Yang et al. (1981)
MFF	max W2H3S/Q2	Davies & Sutherland (1980, 1983)
minimum Froude number	min	Jia (1990)
minimum total energy expenditure	min	Rodríguez-Iturbe et al. (1992)