The river regime generally describes the character of the typical fluctuations of flow of a river, but can also refer to the mathematical relationship between the river discharge and its width, depth and slope. Thus, "river regime" can describe one of two characteristics of a reach of an alluvial river:

• The variability in its discharge throughout the course of a year in response to precipitation, temperature, evapotranspiration and drainage basin characteristics (Beckinsale, 1969)
• A series of characteristic power-law relationships between discharge and width, depth and slope

The latter 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:

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

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

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

${\displaystyle Q}$ 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.

The variability in discharge over the course of a year is commonly represented by a hydrograph with mean monthly discharge variations plotted over the annual time scale. When interpreting such records of discharge, it is important to factor in the time scale over which the average monthly values were calculated. It is particularly difficult to establish a typical annual river regime for rivers with high interannual variability in monthly discharge and/or significant changes in the catchment's characteristics (e.g. tectonic influences or the introduction of water management practices).