ISO/TS 25377:2007
(Main)Hydrometric uncertainty guidance (HUG)
Hydrometric uncertainty guidance (HUG)
ISO/TS 25377:2007 provides an understanding of the nature of measurement uncertainty and its significance in estimating the quality of a measurement or a determination in hydrometry. It is applicable to flow measurements in natural and man-made channels. Rainfall measurements are not covered.
Lignes directrices relatives à l'incertitude en hydrométrie
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Standards Content (Sample)
TECHNICAL ISO/TS
SPECIFICATION 25377
First edition
2007-10-01
Hydrometric uncertainty guidance (HUG)
Lignes directrices relatives à l'incertitude en hydrométrie
Reference number
ISO/TS 25377:2007(E)
©
ISO 2007
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ISO/TS 25377:2007(E)
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ISO/TS 25377:2007(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references. 1
3 Terms and definitions. 1
4 Symbols and abbreviations . 2
5 ISO/IEC Guide 98 (GUM) — Basic definitions and rules. 4
5.1 General. 4
5.2 The uncertainty of sets of measurements. 4
5.3 Random and systematic effects. 4
5.4 Uncertainty models — Probability distributions . 5
5.5 Combining uncertainties — The law of propagation . 5
5.6 Expressing results. 6
6 Open channel flow — Velocity area methods. 6
6.1 General. 6
6.2 Mean velocity, V . 7
x
6.3 Velocity-area determination. 8
6.4 Stationary determination of velocity. 9
6.5 Moving determination of velocity. 10
6.6 Velocity-area uncertainties. 11
**
⎡⎤
6.7 Integration uncertainties uF ,uF . 15
()
()
yz
⎣⎦
6.8 Perimeter flow uncertainties, uQ . 16
()
p
7 Open channel flow — Critical depth methods . 16
7.1 General. 16
7.2 Head and geometry determination. 17
7.3 Iterative calculation. 18
7.4 Evaluating uncertainty . 18
8 Dilution methods. 18
8.1 General. 18
8.2 Continuous feed. 19
8.3 Transient mass. 20
9 Hydrometric instrumentation . 21
9.1 Performance specifications. 21
9.2 Validity of uncertainty statements . 21
9.3 Manufacturer’s performance specifications . 22
9.4 Performance guide for hydrometric equipment for use in technical standard examples . 23
10 Guide for the drafting of uncertainty clauses in hydrometric standards . 24
10.1 General. 24
10.2 Equipment, methods and measurement systems. 24
Annex A (informative) Introduction to hydrometric uncertainty . 26
Annex B (informative) An introduction to Monte Carlo Simulation (MCS). 43
Annex C (informative) Performance guide for hydrometric equipment for use in technical
standard examples . 48
Bibliography . 51
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ISO/TS 25377:2007(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.
In other circumstances, particularly when there is an urgent market requirement for such documents, a
technical committee may decide to publish other types of normative document:
⎯ an ISO Publicly Available Specification (ISO/PAS) represents an agreement between technical experts in
an ISO working group and is accepted for publication if it is approved by more than 50 % of the members
of the parent committee casting a vote;
⎯ an ISO Technical Specification (ISO/TS) represents an agreement between the members of a technical
committee and is accepted for publication if it is approved by 2/3 of the members of the committee casting
a vote.
An ISO/PAS or ISO/TS is reviewed after three years in order to decide whether it will be confirmed for a
further three years, revised to become an International Standard, or withdrawn. If the ISO/PAS or ISO/TS is
confirmed, it is reviewed again after a further three years, at which time it must either be transformed into an
International Standard or be withdrawn.
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/TS 25377 was prepared by the European Committee for Standardization (CEN) Technical Committee
CEN/TC 318, Hydrometry, in collaboration with Technical Committee ISO/TC 113, Hydrometry, in accordance
with the Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
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ISO/TS 25377:2007(E)
Introduction
The management of a natural environment requires knowledge, by measurement, of what is happening. Only
then can effective action be taken and the effectiveness of the action assessed. Much depends on the quality
of the knowledge itself.
