Dynamic analysis of non-revenue water in district metered areas under varying water consumption conditions owing to COVID-19

Abstract

Increasing water demands and high water losses have rendered securing safe water challenging in the 21st century. Although non-revenue water (NRW), as a percentage of system input, has been commonly used by water utilities worldwide, in-depth analyses on the influence of water consumption fluctuation on NRW has never been conducted; instead, taking one-year average NRW volume has been recommended. Thus, this study analyzed the influence of water consumption fluctuation on NRW using the data of five district metered areas (DMAs) in Colombo City, Sri Lanka, and also by the network simulation analysis. The results showed that percentage and volumetric NRWs are strongly correlated with water consumption (r = 0.9373 and 0.9121, respectively) and with each other (r = 0.9977) due to pressure changes in water supply networks caused by water consumption fluctuation. Therefore, dynamic analysis of NRW by plotting DMA inflow and NRW against water consumption was conducted using the aforementioned DMA data and long-term (1956–2021) water consumption and NRW data in Tokyo. This method identified two factors influencing NRW: water consumption fluctuation and network leakage changes, and the results were verified; thus, it can be applied to NRW analysis even under the influence of high water consumption fluctuations.

Abbreviations

MA3

three-month moving average

ADB

Asian Development Bank

AWWA

American Water Works Association

BABE

Burst and Background Estimate

CARL:

Current Annual Real Loss

DMA

District Metered (or Metering) Area

GCWWMIIP

Greater Colombo Water and Wastewater Management Improvement Investment Program

ILI

Infrastructure Leakage Index

IWA

International Water Association

JICA

Japan International Cooperation Agency

MNF

Minimum Night Flow

NRW

Non-Revenue Water

NWSDB

National Water Supply and Drainage Board

UARL:

Unavoidable Real Loss

1. Introduction

Securing safe water is an important challenge in the 21st century [1]. Two-thirds of the global population live under conditions of severe water scarcity for at least 1 month of the year [2]. Owing to population increase and precipitation variability due to climate change, more than 27 % of the 482 largest cities in the world are predicted to have water demands that exceed the available surface water by 2050 [3]. High water losses are prevalent among many water utilities, especially in developing countries [4]. In 2019, the global non-revenue water (NRW) was estimated to be 346 million m³/d, which equals 125 billion m³/y, causing a financial loss of $39 billion (USD) per year [5]. NRW comprises two components, unbilled authorized consumption and water losses, which are further divided into apparent loss (commercial losses including metering inaccuracies, unauthorized consumption, and data handing errors) and real loss (physical losses or leakages) (table S1) [6]. Since the introduction of NRW in 2000, many water utilities have applied the IWA/AWWA water balance to estimate their NRW [4,7,8]. Reducing NRW has been challenging because its drivers, such as population and network length, are beyond the control of water utilities [9], rendering NRW highly variable.

Although many studies reported high fluctuations of NRW [4,7,10,11], no logical reasoning has been provided, possibly because most researchers focused on filling the IWA/AWWA water balance table [11]. Güngör-Demirci and Lee [12] applied the fixed effects panel regression model to understand the impacts of independent variables on NRW; however, they did not evaluate the influence of water consumption. To alleviate NRW fluctuation, taking 1-year averages was recommended [7]. However, taking long-term NRW averages might eclipse the influence of water consumption fluctuations on NRW. Under such circumstances, setting a target value for NRW reduction, such as 23 % [13], might not be reasonable.

Apart from NRW, the IWA Task Force on Water Loss Control proposed the infrastructure leakage index (ILI) to assess the leakage levels of water supply systems [14]. The ILI is the ratio of current annual real losses (CARL) to unavoidable real loss (UARL) estimated by the equation proposed by the IWA Task Force. Using ILI, a physical loss assessment matrix was proposed to categorize water loss levels for developed and developing countries [[15], [16], [17]].

There are also other methods to estimate water loss, such as modified minimum night flow (MNF) and component analysis, which include the Burst and Background Estimate (BABE) methods [18,19]. While Serafeim et al. [20] reported that estimated water losses by the MNF and BABE methods converge when rigorous statistical analysis is performed, MNF requires intensive field work, and the estimated night consumption are rarely accurate [18].

Recently, Cavazzini et al. [21] proposed the Leakage Performance Index, which ranks the nodes in the network based on pressure and flow rate data to minimize leakages by pressure control. Moslehi et al. [22] presented the Short-Run Economic Level of Leakage with respect to active leakage control activities. Although these indicators can be used with NRW, they cannot replace it. In 2019, the AWWA announced that they cannot recommend percentage NRW due to high fluctuation and instead proposed NRW volume per service connection as a key performance indicator [23,24].

Colombo City, the capital of Sri Lanka, had an annual average NRW of 40 % in 2020 [25], which was higher than the average NRW of 35 % in 44 developing counties [26]. Thus, the Asian Development Bank (ADB) funded the Greater Colombo Water and Wastewater Management Improvement Investment Program (GCWWMIIP) in 2013 to reduce NRW below 18 % by 2020 [27]. GCWWMIIP included creating district metered areas (DMAs), replacing old and leaking pipes, installing valves, flow meters, and pressure gauges [28]. The NRW in DMA-1 varied from 6 to 30 % between 2017 and 2018, rendering it difficult to find a representative NRW value [29]. Hence, understanding the cause of unsuccessful NRW reduction in Colombo City is essential.

