ISO 18320:2020
(Main)Hydrometry — Measurement of liquid flow in open channels — Determination of the stage–discharge relationship
Hydrometry — Measurement of liquid flow in open channels — Determination of the stage–discharge relationship
This document specifies methods of determining the stage?discharge relationship for gauging stations. It specifies an accuracy for defining the stage?discharge relationship based on a sufficient number of discharge measurements, complete with corresponding stage measurements. This document considers stable and unstable channels and includes brief descriptions of the effects on the stage?discharge relationship of the transition from inbank to overbank flows, shifting controls, variable backwater and hysteresis. Methods of determining discharge for twin-gauge stations, ultrasonic velocity-measurement stations and other complex rating curves are not described in detail. NOTE These types of rating curves are described separately in other International Standards, Technical Specifications and Technical Reports, which are listed in the Bibliography.
Hydrométrie — Measurage du débit des cours d'eau — Détermination de la relation hauteur–débit
Le présent document spécifie des méthodes permettant de déterminer la relation hauteur?débit pour des stations hydrométriques. Un nombre suffisant de jaugeages, complétés par des mesurages de hauteur correspondants, est nécessaire afin de définir une relation hauteur?débit selon l'exactitude requise par le présent document. Le présent document étudie les chenaux, qu'ils soient stables ou instables, et comporte une brève description des effets hydrauliques sur la relation hauteur?débit de la transition entre l'écoulement sans débordement et l'écoulement avec débordement, des détarages, du remous variable et des effets d'hystérésis. Les méthodes de détermination du débit pour les stations à double échelle, les stations vélocimétriques par ultrasons et les autres courbes de tarage complexes ne sont pas décrites en détails. NOTE Ces types de courbes de tarage sont répertoriés séparément dans d'autres Normes internationales, Spécifications techniques et Rapports techniques, listés dans la Bibliographie.
General Information
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Standards Content (Sample)
DRAFT INTERNATIONAL STANDARD
ISO/DIS 18320
ISO/TC 113/SC 1 Secretariat: BIS
Voting begins on: Voting terminates on:
2018-07-31 2018-10-23
Hydrometry — Determination of liquid flow in open
channels
Hydrométrie - Mesurage du débit des liquides dan les canaux décourts
ICS: 17.120.20
THIS DOCUMENT IS A DRAFT CIRCULATED
This document is circulated as received from the committee secretariat.
FOR COMMENT AND APPROVAL. IT IS
THEREFORE SUBJECT TO CHANGE AND MAY
NOT BE REFERRED TO AS AN INTERNATIONAL
STANDARD UNTIL PUBLISHED AS SUCH.
IN ADDITION TO THEIR EVALUATION AS
ISO/CEN PARALLEL PROCESSING
BEING ACCEPTABLE FOR INDUSTRIAL,
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STANDARDS MAY ON OCCASION HAVE TO
BE CONSIDERED IN THE LIGHT OF THEIR
POTENTIAL TO BECOME STANDARDS TO
WHICH REFERENCE MAY BE MADE IN
Reference number
NATIONAL REGULATIONS.
ISO/DIS 18320:2018(E)
RECIPIENTS OF THIS DRAFT ARE INVITED
TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
RIGHTS OF WHICH THEY ARE AWARE AND TO
©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2018
ISO/DIS 18320:2018(E) ISO/DIS 18320
Contents Page
Foreword. iv
1 Scope .1
2 Normative references .1
3 Symbols .1
4 Principle of the stage-discharge relationship .3
4.1 General .3
4.2 Controls .3
4.3 Governing hydraulic equations .3
5 Stage-discharge calibration of a gauging station .5
5.1 General .5
5.2 Preparation of a stage-discharge relationship .5
5.3 Curve fitting .12
5.5 Stable stage-discharge relationships.14
5.6 Unstable stage-discharge relationships .14
5.7 Shifting controls .15
5.8 Variable-backwater effects .16
6 Methods of testing stage-discharge relationships.19
7 Uncertainty in the stage-discharge relationship.20
7.1 General .20
7.2 Definition of uncertainty.20
7.3 Statistical analysis of the stage-discharge relationship .20
7.4 Uncertainty of predicted discharge .23
Annex A.25
Annex B.26
Annex C .27
Annex D.31
Annex E .33
Annex F .39
Annex G.41
Bibliography .44
© ISO 2018
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iii
ii © ISO 2018 – All rights reserved
ISO/DIS 18320:2018(E)
ISO/DIS 18320
Contents Page
Foreword . iv
1 Scope .1
2 Normative references .1
3 Symbols .1
4 Principle of the stage-discharge relationship .3
4.1 General .3
4.2 Controls .3
4.3 Governing hydraulic equations .3
5 Stage-discharge calibration of a gauging station .5
5.1 General .5
5.2 Preparation of a stage-discharge relationship .5
5.3 Curve fitting . 12
5.5 Stable stage-discharge relationships . 14
5.6 Unstable stage-discharge relationships . 14
5.7 Shifting controls . 15
5.8 Variable-backwater effects . 16
6 Methods of testing stage-discharge relationships . 19
7 Uncertainty in the stage-discharge relationship . 20
7.1 General . 20
7.2 Definition of uncertainty. 20
7.3 Statistical analysis of the stage-discharge relationship . 20
7.4 Uncertainty of predicted discharge . 23
Annex A . 25
Annex B . 26
Annex C . 27
Annex D . 31
Annex E . 33
Annex F . 39
Annex G . 41
Bibliography . 44
iii
ISO/DIS 18320:2018(E)
ISO/DIS 18320
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national
standards bodies (ISO member bodies). The work of preparing International Standards is normally
carried out through ISO technical committees. Each member body interested in a subject for which a
technical committee has been established has the right to be represented on that committee.
International organizations, governmental and non-governmental, in liaison with ISO, also take part in
the work. ISO collaborates closely with the International Electrotechnical Commission (IEC) on all
matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO's adherence to the World Trade Organization (WTO)
principles in the Technical Barriers to Trade (TBT) see the following URL:
www.iso.org/iso/foreword.html.
ISO 18320 was prepared by Technical Committee ISO/113, Hydrometry, Subcommittee SC 1, Velocity
Area Methods.
This edition cancels and replaces precious editions. Most of the clauses have been updated and
technically revised. Major revisions have been made to Clause 5, including a new figure of a stage-
discharge relationship and shift curves., Clause 7 has been revised to be consistent with new standards
on uncertainty.
iv
ISO/DIS 18320:2018(E)
DRAFT INTERNATIONAL STANDARD ISO/DIS 18320
Hydrometry — Measurement of liquid flow in open channels
1 Scope
ISO 18320 specifies methods of determining the stage-discharge relationship for a gauging station. A
sufficient number of discharge measurements, complete with corresponding stage measurements, are
required to define a stage-discharge relationship to the accuracy required by this Standard.
Stable and unstable channels are considered, including brief descriptions of the effects on the
stage-discharge relationship of the transition from inbank to overbank flows, shifting controls, variable
backwater and hysteresis. Methods of determining discharge for twin-gauge stations, ultrasonic
velocity-measurement stations, electromagnetic velocity-measurement stations and other complex
rating curves are not described in detail. These types of rating curves are described separately in other
International Standards, Technical Specifications and Technical Reports, which are listed in the
Bibliography.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 748, Hydrometry — Measurement of liquid flow in open channels using current-meters or floats
ISO 772, Hydrometry — Vocabulary and symbols
ISO 5168, Measurement of fluid flow — Procedures for the evaluation of uncertainties
ISO 9123, Measurement of liquid flow in open channels — Stage-fall-discharge relationships
ISO 15769, Hydrometry—Guidelines for application of acoustic velocity meters using Doppler and echo
correlation methods
ISO/TR 24578, Hydrometry—Acoustic Doppler Profiler—Method and application for the measurement
of flow in open channels
ISO 4373 Hydrometry - water level measuring devices
3 Symbols
For the purposes of this document, the symbols given in ISO 772 and the following apply:
A wet cross-sectional area
B cross-sectional width
power-law exponent (slope on logarithmic plot) of the rating curve
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C coefficient of discharge
D
C Chezy's channel roughness coefficient
e effective gauge height of zero flow
f Darcy-Weisbach friction factor
g acceleration due to gravity
h gauge height of the water surface
(h e) effective depth, this is basically the difference between the cease to flow level and the gauge
reading. For example, for a horizontal control with a gauge zero at the same level as the crest
of the control, e will be effectively zero
H total head (hydraulic head)
k height of roughening above smooth surface
k Nikuradse equivalent sand roughness size
s
n Manning's channel roughness coefficient
N number of stage-discharge measurements (gaugings) used to define the rating curve
p number of rating-curve parameters (Q , , e) estimated from the N gaugings
P wetted perimeter
Q total discharge
Q steady-state discharge
o
Q power-law scale factor of rating curve, equal to discharge when effective depth of flow (h e)
is equal to 1
R hydraulic radius, equal to the effective cross-sectional area divided by the wetted perimeter,
A/P
w (only strictly suitable for inbank flows)
Re Reynolds number ( 4V / )
Note -. some reference texts use a characteristic dimension of four times the hydraulic radius, because it gives
[15]
the same value of Re for the onset of turbulence as in pipe flow, . Other texts use the hydraulic radius as the
characteristic length-scale, with consequently different values of Re for transition and turbulent flow.
S standard error of estimate
S friction slope
f
S bed slope
S water surface slope corresponding to steady discharge
w
t time
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u standard uncertainty
V stream mean velocity (= Q/A)
U expanded uncertainty
V velocity of a flood wave
w
ν kinematic viscosity
4 Principle of the stage-discharge relationship
4.1 General
The relationship at a gauging station between stage and discharge is commonly referred to as the stage-
discharge relationship, rating curve or rating. A stage-discharge relationship is developed to enable the
future production of a time series of discharge based on continuous stage measurements at the gauging
station. It is generally much easier to continuously measure stage than it is to measure discharge.
Hence, once a stable stage–discharge relationship has been established at a gauging station, the creation
of a record of discharge is greatly simplified.
4.2 Controls
The stage-discharge relationship for open-channel flow at a gauging station is governed by channel
conditions at and downstream from the gauge, referred to as a control. Two types of control can exist,
depending on channel and flow conditions. Low flows ie those experienced during dry weather, are
usually controlled by a section control, whereas high flows ie those experienced after stormy and wet
weather, are usually controlled by a channel control. Medium flows can be controlled by either type of
control. At some stages, a combination of section and channel control might occur. These are general
rules, and exceptions can and do occur. Knowledge of the channel features that control the stage-
discharge relationship is important. The development of stage-discharge curves where more than one
control is effective, where control features change and where the number of measurements is limited
requires judgement in interpolating between measurements and in extrapolating beyond the highest or
lowest measurements. This is particularly true where the controls are not stable and tend to shift from
time to time, resulting in changes in the positioning of segments of the stage-discharge relationship.
High flows may cause a channel to overflow its banks and inundate any adjoining floodplains. Under
these circumstances, some of the discharge will be contained in the main river channel and some takes
place over the floodplains. A distinction should therefore be made between when the discharge is
wholly inbank or when flow has exceeded the bankfull capacity. The stage-discharge relationship will
be affected by the transition from inbank to overbank flow arising from the changing hydraulic
conditions. The description of the types of control is given in Annex A
4.3 Governing hydraulic equations
Stage-discharge relationships can be defined according to the type of control that exists. Section
controls, either natural or man-made, are governed by some form of the weir or flume equations. In a
very general and basic form, these equations are expressed as:
Q C BH (1)
D
where
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Q is the discharge, in cubic metres per second;
C is a coefficient of discharge and includes several factors;
D
B is the cross-sectional width perpendicular to the direction of flow, in metres;
H is the hydraulic head, in metres;
is a power-law exponent, dependent on the cross-sectional shape of the control section.
