River regime

The river regime generally refers to the mathematical relationship between the river discharge and its width, depth and slope. Thus, "river regime" describes a series of characteristic power-law relationships between discharge and width, depth and slope

It is described by the fact that the discharge through a river of an approximate rectangular cross-section must, through conservation of mass, equal


 * $$Q = \bar{u} b h$$

where $$Q$$ is the volumetric discharge, $$\bar{u}$$ is the mean flow velocity, $$b$$ is the channel width (breadth) and $$h$$ is the channel depth.

Because of this relationship, as discharge increases, depth, width, and/or mean velocity must increase as well.

Empirically derived relationships between depth, slope, and velocity are:


 * $$b \propto Q^{0.5}$$
 * $$h \propto Q^{0.4}$$
 * $$u \propto Q^{0.1}$$

$$Q$$ refers to a "dominant discharge" or "channel-forming discharge", which is typically the 1–2 year flood, though there is a large amount of scatter around this mean. This is the event that causes significant erosion and deposition and determines the channel morphology.