SIST ISO 1088:2013
Hydrometry - Velocity-area methods using current-meters - Collection and processing of data for determination of uncertainties in flow measurement
Hydrometry - Velocity-area methods using current-meters - Collection and processing of data for determination of uncertainties in flow measurement
This International Standard provides a standard basis for the collection and processing of data for the determination of the uncertainties in measurements of discharge in open channels by velocity-area methods using current-meters. To determine the discharge in open channels by the velocity-area method, components of the flow (velocity, depth and breadth) need to be measured. The component measurements are combined to compute the total discharge. The total uncertainty in the computed discharge is a combination of the uncertainties in the measured components. Clause 4 of this International Standard deals with the types of errors and uncertainties involved. Clauses 5 and 6 present a standard procedure to estimate the component uncertainties by the collection and processing of the necessary data. This International Standard is intended to be applied to velocity-area methods that involve measurement of point velocities at a relatively small number of discrete depths and transverse positions in the flow crosssection, as described in ISO 748. This International Standard is not intended to be applied to measurements made by Acoustic Doppler Velocity Profilers (ADVP) or other instruments that produce essentially continuous velocity profiles of the flow field.
Durchflussmessung in offenen Gerinnen - Geschwindigkeitsflaechenmethoden - Datensammlung und. -verarbeitung zur Bestimmung von Messfehlern
Hydrométrie - Méthodes d'exploration du champ des vitesses à l'aide de moulinets - Recueil et traitement des données pour la détermination des incertitudes de mesurage du débit
Hidrometrija - Metode hitrost-prerez z uporabo merilnikov tokov - Zbiranje in obdelovanje podatkov za ugotavljanje negotovosti pri meritvah pretokov
Ta mednarodni standard zagotavlja standardno podlago za zbiranje in obdelovanje podatkov za ugotavljanje negotovosti pri meritvah izpusta v odprtih kanalih z metodami hitrost-prerez z uporabo merilnikov tokov. Za določanje izpusta v odprtih kanalih z metodo hitrost-prerez je treba izmeriti komponente pretoka (hitrost, globina in širina). Meritve komponent se združijo za izračun skupnega izpusta. Skupna negotovost v izračunanem izpustu je kombinacija negotovosti v izmerjenih komponentah. Točka 4 tega mednarodnega standarda obravnava vrste prisotnih napak in negotovosti. V točkah 5 in 6 je predstavljen standardni postopek za določanje negotovosti komponent z zbiranjem in obdelavo potrebnih podatkov. Ta mednarodni standard se uporablja z metodami hitrost-prerez, ki vključujejo meritve točk hitrosti pri relativno majhnem številu diskretnih globin in transverzalnih položajev v preseku tokov, kot je opisano v standardu ISO 748. Ta mednarodni standard se ne uporablja za meritve, opravljene z akustičnim Dopplerjevim merilnikom pretoka (ADVP) ali drugimi napravami, ki v osnovi izvajajo neprekinjene meritve hitrosti pretoka.
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INTERNATIONAL ISO
STANDARD 1088
Third edition
2007-07-01
Hydrometry — Velocity-area methods
using current-meters — Collection and
processing of data for determination of
uncertainties in flow measurement
Hydrométrie — Méthodes d'exploration du champ des vitesses à l'aide
de moulinets — Recueil et traitement des données pour la
détermination des incertitudes de mesurage du débit
Reference number
ISO 1088:2007(E)
©
ISO 2007
---------------------- Page: 1 ----------------------
ISO 1088:2007(E)
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ii © ISO 2007 – All rights reserved
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ISO 1088:2007(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Symbols and abbreviated terms . 2
4 Types of errors and procedure for estimating the uncertainties in flow measurement. 3
4.1 Principle. 3
4.2 Occurrence of error . 4
4.3 Sources of error . 5
4.4 Determination of the individual components of the uncertainty . 6
4.5 Total uncertainty in discharge. 7
5 Collection and processing of data for the investigation of component uncertainties – type
A evaluation of uncertainties. 8
5.1 Data on the local point velocity. 8
5.2 Data on the average velocity . 9
5.3 Data on the velocity-area method . 10
5.4 Integration method . 11
5.5 Calibration curves. 11
5.6 Distance measurements . 11
5.7 Depth measurements . 12
6 Data processing. 12
6.1 General. 12
6.2 Error-type i. 13
6.3 Error-type ii — Approximation of mean velocity in the vertical. 15
6.4 Error-type iii — Limited number of verticals.17
Annex A (informative) Characteristics of rivers from which data were collected . 21
Annex B (normative) Effect of increasing measuring time on uncertainty. 26
Annex C (normative) Local point velocity measurements - Report form. 27
Annex D (normative) Average velocity measurements — Report form . 31
Annex E (normative) Velocity-area method — Report form . 34
Annex F (informative) Examination of Error Types i, ii, and iii. 38
Annex G (informative) Uncertainties in velocity-area measurement components. 41
Annex H (informative) Calculation of the uncertainty in a current-meter gauging. 45
Bibliography . 48
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ISO 1088:2007(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 1088 was prepared by Technical Committee ISO/TC 113, Hydrometry, Subcommittee SC 5, Instruments,
equipment and data management.
