1、Designation: D 5541 94 (Reapproved 2008)Standard Practice forDeveloping a Stage-Discharge Relation for Open ChannelFlow1This standard is issued under the fixed designation D 5541; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the
2、 year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers the development of a curve relatingstage (elevation) to discharge. Standard test methods
3、 have beendocumented for measuring discharge and for measuring stage(see Practice D 3858, and Test Methods D 5129, D 5130,D 5243, D 5388, and D 5413). This practice takes the dis-charge and stage determined by each respective test methodand shows a relation between them using a curved line. Thiscurv
4、ed line is called a stage-discharge relation or rating curve.1.2 The procedures described in this practice are usedcommonly by those responsible for investigations of stream-flow, for example, the U.S. Geological Survey, Army Corps ofEngineers, Bureau of Reclamation, and U.S Agriculture Re-search Se
5、rvice. For the most part, these procedures are adaptedfrom reports of the U.S. Geological Survey.2,31.3 The procedures described in this practice apply only tosimple freely flowing open-channel flow. Ratings for complexhydraulic conditions of extremely low slope channels usingmultiple-stage inputs,
6、channels affected by man-induced regu-lation, or tidal conditions are not described. These types ofratings are described in detail in the documents listed inFootnotes 2 and 3.1.4 This practice uses the results of current-meter dischargemeasurements or indirect discharge measurements and thecorrespon
7、ding measured stage to define as much of thestage-discharge relation curve as possible. A theoretical curveis developed for the full range of stage and discharge to shapethe curve.1.5 The values stated in inch-pound units are to be regardedas standard. The values given in parentheses are mathematica
8、lconversions to SI units that are provided for information onlyand are not considered standard.1.6 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health pr
9、actices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:4D 1129 Terminology Relating to WaterD 3858 Test Method for Open-Channel Flow Measurementof Water by Velocity-Area MethodD 5129 Test Method for Open Channel Flow Measurementof Wa
10、ter Indirectly by Using Width ContractionsD 5130 Test Method for Open-Channel Flow Measurementof Water Indirectly by Slope-Area MethodD 5243 Test Method for Open-Channel Flow Measurementof Water Indirectly at CulvertsD 5388 Test Method for Indirect Measurements of Dis-charge by Step-Backwater Method
11、D 5413 Test Methods for Measurement of Water Levels inOpen-Water Bodies2.2 ISO Standard:5ISO 1100/2 Liquid Flow Measurement in Open ChannelsPart 2, Determination of Stage-Discharge Relation3. Terminology3.1 Definitions: For definitions of terms used in this prac-tice, refer to Terminology D 1129.3.2
12、 Symbols:3.2.1 GHgauge height or stage, ft (m).3.2.2 Qdischarge, ft3/s (m3/s).4. Summary of Practice4.1 The stage-discharge relation is developed by plottingstage versus discharge from discharge measurements or otherdeterminations of flow, either manually or through the use ofcomputer programs and f
13、itting a curve to these points. The1This practice is under the jurisdiction of ASTM Committee D19 on Water andis the direct responsibility of Subcommittee D19.07 on Sediments, Geomorphology,and Open-Channel Flow.Current edition approved Oct. 1, 2008. Published November 2008. Originallyapproved in 19
14、94. Last previous edition approved in 1998 as D 5541 94(1998).2Kennedy, E. J., “Discharge Ratings at Gaging Stations: U.S. GeologicalSurvey,” Techniques of Water-Resource Investigations , Book 3, Chapt. A10, 1984,p. 59.3Rantz, S. E., et al., Measurement and Computation of Streamflow: Vol 2,Computati
15、on of Discharge, U.S. Geological Survey, Water-Supply Paper No. 2175,1982, p. 631.4For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary pag
16、e onthe ASTM website.5Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036, http:/www.ansi.org.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.stage should be determined at a singl
17、e gage datum for the entirerange in stage. Stages determined in stilling wells, at outsidegages, and at bridge abutments can be significantly differentand should not be interchanged. Discharge measurements maynot be available for the entire range in stage of the stage-discharge relation. A theoretic
18、al rating curve should be devel-oped for the entire range in stage using Test Method D 5388.This theoretical curve is used as a guide to shape the stage-discharge relation at places where discharge measurements arenot available.5. Significance and Use5.1 This practice is particularly useful for dete
