ISO 2425:2010

INTERNATIONAL ISO
STANDARD 2425
Third edition
2010-12-01
Hydrometry — Measurement of liquid
flow in open channels under tidal
conditions
Hydrométrie — Mesurage du débit des liquides dans les canaux
découverts dans des conditions de marée

Reference number
©
ISO 2010
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ii © ISO 2010 – All rights reserved

Contents Page
Foreword .iv
1 Scope.1
2 Normative references.1
3 Terms and definitions .1
4 Abbreviated terms.2
5 Principles of methods of measurement.2
5.1 General .2
5.2 Single measurement methods .2
5.3 Continuous measurement methods.2
6 Special considerations and choice of method.3
6.1 Special considerations .3
6.2 Choice of method .4
7 Measurement of tidal flow .6
7.1 Techniques for single measurements of tidal flow.6
7.2 Techniques appropriate for continuous measurement of tidal flow.10
8 Uncertainties in tidal flow measurement .12
8.1 General .12
8.2 Uncertainties in measurement by velocity area method.12
Annex A (informative) Measurement of tidal flow by cubature method.16
Annex B (informative) Measurement methods suitable for tidal flow conditions.20
Annex C (informative) Record of velocity measurement of a tidal river (see 7.1).22
Annex D (informative) Measurement of tidal flow using an acoustic Doppler velocity meter
(see 7.1) .24
Bibliography.27

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 2425 was prepared by Technical Committee ISO/TC 113, Hydrometry, Subcommittee SC 1, Velocity area
methods.
This third edition cancels and replaces the second edition (ISO 2425:1999), which has been technically
revised. It also incorporates the Amendment ISO 2425:1999/Amd.1:2003. Annex D on measurement of tidal
flow using an acoustic Doppler velocity meter has been added.

iv © ISO 2010 – All rights reserved

INTERNATIONAL STANDARD ISO 2425:2010(E)

Hydrometry — Measurement of liquid flow in open channels
under tidal conditions
1 Scope
This International Standard provides a summary of recommended methods for the determination of liquid flow
in tidal channels, special consideration being given to those techniques that are either unique to or particularly
appropriate for application under tidal conditions, including treatment of uncertainties.
Reference is also made, where appropriate, to methods for the determination of flow in non-tidal channels, but
attention is drawn to their limitations with respect to practicality and/or uncertainty.
This International Standard does not describe alternative methods, such as the use of weirs, flumes, dilution
gauging, salt velocity and floats, although they might be suitable under certain conditions, especially where
the effect of tides only impedes and does not stop or reverse the passage of stream flow. These methods are
described in detail in other International Standards.
This International Standard specifies two types of technique:
a) techniques for single measurements of tidal flow;
b) techniques for continuous measurement of tidal flow.
Annex A specifies the cubature method of measurement. Annex B specifies methods for the determination of
flow under tidal conditions, and Annex C gives an example of the computation for a single vertical. Similar
computations are possible for other verticals. Annex D describes the determination of tidal flow using an
acoustic Doppler velocity meter.
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 748:2007, Hydrometry — Measurement of liquid flow in open channels using current-meters or floats
ISO 772, Hydrometry — Vocabulary and symbols
ISO 1100-1, Measurement of liquid flow in open channels — Part 1: Establishment and operation of a gauging
station
ISO 6416, Hydrometry — Measurement of discharge by the ultrasonic (acoustic) method
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 772 apply.
4 Abbreviated terms
ADCP acoustic Doppler current profiler
ADP acoustic Doppler profiler
ADV acoustic Doppler velocimeter
ADVM acoustic Doppler velocity meter
5 Principles of methods of measurement
5.1 General
Tidal flow measurement can be an instantaneous rate of flow or a total volume of flow during a flood or ebb
tide. The unsteady nature and change in direction of flow under tidal conditions create problems of
measurement additional to those associated with the measurement of the discharge of unidirectional streams.
