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on 09 May 2022© 2022 The Authors Water Practice & Technology Vol 17 No 1, 14 doi: 10.2166/wpt.2021.124
Impact of active night population and leakage exponent on leakage estimation
in developing countries
Peace Korshiwor Amoatey a,*, Abena Agyeiwaa Obiri-Yeboah b
and Maxwell Akosah-Kusi c
a Department of Agricultural Engineering, University of Ghana, Legon. P. O. Box LG 77, Legon Accra, Ghana
b Department of Civil Engineering, Kumasi Technical University (KsTU), Kumasi, Ghana
c Ghana Water Company Limited (GWCL), Accra, Ghana
*Corresponding author. E-mails: pkamoatey@ug.edu.gh; pkamoatey@gmail.com
PKA, 0000-0002-2794-9721; AAO-Y, 0000-0002-5839-0553ABSTRACT
Methods for network leakage estimation include water balance, component analysis and minimum night flow (MNF) methods,
the latter of which involves subtracting the customer night use (QCNU) from night leakage and multiplying by the hour day factor
(HDF). QCNU and HDF respectively depend on Active Night Population (ANP) and leakage exponent (N1). In most developing
countries, these parameters are assumed in the MNF method, thus introducing errors which makes setting realistic leakage
reduction targets and key performance indicators (KPI) problematic. In this study, QCNU and HDF were evaluated by determining
the relative error associated with ANP and N1 to establish localized rates for accurately estimating leakage in water networks.
Between 7 and 11% relative error was associated with every 1% higher or lower ANP while up to 4% relative error was observed
for every N1 step considered. A linear relationship exists between the relative error associated with both N1 and ANP although
that of ANP is twice as high as N1: This has technical implications for setting water loss reduction targets and investing in the
water infrastructure. It is recommended that water utilities must establish localized ANP and N1 values for accurate leakage
estimation in water networks.
Key words: active night population, customer night use, hour-day factor, leakage exponent, performance indicators, relative
error
HIGHLIGHTS
• Customer night use and Hour-day factor, which respectively depend on active night population and leakage exponent, are
key parameters for use in the minimum night flow method.
• Active night population rate and leakage exponents will enhance the accuracy of the amount of leakage estimated.
• Key Performance indicators computed, realistic targets set and infrastructure investments for water loss reduction ensured.This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits
copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://
creativecommons.org/licenses/by-nc-nd/4.0/).
aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022GRAPHICAL ABSTRACT1. INTRODUCTION
An estimated 666 million people lack improved drinking water worldwide (Ritchie & Roser 2019); amid the
Sustainable Development Goals, SDG 6 aims at ensuring available and sustainable water for all by 2030. Van
den Berg (2014) reports that huge volumes of treated water are physically and commercially lost from urban
water supply systems annually as earlier reported by Kingdom et al. (2008). This loss amounts to 45 million
cubic meters daily, costs the world approximately $5 billion a year, and is sufficient to serve nearly 200 million
people worldwide (Kingdom et al. 2006).
Global leakage rates reported by Kingdom et al. (2006) have been corroborated by many other researchers.
Burst losses and leaks contributed 13% out of 39% non-revenue water (NRW) in Sana, Yemen, 43% out of
51% NRW in Pirot, Serbia and 44% out of 50% NRW in Blantyre, Malawi (Kofodya 2010; Al-Washali et al.
2018; Radivojević et al. 2020). 67% in Selangor State, Malaysia. 59% in Kazerun, Iran, between 25 and 60%
in five Bosnia-Herzegovinian utilities, 92% in Kafubu, Zambia and 44% in Kampala, Uganda (Chiipathenga
2008; Kamani et al. 2012; Vučijak et al. 2013). The reasons for these huge losses may be technical, socio-political
and economic.
Studies byKnobloch et al. (2014) and Farley et al. (2011) indicate that the steps in addressing the leakage problem
are fourfold; identify how much is lost, where the losses occur, why they occur and how they can be reduced. To
determine how much is lost, three methods, namely –water balance (Farley et al. 2011; Knobloch et al. 2014), mini-
mumnight flow (MNF) (García et al. 2006; Tabesh et al. 2009; Xin et al. 2014) and component analysis also knownas
the Burst and Background Estimates (BABE) (McKenzie 2003; Fanner& Thornton 2005; Özdemir et al. 2021), have
been identified and have been applied to the case study network in Amoatey et al. (2018).