This third edition cancels and replaces the second edition (ISO 1088:1985), which has been revised to
incorporate ISO/TR 7178 (based on ISO/DATA No. 2) and edited in accordance with ISO/IEC Guide 98:1995,
Guide to the expression of uncertainty in measurement (GUM). This third edition of ISO 1088 also cancels
and replaces ISO/TR 7178, all provisions of which have been incorporated into this edition.
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ISO 1088:2007(E)
Introduction
All measurements of physical quantities are subject to uncertainties, which can be due to biases (systematic
errors) introduced in the manufacture, calibration, and maintenance of measurement instruments, or to
random scatter caused by a lack of sensitivity of the instruments, and to other sources of error.
During the preparation of the first edition of ISO 748, much discussion was given to the question of the
magnitude of errors in measurements, and it was concluded that recommendations could only be formulated
on the basis of an analysis of sufficient data. Moreover, it was recognized that to be able to analyze such data
statistically, it was essential that the data be collected and recorded on a standardized basis and in a
systematic manner, and this recognition led to the preparation of ISO 1088 and ISO/TR 7178.
On the basis of the procedures given in the first editions of ISO 748 (1968) and ISO 1088 (1973), data were
subsequently collected and processed from the following rivers (see Annex A for the characteristics of these
rivers) and ISO/TR 7178 was accordingly published:
a) Rivers Ganga, Jalangi, Yamuna, and Visvesvaraya Canal, in India;
b) River IJssel, in the Netherlands;
c) Rivers Derwent, Eden, Lambourne, Ouse, Tyne, and Usk in the United Kingdom;
d) Rivers Columbia and Mississippi, in the United States.
Further data obtained on the Rivers Ganga and Krishna, in India, and the Spey,Tay, Tweed, Tyne, Gala Water,
Yarrow Water, Ettrick Water, and the Clyde, in the United Kingdom, were received later, but could not be
included in the processing.
The procedures for estimating the component uncertainties and the uncertainty in discharge in this
International Standard conform to the ISO/IEC Guide 98, Guide to the expression of uncertainty in
measurement (GUM).
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INTERNATIONAL STANDARD ISO 1088:2007(E)
Hydrometry — Velocity-area methods using current-meters —
Collection and processing of data for determination of
uncertainties in flow measurement
1 Scope
This International Standard provides a standard basis for the collection and processing of data for the
determination of the uncertainties in measurements of discharge in open channels by velocity-area methods
using current-meters.
To determine the discharge in open channels by the velocity-area method, components of the flow (velocity,
depth and breadth) need to be measured. The component measurements are combined to compute the total
discharge. The total uncertainty in the computed discharge is a combination of the uncertainties in the
measured components.
Clause 4 of this International Standard deals with the types of errors and uncertainties involved. Clauses 5
and 6 present a standard procedure to estimate the component uncertainties by the collection and processing
of the necessary data.
This International Standard is intended to be applied to velocity-area methods that involve measurement of
point velocities at a relatively small number of discrete depths and transverse positions in the flow cross-
section, as described in ISO 748. This International Standard is not intended to be applied to measurements
made by Acoustic Doppler Velocity Profilers (ADVP) or other instruments that produce essentially continuous
velocity profiles of the flow field.
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, Measurement of liquid flow in open channels — Velocity-area methods
ISO 4363, Measurement of liquid flow in open channels — Methods for measurement of characteristics of
suspended sediment
ISO 4364, Measurement of liquid flow in open channels — Bed material sampling
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ISO 1088:2007(E)
3 Symbols and abbreviated terms
a coefficient of linear regression, slope of trend line
b breadth (width) of segment i
i
d depth at vertical in segment i
i
L number of sets of measurements (error type ii)
J number of measurements per set (error types ii and iii)
k′ time displacement in autocorrelation function (of time interval, etc.)
k coverage factor for expanded uncertainty (taken as 2, corresponding to a level of confidence of
approximately 95 %)
m number of verticals or sections per measurement cross-section
n multiple of basic exposure-time for velocity measurement (error type i)
n number of depths in vertical i at which velocity measurements are made
i
Q discharge
Q discharge of measurement j in a set of measurements (error type iii)
j
S standard deviation of the relative mean velocities (error type ii)
rel
S mean standard deviation of all measurement sets together due to velocity fluctuations (error
F
type ii)
S standard deviation of sampling error in measurement set i (error type ii)
F,i
S standard deviation of the sampling error due to the computation rule (error type ii)
s
S stochastic sampling error of mean velocity in vertical i (error type ii)
i
S unobservable random sampling error of mean velocity in vertical i (error type ii)
vi,
S (m) standard deviation of relative error when m verticals are applied (error type iii)
s,hd
t instant of time of observation i (error type i)
i
t initial measuring time (basic time interval)
0
t mean of observation times t in a linear trend segment (error type i)
i
u standard relative (percentage) uncertainty in uncertainty component i
i
u standard relative (percentage) combined uncertainty of measurement
U expanded relative (percentage) uncertainty with coverage factor k
u standard relative (percentage) uncertainty due to responsiveness of current-meter
c
u standard relative (percentage) uncertainty in width measurement
b
u standard relative (percentage) uncertainty in depth measurement
d
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ISO 1088:2007(E)
u standard relative (percentage) uncertainty due to velocity fluctuations
e
u standard relative (percentage) uncertainty due to limited number of verticals
m
u standard relative (percentage) uncertainty due to limited number of depths at which velocity is
p
measured
u standard relative (percentage) uncertainty due to instrument calibration errors
s
v velocity at time t or in vertical i
i i
V actual velocity at time t or in vertical i
i i
′
v corrected velocity from which trend has been removed (error type i)
i
vtˆ() trend-line velocity (error type i)
v mean velocity in vertical i or at point i;
i
V mean of the relative mean velocities (error type ii)
rel
th
V mean relative velocity in the j profile (error type ii)
rel, j
µˆ mean sampling error for the entire series of measurement sets (error type ii)
s
µ mean sampling error in measurement set i (error type ii)
s,i
µˆ()m mean relative error when m verticals are applied (error type iii)
σ standard deviation of velocity fluctuations (error type i)
F
Additional symbols are defined in the text.
