Discharge Measurement

Discharge (flow) is the volume of water passing a point on a stream per unit of time, most commonly reported as cubic feet per second (cfs). Discharge measurements are conducted during site visits, typically by measuring the width, depth, and velocity of the water at multiple points across the stream (Velocity-Area Method). Discharge can also be measured using weirs or with dilution gaging (adding a batch of salt to the stream and measuring specific conductivity downstream).

Site selection is the most critical step for conducting an accurate discharge measurement. The best sites are relatively straight without cross-channel flow, backwater, overhanging banks, or debris. If a stage logger is present, discharge needs to be measured relatively close to the logger so that gains or losses of flow do not occur between the stage logger and the discharge measurement location.

The most common measurement equipment will include a velocity meter that is mounted on a top setting rod. The top setting rod allows for measuring depth and setting the depth of the velocity sensor. The average velocity in a stream is typically at 60% of the distance from the surface to the bottom. The top setting rod is constructed to make it easy to set the probe depth at 60%.

A relatively simple 2-page standard operating procedure for measuring discharge with the Velocity-Area method using a Marsh McBirney Flo-Mate is available here. For an authoritative technical guide on measuring discharge, see the USGS technical report titled Discharge Measurement at Gaging Stations (Turnipseed and Sauer, 2010).

Stage measurement

Stage is the depth of water at a site and is typically measured to estimate discharge for the periods between site visits, using the relationship between stage and discharge. Stage data for creating hydrographs is commonly measured and recorded by a logger every hour, or sometimes more frequently.

Outside the USGS, pressure sensors have become perhaps the most common method for monitoring stage, but bubblers, floats, sonic distance sensors and other methods are also used. Stage loggers have traditionally been installed in stilling wells, which are basically a vertical pipe in the stream that provides a protected location for a stage recorder and a water surface protected from wave action. Stilling wells or installation locations should be configured so users can easily be reassured that the logger is going back into the exact same location when reinstalled after downloading data.

One of the biggest challenges in estimating discharge from stage is when changes in channel conditions or disturbance of the stage recorder result in changes to measured water depth for a given discharge rate. Estimating discharge from stage hinges on a given water level indicating a specific discharge, so stage gaging locations need to be located where non-flow related water level changes are minimal. Below are a few common causes for a change in measured stage without a change in discharge and ways to avoid the issue.

  1. Debris flowing down the stream catches on the stilling well and backs up water over the stage logger.
    • Make observations about the most likely path of debris moving down a channel and install stilling wells away from those stream positions. For pressure transducers, consider installing short pieces of pipe to house the loggers that do not extend above the water surface, perhaps bolted to rocks or infrastructure.
  2. Debris accumulates near the stilling well and backs up water over the stage logger.
    • Avoid installing stage loggers in locations where debris is present or in areas near obvious debris catching features.
  3. Macrophytes grow in the channel during the summer and displace water upwards resulting in higher stage for the same amount of discharge.
    • Scouting for macrophyte growth during peak growing season (July-September) prior to logger installation is ideal but often not possible for the first year of installation. Macrophyte growth is common in streams with high nutrient loads, in stream reaches with a lot of light, and with finer textured substrate.
  4. A high flow event erodes or deposits sediment from the channel bottom or banks near the site and changes the stage at the logger for a given discharge rate.
    • Look for sites with evidence of stable banks and channel bottom. Avoid installing stage loggers in stream sections with actively eroding banks or point bar formation.
  5. The position of the stage logger is disturbed by livestock rubbing on a stilling well or stepping on the logger.
    • Select sites without livestock access or install loggers in stream locations unlikely to be accessed by livestock.

Barometric pressure data is necessary to use pressure for measuring stage, to correct for changes in air pressure. Barometric pressure data must be available at the same logging interval as the water pressure data, which is a good reason to set pressure loggers to collect data on the hour for easy alignment of measurements. Installing a barometric pressure logger at a site is perhaps the most straightforward option. Barometric pressure data from a local weather station can also be used if it is representative of pressure for the monitoring site (perhaps within 5 miles and not at a vastly different elevation). A handheld barometer can be used during site scouting to assess now similar barometric pressure at a site is to pressure reported from a local weather station. Some water pressure loggers are equipped with a tube that vents to the surface so they can collect air pressure. Vented loggers are convenient for the barometric correction, but reduce opportunities for sleek installations in short pieces of pipe bolted to rocks to avoid debris catch issues. For context on importance of barometric pressure correction, one Kilopascal of air pressure is equivalent to the pressure from about 10 cm (4 in) of water pressure. Daily barometric pressure measurements for the Montana Mesonet station near Manhattan MT ranged between 84.4 and 88.2 over the last few years, which if unaccounted for, would translate to 38 cm (15 in) of error in recorded water levels.

Loggers should be downloaded on a regular interval and data should be backed up in multiple locations. If a logger has sufficient data storage capacity, consider scheduling regular downloads through the season but also leaving all data on the logger for a full monitoring season. Regular downloads are important to allow for timely troubleshooting of data logging issues that may arise during the season. Keeping all data on the logger for the full season allows for a single downloaded file at the end of the season to contain all data to avoid needing to splice data files together for analysis. Leaving data on the logger also provides redundancy if any data files are lost from the field computer used to download loggers.