Although NRW has been used as an indicator of water losses, in-depth analysis has not been conducted yet to identify the relationship between water consumption and NRW. Therefore, this study aimed to (1) analyze the relationship between percentage and volumetric NRWs and water consumption; (2) examine the influence of water consumption, leakages, and pipe replacement on the ILI; and (3) propose a dynamic analysis method of NRW fluctuations as a function of billed water consumption to discern the influence of fluctuating water consumption on the reduction or increase of potential NRW levels. This study makes a novel contribution to the literature by quantitatively analyzing the influence of water consumption fluctuation on percentage and volumetric NRW. To verify the dynamic analysis method, the DMA inflow, water consumption, and NRW datasets in the five newly commissioned DMAs in Colombo City, Sri Lanka, were obtained during the period influenced by COVID-19, when water consumption varied extensively [30,31].

2. Materials and methods

Fig. 1 shows the flow chart of this study. The data source and analysis methods are described below.

Fig. 1.

Research flow chart.

2.1. Study area

As of 2019, the population of Colombo City in Sri Lanka was 2.45 million [32] and had a piped water coverage of 99.6 % [33]. The governmental water utility (National Water Supply and Drainage Board, NWSDB) supplies water to urban areas including Colombo City. It has attempted to reduce NRW in Colombo City by implementing projects such as GCWWMIIP and Enhancement of Operational Efficiency and Asset Management Capacity of Regional Support Center-Western South Region of NWSDB [25,34].

Four NRW reduction packages have been conducted under the GCWWMIIP. Five DMAs in Package 1 (Fig. 2), i.e., DMA-1, DMA-2A, DMA-2B, DMA-3, and DMA-4A, were selected in this study (Table 1); DMA-3 was the smallest DMA, with 728 and 756 connections and pipe length of 4613 and 3836 m before and after DMA completion, respectively. Other DMAs had 1200–3500 connections and pipe lengths of 4700–20000 m. The service connections increased in DMA-1, DMA-2B, and DMA-3 by 3.8–9.2 % and decreased by 2.1 % and 60.0 % in DMA-2A and DMA-4A, respectively, due to a large development and relocation program. In all DMAs, the pipe length decreased by an average of 10.5 % after construction. However, the changes in the pipe length highly varied among the DMAs, from 51.3 % decrease in DMA-4A to 11.4 % increase in DMA-2A.

Fig. 2.

Location map of the five district metered areas (DMA) in the Package 1 area for the study in Colombo City, Sri Lanka. Map is from the 2021 data of the Greater Colombo Water and Wastewater Management Improvement Investment Program. The numbers in black and purple are pipe lengths in 2018 (before the commencement of DMA construction) and January 2021 (in the intermediate stage), respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Table 1.

Attributes of the five district metered areas (DMA).

DMA	Connections		Pipe length			Commissioned in3)	Data period
	Number1) before/after	Change (%)	Before/after1) (m)	DMA2) design (m)	Change (%)		From – To	months
DMA-1	2347	4.8 %	11272	10909	−18.9 %	October 2019	August 2019–April 2022	33
	2460		9141
DMA-2A	3293	−2.1 %	20311	18678	−11.4 %	July 2020	November 2019 –April 2022	31
	3225		17992
DMA-2B	3188	9.2 %	16462	12635	22.0 %	October 2019	August 2019–April 2022	33
	3482		20079
DMA-3	728	3.8 %	4613	5167	−16.8 %	October 2018	January 2019 –April 2022	40
	756		3836
DMA-4A	3166	−60.0 %	9610	9010	−51.3 %	July 2020	January 2019 –April 2022	40
	1266		4678
Total	13071	−12.0 %	62268	56399	−10.5 %			175
	10888		55726

Note: 1) Upper and lower rows denote before and after DMA construction, respectively. 2) Pipe length during the design stage of DMAs, which differed from after DMA construction. 3) “Commissioned in” refers to the DMA handover to the water utility after isolation and testing.

2.2. Data analyses

The net inflow (hereafter inflow), namely inflow minus outflow, and billed water consumption (hereafter billed consumption) of the five DMAs were obtained for 31–40 months between 2019 and 2022 (Table 1). The NRW was calculated by subtracting the billed consumption from the inflow and plotted as a monthly time-series data together with the inflow and the billed consumption. However, monthly billed water consumption inherently included meter-reading errors; the errors were higher in the months when meter readers entered the estimated water consumption due to COVID-19 lockdown. Those meter-reading errors were rectified when the meter readers visited the customers’ homes to read meters in the following months. Thus, to alleviate fluctuation of the monthly data, 3-month moving averages (MA3) of inflow, billed consumption, and NRW were also plotted as time-series data.

The percentage NRW is a ratio indicator calculated by the following equation (Eq. 1):

$$\text{NRW}(\%)=\frac{volumetricNRW}{inflow}\times 100=\frac{volumetricNRW}{billedconsumption+volumetricNRW}\times 100$$ (1)

To determine the influence of water consumption fluctuation on percentage and volumetric NRWs, their correlation with billed water consumption were analyzed by linear regression analysis of NRWs plotted against billed water consumption. After confirming the absence of outliers and the normality of the data by Shapiro-Wilk test (the null hypothesis H₀: the population is normally distributed) at a significance level of 5 %, the Pearson correlation coefficients (r) were calculated using R v.4.2.2 [35]. The coefficient of variation (CV) was calculated to compare the variation of the number of customer connections, water inflow to the distribution networks, billed water consumption, and NRW.