Due to the statistical nature of this International Standard, it is necessary to have symbols representing
observed values and true values of variables. The symbols therefore might not conform to ISO 772.
4 Types of errors and procedure for estimating the uncertainties in flow
measurement
4.1 Principle
The principle of the velocity-area method consists in determining from measurements the distribution of the
flow velocity in the cross-section and the area of the cross-section, and using these observations for the
computation of the discharge.
The measurements of the velocity are made in a number of verticals. In each vertical the mean velocity is
determined from measurements at a selected number of points. The discharge per unit width can be found by
multiplying the mean velocity by the depth in the vertical considered.
Each vertical is assumed to be representative of a segment of the cross-sectional area. The selection of the
number and location of the verticals determines the width of these segments. Recommendations on the
number of verticals required are given in 4.4.3 c).
Assuming that the discharge has remained constant during the measurements, summation of the discharge in
the various segments gives the total discharge through the section.
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ISO 1088:2007(E)
4.2 Occurrence of error
In general, the result of a measurement is only an estimate of the true value of the quantity subjected to
measurement. The discrepancy between the true and measured values is the measurement error. The
measurement error, which cannot be known, causes an uncertainty about the correctness of the
measurement result.
The measurement error is a combination of component errors, which arise during the performance of various
elementary operations during the measurement process. For measurements of composite quantities, which
depend on several component quantities, the total error of the measurement is a combination of the errors in
all component quantities. Determination of measurement uncertainty involves identification and
characterization of all components of error, and the quantification and combination of the corresponding
uncertainties.
ISO/IEC Guide 98 treats measurement uncertainty using concepts and formulas for probability distributions,
expected values, standard deviations, and correlations of random variables. The standard deviation of the
measurement error is taken as the quantitative measure of uncertainty.
ISO/IEC Guide 98 does not make use of the traditional categorization of errors as random and systematic.
That categorization can be difficult to apply in practice. For example, an error that is systematic in one
measurement process might become random in a different process. The essential characteristic of systematic
errors is that they are not reduced by averaging of replicate measurements. The guide makes it clear that
accurate description of the measurement process and correct mathematical formulation of the uncertainty
equations are sufficient to account for the fact that some uncertainty sources are not reduced by averaging of
replicate measurements whereas others are reduced, without reliance on the concepts of systematic and
random error.
The components of uncertainty are characterized by estimates of standard deviations, which are termed
standard uncertainty, with recommended symbol u , where i identifies the component in question, and which
i
2
are equal to the positive square root of the estimated variance, u . The uncertainty components are
i
combined using formulas for combination of standard deviations of possibly correlated random variables. The
resultant uncertainty, which takes all sources and components of uncertainty into account, is called the
combined uncertainty and is denoted as u.
ISO/IEC Guide 98 introduces the concepts of Type A and Type B methods of evaluation of uncertainty to
make a distinction between uncertainty evaluation by statistical analysis of replicate measurements and
uncertainty evaluation by other (perhaps subjective or judgmental) means. Type A evaluation of uncertainty is
by statistical analysis of repeated observations to obtain statistical estimates of the standard deviations of the
observations; this evaluation commonly can be carried out automatically during the measurement process by
data loggers or other instrumentation. Type B evaluation is by calculation of the standard deviation of an
assumed probability distribution based on scientific judgment and consideration of all available information,
which might include previous measurement and calibration data and experience or general knowledge of the
behaviour and properties of relevant instruments. By proper consideration of correlations, either Type A or
Type B method of evaluation can be used for evaluation of either systematic or random uncertainty
components.
In this International Standard, all uncertainties are expressed numerically as percentages. Standard
uncertainty values thus correspond to percentage coefficients of variation (standard deviation divided by the
mean). Expanded uncertainties are explicitly identified as such, and are taken with coverage factor 2,
corresponding to a level of confidence of approximately 95 %.
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ISO 1088:2007(E)
4.3 Sources of error
Theoretically, the discharge can be expressed as
Qv= x,dy xdy (1)
( )
∫∫
where
Q is the true discharge;
v(x,y) is the velocity field over the width, x, and depth, y, of the cross section.
