Stream Gaging and Rating Curves
I. Objective
The process of
measuring stream flow is called stream
gaging. Precisely measuring the discharge of a stream or river is
one of the fundamental tasks in surface water hydrology. Directly measuring the
discharge is accomplished by measuring the average flow velocity with a flow
meter within subsections of a stream's cross-section (discharge = velocity x
cross-sectional area). However, this process can be time consuming, and
occasionally dangerous, especially during flooding events. Therefore, it is
practical to develop indirect methods for determining discharge. Measurement of
stage (depth of the water at a
particular point along the stream) is quick and easy, and can provide fairly
precise measure of discharge if the relationship between stage and discharge is
known. Hydrologists must therefore develop a rating
curve that relates stage to discharge at a particular point along a
stream.
Above/Right: Stream gaging along the Verde River, Arizona
IIa. Background - Stream Gaging
Consider a cross section of a stream that is oriented perpendicular to the flow direction. Since the velocity varies so greatly across the section (approximately zero at the channel bottom and near obstacles to the maximum near the surface away from the banks), finding a value for the average velocity of the stream is quite difficult. Therefore, it is practical to divide the stream into a number of imaginary subsections and measure the average velocity for that subsection. If the width and depth dimensions are known, a discharge measurement for the subsection is determined by multiplying the cross-sectional area of the subsection (width x depth) by the average velocity of the subsection. The discharge for the entire stream is therefore the summation of all of the subsection discharge measurements.
What is the average velocity of a subsection? On the basis of field and laboratory tests, the velocity variation along a vertical line running from the stream bed to the stream surface is such that average velocity is found at 0.6 depth (6/10 of the way down from the surface to the stream bed), or at the average of the velocities found at the 0.2 and 0.8 depths. For example, if the subsection was 1 foot deep, the average velocity of the subsection would be found 0.6 feet down from the surface (or 0.4 feet up from the bottom). As a general rule of thumb, use the 0.6 depth velocity reading as the average if the stream is less than 1.5 feet deep, and use the average of the 0.2 and 0.8 depth velocity readings as the average if the stream is more than 1.5 feet deep.
Above: Diagram of a stream cross section showing the location of velocity measurements (white dots) that must be acquired during gaging. The profile has a width of 15 feet, and is therefore divided into 1-foot wide sections to provide at least 15 subsections for gaging. Velocity is measured in the center of each subsection (at 0.5', 1.5', 2.5'. etc.) at 0.6D if D is less than 1.5 feet, or at 0.2 and 0.8D if D is greater than 1.5 feet.
How many subsections should the stream be divided into? There are a couple of considerations that dictate the number of subsections that should be measured to determine the discharge of a stream.
1) the stream should be divided into a minimum of 15 subsections.
2) no subsection should have a width less than 3/10 of a foot.
3) no subsection may have more than 10% of the total stream flow
4) the number of subsections must be limited to those that can be measured in a reasonable amount of time.
For example, if a stream is 32 feet wide then it may be prudent to divide it into 16 sections that are 2-feet wide each. However, some small ditches, streams and channels may be so narrow that it is not possible to divide them into 15 or more sections that are at least 3/10 of a foot wide. If this is the case, then divide the stream into as many 3/10 of a foot sections as possible. Thus, a 1.2 foot wide ditch would be divided into four 3/10 of a foot subsections.
Depending on the shape of the channel, it may be necessary to sub-divide some of the deeper subsections into even smaller subsections to prevent measuring more than 10% of the total flow in a single subsection. For example, if you are gaging the 32 foot wide stream mentioned above and notice that two of your 16 2-foot wide subsections are quite deep and likely will contain more than 10% of the total flow, it is entirely acceptable to divide these two 2-foot wide subsections into 4 one-foot wide subsections. Thus, you would measure 14 2-foot wide subsections and 4 one-foot wide subsections. It is not necessary to have all subsections the same width!
IIb. Background - Rating Curves
In order to produce a rating curve that easily allows a hydrologist to relate a stage measurement to discharge, one must acquire a number of different discharge and associated stage measurements at a particular cross-section along a natural stream. Stage is measured by reading the position of a water surface on a ruler-like staff gage or with bubbler-type instruments that directly measure water pressure and relate this value to stage.
Far Left: USGS gaging station at Spearfish
Creek. The station continually measures stage by using a bubbler-type
instrument that relates the pressure needed to force air through a tube to the
depth of water over the tube. Left: Pipe containing air tube for the bubbler at
the base of the large rock, immediately adjacent to the gaging station. The
pipe protects the tube and helps keep it in position.