If a stage monitoring site has a high likelihood for disturbance, and/or is intended to be used for many years, consider measuring the height of the logger installation relative to a stable location (a datum). Candidates for local datums include large concrete infrastructure, bedrock outcrops, or robustly installed off-channel fence posts. Measuring the elevation of the stage logger relative to a datum in close proximity is possible with a simple survey level and transit rod. If a high accuracy GPS system is available, the datum could be sea level.

For an authoritative technical guide on measuring stage, see the USGS technical report titled Stage Measurement at Gaging Stations (Sauer and Turnipseed, 2010).

Continuous discharge

Producing hydrographs with daily (or higher frequency) discharge values are a common goal of monitoring projects. Daily discharge data requires daily stage data in combination with direct discharge measurements and a “rating curve” that establishes the relationship between stage and discharge at a site.

Discharge measurements and associated stage values for multiple visits over a season are plotted with discharge on the X axis and stage on the Y axis. A line is fit through the points, to produce a “rating curve,” which is an equation relating stage to discharge. Stage values measured by a data logger are plugged into the rating curve equation to estimate discharge on a daily or hourly basis.

Rating curves change over time, especially related to high flow events that commonly reshape channels. USGS guidance suggests a minimum of 10 discharge measurements per year for a rating to meet their data quality standards. For monitoring programs with more intermediate data rigor goals, ensuring at least five measurements per year might be a more practical minimum number of measurements.

Discharge estimates are not accurate for values outside the range of discharge measurements used to create rating curves. This means hydrographs are not accurate for estimating flows higher than the highest flow measured during a site visit, and are not accurate for flows lower than the lowest flow measured. This should be considered for scheduling field visits to cover the largest flow range that is practical and safe. The lowest flows may occur in late summer, so visits should be scheduled during this time if low flows are intended to be accurate on the hydrograph. High flow occurs with peak snowmelt in most Montana streams, but the highest flows often produce unsafe conditions for measurements. This means that without specialized focus on estimating discharge at peak flows, hydrographs will not be accurate for discharge above levels where it is safe to make field measurements.

Installing a manual staff gage at the same location where stage recorders are deployed is highly recommended. A manual staff gage reading should be taken during every site visit when discharge is measured. This allows for creation of a rating curve with both the stage from the manual readings and from the stage logger. If issues arise in the rating curve based on manual stage readings, issues are typically related to local controls on stage (debris, macrophytes, etc.). If the manual stage rating curve looks good, but the rating curve with stage values from the data logger has problems, the issue is typically related to the data logger.

Changes or “shifts” in a rating curve are expected to occur over time as the channel form changes, but shifts can also occur on a seasonal basis due to aquatic vegetation growth. Application of shifts to data within a monitoring season can be complex and likely requires engaging a hydrologist. Taking time to select stations and install stage loggers to minimize likelihood of shifts is important to make the rating curve analysis as straight-forward as possible. When starting the process of rating curve development for a new year with an established monitoring site, it is reasonable to include the points from the previous year’s rating curve. It is important to fit separate curves for the different years however to assess whether the channel has changed enough that the previous year’s points need to be discarded.

It is important to plot measured discharge values on the same plot with discharge values estimated from stage and the rating curve to get a sense for the uncertainty in the hydrograph. Assess the difference between the measured and estimated values for each field visit discharge value. Do not expect your hydrograph to be more accurate than those difference values. The R^2 value of a rating curve line can also provide a rough idea of the uncertainty in discharge values estimated from the rating curve, as long as a minimum of five discharge measurements are included. Hydrographs produced by these methods can be very insightful for interpreting patterns in discharge, but it is important to be weary of over-interpreting the accuracy of individual modeled discharge values if rigorous quality assurance measures are not in place.

For an authoritative technical guide on calculating discharge using rating curves, see the USGS technical report titled Measurement and Computation of Streamflow: Volume 2. Computation of Discharge (Rantz, 1982).


  • EPA, 2008, Surface Water Flow Measurement for Water Quality Monitoring Projects. Technotes, Issue Number 3. https://www.epa.gov/sites/default/files/2016-05/documents/tech_notes_3_dec2013_surface_flow.pdf (16 page factsheet overviewing methods and considerations for monitoring flow related to water quality)
  • Rantz, S.E., 1982, Measurement and Computation of Streamflow: Volume 2. Computation of Discharge. https://pubs.usgs.gov/wsp/wsp2175/wsp2175_vol2.pdf (373 page technical report on calculating flow to create hydrographs from direct flow measurements and high frequency stage data)
  • Sauer, V.B., 2002, Standards for the Analysis and Processing of Surface-Water Data and Information Using Electronic Methods: U.S. Geological Survey Water-Resources Investigations Report 01–4044, 91 p. https://water.usgs.gov/osw/pubs/WRIR01-4044.pdf (a 106 page technical report covering data entry, rating curve development, shifts, etc.)
  • Sauer, V.B., and Turnipseed, D.P., 2010, Stage measurement at gaging stations: U.S. Geological Survey Techniques and Methods book 3, chap. A7, 45 p. http://pubs.usgs.gov/tm/tm3-a7/ (60 page technical report describing measurement of high frequency stage data)
  • Turnipseed, D.P., and Sauer, V.B., 2010, Discharge measurements at gaging stations: U.S. Geological Survey. Techniques and Methods book 3, chap. A8, 87 p. http://pubs.usgs.gov/tm/tm3-a8/. (106 page technical report describing methods for making direct discharge measurements during site visits)