Figure 1 — Definition sketch
In practice, the integral is approximated by the summation
m
Qb=⋅dvF (2)
()
∑ ii i
i=1
where
Q is the calculated discharge;
th
b is the width of the i section;
i
th
d is the depth of the i vertical;
i
th
v is the mean velocity in the i vertical;
i
F is a factor, conventionally assumed as unity, that relates the discrete sum of the finite number of
verticals to the integral of the continuous function over the cross-section (see ISO 748);
m is the number of verticals.
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ISO 1088:2007(E)
Errors in Q are due to
a) errors in the measurement of quantities b and d and of the individual measurements of the velocity
i i
necessary for the determination of the average velocity, v , and
i
b) errors in approximation of the integral equation [Equation (1)] by the summation equation [Equation (2)].
4.4 Determination of the individual components of the uncertainty
4.4.1 Uncertainties in width
The measurement of the width between verticals is normally made by measuring distances from a reference
point on the bank. When a tape or tag-line is used, or the movement of the wire attached to a trolley is
observed, the uncertainty depends on the distance but is usually negligible. Where optical means are used,
the uncertainties also depend on the distance measured but can be greater.
Where the distance is measured by electronic means, a constant uncertainty and an uncertainty depending on
the distance measured occurs.
The uncertainties result mainly from instrument errors.
4.4.2 Uncertainties in depth
Some uncertainties depend on the type and use of the instrument applied. Such uncertainties are not included
in this International Standard.
Uncertainties also arise due to the interpolation of the depth between verticals at which depths are measured.
4.4.3 Uncertainties in the determination of the mean velocity
Apart from instrument calibration errors, the error in the mean flow velocity can be considered as consisting of
three independent types of error.
a) Error Type i — Pulsations: The uncertainty due to the limited measuring time of the local point velocity
in each vertical. Because of turbulence, the velocity fluctuates continuously over the wet cross-section.
The mean velocity at any point, determined from measurement during a certain time interval, is an
approximation of the true mean velocity at that particular point. In this International Standard,
uncertainties of this nature are referred to as “error type i”. Pulsations in flow are not independent of each
other. The velocity at time t is influenced by the velocity at time t . This influence will decrease as the
2 1
time interval t − t increases. The effect of increasing the measuring time on the uncertainty is given in
2 1
Annex B.
b) Error Type ii — Number of points in the vertical: The uncertainty arising from the use of a limited
number of sampling points in a vertical. Computation of the mean velocity in a vertical as an average or
weighted average of a number of point velocities results in an approximation of the true mean velocity in
the vertical considered. In this International Standard, uncertainties of this nature are referred to as “error
type ii”.
c) Error Type iii — Number of verticals: The uncertainty from the limited number of verticals in which
velocities are measured. The horizontal velocity profile and bed profile between two verticals have to be
determined by interpolation, which introduces an uncertainty (see Annex F). In this International Standard,
uncertainties of this nature are referred to as “error type iii”.
NOTE The types of errors referred to in this International Standard are not related to statistical Type i and Type ii
errors.
To determine the influence of the distribution of horizontal velocity and depth between the verticals on the total
uncertainty in discharge, it is necessary to make a detailed measurement of the cross-section and to locate
the verticals for the velocity measurement at intervals of no more than 0,25 m or 1/50 of the total width,
whichever is greater.
6 © ISO 2007 – All rights reserved
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ISO 1088:2007(E)
The values of depth d , breadth b , and mean velocity v in the vertical are used to determine the discharge
i i i
per unit width and discharge through segment i. Summation of the discharges through each segment
according to Equation (2) results in an approximation of the true total discharge.
4.5 Total uncertainty in discharge
The uncertainties in the individual components of discharge are expressed as relative standard uncertainties
in percent, corresponding to percentage coefficients of variation (standard deviation of error divided by
expected value of the measured quantity).
The relative (percentage) combined standard uncertainty in the measurement is given by the following
equation (ISO 748):
m 2
22 2
bd v u ++u u
()
∑()ii i()b,i d,i v,i
2 i=1
22
uQ =+u u+ (3)
()
ms
2
m
⎛⎞
bd v
⎜⎟
∑ ii i
i=1
⎝⎠
where
u(Q) is the relative (percentage) combined standard uncertainty in discharge;
uuu,, are the relative (percentage) standard uncertainties in the breadth, depth, and mean
b,iid, v,i
velocity measured at vertical i;
u is the relative uncertainty due to calibration errors in the current-meter, breadth
s
measurement instrument, and depth sounding instrument;
u is the relative uncertainty due to the limited number of verticals;
m
m is the number of verticals.
2 2 2 1/2
The relative uncertainty due to calibration errors, u , can be expressed as u = (u + u + u ) , where
s s cm bm ds
u , u , and u are the relative uncertainties due to calibration errors in the current-meter, breadth
cm bm ds
measurement instrument, and depth sounding instrument, respectively. An estimated practical value of 1 %
can be taken for the value of u .
s
The mean velocity v at vertical i is the average of point measurements of velocity made at several depths in
i
the vertical. The uncertainty in v is computed as follows:
i
⎛⎞
2 1
222
uv =+u u +u (4)
()
⎜⎟
iip, ()c,i e,i
n
⎝⎠i
where
u is the uncertainty in mean velocity v due to the limited number of depths at which velocity
p,i i
measurements are made at vertical i;
n is the number of depths in the vertical i at which velocity measurements are made;
i
u is the uncertainty in point velocity at a particular depth in vertical i due to variable responsiveness
c,i
of current-meter;
u is the uncertainty in point velocity at a particular depth in vertical i due to velocity fluctuations
e,i
(pulsations) in the stream.