Stage-discharge relationships for channel controls with uniform flow are typically governed by the
Manning, (in Europe this is sometimes known as Manning- Strickler equation), Chezy, and Darcy-
Weisbach equation as they apply to the reach of the controlling channel upstream and downstream
from a gauge.
The Manning equation is:
0.67 0.5
Q = (AR S ) / n (2)
f
where
A is the cross-sectional area, in square metres;
R is the hydraulic radius, in metres;
S is the friction slope;
f
n is the Manning’s channel roughness.
Note that the Strickler coefficient is just the inverse of Manning’s n.
The Chezy equation is:
0.5 0.5
Q CAR S (3)
f
where C is the Chezy form of roughness.
The Darcy-Weisbach equation is:
0 .5
8 g
0 .5 0 .5
(4)
Q AR S
f
f
where g is acceleration due to gravity, and f is the friction factor, given by the Colebrook- White
equation, which may be used for open channels:
1 k 2 .51
s
2 .0 log
(5)
14 .8 R
f 4V R / f
where V is the mean stream velocity, k = Nikuradse roughness size and ν = kinematic viscosity.
s
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The variation of f with relative roughness (= k /4R) and Reynolds number, ( ) is often shown
s R 4V /
e
plotted in the form of the so-called ‘Moody diagram’ (f versus Re and k /4R). The roughness of any
s
surface is then characterised by k , the so-called Nikuradse equivalent sand roughness size. The
s
Colebrook-White equation is physically well founded, since it tends towards two theoretically limiting
cases, one for hydraulically smooth surfaces and another for hydraulically rough surfaces; and the
shape of the channel is captured through use of appropriate coefficients.
The above equations are generally applicable for steady or quasi-steady inbank flows. For highly
unsteady flow, such as tidal or dam-break flow, equations such as the Saint-Venant unsteady-flow
equations would be necessary. However, these are seldom used in the development of stage-discharge
relationships and are not described in this standard. Overbank flows typically require special attention
due to the strong interaction between the flows in different regions of the channel, giving rise to
significant lateral momentum transfer effects. For overbank flows, the hydraulic radius (R = A/P)
adopted in the equations (2) to (4) is no longer appropriate for characterising the cross-section of the
channel as P will increase at a higher rate with stage than A due to the additional wetted perimeter of
the floodplain as the flow goes overbank. This in turn will lead to a dramatic reduction in R at the
bankfull stage and a consequent apparent decrease in the resistance coefficient for the whole section,
even though the actual hydraulic roughness increases. Under these circumstances, the individual
resistance coefficients for the main channel and floodplains also need re-defining, as explained further
in Annex E and Equation (6).
A full description of the complexities of stage–discharge relationships is given in Annex B.
5 Stage-discharge calibration of a gauging station
5.1 General
The primary object of a stage-discharge gauging station is to provide a record of the discharge of the
open channel or river at which the water level gauge is sited. This is achieved by measuring the stage
and converting this stage to discharge by means of a stage-discharge relationship which correlates
discharge and water level. In some instances, other parameters, such as index velocity, water surface
fall between two gauges or rate-of-change in stage, can also be used in rating-curve calibrations as given
in ISO 15769 and ISO 9123. Stage-discharge relationships are usually calibrated by measuring discharge
and the corresponding gauge height. Theoretical computations can also be used to aid in the shaping
and positioning of the rating curve. Stage-discharge relationships from previous time periods should
also be considered as an aid in the shaping of the rating curve.
5.2 Preparation of a stage-discharge relationship
5.2.1 General
The relationship between stage and discharge is defined by plotting measurements of discharge with
corresponding observations of stage, taking into account whether the discharge is steady, increasing or
decreasing, and also noting the rate of change in stage. This can be done either manually by plotting on
paper or automatically using computerized plotting techniques (see Annex C). The plotting scale used
can be an arithmetic scale or a logarithmic scale. Each has certain advantages and disadvantages, as
explained in 5.2.3 and 5.2.4. Most national hydrological services plot the stage as ordinate (Y axis) and
the discharge as abscissa (X axis). However, when using the stage-discharge relationship to derive
discharge from a measured value of stage, the stage is treated as the independent variable.
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For gauging sites where there is significant flow in the floodplain, through multiple channels or via
submerged structures, the determination of the composite stage discharge relationship is prone to
difficulty. Poor or unsafe access can mean that flood flows cannot be adequately measured. In addition
to this, flow across a floodplain can be complex, and is impacted by changes in storage as a flood builds
up or ebbs. The extent of these complexities can mean that theoretical considerations have to be used in
conjunction with the limited measurements when determining the stage-discharge relationship.
5.2.2 List of discharge measurements
The first step prior to plotting a stage-discharge relationship is the preparation of a list of discharge
measurements that will be used for the plot. The measurements should be checked to ensure that the
recorded stages are related to a common datum and that the discharge calculations are accurate. As a
minimum, this list should include 15 measurements, all taken during the period of analysis. More
measurements would be required for a compound rating curve, i.e. one that is represented by multiple
hydraulic controls, or if the site experiences an extreme range in stage. For a general purpose gauging
station, these measurements should be well distributed over the range of gauge heights experienced.
Alternatively, where a specific flow range is to be observed, the measurements should cover that range.
For example, at low flows for a site that is intended to inform a low flow management system, or at high
flows where flood flows are to be monitored and managed. The list of measurements should include low
and high measurements across the desired flow range, particularly if extrapolation of the rating curve is
to be done.
For each discharge measurement in the list, the following items are required (see Table 1):
1. a unique identification name of site, and gauging number;
2. the date of measurement and time of start and time of finish of gauging;
3. The name of the person undertaking or leading the gauging, as well as the type of instruments
used to measure the discharge, the average gauge height, based on a minimum of the readings at
the start and end of the complete gauging.
4. the total discharge;
5. an indication of the likely accuracy of measurement, as determined by the person leading the
gauging e.g. was the channel heavy with weed, were extensive vortices evident in the flow
pattern, was the cross section uniform, was the flow steady. Documentary evidence of the
channel and flow conditions at the time of each gauging can also be compiled using
photographic or video recordings.
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Table 1 — List of discharge measurements made by a hydrometric practitioner using
current meters and depth soundings
2 3
m m m/s m m m /s m/h
0,2/0,8
0,6/0,2/0,
12 78/04/08 MEF 36,27 77,94 1,272 2,682 2,080 99,12 22 0,082 GOOD
183 85/02/06 GTC 33,53 78,41 1,405 2,786 2,186 110,2 22 0,047 GOOD
0,6/0,2/0,
201 87/02/04 AJB 28,96 21,92 1,511 2,002 1,402 33,13 8 21 0,013 POOR
260 93/03/13 GMP 26,52 21,46 1,400 1,981 1,381 30,02 0,6 22 0,020 GOOD
313 96/08/24 HFR 30,18 42,08 1,602 2,374 1,774 67,40 0,6/0,2/0, 22 0,006 GOOD
366 03/08/21 MAF 28,96 14,86 0,476 1,557 0,957 7,080 21 0 GOOD
0,6
367 03/10/10 MAF 28,96 13,66 0,361 1,490 0,890 4,928 21 0 GOOD
0,6
368 03/11/26 MAF 29,26 14,21 0,373 1,509 0,909 5,296 18 0 GOOD
0,6
369 04/02/19 MAF 29,87 16,26 1,291 1,838 1,238 20,99 21 0 GOOD
0,6
370 04/04/09 MAF 29,26 21,27 0,805 1,780 1,180 17,13 21 0 GOOD
0,6/0,2/0,
371 04/05/29 MAF 29,57 19,69 0,688 1,710 1,110 13,54 21 0 GOOD
372 04/07/10 MAF 28,96 16,81 0,458 1,573 0,973 7,703 21 0 GOOD
0,6
373 04/08/22 MAF 29,26 15,79 0,481 1,570 0,970 7,590 21 0 GOOD
0,6
374 08/10/01 MAF 29,26 13,19 0,264 1,414 0,814 3,483 21 0 GOOD
0,6
375 09/11/11 MAJ 28,96 11,71 0,283 1,396 0,796 3,313 21 0 GOOD
0,6
382 10/10/01 MAF 30,48 43,76 1,598 2,432 1,832 69,95 21 0,017 GOOD
0,6
0,2/0,8
NOTES 1. Discharge measurements made with acoustic Doppler current profilers require additional parameters, including
the number of transects and the range of discharges measured during the transects (see ISO/TS 24578).
2. In terms of uncertainty of the stage discharge relationship, a relationship is regarded as ‘poor if its uncertainty is >15%. A
‘good’ relationship has uncertainty of +/- 5%
5.2.3 Arithmetic plotting scales
The simplest type of plot uses an arithmetically divided plotting scale, as shown in Figure 1. Scale
subdivisions should be chosen to cover the complete range of gauge height and discharge expected to
occur at the gauging site. Scales should be subdivided in uniform increments that are easy to read and
interpolate. The choice of scale should also produce a rating curve that is not unduly steep or flat. If the
range in gauge height or discharge is large, it may be necessary to plot the rating curve in two or more
segments to provide scales that are easily read with the necessary precision. This procedure can result
in separate curves for low water, medium water and high water.
Where a hand derived relationship is required, graph paper with arithmetic scales is convenient to use
and easy to read. Such scales are ideal for displaying a rating curve and have an advantage over
logarithmic scales in that zero values of gauge height and/or discharge can be plotted. However, for
analytical purposes, arithmetic scales have practically no advantage. A stage-discharge relationship on
arithmetic scales is usually a curved line, concave downward, which is difficult to shape correctly if only
a few discharge measurements are available. Logarithmic scales, on the other hand, have a number of
analytical advantages as described in 5.2.4. Generally, a stage-discharge relationship is first drawn on
logarithmic plotting paper for shaping and analytical purposes and then later transferred to arithmetic
plotting paper if a display plot is needed.
ID number
Date
(yy/mm/dd
)
Made by
Width
Area
Mean
velocity
Average
gauge
height
Effective
depth
Discharge
Method
Number of
verticals
Gauge
height
change
Rated
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Key
X discharge, Q, in cubic metres per second
Y effective depth, (h e), in metres
NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1.
Figure 1 — Arithmetic plot of stage-discharge relationship
5.2.4 Logarithmic plotting scales
Most stage-discharge relationships, or segments thereof, can be analysed graphically through the use of
logarithmic plotting. There are two methods that can be used to fully utilize this procedure; by plotting
effective
depth of flow, also known as hydraulic head, versus discharge, or by applying scale offsets to the gauge
height axis and plotting gauge height versus discharge. Effective depth of flow on the control, or
hydraulic head, for a section control is computed by subtracting the gauge height of zero discharge (also
known as cease to flow gauge height) from the gauge height associated with the measured discharge. In
theory, a straight line relation in log space can be achieved by plotting the effective depth versus
discharge. Similarly, the gauge height of zero discharge for a section control, can be used as a scale
offset for the gauge height axis in log space to also achieve a straight line segment. The offset approach
allows for plotting of actual gauge height versus discharge which provides some simplification to the
process as real data does not need to be transformed.
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The approaches discussed above are simple to apply for section type controls. Channel type controls
present a more complicated situation. When a reach is under channel control there is not a single cross
section of the channel that is controlling the height of the water at the gauge, rather the reach
characteristics, including geometry, slope, and roughness, where the gauge is located controls the
height of water. Because of this, it is not feasible to measure and determine the gauge height of zero
discharge (cease to flow) of the channel control. Without this determination, one is unable to plot the
effective depth (hydraulic head) versus discharge in log space. For the offset approach, the
determination of the proper offset must be made through a trial-and-error approach. The trial-and-
error approach is applied by iteratively adjusting the offset on the gauge height axis and visually
examining the plot of actual gage height versus discharge for measurements under the channel control
for a straight line relation. For gauges that experience multiple hydraulic controls, such as section and
channel, multiple offsets are required to obtain straight line segments for each control.
