View source for Discharge (hydrology)

{{Short description|Flow rate of water that is transported through a given cross-sectional area}}
{{More citations needed|date=December 2023}}
In [[hydrology]], '''discharge''' is the [[volumetric flow rate]] (volume per time, in units of m<sup>3</sup>/h or ft<sup>3</sup>/h) of a [[stream]]. It equals the product of average [[flow velocity]] (with dimension of length per time, in m/h or ft/h) and the [[cross-sectional area]] (in m<sup>2</sup> or ft<sup>2</sup>).<ref>Buchanan, T.J. and Somers, W.P., 1969, [https://pubs.usgs.gov/twri/twri3a8/pdf/twri_3-A8_a.pdf#page=7&zoom=auto,-52,304 Discharge Measurements at Gaging Stations: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chapter A8, p. 1.]</ref> It includes any suspended solids (e.g. sediment), dissolved chemicals like {{chem|Ca|C|O|3|link=calcium carbonate}}(aq), or biologic material (e.g. [[diatom]]s) in addition to the water itself. Terms may vary between disciplines. For example, a fluvial hydrologist studying natural river systems may define discharge as [[streamflow]], whereas an engineer operating a reservoir system may equate it with '''outflow''', contrasted with '''inflow'''.

==Formulation==
A discharge is a measure of the quantity of any fluid flow over unit time. The quantity may be either volume or mass. Thus the water discharge of a tap (faucet) can be measured with a measuring jug and a stopwatch. Here the discharge might be 1 litre per 15 seconds, equivalent to 67 ml/second or 4 litres/minute. This is an average measure. For measuring the discharge of a river we need a different method and the most common is the 'area-velocity' method. The area is the cross sectional area across a river and the average velocity across that section needs to be measured for a unit time, commonly a minute. Measurement of cross sectional area and average velocity, although simple in concept, are frequently non-trivial to determine.

The [[units of measurement|units]] that are typically used to express discharge in streams or rivers include m<sup>3</sup>/s (cubic meters per second), ft<sup>3</sup>/s (cubic feet per second or cfs) and/or [[acre-feet]] per day.<ref>[[Thomas Dunne (geologist)|Dunne, T.]], and [[Luna Leopold|Leopold, L.B.]], 1978, Water in Environmental Planning: San Francisco, Calif., W.H. Freeman, pp. 257–258.</ref>

A commonly applied methodology for measuring, and estimating, the discharge of a river is based on a simplified form of the [[continuity equation]].  The equation implies that for any incompressible fluid, such as liquid water, the discharge (Q) is equal to the product of the stream's cross-sectional area (A) and its mean velocity (<math>\bar{u}</math>), and is written as:
:<math>Q=A\,\bar{u}</math>
where
*<math>Q</math> is the discharge ([L<sup>3</sup>T<sup>−1</sup>]; m<sup>3</sup>/s or ft<sup>3</sup>/s)
*<math>A</math> is the cross-sectional [[area]] of the portion of the channel occupied by the flow ([L<sup>2</sup>]; m<sup>2</sup> or ft<sup>2</sup>)
*<math>\bar{u}</math> is the average [[flow velocity]] ([LT<sup>−1</sup>]; m/s or ft/s)

For example, the average discharge of the [[Rhine]] river in Europe is {{convert|2200|m3/s|cuft/s}} or {{convert|190000000|m3|acre.ft}} per day.

Because of the difficulties of measurement, a [[stream gauge]] is often used at a fixed location on the stream or river.

==Hydrograph==
{{excerpt|Hydrograph}}

==Catchment discharge==
[[File:Pescone alla foce.jpg|thumb|Torrente Pescone, one of the inflows of [[Lake Orta]] ([[Italy]]).]]
The [[drainage basin|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 are aided 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 rainfall (e.g., half an inch over one hour). The amount of precipitation correlates to the volume of water (depending on the area of the catchment) that subsequently flows out of the river. Using the unit hydrograph method, actual historical rainfalls can be modeled mathematically to confirm characteristics of historical floods, and hypothetical "design storms" can be created for comparison to observed stream responses.

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.

Larger flows (higher discharges) can [[sediment transport|transport]] more [[sediment]] and larger particles downstream than smaller flows due to their greater force. Larger flows can also erode stream banks and damage public infrastructure.