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ISO 1088:2007(E)
Combining Equations (3) and (4) yields:
⎛⎞
⎛⎞
⎛⎞
m
2 1
22 2 2 2
⎜⎟
bd v⎜⎟u ++u u + u +u
() ⎜⎟
()
∑ ii i b,i d,i p,i c,i e,i
i=1⎜⎟
⎜⎟
n
i
2 ⎝⎠
⎝⎠
22⎝⎠
uQ =+u u+ (5)
()
ms
2
m
⎛⎞
bd v
⎜⎟
∑ ii i
i=1
⎝⎠
If the measurement verticals are placed so that the segment discharges (b d v ) are approximately equal and
i
i i
if the component uncertainties are equal from vertical to vertical, then Equation (5) simplifies to:
1
⎡⎤ 2
⎛⎞
⎛⎞11⎛ ⎞
22 2 2 2 2 2
uQ=+u u+ uuu+ + + u+u (6)
()
⎢⎥⎜⎟
ms ⎜⎟ b d p ⎜ ⎟()c e
mn
⎢⎥⎝⎠ ⎝ ⎠
⎝⎠
⎣⎦
Equation (6) can be used for uncertainty computation for a particular measurement if the segment discharges
(b d v ) and the component uncertainties are nearly equal from vertical to vertical. More generally, however,
i i i
Equation (6) is useful for developing a qualitative understanding of how the various component uncertainties
contribute to the total uncertainty discharge measurement. Equation (5) is needed to properly account for the
effects of unequal distribution of flow among the segments.
From the above equations, it can be seen that the total standard uncertainty may be reduced by increasing
the number of verticals, improving the measurement of the individual components, or both.
It is reco
...
SLOVENSKI STANDARD
SIST ISO 1088:2013
01-april-2013
Hidrometrija - Metode hitrost-prerez z uporabo merilnikov tokov - Zbiranje in
obdelovanje podatkov za ugotavljanje negotovosti pri meritvah pretokov
Hydrometry - Velocity-area methods using current-meters - Collection and processing of
data for determination of uncertainties in flow measurement
Durchflussmessung in offenen Gerinnen - Geschwindigkeitsflaechenmethoden -
Datensammlung und. -verarbeitung zur Bestimmung von Messfehlern
Hydrométrie - Méthodes d'exploration du champ des vitesses à l'aide de moulinets -
Recueil et traitement des données pour la détermination des incertitudes de mesurage
du débit
Ta slovenski standard je istoveten z: ISO 1088:2007
ICS:
17.120.20 Pretok v odprtih kanalih Flow in open channels
SIST ISO 1088:2013 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO 1088:2013
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SIST ISO 1088:2013
INTERNATIONAL ISO
STANDARD 1088
Third edition
2007-07-01
Hydrometry — Velocity-area methods
using current-meters — Collection and
processing of data for determination of
uncertainties in flow measurement
Hydrométrie — Méthodes d'exploration du champ des vitesses à l'aide
de moulinets — Recueil et traitement des données pour la
détermination des incertitudes de mesurage du débit
Reference number
ISO 1088:2007(E)
©
ISO 2007
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SIST ISO 1088:2013
ISO 1088:2007(E)
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
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Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Symbols and abbreviated terms . 2
4 Types of errors and procedure for estimating the uncertainties in flow measurement. 3
4.1 Principle. 3
4.2 Occurrence of error . 4
4.3 Sources of error . 5
4.4 Determination of the individual components of the uncertainty . 6
4.5 Total uncertainty in discharge. 7
5 Collection and processing of data for the investigation of component uncertainties – type
A evaluation of uncertainties. 8
5.1 Data on the local point velocity. 8
5.2 Data on the average velocity . 9
5.3 Data on the velocity-area method . 10
5.4 Integration method . 11
5.5 Calibration curves. 11
5.6 Distance measurements . 11
5.7 Depth measurements . 12
6 Data processing. 12
6.1 General. 12
6.2 Error-type i. 13
6.3 Error-type ii — Approximation of mean velocity in the vertical. 15
6.4 Error-type iii — Limited number of verticals.17
Annex A (informative) Characteristics of rivers from which data were collected . 21
Annex B (normative) Effect of increasing measuring time on uncertainty. 26
Annex C (normative) Local point velocity measurements - Report form. 27
Annex D (normative) Average velocity measurements — Report form . 31
Annex E (normative) Velocity-area method — Report form . 34
Annex F (informative) Examination of Error Types i, ii, and iii. 38
Annex G (informative) Uncertainties in velocity-area measurement components. 41
Annex H (informative) Calculation of the uncertainty in a current-meter gauging. 45
Bibliography . 48
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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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
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.
ISO 1088 was prepared by Technical Committee ISO/TC 113, Hydrometry, Subcommittee SC 5, Instruments,
equipment and data management.