2.3. Dynamic analysis using normalized plot

Subsequently, the relationship of inflow and NRW with billed consumption was analyzed graphically (Fig. 3). The NRW volume decreases when water consumption increases because of greater head loss at high flow rates, assuming that apparent loss is a minor fraction of NRW; contrarily, NRW volume increases with decreased billed consumption (Fig. 3). When the inflow line in Fig. 3 is extended to the larger inflow, it will eventually meet the hypothetical line of zero water loss. To compare different DMAs, we drew normalized plots using the inflow and billed consumption data divided by the values at the above-mentioned meeting points with zero-water-loss lines. The slopes of the inflow lines in the DMAs represent the tendencies of inflow and NRW changes to the fluctuation of billed consumption; thus, from the slopes of DMAs, we can compare water loss characteristics. Namely, the larger the slope of inflow, the smaller the NRW, and vice versa. This dynamic analysis method was verified using the data of the aforementioned five DMAs. It was also applied to the data on water consumption, supply volume, and NRW obtained for 65 years (1956–2021) in Tokyo, Japan, to demonstrate its applicability to long-term data.

Fig. 3.

Schematic illustration of inflow, non-revenue water (NRW), and billed consumption of a district metered area (DMA).

2.4. Network simulation

Fig. 4 shows the network model of DMA-1 for the EPANET simulation [36]. Water enters the DMA-1 inlet (the large violet circle) by gravity flow from the elevated water reservoir, and then distributed via ductile iron (DI) or high-density polyethylene (HDPE) pipes. The simulation conditions are listed in Table 2. The node demand was varied at five levels between the minimum and maximum water consumption (16.26–23.64 m³/d) reported in August 2019–April 2022 (Table 1). The water demand was allocated equally to all the nodes, and the emitter coefficient (EC) was assigned to all the nodes at three levels, 0.5, 1.0, and 1.5, to compare the effect of water loss changes on NRW and inflow volume.

Fig. 4.

EPANET simulation model for DMA-1, the area surrounded by the yellow color lines. Violet, green, and black lines show the locations of the 250 mm ductile iron pipes, 250 mm HDPE pipe, and 90 and 62 mm HDPE pipes, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Table 2.

EPANET simulation model for DMA-1.

Parameter	Value
Distribution mains	ductile iron pipe, nominal diameter 250 mm HDPE pipe, nominal diameter 160 mm length 1325 m
Branch pipe	HDPE pipes, nominal diameters 90 mm or 63 mm length 5323 m
Number of pipes	148
Hazen Williams C	100 for DI pipes and 140 for the HDPE pipes
Ground levels	7 m at the DMA inlet, 5–9 m at the junctions
Water head at the inlet	Varied at five levels between 22 m and 32 m
Number of nodes (junctions)	121
Node demand (base demand)	Varied at five levels in 16.26–23.64 m3/d The total demand was allocated equally to all nodes.
Emitter coefficient	Simulated at three levels: 0.5, 1.0, and 1.5 Assigned to all nodes.

Note: The EPANET model is based on the DMA design map; hence, the total pipe length of the model (6648 m) was shorter than the final pipe length of DMA-1 (9141 m).

2.5. UARL and ILI

ILI is defined by the ratio of CARL to UARL that is characterized by:

$$\text{UARL}=\left(18\times L_m+0.80\times N_c+25\times L_p\right)\times P$$ (2)

where,

L_m = mains length (km)

Nc = number of service connection (No.)

Lp = total length of underground pipe between the edge of the street and customer meters (m), and.

P = pressure (m).

The mains lengths and the numbers of service connection were obtained from the National Water Supply and Drainage Board of Sri Lanka for the five DMAs and from the Tokyo Metropolitan Waterworks Bureau. The Lp of the DMAs in Colombo and Tokyo were assumed to be 2.0 and 1.5 m, respectively. Based on monitoring data, the average network pressure was assumed to be 20 and 30 m for Colombo and Tokyo, respectively.

3. Results and discussion

3.1. Monthly and MA3 data of inflow, billed consumption, and NRW

Fig. 5a shows the time-series of monthly inflow, billed consumption, and NRW, in volume and percentage, of DMA-1. These monthly data varied extensively, especially with the sudden water consumption increases and NRW drops in May 2020 and February 2021 due to the COVID-19 lockdowns. Meter readers overestimated billed water consumptions because they were not allowed to visit customers’ homes, which became greater than the inflow into DMA-1. Thus, both percentage and volumetric NRWs were negative in May 2020 and February 2021. During the 33-month data period, percentage NRW varied from −14.3 % to 29.0 %, while NRW per connection varied from −4.46 to 8.67 m³/connection/month. These high variations render it difficult to select representative NRW values to be compared with the target NRW of 18 %. Similar problems of overestimation of billed consumption occurred in other DMAs as well (Fig. 1, fig. S1).

Fig. 5.

Inflow, billed consumption, and non-revenue water (NRW) in DMA-1 for (a) monthly data and (b) 3-month moving average (MA3). Data period is 33 months from August 2019 to April 2022.

To reduce the influence of meter reading errors, MA3 averages of inflow, consumption, and NRW were plotted (Fig. 5b). Although the sharp peaks and bottoms of the monthly plot were smoothed, inflow, consumption, and NRW still varied due to water consumption fluctuations caused by COVID-19 [31].