The quality of measurable knowledge is stated in terms of measurement uncertainty. The internationally
agreed method for assessing measurement quality is the Guide to the estimation of uncertainty in
measurement (GUM). Without this uniformity of measurement standards, equitable sharing of the environment
is not possible and international obligations to care for the environment would be weakened.
The essential purpose of the GUM is that a statement of the quality of a measurement result will be presented
with all measurements described in technical standards. Without this, no two measurements can be compared
or standards set. Whereas the GUM is a reference document serving the universal requirements of metrology,
the Hydrometric uncertainty guidance (HUG) document is specific to hydrometry, i.e. to the measurement of
the components of the hydrological cycle. It borrows from the GUM the methods that are the most applicable
to hydrometry and applies them to techniques and equipment used in hydrometry.
In the past, error analysis has provided an indication of measurement quality, but such statements cannot
properly convey the quality of the result because it presupposes a knowledge of a true, error-free, value
against which the measured result can be compared. The true value can never be known. Uncertainty
therefore remains. For this reason, the GUM uses the concept of uncertainty and uses it for all stages and
components of the measurement process. This ensures consistency.
The GUM defines standard uncertainty of a result as being equivalent to a standard deviation. This can be the
standard deviation of a set of measured values or of probable values. This is broadly similar to the approach
used in error analysis that preceded the uncertainty technique. However, the GUM provides additional
methods of estimating uncertainty based on probability models. The two approaches are equivalent but
uncertainty requires only a knowledge or estimate of the dispersion of measurement about its mean value,
and not the existence of a true value. It is assumed that a careful evaluation of the components of
measurement uncertainty brings the mean value close to a probable true value, at least well within its margin
of uncertainty.
In more general terms, uncertainty is a parameter that characterizes the dispersion of measurable values that
can be attributed to their mean value.
By treating standard deviations and probability models as if they approximated to Gaussian (or normal)
distributions, the GUM provides a formal methodology for combining components of uncertainty in
measurement systems where several input variables combine to determine the result.
Within this formal framework, the GUM can be consistently applied to a range of applications and, thereby, be
used to make meaningful comparisons of results.
The HUG seeks to promote an understanding of the nature of measurement uncertainty and its significance in
estimating the ‘quality’ of a measurement or a determination in hydrometry.
Hydrometry is principally concerned with the determination of flow in rivers and man-made channels. This
includes
⎯ environmental hydrometry, i.e. the determination of the flow of natural waters (largely concerned with
hydrometric networks, water supply and flood protection),
⎯ industrial hydrometry, i.e. the determination of flows within industrial plants and discharges into the
natural environment (largely concerned with environment protection and also irrigation).
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ISO/TS 25377:2007(E)
Both are the subject of international treaties and undertakings. For this reason, measured data needs to
conform to the GUM to assure that results can be compared.
Hydrometry is also concerned with the determination of rainfall, the movement/diffusion of groundwater and
the transport by water flow of sediments and solids. This version of the HUG is concerned with flow
determination only.
The results from hydrometry are used by other disciplines to regulate and manage the environment. If
knowledge is required of biomass, sedimentary material, toxins, etc., the concentration of these components
is determined and their uncertainty estimated. The uncertainty of mass-load can then be determined from the
uncertainty of flow determination. The components of this calculation are made compatible through
compliance with the GUM.
For practitioners of hydrometry and for engineers, the GUM is not a simple document to refer to. The
document has been drafted to provide a legal framework for professional metrologists with a working
knowledge of statistical methods and their mathematical representation. A helpful document, NIST Technical
[12]
Note 1297 , is an abbreviated version of the GUM written to be more accessible to engineers and to
specialists in fields other than metrology.
The HUG, although simplifying the concepts, in no way conflicts with the principles and methods of the GUM.
