Discharge (hydrology)

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In hydrology, the discharge or outflow of a river is the volume of water transported by it in a certain amount of time. It is contrasted with inflow. The unit used is usually m³/s (cubic meters per second, or cumecs). For example, the average discharge of the Rhine river is 2200 m³/s.

The discharge of a river can be estimated by:

$Q=A\,\bar{v}$

where

$Q$ is the discharge ([L³T⁻¹]; m³/s or ft³/s)
$A$ is the cross-sectional area ([L²]; m² or ft²)
$\bar{v}$ is the average linear velocity ([LT⁻¹]; m/s or ft/s)

[edit] Catchment discharge

The catchment of a river above a certain location is determined by the surface area of all land which drains toward the river from above that point. The river's discharge at that location depends on the rainfall on the catchment or drainage area and the inflow or outflow of groundwater to or from the area, stream modifications such as dams and irrigation diversions, as well as evaporation and evapotranspiration from the area's land and plant surfaces. In storm hydrology an important consideration is the stream's discharge hydrograph, a record of how the discharge varies over time after a precipitation event. The stream rises to a peak flow after each precipitation event, then falls in a slow recession. Because the peak flow also corresponds to the maximum water level reached during the event, it is of interest in flood studies. Analysis of the relationship between precipitation intensity and duration, and the response of the stream discharge is mmm by the concept of the unit hydrograph which represents the response of stream discharge over time to the application of a hypothetical "unit" amount and duration of rain, for example 1 cm over the entire catchment for a period of one hour. This represents a certain volume of water (depending on the area of the catchment) which must subsequently flow out of the river. Using this method either actual historical rainfalls or hypothetical "design storms" can be modelled mathematically to confirm characteristics of historical floods, or to predict a stream's reaction to a predited storm.

The relationship between the discharge in the stream at a given cross-section and the level of the stream is described by a rating curve. Average velocities and the cross-sectional area of the stream are measured for a given stream level. The velocity and the area give the discharge for that level. After measurements are made for several different levels, a rating table or rating curve may be developed. Once rated, the discharge in the stream may be determined by measuring the level, and determining the corresponding discharge from the rating curve. If a continuous level-recording device is located at a rated cross-section, the stream's discharge may be continuously determined.

In absolute terms, the greater the discharge of a river, the more sediment it may carry. In relative terms the ability to carry sediments depends on the settling velocity, the speed of the flow.