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In “Introduction to USGS Streamgaging,” they write:

“How Streamflow is Measured

“As you’re enjoying yourself sitting on the peaceful bank of a local river, one question you may ask yourself is ‘How much water is flowing in this river?’ You’ve come to the right place for an answer. The USGS has been measuring streamflow on thousands of rivers and streams for many decades and by reading this set of Web pages you can find out how the whole streamflow-measurement process works.

“Often during a large rainstorm you can hear an announcement on the radio like ‘Peachtree Creek is expected to crest later today at 14.5 feet.’ The 14.5 feet the announcer is referring to is the stream stage. Stream stage is important in that it can be used (after a complex process described below) to compute streamflow, or how much water is flowing in the stream at any instant.

“Stream stage (also called stage or gage height) is the height of the water surface, in feet, above an established altitude where the stage is zero. The zero level is arbitrary, but is often close to the streambed. You can get an idea of what stream stage is by looking at a picture of a common staff gage, which is used to make a visual reading of stream stage. The gage is marked in 1/100th and 1/10th foot intervals.

Streamgaging generally involves 3 steps:

1. Measuring stream stage—obtaining a continuous record of stage—the height of the water surface at a location along a stream or river
2. The discharge measurement—obtaining periodic measurements of discharge (the quantity of water passing a location along a stream)
3. The stage-discharge relation—defining the natural but often changing relation between the stage and discharge; using the stage-discharge relation to convert the continuously measured stage into estimates of streamflow or discharge

“The discharge measurement

“Discharge is the volume of water moving down a stream or river per unit of time, commonly expressed in cubic feet per second or gallons per day. In general, river discharge is computed by multiplying the area of water in a channel cross section by the average velocity of the water in that cross section:

discharge = area x velocity

“The USGS uses numerous methods and types of equipment to measure velocity and cross-sectional area, including the following current meter and Acoustic Doppler Current Profiler.”

Their description: “Diagram of Channel Cross Section With Subsections.The most common method used by the USGS for measuring velocity is with a current meter. However, a variety of advanced equipment can also be used to sense stage and measure streamflow. In the simplest method, a current meter turns with the flow of the river or stream. The current meter is used to measure water velocity at predetermined points (subsections) along a marked line, suspended cableway, or bridge across a river or stream. The depth of the water is also measured at each point. These velocity and depth measurements are used to compute the total volume of water flowing past the line during a specific interval of time. Usually a river or stream will be measured at 25 to 30 regularly spaced locations across the river or stream.” (From https://www.usgs.gov/special-topics/water-science-school/science/how-streamflow-measured)

Current Meter

“One method that has been used for decades by the USGS for measuring discharge is the mechanical current-meter method. In this method, the stream channel cross section is divided into numerous vertical subsections. In each subsection, the area is obtained by measuring the width and depth of the subsection, and the water velocity is determined using a current meter. The discharge in each subsection is computed by multiplying the subsection area by the measured velocity. The total discharge is then computed by summing the discharge of each subsection.

“The stage-discharge relation

“Streamgages continuously measure stage, as stated in the “Measuring Stage”” section. This continuous record of stage is translated to river discharge by applying the stage-discharge relation (also called rating). Stage-discharge relations are developed for streamgages by physically measuring the flow of the river with a mechanical current meter or ADCP at a wide range of stages; for each measurement of discharge there is a corresponding measurement of stage. The USGS makes discharge measurements at most streamgages every 6 to 8 weeks, ensuring that the range of stage and flows at the streamgage are measured regularly. Special effort is made to measure extremely high and low stages and flows because these measurements occur less frequently. The stage-discharge relation depends upon the shape, size, slope, and roughness of the channel at the streamgage and is different for every streamgage.

“Streamflow summary

“Streamgaging involves obtaining a continuous record of stage, making periodic discharge measurements, establishing and maintaining a relation between the stage and discharge, and applying the stage-discharge relation to the stage record to obtain a continuous record of discharge. The USGS has provided the Nation with consistent, reliable streamflow information for over 115 years. USGS streamflow information is critical for supporting water management, hazard management, environmental research, and infrastructure design.”