Regardless of the approach taken, a rating-curve segment for a given control will then tend to plot as a
straight. The slope of the straight line should conform to the type of control section, thereby providing
valuable information for correctly shaping the rating-curve segment. Additionally, this feature allows
the analyst to calibrate the stage-discharge relationship with fewer discharge measurements. The slope
of a rating curve is the ratio of the horizontal distance to the vertical distance. This method of
measuring the slope is used since the dependent variable (discharge) is always plotted as the abscissa.
Figure 2 is a logarithmic plot of an actual rating curve, using the measurements shown in Table 1. This
rating curve is for a stream where section control exists throughout the range of flow, including the
high-flow measurements. The effective gauge height of zero flow, e, for this stream is 0,6 m, which is
subtracted from the gauge height of the measurements to define the effective depth of flow at the
control. The slope of the rating curve below 1,4 m is about 4,3, which is greater than 2 and conforms to
a section control. Above 1,5 m, the slope is 2,8, which also conforms to a section control. The change in
slope of the rating curve above about 1,5 m is caused by a change in the shape of the control cross-
section.
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Key
X discharge, Q, in cubic metres per second
Y effective depth, (h e), in metres
NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1.
Figure 2 — Logarithmic plot of stage-discharge relationship
Rating curves for section controls such as weirs or flumes conform to Equation (1) in 4.3 and, when
plotted logarithmically, will have a slope of 1.5 or greater, depending on control shape, velocity of
approach and minor variations of the coefficient of discharge. Horizontal crested structures will have a
slope of about 1.5 , whereas V shaped structures will have slopes of about 2.5.Rating curves for channel
controls are governed by one of the standard equations (2) - (4) and, when plotted as effective depth
versus discharge, the slope is usually between 1.5 and 2. Variations in the slope of the rating curve
when channel control exists are the result of changes in roughness and friction slope as depth changes.
The effective depth is sometimes not known for channel controls. It can be determined mathematically
and statistically during the stage-discharge development process using an iterative process whereby
the parameters C, β and e are optimised to give the best fitting relationship taking due account of the
physical properties of the channel.
5.2.5 Commercially available software
There are a number of commercially available software packages that can analyse a series of stage and
discharge measurements and derive the best stage-discharge relationship (see Annex C). Most
ISO/DIS 18320:2018(E)
ISO/DIS 18320
packages also give the statistics relating to the standard error and uncertainty of the derived
relationship. This also applies to the use of logarithmic stage to flow relationships as covered in 5.2.4
5.2.6 Rating-curve shape
5.2.6.1 General
The details provided in 5.2.2 to 5.2.4 apply to control sections of regular shape (trapezoidal, parabolic,
etc.). However, natural channels are rarely regular in section hence the practitioner should be aware of
where ‘step changes’ in the stage-discharge relationship are likely to occur. Where a significant change
in shape or flow control occurs, there will be a change in the rating-curve slope at that point. These
changes are usually defined by short curved segments of the rating curve, referred to as transitions.
This information about the plotting characteristics of a rating curve is extremely useful in the
calibration and maintenance of the rating curve and in later analysis of shifting control conditions. By
knowing the kind of control (section or channel), and the shape of the control, the analyst can define the
correct hydraulic shape of the rating curve with greater precision. Additionally, this information allows
the analyst to extrapolate accurately a rating curve or, conversely, to know when extrapolation is likely
to lead to a large uncertainty.
Examples of a hypothetical rating curves are given in Annex D
5.2.6.2 Gauge height of zero flow
The actual gauge height of zero flow is the gauge height of the lowest point in the control cross-section
for a section control [sometimes referred to as the cease-to-flow or CTF value. For natural channels, this
value can sometimes be measured in the field by measuring the depth of flow at the deepest place in the
control section and subtracting this depth and the velocity head from the gauge height at the time of
measurement.
The effective gauge height of zero flow is a value that, when subtracted from the mean gauge heights of
the discharge measurements, will cause the logarithmic rating curve segment for specific to that control
to plot as a straight line. Thus, it should be determined for each rating-curve segment. For regularly
shaped section controls, this value will be close to the actual gauge height of zero flow. For channel
controls there is not a single cross section that controls the stage discharge relation. For these controls,
the effective gage height of zero flow is determined by a trial-and-error method of plotting. A value is
assumed and adjusted gauge heights are plotted based on this assumed value. If the resulting curve
shape is concave upward, then a somewhat larger value for the effective gauge height of zero flow
should be used. A somewhat smaller value should be used if the curve plots concave downward. Usually
only a few trials are needed to find a value that results in a straight line for the rating-curve segment.
Logarithmic (power-law) equation
The equation for a rating curve that plots as a straight line on logarithmic plotting paper is:
Q Q (h e) (6)
where
(h e) is the effective depth of water on the control;
h is the gauge height of the water surface;
e is the effective gauge height of zero flow or offset;
ISO/DIS 18320:2018(E)
ISO/DIS 18320
is the slope of the rating curve when plotted on logarithmic paper if discharge is plotted on the
abscissa.
Q is a scale factor that is numerically equal to the discharge when the effective depth of flow
(h e) is equal to 1.
5.3 Curve fitting
5.3.1 General
There are a number of commercially available software packages (see Annex C) to aid the creation of
the stage-discharge relationship given a series of flow measurements at specific stages at the
observation site. Such packages contain additional analytical tools that help describe the accuracy and
standard errors associated with the rating curve. However, for proponents of hand-based curve fitting,
the curve-fitting process for stage-discharge relationships includes the actual drawing, positioning and
shaping of the rating curve. Hydraulic-analysis and line-fitting applications can be used to aid in the
curve-fitting process but the stage-discharge relationship should represent the best fit of the calibration
measurements over the range of measurements and with considerations for the quality or uncertainty
of the measurements.
Nevertheless, for a site with a varying flow control due to, for example, seasonal weed growth, every
measurement does not need to fit on the same rating curve. A particular gauge location can have a
number of ratings that apply to specific control conditions in the channel. The curves produced by the
curve fitting process should give stage-discharge relationships that reflect the particular control
changes. Further, only measurements made under similar control conditions should be used when
developing the rating curve. For example, measurements associated with weeds on the control should
not be included with measurements associated with clear control (no weeds) conditions when
developing a rating curve for clear control conditions.
5.3.2 Hydraulic-equation curves
The shape of stage-discharge relationships can be defined through the use of hydraulic equations,
namely Equations (1), (2), (3) and (4) in 4.3. Where section control exists, the weir equation,
Equation (1), can be used to compute rating-curve points. Coefficients of discharge, C , have been
D
defined in other International Sta
...
INTERNATIONAL ISO
STANDARD 18320
First edition
2020-07
Hydrometry — Measurement of
liquid flow in open channels —
Determination of the stage–discharge
relationship
Hydrométrie — Measurage du débit des cours d'eau — Détermination
de la relation hauteur–débit
Reference number
©
ISO 2020
© ISO 2020
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting
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below or ISO’s member body in the country of the requester.
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Published in Switzerland
ii © ISO 2020 – All rights reserved
Contents Page
Foreword .v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions and symbols . 1
3.1 Terms and definitions . 1
3.2 Symbols . 1
4 Principle of the stage–discharge relationship . 2
4.1 General . 2
4.2 Controls . 3
4.3 Governing hydraulic formulae . 3
5 Stage–discharge calibration of a gauging station . 5
5.1 General . 5
5.2 Preparation of a stage–discharge relationship. 5
5.2.1 General. 5
5.2.2 List of discharge measurements. 5
5.2.3 Arithmetic plotting scales . 7
5.2.4 Logarithmic plotting scales . 8
5.2.5 Commercially available software .10
5.2.6 Rating-curve shape .11
5.3 Curve fitting .12
5.3.1 General.12
5.3.2 Hydraulic-formula curves .12
5.3.3 Mathematical rating curves .13
5.3.4 Software packages to aid the determination of the rating curve .13
5.4 Combination-control stage–discharge relationships .13
5.5 Stable stage–discharge relationships .13
5.6 Unstable stage–discharge relationships .14
5.7 Shifting controls .14
5.8 Variable-backwater effects .15
5.8.1 General.15
5.8.2 Downstream backwater influences .15
5.8.3 Hysteresis effects or loop rating curves .15
5.9 Extrapolation of the stage–discharge relationship .18
6 Methods of testing stage–discharge relationships .18
7 Uncertainty in the stage–discharge relationship .19
7.1 General .19
7.2 Definition of uncertainty .19
7.3 Statistical analysis of the stage–discharge relationship .20
7.3.1 General.20
7.3.2 Standard error of estimate .20
7.3.3 Standard uncertainty .21
7.4 Uncertainty of predicted discharge .22
Annex A (informative) Types of control .23
Annex B (informative) Complexities of stage–discharge relationships .24
Annex C (informative) Software packages available to evaluate the stage–discharge relationship 25
Annex D (informative) Examples of a hypothetical rating curve .29
Annex E (informative) Example of how hydraulic properties of a river channel properties
vary with stage .31
Annex F (informative) Use of shift controls .37
Annex G (informative) Extrapolation of a stage–discharge relationship .39
Annex H (informative) Uncertainty in the stage–discharge relationship and in a continuous
measurement of discharge .41
Bibliography .44
iv © ISO 2020 – All rights reserved
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www .iso .org/ directives).
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www .iso .org/ patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to the
World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT) see www .iso .org/
iso/ foreword .html.
This document was prepared by Technical Committee ISO/TC 113, Hydrometry, Subcommittee SC 1,
Velocity area methods.
This first edition of ISO 18320 cancels and replaces ISO 1100-2:2010, which has been technically revised.
The main changes compared to the previous edition are as follows.
— Major revisions have been made to Clause 5, including a new figure of a stage–discharge relationship
and shift curves.
— Clause 7 has been revised to be consistent with new standards on uncertainty.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www .iso .org/ members .html.
INTERNATIONAL STANDARD ISO 18320:2020(E)
Hydrometry — Measurement of liquid flow in open
channels — Determination of the stage–discharge
relationship
1 Scope
This document specifies methods of determining the stage–discharge relationship for gauging stations.
It specifies an accuracy for defining the stage–discharge relationship based on a sufficient number of
discharge measurements, complete with corresponding stage measurements.
This document considers stable and unstable channels and includes brief descriptions of the effects
on the stage–discharge relationship of the transition from inbank to overbank flows, shifting controls,
variable backwater and hysteresis. Methods of determining discharge for twin-gauge stations,
ultrasonic velocity-measurement stations and other complex rating curves are not described in detail.
NOTE These types of rating curves are described separately in other International Standards, Technical
Specifications and Technical Reports, which are listed in the Bibliography.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies. For
undated references, the latest edition of the referenced document (including any amendments) applies.
ISO 748, Hydrometry — Measurement of liquid flow in open channels using current-meters or floats
ISO 772, Hydrometry — Vocabulary and symbols
3 Terms, definitions and symbols
3.1 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at http:// www .electropedia .org/
3.2 Symbols
For the purposes of this document, the symbols given in ISO 772 and the following apply.
Symbol Definition
A wet cross-sectional area
B cross-sectional width
β power-law exponent (slope on logarithmic plot) of the rating curve
C coefficient of discharge
D
a
Some reference texts use a characteristic dimension of four times the hydraulic radius, because it gives the same value
[16]
of Re for the onset of turbulence as in pipe flow . Other texts use the hydraulic radius as the characteristic length-scale,
with consequently different values of Re for transition and turbulent flow.
Symbol Definition
C Chezy's channel roughness coefficient
e effective gauge height of zero flow
f Darcy-Weisbach friction factor
g acceleration due to gravity
h gauge height of the water surface
(h − e) effective depth, this is basically the difference between the cease to flow level and the gauge reading.