The methods specified in ISO 748, ISO 1100-1, ISO 4369, ISO 9123, ISO/TR 9823 and ISO 9825 cannot
therefore always be applied to tidal channels. Any change in water quality brought about by tidal conditions
can affect the methods specified in ISO 6416 and ISO 9213.
For various reasons, direct measurements of velocity in tidal channels are more liable to greater uncertainty
than those made under conditions of unidirectional flow.
The methods of measurement in this International Standard can be grouped into either single or continuous
measurements.
5.2 Single measurement methods
5.2.1 Velocity area method
At a chosen gauging site, the velocity of flow and the area of cross-section of the channel are measured. The
product of these measurements at any instant is the rate of flow or discharge past the gauging site at that
instant. It is referred to as the velocity area method and includes the following techniques.
a) current meter from a fixed station;
b) acoustic Doppler profiler or acoustic Doppler velocity meter from a fixed station;
c) current meter from a moving station (moving boat);
d) acoustic Doppler current profiler from a moving station (moving boat).
5.2.2 Cubature method
In an area that includes a stretch of river channel and its flood plain, surface areas and rise in water level of
stored water are measured at known time intervals. Volumes of stored water are computed, and the flow into
the upstream stretch of river is estimated, from which the average rate of flow is determined (see Annex A).
5.3 Continuous measurement methods
5.3.1 Ultrasonic method (ISO 6416)
Transducers are positioned on each bank of the river channel, such that the acoustic path is at an oblique
angle to the direction of flow. The time taken for a pulse of sound to travel in both directions is measured and
2 © ISO 2010 – All rights reserved

compared. From these two times, the velocity of the water can be computed. Knowledge of the cross-
sectional area allows computation of discharge.
5.3.2 Electromagnetic method (ISO 9213)
A horizontal coil is constructed above or below a river channel. A magnetic field is generated by an alternating
current and voltages are induced in the flowing water, which acts as an electrical conductor. After calibration,
measurements of electrical parameters and water depth provide a means of determining the discharge.
5.3.3 Acoustic Doppler velocity method from a fixed station
Acoustic Doppler velocity meters (ADVMs) may be horizontally or vertically oriented and shall be fixed to a
bridge pier or abutment, or other stable mountable structure for horizontal mountings, or to the channel bed for
vertical mountings. The ADVMs measure an index velocity that is related to the measured average velocity of
the channel (mean velocity) determined from current meter measurements and channel cross-sectional area.
A separate water level-to-area relation is developed from regularly measured cross-sectional geometry at or
near the location of the ADVM. Discharge is computed as a product of the mean velocity and cross-sectional
area. The acoustic Doppler velocity method can be implemented using the following techniques:
a) horizontal measurement from a fixed station or stations;
b) vertical measurement from a fixed station or stations;
c) a combination of the horizontal and vertical methods at a fixed station.
5.3.4 Unsteady flow models
Unsteady flow models may be used for computing continuous records of discharge in open channels in both
tidal and non-tidal conditions. These models, however, are not applicable where a longitudinal density
gradient, such as a salt-water wedge, is present.
Unsteady flow models are based on the numerical solution of non-linear partial differential equations that
describe gradually varied unsteady flow in open channels. The available models employ one or more of
several numerical computation techniques. Data requirements, which can be substantial, depend on the
numerical techniques employed by the model selected. It is necessary that techniques for the application of
unsteady flow models and the data requirements be clearly defined and understood for successfully
computing discharges.
6 Special considerations and choice of method
6.1 Special considerations
Changes in water level at the mouth of a river due to tidal action cause backwater effects in the channel.
These changes can alter water level and flow magnitude only, or water level, flow magnitude, and direction of
flow. The entire flow might be reversed in direction, or only some of the flow might be reversed due to
variations in the density gradient.