The challenge these methods pose is their application to water networks with inadequate data, thus compelling
water utilities to assume International Water Association (IWA) established parameters that may be sensitive to
estimated leakage due to differing local conditions (Amoatey et al. 2018; Negharchi & Shafaghat 2020). Foraponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022example, the infrastructure condition factor (ICF) and burst flow rates, used in the BABE method, must be deter-
mined per particular networks. However, in most developing countries, these factors have not been established,
thus IWA rates, which are based on UK water networks, are used. Therefore, there is a need for water utilities in
developing countries to develop local factors and rates for leakage estimation (Amoatey et al. 2018).
Similarly, the MNF method estimates leakage as the difference between night leakage (QL) and customer night
use (QCNU), multiplied by the hour day factor (HDF). The active night population (ANP), is the percentage of
customers that use water at night between 12:00 midnight and 04:00 am while the HDF accounts for the pressure
variations during the day. The parameters, QCNU and HDF depend respectively on the ANP and the leakage
exponent (N1). QCNU is also known as legitimate Night Consumption (LNC) and presupposes that customers
with toilet flushing systems within a particular water distribution network, contribute to night flows. However,
some people do not use toilet flushing systems which called for categorization of night users. These toilet-flusing
and non-toilet flushing categories of night users is reported in earlier studies (Amoatey et al. 2014, 2018). The
leakage exponent on the other hand depends on the pipe material, pipe age and environmental conditions of
the network. As pipes of certain material advance in age, their response to changes in pressure varies and this
can influence leakage exponent (Cheung et al. 2010; Lambert & Thornton 2012; De Marchis et al. 2016). There-
fore, its influence in the estimation of leakage using the MNF method is being investigated in this study.
The influence of water loss (and NRW) parameters has been anticipated and have been the reason for various
adaptations, modifications and re-definition of key concepts based on local network situations reported in pre-
vious studies (Tabesh & Asadiani Yekta (2005); Tsitsifli & Kanakoudis 2010; Al-Washali et al. 2020;
Negharchi & Shafaghat 2020). Al-Washali et al. (2020) intimated that these have led to the introduction of cor-
rection factors, uncertainty, normalization, recognition of intermittent supply for among others.
It must be indicated that much has been reported on factors influencing apparent losses than have been
reported on real losses. Fontanazza et al. (2015) identified meter age, meter inaccuracies, metering and billing
errors incorrect installation practices, lack of maintenance or calibration, incorrect meter type and class and
incorrect meter sizing as crucial for accurate estimation of apparent losses. The authors modeled the effect of
private water tanks on apparent losses and recommended the use of unmeasured flow reducers (UFR) in such
areas. Earlier authors like Tsitsifli & Kanakoudis (2010), Arregui et al. (2006), Tabesh & Asadiani Yekta
(2005), Rizzo & Cilia (2005), Thornton & Rizzo (2002); have reported same.
With respect to real losses, though must has been studied on how to estimate the amount of leakage, not much
has been explored as regards the influence of the factors used in these methods. Amoatey et al. (2018) identified
the factors that influence all three leak estimation methods without analyzing the influence of the factors. The
only study that has assessed the influence of some leak estimation parameters using the MNF method is that
of García et al. (2006). The authors explored the influence of average zone pressure (AZP), the N1 and the
MNF hour on the leakage level error and proposed guidelines to improve the assessment of daily leakage
rates using the MNF method.
Amoatey et al. (2014, 2018) studies identifed QCNU to be crucial in the MNF procedure in developing country
water networks and argues that, an assumption of the parameter may not depict the actual local situation and
could lead to inaccurate estimation of losses, resulting in setting inaccurate water loss reduction targets.