To examine the variation of NRW and other parameters, coefficients of variation (CV) were calculated (Table 3). The number of connections varied slightly with CVs at 1.3–2.8 % except for DMA-4A (27.8 %), where residents were relocated owing to redevelopment. We used Wilcoxon rank-sum test (H_0: There is no difference in the distributions of two populations.) to compare the CV values of inflow and water consumption because they did not follow the normal distribution. The inflow CV (4.6–10.4 %) was significantly smaller than consumption CV (11.9–41.1 %) (Wilcoxon rank-sum test, p < 0.05), indicating that, despite water consumption variations, the inflow did not vary as much, similar to reports in Zimbabwe [7]. This may be due to two possible reasons: water consumption overestimation and NRW reduction by increased water consumption. If the billed water consumption was overestimated, the inflow did not increase as much as the water consumption.

Table 3.

Coefficients of variation (CV) for connection, inflow, water consumption and non-revenue water (NRW) in five district metered areas (DMA).

Data	Parameter	DMA-1	DMA-2A	DMA-2B	DMA-3	DMA-4A
Monthly data	Connection	1.3 %	1.7 %	2.8 %	1.4 %	27.8 %
	Inflow	4.6 %	4.6 %	6.6 %	6.8 %	10.4 %
	Consumption	11.9 %	11.7 %	12.5 %	41.1 %	13.6 %
Monthly NRW	NRW (m3)	65.6 %	105.8 %	158.9 %	95.7 %	47.4 %
	NRW (%)	63.8 %	106.4 %	160.0 %	97.4 %	43.4 %
	NRW (m3/conn.)	65.9 %	105.5 %	161.2 %	95.5 %	61.8 %
moving average (MA3) NRW	NRW (m3)	38.1 %	76.9 %	66.6 %	58.9 %	31.0 %
	NRW (%)	38.3 %	77.3 %	66.4 %	57.0 %	28.3 %
	NRW (m3/conn.)	38.6 %	76.8 %	67.3 %	59.3 %	48.9 %

Note: Data periods are August 2019–April 2022 for DMA-1 and DMA-2B, November 2019–April 2022 for DMA-2A, and June 2019–April 2022 for DMA-3 and DMA-4A.

Although the CVs varied extensively among the five DMAs, the CVs of percentage and volumetric NRW were similar in each DMA for both monthly and MA3 data, indicating that despite selecting volumetric NRW per connection as an indicator, NRW fluctuates when water consumption fluctuation is unavoidable.

3.2. Comparison of yearly averages of inflow, billed consumption, and NRW

The high variations of percentage and volumetric NRW rendered the use of NRW indicators challenging. Use of 1-year average NRW values was recommended to alleviate NRW fluctuation [37]; thus, 1-year averages of inflow, consumption, and NRW were compared between 2020 and 2021 for the five DMAs (Table 4). The variations of inflow from 2020 to 2021 were small, at 6.9 % in DMA-4A and −4.5 % in DMA-3. The billed consumption changed more than the changes of the inflow, at 10.2 % in DMA-1 and −5.3 % in DMA-4A. The changes of percentage and volumetric NRWs (−48.9 to 36.8 % and −50.1 to 44.7 %, respectively) were significantly greater than those of inflow and billed consumptions. These results indicate that small fluctuations in water consumption magnified the fluctuation of both percentage and volumetric NRWs at nearly identical magnitudes. Thus, even with the use of volumetric NRW as an indicator, high NRW fluctuations cannot be avoided in cases of extensive water consumption fluctuations. fig. S2 shows the monthly variation of inflow and water consumption in DMA-1; higher water consumption was recorded in 2021–2022 than in 2019–2020, while the variation of inflow was moderate.

Table 4.

Comparison of yearly averages for inflow, billed consumption, non-revenue water (NRW) percentages and NRW per connection between 2020 and 2021 in five district metered areas (DMA).

DMA	Inflow			Billed consumption			NRW (%)				NRW per connection
	2020	2021	Change (%)	2020	2021	Change (%)	2020	2021	Difference	Change (%)	2020	2021	Difference	Change (%)
1	69784	69522	−0.4 %	56248	61971	10.2 %	19.5 %	10.7 %	−8.9 %	−45.4 %	5.62	3.09	−2.53	−45.0 %
2A	86546	89171	3.0 %	78327	81593	4.2 %	9.5 %	8.2 %	−1.3 %	−14.0 %	2.46	2.22	−0.24	−9.9 %
2B	78668	80324	2.1 %	70495	74646	5.9 %	10.4 %	6.9 %	−3.5 %	−33.4 %	2.45	1.65	−0.80	−32.8 %
3	24746	23632	−4.5 %	21963	22228	1.2 %	11.1 %	5.7 %	−5.4 %	−48.9 %	3.74	1.87	−1.88	−50.1 %
4A	70100	74918	6.9 %	52814	50029	−5.3 %	24.1 %	32.9 %	8.9 %	36.8 %	5.49	7.95	2.46	44.7 %
Average	65969	67513	1.4 %	55969	58093	3.2 %	14.9 %	12.9 %	−2.1 %	−21.0 %	3.95	3.35	−0.60	−18.6 %

Note: DMA commission months were October 2019, July 2020, October 2019, October 2018, and July 2019 for DMA-1, DMA-2A, DMA-2B, DMA-3, and DMA-4A, respectively.