Most flow-gauging techniques are generally best suited to conditions closely approximating to steady flow, but
unsteady flow causes additional difficulties, as follows.
a) At any section, water levels continuously change.
b) At any point in a vertical, velocities continuously change either with or without change in direction.
c) In any vertical, the continuously changing velocities could create greater velocity gradients than in
channels with steady uniform flow.
d) During the period of transition in flow direction (flood to ebb or ebb to flood), zero velocity can occur at a
succession of points over the changing velocity profile.
e) High water and low water might not take place at the same time as the reversal in flow direction.
f) The change in direction of flow might not take place at the same time throughout the wetted cross-section
and the flood and ebb channels might be positioned differently in a wide cross-section.
g) When the direction of flow changes, the characteristics of the approach conditions from the upstream and
the downstream can be different and can result in divergence (when the angle between the flood and the
ebb flow is other than 180°) between the flood and ebb flow.
h) Flow can be stratified, with liquids of different densities in each layer. While the liquid in the upper stratum
may flow in one direction, the denser liquid in the lower stratum may flow at a different speed in the same
or opposite direction. When a density difference due to a salt-water wedge occurs, the maximum velocity
in each layer can occur at different times.
i) At any section in a channel, variations in water level can cause changes in width and cross-section of flow.
j) An increase in the number of measurements is required to make an estimate of discharge.
k) During a tidal cycle there can be variations in salinity, leading to changes in the speed of sound and
conductivity of the water, and these can adversely affect ultrasonic, acoustic Doppler velocity meter, and
electromagnetic methods.
l) During a tidal cycle there can be water column variations in temperature and/or conductivity that can
cause acoustic beam direction changes that can adversely affect ultrasonic and acoustic Doppler velocity
meter methods.
m) Spatial flow patterns during ebb flow can sometimes be significantly different from the flow conditions
during flood tide (e.g. separate ebb and flood gullies in a tidal estuary).
6.2 Choice of method
6.2.1 General
In channels with steady flow, one of the main factors affecting the choice of gauging method is the frequency
of measurements of discharge in the channel. Observations may be repeated over months or years (continual
or repeated measurements), or as little as once only (occasional measurements). Under variable or unsteady
conditions, the frequency of measurement, although affecting the cost of each gauging and important
economically, shall not be compromised. The physical conditions of flow and waterway dominate the choice.
6.2.2 Physical conditions
The physical conditions that affect the choice of gauging method are:
a) tidal range including level, flow and velocity;
b) width of channel;
c) variation in width along a channel and with time;
d) depth of channel;
e) shape of channel;
f) change in flow direction during a tidal cycle including flow reversal or backwater effects;
4 © ISO 2010 – All rights reserved

g) density of river traffic;
h) the number of experienced staff available;
i) the number of boats and gauging equipment available;
j) environmental considerations;
k) the intrusion of a salt-water wedge;
l) a temperature gradient in the water;
m) the incidence of seiches and wind-induced waves;
n) health and safety of personnel (including the availability of lighting during hours of darkness);
o) the number of observations to be made, e.g. current meter gauging requires a considerable number of
observations at one cross-section;
Guidance on the selection of the gauging method is summarized in Table B.1.
6.2.3 Selection and demarcation of site
6.2.3.1 General
The site should contain all stages of flow that occur or that need to be measured. Ideally, sites should conform
to the following requirements.
a) Sites where aquatic vegetation grows should be avoided or kept free from aquatic vegetation to ensure
there is no obstruction to the gauging operation, unless the method is tolerant to the presence of aquatic
vegetation, e.g. electromagnetic method.
b) There should be no vortices, dead water, or strong cross-currents.
c) Sites where ice accumulates should be avoided.
d) The site should be accessible for personnel and equipment at all stages of flow.
6.2.3.2 Preliminary reconnaissance surveys
A preliminary reconnaissance survey of all potential sites should be made to eliminate those that are
unsuitable and to ensure that the hydraulic and topographic features of the remainder conform to the
requirements of the International Standards pertaining to the method of measurement to be used.
Inspections under different flow conditions might be necessary to ensure that conditions unsuitable for the
method of measurement do not occur when observations are being made.
6.2.3.3 Survey of chosen site
A permanent benchmark should be established and related to a standard datum in general use in the area. All
subsequent levelling surveys should be reduced to the standard datum.