Accordingly, the HUG interprets the GUM to apply its requirements to hydrometry in a practical way, and,
hopefully, in a way accessible to engineers and those responsible for managing the environment.
In addition, the HUG introduces and develops Monte Carlo Simulation, a complementary technique, which has
benefits for hydrometry, insomuch as complex measurement systems can be represented realistically.
The HUG summarizes basic hydrometric methods defined in various technical standards. The HUG develops
uncertainty estimation formulae from the GUM for these basic methods. The basic hydrometric methods
described in the HUG may not be identical to those recited in the published technical standards. In such cases,
the methods described in these standards are to be taken as authoritative. However, clauses in technical
standards that concern uncertainty should be adapted to be in accordance with the HUG.
NOTE There is no unified definition of space coordinates within the hydrometric standards. The textbook
conventional axes are adopted in this document when describing open channel flow: the x axis being horizontal and
positive in the mean flow direction, the y axis being orthogonal to the x axis in the horizontal plane and the z axis being
vertical positive.
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TECHNICAL SPECIFICATION ISO/TS 25377:2007(E)
Hydrometric uncertainty guidance (HUG)
1 Scope
This Technical Specification provides an understanding of the nature of measurement uncertainty and its
significance in estimating the ‘quality’ of a measurement or a determination in hydrometry.
It is applicable to flow measurements in natural and man-made channels. Rainfall measurements are not
covered.
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 772, Hydrometric determinations — Vocabulary and symbols
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 772 and the following apply.
NOTE For a complete appreciation of the scope of definitions used in measurement uncertainty, the reader is
[10] [12]
referred to the GUM or to NIST Technical Note 1297 .
3.1
standard uncertainty
uncertainty of the result of a measurement expressed as a standard deviation
3.2
type A evaluation of uncertainty
method of evaluation uncertainty by the statistical analysis of a series of observations
3.3
type B evaluation of uncertainty
method of evaluation uncertainty by means other than the statistical analysis of a series of observations
3.4
combined standard uncertainty
standard uncertainty of the result of a measurement when that result is obtained from the values of a number
of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or
covariances of these other quantities weighted according to how the measurement result varies with changes
in these quantities
3.5
expanded uncertainty
quantity defining an interval about the result of a measurement that may be expected to encompass a large
fraction of the values that could be attributed to the measurand
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ISO/TS 25377:2007(E)
3.6
coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded
uncertainty
4 Symbols and abbreviations
α coefficient representing the effects of non-uniform energy (velocity) in a channel
γγ,,γ angles between boat axes and the x axis.
xxxy xz
σ standard deviation
′′
∆∆xy, dispersion of measurement from the mean value of the set of x,y measurements for a
symmetric distribution: ∆=′xx0,5 −x , etc.
( )
max min
+−
∆∆′′xx, ± dispersion about the mean value, x , for an asymmetric distribution of measurements
+ −
′ ′
where ∆=xx −x and ∆=xx−x .
( ) ( )
max min
∆ small difference in a measured quantity ∆QhT,,∆∆, etc.
∆∆yz, notional small distances in the y and z directions at a cross-section in the channel
Dc in the dilution method, the downstream mixed change (c − c ) of concentration of the
2 m b
tracer
A, A(z), A(h) cross-section area (in the y,z plane) of the flow
B channel width
b contracted channel width or flume throat width
c dilution method, the background concentration of tracer
b
c dilution method, the feed concentration of tracer
T
c dilution method, the downstream mixed concentration of the tracer
m
C discharge coefficient
C velocity coefficient
v
d deviation of an measurement (the ith measurement of a series) from the mean value of
i
that series
E datum elevation of a range measuring device
f(h) relationship between head, h, and cross-section area, A
F , F multiplying factors to be applied to the summation of velocity-area elements to account
x y
for the approximation of a summation process to a true integration of continuously
varying parameters.