Negharchi & Shafaghat (2020) also investigated the influence of QCNU and N1 on the amount of leakage esti-
mated using the BABE and MNF methods in a network where domestic customers use water tanks. The
authors found that changing N1 by 0.1, alters the estimated leakage by 1%, while changing QCNU by one step,
alters the calculated leakage by 14% although it is not clear what a step is in that study.
This study, therefore, seeks to investigate the influence of ANP and N1 onQCNU and HDF respectively and how
both parameters subsequently influence estimated leakages. This is necessary since in the case study network,
there are no automatic meter reading (AMR) systems that help identify typical night users and key water uses
are not yet installed in the water network.1.1. Active night population (ANP)
Farley (2001) recommends an ANP of 6% and this has been adopted in several studies (Fanner & Thornton 2005;
Tabesh et al. 2009). ANP is the percentage of active consumers who use water between 12:00–4:00 am. The typi-
cal activities range are flushing of toilets, use of faucets, showers and use of washing machines is known as QCNU
(Fantozzi & Lambert 2012). This parameter has been known to differ for different water networks and countries.aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022A summary of customer night use rates for different countries is documented in Amoatey et al. (2014) and
updated by Negharchi & Shafaghat (2020).
Loureiro et al. (2012), identified social demographic factors such as property type, household size, daily habits
of customers as well as technical, climatic factors and maintenance program of water utility as factors that influ-
ence QCNU and studied these extensively in Portugal. This makes the determination of ANP crucial for obtaining
QCNU . Amoatey et al. (2018) identified three ways by which QCNU can be estimated but recommends using Auto-
matic Meter Infrastructure (AMI) to identify the typical night uses and the active night population.
Fantozzi & Lambert (2012) carried out a study using smart metering systems in Australia and found ANP to be
3% confirming the fact that the recommendation to use 6% in earlier studies (Farley 2001; AL-Washali et al.
2019) might not be the same for all networks. This paper therefore posits that, some water networks especially
in developing countries may have lower ANPs than the recommended 6% and the measured 3% (Fantozzi &
Lambert 2012). Again, it is possible that with an increase in socio-economic activities coupled with the new
way of working since the SARS-CoV 2 pandemic struck, ANP may be relatively higher in some networks than
that found in the Fantozzi & Lambert (2012) study. Thus, it is imperative that water utilities know how far the
leakage situation in the network is from reality. Since most developing country networks do not have AMI or
smart metering systems, and not all consumers use toilet flushing systems, it is essential to investigate what rela-
tive error exists with the choice of an ANP rate.
1.2. Hour day factor
Another parameter under investigation is the HDF sometimes called night day factor (NDF) is a dimensionless par-
ameter that presupposes that leakage and pressure are related, thus, by controlling pressure, water losses can be
reduced (García et al. 2006; Cheung et al. 2010; Al-Washali et al. 2019; Özdemir et al. 2021). It is known from the
Morrison et al. (2007) study that, gravity-fed networks and low-pressure gravity systems usually have HDF less than
or equal to 24 hours per day due to high frictional head losses. HDFs depends on N1 and are estimated in the UK to
range between 15 and 30, with an average of 22, and between 18 to 22 in South Africa (García et al. 2006; Cheung
et al. 2010; Lambert & Thornton 2012). In a study in Kayseri, Turkey, Özdemir et al. (2021) found HDF to be 22.5.
SinceN1 shows the interdependency of leakage on pressure, theoretically, leakage rates in water distribution sys-
tems varywith the square root of pressure (Lambert 2001; Cheung et al. 2010). Practically, however, tests in various
countries have yielded higher N1 values due to changing flow conditions (laminar, transition or turbulent) and
changing orifice area and size in terms of holes, slots or cracks of leaks (Lambert 2001). The determination of
N1 is specific to any distribution network and is obtained from field studies by gradually reducing flow into a section
of the network and recording changes in pressure over a period of time (Lambert 2001; Tabesh & Asadiani Yekta
2005; García et al. 2006; Thornton et al. 2008; Cheung et al. 2010). N1 values have been found to typically range
from 0.5 to 2.5 (García et al. 2006; Tabesh et al. 2009; Cheung et al. 2010; Negharchi & Shafaghat 2020; Özdemir
et al. 2021) depending on pipematerial and level of leakage. Themore rigid the pipematerial, the closer theN1 is to
0.5. Networks with mixed materials range between 0.5 and 2.5. An established value of 1.15 is reported in Japan,
1.13 in UK distribution systems and close to 1.5 in Australia and New Zealand systems (Lambert 2001; Thornton
&Lambert 2005; Lambert & Thornton 2012). Schwaller & van Zyl (2015) foundN1 values between 0.46 and 1.67,
with the vast majority of values lying between 0.5 and 1.5 in amodel of the distribution of individual leaks and their
parameters. It must be indicated therefore that the effect of age and material type of pipes has an indirect influence
on N1 of the network (De Marchis et al. 2016).