3.3. Influence of billed consumption on volumetric and percentage NRW

As per the recommendation by IWA and AWWA to use volumetric NRW per connection instead of percentage NRW, after checking the normality of these two NRW indicators (Shapiro-Wilk test: p = 0.125 and p = 0.151, respectively) and billed water consumption (Shapiro-Wilk test: p = 0.246), they were compared and the results are presented in Fig. 6a and b. Both percentage and volumetric NRW per connection were inversely correlated with billed water consumption (Fig. 6a). As the water consumption increased, water pressure in the pipe networks decreased due to greater head loss at high flow rates resulting in lower water loss in the distribution networks (Fig. 3). The water losses decreased both percentage and volumetric NRWs because they were strongly correlated (Fig. 6b). The results for other DMAs (Fig. 2) are shown in fig. S3. Although previous studies reported that distribution pipe length, number and length of service connections, and pressure influence NRW [14,23,24,38], the influence of water consumption fluctuation on NRW fluctuation has not been elucidated [23]. Thus, this study delineated, for the first time, the quantitative influence of water consumption fluctuation on percentage and volumetric NRW.

Fig. 6.

Correlation between (a) non-revenue water (NRW) percentages and NRW per connection with billed water consumption of 3-month moving average (MA3) data in DMA-1 and (b) NRW percentages and NRW per connection of MA3 data in DMA-1. Data period is 31 months from September 2019 to March 2022.

3.4. Distribution network simulation

Fig. 7a shows the influence of water consumption variation on the inflow, pressure, and percentage and volumetric NRWs. In the simulation, we used water consumption instead of billed consumption because no billing process was considered and NRW was equal to real water loss assuming no apparent losses. When the water consumption increased, the inflow also increased linearly with a slope of 0.876, which verified the model presented in Fig. 3 and the data presented in Fig. 6a. However, both percentage and volumetric NRWs decreased with increasing water consumption because of decreasing water pressure due to the head loss at higher flow rates. Pressure loss solely depended on the inflow, not on the inlet pressure (Fig. S4). These results indicate the challenge in finding representative values of percentage and/or volumetric NRWs in DMAs under fluctuating water consumption.

Fig. 7.

EPANET simulation results of DMA-1. Correlation between (a) inflow, non-revenue water (NRW) percentage, NRW per connection, and pressure in the network with water consumption (BPD 90 mm, EC 1.0, IP 25 m), (b) inflow and NRW percentage against water consumption at different emitter coefficients (BPD 90 mm, IP 25 m, EC 0.5, 1.0. 1.5), (c) inflow and NRW per connection against water consumption at different emitter coefficients (BPD 90 mm, IP 25 m, EC 0.5, 1.0. 1.5), and (d) NRW percentage and NRW per connection at different emitter coefficients (IP 15–25 m, EC 0.5, 1.0. 1.5). BPD: branch pipe diameter; EC: emitter coefficient; IP: DMA inlet pressure.

Although EC 1.0 provided NRW and inflow data close to the actual data, the EC was varied to show the influence on inflow and NRW. Fig. 7b presents inflow and percentage NRW at different EC of 0.5, 1.0, and 1.5. The inflow shifted upwards with increasing EC, while maintaining a linear relationship with water consumption. The NRW percentages also upsifted with increasing EC. These results indicate that the status of water supply networks under fluctuating water consumption can be assessed by comparing the regression lines of inflow and/or NRW with water consumption by drawing a graph similar to that in Fig. 7b.

Fig. 7c shows that the volumetric NRW also shift with changes in EC, similar to the percentage NRW (Fig. 7b); thus, the use of volumetric NRW per connection does not eliminate the influence of fluctuating water consumption. The percentage and volumetric NRWs were closely correlated (Fig. 7d), as shown in fig. 6b and S3. Therefore, the inability to obtain representative values of percentage and/or volumetric NRWs in distribution networks under fluctuating water consumption was also verified by the network simulation. Thus, it is necessary to find an alternative method to analyze NRW under fluctuating water consumption.

3.5. UARL and ILI

Table 5 shows the UARL and ILI values for the five DMAs in Colombo City and Tokyo. In the five DMAs, UARL (L/d) depended on the scale of the distribution networks and the numbers of service connections (Table 1); thus, the UARLs in DMA-2A and DMA-2B were large and that in DMA-3 was the smallest. However, UARLs per connection were similar in all DMAs, averaging 17.8 (min.–max.: 17.4–19.7) L/conn./d and 17.9 (17.7–19.1) L/conn./d before and after the DMA construction, respectively. UARL per connection in DMA-3 was slightly higher than that in other DMAs because of the smaller number of connections per pipe length than other DMAs (Table 1).

Table 5.

Unavoidable real loss (UARL) and Infrastructure leakage index (ILI) in district metered areas (DMA).

DMA	Before DMA construction			After DMA construction			Difference before and after
	UARL1)		ILI	UARL		ILI	UARL		ILI
	L/d	L/conn/d	(−)	L/d	L/conn/d	(−)	L/d	L/conn/d	change %
DMA-1	42,610	18.2	7.04	43,651	17.7	7.95	2.4 %	−2.26 %	12.9 %
DMA-2A	61,000	18.5	4.42	59,077	18.3	4.99	−3.2 %	−1.11 %	12.9 %
DMA-2B	57,934	18.2	0.90	63,940	18.4	3.06	10.4 %	1.05 %	239.6 %
DMA-3	14,309	19.7	13.24	14,477	19.1	5.94	1.2 %	−2.57 %	−55.1 %
DMA-4A	55,116	17.4	6.09	22,940	18.1	28.16	−58.4 %	4.09 %	362.4 %
All DMAs	226,968	17.8	5.05	200,085	17.9	7.84	−11.8 %	0.23 %	55.2 %
Tokyo (1956, 2021)2)	26.5 million	27.2	24.07	202.0 million	25.9	0.72	662.0 %	−4.82 %	−97.0 %

Note: 1) Non-revenue water (NRW) was unknown in each DMA before their construction. Thus, it was assumed to be the same as the NRW after the DMA construction. 2) Water Statistics Book, Japan Water Works Association, 1956–2021. Tokyo Metropolitan Water Works Bureau.