g gravitation acceleration
h head of water relative to a defined datum level in the channel
H total head relative to a defined datum level in the channel
i,j indices of a count i = 1 to n, or j = 1 to m of a series
J false measurement detection factor
K constant of a flow determination equation for a weir or flume
k , k constants for the determination of flow by the dilution method
1 2
M dilution method, the mass of tracer introduced into the stream
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ISO/TS 25377:2007(E)
n exponent of a flow determination equation for a weir or flume
n, m number of measurement in a series
p(x) probability function
Q flow
Q estimated flow passing close to boundaries or any region where measurement cannot be
p
determined by the primary means
Q dilution method, the flow of tracer into the stream
T
S standard deviation of a set of measurements
t factor to be applied to small numbers of samples to enable the standard deviation to be
e
representative of large numbers of samples (see Annex A)
t , t in the dilution method, the interval during which a change in concentration is detectable
1 2
T absolute temperature, in Kelvin
T Grubbs’ test parameter
n
U(x), u(y) uncertainty of measured variables x, y, etc.
u (p), u (q) the combined uncertainty of determined results p, q, etc.
c c
*
ux the percentage uncertainty of a measurement of any quantity x
()
U measurement uncertainty expanded to the 95 % level of confidence
95
V mean velocity through a yx plane intersecting a channel cross-section of the channel
x
Vy,z velocity in the x direction at point y, z in the channel
( )
x
→
V water velocity vector relative to channel
→
V boat velocity vector relative to the channel
b
′
→
V water velocity vector relative to boat
′′ ′
VV,,V water velocity components relative to boat along boat coordinate axes
′
x yz
′′ ′
VV,,V components of boat velocity relative the boat axes
′
bbx yzb
γγγ,, angles between boat axes and the channel x axis.
xxxyxz
x,y,z channel coordinates
x’,y’,z’ boat coordinates
x,y measurable variables
In this document, the term “uncertainty” refers to measurement uncertainty and the following forms of equation
are used to signify
n
⎯ a sum of n values of x xx+++x .x+ .x= x ,
12 3 in i
∑
i=1
df
∆x,
⎯ a difference, ∆f()x , in the function, f (x), due to a small change, in the value x ∆=fxx∆ ,
()
dx
x
n
⎯ a value of an integral, F, of a function, f x , between, x = x , and x = x F = fx d.x
( ) ()
1 n
∫
x
1
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ISO/TS 25377:2007(E)
5 ISO/IEC Guide 98 (GUM) — Basic definitions and rules
5.1 General
This section summarizes the methods described in the GUM for the expression of uncertainty in measurement.
For a general introduction to measurement uncertainty, refer to Annex A.
5.2 The uncertainty of sets of measurements
The GUM describes measurement uncertainty as a value that characterizes the dispersion of measurements
that could reasonably be attributed to the result. The GUM goes on to define standard uncertainty as
uncertainty expressed as a standard deviation, s.
So, for a set of n measurements, uncertainty is related to the difference between each measured value, x ,
i
from the average value, x, of the set. The standard deviation, and hence the uncertainty,ux , is:
()
1 222 2
⎡⎤
ux=s= x−x + x−+x x−+x . x−x
() () () () ()
12 3 n
⎢⎥
n −1⎣⎦
2
where components xx− are the deviation of the ith measurement, x , from the mean value, x.
()
i
i
Or, more concisely:
1 n
2
ux()==s d (1)
i
∑
1
n −1
where dx=−x is the deviation of the ith measurement from the mean value, x,
ii
and
1 n
xx= (2)
i
∑
i=1
n
The larger the number, n, of measurements used to calculate the mean value, x, the greater is the
expectation that the mean value approaches the ‘true’ value. Therefore, the uncertainty of the mean value,
ux , decreases as the number of measurements, n, increases. The GUM relationship for this is
( )
1
ux = u x (3)
() ()
n
5.3 Random and systematic effects
Equation (3) applies only to the random variations of the measured quantity. This random effect is determined
from the measured data and, as such, is evaluated after a set of measurements have been taken. Random
effects can be determined from analysis of the historic data or by the instrumentation itself if it is designed to
analyse the data in real time. Random effects diminish the average value of a set of n measurements by the
1
factor . Random conditions often exist as natural turbulence. However, random variation can sometimes
n
occur through human interpretation of a reading of an indicator, such as a staff gauge.
