River regime

This article is about the mathematical relationship between the river discharge and its width, depth and slope. For the annual pattern of a river's discharge, see Discharge 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

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

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.