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 where is the volumetric discharge, is the mean flow velocity, is the channel width and 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: 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 annualtime 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.
Simple regimes can be nival, pluvial or glacial, depending on the origin of the water. Simple regime is where all rivers have one peak discharge per year ;Glacial regime The glacial regime is characterised by:
Very low discharge from the end of autumn to early spring
Amplitude of monthly variation of discharge greater than 25
Very high daily variability in discharge during the year
High flow
It is found at high altitudes, above. Example: Rhône at Brigue. ;Nival The nival regime is similar to the glacial, but attenuated and the maximum takes place earlier, in June. It can be mountain or plain nival. The characteristics of the plain nival are:
Short and violent flood in April–May following massive spring thawing ofwinter snows
Great daily variability
Very great variability over the course of the year
Great inter-annual variability
Significant flow
;Pluvial The pluvial regime is characterized by:
high water in winter and spring
low discharge in summer
great inter-annual variability
flow is generally rather weak
It is typical of rivers at low to moderate altitude. Example: Seine. ;Tropical pluvial The tropical pluvial regime is characterized by:
very low discharge in the cold season and abundant rainfall in the warm season
The complex regime is characteristic of large rivers, the flow of which is diversely influenced by numerous tributaries from different altitudes, climates etc. The influences diminish extreme discharges and increase the regularity of the mean monthly discharge from upstream to downstream.