For example, for a horizontal control with a gauge zero at the same level as the crest of the control,
e will be effectively zero
H total head (hydraulic head)
k height of roughening above smooth surface
k Nikuradse equivalent sand roughness size
s
n Manning's channel roughness coefficient
N number of stage–discharge measurements (gaugings) used to define the rating curve
p number of rating-curve parameters (Q , β, e) estimated from the N gaugings
Pw wetted perimeter
Q total discharge
Q steady-state discharge
o
Q power-law scale factor of rating curve, equal to discharge when effective depth of flow (h − e) is
equal to 1
r hydraulic radius, equal to the effective cross-sectional area divided by the wetted perimeter, A/P
h w
(only strictly suitable for inbank flows)
a
Re Reynolds number (= 4Vv/ )
S standard error of estimate
S friction slope
f
S bed slope
S water surface slope corresponding to steady discharge
w
t time
u standard uncertainty
stream mean velocity (= Q/A)
V
U expanded uncertainty
V velocity of a flood wave
w
ν kinematic viscosity
a
Some reference texts use a characteristic dimension of four times the hydraulic radius, because it gives the same value
[16]
of Re for the onset of turbulence as in pipe flow . Other texts use the hydraulic radius as the characteristic length-scale,
with consequently different values of Re for transition and turbulent flow.
4 Principle of the stage–discharge relationship
4.1 General
The relationship at a gauging station between stage and discharge is commonly referred to as the
stage–discharge relationship, rating curve or rating. A stage–discharge relationship is developed to
enable the future production of a time series of discharge based on continuous stage measurements
at the gauging station. It is generally much easier to continuously measure stage than it is to measure
discharge. Hence, once a stable stage–discharge relationship has been established at a gauging station,
the creation of a record of discharge is greatly simplified.
2 © ISO 2020 – All rights reserved
4.2 Controls
The stage–discharge relationship for open-channel flow at a gauging station is governed by channel
conditions at and downstream from the gauge, referred to as a control. Two types of control can exist,
depending on channel and flow conditions. Low flows, that is, those experienced during dry weather,
are usually controlled by a section control, whereas high flows, that is, those experienced after stormy
and wet weather, are usually controlled by a channel control. Medium flows can be controlled by either
type of control. At some stages, a combination of section and channel control might occur. These are
general rules, and exceptions can and do occur. Knowledge of the channel features that control the
stage–discharge relationship is important. The development of stage–discharge curves where more
than one control is effective, where control features change and where the number of measurements
is limited requires judgement in interpolating between measurements and in extrapolating beyond the
highest or lowest measurements. This is particularly true where the controls are not stable and tend
to shift from time to time, resulting in changes in the positioning of segments of the stage–discharge
relationship.
High flows may cause a stream or river to overflow its banks and inundate any adjoining floodplains.
Under these circumstances, some of the discharge will be contained in the main river channel and some
takes place over the floodplains. A distinction should therefore be made between when the discharge
is wholly inbank or when flow has exceeded the bankfull capacity. The stage–discharge relationship
will be affected by the transition from inbank to overbank flow arising from the changing hydraulic
conditions. The description of the types of control is given in Annex A.
4.3 Governing hydraulic formulae
Stage–discharge relationships can be defined according to the type of control that exists. Section
controls, either natural or man-made, are governed by some form of the weir or flume formulae. In a
very general and basic form, these formulae are expressed as shown by Formula (1):
β
QC= BH (1)
D
where
Q is the discharge, in cubic metres per second;
C is a coefficient of discharge and includes several factors;
D
B is the cross-sectional width perpendicular to the direction of flow, in metres;
H is the hydraulic head, in metres;
β is a power-law exponent, dependent on the cross-sectional shape of the control section.
Stage–discharge relationships for channel controls with uniform flow are typically governed by the
Manning (in Europe this is sometimes known as Manning-Strickler formula), Chezy, and Darcy-
Weisbach formulae, as they apply to the reach of the controlling channel upstream and downstream
from a gauge.
The Manning formula is shown by Formula (2):
06,,70 5
QA= rS /n (2)
()
hf
where
A is the cross-sectional area, in square metres;
r is the hydraulic radius, in metres;
h
S is the friction slope;
f
n is the Manning’s channel roughness.
NOTE The Strickler coefficient is just the inverse of Manning’s n.
The Chezy formula is shown by Formula (3):
05,,05
QC= Ar S (3)
hf
where C is the Chezy form of roughness.
The Darcy-Weisbach formula is shown by Formula (4):
05,
05,,05
Qg={}8 /fArS (4)
hf
where
g is acceleration due to gravity;
f is the friction factor, given by the Colebrook-White formula,
which may be used for open channels, see Formula (5):
−05,,05
f =−21log/kr40,,82+ 51//4Vr vf (5)
{}() ()
10 sh h
where
is the mean stream velocity;
V
k is the Nikuradse roughness size;
s
ν is the kinematic viscosity.
The variation of f with relative roughness (= k /4 r ) and Reynolds number is often shown plotted in the
s h
form of the so-called “Moody diagram”. The roughness of any surface is then characterized by k , the
s
so-called “Nikuradse equivalent sand roughness size”. The Colebrook-White formula is physically well
founded, since it tends towards two theoretically limiting cases, one for hydraulically smooth surfaces
and another for hydraulically rough surfaces, and the shape of the channel is captured through use of
appropriate coefficients.
The above formulae are generally applicable for steady or quasi-steady inbank flows. For highly unsteady
flow, such as tidal or dam-break flow, formulae, such as the Saint-Venant unsteady-flow formulae, would
be necessary. However, these are seldom used in the development of stage–discharge relationships
and are not described in this document. Overbank flows typically require special attention due to
the strong interaction between the flows in different regions of the channel, giving rise to significant
4 © ISO 2020 – All rights reserved
lateral momentum transfer effects. For overbank flows, the hydraulic radius adopted in Formulae (2) to
(4) is no longer appropriate for characterizing the cross-section of the channel as Pw will increase at a
higher rate with stage than A due to the additional wetted perimeter of the floodplain as the flow goes
over bank. This in turn will lead to a dramatic reduction in r at the bankfull stage and a consequent
h
apparent decrease in the resistance coefficient for the whole section, even though the actual hydraulic
roughness increases. Under these circumstances, the individual resistance coefficients for the main
channel and floodplains also need re-defining, as explained further in Annex E and Formula (6).
A full description of the complexities of stage–discharge relationships is given in Annex B.
5 Stage–discharge calibration of a gauging station
5.1 General
The primary objective of a stage–discharge gauging station is to provide a record of the discharge of the
open channel or river at which the water level gauge is sited. This is achieved by measuring the stage
and converting this stage to discharge by means of a stage–discharge relationship which correlates
discharge and water level. In some instances, other parameters, such as index velocity, water surface
fall between two gauges or rate-of-change in stage, can also be used in rating-curve calibrations, as
given in ISO 15769 and ISO 9123. Stage–discharge relationships are usually calibrated by measuring
discharge and the corresponding gauge height. Theoretical computations can also be used to aid in the
shaping and positioning of the rating curve. Stage–discharge relationships from previous time periods
should also be considered as an aid in the shaping of the rating curve.
5.2 Preparation of a stage–discharge relationship
5.2.1 General
The relationship between stage and discharge is defined by plotting measurements of discharge with
corresponding observations of stage, taking into account whether the discharge is steady, increasing
or decreasing, and also noting the rate of change in stage. This can be done either manually by plotting
on paper or automatically using computerized plotting techniques (see Annex C). The plotting scale
used can be an arithmetic scale or a logarithmic scale. Each has certain advantages and disadvantages,
as explained in 5.2.3 and 5.2.4. Most national hydrological services plot the stage as ordinate (y-axis)
and the discharge as abscissa (x-axis). However, when using the stage–discharge relationship to derive
discharge from a measured value of stage, the stage is treated as the independent variable.
For gauging sites where there is significant flow in the floodplain, through multiple channels or via
submerged structures, the determination of the composite stage discharge relationship is prone to
difficulty. Poor or unsafe access can mean that flood flows cannot be adequately measured. In addition
to this, flow across a floodplain can be complex, and is impacted by changes in storage as a flood builds
up or ebbs. The extent of these complexities can mean that theoretical considerations should be used in
conjunction with the limited measurements when determining the stage–discharge relationship.
5.2.2 List of discharge measurements
The first step prior to plotting a stage–discharge relationship is the preparation of a list of discharge
measurements that will be used for the plot. The measurements should be checked to ensure that the
recorded stages are related to a common datum and that the discharge calculations are accurate. As a
general rule, this first list shall include a minimum of 15 measurements, all taken during the period of
analysis. More measurements will be required for a compound rating curve, i.e. one that is represented
by multiple hydraulic controls, if the site experiences an extreme range in stage, is governed by a shifting
control due to sedimentation, erosion or seasonal vegetation growth, or if the gauging site is otherwise
problematical and the uncertainties in measurement could be high. For a general purpose gauging
station, these measurements should be well distributed over the range of gauge heights experienced.
Alternatively, where a specific flow range is to be observed, the measurements should cover that range.
For example, at low flows for a site that is intended to inform a low flow management system, or at high
flows where flood flows are to be monitored and managed. The list of measurements should include
low and high measurements across the desired flow range, particularly if extrapolation of the rating
curve is to be done.
Uncertainty analysis (see Clause 7) should be undertaken when developing and analysing the stage–
discharge relationship such that it takes due cognisance of the quality of the gauging data and the
performance of the rating. If the potential uncertainties are considered to be relatively high, i.e. greater
than 10 % to 15 % at the 95 % confidence level, then more frequent gaugings may be required targeting
the critical stage range(s) of concern.
For each discharge measurement in the list, the following items are required (see Table 1).
a) A unique identification name of site, and gauging number.
b) The date of measurement and time of start and time of finish of gauging.
c) The name of the person undertaking or leading the gauging, as well as the type of instruments used
to measure the discharge, the average gauge height, based on a minimum of the readings at the
start and end of the complete gauging.
d) The total discharge.
e) An indication of the likely accuracy of measurement, as determined by the person leading the
gauging, e.g. whether the channel was heavy with vegetation, whether extensive vortices were
evident in the flow pattern, whether the cross section was uniform, whether the flow was steady.
Documentary evidence of the channel and flow conditions at the time of each gauging can also be
compiled using photographic or video recordings.
Table 1 — List of discharge measurements made by a hydrometric practitioner using current
meters and depth soundings
Aver-
ID Effec- Gauge
Date (yy/ Made Mean age Dis- Number of
num- Width Area tive Method height Rated
mm/dd) by velocity gauge charge verticals
ber depth change
height
2 3
m m m/s m m m /s m/h
12 78/04/08 MEF 36,27 77,94 1,272 2,682 2,080 99,12 0,2/0,8 22 −0,082 GOOD
183 85/02/06 GTC 33,53 78,41 1,405 2,786 2,186 110,2 0,6/0,2/0,8 22 −0,047 GOOD
201 87/02/04 AJB 28,96 21,92 1,511 2,002 1,402 33,13 0,6/0,2/0,8 21 −0,013 POOR
260 93/03/13 GMP 26,52 21,46 1,400 1,981 1,381 30,02 0,6 22 −0,020 GOOD
313 96/08/24 HFR 30,18 42,08 1,602 2,374 1,774 67,40 0,6/0,2/0,8 22 +0,006 GOOD
366 03/08/21 MAF 28,96 14,86 0,476 1,557 0,957 7,080 0,6 21 0 GOOD
367 03/10/10 MAF 28,96 13,66 0,361 1,490 0,890 4,928 0,6 21 0 GOOD
368 03/11/26 MAF 29,26 14,21 0,373 1,509 0,909 5,296 0,6 18 0 GOOD
369 04/02/19 MAF 29,87 16,26 1,291 1,838 1,238 20,99 0,6 21 0 GOOD
370 04/04/09 MAF 29,26 21,27 0,805 1,780 1,180 17,13 0,6/0,2/0,8 21 0 GOOD
371 04/05/29 MAF 29,57 19,69 0,688 1,710 1,110 13,54 0,6 21 0 GOOD
372 04/07/10 MAF 28,96 16,81 0,458 1,573 0,973 7,703 0,6 21 0 GOOD
373 04/08/22 MAF 29,26 15,79 0,481 1,570 0,970 7,590 0,6 21 0 GOOD
374 08/10/01 MAF 29,26 13,19 0,264 1,414 0,814 3,483 0,6 21 0 GOOD
375 09/11/11 MAJ 28,96 11,71 0,283 1,396 0,796 3,313 0,6 21 0 GOOD
382 10/10/01 MAF 30,48 43,76 1,598 2,432 1,832 69,95 0,2/0,8 21 +0,017 GOOD
NOTE 1 Discharge measurements made with acoustic Doppler current profilers require additional parameters, including the number of
transects and the range of discharges measured during the transects (see ISO/TR 24578).