This third edition cancels and replaces the second edition (ISO 1088:1985), which has been revised to
incorporate ISO/TR 7178 (based on ISO/DATA No. 2) and edited in accordance with ISO/IEC Guide 98:1995,
Guide to the expression of uncertainty in measurement (GUM). This third edition of ISO 1088 also cancels
and replaces ISO/TR 7178, all provisions of which have been incorporated into this edition.
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Introduction
All measurements of physical quantities are subject to uncertainties, which can be due to biases (systematic
errors) introduced in the manufacture, calibration, and maintenance of measurement instruments, or to
random scatter caused by a lack of sensitivity of the instruments, and to other sources of error.
During the preparation of the first edition of ISO 748, much discussion was given to the question of the
magnitude of errors in measurements, and it was concluded that recommendations could only be formulated
on the basis of an analysis of sufficient data. Moreover, it was recognized that to be able to analyze such data
statistically, it was essential that the data be collected and recorded on a standardized basis and in a
systematic manner, and this recognition led to the preparation of ISO 1088 and ISO/TR 7178.
On the basis of the procedures given in the first editions of ISO 748 (1968) and ISO 1088 (1973), data were
subsequently collected and processed from the following rivers (see Annex A for the characteristics of these
rivers) and ISO/TR 7178 was accordingly published:
a) Rivers Ganga, Jalangi, Yamuna, and Visvesvaraya Canal, in India;
b) River IJssel, in the Netherlands;
c) Rivers Derwent, Eden, Lambourne, Ouse, Tyne, and Usk in the United Kingdom;
d) Rivers Columbia and Mississippi, in the United States.
Further data obtained on the Rivers Ganga and Krishna, in India, and the Spey,Tay, Tweed, Tyne, Gala Water,
Yarrow Water, Ettrick Water, and the Clyde, in the United Kingdom, were received later, but could not be
included in the processing.
The procedures for estimating the component uncertainties and the uncertainty in discharge in this
International Standard conform to the ISO/IEC Guide 98, Guide to the expression of uncertainty in
measurement (GUM).
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INTERNATIONAL STANDARD ISO 1088:2007(E)
Hydrometry — Velocity-area methods using current-meters —
Collection and processing of data for determination of
uncertainties in flow measurement
1 Scope
This International Standard provides a standard basis for the collection and processing of data for the
determination of the uncertainties in measurements of discharge in open channels by velocity-area methods
using current-meters.
To determine the discharge in open channels by the velocity-area method, components of the flow (velocity,
depth and breadth) need to be measured. The component measurements are combined to compute the total
discharge. The total uncertainty in the computed discharge is a combination of the uncertainties in the
measured components.
Clause 4 of this International Standard deals with the types of errors and uncertainties involved. Clauses 5
and 6 present a standard procedure to estimate the component uncertainties by the collection and processing
of the necessary data.
This International Standard is intended to be applied to velocity-area methods that involve measurement of
point velocities at a relatively small number of discrete depths and transverse positions in the flow cross-
section, as described in ISO 748. This International Standard is not intended to be applied to measurements
made by Acoustic Doppler Velocity Profilers (ADVP) or other instruments that produce essentially continuous
velocity profiles of the flow field.
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, Measurement of liquid flow in open channels — Velocity-area methods
ISO 4363, Measurement of liquid flow in open channels — Methods for measurement of characteristics of
suspended sediment
ISO 4364, Measurement of liquid flow in open channels — Bed material sampling
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3 Symbols and abbreviated terms
a coefficient of linear regression, slope of trend line
b breadth (width) of segment i
i
d depth at vertical in segment i
i
L number of sets of measurements (error type ii)
J number of measurements per set (error types ii and iii)
k′ time displacement in autocorrelation function (of time interval, etc.)
k coverage factor for expanded uncertainty (taken as 2, corresponding to a level of confidence of
approximately 95 %)
m number of verticals or sections per measurement cross-section
n multiple of basic exposure-time for velocity measurement (error type i)
n number of depths in vertical i at which velocity measurements are made
i
Q discharge
Q discharge of measurement j in a set of measurements (error type iii)
j
S standard deviation of the relative mean velocities (error type ii)
rel
S mean standard deviation of all measurement sets together due to velocity fluctuations (error
F
type ii)
S standard deviation of sampling error in measurement set i (error type ii)
F,i
S standard deviation of the sampling error due to the computation rule (error type ii)
s
S stochastic sampling error of mean velocity in vertical i (error type ii)
i
S unobservable random sampling error of mean velocity in vertical i (error type ii)
vi,
S (m) standard deviation of relative error when m verticals are applied (error type iii)
s,hd
t instant of time of observation i (error type i)
i
t initial measuring time (basic time interval)
0
t mean of observation times t in a linear trend segment (error type i)
i
u standard relative (percentage) uncertainty in uncertainty component i
i
u standard relative (percentage) combined uncertainty of measurement
U expanded relative (percentage) uncertainty with coverage factor k
u standard relative (percentage) uncertainty due to responsiveness of current-meter
c
u standard relative (percentage) uncertainty in width measurement
b
u standard relative (percentage) uncertainty in depth measurement
d
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u standard relative (percentage) uncertainty due to velocity fluctuations
e
u standard relative (percentage) uncertainty due to limited number of verticals
m
u standard relative (percentage) uncertainty due to limited number of depths at which velocity is
p
measured
u standard relative (percentage) uncertainty due to instrument calibration errors
s
v velocity at time t or in vertical i
i i
V actual velocity at time t or in vertical i
i i
′
v corrected velocity from which trend has been removed (error type i)
i
vtˆ() trend-line velocity (error type i)
v mean velocity in vertical i or at point i;
i
V mean of the relative mean velocities (error type ii)
rel
th
V mean relative velocity in the j profile (error type ii)
rel, j
µˆ mean sampling error for the entire series of measurement sets (error type ii)
s
µ mean sampling error in measurement set i (error type ii)
s,i
µˆ()m mean relative error when m verticals are applied (error type iii)
σ standard deviation of velocity fluctuations (error type i)
F
Additional symbols are defined in the text.
