ISO 1088:2007

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 2007
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©  ISO 2007
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ii © ISO 2007 – All rights reserved

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

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.

iv © ISO 2007 – All rights reserved

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).
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

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)
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
2 © ISO 2007 – All rights reserved

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.
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
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 %.

4 © ISO 2007 – All rights reserved

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.
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

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
uQ =+u u+ (3)
()
ms
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
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.
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
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:
⎡⎤ 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 recommended that, whenever possible, the user shall determine independently the values of the
component uncertainties in the above equations. However, for routine gauging, values are given in Annex E of
ISO 748:1997 that are the result of many investigations carried out since the publication of the first edition of
ISO 748 in 1968. These results are included in Annex G, re-expressed in terms of standard uncertainties
(level of confidence approximately 68 %) for conformance with ISO/IEC Guide 98.
It should be noted that since the individual components of uncertainty presented in Annex G are based on
statistical analyses of the spread of replicate measurements, on prior observations, rather than on repeated
observations during the actual course of the measurement of discharge, they shall be considered as Type B
evaluations of uncertainties (see 4.2).
A simplified example of the calculation of the uncertainty in a velocity-area gauging using Equation (6) and the
relevant component uncertainties given in Annex G is presented in Annex H.
5 Collection and processing of data for the investigation of component
uncertainties – type A evaluation of uncertainties
5.1 Data on the local point velocity
To judge the uncertainty of a single point velocity measurement, the following procedure is required at each of
three verticals.
At each point of measurement on a vertical, an uninterrupted observation of the velocity over a period of
2 000 s, or for a period during which the discharge does not change by more than 5 % of the initial value,
whichever is the less, shall be made with a current-meter. Every 10 s, a reading of the instrument should be
taken, thus giving a total of 200 readings. When pulses are emitted by the current-meter, the number of pulses
should be recorded every 10 s; or, when the time is measured at a fixed number of pulses, this time interval
should average 10 s. When a continuous record is produced, the complete record should be given and the
response characteristics of the electronic instrument stated.
8 © ISO 2007 – All rights reserved