Their description: “USGS Stage-Discharge Relation Example.The continuous record of stage is converted to streamflow by applying a mathematical rating curve. A rating curve (fig. 3) is a graphic representation of the relation between stage and streamflow for a given river or stream. USGS computers use these site-specific rating curves to convert the water-level data into information about the flow of the river.” (From https://www.usgs.gov/special-topics/water-science-school/science/how-streamflow-measured)

In “Hydrometry: measuring the flow rate of a river, why and how?” (Lallement, Christian (February 7, 2019), Hydrometry: measuring the flow rate of a river, why and how?, Encyclopedia of the Environment, Accessed March 1, 2023 [online ISSN 2555-0950]) they write:

“Direct flow measurement is a complex operation that can only be performed occasionally. Except in very specific cases, direct and continuous monitoring of the flow cannot be carried out. It is the water level that is measured continuously, after having previously connected it to the flow rate by a calibration curve. This is why hydrometry is a 4-step process:

  • the continuous measurement of heights upstream of a hydraulic control (see Figure 3), or at another location where a unique height-flow relationship can be established,
  • the realization of periodic gauges to build this relationship (calibration curve), allowing to convert the heights into flows,
  • the layout of this calibration curve and the detection of its evolutions,
  • then, after conversion of heights into flow, critical analysis of spatial and temporal fluctuations, then their archiving.

“The most delicate link is the setting curve, the relationship between height and flow (Figure 10). For a long time manually drawn, according to the operators’ expertise alone, the definition of this curve now calls for decision support tools, tools combining statistical approaches, taking into account metrological uncertainties on gauging, hydraulic models.

From https://www.encyclopedie-environnement.org/en/water/hydrometry-measuring-flow-river-why-how/

“The height-flow relationship, if it is considered stable over a given period of time, is not necessarily stable over time, especially when the hydraulic control is not constituted by an artificial structure. Vegetation, human intervention, flooding – through the associated mechanisms of solid transport, erosion or deposition – more or less often modify the flow profile of the river. Monitoring the setting curve thus conditions a real gauging strategy, to be adapted both temporally (frequency of gauging) and according to water conditions (low water, average water, floods). Monitoring and plotting the calibration curve is the core business of hydrometry.

“The state of the art has recently evolved with indwelling devices that allow continuous speed measurement, either on the surface (speed radar) or indwelling in the flow (transit timeultrasound or Doppler effect). The principles of hydrometry are not fundamentally changed: a calibration relationship of height, velocity(s), flow rate remains to be calibrated throughout the operation of the measurement site. These systems were already implemented when a unique relationship between height and flow was not verified (rivers regulated by navigation and/or subject to tide), but current technological developments make it less costly to distribute this type of installation.

“New imaging technologies bring a promising innovation: video image processing to determine the field of surface velocities of a river (Figure 11). We use here the displacement of all solid bodies transported on the surface (twigs, bubbles, leaves…) as well as the turbulence of the flow. This technique is derived from the Particle Image Velocimetry (PIV) used in the laboratory, but for a study on large-scale river-type objects, hence its name Large-Scale PIV (LSPIV). This includes:

  • recording time-stamped image sequences ofthe flow,
  • geometric correction of the images to avoid perspective distortions,
  • calculation of the displacement of the flow tracers using a statistical analysis in correlation with the patterns.

“Knowing the geometry of the river section and assuming a vertical velocity distribution model, the total flow is estimated from the LSPIV velocity field.

“This technique of the future opens the way to a densification of flood measures: the fleeting nature of the episodes, the difficulties of access (flooded roads), the security conditions (violent flows) not allowing the teams to intervene as much as necessary. However, it cannot yet be implemented in case of poor visibility (night, fog).”

From https://www.encyclopedie-environnement.org/en/water/hydrometry-measuring-flow-river-why-how/

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