# Discharge (hydrology)

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In hydrology, discharge is the volumetric flow rate of water that is transported through a given cross-sectional area. [1] It includes any suspended solids (e.g. sediment), dissolved chemicals (e.g. CaCO3(aq)), or biologic material (e.g. diatoms) 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.

## Theory and calculation

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 that are typically used to express discharge in streams or rivers include m3/s (cubic meters per second), ft3/s (cubic feet per second or cfs) and/or acre-feet per day. [2]

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 (${\displaystyle {\bar {u}}}$), and is written as:

${\displaystyle Q=A\,{\bar {u}}}$

where

• ${\displaystyle Q}$ is the discharge ([L3T−1]; m3/s or ft3/s)
• ${\displaystyle A}$ is the cross-sectional area of the portion of the channel occupied by the flow ([L2]; m2 or ft2)
• ${\displaystyle {\bar {u}}}$ is the average flow velocity ([LT−1]; m/s or ft/s)

For example, the average discharge of the Rhine river in Europe is 2,200 cubic metres per second (78,000 cu ft/s) or 190,000,000 cubic metres (150,000 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

A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second (cms or cfs).

It can also refer to a graph showing the volume of water reaching a particular outfall, or location in a sewerage network. Graphs are commonly used in the design of sewerage, more specifically, the design of surface water sewerage systems and combined sewers.

## 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 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 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. [3] and on land use affecting river discharge and bedload supply. [4]

## Inflow and the Hydrologic Cycle

Inflow [5] is a process within the hydrologic cycle that helps maintain the water levels within all bodies of water.

The hydrologic cycle, [6] or water cycle, has no true starting point. However, it’s easiest to start with the ocean, as the ocean makes up the majority of Earth’s water. The sun is the main aspect of the hydrologic cycle, as it is responsible for warming the water and causing evaporation. As water evaporates into the air and the rising air currents take the evaporated water into the atmosphere. Once the evaporated water reaches high enough in the atmosphere, it reaches cooler temperatures, which cause the vapor to condense into clouds.

Air currents are capable of moving clouds around the globe, but typically cloud particles collide and fall out of the sky as precipitation. Even though precipitation can fall in many forms and in many locations, most precipitations either ends up back into a body of water or on land as surface runoff. [7] A portion of runoff enters back into streams and rivers, which over time lead back to the ocean. Another portion of runoff soaks into the ground as groundwater seepage, and are stored in freshwater lakes. [8] The other portion of runoff soaks into the ground as infiltration, some of this water will infiltrate deep into the ground and replenish aquifers. [6]

So how does inflow play a role in the hydrologic cycle? Inflow is the adding of water to the different aspects of the hydrologic system. Consequently, outflow is the removal of water from the hydrological cycle. Inflow adds water to different aspects of the hydrologic cycle that returns water storage to an even level. Water storage is the retention of water throughout different aspects of the hydrologic cycle. Due to the fact that water movement is cyclical, [9] inflow, outflow, and storage are all aspects of the hydrologic cycle.

Inflow = Outflow +/- Changes in Storage [9]

## Related Research Articles

Hydrology is the scientific study of the movement, distribution, and management of water on Earth and other planets, including the water cycle, water resources, and environmental watershed sustainability. A practitioner of hydrology is called a hydrologist. Hydrologists are scientists studying earth or environmental science, civil or environmental engineering, and physical geography. Using various analytical methods and scientific techniques, they collect and analyze data to help solve water related problems such as environmental preservation, natural disasters, and water management.

A stream gauge, streamgage or stream gauging station is a location used by hydrologists or environmental scientists to monitor and test terrestrial bodies of water. Hydrometric measurements of water level surface elevation ("stage") and/or volumetric discharge (flow) are generally taken and observations of biota and water quality may also be made. The locations of gauging stations are often found on topographical maps. Some gauging stations are highly automated and may include telemetry capability transmitted to a central data logging facility.