The verticals to be taken for this measurement should be the vertical situated at the deepest point and the
verticals situated at places where the depths are 0,6 and 0,3 times the maximum depth, both located on the
side of the greater segment of the width from the deepest point.
In each vertical this procedure should be carried out at 0,2, 0,6, and 0,8 and, where possible, at 0,9 times the
depth, all measured from the surface. The data shall be obtained, where possible, during the same 2 000 s
period.
The data thus obtained shall be indicated in the report format as illustrated in Annex C. In the case of a
continuous recorder, the values at intervals of 10 s shall be given, indicating the method of determination.
5.2 Data on the average velocity
5.2.1 General
The average velocity in a vertical can be obtained in various ways. The velocity distribution method, however,
is taken as a basis for comparison with the results of other methods generally used or special methods
adopted owing to special circumstances.
The following procedure is required for investigating the average velocity in each of the three verticals.
5.2.2 Location of the verticals
The location of the verticals for this measurement shall normally be determined from the known velocity
distribution in the gauging cross-section, so as to give velocities which are representative of the whole cross-
section.
When the velocity distributions in the gauging cross-section are not known, the verticals taken for this
measurement shall be that at maximum depth in the cross-section and at places where the depths are 0,6 and
0,3 times the maximum depth respectively, at the side of the greater segment and not too close to the bank.
5.2.3 Distribution of measuring points in the vertical
Velocity measurements shall be made at the following depths in each vertical:
1) immediately below the surface
2) at 0,2 times the depth
3) at 0,3 times the depth
4) at 0,4 times the depth
5) at 0,5 times the depth
6) at 0,6 times the depth
7) at 0,7 times the depth
8) at 0,8 times the depth
9) at 0,9 times the depth
10) near the bed
In channels containing weed growth, great care shall be taken to ensure that measurements made in the
vicinity of the bed are not affected by weed fouling the current-meter.
5.2.4 Period of measurement of local point velocities
The period of measurement of local point velocity at any point should be 60 s, or the number of pulses should
be that observed in 60 s at 0,6 times the depth.
5.2.5 Number of measurements
The measurements in each of the verticals should be made at least five times, preferably consecutively.
Measurements affected by navigation should be indicated.
These sets of observations should be made for various discharges.
5.2.6 Presentation of data
Compilation of data should be made in the format illustrated in Annex D.
The mean velocity should be determined with the use of a planimeter from an adequately large graphical plot
(preferably not less than 300 cm ). The type and accuracy of the planimeter should be given, together with the
scale of the discharge. The accuracy of the graph paper should be checked.
The velocity profiles should be drawn to a scale in such a way that the maximum velocity and the depth are
represented by 0,10 m and 0,20 m respectively.
5.3 Data on the velocity-area method
5.3.1 General
There are two possible ways of determining the uncertainty of the velocity-area method, one requiring special
measurements, the other mainly using routine measurements.
Wherever possible, data for both should be produced.
5.3.2 Measurement at 0,6 times the depth
In this method, the continuous profile of the cross-section at the measuring site is required. This can be
obtained by echo-sounder measurements or by measuring the depth with a rod at intervals of no more than
0,25 m or 1/50 of the total width, whichever is greater.
The horizontal velocity distribution shall be observed by taking velocity readings at 0,6 times the depth at
intervals of no more than 0,25 m or 1/50 of the total width, whichever is greater. The readings of the current-
meter shall be made over a period of 120 s.
In addition, readings shall be taken from a reference current-meter at a fixed point, preferably at 0,6 times the
depth in the vertical of maximum depth. The readings shall be made every 60 s.
5.3.3 Velocity-distribution method
In this method, the normal procedure for discharge measurement may be used provided the velocity-
distribution method or integration method is used for the determination of the average velocity in the vertical.
Readings shall be taken every 60 s, from a reference current-meter at a fixed point, preferably at 0,6 times the
depth in the vertical at maximum depth.
In addition to the data on the depth obtained by the normal discharge measurement, a continuous profile of
the cross-section at the measuring site shall be provided, as indicated in 5.3.5.
10 © ISO 2007 – All rights reserved