NOTE 2 In terms of uncertainty of the stage discharge relationship, a relationship is regarded as ‘poor if its uncertainty is > 15 %. A “good”
relationship has uncertainty of ± 5 %.
6 © ISO 2020 – All rights reserved
5.2.3 Arithmetic plotting scales
The simplest type of plot uses an arithmetically divided plotting scale, as shown in Figure 1. Scale
subdivisions should be chosen to cover the complete range of gauge height and discharge expected to
occur at the gauging site. Scales should be subdivided in uniform increments that are easy to read and
interpolate. The choice of scale should also produce a rating curve that is not unduly steep or flat. If the
range in gauge height or discharge is large, it may be necessary to plot the rating curve in two or more
segments to provide scales that are easily read with the necessary precision. This procedure can result
in separate curves for low water, medium water and high water.
Where a hand derived relationship is required, graph paper with arithmetic scales is convenient to
use and easy to read. Such scales are ideal for displaying a rating curve and have an advantage over
logarithmic scales in that zero values of gauge height and/or discharge can be plotted. However, for
analytical purposes, arithmetic scales have practically no advantage. A stage–discharge relationship on
arithmetic scales is usually a curved line, concave downward, which is difficult to shape correctly if only
a few discharge measurements are available. Logarithmic scales, on the other hand, have a number of
analytical advantages as described in 5.2.4. Generally, a stage–discharge relationship is first drawn on
logarithmic plotting paper for shaping and analytical purposes and then later transferred to arithmetic
plotting paper if a display plot is needed.
Key
Y effective depth, (h − e), in metres
X discharge, Q, in cubic metres per second
NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1.
Figure 1 — Arithmetic plot of stage–discharge relationship
5.2.4 Logarithmic plotting scales
Most stage–discharge relationships, or segments thereof, can be analysed graphically through the
use of logarithmic plotting. There are two methods that can be used to fully utilize this procedure; by
plotting effective depth of flow, also known as hydraulic head, versus discharge, or by applying scale
offsets to the gauge height axis and plotting gauge height versus discharge. Effective depth of flow
on the control, or hydraulic head, for a section control is computed by subtracting the gauge height
of zero discharge (also known as cease to flow gauge height) from the gauge height associated with
the measured discharge. In theory, a straight line relation in log space can be achieved by plotting the
effective depth versus discharge. Similarly, the gauge height of zero discharge for a section control, can
be used as a scale offset for the gauge height axis in log space to also achieve a straight line segment.
The offset approach allows for plotting of actual gauge height versus discharge which provides some
simplification to the process as real data does not need to be transformed.
The approaches discussed above are simple to apply for section type controls. Channel type controls
present a more complicated situation. When a reach is under channel control there is not a single
8 © ISO 2020 – All rights reserved
cross section of the channel that is controlling the height of the water at the gauge, rather the reach
characteristics, including geometry, slope, and roughness, where the gauge is located controls the height
of water. Because of this, it is not feasible to measure and determine the gauge height of zero discharge
of the channel control. Without this determination, one is unable to plot the effective depth versus
discharge in log space. For the offset approach, the determination of the proper offset shall be made
through a trial-and-error approach. The trial-and-error approach is applied by iteratively adjusting the
offset on the gauge height axis and visually examining the plot of actual gage height versus discharge
for measurements under the channel control for a straight line relation. For gauges that experience
multiple hydraulic controls, such as section and channel, multiple offsets are required to obtain straight
line segments for each control.
Regardless of the approach taken, a rating-curve segment for a given control will then tend to plot as
a straight line. The slope of the straight line should conform to the type of control section, thereby
providing valuable information for correctly shaping the rating-curve segment. Additionally, this feature
allows the analyst to calibrate the stage–discharge relationship with fewer discharge measurements.
The slope of a rating curve is the ratio of the horizontal distance to the vertical distance. This method of
measuring the slope is used since the dependent variable (discharge) is always plotted as the abscissa.
Figure 2 is a logarithmic plot of an actual rating curve, which is plots effective depth (not gauge height)
versus discharge, using the measurements shown in Table 1. This rating curve is for a stream where
section control exists throughout the range of flow, including the high-flow measurements. The effective
gauge height of zero flow, e, for this stream is 0,6 m, which is subtracted from the gauge height of the
measurements to define the effective depth of flow at the control. The slope of the rating curve below
1,4 m is about 4,3, which is greater than 2 and conforms to a section control. Above 1,5 m, the slope is
2,8, which also conforms to a section control. The change in slope of the rating curve above about 1,5 m
is caused by a change in the shape of the control cross-section or another section control downstream
from the low-water section control.
Key
Y effective depth, (h − e), in metres
X discharge, Q, in cubic metres per second
NOTE The numbers indicated against the plotted observations are the ID numbers given in Table 1.
Figure 2 — Logarithmic plot of stage–discharge relationship
Rating curves for section controls such as weirs or flumes conform to Formula (1) and, when plotted
logarithmically, will have a slope of 1,5 or greater, depending on control shape, velocity of approach
and minor variations of the coefficient of discharge. Horizontal crested structures will have a slope
of about 1,5, whereas V shaped structures will have slopes of about 2,5. Rating curves for channel
controls are governed by one of the standard Formulae (2) to (4) and, when plotted as effective depth
versus discharge, the slope is usually between 1,5 and 2. Variations in the slope of the rating curve
when channel control exists are the result of changes in roughness and friction slope as depth changes.
The effective depth is sometimes not known for channel controls. It can be determined mathematically
and statistically during the stage–discharge development process using an iterative process whereby
the parameters C, β and e are optimised to give the best fitting relationship taking due account of the
physical properties of the channel.
5.2.5 Commercially available software
There are a number of commercially available software packages that can analyse a series of stage and
discharge measurements and derive the best stage–discharge relationship (see Annex C). Most packages
also give the statistics relating to the standard error and uncertainty of the derived relationship. This
also applies to the use of logarithmic stage to flow relationships as covered in 5.2.4
10 © ISO 2020 – All rights reserved
5.2.6 Rating-curve shape
5.2.6.1 General
The details provided in 5.2.2 to 5.2.4 apply to control sections of regular shape (trapezoidal, parabolic,
etc.). However, natural channels are rarely regular in section hence the practitioner should be aware
of where “step changes” in the stage–discharge relationship are likely to occur. Where a significant
change in shape or flow control occurs, there will be a change in the rating-curve slope at that point.
These changes are usually defined by short curved segments of the rating curve, referred to as
transitions. This information about the plotting characteristics of a rating curve is extremely useful in
the calibration and maintenance of the rating curve and in later analysis of shifting control conditions.
By knowing the kind of control (section or channel), and the shape of the control, the analyst can define
the correct hydraulic shape of the rating curve with greater precision. Additionally, this information
allows the analyst to extrapolate accurately a rating curve or, conversely, to know when extrapolation
is likely to lead to a large uncertainty.
Examples of a hypothetical rating curves are given in Annex D.
5.2.6.2 Gauge height of zero flow
The actual gauge height of zero flow is the gauge height of the lowest point in the control cross-section
for a section control. This is sometimes referred to as the cease-to-flow. For natural channels, this value
can sometimes be measured in the field by measuring the depth of flow at the deepest place in the
control section and subtracting this depth and the velocity head from the gauge height at the time of
measurement.
The effective gauge height of zero flow is a value that, when subtracted from the mean gauge heights
of the discharge measurements, will cause the logarithmic rating curve segment for specific to that
control to plot as a straight line. Thus, it should be determined for each rating-curve segment. For
regularly shaped section controls, this value will be close to the actual gauge height of zero flow. For
channel controls there is not a single cross section that controls the stage discharge relation. For these
controls, the effective gage height of zero flow is determined by a trial-and-error method of plotting. A
value is assumed and adjusted gauge heights are plotted based on this assumed value. If the resulting
curve shape is concave upward, then a somewhat larger value for the effective gauge height of zero flow
should be used. A somewhat smaller value should be used if the curve plots concave downward. Usually,
only a few trials are needed to find a value that results in a straight line for the rating-curve segment.
Formula (6) shows a rating curve that plots as a straight line on logarithmic paper:
β
QQ=−he (6)
()
where
(h − e) is the effective depth of water on the control;
h is the gauge height of the water surface;
e is the effective gauge height of zero flow or offset;
β is the slope of the rating curve when plotted on logarithmic paper if discharge is plotted
on the abscissa;
Q is a scale factor that is numerically equal to the discharge when the effective depth of flow
(h − e) is equal to 1.
5.3 Curve fitting
5.3.1 General
There are a number of software packages (see Annex C) to aid the creation of the stage–discharge
relationship given a series of flow measurements at specific stages at the observation site. Such packages
contain additional analytical tools that help describe the accuracy and standard errors associated with
the rating curve. However, for proponents of hand-based curve fitting, the curve-fitting process for
stage–discharge relationships includes the actual drawing, positioning and shaping of the rating curve.
Hydraulic-analysis and line-fitting applications can be used to aid in the curve-fitting process but the
stage–discharge relationship should represent the best fit of the calibration measurements over the
range of measurements and with considerations for the quality or uncertainty of the measurements, as
well as the conditions of the hydraulic control.
Nevertheless, for a site with a varying flow control due to, for example, seasonal vegetation growth,
every measurement does not need to fit on the same rating curve. A particular gauge location can have
a number of ratings that apply to specific control conditions in the channel. The curves produced by
the curve fitting process should give stage–discharge relationships that reflect the particular control
changes. Further, only measurements made under similar control conditions should be used when
developing the rating curve. For example, measurements associated with vegetation on the control
should not be included with measurements associated with clear control (no vegetation) conditions
when developing a rating curve for clear control conditions.
5.3.2 Hydraulic-formula curves
The shape of stage–discharge relationships can be defined through the use of hydraulic formulae, namely
Formulae (1), (2), (3) and (4). Where section control exists, the weir formula, Formula (1), can be used
to compute rating-curve points. Coefficients of discharge, C , have been defined in other International
D
Standards for certain types of weirs and flumes, so a reasonably accurate rating curve can be computed
that will conform to correct hydraulics. For natural section controls, such as a rock outcrop or gravel
bar, the coefficient of discharge can be estimated on the basis of calibration measurements. Widths and
depths can be determined
...