A topographical survey of the channel at the proposed gauging site should be made. This should include a
plan of the site indicating the width of the water surface at a stated stage, date and time, the edges of the
natural banks of the channel or channels, the line of any definite discontinuity of the slope of these banks, and
the toe and crest of any artificial flood bank.
The survey of the stretch of channel should be extended through the floodway to an elevation above the
highest anticipated flood level. The spacing of levels or soundings should be close enough to reveal any
abrupt change of the contour of the channel. The bed of the channel should be examined for the presence of
rocks or boulders, particularly near positions where measurements will be made.
6.2.3.4 Additional site selection criteria for ADVMs
The ADVM is a device for measuring an index velocity from a fixed location. For tidal measurement, the site
requirements such as minimum depth and velocities are largely dependent on the transducer frequency,
sensor orientation (horizontal or vertical), and the mode of operation (how the instrument processes the
acoustic signals and what setup parameters are used). Further guidance should be available from the
manufacturer's instruction manual.
The ideal ADVM site satisfies the following criteria.
a) The general course of the stream is straight for sufficient distance upstream and downstream from the
ADVM site to be outside the hydraulic effects of any flow control associated with the station.
b) If possible, the total flow is confined to one channel at all stages, and no flow bypasses the site during all
normal tidal phases or storm tides. At the mouth/delta of a river system entering an ocean tidal
environment this will be in the vicinity of a flow control structure such as a bridge.
c) The streambed is not subject to scour or accretion and is free of excessive aeration, turbulence or aquatic
vegetation.
d) A satisfactory reach for measuring discharge at all stages is available within reasonable proximity of the
gauge site.
Rarely will an ideal site be found, and judgment shall be exercised in choosing between adequate sites, each
of which has some shortcomings. Often, adverse conditions exist at all possible sites, and it is necessary to
accept such a site.
7 Measurement of tidal flow
7.1 Techniques for single measurements of tidal flow
7.1.1 Measurement of tidal flow by velocity area methods
7.1.1.1 Site requirements
Details of the methods are provided in ISO 748, ISO 1100-1, ISO 3454, ISO 4366, ISO 4369, ISO 4375,
ISO/TR 7178, ISO/TR 8363 and ISO/TR 9209.
The conditions in ISO 748 for selection of site might be difficult to achieve for tidal rivers, since the flow is
unsteady and can reverse. Reversal of flow implies different approach conditions for flood and ebb at the
measuring cross-section, making it difficult to obtain the idealized flow conditions specified in ISO 748.
However, the site for measurement of tidal flow should be chosen to have as far as possible the following
features.
a) The direction of velocities at all points, particularly during the period of maximum flow, should be at right
angles to the measuring section.
b) The channel upstream and downstream of the gauging site should be straight and of uniform cross-
section.
c) The depth of water in the selected length should, at low stages of flow, be sufficient to provide for the
effective immersion of current meters (ISO 748). This also applies to ADVMs.
6 © ISO 2010 – All rights reserved

d) The view from the gauging site should be unobstructed by trees or other obstacles.
e) The bed of the channel should not be subject to significant changes during the tidal cycle.
f) The location of cross-sections, particularly the measuring cross-section, should be marked with clearly
visible and readily identifiable markers of sufficient durability to last the lifetime of the gauging station.
g) One or more staff gauges should be installed to provide a means of measuring all stages of flow. The
gauge should be related by precise levelling to the standard datum.
h) Where there might be a significant difference in the level of the water surface between the two banks, an
auxiliary gauge should be installed on the opposite bank, particularly in the case of wide rivers. The mean
of the measurements taken from the two gauges should be taken as the mean level of the water surface.
7.1.1.2 Measurement of cross-sectional area
ISO 748 shall be applied without alteration.
7.1.1.3 Measurement of velocity by fixed current meter method
7.1.1.3.1 Measurement procedure
ISO 748, ISO 4375 and ISO 5168 provide details of the method, equipment and uncertainties in the results.
When using a current meter to measure velocities at chosen locations across a channel subject to tidal flow,
speed of measurement is important. Many procedures considered essential to achieve accuracy in
unidirectional flow measurements might have to be abandoned for practical and economic reasons in favour
of those that will accelerate the gauging procedure.