19、rmining thedischarge at a gaging station or a location where dischargeinformation is repeatedly needed.5.2 This practice is applicable only for open-channel flowconditions where channel hydraulics permit a stable relationbetween stage and discharge.6. Channel Hydraulics6.1 The stage-discharge relati
20、on for open-channel flow at agaging station or other stage reference point is governed bychannel conditions downstream from that point, referred to asa control. Knowledge of the channel features that control thestage-discharge relation is important. The development ofstage-discharge curves where mor
21、e than one control is effec-tive, control features change, and the number of measurementsis limited usually requires judgment in interpolating betweenmeasurements and in extrapolating beyond the highest orlowest measurements.6.1.1 Section ControlsA section control is a specific crosssection of the s
22、tream channel that controls the relation betweenstage and discharge at that point in the channel. A sectioncontrol can be a natural feature such as a rock ledge, sand bar,or severe constriction in the channel. A section control canlikewise be a manmade feature such as a small dam, weir,flume, or ove
23、rflow spillway. Section controls can frequently beidentified visually in the field by observing a riffle, or pro-nounced drop in the water surface, as the flow passes over thecontrol. As stage increases because of higher flows, the sectioncontrol will frequently become submerged to the extent that i
24、tno longer controls the relation between stage and discharge. Atthis point, the riffle is no longer observable, and flow is thencontrolled by either another section control further downstreamor by channel control.6.1.2 Channel ControlsA channel control consists of acombination of features throughout
25、 a reach downstream from agage. These features include channel size, shape, curvature,slope, and roughness. The length of channel reach that controlsa stage-discharge relation varies. The stage-discharge relationfor relatively steep channels may be controlled by a relativelyshort channel reach, wher
26、eas the relation for a relatively flatchannel may be controlled by a much longer channel reach. Inaddition, the length of a channel control will vary depending onthe magnitude of flow. Precise definition of the length of achannel-control reach is usually not possible or necessary.6.1.3 Combination C
27、ontrolsThe stage-discharge relationmay be governed by a combination of section and channelcontrols. This usually occurs for a short range in stage betweena section-controlled segment of the rating and a channel-controlled segment of the rating. This part of the rating iscommonly referred to as a tra
28、nsition zone of the rating andrepresents the change from section control to channel control.In other instances, a combination control may consist of twosection controls, where each has partial controlling effect.Combination controls or transition zones, or both, occur forvery limited parts of a stag
29、e-discharge relation and can usuallybe defined by plotting procedures. In particular, transitionzones represent changes in the slope or shape of a stage-discharge relation.6.2 Low flows are usually controlled by a section control,whereas high flows are usually controlled by a channel control.Medium
30、flows may be controlled by either type of control. Acombination of section and channel control may occur at somestages. These are general rules, and exceptions can and dooccur.7. Interferences7.1 The stage-discharge relation may be affected by thedeposition or removal of stream bed or bank material
31、byflowing water, usually at high flow conditions or manmadechanges. Large changes may require a redefinition of the ratingcurve. Small, transitory changes may be facilitated by adjust-ments to the stage observations. An example of a temporaryshift would be a beaver dam on a section control or debris
32、deposited on a dam or bridge piling that would be expected tobe removed or eventually wash away.7.2 Aquatic growth may develop in a stream during thegrowing season. This growth would result in a temporarybackwater situation. Adjustments to stage observations wouldnormally be made during these period
33、s.7.3 Ice cover changes river hydraulics and alters the stage-discharge relation.7.4 Hysteresis may affect the high flow stage-dischargerelation when the water surface slope changes due to eitherrapidly rising or rapidly falling water levels in a channelcontrol reach. Hysteresis is sometimes referre
34、d to as loopratings and is most pronounced in relatively flat slopedstreams. The water surface slope on rising stages is signifi-cantly steeper than that for steady flow conditions, resulting ingreater discharge than indicated by the steady flow rating. Thereverse is true for falling stages. If disc