NORME ISO
INTERNATIONALE 18320
Première édition
2020-07
Hydrométrie — Measurage du débit
des cours d'eau — Détermination de la
relation hauteur–débit
Hydrometry — Measurement of liquid flow in open channels —
Determination of the stage–discharge relationship
Numéro de référence
©
ISO 2020
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2020
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Publié en Suisse
ii © ISO 2020 – Tous droits réservés
Sommaire Page
Avant-propos .v
1 Domaine d’application . 1
2 Références normatives . 1
3 Termes, définitions et symboles . 1
3.1 Termes et définitions . 1
3.2 Symboles . 2
4 Principe de la relation hauteur–débit . 3
4.1 Généralités . 3
4.2 Contrôles hydrauliques . 3
4.3 Principales formules hydrauliques . 4
5 Calage hauteur–débit d’une station hydrométrique . 5
5.1 Généralités . 5
5.2 Préparation d’une relation hauteur–débit . 6
5.2.1 Généralités . 6
5.2.2 Liste des jaugeages. 6
5.2.3 Échelles arithmétiques . 7
5.2.4 Échelles logarithmiques . 9
5.2.5 Logiciels disponibles à la vente .11
5.2.6 Forme de la courbe de tarage .11
5.3 Calage de la courbe .12
5.3.1 Généralités .12
5.3.2 Courbes relatives aux formules hydrauliques .12
5.3.3 Courbes de tarage mathématiques .13
5.3.4 Progiciels d’aide à la détermination de la courbe de tarage .13
5.4 Relations hauteur–débit pour contrôle composé .13
5.5 Relations hauteur–débit stables .14
5.6 Relations hauteur–débit instables .14
5.7 Détarages .15
5.8 Effets liés à un remous variable.16
5.8.1 Généralités .16
5.8.2 Influences liées aux remous en aval .16
5.8.3 Effets de l’hystérésis ou courbes de tarage en boucle .16
5.9 Extrapolation de la relation hauteur–débit .19
6 Méthodes de vérification des relations hauteur–débit .19
7 Incertitude de la relation hauteur–débit .20
7.1 Généralités .20
7.2 Définition de l’incertitude .21
7.3 Analyse statistique de la relation hauteur–débit .21
7.3.1 Généralités .21
7.3.2 Erreur-type d’estimation .21
7.3.3 Incertitude-type.22
7.4 Incertitude d’une prévision de débit .23
Annexe A (informative) Types de contrôles .25
Annexe B (informative) Difficultés liées aux relations hauteur–débit .26
Annexe C (informative) Progiciels disponibles pour l’évaluation de la relation hauteur–débit.27
Annexe D (informative) Exemples de courbes de tarage hypothétiques .31
Annexe E (informative) Exemple de variation des propriétés hydrauliques d’un chenal de
rivière en fonction de la hauteur .33
Annexe F (informative) Utilisation des décalages de contrôles .39
Annexe G (informative) Extrapolation d’une relation hauteur–débit.41
Annexe H (informative) Incertitude dans la relation hauteur–débit et dans un mesurage
continu du débit .43
Bibliographie .46
iv © ISO 2020 – Tous droits réservés
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes
nationaux de normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est
en général confiée aux comités techniques de l'ISO. Chaque comité membre intéressé par une étude
a le droit de faire partie du comité technique créé à cet effet. Les organisations internationales,
gouvernementales et non gouvernementales, en liaison avec l'ISO participent également aux travaux.
L'ISO collabore étroitement avec la Commission électrotechnique internationale (IEC) en ce qui
concerne la normalisation électrotechnique.
Les procédures utilisées pour élaborer le présent document et celles destinées à sa mise à jour sont
décrites dans les Directives ISO/IEC, Partie 1. Il convient, en particulier, de prendre note des différents
critères d'approbation requis pour les différents types de documents ISO. Le présent document a été
rédigé conformément aux règles de rédaction données dans les Directives ISO/IEC, Partie 2 (voir www
.iso .org/ directives).
L'attention est attirée sur le fait que certains des éléments du présent document peuvent faire l'objet de
droits de propriété intellectuelle ou de droits analogues. L'ISO ne saurait être tenue pour responsable
de ne pas avoir identifié de tels droits de propriété et averti de leur existence. Les détails concernant
les références aux droits de propriété intellectuelle ou autres droits analogues identifiés lors de
l'élaboration du document sont indiqués dans l'Introduction et/ou dans la liste des déclarations de
brevets reçues par l'ISO (voir www .iso .org/ brevets).
Les appellations commerciales éventuellement mentionnées dans le présent document sont données
pour information, par souci de commodité, à l’intention des utilisateurs et ne sauraient constituer un
engagement.
Pour une explication de la nature volontaire des normes, la signification des termes et expressions
spécifiques de l'ISO liés à l'évaluation de la conformité, ou pour toute information au sujet de l'adhésion
de l'ISO aux principes de l’Organisation mondiale du commerce (OMC) concernant les obstacles
techniques au commerce (OTC), voir www .iso .org/ avant -propos.
Le présent document a été élaboré par le comité technique ISO/TC 113, Hydrométrie, sous-comité SC 1,
Méthodes d’exploration du champ des vitesses.
Cette première édition de l’ISO 18320 annule et remplace l’ISO 1100-2:2010, dont elle constitue une
révision technique.
Les principales modifications par rapport à l’édition précédente sont les suivantes:
— l’Article 5 a fait l’objet d’une révision importante, avec l’inclusion d’un nouveau chiffre pour la
relation hauteur–débit et les courbes filles;
— l’Article 7 a été révisé pour s’aligner sur les nouvelles normes relatives à l’incertitude.
Il convient que l’utilisateur adresse tout retour d’information ou toute question concernant le présent
document à l’organisme national de normalisation de son pays. Une liste exhaustive desdits organismes
se trouve à l’adresse www .iso .org/ fr/ members .html.
NORME INTERNATIONALE ISO 18320:2020(F)
Hydrométrie — Measurage du débit des cours d'eau —
Détermination de la relation hauteur–débit
1 Domaine d’application
Le présent document spécifie des méthodes permettant de déterminer la relation hauteur–débit pour
des stations hydrométriques. Un nombre suffisant de jaugeages, complétés par des mesurages de
hauteur correspondants, est nécessaire afin de définir une relation hauteur–débit selon l’exactitude
requise par le présent document.
Le présent document étudie les chenaux, qu’ils soient stables ou instables, et comporte une brève
description des effets hydrauliques sur la relation hauteur–débit de la transition entre l’écoulement
sans débordement et l’écoulement avec débordement, des détarages, du remous variable et des effets
d’hystérésis. Les méthodes de détermination du débit pour les stations à double échelle, les stations
vélocimétriques par ultrasons et les autres courbes de tarage complexes ne sont pas décrites en détails.
NOTE Ces types de courbes de tarage sont répertoriés séparément dans d’autres Normes internationales,
Spécifications techniques et Rapports techniques, listés dans la Bibliographie.
2 Références normatives
Les documents suivants cités dans le texte constituent, pour tout ou partie de leur contenu, des
exigences du présent document. Pour les références datées, seule l’édition citée s’applique. Pour les
références non datées, la dernière édition du document de référence s’applique (y compris les éventuels
amendements).
ISO 748, Hydrométrie — Mesurage du débit des liquides dans les canaux découverts au moyen de moulinets
ou de flotteurs
ISO 772, Hydrométrie — Vocabulaire et symboles
3 Termes, définitions et symboles
3.1 Termes et définitions
Aucun terme n’est défini dans le présent document.
L’ISO et l’IEC tiennent à jour des bases de données terminologiques destinées à être utilisées en
normalisation, consultables aux adresses suivantes:
— ISO Online browsing platform: disponible à l’adresse https:// www .iso .org/ obp
— IEC Electropedia: disponible à l’adresse http:// www .electropedia .org/
3.2 Symboles
Pour les besoins du présent document, les symboles décrits dans l’ISO 772 ainsi que les suivants
s’appliquent:
Symbole Définition
A surface mouillée de la section transversale
B largeur de la section transversale
β exposant (pente sur une courbe logarithmique) de la courbe de tarage
C coefficient de débit
D
C coefficient de rugosité de Chézy pour le chenal
e hauteur à l’échelle efficace du débit nul
f coefficient de frottement de Darcy-Weisbach
g accélération due à la gravité
h hauteur à l’échelle de la surface de l’eau
(h − e) profondeur efficace, il s’agit essentiellement de la différence entre le niveau d’arrêt de l’écoulement
et le relevé sur l’échelle. Par exemple, pour un contrôle hydraulique horizontal avec une échelle nulle
au même niveau que le seuil du contrôle, la valeur efficace de e sera nulle
H charge totale (charge hydraulique)
k hauteur de rugosité au-dessus de la surface lisse
k taille de rugosité (en équivalent sable) de Nikuradse
s
n coefficient de rugosité de Manning pour le chenal
N nombre de mesurages de hauteur–débit (jaugeages) utilisés pour définir la courbe de tarage
p nombre de paramètres de la courbe de tarage (Q , β, e) estimés à partir des N jaugeages
Pw périmètre mouillé
Q débit total
Q débit stationnaire
o
Q facteur d’échelle à loi exponentielle de la courbe de tarage, égal au débit lorsque la profondeur efficace
de l’écoulement (h − e) est égale à 1
r rayon hydraulique, égal à la surface efficace de section transversale divisée par le périmètre mouillé,
h
A/P (convient uniquement aux écoulements sans débordement)
w
a
Re nombre de Reynolds (= 4Vv/ )
S erreur-type d’estimation
S pente de frottement
f
S pente du fond
S pente de la surface de l’eau correspondant à un débit permanent
w
t temps
u incertitude-type
vitesse moyenne du cours d’eau (= Q/A)
V
U incertitude élargie
V vitesse d’une onde de crue
w
ν viscosité cinématique
a
Certains textes de référence utilisent une dimension caractéristique de quatre fois le rayon hydraulique, car Re
[16]
adopte alors la même valeur pour le début des turbulences que pour l’écoulement en charge . D’autres textes utilisent le
rayon hydraulique en tant qu’échelle de longueur caractéristique, avec par conséquent des valeurs de Re différentes pour
l’écoulement de transition et l’écoulement turbulent.
2 © ISO 2020 – Tous droits réservés
4 Principe de la relation hauteur–débit
4.1 Généralités
La relation entre la hauteur et le débit pour une station hydrométrique donnée est généralement
appelée relation hauteur–débit, courbe de tarage ou barème. Une relation hauteur–débit est établie
afin de permettre la production future d’une série temporelle de débit (hydrogramme), basée sur
des mesurages continus de la hauteur (limnigramme) à la station hydrométrique. Il est généralement
plus aisé de mesurer en continu la hauteur que le débit. L’élaboration d’une chronique de débit est
donc grandement facilitée dès lors qu’une relation hauteur–débit stable a été établie à une station
hydrométrique.
4.2 Contrôles hydrauliques
La relation hauteur–débit pour un cours d’eau à une station hydrométrique est régie par les conditions,
aussi appelées «contrôles hydrauliques», présentes au sein du chenal, au droit et en aval de l’échelle.
Il peut exister deux types de contrôle, selon les conditions du chenal et les conditions d’écoulement.
Les écoulements faibles, c’est-à-dire ceux rencontrés par temps sec, sont généralement contrôlés par
un contrôle dit «par section», tandis que les écoulements importants, c’est-à-dire ceux rencontrés
par temps pluvieux, sont habituellement contrôlés par un contrôle dit «par chenal». Les écoulements
moyens peuvent être contrôlés par les deux types de contrôle. Pour certaines hauteurs, une combinaison
de contrôles par section et par chenal peut être utilisée. Il s’agit de règles générales, mais certaines
exceptions existent et peuvent survenir. La connaissance des caractéristiques du chenal qui contrôle la
relation hauteur–débit est essentielle. L’interpolation entre les jaugeages et l’extrapolation au-delà des
jaugeages les plus élevés ou les plus bas des courbes de hauteur–débit exigent un certain discernement,
notamment en présence de plus d’un contrôle effectif, de caractéristiques de contrôle variables et d’un
nombre de jaugeages limité. Cela s’avère particulièrement vrai lorsque les contrôles ne sont pas stables
et tendent à varier, occasionnant des changements dans le positionnement des segments de la relation
hauteur–débit.
Les écoulements importants peuvent entraîner le débordement du cours d’eau ou de la rivière et
l’inondation de tout lit majeur adjacent. Dans ces circonstances, une partie du débit sera contenue
dans le lit mineur de la rivière et une autre partie envahira le lit majeur. Par conséquent, il convient
d’établir une distinction entre la situation où le débit est entièrement contenu dans le lit mineur et celle
où le débit excède cette capacité de plein bord. Le changement de conditions hydrauliques découlant de
cette transition d’un écoulement sans débordement vers un écoulement avec débordement affectera la
relation hauteur–débit. Une description des types de contrôles est donnée dans l’Annexe A.