The UARL decreased by 58.4 % in DMA-4A after the DMA construction because the number of connections and the pipe length decreased by 60.0 % and 51.3 %, respectively (Table 1), while UARL in DMA-2B increased because the number of connections increased by 9.2 % and extended pipe length by 22.0 % (Table 1). In other DMAs, the UARL was nearly identical before and after construction. However, the UARL per connection increased slightly by 4.09 % in DMA-4A.

The ILIs varied extensively among the five DMAs, with the smallest being in DMA-2B and the largest in DMA-3 and DMA-4B before and after the construction, respectively. The lowest ILI in DMA-2B was due to the possible underestimation of NRW at 2.0 % before the construction. Nevertheless, ILI in DMA-2B was the lowest at 3.06 with the reliable data after the DMA construction. Thus, the largest increase of ILI in DMA-2B (239.6 %) was due to underestimation of ILI before the DMA construction.

After the construction, the ILI in DMA-4A increased significantly by 362.4 % because of the decease of the UARL as mentioned above. The ILI in DMA-3 decreased from 13.24 to 5.94 by 55.1 % as an outcome of the NRW reduction because UARL did not change before and after the construction. However, ILIs in DMA-1 and DMA-2A increased only by 12.9 % before and after.

In all five DMAs, the UARL decreased by 11.8 %, which agrees with the reduction in the number of connections (12.0 %) and pipe length (10.5 %). However, the ILI increased by 55.2 % from 5.05 to 7.84, which resulted in uncertainty with respect to the use of ILI as an indicator of the NRW reduction projects. The two possible reasons for the increased ILI after the water loss reduction projects were: decreased UARL after DMA construction and non-representativeness of the estimated NRW owing to water consumption fluctuations. The UARL decreased only by 11.8 % after the DMA construction; hence, it cannot account for 55 % increase of ILI. It is likely that the estimated NRWs did not represent water losses in the DMAs.

In Tokyo, most of the distribution pipes, namely cast-iron and asbestos cement pipes, were replaced with ductile iron pipes and the distribution pipe length increased by 272 % in 65 years between 1956 and 2021; thus, the UARL in Tokyo increased from 26.5 million L/d to 202.0 million L/d by 662.0 %. However, UARL per connection decreased by 4.82 % owing to the increase in the number of connections by 543 % during the same period. Even though new ductile iron pipes resistant to corrosion were installed during this period, UARL did not reflect the pipe materials and structures; thus, the estimated values of UARL could be significantly greater than the actual “unavoidable” water loss with new pipes [39], which was verified by the lower ILI (0.72) of the present-day in Tokyo than unity; namely, in principle, ILI must be equal or greater than unity if the UARL is actually unavoidable water loss.

3.6. Time-series data of Tokyo

Fig. 8a shows the water supply volume, consumption and loss in Tokyo, Japan, between 1956 and 2021. The water consumption and supply volume increased from the 1950s to the 1970s. The water supply volume then reached a peak in 1978, 14 years before the water consumption reached the maximum in 1992. The water loss increased from 1956 to 1971, then eventually decreased. Between 1978 and 1992, although the water demand increased, the supply volume was almost stable because water loss had started to decrease. Between 1992 and 2012, the water supply volume, water demand, and water loss had decreased, eventually reaching stable levels.

Fig. 8.

Data time-series of Tokyo Metropolitanwater Works (1956–2021) on (a) water supply, consumption, water loss volumes, and water loss percentage, (b) unavoidable real loss (UARL), infrastructure leakage index (ILI), pipe length, and service connection. (c) water loss volume against ILI, and (d) water loss percentage against ILI. Data are from JWWA Water Statistics and Tokyo Metropolitan Waterworks.

During the whole period, the water loss percentage gradually decreased except for short periods of plateaus from 1975 to 1983 and 2014–2021. From 1956 to 1971, the water loss percentage decreased despite increased water loss volume because the increase in water demand was more than the loss of water. Then, after the period of nearly constant water loss from 1975 to 1983, the water loss percentage decreased steadily along water loss volume.

In Fig. 8b, UARL per connection and ILI are plotted for the same period as that in Fig. 8a. The UARL per connection had been almost constant for 65 years from 1956 to 2021, showing only a small decrease by 4.7 % from 27.2 L/conn./d in 1956 to 25.9 L/conn./d in 2021; these changes occurred despite the pipe replacements from cast iron and asbestos cement pipes to anti-seismic corrosion-proof ductile iron pipes with inside lining and outside polyethylene sleeve. This is because the UARL does not consider the pipe materials and age, and it only reflects the distribution pipe length, number of connections, length of service pipes, and water supply pressure.

Despite almost constant UARL per connection, ILI decreased since 1971, after the nearly constant period of 1956–1970; as ILI is the ratio of CARL to UARL, it decreased by decrease in CARL and increase in UARL during this period (Fig. 8a, Table 5). The effects of extending the pipe length and increasing the number of connections is especially noticeable between 1975 and 1983 (Fig. 8b), wherein ILI decreased significantly while the water loss, both in percentage and volume, did not (Fig. 8a).

