ISO 18320:2020

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

• Status: Published
• Publication Date: 02-Aug-2020
• ICS: 17.120.20 - Flow in open channels
• Technical Committee: ISO/TC 113/SC 1 - Velocity area methods
• Drafting Committee: ISO/TC 113/SC 1/WG 7 - Determination of the stage-discharge relationship
• Current Stage: 6060 - International Standard published
• Start Date: 23-Apr-2020
• Completion Date: 03-Aug-2020

RELATIONS

• Replaces: ISO 1100-2:2010 - Hydrometry — Measurement of liquid flow in open channels — Part 2: Determination of the stage-discharge relationship
• Effective Date: 26-May-2012
• Consolidated By: ISO 4957:2018 - Tool steels
• Effective Date: 06-Jun-2022

Standards Content (sample)

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 18320:2020(E)
ISO 2020
---------------------- Page: 1 ----------------------
ISO 18320:2020(E)
COPYRIGHT PROTECTED DOCUMENT
© 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

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
ii © ISO 2020 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 18320:2020(E)
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

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ISO 18320:2020(E)

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
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ISO 18320:2020(E)
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.
© ISO 2020 – All rights reserved v
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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

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.
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ISO 18320:2020(E)
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
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

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)
Re Reynolds number (= 4Vv/ )
S standard error of estimate
S friction slope
S bed slope
S water surface slope corresponding to steady discharge
t time
u standard uncertainty
stream mean velocity (= Q/A)
U expanded uncertainty
V velocity of a flood wave
ν kinematic viscosity

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.
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ISO 18320:2020(E)
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):

QC= BH (1)
where
Q is the discharge, in cubic metres per second;
C is a coefficient of discharge and includes several factors;

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.
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ISO 18320:2020(E)
The Manning formula is shown by Formula (2):
06,,70 5
QA= rS /n (2)
where
A is the cross-sectional area, in square metres;
r is the hydraulic radius, in metres;
S is the friction slope;
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)
where C is the Chezy form of roughness.
The Darcy-Weisbach formula is shown by Formula (4):
05,
05,,05
Qg={}8 /fArS (4)
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;
k is the Nikuradse roughness size;
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

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
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ISO 18320:2020(E)

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

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

© ISO 2020 – All rights reserved 5
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ISO 18320:2020(E)

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 33,1
...

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,
TECHNOLOGICAL, COMMERCIAL AND
USER PURPOSES, DRAFT INTERNATIONAL
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
---------------------- Page: 1 ----------------------
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

COPYRIGHT PROTECTED DOCUMENT
© ISO 2018

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

on the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address

below or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Fax: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland
© ISO 2018 – All rights reserved
iii
ii © ISO 2018 – All rights reserved
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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 – All rights reserved
iii
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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.
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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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ISO/DIS 18320:2018(E)
ISO/DIS 18320
C coefficient of discharge
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
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

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
S bed slope
S water surface slope corresponding to steady discharge
t time
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ISO/DIS 18320:2018(E)
ISO/DIS 18320
u standard uncertainty
V stream mean velocity (= Q/A)
U expanded uncertainty
V velocity of a flood wave
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)
where
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ISO/DIS 18320:2018(E)
ISO/DIS 18320
Q is the discharge, in cubic metres per second;
C is a coefficient of discharge and includes several factors;

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)
where
A is the cross-sectional area, in square metres;
R is the hydraulic radius, in metres;
S is the friction slope;
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)
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
 
 

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
  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.

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ISO/DIS 18320:2018(E)
ISO/DIS 18320

The variation of f with relative roughness (= k /4R) and Reynolds number, ( ) is often shown

s R  4V /

plotted in the form of the so-called ‘Moody diagram’ (f versus Re and k /4R). The roughness of any

surface is then characterised by k , the so-called Nikuradse equivalent sand roughness size. The

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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ISO/DIS 18320

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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ISO/DIS 18320:2018(E)
ISO/DIS 18320

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
...

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 18320:2020(F)
ISO 2020
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ISO 18320:2020(F)
DOCUMENT PROTÉGÉ PAR COPYRIGHT
© ISO 2020

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ISO 18320:2020(F)
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

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ISO 18320:2020(F)

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

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ISO 18320:2020(F)
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.
© ISO 2020 – Tous droits réservés v
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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/
© ISO 2020 – Tous droits réservés 1
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ISO 18320:2020(F)
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
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
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

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,

A/P (convient uniquement aux écoulements sans débordement)
Re nombre de Reynolds (= 4Vv/ )
S erreur-type d’estimation
S pente de frottement
S pente du fond
S pente de la surface de l’eau correspondant à un débit permanent
t temps
u incertitude-type
vitesse moyenne du cours d’eau (= Q/A)
U incertitude élargie
V vitesse d’une onde de crue
ν viscosité cinématique

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
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ISO 18320:2020(F)
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.

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ISO 18320:2020(F)
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):
QC= BH (1)
Q est le débit, en mètres cubes par seconde;
C est un coefficient de débit et inclut plusieurs facteurs;

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)
A est la surface mouillée, en mètres carrés;
r est le rayon hydraulique, en mètres;
S est la pente de la ligne de charge;
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)
où C est le coefficient de rugosité de Chézy.
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ISO 18320:2020(F)
La formule de Darcy-Weisbach est donnée dans la Formule (4):
05,
05,,05
Qg={}8 /fArS (4)
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
est la vitesse moyenne du cours d’eau;
k est la taille de rugosité de Nikuradse;
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

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

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

© ISO 2020 – Tous droits réservés 5
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ISO 18320:2020(F)

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
...