Due to the statistical nature of this International Standard, it is necessary to have symbols representing
observed values and true values of variables. The symbols therefore might not conform to ISO 772.
4 Types of errors and procedure for estimating the uncertainties in flow
measurement
4.1 Principle
The principle of the velocity-area method consists in determining from measurements the distribution of the
flow velocity in the cross-section and the area of the cross-section, and using these observations for the
computation of the discharge.
The measurements of the velocity are made in a number of verticals. In each vertical the mean velocity is
determined from measurements at a selected number of points. The discharge per unit width can be found by
multiplying the mean velocity by the depth in the vertical considered.
Each vertical is assumed to be representative of a segment of the cross-sectional area. The selection of the
number and location of the verticals determines the width of these segments. Recommendations on the
number of verticals required are given in 4.4.3 c).
Assuming that the discharge has remained constant during the measurements, summation of the discharge in
the various segments gives the total discharge through the section.
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4.2 Occurrence of error
In general, the result of a measurement is only an estimate of the true value of the quantity subjected to
measurement. The discrepancy between the true and measured values is the measurement error. The
measurement error, which cannot be known, causes an uncertainty about the correctness of the
measurement result.
The measurement error is a combination of component errors, which arise during the performance of various
elementary operations during the measurement process. For measurements of composite quantities, which
depend on several component quantities, the total error of the measurement is a combination of the errors in
all component quantities. Determination of measurement uncertainty involves identification and
characterization of all components of error, and the quantification and combination of the corresponding
uncertainties.
ISO/IEC Guide 98 treats measurement uncertainty using concepts and formulas for probability distributions,
expected values, standard deviations, and correlations of random variables. The standard deviation of the
measurement error is taken as the quantitative measure of uncertainty.
ISO/IEC Guide 98 does not make use of the traditional categorization of errors as random and systematic.
That categorization can be difficult to apply in practice. For example, an error that is systematic in one
measurement process might become random in a different process. The essential characteristic of systematic
errors is that they are not reduced by averaging of replicate measurements. The guide makes it clear that
accurate description of the measurement process and correct mathematical formulation of the uncertainty
equations are sufficient to account for the fact that some uncertainty sources are not reduced by averaging of
replicate measurements whereas others are reduced, without reliance on the concepts of systematic and
random error.
The components of uncertainty are characterized by estimates of standard deviations, which are termed
standard uncertainty, with recommended symbol u , where i identifies the component in question, and which
i
2
are equal to the positive square root of the estimated variance, u . The uncertainty components are
i
combined using formulas for combination of standard deviations of possibly correlated random variables. The
resultant uncertainty, which takes all sources and components of uncertainty into account, is called the
combined uncertainty and is denoted as u.
ISO/IEC Guide 98 introduces the concepts of Type A and Type B methods of evaluation of uncertainty to
make a distinction between uncertainty evaluation by statistical analysis of replicate measurements and
uncertainty evaluation by other (perhaps subjective or judgmental) means. Type A evaluation of uncertainty is
by statistical analysis of repeated observations to obtain statistical estimates of the standard deviations of the
observations; this evaluation commonly can be carried out automatically during the measurement process by
data loggers or other instrumentation. Type B evaluation is by calculation of the standard deviation of an
assumed probability distribution based on scientific judgment and consideration of all available information,
which might include previous measurement and calibration data and experience or general knowledge of the
behaviour and properties of relevant instruments. By proper consideration of correlations, either Type A or
Type B method of evaluation can be used for evaluation of either systematic or random uncertainty
components.
In this International Standard, all uncertainties are expressed numerically as percentages. Standard
uncertainty values thus correspond to percentage coefficients of variation (standard deviation divided by the
mean). Expanded uncertainties are explicitly identified as such, and are taken with coverage factor 2,
corresponding to a level of confidence of approximately 95 %.
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4.3 Sources of error
Theoretically, the discharge can be expressed as
Qv= x,dy xdy (1)
( )
∫∫
where
Q is the true discharge;
v(x,y) is the velocity field over the width, x, and depth, y, of the cross section.
Figure 1 — Definition sketch
In practice, the integral is approximated by the summation
m
Qb=⋅dvF (2)
()
∑ ii i
i=1
where
Q is the calculated discharge;
th
b is the width of the i section;
i
th
d is the depth of the i vertical;
i
th
v is the mean velocity in the i vertical;
i
F is a factor, conventionally assumed as unity, that relates the discrete sum of the finite number of
verticals to the integral of the continuous function over the cross-section (see ISO 748);
m is the number of verticals.