If the equipment is available, it is recommended that an acoustic Doppler profiler be used for measurements
at tidal sites.
To limit the risk of error due to changes in the direction of flow, the use of a direction-indicating current meter
is recommended. Since the direction of flow might not be the same at different levels in the vertical, the depths
at which the directions of flow are measured should also be recorded, and the measurement made at a
number of points (at least surface, mid-depth and bed) in the vertical. An alternative but less reliable method
of determining the direction of flow is to use a subsurface float.
Velocity measurements should be made at as many verticals as practicable depending on the availability of
staff, instruments and equipment. Measurements should be made at not less than three verticals, using the
following procedure.
a) Synchronize the watches and clocks of all sensors and observers.
b) Survey the gauging cross-section.
c) Mark the positions of the selected verticals with mooring buoys using both flood and ebb anchors to
restrict the movement of the buoy, if the gauging is to be carried out from a boat. If gauging is to be
carried out from a bridge or cableway, the positions should be marked on the structures. If gauging is by
wading (rarely possible except in the upper reaches of small tidal rivers), stakes should be driven into
each bank of the river to denote the measurement section and each gauging position related to such
stakes.
d) Measure the depth of water and the clock time at the first vertical.
e) Measure velocities, in magnitude and direction, near the surface, at depths of 0,2, 0,4, 0,6 and 0,8 of the
total depth and near the bed. Repeat the measurement near the surface. If the depth exceeds about 15 m,
measure velocities at intervals of one tenth of the depth between 0,1 and 0,9 of the total depth, and
repeat the measurement at 0,1 of the depth. Record the clock time of every measurement.
f) Measure depth of water and clock time at the first vertical again, and then move the gauging equipment
as quickly as possible to the second vertical.
g) Repeat the measurements of depth, velocity and time at the second vertical as specified in d), e) and f),
before proceeding to the third vertical to repeat the procedure. Continue this procedure until
measurements have been made at all verticals. Return to the first vertical to repeat the procedure.
h) If more than one gauging team is available, measurements may be made at two or more verticals
simultaneously. Each team should carry out observations on preselected verticals to avoid interfering with
one another as specified in d) to g).
i) The measurements of depth, velocity and time at the verticals should be continued for a period of at least
2 h longer than the tidal cycle (i.e. 1 h before and 1 h after the tide cycle). Where there is diurnal
inequality, observations should be taken over at least 25 h.
j) At intervals of not more than 15 min, observe water level and clock time. These observations should
begin before the survey of the cross-section is started, and should continue until after the last
measurement on a vertical has been made.
k) Resurvey the cross-section.
l) Where oblique flow is unavoidable, the angle of the direction of flow to the perpendicular to the cross-
section shall be measured and the measured velocity corrected. Special instruments are available for
measuring both angle and velocity at a point simultaneously.
Where these instruments are not available and there is insignificant wind, the angle of flow throughout the
vertical may be taken to be the same as that observed on the surface. If the channel is very deep, or if the
local bed profile is changing rapidly, this assumption shall not be accepted without checking. If the measured
angle to the perpendicular is γ, then:
V = V cos γ
corrected measured
7.1.1.3.2 Computation of discharge for fixed current meter method
For each set of verticals, the following calculations and plots are necessary.
a) Choose a convention for flow direction. For each vertical, adjust the values of measured velocities to the
time of the first velocity measurement, and calculate the mean velocity over the vertical.