This paper seeks to establish the influence of ANP in the QCNU and N1 in HDF parameters on the estimated
leakage volume in developing country water networks. It emphasizes the need to establish these parameters for
particular networks. The relative error associated with an assumed ANP and N1 is investigated to establish how
changes in these parameters influence leakage volumes in a network. It is expected that water utilities in devel-
oping countries will adopt localized parameters to determine actual leakage levels so as to be able to accurately
determine key performance indicators and set leakage reduction strategies.2. MATERIALS AND METHODS
2.1. Case study area
The Baifikrom water network is located mainly in the Mfantsiman Municipal Assembly in the Central Region of
Ghana and was selected as the study area for this work because the network had been zoned, expanded andaponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022rehabilitated. It supplies 32 communities with a population of about 122,000 (AVRL 2008), some of which are
rural over an area of approximately 250 km2. The design per capita consumption rates range from 30–75
litres/capita/day (Adombire 2007). The total demand is 318 m3/h. Pipes are made of Asbestos Cement (AC),
High Density Polyethylene (HDPE) and Polyvinyl Chloride (PVC) making about 150 km in length.
The pipe sizes range from 75–500 mm (AVRL 2008). The network (Figure 1) has approximately 5,700 service
connections and 85% customer metering. Water is pumped from the Treatment Plant (WTP) into 4 reservoirsFigure 1 | Water distribution network for Baifikrom.
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on 09 May 2022sited at the highest points (on hills) within the supply area. Water then flows under gravity from these reservoirs
into the towns and communities. Rural communities are mainly served through public standpipes as some cannot
afford a water meter connection. Also fixed outlet pressure reducing valves (PRVs) set at pressures between 10
and 30 m reduce flow to communities that branch off from the transmission mains.
Out of the 32 towns, 3 of them – Mankessim, Saltpond and Anomabo – are the most vibrant, with the remain-
ing being rural farming and fishing communities. There is the market at Mankessim where vibrant commercial
activities take place mainly during the day. It is the most populous town with a few commercial and rural
banks. Saltpond and Anomabo have much smaller markets where fish, sea foods and salt are major commodities.
There are a number of Secondary/High schools in these three towns. These towns are the most likely to have a
section of their populace using toilet flushing systems. Most rural communities rely on public stand pipes and that
accounts for the high number of stand pipes in this water network.
According to Mfantsiman Municipal Council (2012) assembly, only 10% of households use toilet flushing sys-
tems in this network. For this reason, the MNF procedure was modified to make it applicable to this network in
an earlier study (Amoatey et al. 2018). The Baifikrom water network reports annual non-revenue water (NRW) of
about 50% and this had not been broken down into its major components – leakage (physical) and apparent
(commercial) losses (GWCL 2014). The NRW of the Baifikrom network is similar to other networks like
Mwanza, Tanzania, Sana’a, Yemen and Zarqa, Jordan (Al-Washali et al. 2019).
After 3 months, the minimum night flow rate for the network was measured to be 40 m3/h. N1 was found to be
2.4 resulting and anHDFof 20 obtained frompressuremeasurements taken over threeweeks (Amoatey et al. 2012).
Because the pipe materials in the case study network are 70% plastic, an N1 of 1.0 was theoretically expected
(García et al. 2006; Lambert & Thornton 2012; De Marchis et al. 2016). In analyzing the relative error of leakage
estimated for N1, for each ANP rate considered, a range of values 0.5 to 2.5 in steps of 0.5 is considered.