Uncertainties that are inherent to the measurement equipment or to the method are systematic. Systematic
effects cannot be diminished by the use of Equation (3). During each measurement session, systematic
effects can usually be taken as constant for the measurement device. Systematic components are
a) assessed as part of an installation or commissioning procedure, and/or
b) specified beforehand for the equipment by the manufacturer. Refer to Clause 9.
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ISO/TS 25377:2007(E)
Refer to A.6 in Annex A for more information on random and systematic effects.
For the evaluation of the uncertainty of a continuous process, include unsteady effects as a random
component. The quantity being measured may be varying slowly during the measurement process. This will
widen the dispersion of measured values and hence add to the assessment of the random component. Such
variation shall be part of the randomness of the measurement. If during the measurement process the rate of
change is such that it significantly exceeds the natural dispersion of measurements, then the result shall be
discarded.
5.4 Uncertainty models — Probability distributions
In hydrometry, measurements are often made using automated instruments. They have a margin of
measurement within which measured values can vary randomly in steady conditions. If this uncertainty is
inherent to the measurement process, it is a systematic component. It is commonly expressed as a probability
distribution. Probability distributions have standard deviations about the mean value which are equivalent to
the standard deviation of discrete measurements as defined above. The probability distributions equivalent to
Equations (1) and (2) are
∆x
2
ux=⋅d x px dx (4)
() () ()
∫
−∆x
and
∆x
xx′=⋅px dx (5)
()
∫
−∆x
wherepx is a probability function and d is the dispersion. Refer to Annex A for details.
()
5.5 Combining uncertainties — The law of propagation
The GUM also defines a rule for combining uncertainties from several sources. It is called ‘the law of the
propagation of uncertainties’. For a relationship, f, between a result, y, and variables, xx, .x , defined
12 n
as y =fxx(), .x , the combined uncertainty, uy( ), of y is
12 n c
2
in=
2 ⎛⎞∂f
uy = ux
() ()
c ∑⎜⎟i
∂xi
⎝⎠
i=1
or
22 2
⎛⎞⎛ ⎞ ⎛⎞
∂∂ff ∂f
2
u y=+ux u x+ .+ ux (6.A)
() () () ()
⎜⎟⎜ ⎟ ⎜⎟
c1 2 n
∂∂xx ∂x
⎝⎠12⎝ ⎠ ⎝⎠n
where xx, .x are independent variables.
12 n
Equation (6.A) applies only where the variables xx, .x are uncorrelated, i.e. if variable x changes value,
12 n
i
no other x variable is affected by that change. If two or more variables x do influence each other (i.e. they are
correlated), then an additional component of uncertainty exists. Equation (6.A) then becomes
2
jn=
in==i n−1
∂∂ff∂f
2 ⎛⎞
u y=+ux 2 uxx (6.B)
() ()
()
c∑∑⎜⎟ii∑ j
∂∂xxii∂xj
⎝⎠
ii==11j=i+1
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ISO/TS 25377:2007(E)
Almost all hydrometric uncertainty estimations require the use of the simpler form, i.e. Equation (6.A).
∂f
The components can be random or systematic. The partial derivatives are referred to as ‘sensitivity
∂x
n
coefficients’.
5.6 Expressing results
Equation (6.A) expresses the final result in terms of standard uncertainty. For the Gaussian probability, used
as a model distribution for general analysis, one standard deviation covers only 68 % of the range of possible
results. This means that for a result expressed as
Flow rate = 10,8 l/s ± 0,6 l/s
or
QQ=±uQ
()
Onl
...
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