5.3.4 Presentation of data
Compilation of data should be made in the format illustrated in Annex E.
Correction factors in the table on velocity at the reference point can best be based on the average value of
velocity at the reference point. In this table, the factors are set as a function of time. To obtain the corrected
velocity in the table “Mean velocity at verticals”, the velocity column shall be multiplied by this correction factor.
A graphical representation of the cross-section shall be drawn to an adequate scale; the width of the river on
the drawing shall be not less than 0,5 m. The representation shall indicate the numerical values of depth at the
measuring points when a rod has been used, and shall show the location of the verticals and of the reference
current-meter.
A graphical representation of the measured velocity profiles should also be given. This should indicate the
numerical values of the velocities at the measuring points.
5.3.5 General data
To facilitate the interpretation of deviations from the normal pattern of the various errors, relevant information
on the geometry and morphology of the river concerned is required: for example, a map of scale 1/10 000 of
the river approximately 50 times the width of the river upstream and downstream of the measuring site, and a
continuous profile of the cross-section at the measurement site.
5.4 Integration method
To determine the standard error in the mean velocity in the verticals obtained by the integration method, a
sufficient number of measurements (for example, 50) should be carried out at steady stage in three verticals
and the results should be tabulated.
The verticals to be taken for this measurement should be the vertical situated at the maximum depth and the
verticals situated at places where the depths are 0,6 and 0,3 times the maximum depth, both located on the
side of the greater segment of the width from the deepest point.
The measurements should be repeated for different discharges. Data of a general character can be compiled
in a report form similar to that given in Annex C.
5.5 Calibration curves
In connection with the study of the instrument error, calibration curves together with all calibration points
should be given, especially data of successive calibrations of a representative current-meter with dates and
years of calibration and the intensity of use.
5.6 Distance measurements
No generally applicable method of determining the uncertainty of distance measurements can be given at
present. Detailed description of the method of distance measurement should be given, together with the
distances involved, and other relevant factors should be given for theoretical examination.
Electronic distance measuring devices give an almost absolutely accurate standard of comparison for
distance measurements. Where these instruments are available, independent research programmes,
concerning the uncertainty of different methods of distance measurement, may be carried out and the results
stated.
The conditions under which the study is carried out should be similar to normal operating conditions in the
field.
5.7 Depth measurements
The uncertainty of depth measurement is dependent on the channel conditions and the method of
measurement. In the case of lined channels, the bed conditions are not likely to influence the uncertainty of
the measurement.
In natural channels, for example rivers, the configuration of the bed varies in the longitudinal as well as in the
transverse direction.
In relation to the measuring procedure, it is important to know whether the measurement is carried out from a
rigid position or from an anchored launch. In the latter case, the influence of the irregularity of the bed can
result in a greater contribution to the total uncertainty of the depth measurement.
Owing to the complex nature of the depth measurements, general directives cannot be given. In carrying out a
study, the following considerations give guidance.
a) In a river with a shifting bed, consecutive measurements at one point should be avoided.
b) It is advisable to study the bed configuration in the vicinity of the actual measuring point by determining
longitudinal and transverse sections.
c) For all instruments, the uncertainty of the reading in relation to the scale intervals should be determined.
d) Sounding rods yield errors due to
1) penetration into the bed;
2) deviation from the vertical position;
3) velocity-head pile-up due to velocity stagnation.
e) Sounding lines (including suspended current-meters) yield errors due to
1) penetration into the bed;
2) deviations from the ideal conditions for which the correction for downstream drift has been
calculated;
3) shape and suspension point of the sounding instrument.
f) Echo-sounders yield errors due to
1) beam width of the transmitted pulse at the bottom;
2) penetration of the pulse into the bed, which is a function of the frequency of the pulse and of bed
consistency.
6 Data processing
6.1 General
The method of data processing for the Type A evaluation of component and total uncertainties in the
discharge measurement by velocity area methods is given. Although the availability of computers is assumed,
it is possible to perform the computation process with less advanced means. Some of these alternatives are
indicated.
12 © ISO 2007 – All rights reserved

When processing the data, steady-flow conditions are assumed, which means that the true mean value of
each of the various quantities remains constant with time. The existence of non-steady conditions shall be
appraised by plotting the data versus time. Any non-steady trends shall be removed from the data before
processing (see 6.2.2).
6.2 Error-type i
6.2.1 Finite measuring time and distribution of results
The standard deviation of the fluctuation error due to a finite measuring time is calculated.
It is assumed that the means found from the actual measurements are equal to the hypothetical means over
infinite measuring time and that the distribution of the results is of normal (Gaussian) nature.
6.2.2 Correction for non-steady conditions
When the velocity v is plotted against time t, it can be seen from the graph whether the magnitude of v shows
any trend which indicates that the conditions during the measurements were not steady. If so, the observed
velocities shall be corrected by removing the trend as follows:
′ ˆ
vv=−v()t (7)
ii i
′ ˆ
where v is the corrected velocity, v the corresponding observed velocity, and vt() is the trend velocity at the
i i
i
corresponding time t . The corrected velocity v′ thus is the residual or deviation of the observed velocity from
i i
the trend line. If trends are removed, the corrected velocities should be used in subsequent processing; that is,
v′ should be substituted for v in the equations in the following sections.
i i
If the trend consists of (or can be approximated by) one or more linear trend segments, the trend line for each
segment can be fitted by least squares, with the following result:
ˆ
vt()=+v a⋅(t−t) (8)
where v is the mean of the velocity observations v in the linear trend segment, t is the mean of the
i
corresponding observation times t , and a is the slope of the least squares line, as follows:
i
n
v
∑ i
i=1
v = (9)
n
n
t
∑ i
i=1
t = (10)
n
n
vt⋅−t
()()
∑ ii
i=1
a = (11)
n 2
...