QCNU was estimated for two categories of night users and summed up in the same way as in the pilot study
reported by Amoatey et al. (2014). Total QCNU was estimated for 1–6% ANP and used to estimate leakage.
The relative error associated with each ANP rate was computed for N1, range of values based on the modified
MNF method is assessed (Amoatey et al. 2014, 2018).
2.2. Method
2.2.1. Customer night use (QCNU) and leakage
García et al. (2006) determined uncertainties associated with the MNF reference hour and leakage exponent N1
on the estimated leakage using the relative error method. Negharchi & Shafaghat (2020) agree that some errors
may be associated with the volume of leakage estimated due to initial assumptions and recommends that QCNU
and N1 be established for network-specific uses. The method is used in this study to determine the error associ-
ated with assuming an ANP rate if the actual is lower or higher. In essence, how leakage is being under or
overestimated if an assumed ANP is respectively lower or higher than the actual. The MNF procedure used in
this study is described by Equations (2) and (3) (Amoatey et al. 2014, 2018) which is modified after Equation (1)
(García et al. 2006; Cheung et al. 2010). The modification was necessary because most customers in the Baifikrom
network do not use toilet flushing systems and therefore do not use the same amount of water during the minimum
night period (12:00–4:00 am).
QL ¼ QDMA QCNU (1)
where,
QL¼ leakage rate [m3/h];
QDMA¼ flow rate into a District Metered Area [m3/h]; and
QCNU¼ customer night use [m3/h].
QL is the total leakage rate for the network, which is not evenly distributed during the day due to pressure vari-
ation. QL is therefore distributed throughout the day using the HDF (Equation (2)).
VL ¼ QL  HDF (2)aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022where,
VL¼ average daily leakage rate [m3/h];
QL¼ leakage rate [m3/h]; and
HDF¼ hour-day factor [-].
For each category, QCNU was computed by summing up the product of the assumed ANP by typical consump-
tion volumes per typical night use (flushing toilets, washing of hands). The results and how it relates to similar
studies have been discussed extensively in Amoatey et al. (2014). Therefore, the influence of ANP rate in
QCNU and how it affects the amount of leakage cannot be overlooked.
QL ¼ QDMA  (QCNUWC þQCNU (3)NonWC )
where,
Q 3CNUWC ¼ night use for customers who use WC [m /h];
QCNUNonWC ¼ night use for customers who do not use WC [m3/h].
Just as ANP rates influence QCNU , HDF is also related to the N1 and is given by Equations (4) and (5). It shows
how flow rates through existing leaks change from Q0 to Q1, as pressure changes from P0 to P1 at a rate of the
leakage exponent N1 (Lambert 2001; Al-Washali et al. 2019). Thus, this study is also investigating how changes in
N1 steps influence the amount of leakage.

 
Q N11 ¼ P1 (4)
Q0 P0
where,
Q0¼ flow rate in association with P0 pressure;
Q1¼ flow rate in association with P1 pressure; and
N1¼ leakage exponent.
X24 
 P N1
HDF ¼ i (5)
P
i¼0 MNF hour
where,
Pi is the average pressure in one observed point for each i time [m];
PMNF hour is the average pressure during minimum night hour [m]; and
N1 is the leakage exponent [].
2.2.2. Relative error analysis
After estimating the amount of leakage for each ANP rate and each N1 step, relative to an assumed ANP rate and N1
step respectively, it was necessary to determine how incorrect a quantity is from a number considered to be true (Centre
for Teaching & Learning 2015). It is estimated as the ratio of the difference between the amount of leakage estimated
with a range of ANPs (QL (ANP )) and that estimated using an assumed rate of ANP to leakage estimated with ani
assumed ANP rate expressed in Equation (6) as follows (García et al. 2006; Centre for Teaching & Learning 2015):
Relative error e(%) ¼ QL(assumed rate of ANP)QL (ANPi) (6)
QL(assumed rate of ANP)
where,
1%  i  6%;
QL(assumed rate of ANP) ¼ leakage estimated at an assumed rate of ANP at each step; and
QL (ANP 16%) ¼ leakage estimated at each ANP value.