VV− tt−
1 r n 1
VV=+ ⋅ ⋅V
nn n
a
Vt −t
rr 1
⎡⎤
VV=+V+ .+V
ma12a
ra−1
⎢⎥()
⎣⎦
r −1
where
t is the time of first observation at surface;
t is the time of nth observation;
n
t is the time of repeat observation at surface;
r
V is the first measured velocity at surface;
8 © ISO 2010 – All rights reserved

V is the measured velocity at time t ;
n n
V is the repeat measured velocity at surface;
r
V is the adjusted value of measured velocity V ;
n n
a
V is the mean of adjusted velocities;
m
r−1 is the number of points in the vertical.
b) Plot cross-sections.
c) Plot depth of each vertical against time.
d) Tabulate mean velocities for each vertical against clock times of first and last observations of velocity in
that set.
e) For each vertical, plot mean velocity against the mean of the clock times for each set of velocity
measurements.
f) For clock times at intervals of not more than 30 min, tabulate:
1) clock time;
2) water level;
3) area of cross-section (computed from cross-section and water level);
4) mean velocity on each vertical [interpolated from plot in e) above];
5) discharge at each clock time calculated from:
Q = (V A + V A + … V A )
1 1 2 2 n n
where
Q is the discharge at specified clock time;
n is the number of verticals;
A is the area of cross-section 1;
A is the area of cross-section 2;
V is the mean velocity at vertical 1;
V is the mean velocity at vertical 2, etc.
g) Plot discharge against clock time.
The volume of water passing the gauging section is equal to the area under the discharge/time plot during the
period of flood tide or ebb tide.
NOTE The volume of ebb flow normally exceeds the volume of flood flow by an amount qT unless there is a
significant seepage out of the banks,
where
q is the freshwater flow (m /s) measured upstream of the limit of tidal influence;
T is the duration of the tidal cycle(s).
Annex C shows a typical tabulation for one segment, but methods of utilizing computing aids can be evolved.
7.1.2 Measurement of tidal flow by moving boat method
ISO 4369 specifies this method of measurement using a moving boat.
This method is suitable for gauging flow in tidal rivers that are wide and deep enough to permit the use of a
small powered boat. The relationship between surface and mean velocity should be established as described
in ISO 4369.
The direction of the flow may be measured as specified in 7.1.1.3.1. This introduces much additional work,
which the moving boat method is designed to eliminate. A simpler but less accurate method is to anchor three
or more buoys in the channel.
The position of a buoy relative to the cross-section will indicate whether the net direction of flow is landward or
seaward. This method will not indicate the difference in the direction of flow near the surface and the bed.
7.2 Techniques appropriate for continuous measurement of tidal flow
7.2.1 Measurement of tidal flow by acoustic Doppler method
Computation of a discharge time series in a tidally affected area using an acoustic Doppler velocity meter
(ADVM) is basically a two-step process. First, the cross-sectional area near or at the location of the ADVM is
computed on the basis of a measured cross-sectional area and measured water levels. A relation between
water level and cross-sectional area is determined using regression techniques. The measured cross-
sectional area is checked periodically to ensure a stable relation between water level and area. Secondly, a
relation between the mean cross-sectional velocity and the index velocity from the ADVM is determined using
regression techniques. The mean cross-sectional velocity is computed on the basis of discharge
measurements and computed cross-sectional area. Then, continuous discharge is computed as the product of
the water-level computed area and the computed mean cross-sectional velocity.
7.2.2 Measurement of tidal flow by ultrasonic (acoustic) method
Refer to ISO 1100-1 and ISO 6416 for specifications on the requirements for gauging stations using ultrasonic
equipment.
Ultrasonic gauging stations may be constructed specifically for the purpose of measuring reverse flow in a
narrow channel. The following features are necessary.
a) Electric power should normally be available, although some new designs can operate from batteries or
solar cell and battery systems.
b) Abrupt bends in the channel should be avoided if possible, but these may be acceptable provided that
condition c) is satisfied.
c) At cross-sections taken in the area between the positions of the upstream and downstream transducer
mountings, the velocity distribution should be similar under all flow conditions both positive and negative.
10 © ISO 2010 – All rights reserved

d) The bed should not progressively scour or accrete, and preferably should not show appreciable changes
in its level over the range of flows.
e) Measurement might not be possible if the concentration of suspended sediment exceeds about
1 000 mg/l. Table B.2 specifies the limits of maximum sediment concentration under which varying
combinations of transducer frequency and path length will operate successfully.
f) The water should be well mixed and should not contain pockets of saline water or waters of different
temperatures.
g) The water should be free of bubbles such as occur downstream of a weir or sluice.