==Catchment effects on discharge and morphology==
[[G. H. Dury]] and M. J. Bradshaw are two [[geographers]] who devised models showing the relationship between discharge and other variables in a river. The [[Bradshaw model]] described how pebble size and other variables change from source to mouth; while Dury considered the relationships between discharge and variables such as [[stream slope]] and friction. These follow from the ideas presented by Leopold, Wolman and Miller in ''Fluvial Processes in Geomorphology''.<ref>L. B. Leopold, M. G. Wolman J. P. and Miller, ''Fluvial Processes in Geomorphology'', W. H. Freeman, San Francisco, 1964.</ref> and on land use affecting river discharge and bedload supply.<ref>G. M. Kondolf, H. Piégay and N. Landon, "Channel response to increased and decreased bedload supply from land use change: contrasts between two catchments", ''Geomorphology'', 45/1–2, pp. 35–51.</ref>

== Inflow ==
{{section rewrite|date=December 2023}}
[[File:Watercyclesummary.jpg|thumb|Visual description of Hydrologic Cycle]]
Inflow is the sum of processes within the [[Water cycle|hydrologic cycle]] that increase the water levels of bodies of water.<ref>{{Cite web|title=The Hydrologic Cycle {{!}} Freshwater Inflows|url=https://www.freshwaterinflow.org/hydrologic-cycle|access-date=2020-12-09|website=freshwaterinflow.org}}</ref>
Most [[precipitation]] occurs directly over bodies of water such as the oceans, or on land as [[surface runoff]].<ref>{{Cite web|last=DOC|first=NOAA|title=Description of the Hydrologic Cycle|url=https://www.nwrfc.noaa.gov/info/water_cycle/hydrology.cgi|access-date=2020-12-09|website=www.nwrfc.noaa.gov|language=en}}</ref> A portion of runoff enters streams and rivers, and another portion soaks into the ground as [[Soil mechanics#Seepage|groundwater seepage]].<ref>{{Cite web|title=Groundwater Flows Underground|url=https://www.usgs.gov/special-topic/water-science-school/science/groundwater-flows-underground?qt-science_center_objects=0#qt-science_center_objects|access-date=2020-12-09|website=usgs.gov}}</ref> The rest soaks into the ground as infiltration, some of which infiltrates deep into the ground to replenish aquifers.<ref name=":0">{{Cite web|title=Precipitation and the Water Cycle|url=https://www.usgs.gov/special-topic/water-science-school/science/precipitation-and-water-cycle?qt-science_center_objects=0#qt-science_center_objects|access-date=2020-12-09|website=usgs.gov}}</ref>

==See also==
* [[List of rivers by discharge]]
* [[Groundwater discharge]]
* [[Submarine groundwater discharge]]
* [[Stream gauge]]
*[[Hydrology]]

==References==
<references />

==External links==
*{{cite book |title=USDA NRCS National Engineering Handbook |chapter-url=https://www.wcc.nrcs.usda.gov/ftpref/wntsc/H%26H/NEHhydrology/ch14.pdf |chapter=Chapter 14: Stage-Discharge Relationships |date=April 2012 |series=Part 630: Hydrology |publisher=[[United States Department of Agriculture|USDA]] |access-date=2017-09-11 |archive-date=2021-04-19 |archive-url=https://web.archive.org/web/20210419113655/https://www.wcc.nrcs.usda.gov/ftpref/wntsc/H%26H/NEHhydrology/ch14.pdf |url-status=dead }}
*{{cite book |title=USDA NRCS National Engineering Handbook |url=https://directives.sc.egov.usda.gov/viewerFS.aspx?hid=21422 |date=May 2012 |series=Part 630: Hydrology |publisher=[[United States Department of Agriculture|USDA]] |access-date=2017-09-11 |archive-date=2022-01-14 |archive-url=https://web.archive.org/web/20220114201859/https://directives.sc.egov.usda.gov/ViewerFS.aspx?hid=21422 |url-status=dead }}

{{Rivers, streams and springs}}

[[Category:Hydrology]]
[[Category:Rivers]]
[[Category:Temporal rates]]
[[Category:Physical quantities]]