4.3 Principales formules hydrauliques
La relation hauteur–débit peut être définie en fonction du type de contrôle existant. Les contrôles par
section, d’origine naturelle ou humaine, sont régis par certaines formes de formules liées aux déversoirs
ou aux canaux jaugeurs. Sous une forme très générale et basique, ces formules sont exprimées comme
indiqué dans la Formule (1):
β
QC= BH (1)
D
où
Q est le débit, en mètres cubes par seconde;
C est un coefficient de débit et inclut plusieurs facteurs;
D
B est la largeur de la section transversale perpendiculaire à la direction de l’écoulement, en
mètres;
H est la charge hydraulique, en mètres;
β est un exposant dépendant de la forme de la section transversale de la section de contrôle.
Les relations hauteur–débit pour les contrôles par chenal avec écoulement uniforme sont habituellement
régies par les formules de Manning (parfois appelée «formule de Manning-Strickler» en Europe), de
Chézy et de Darcy-Weisbach dans la mesure où elles s’appliquent au tronçon du chenal de contrôle situé
en amont et en aval d’une échelle.
La formule de Manning est donnée dans la Formule (2):
06,,70 5
QA= rS /n (2)
()
hf
où
A est la surface mouillée, en mètres carrés;
r est le rayon hydraulique, en mètres;
h
S est la pente de la ligne de charge;
f
n est la rugosité de Manning pour le chenal.
NOTE Le coefficient de Strickler est exactement l’inverse du «n» de Manning.
La formule de Chézy est donnée dans la Formule (3):
05,,05
QC= Ar S (3)
hf
où C est le coefficient de rugosité de Chézy.
4 © ISO 2020 – Tous droits réservés
La formule de Darcy-Weisbach est donnée dans la Formule (4):
05,
05,,05
Qg={}8 /fArS (4)
hf
où
g est l’accélération due à la gravité;
f est le coefficient de frottement, donné par la formule de Colebrook-White,
qui peut être utilisée pour les cours d’eau, voir la Formule (5):
−05,,05
f =−21log/kr40,,82+ 51//4Vr vf (5)
{}() ()
10 sh h
où
est la vitesse moyenne du cours d’eau;
V
k est la taille de rugosité de Nikuradse;
s
ν est la viscosité cinématique.
La variation de f avec une rugosité relative (= k /4 r ) et le nombre de Reynolds est souvent représentée
s h
sous la forme d’une courbe appelée «diagramme de Moody». La rugosité de toute surface est alors
caractérisée par k , aussi appelé taille de rugosité (en équivalent sable) de Nikuradse. La formule de
s
Colebrook-White dispose de bases physiques solides. Elle tend en effet vers deux cas limites théoriques,
l’un concernant les surfaces hydrauliquement lisses et l’autre les surfaces hydrauliquement rugueuses,
et la forme du chenal est prise en compte grâce à l’utilisation de coefficients appropriés.
Les formules ci-dessus sont généralement applicables aux écoulements sans débordement permanents
ou quasi-permanents. Dans le cas d’écoulements extrêmement instationnaires, tels que ceux liés
aux marées ou à une rupture de barrage, des formules telles que les formules de Saint-Venant pour
écoulements transitoires sont nécessaires. Toutefois, ces dernières ne sont que rarement utilisées
dans l’élaboration des relations hauteur–débit et ne sont pas décrites dans le présent document. Les
écoulements avec débordement nécessitent en principe une attention particulière en raison de la
forte interaction entre les écoulements de différentes régions du chenal, donnant lieu à d’importants
effets de transfert latéral de quantité de mouvement. Pour les écoulements avec débordement, le
rayon hydraulique adopté dans les Formules (2) à (4) n’est plus approprié pour caractériser la section
transversale du chenal, dans la mesure où Pw va augmenter bien plus rapidement avec la hauteur que
A en raison du périmètre mouillé supplémentaire lié au lit majeur à mesure que l’écoulement dépasse
la capacité de plein bord. Cela peut alors entraîner une réduction considérable de r au niveau de
h
débordement, ainsi qu’une apparente diminution consécutive du coefficient de résistance pour la
section entière, bien que la rugosité hydraulique réelle augmente. Dans ces conditions, il est également
nécessaire de redéfinir les coefficients de résistance individuels pour le lit mineur et les lits majeurs,
comme expliqué plus en détail dans l’Annexe E et la Formule (6).
Une description complète des aspects les plus complexes des relations hauteur–débit est donnée dans
l’Annexe B.
5 Calage hauteur–débit d’une station hydrométrique
5.1 Généralités
Le principal objectif d’une station hydrométrique à relation hauteur–débit est d’obtenir un
enregistrement du débit du cours d’eau par l’intermédiaire de la mesure de hauteur d’eau au droit de
l’échelle de référence. Pour ce faire, la hauteur est mesurée, puis convertie en débit à l’aide d’une relation
hauteur–débit qui met en corrélation le débit et la hauteur d’eau à l’échelle. Dans certains cas, d’autres
paramètres, comme la vitesse témoin, la dénivelée de la ligne d’eau entre deux échelles ou le taux de
variation de la hauteur, peuvent également être utilisés lors du calage de la courbe de tarage, comme
indiqué dans l’ISO 15769 et l’ISO 9123. Les relations hauteur–débit sont généralement étalonnées en
mesurant le débit et la hauteur à l’échelle correspondante. Des calculs théoriques peuvent également
être utilisés afin de contribuer à la création et au positionnement de la courbe de tarage. Il convient en
outre de tenir compte des relations hauteur–débit de périodes précédentes pour aider à l’élaboration de
la courbe.
5.2 Préparation d’une relation hauteur–débit
5.2.1 Généralités
La relation entre la hauteur et le débit est définie en réalisant le tracé des jaugeages avec les observations
de hauteur correspondantes, en tenant compte de la stabilité, de l’augmentation ou de la diminution du
débit et en notant le taux de variation de la hauteur. Cela peut être réalisé manuellement en traçant sur
papier, ou automatiquement en ayant recours à des techniques de traçage informatisées (voir Annexe C).
Le tracé peut utiliser une échelle arithmétique ou logarithmique. Chacune présente des avantages et des
inconvénients, comme décrit dans les paragraphes 5.2.3 et 5.2.4. La plupart des services hydrologiques
nationaux utilisent la hauteur en ordonnées (axe y) et le débit en abscisse (axe x). Toutefois, lorsque la
relation hauteur–débit est utilisée pour obtenir le débit à partir du mesurage d’une valeur de hauteur, la
hauteur est traitée comme la variable indépendante.
Pour les sites hydrométriques présentant un écoulement significatif en lit majeur, dû à de nombreux
chenaux ou à des structures immergées, la détermination de la relation hauteur–débit composite peut
s’avérer difficile. Le débit de crue peut ne pas être mesuré de façon appropriée en raison d’un accès
insuffisant ou dangereux. Par ailleurs, un écoulement traversant un lit majeur peut être complexe et
est affecté par des variations de stockage à mesure qu’une crue se forme ou se retire. Ces difficultés
peuvent avoir une ampleur telle qu’il convient d’utiliser des considérations théoriques en association
avec les mesurages limités lors de la détermination de la relation hauteur–débit.
5.2.2 Liste des jaugeages
La première étape préalable au traçage d’une relation hauteur–débit est la préparation d’une liste des
jaugeages qui seront utilisés pour la courbe. Il convient de vérifier les jaugeages afin de s’assurer que
les hauteurs enregistrées soient associées à une date commune et que les calculs de débit soient exacts.
En règle générale, cette première liste doit comprendre au moins 15 jaugeages, tous réalisés durant la
période d’analyse. Davantage de jaugeages sont requis pour une courbe de tarage composée, c’est-à-
dire une courbe représentée par plusieurs contrôles hydrauliques, dans le cas où le site serait soumis
à un marnage important, dans le cas où des techniques de détarages seraient utilisés en raison de la
sédimentation, de l’érosion ou de la croissance saisonnière de la végétation, ou encore dans le cas d’un
site hydrométrique posant tout autre problème pouvant entraîner des incertitudes de jaugeage élevées.
Pour une station hydrométrique d’usage général, il convient que ces jaugeages soient harmonieusement
répartis sur toute la gamme de hauteur à l’échelle rencontrée. Sinon, lorsque l’observation porte sur une
gamme d’écoulement spécifique, il convient que les jaugeages couvrent cette gamme. Par exemple, à
débit réduit pour un site destiné à informer un système de gestion de faible débit, ou à débit important
lorsque des débits de crue doivent être surveillés et gérés. Il convient que les jaugeages soient effectués
pour toute la gamme de débits attendus, notamment si une extrapolation de la courbe de tarage doit
être réalisée.
Il convient d’entreprendre une analyse de l’incertitude (voir Article 7) lors de l’élaboration et de l’analyse
de la relation hauteur–débit de manière à reconnaître convenablement la qualité des données de
jaugeage et la performance du barème. S’il apparaît que les incertitudes potentielles sont relativement
élevées, c’est-à-dire supérieures à 10 % à 15 % à un niveau de confiance de 95 %, il peut être nécessaire
d’effectuer des jaugeages plus fréquents ciblant la ou les gamme(s) de hauteur critique(s) posant
problème.
6 © ISO 2020 – Tous droits réservés
Pour chaque jaugeage figurant sur la liste, les éléments suivants sont requis (voir Tableau 1):
a) un nom unique identifiant le site, ainsi qu’un numéro de jaugeage;
b) la date de jaugeage, ainsi que l’heure de début et l’heure de fin du jaugeage;
c) le nom de la personne réalisant ou dirigeant le jaugeage, ainsi que le type d’instruments utilisé
pour mesurer le débit, la hauteur à l’échelle moyenne basée au minimum sur les relevés au début et
à la fin de l’opération de jaugeage complète;
d) le débit total;
e) une indication de l’incertitude vraisemblable du jaugeage, telle que déterminée par la personne
dirigeant le jaugeage. Par exemple, si le chenal était envahi de végétation aquatique, si le motif
d’écoulement présentait de nombreux tourbillons, si la section transversale était uniforme, si
l’écoulement était permanent, etc. Des documents attestant des conditions du chenal et d’écoulement
au moment de chaque jaugeage doivent également être établis au moyen d’enregistrements
photographiques ou vidéo.
Tableau 1 — Liste des jaugeages effectués par un technicien d’hydrométrie utilisant des
instruments et des mesures de profondeur
Nombre Change-
Hau-
Numéro Date (jj/ Profon- de ment de
Réalisé Vitesse teur à
d’identi- mm/ Largeur Surface deur Débit Méthode verti- hau- Qualité
par moyenne l’échelle
fication aaaa) efficace cales de teur à
moyenne
mesure l’échelle
2 3
m m m/s m m m /s m/h
12 78/04/08 MEF 36,27 77,94 1,272 2,682 2,080 99,12 0,2/0,8 22 −0,082 BON
183 85/02/06 GTC 33,53 78,41 1,405 2,786 2,186 110,2 0,6/0,2/0,8 22 −0,047 BON
201 87/02/04 AJB 28,96 21,92 1,511 2,002 1,402 33,13 0,6/0,2/0,8 21 −0,013 MAUVAIS
260 93/03/13 GMP 26,52 21,46 1,400 1,981 1,381 30,02 0,6 22 −0,020 BON
313 96/08/24 HFR 30,18 42,08 1,602 2,374 1,774 67,40 0,6/0,2/0,8 22 +0,006 BON
366 03/08/21 MAF 28,96 14,86 0,476 1,557 0,957 7,080 0,6 21 0 BON
367 03/10/10 MAF 28,96 13,66 0,361 1,490 0,890 4,928 0,6 21 0 BON
368 03/11/26 MAF 29,26 14,21 0,373 1,509 0,909 5,296 0,6 18 0 BON
369 04/02/19 MAF 29,87 16,26 1,291 1,838 1,238 20,99 0,6 21 0 BON
370 04/04/09 MAF 29,26 21,27 0,805 1,780 1,180 17,13 0,6/0,2/0,8 21 0 BON
371 04/05/29 MAF 29,57 19,69 0,688 1,710 1,110 13,54 0,6 21 0 BON
372 04/07/10 MAF 28,96 16,81 0,458 1,573 0,973 7,703 0,6 21 0 BON
373 04/08/22 MAF 29,26 15,79 0,481 1,570 0,970 7,590 0,6 21 0 BON
374 08/10/01 MAF 29,26 13,19 0,264 1,414 0,814 3,483 0,6 21 0 BON
375 09/11/11 MAJ 28,96 11,71 0,283 1,396 0,796 3,313 0,6 21 0 BON
382 10/10/01 MAF 30,48 43,76 1,598 2,432 1,832 69,95 0,2/0,8 21 +0,017 BON
NOTE 1 Les jaugeages effectués à l’aide de profileurs de courant à effet Doppler nécessitent des paramètres supplémentaires, dont le
nombre de transects et la gamme de débits mesurée pendant les transects (voir ISO/TR 24578).