This enables water utilities to see howmuchANPandN1 contribute to the volume of leakage. Therefore, in this study,
leakagewas estimated for a1–6%rangeofANPand foreachN1step in the range, as indicated earlier.As indicated earlier,aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022the rangeofANPvalues considered, testing the uncertaintyof in the range appears realistic forwater networks around the
world(Farley2001;Fantozzi&Lambert2012).ThesensitivityofANPforeachN1value in therangeconsideredwasdeter-
mined by assuming a rate of 3%. The absolute error for the volume of leakage estimated determined for each ANP rate is
compared with that of the assumed rate (Reuter & Liebsche 2008; Saltelli et al. 2008).
Ikonen (2016) proposed a one-factor-at-a-time (OAT) method, which determines the change in model output
values that results from modest changes in model input values. However, since both ANP and N1 are necessary
at the same time in the MNF method, both parameters interact to affect the precision of the amount of leakage
estimated. In such a case, Loucks & Van Beek (2005) proposed a multivariate linear analysis to evaluate the
approximate impact. This approach, however, requires a definition of the probability distributions of the par-
ameter sets (N1 and ANP) which is difficult to establish in this study.
2.3. Limitations of the study
The challenge of finding other methods which could be confirmatory and more robust can be identified as a limit-
ation of this study. The authors will consider some mathematical theorems and assumption that could explain such
problems if the future. Many studies have been conducted on factors that influence accurate estimate of apparent
losses (Thornton & Rizzo 2002; Tabesh & Asadiani Yekta 2005; Rizzo & Cilia 2005; Arregui et al. 2006; Tsitsifli &
Kanakoudis 2010) but for real losses, only García et al. (2006) and Negharchi & Shafaghat (2020) have studied
some leak estimation parameters, the later however, used actual measurements and no uncertainty analysis in
particular.
3. RESULTS AND DISCUSSION
The results presented in Table 1 below have 3 parts as indicated by the solid lines, long dashes and short broken
lines. The first part indicates the computation of QCNU per capita and for the entire population in the network for
the two categories of night users – toilet flushing and non-toilet flushing customers. Following the procedure
described earlier, QCNU for toilet flushing customers was found to range between 0.16 L/h and 0.71 L/h, whereas
non-toilet flushing customers ranged between 0.03 L/h and 0.08 L/h respectively for ANP of 1%–6%. The per
capita QCNU obtained was reported and discussed in Amoatey et al. (2014) study in comparison with similar
rates from Uganda Mutikanga et al. (2010); and ASEAN region (Fantozzi & Lambert 2012).
The QCNU for the population per category was then computed and summed up, and the total QCNU for 3% ANP
was found to be 9,845.4 L/h. QCNU estimates obtained were compared with a similar study in Kampala, Uganda
and found to be realistic (Amoatey et al. 2014, 2018). These were subsequently used together with the measured
night leakage and HDF to determine the leakage volume. The total daily leakage indicated by the region with
long dashes was computed for each ANP over a range of five N1 with corresponding HDF values.
Leakage volume for Baifikrom network for N1 of 2.4 which translates into an HDF of 20 was found to be
663,401 L/day at 3% ANP (shown by the circled value). The third region (indicated by the short dashes), contains
the percent leakage relative to the amount supplied for each N1 (with corresponding HDF) over 1–6% ANP. The
percent leakage for each ANP for the expected theoretical N1 ¼ 1:0 is between 9-14% and for the field-deter-
mined N1 ¼ 2:4, leakage ranges between 8 and 13% of the supplied volume (see Table 1). Therefore, for an
ANP of 3%, and N1 of 1.0, leakage is 12.4%, which indicates that leakage in the Baifikrom network is relatively
lower in comparison with total leakage. The differences in leakage obtained per ANP rate reveal the importance
of establishing actual rates for every network.