As shown in Fig. 8c, the water loss volume increased while ILI barely varied in 1956–1969. This was because the UARL during this period increased along with the water loss volume owing to extended distribution pipe lengths and service connection number growths. From 1970 until 1982, contrary to the preceding period, ILI decreased significantly by 63 % mainly because of a large increase in UARL owing to rapid extension of pipe length and customer connections, while water loss decreased by only 22 %. Thus, ILI is highly influenced, not only by reductions of water losses but also by the changes of the pipe length and the number of service connections, especially during rapid developmental phases. After 1983, the water loss decreased along with the ILI because of small increases to pipe length and service connections. Although water loss percentage decreased slightly between 1956 and 1969 (Fig. 8d), the trends after 1970 remained the same as water loss volume presented in Fig. 8c.

Although ILI has been used to classify or compare water losses of utilities in different countries [[15], [16], [17]], the results of this study indicate that ILI does not represent water loss during rapid network extensions and pipe renovation periods because UARL increases with pipe lengths and connection numbers but does not consider the age and materials of pipe networks. The decreasing water loss volume while extending pipes and increasing the number of connections in Tokyo's 65-year history indicates the careful use of UARL and ILI as indicators to measure water loss in water supply networks.

3.7. Inflow and NRW against billed consumption in DMAs in Colombo and Tokyo

To verify the relationship between water consumption and inflow or NRW established by the network simulation (Fig. 7a and b), MA3 data of DMA-1 were plotted (Fig. 9a). As shown in Fig. 6, Fig. 7a–b, NRW was inversely correlated with billed consumption (r = −0.9373, p < 0.05), while inflow was positively correlated with water consumption (r = 0.5135, p < 0.05). It should be noted that the slope of the linear regression equation for inflow was 0.2178, significantly smaller than unity, which means that inflow increased only 0.2178 times the increase in billed water consumption because NRW decreased when water consumption increased as inflow is the sum of billed consumption and NRW.

Fig. 9.

Relationship of net-inflow and non-revenue water (NRW) against billed water consumption in (a) DMA-1 3-month moving average (MA3) data in Colombo, and (b) Tokyo Metropolitan Waterworks. Data period is 1964–2021.

The parameters of linear regression analysis for the five DMAs, as shown in Fig. 9a and fig. S5, are listed in Table 6. Although the linear regression for inflow in DMA-2A and DMA-4A were not significant (p > 0.05), the regression analyses of NRW was significant for all DMAs (p < 0.05). In addition, the correlation coefficients (r) were greater for the NRW than for the inflow. These results indicate that NRW is more sensitive to the fluctuation of billed consumption than is inflow.

Table 6.

Linear regression parameters of non-revenue water (NRW) and inflow with billed consumption.

X: billed consumption	Y: inflow	Y: NRW
DMA-1	y = 0.2178x + 56130 r = 0.5135, p = 3.128 × 10−3	y = −0.0012x + 84284 r = −0.9373, p = 8.300 × 10−15
DMA-2A	y = 0.0768x + 81337 r = 0.2368, p = 2.250 × 10−1	y = −0.0011x + 94.686 r = −0.9606, p = 5.634 × 10−16
DMA-2B	y = 0.2626x + 59545 r = 0.1651, p = 2.329 × 10−2	y = −0.0010x + 77.961 r = −0.8117, p = 3.010 × 10−8
DMA-3	y = 0.3849x + 16225 r = 0.3777, p = 1.937 × 10−2	y = −0.0027x + 70.390 r = −0.6253, p = 2.703 × 10−5
DMA-4A	y = 0.1082x + 66831 r = 0.1307, p = 4.343 × 10−1	y = −0.0013x + 95.055 r = 0.8236, p = 2.161 × 10−10

Fig. 9b shows the percentage NRW and inflow supply volume against billed water consumption in Tokyo for 65 years between 1956 and 2020. There are three distinctively different trends in both NRW and inflow: 1) from 1956 to 1971, NRW volume increased with increasing water consumption due to more leakages; thus, the slope for inflow was greater than unity at 1.27. However, the percentage NRW decreased because the increase in water consumption was more than that in NRW volume. 2) From 1972 to 1992, similar to the DMA-1 in Colombo City, NRW decreased with increasing water consumption, while inflow increased with water consumption with the slope of the regression line at 0.32, which is less than unity. 3) Since 1993, although water consumption has been steady, both inflow and NRW plummeted.

These different trends during the three periods indicated that the dynamic analysis method presented in Fig. 9b can aid in the segregation of the influence of increases in water consumption and pipe replacement on the total reduction of NRW. The larger slope of inflow than the unity between 1956 and 1971 indicated increasing NRW volume despite increasing water consumption; NRW then decreased with increasing water consumption until 1992, which was the same as those of Colombo City. After 1993, NRW plummeted to a steady water consumption, clearly indicating the successful outcome of water loss reduction projects in Tokyo.

3.8. Normalized plot for inflow and NRW against billed consumption

Normalized plots of inflow and NRW percentage against billed consumption are illustrated in Fig. 10a and b, respectively, following the methods written in Section 2.3. The slope and intercept values of the linear regression lines (Table 6) of MA3 data for each DMA were used to build the normalized plots. The range between the symbols, such as circles and triangles, indicate the ranges wherein the water consumption, inflow, and NRW varied in the DMAs.

Fig. 10.

Normalized plot of (a) billed consumption and inflow and (b) billed consumption and non-revenue water (NRW). 3-month moving average (MA3) for district metered areas (DMA) in Colombo City and Tokyo 1972–1992 and 1993–2021. The interval between symbols indicates the data range for each DMA.