NOTE 2 En termes d’incertitude de la relation hauteur–débit, une relation est considérée comme «mauvaise» lorsque son incertitude
est > 15 %. L’incertitude d’une «bonne» relation est de ± 5 %.
5.2.3 Échelles arithmétiques
Le type de courbe le plus simple utilise une échelle de traçage divisée arithmétiquement, comme
indiqué en Figure 1. Il convient que l’emplacement et la graduation des échelles soient choisis de manière
à couvrir l’ensemble de la gamme des hauteurs d’eau et des débits attendus au niveau de la station
hydrométrique. Il convient que les échelles soient subdivisées en incréments réguliers afin de faciliter
la lecture et l’interpolation. Il convient que le choix de l’échelle produise une courbe de tarage qui ne
soit pas exagérément abrupte ou plate. Si la gamme de hauteur à l’échelle ou de débit est importante,
il peut être nécessaire d’adapter l’échelle du graphique de la courbe de tarage (deux segments ou plus)
pour obtenir des courbes facilement lisibles et disposant de la précision requise. Cette procédure peut
se traduire par des courbes séparées pour des eaux basses, moyennes et hautes.
S’il s’avère nécessaire d’obtenir une relation réalisée à la main, le papier millimétré à échelles
arithmétiques est à la fois pratique à utiliser et à lire. De telles échelles sont idéales pour représenter
une courbe de tarage et, contrairement aux échelles logarithmiques, ont pour avantage de permettre le
traçage des valeurs nulles de la hauteur à l’échelle et/ou du débit. Toutefois, les échelles arithmétiques
ne présentent pratiquement aucun avantage lorsqu’elles sont utilisées à des fins analytiques. Une
relation hauteur–débit sur échelle arithmétique est habituellement représentée par une ligne
courbe, concave vers le bas, difficile à former correctement lorsque seuls quelques jaugeages sont
disponibles. À l’inverse, les échelles logarithmiques présentent une grande valeur analytique, comme
décrit en 5.2.4. De manière générale, une relation hauteur–débit est tout d’abord tracée sur papier
millimétré logarithmique à des fins de mise en forme et d’analyse, puis transférée sur papier millimétré
arithmétique si une représentation graphique est nécessaire.
Légende
Y profondeur efficace, (h − e), en mètres
X débit, Q, en mètres cubes par seconde
NOTE Les chiffres indiqués le long du tracé correspondent aux numéros d’identification spécifiés dans le
Tableau 1.
Figure 1 — Tracé arithmétique d’une relation hauteur–débit
8 © ISO 2020 – Tous droits réservés
5.2.4 Échelles logarithmiques
La plupart des relations hauteur–débit, ou des segments qui en sont issus, peuvent être analysé(e)s
graphiquement à l’aide d’un tracé logarithmique. Deux méthodes peuvent être employées afin d’exploiter
pleinement cette procédure: en réalisant un tracé de la profondeur d’écoulement efficace (également
appelée charge hydraulique) en fonction du débit, ou en appliquant des offsets d’échelle à l’axe de la
hauteur à l’échelle, puis en traçant la courbe de hauteur à l’échelle en fonction du débit. La profondeur
d’écoulement efficace sur le contrôle, ou charge hydraulique, pour un contrôle par section est calculée
en retranchant la hauteur à l’échelle du débit nul (également appelée hauteur à l’échelle d’arrêt de
l’écoulement) de la hauteur à l’échelle associée au débit mesuré. En théorie, il est possible d’obtenir une
relation en ligne droite dans l’espace logarithmique en traçant la courbe de la profondeur efficace en
fonction du débit. De la même manière, la hauteur à l’échelle du débit nul d’un contrôle par section peut
être utilisée comme offset d’échelle pour l’axe de hauteur à l’échelle dans l’espace logarithmique, afin
d’obtenir un segment en ligne droite. Grâce à l’approche par offset, il est possible de tracer la courbe
réelle de hauteur à l’échelle en fonction du débit, ce qui permet de simplifier le processus car les données
réelles n’ont alors pas besoin d’être transformées.
Les approches mentionnées ci-dessus sont facilement applicables pour la catégorie des contrôles par
section. Le cas des contrôles par chenal est cependant plus complexe. Lorsqu’un tronçon de cours d'eau
est soumis à un contrôle par chenal, la hauteur de l’eau au niveau de l’échelle n’est pas contrôlée par
une unique section transversale du chenal. Au lieu de cela, ce sont les caractéristiques du tronçon de
cours d'eau, dont la géométrie, la pente et la rugosité, qui contrôlent la hauteur de l’eau à l’emplacement
de l’échelle. Pour cette raison, le mesurage et la détermination de la hauteur à l’échelle du débit nul
du contrôle par chenal ne sont pas réalisables. Sans cette détermination, il est impossible de tracer la
courbe de la profondeur efficace en fonction du débit dans l’espace logarithmique. Pour l’approche par
offset, la détermination de l'offset approprié doit résulter d’une approche par tâtonnement. L’approche
par tâtonnement est appliquée en ajustant l'offset de manière itérative sur l’axe de la hauteur à l’échelle
et en examinant visuellement la courbe de la hauteur à l’échelle réelle en fonction du débit pour les
jaugeages réalisés en contrôle par chenal jusqu’à observer une relation en ligne droite. Pour les échelles
soumises à plusieurs contrôles hydrauliques, tels que par section ou par chenal, différents offsets sont
nécessaires pour obtenir des segments de courbe droits pour chaque contrôle.
Indépendamment de l’approche choisie, le tracé d’un segment de courbe de tarage d’un contrôle donné
aura alors tendance à représenter une ligne droite. Il convient que la pente de la ligne droite soit
conforme au type de section de contrôle, afin de fournir les précieuses informations qui permettront
de former correctement le segment de courbe de tarage. Cette caractéristique permet en outre à
l'opérateur d’étalonner la relation hauteur–débit avec un nombre réduit de jaugeages. La pente d’une
courbe de tarage est le ratio de la distance horizontale par rapport à la distance verticale. Cette méthode
de mesure de la pente est utilisée car la variable dépendante (le débit) est toujours représentée en
abscisse.
La Figure 2 est un tracé logarithmique d’une courbe de tarage réelle qui représente la profondeur
efficace (et non la hauteur à l’échelle) en fonction du débit, en utilisant les jaugeages figurant dans le
Tableau 1. Cette courbe de tarage correspond à un écoulement contrôlé par section sur toute la gamme
des débits y compris les plus importants. La hauteur à l’échelle efficace du débit nul, e, est de 0,6 m pour
ce cours d’eau. Elle est soustraite de la hauteur à l’échelle des jaugeages afin de définir la profondeur
d’écoulement efficace au contrôle. Au-dessous de 1,4 m, la pente de la courbe de tarage est d’environ 4,3.
Ce résultat est supérieur à 2 et conforme à un contrôle par section. Au-dessus de 1,5 m, la pente est
de 2,8 et est également conforme à un contrôle par section. La variation de la pente de la courbe de
tarage au-delà de 1,5 m environ résulte d’un changement de forme de la section transversale du contrôle
ou d’un autre contrôle par section en aval du contrôle par section en basses eaux.
Légende
Y profondeur efficace, (h − e), en mètres
X débit, Q, en mètres cubes par seconde
NOTE Les chiffres indiqués le long du tracé correspondent aux numéros d’identification spécifiés dans le
Tableau 1.
Figure 2 — Tracé logarithmique d’une relation hauteur–débit
Les courbes de tarage des contrôles par section tels que les déversoirs ou les canaux jaugeurs sont
conformes à la Formule (1) et, lors d’un traçage logarithmique, auront une pente de 1,5 ou plus, en
fonction de la forme du contrôle, de la vitesse d’approche et de variations mineures du coefficient de
débit. Les structures à seuil horizontal auront une pente d’environ 1,5 alors que les structures en forme
de V présenteront des pentes d’environ 2,5. Les courbes de tarage des contrôles par chenal sont régies
par une des Formules (2) à (4) types et, lorsqu’elles représentent la profondeur efficace en fonction du
débit, la pente se situe généralement entre 1,5 et 2. Les variations de la pente de la courbe de tarage
en présence d’un contrôle par chenal résultent des variations de rugosité et de la pente de frottement
à mesure que la profondeur évolue. Il arrive que la profondeur efficace ne soit pas connue pour les
contrôles par chenal. Elle peut être déterminée mathématiquement ou statistiquement pendant
l’élaboration de la relation hauteur–débit en employant un processus itératif par lequel les paramètres
C, β et e sont optimisés de façon à donner la relation la plus adaptée en tenant compte des propriétés
physiques du chenal.
10 © ISO 2020 – Tous droits réservés
5.2.5 Logiciels disponibles à la vente
Il existe différents progiciels disponibles à la vente permettant d’analyser une série de jaugeages de
hauteur et de débit, puis d’en déduire la meilleure relation hauteur–débit (voir Annexe C). La plupart des
progiciels permet également d’obtenir les données statistiques relatives à l’erreur-type et à l’incertitude
de la relation obtenue. Cela s’applique également à l’utilisation de relations logarithmiques hauteur–
débit, comme décrit en 5.2.4.
5.2.6 Forme de la courbe de tarage
5.2.6.1 Généralités
Les détails fournis dans les paragraphes 5.2.2 à 5.2.4 s’appliquent aux sections de contrôle de forme
régulière (trapézoïdale, parabolique, etc.). Cependant, la section des chenaux naturels est rarement
régulière, il convient donc que l'analyste ait connaissance des endroits où des variations importantes
dans la relation hauteur–débit sont susceptibles de survenir. Une modification significative de la forme
ou du contrôle de l’écoulement se traduira par une variation de la pente hauteur–débit à ce point. Ces
variations sont généralement représentées par de courts segments incurvés sur la courbe de tarage,
que l’on appelle des transitions. Cette information relative aux caractéristiques du tracé d’une courbe
de tarage est extrêmement utile pour le calage et la maintenance de la courbe de tarage, ainsi que pour
l’analyse ultérieure de détarages. La connaissance du type de contrôle (par section ou par chenal) et
de la forme du contrôle permet à l'opérateur de définir avec une précision accrue la forme hydraulique
correcte de la courbe de tarage. Cette information permet en outre à l'opérateur d’extrapoler avec
exactitude une courbe de tarage ou, à l’inverse, de savoir quand l’extrapolation sera susceptible
d’occasionner une incertitude importante.
Des exemples de courbes de tarage hypothétiques sont fournis dans l’Annexe D.
5.2.6.2 Hauteur à l’échelle du débit nul
La hauteur à l’échelle réelle du débit nul est la ha
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