Considering that water loss for the entire study network is about 50%, the amount of leakage estimated appears
to be small (Amoatey et al. 2018) even though similar in comparison with Al-Washali et al. (2019) findings for
Zarqa (Jordan) and Mwanza (Tanzania) with average leakage of 15 and 11% respectively as against 66 and
46% NRW. It can therefore be seen that apparent losses are about three times higher than physical losses similar
to other reports from Asia and Africa (Lievers & Barendregt 2009; Mutikanga et al. 2010).
Again, from Table 1, the relative error associated with the volume of leakage estimated for the range of ANP
and N1 values using 3% and 1.5 as the nominal values respectively is indicated by the long dash double dot area.
It can be seen that a 1% higher or lower ANP results in an 8% under-or overestimation of leakage. This implies
that if AMR reveals that the actual ANP for the case study network is 2% instead of the 3% assumed nominal, the
amount of leakage overestimated by 8% of the assumed nominal of 12%.
Although the Negharchi & Shafaghat (2020) did not investigate active night population in particular, the
authors found that changing the measured legitimate night consumption (QCNU) by one step alters the calculatedaponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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Table 1 | Leakage estimation for Baifikrom water network
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on 09 May 2022leakage by 14%. Again, because the authors were also interested in the influence of private water tanks on QCNU ,
the results were 14 times higher than the 1.7 litre/connection/hr recommended in the UK Water Industry (1994)
report. In a summary of different customer night consumption values presented in Amoatey et al. (2014), it can be
realized that studies in Ottawa, Canada, Malaysia were also higher than 1.7 lit/connection/hr. Again, though the
premise of the Negharchi & Shafaghat (2020) study is not directly comparable with this study, it buttresses the
fact that every water network is characteristic, and therefore cannot adapt parameters established elsewhere.
Similarly, the relative error associated with N1 of 1.5 as the nominal leakage exponent results in a maximum of
4% over or underestimation for a 0.5 lower or higher step respectively. It can be realized that there is an increas-
ing linear relationship between a relative error of ANP and N1 irrespective of the assumed rate confirming the
findings of García et al. (2006) for N1. With actual measurements, Negharchi & Shafaghat (2020) found that
a 0.1 change in N1 results in a 1% change in leakage. Comparing the results of this study with the Negharchi
& Shafaghat (2020) work, the results are similar, in that, since a linear relationship is linear relationship exist
between N1, and leakage in this study, it can be inferred that a 0.1 step N1 results in a 0.8% leakage which is
approximately 1%. The García et al. (2006) study however, reports a 10 times greater error for a +10%
change in N1 than N1 ¼ 1:0 which is higher and probably more sensitive than this and the Negharchi & Shafa-
ghat (2020) study. This supports the fact that networks differ and respond differently depending on the type of
leak(s) predominant within the network.aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf
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on 09 May 2022With the arguments above, it can be seen that the accuracy of both parameters is crucial for quantifying leakage in
water networks and this shouldbeensuredbywater utilities. Accurately estimating leakagehas technical and research
implications in that water utilities around theworld are striving for efficiency in their services and in themanagement
of the utility. In view of this, water utilities calculate key performance indicators (KPI) and set targets for leakage
reduction and investment priorities. This makes the water utilities comparable with others around the world.
Again, since water loss is made up of leakage and apparent losses, the water utility can plan how to tackle
apparent losses while it reduces leakage. For this reason, over or underestimating leakage further affects leakage
reduction targets, and planning of maintenance investment priorities. Further research will consider a survey of
ANP in the Baifikrom study network will be conducted to reduce leakage estimation uncertainties.4. CONCLUSION
This paper investigated the relative error in leakage estimation using the minimum night flow method in the Bai-
fikrom water network where some parameters have not yet been established and localized. Changes in the
amount of leakage when a range of ANP rates for calculating QCNU and N1 values for estimating HDF was inves-
tigated. It was found that a linear relationship exists between the relative error of ANP and N1, although ANP is
more crucial. It is recommended that water utilities must establish localized ANP and N1 values for accurate
leakage estimation in water networks.DATA AVAILABILITY STATEMENT
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First received 8 June 2021; accepted in revised form 30 November 2021. Available online 13 December 2021aponline.com/wpt/article-pdf/17/1/14/990229/wpt0170014.pdf