Because the process of acquiring a sufficient number of discharge/stage measurements can be time consuming (especially if one must wait for meteorological conditions to change), it is typically preferable to install a flume or a weir. Flumes and weirs are devices installed in streams that force all discharge through an opening of known dimension whose stage/discharge relationships are precisely-known. A weir is essentially a dam built across an open channel over which the water flows through an opening or notch (v-notch, rectangular, trapezoidal). A flume is a specially shaped open flow channel that is different from the rest of the channel, and typically has a converging section where the flow is constricted, a throat section of constant width and depth where stage is measured, and a diverging section. The H-flume is a hybrid between a weir and a flume, requiring a fairly uniform reach, yet forcing water through a modified v-notch (see photos below). The time involved in installing a flume or a weir is typically MUCH less than constructing a rating curve from scratch along a natural stream. Rating curves for flumes and weirs of various sizes and geometries can be found in the Isco Open Channel Flow Measurement Handbook by D.M. Grant and B.D. Dawson.
IIIa - Procedure - Stream Gaging
A. Choosing a cross-section - Look for a
cross-section that
1. Lacks eddies or near-zero velocity conditions and is perpendicular to the main direction of flow
2. Lacks obstacles
3. That has a relatively smooth cross-sectional profile (lacks wild changes in depth)
4. Has a velocity and depth that does not exceed the range of the measuring devices
Above/Right: Example of an ideal cross
section for gaging. Note the lack of obstacles and zero-flow conditions, as
well as the smooth cross section profile.
Remember that you are a measuring device, every bit as much as the flow meter! In other words, do not choose a cross-section that has depth of 6 feet if you are 5'8" and have a 4 foot wading rod and hip boots that are 3'6" high!! Obviously, continue looking for cross section with a maximum depth of 3'6", or find a taller partner with taller boots.
Above/Right: Example of a poor cross section for gaging. Note the obstacles, zero-flow conditions between the obstacles, deep water near the far bank, and the overhanging trees that could interfere with the wading rod.
Rule of 10 for wading stream gagers! Bob Seykora, a Water Resource Specialist with Arizona State Parks, taught me one of the most useful rules in stream gaging - the rule of 10. If the product of depth times average velocity is greater than 10, then you will be going for a ride that you didn't plan on. In other words, if D x V > 10 then you will not be able to stand upright in the flow. Therefore, if you are gaging a stream and the product of D and V is approaching 10, it would be wise to stop and find a different cross-section especially if there are unmeasured subsections that appear deeper and/or faster!
B. Dividing into subsections
1. Measure the width of the cross-section perpendicular to the main flow direction with a tape measure. Anchor both ends of the tape on opposite banks so that the tape is suspended a foot or two above the water. You will be using this tape to determine where to acquire your velocity measurements (see the photo at the top of the page).
2. Divide the cross-section into at least 15 sections that are at least 3/10 foot wide (if the stream is too narrow to permit fifteen 3/10 sections, do as many 3/10 sections as possible). Remember that equal-width sections are the easiest to measure.
3. If any of these equal-width subsections could contain >10% of the total discharge, then subdivide these subsections.
C. Field Notes
Because discharge is a variable that can change rapidly in most streams, it is important to include some basic field data with each discharge determination. The following data should be taken with each stream discharge measurement
1. Date
2. Name of stream
3. Location of cross-section (GPS coordinates or map location (township/range)
4. Time of measurement
5. Personnel involved
6. Weather conditions
7. Equipment used (type of meter, wading rod, etc.)
Remember that many hydrologic projects are potentially contentious and thus could end up in the court system, so make sure your data are of sufficiently high quality to reflect positively on you should you ever have to defend your data, methods, and/or reputation.
D. Set up of the flow meter
For Black Hills State University students, please consult the online tutorial for setting up the Price AA flow meter and top-setting wading rod by clicking here.
E. Data Acquisition
For each subsection, the gager must acquire the following data. The example data would represent a portion of the data required if the stream was divided into 2 foot subsections. Remember, data is acquired from the center of the subsection (velocity and depth would be measured in the first 2 foot subsection at a distance of 1 foot from the bank)
The total discharge of the stream is the summation of the discharge measurements for each subsection (last column).
IIIb - Procedure - Rating Curves
A. Stage placement
To establish a useful stage-discharge relation, stage must be measured
1) within a few feet stream widths of the discharge-measurement cross-section,
2) where it is sensitive to discharge variations
3) where it can be accurately measured to within 0.01 ft
4) where erosion is unlikely to disrupt the stage-discharge relationship
These conditions are usually met in an area of quiet water not far upstream from a reach of accelerating flow and near the bank where wave conditions are minimal (Dingman, 1994).
B. Establishment of an empirical stage-discharge relationship
A sufficient number of discharge and associated stage measurements must be acquired to provide the hydrologist with a rating curve that accurately relates the easily measured stage with discharge. The number of associated measurements will vary according to the size of the stream and the purpose of study. The result is a table (abbreviated example below) that relates stage to discharge.
IV. References
Dingman, S.L., 1994. Physical Hydrology, Prentice Hall, Upper Saddle River, New Jersey, 575p.
D.M. Grant and B.D. Dawson, 1997. Isco Open Channel Flow Measurement Handbook, 5th edition, ISCO, Inc. Lincoln, Nebraska, 501p.