The normalized plots shown in Fig. 10a and b enable comparison of the differences in NRWs among the DMAs, as well as among different cities, even if their water inflow and billed consumption are significantly different. Thus, the normalized plots are useful for benchmarking different cities and/or comparing the NRWs of different years of a city where water demand has increased significantly. Graphically in Fig. 10a, the greater the slopes, the smaller the NRWs, because the regression lines approach the line of zero water loss (Fig. 2). In Fig. 10b, the smaller the absolute values of the slopes, the smaller the NRW. Thus, DMA-3 showed the best performance in NRW reduction, followed by DMA-2B and DMA-1, while DMA-2A and DMA-4A exhibited the worst performance.

Although DMA-2A and DMA-4A followed the same line, NRW in DMA-4A was larger than that in DMA-2A because of the different ranges of water consumption variations. Thus, two reasons of large NRW in DMA-4A were the small slope of the regression line (Fig. 10a) and the large absolute value of the slope (Fig. 10b), and the large variation of water consumption.

The data on Tokyo Metropolitan Waterworks (1972–1992 and 1993–2021) were also plotted together with the DMA in Colombo (Fig. 10b). The slope of the line for Tokyo in 1972–1992 was found to be almost the same as the slope of DMA-2B in Colombo City. However, after 1993, NRW plummeted from 12.0 % to 3.0 % with similar water consumption, verifying the outcome of water loss reduction programs implemented by Tokyo Metropolitan Waterworks since 1995 [40].

The dynamic analysis of NRW shown in Fig. 10a and b can help to segregate two factors influencing NRW: water consumption fluctuation and outcomes of water loss reduction projects. The outcomes of NRW reduction projects should be evaluated by the slope changes of the regression lines shown in Fig. 10a and b; the greater the slope, the more successful the NRW reduction projects (Fig. 10a), and vice versa (Fig. 10b).

The NRW varied extensively in many cities. Chawira et al. [7] (2022) analyzed data obtained from 2012 to 2020, and found that NRW had fluctuated between 7.1 % and 35.9 %; in addition, the data collected in their study in 2020 showed much higher NRW with the maximum of 42.0 %. However, they did not analyze the factors influencing such a high variation of NRW. Recently smart water meters are available to measure water consumption more frequently, such as hourly monitoring. Alvisi et al. [41] used smart meters, in combination with a water flow meter at the inlet of DMA to estimate water loss more accurately. However, they did not analyze the relationship between water consumption and water loss.

The Comparison of Flow Pattern Distribution (CFPD) method was proposed to estimate the background and unpredicted water leakages using only the DMA inflow data; however, this method requires that the water consumption patterns are nearly the same in the DMAs [42]. Thus, this method cannot be used in DMAs having different water consumption patterns, which is often true in different areas of cities. In addition, this method does not analyze the relationship between billed water consumption and water loss (or NRW) because it assumes the water consumption pattern to be unchanged. Therefore, the dynamic model presented in this study is novel because it enables analysis of the relationship between billed water consumption and NRW.

The assumption of the dynamic model presented in this study is valid for real (physical) losses but may not be for apparent (commercial) losses. Although it is reported that real losses are significantly greater than apparent losses in many countries [7], the linearity of network inflow and NRW with water consumption should be carefully examined before adapting the dynamic model presented in this paper. Data variations could be attenuated by considering longer-term moving averages for more than 3 months; however, the influence of water consumption fluctuation on NRW are gradually diminished when longer-term moving averages are considered. Thus, 3–5 months moving averages would be sufficient to diminish meter-reading errors.

Service meter malfunctioning and connections without water meters render accurate measurement of water consumption in many cities [43,44]; thus, installation of customer meters and regular checking and cleaning of water meters are fundamental steps for NRW reduction.

4. Conclusion

To counter NRW fluctuations owing to water consumption variations, it is recommended to consider 1-year average NRWs. However, this study proved that NRW averages eclipse and obscure the influence of water consumption variations on estimated NRW, leading to a false understanding and evaluation of NRW reduction projects. A dynamic analysis method of fluctuating NRW was presented and verified using 3-year data obtained from the five DMAs in Colombo City, Sri Lanka, and 65-year date from Tokyo, Japan. The following conclusions were realized from this study.

• 1)Although volumetric NRW per connection is recommended, volumetric NRW also fluctuates to the same extent as does percentage NRW, as validated by CVs and correlation analysis.
• 2)ILI does not represent water loss during rapid network extension and pipe renovation periods because UARL increases with pipe lengths and connection numbers but does not consider the age and materials of pipe networks.
• 3)The proposed dynamic analysis method enables the evaluation of two factors influencing NRW: water consumption fluctuation and status changes of the water distribution network owing to NRW reduction projects or aging.

The dynamic analysis method presented in this paper can be easily applied to analyze water loss in water supply networks with large variation of water consumption. Although this study proposed and verified the dynamic analysis method of real water losses, the influence of water consumption fluctuation on apparent water losses were not independently evaluated; thus, it is expected that future studies will clarify such influences.

Funding

This research was supported by the scholarship provided by Japan International Corporation Agency, and by the Grant-in-Aid for Scientific Research (No. 22H01621) provided by the Japan Society for the Promotion of Sciences (JSPS).

Data availability statement

Data will be made available on request.

CRediT authorship contribution statement

Ashan Pathirane: Writing - original draft, Investigation, Data curation. Shinobu Kazama: Writing - review & editing, Methodology, Conceptualization. Satoshi Takizawa: Writing - review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article.