The water cycle, also known as the hydrologic cycle or the hydrological cycle, is a biogeochemical cycle that describes the continuous movement of water on, above and below the surface of the Earth. The mass of water on Earth remains fairly constant over time but the partitioning of the water into the major reservoirs of ice, fresh water, saline water and atmospheric water is variable depending on a wide range of climatic variables. The water moves from one reservoir to another, such as from river to ocean, or from the ocean to the atmosphere, by the physical processes of evaporation, transpiration, condensation, precipitation, infiltration, surface runoff, and subsurface flow. In doing so, the water goes through different forms: liquid, solid (ice) and vapor. The ocean plays a key role in the water cycle as it is the source of 86% of global evaporation.

A hydrograph is a graph showing the rate of flow (discharge) versus time past a specific point in a river, channel, or conduit carrying flow. The rate of flow is typically expressed in cubic meters or cubic feet per second . It can also refer to a graph showing the volume of water reaching a particular outfall, or location in a sewerage network. Graphs are commonly used in the design of sewerage, more specifically, the design of surface water sewerage systems and combined sewers.

Ecohydrology is an interdisciplinary scientific field studying the interactions between water and ecological systems. It is considered a sub discipline of hydrology, with an ecological focus. These interactions may take place within water bodies, such as rivers and lakes, or on land, in forests, deserts, and other terrestrial ecosystems. Areas of research in ecohydrology include transpiration and plant water use, adaption of organisms to their water environment, influence of vegetation and benthic plants on stream flow and function, and feedbacks between ecological processes, the soil carbon sponge and the hydrological cycle.

Isotope hydrology is a field of geochemistry and hydrology that uses naturally occurring stable and radioactive isotopic techniques to evaluate the age and origins of surface and groundwater and the processes within the atmospheric hydrologic cycle. Isotope hydrology applications are highly diverse, and used for informing water-use policy, mapping aquifers, conserving water supplies, assessing sources of water pollution, and increasingly are used in eco-hydrology to study human impacts on all dimensions of the hydrological cycle and ecosystem services.

Drainage density is a quantity used to describe physical parameters of a drainage basin. First described by Robert E. Horton, drainage density is defined as the total length of channel in a drainage basin divided by the total area, represented by the following equation:

Infiltration is the process by which water on the ground surface enters the soil. It is commonly used in both hydrology and soil sciences. The infiltration capacity is defined as the maximum rate of infiltration. It is most often measured in meters per day but can also be measured in other units of distance over time if necessary. The infiltration capacity decreases as the soil moisture content of soils surface layers increases. If the precipitation rate exceeds the infiltration rate, runoff will usually occur unless there is some physical barrier.

The United States Environmental Protection Agency (EPA) Storm Water Management Model (SWMM) is a dynamic rainfall–runoff–subsurface runoff simulation model used for single-event to long-term (continuous) simulation of the surface/subsurface hydrology quantity and quality from primarily urban/suburban areas. It can simulate the Rainfall- runoff, runoff, evaporation, infiltration and groundwater connection for roots, streets, grassed areas, rain gardens and ditches and pipes, for example. The hydrology component of SWMM operates on a collection of subcatchment areas divided into impervious and pervious areas with and without depression storage to predict runoff and pollutant loads from precipitation, evaporation and infiltration losses from each of the subcatchment. Besides, low impact development (LID) and best management practice areas on the subcatchment can be modeled to reduce the impervious and pervious runoff. The routing or hydraulics section of SWMM transports this water and possible associated water quality constituents through a system of closed pipes, open channels, storage/treatment devices, ponds, storages, pumps, orifices, weirs, outlets, outfalls and other regulators.

The law of water balance states that the inflows to any water system or area is equal to its outflows plus change in storage during a time interval. In hydrology, a water balance equation can be used to describe the flow of water in and out of a system. A system can be one of several hydrological or water domains, such as a column of soil, a drainage basin, an irrigation area or a city. Water balance can also refer to the ways in which an organism maintains water in dry or hot conditions. It is often discussed in reference to plants or arthropods, which have a variety of water retention mechanisms, including a lipid waxy coating that has limited permeability.