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Errors in Q are due to
a) errors in the measurement of quantities b and d and of the individual measurements of the velocity
i i
necessary for the determination of the average velocity, v , and
i
b) errors in approximation of the integral equation [Equation (1)] by the summation equation [Equation (2)].
4.4 Determination of the individual components of the uncertainty
4.4.1 Uncertainties in width
The measurement of the width between verticals is normally made by measuring distances from a reference
point on the bank. When a tape or tag-line is used, or the movement of the wire attached to a trolley is
observed, the uncertainty depends on the distance but is usually negligible. Where optical means are used,
the uncertainties also depend on the distance measured but can be greater.
Where the distance is measured by electronic means, a constant uncertainty and an uncertainty depending on
the distance measured occurs.
The uncertainties result mainly from instrument errors.
4.4.2 Uncertainties in depth
Some uncertainties depend on the type and use of the instrument applied. Such uncertainties are not included
in this International Standard.
Uncertainties also arise due to the interpolation of the depth between verticals at which depths are measured.
4.4.3 Uncertainties in the determination of the mean velocity
Apart from instrument calibration errors, the error in the mean flow velocity can be considered as consisting of
three independent types of error.
a) Error Type i — Pulsations: The uncertainty due to the limited measuring time of the local point velocity
in each vertical. Because of turbulence, the velocity fluctuates continuously over the wet cross-section.
The mean velocity at any point, determined from measurement during a certain time interval, is an
approximation of the true mean velocity at that particular point. In this International Standard,
uncertainties of this nature are referred to as “error type i”. Pulsations in flow are not independent of each
other. The velocity at time t is influenced by the velocity at time t . This influence will decrease as the
2 1
time interval t − t increases. The effect of increasing the measuring time on the uncertainty is given in
2 1
Annex B.
b) Error Type ii — Number of points in the vertical: The uncertainty arising from the use of a limited
number of sampling points in a vertical. Computation of the mean velocity in a vertical as an average or
weighted average of a number of point velocities results in an approximation of the true mean velocity in
the vertical considered. In this International Standard, uncertainties of this nature are referred to as “error
type ii”.
c) Error Type iii — Number of verticals: The uncertainty from the limited number of verticals in which
velocities are measured. The horizontal velocity profile and bed profile between two verticals have to be
determined by interpolation, which introduces an uncertainty (see Annex F). In this International Standard,
uncertainties of this nature are referred to as “error type iii”.
NOTE The types of errors referred to in this International Standard are not related to statistical Type i and Type ii
errors.
To determine the influence of the distribution of horizontal velocity and depth between the verticals on the total
uncertainty in discharge, it is necessary to make a detailed measurement of the cross-section and to locate
the verticals for the velocity measurement at intervals of no more than 0,25 m or 1/50 of the total width,
whichever is greater.
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The values of depth d , breadth b , and mean velocity v in the vertical are used to determine the discharge
i i i
per unit width and discharge through segment i. Summation of the discharges through each segment
according to Equation (2) results in an approximation of the true total discharge.
4.5 Total uncertainty in discharge
The uncertainties in the individual components of discharge are expressed as relative standard uncertainties
in percent, corresponding to percentage coefficients of variation (standard deviation of error divided by
expected value of the measured quantity).
The relative (percentage) combined standard uncertainty in the measurement is given by the following
equation (ISO 748):
m 2
22 2
bd v u ++u u
()
∑()ii i()b,i d,i v,i
2 i=1
22
uQ =+u u+ (3)
()
ms
2
m
⎛⎞
bd v
⎜⎟
∑ ii i
i=1
⎝⎠
where
u(Q) is the relative (percentage) combined standard uncertainty in discharge;
uuu,, are the relative (percentage) standard uncertainties in the breadth, depth, and mean
b,iid, v,i
velocity measured at vertical i;
u is the relative uncertainty due to calibration errors in the current-meter, breadth
s
measurement instrument, and depth sounding instrument;
u is the relative uncertainty due to the limited number of verticals;
m
m is the number of verticals.
2 2 2 1/2
The relative uncertainty due to calibration errors, u , can be expressed as u = (u + u + u ) , where
s s cm bm ds
u , u , and u are the relative uncertainties due to calibration errors in the current-meter, breadth
cm bm ds
measurement instrument, and depth sounding instrument, respectively. An estimated practical value of 1 %
can be taken for the value of u .
s
The mean velocity v at vertical i is the average of point measurements of velocity made at several depths in
i
the vertical. The uncertainty in v is computed as follows:
i
⎛⎞
2 1
222
uv =+u u +u (4)
()
⎜⎟
iip, ()c,i e,i
n
⎝⎠i
where
u is the uncertainty in mean velocity v due to the limited number of depths at which velocity
p,i i
measurements are made at vertical i;
n is the number of depths in the vertical i at which velocity measurements are made;
i
u is the uncertainty in point velocity at a particular depth in vertical i due to variable responsiveness
c,i
of current-meter;
u is the uncertainty in point velocity at a particular depth in vertical i due to velocity fluctuations
e
...
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