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^[1]

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

${\displaystyle Q={\bar {u}}bh}$

where ${\displaystyle Q}$ is the volumetric discharge, ${\displaystyle {\bar {u}}}$ is the mean flow velocity, ${\displaystyle b}$ is the channel width (breadth) and ${\displaystyle h}$ 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:^[1]

${\displaystyle b\propto Q^{0.5}}$

${\displaystyle h\propto Q^{0.4}}$

${\displaystyle u\propto Q^{0.1}}$

${\displaystyle Q}$ 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.