ISO 6416 provides details of ultrasonic gauging equipment and methods.
Time series data from an ultrasonic gauging station provide the basic information for computing the volume of
flood or ebb flow past the station.
7.2.3 Measurement of tidal flow by electromagnetic method
ISO 9213 provides specifications on the requirements for gauging stations using the electromagnetic method.
The station should not be located at a point where there is a saline wedge or where rapid changes in electrical
conductivity of the water occur, and should be:
a) at least 100 m from sources of electrical interference (power cables, electric railways, etc.);
b) at least 3 km from a longwave public broadcast radio station;
c) upstream of the limit of saline intrusion, including saline density differences, and at a point where the
specific conductivity of the water is low;
d) able to access a 1 kW source of electrical power;
e) able to be calibrated by another method of flow measurement (see 7.1).
Time series data from an electromagnetic gauging station provide the basic information for computing the
volume of flood or ebb flow past the station.
7.2.4 Computations
The tabulation and graphing of discharge data versus time over the tidal cycle should be accomplished by the
following two simple steps.
a) Tabulate:
1) clock time at intervals of 15 min for a period of the tidal cycle plus 2 h;
2) discharge at clock times.
b) Plot discharge against clock time.
The volume of flow past the gauging station over a flood tide or an ebb tide is equal to the area under the
discharge/time plot during the period of the flood tide or ebb tide respectively.
NOTE The volume of ebb flow usually exceeds the volume of flood flow by an amount qT, unless there is significant
seepage of water into or out of the channel between the seaward section and the inland section, where
q is the freshwater flow (m /s) measured upstream of the limit of tidal influence;
T is the duration of the ebb flow(s).
8 Uncertainties in tidal flow measurement
8.1 General
Reference should be made to ISO 748 for information on the calculation of the uncertainty in the velocity area
method of measurement and to ISO 1088, ISO 5168 and ISO/IEC Guide 98-3. Subclause 8.2 provides
additional information on the computation of uncertainties for the velocity area method (current meters).
8.2 Uncertainties in measurement by velocity area method
8.2.1 Sources of uncertainty
Reference should be made to Clause 9 of ISO 748:2007, in which the necessary definitions and a general
outline of the method of calculation are given. The following extends the method to tidal flow. Estimates of the
magnitude of the additional error components cannot be given with the present state of knowledge.
The generalized form given in ISO 748 for determining the discharge, Q, is extended to read:
im=
Qb= dv cosλ
()
ti∑ ii
i
t
i=1
where
Q is the discharge at one particular moment of the tidal cycle;
t
λ is the mean in a vertical of the angles between the single measured velocity and the normal
to the cross-section;
b , d and v are the width, depth and velocity of water in the ith verticals, of the vertical in which the
i i i
cross-section is divided.
The overall uncertainty in the tidal (ebb or flood) volume is then composed of the following uncertainties,
expressed as percentage random uncertainties:
a) uncertainties in the assessment of width;
b) uncertainties in the assessment of sounding of depth, both of individual soundings and readings of the
water level;
These should be determined having regard to ISO 748.
NOTE 1 Uncertainties originating from the variation of depth and width with time can be neglected.
c) uncertainties in the determination of individual velocities;
These will depend on the accuracy of the equipment, the technique employed (ISO 748) and the
irregularity of the velocity distribution with time and space, and on the magnitude of dv /dt, i.e. the rate of
i
change of the average velocity v with time.
i
NOTE 2 These uncertainties occur, particularly during the slack-water period, due to the limitation of the current-
meter in measuring velocities below 0,15 m/s.
12 © ISO 2010 – All rights reserved

d) uncertainties in the use of the velocity-area method, particularly those concerned with the number of
verticals and the number of points in each vertical;
These uncertainties will also depend on the width of the channel, the ratio of width to depth, and on the
method of computation used.
e) uncertainties in the determination of the angle (in a horizontal plane) between the single velocity vector
and the normal to the cross-section;
f) uncertainties due to the reduction of the individual measurements in the vertical to the same instant;
g) uncertainties arising from interpolation to the same instant of mean velocities in the vertical, in cases
where the velocity distributions are not measured simultaneously;
h) uncertainties arising from the reduction of mean velocities from one tide to another tide.