Streamflow, or channel runoff, is the flow of water in streams and other channels, and is a major element of the water cycle. It is one component of the movement of water from the land to waterbodies, the other component being surface runoff. Water flowing in channels comes from surface runoff from adjacent hillslopes, from groundwater flow out of the ground, and from water discharged from pipes. The discharge of water flowing in a channel is measured using stream gauges or can be estimated by the Manning equation. The record of flow over time is called a hydrograph. Flooding occurs when the volume of water exceeds the capacity of the channel.

A cubic metre per second is the unit of volumetric flow rate in the International System of Units (SI) equal to that of a stere or cube with sides of one metre (39.37 in) in length exchanged or moving each second. It is popularly used for water flow, especially in rivers and streams, and fractions for HVAC values measuring air flow.

A perennial stream is a stream that has continuous flow of surface water throughout the year in at least parts of its catchment during seasons of normal rainfall, as opposed to one whose flow is intermittent. In the absence of irregular, prolonged or extreme drought, a perennial stream is a watercourse, or segment, element or emerging body of water which continually delivers groundwater. For example, an artificial disruption of stream, variability in flow or stream selection associated with the activity in hydropower installations, do not affect this status. Perennial streams do not include stagnant water, reservoirs, cutoff lakes and ponds that persist throughout the year. All other streams, or parts of them, should be considered seasonal rivers or lakes. The stream can cycle from intermittent to perpetual through multiple iterations.

A runoff model is a mathematical model describing the rainfallrunoff relations of a rainfall catchment area, drainage basin or watershed. More precisely, it produces a surface runoff hydrograph in response to a rainfall event, represented by and input as a hyetograph. In other words, the model calculates the conversion of rainfall into runoff.
A well known runoff model is the linear reservoir, but in practice it has limited applicability.
The runoff model with a non-linear reservoir is more universally applicable, but still it holds only for catchments whose surface area is limited by the condition that the rainfall can be considered more or less uniformly distributed over the area. The maximum size of the watershed then depends on the rainfall characteristics of the region. When the study area is too large, it can be divided into sub-catchments and the various runoff hydrographs may be combined using flood routing techniques.

A hydrologic model is a simplification of a real-world system that aids in understanding, predicting, and managing water resources. Both the flow and quality of water are commonly studied using hydrologic models.

Agricultural hydrology is the study of water balance components intervening in agricultural water management, especially in irrigation and drainage.

The following outline is provided as an overview of and topical guide to hydrology:

Catchment hydrology is the study of hydrology in drainage basins. Catchments are areas of land where runoff collects to a specific zone. This movement is caused by water moving from areas of high energy to low energy due to the influence of gravity. Catchments often do not last for long periods of time as the water evaporates, drains into the soil, or is consumed by animals.

DPHM-RS is a semi-distributed hydrologic model developed at University of Alberta, Canada.

In hydrology, routing is a technique used to predict the changes in shape of a hydrograph as water moves through a river channel or a reservoir. In flood forecasting, hydrologists may want to know how a short burst of intense rain in an area upstream of a city will change as it reaches the city. Routing can be used to determine whether the pulse of rain reaches the city as a deluge or a trickle.

## References

1. Buchanan, T.J. and Somers, W.P., 1969, Discharge Measurements at Gaging Stations: U.S. Geological Survey Techniques of Water-Resources Investigations, Book 3, Chapter A8, p. 1.
2. Dunne, T., and Leopold, L.B., 1978, Water in Environmental Planning: San Francisco, Calif., W.H. Freeman, pp. 257–258.
3. L. B. Leopold, M. G. Wolman J. P. and Miller, Fluvial Processes in Geomorphology, W. H. Freeman, San Francisco, 1964.
4. 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.
5. "The Hydrologic Cycle | Freshwater Inflows". www.freshwaterinflow.org. Retrieved 2020-12-09.
6. "Precipitation and the Water Cycle". www.usgs.gov. Retrieved 2020-12-09.
7. DOC, NOAA. "Description of the Hydrologic Cycle". www.nwrfc.noaa.gov. Retrieved 2020-12-09.
8. "Groundwater Flows Underground". www.usgs.gov. Retrieved 2020-12-09.
9. "Water Research Center - Watershed and Water Resource Budgets". water-research.net. Retrieved 2020-12-09.