35、harge measurements aremade at both rising and falling stages, a single curve splittingthese measurements will generally result in satisfactory accu-racy. It may be necessary to use separate curves for rising andfalling conditions in extreme cases.8. Sampling8.1 Sampling as defined in Terminology D 1
36、129 is notapplicable in this practice.9. Calibration9.1 Verify the stage-discharge relation periodically withcurrent-meter or indirect discharge measurements to ascertainthat the relation has not changed. Large floods are most likelyto cause erosion or filling of the channel and cause the relationto
37、 shift. The frequency of current meter measurements dependsD 5541 94 (2008)2on the stability of a stream and is based in part on pastexperience. As a rule of thumb, monthly measurements shouldbe made at a new site, at least until the range of stage iscovered.10. Procedure10.1 If sufficient current-m
38、eter discharge measurements areavailable for the entire range in stage and discharge that isnecessary, develop the entire rating curve by plotting stageversus discharge on logarithmic or rectangular coordinateplotting paper. Logarithmic plotting paper is preferred because,in the usual situation of c
39、ompound controls, changes in theslope of the logarithmically plotted rating identify the range instage for which the effective controls exist. Select a convenientstage scale on the logarithmic paper so that all of the dischargemeasurements below bankfull stage plot in a relatively straightline. Ther
40、e are three segments for a rating curve as a generalrule, and they are identified by the changes in slope of thecurve. A typical rating curve is shown in Fig. 1. At low stages,the curve is straight and relatively flat until the channel widthis full (1.8 ft (0.55 m). From this point until bankfull (2
41、.34 ft(0.71 m), the curve is much steeper.Above bankfull, the waterwill spread out and the curve will be flat and straight.10.1.1 It is often desirable to plot the low-flow componentof the rating on rectangular coordinate plotting paper. Thispresents an opportunity to plot at an expanded scale. For
42、smallstreams that go dry or nearly so, the point of zero flow can beplotted to help shape the extreme low-flow portion of thecurve. A rectangular plot is shown in Fig. 1.10.2 If sufficient discharge measurements are not availablefor the entire range in stage and discharge that is necessary,develop a
43、 theoretical rating curve using the stepbackwater testmethod. This theoretical curve is used as a guide to shape therating curve. Plot the theoretical rating curve on logarithmicplotting paper. All of the current-meter discharge measure-ments are plotted on the same paper. Adjust the theoreticalcurv
44、e to go through the current-meter measurements. Theadjustments to the theoretical curve may not be the same at theupper, middle, and lower sections of the curve.10.3 Discharge measurements are sometimes made underundesirable conditions. The hydrographer making the measure-ment may rate the measureme
45、nt excellent, good, fair, or poor.A measurement that is rated excellent, good, fair, or poor isbelieved to be within 2, 5, 8, and over 8 % of the correct value,respectively. When adjusting the theoretical rating to gothrough the measurements, give consideration to how accuratethe measurements are be
46、lieved to be.11. Precision and Bias11.1 Determination of the precision and bias for this prac-tice is not possible due to the high degree of instability ofopen-channel flow. A minimum bias, measured under idealconditions, is related directly to the bias of the equipment usedto obtain stage and disch
47、arge values.Amaximum precision andbias cannot be estimated due to the variability of the sources ofpotential errors and the temporal and spatial variability ofopen-channel flow. Any estimate of these errors could be verymisleading to the user.11.2 Stage-discharge relations represent hydraulic functi
48、onsthat are subject to frequent changes, as described in Section 7.Each discharge measurement represents a variable range ofprecision as well as defining a unique hydraulic condition.FIG. 1 Typical rating-curve sheet.D 5541 94 (2008)3Various statistical tests have been used to test for bias. Userssh
49、ould always consider what is happening to controllinghydraulic characteristics and make decisions on this basisrather than arbitrarily using statistical techniques.11.3 A comprehensive discussion of tests for bias is pre-sented in ISO 1100/2.12. Keywords12.1 discharge; rating curve; stage; stage-discharge relationASTM International takes no position respecting the validity of any patent rights asserted in connection with any item mentionedin this standard. Users of this standard are expressly advised that determination of the validity of any such patent rights, and the ri