8.2.2 Individual components of errors
1)
In ISO 748:1979 , the following components have been presented and remain essentially the same:
⎯ uncertainties in width X ′ ;
()
b
i
′
⎯ uncertainties in depth X ;
( d )
i
⎯ uncertainties in the determination of local point velocities X ′ ;
( )
v
⎯ uncertainties in the determination of the mean velocities composed of:
⎯ number of points (X′ );
o
⎯ mean velocity in a vertical X ′ v , to be derived from:
( )
i
′′ ′
Xv=+Xv X
i o
⎯ number of verticals (X′ ).
m
To these components, the following shall be added for tidal flow:
⎯ uncertainties in the mean of the angles between the velocity vectors and the normal to the cross-section
X ′ϕ .
()
′
If X′ϕ is the uncertainty in the angle of a single velocity, then the uncertainty X ϕ for a vertical is
determined from:
X ′ϕ
∑
′
X ϕ =
m
where m is the number of velocities measured in the vertical;
⎯ uncertainties arising from insufficiencies in the applied method (X′ ).
s
1) These terms (defined as X′) were not used in ISO 748:2007. They represent individual components of uncertainty
errors and not the uncertainty errors.
Under this heading are considered the uncertainties under f), g) and h) of 8.2.1 and indicated by X′ , X′
(i) (ii)
and X′ respectively. (X′ ) is to be determined from:
(iii) s
22 2
′
′′ ′
XX=+X +X
s iii iii
() ( ) ( )
Each of the constituent uncertainties in this formula may be omitted when not applicable. X′ is usually
(i)
negligible. X′ might be large; this implies that the method it arises from should only be used if X′ is
(iii) (iii)
known. X′ is to be derived from:
(ii)
dv
XX′′==v X′
()ii t t
dt
where
′
X v is the uncertainty in the mean velocity v of a vertical for which v has been determined by
t
interpolation;
X′ is the uncertainty of time measurement (percentage error relative to the time interval
t
between measurements of verticals, and due to synchronization of watches, etc.);
dv
is the slope of the velocity-time curve.
dt
The uncertainty arising from taking “limited number” of discharge measurement during the tidal period can be
disregarded.
8.2.3 Resultant random uncertainty in measurement of flow
′
The percentage resultant random uncertainty X in measurement of flow at time t shall be calculated in
Q
t
accordance with ISO 748, as follows:
im=
⎡⎤
⎛⎞
′′
2 XX
22 2
′′
⎢⎥bd v cosϕϕ⎜⎟X ++X + tan
()
∑ ii i i b d i
ii
⎜⎟
v ϕ
⎢⎥
ii
⎝⎠
2 i=1⎣⎦ 2
′′ ′
XX=+ +X
Qm s
t im=
bd v cosϕ
()
ii i i
∑
t
i=1
The use of a simplified formula based on that presented in ISO 748 is not recommended.
8.2.4 Resultant systematic uncertainty in measurement flow
The above equations are satisfactory for estimating the precision of the measurement but do not take account
of the possibility of systematic errors. Systematic errors which behave as random uncertainties shall be
estimated separately and may be combined as follows:
22 2 2
XX′′=+′′ X ′′+X ′′v+X ′′ϕ
Qb d
where X″ , X″ , X″ v and X″ϕ are the percentage systematic uncertainties in b, d, v and ϕ respectively.
b d
NOTE It is a question here of systematic errors due to the instruments, which vary randomly from instrument to
instrument, and not of systematic errors inherent in the type of instrument or measurement which can be eliminated or
determined only if a superior instrument or improved method is available.
14 © ISO 2010 – All rights reserved

8.2.5 Combined uncertainty at the 95 % confidence level
The overall estimate of the uncertainty of the discharge will then be:
′′′
SX=+X X
volQQ Q
tt
This v
...