Assessing the impact of working pressure on water meter registration

Fluctuations in the network pressure of water supply systems affect hydraulic performance and water meter accuracy. The development of metering error curves requires steady-state conditions which are extremely rare in water distribution systems characterized by intermittent supply. Simple deterministic models are suggested and developed from monthly data collected over a 4-year period (2010 – 2014) for three most dominant meter models (Models 1 – 3) in the Kampala Water Distribution System (KWDS), Uganda. This study combines pressure and billing information at the same time to understand metering accuracy. Results showed that metering accuracy increased by 4.2, 8.4 and 2.9% when pressure was increased from 10 to 50 m for Models 1 – 3, respectively. Age did not in ﬂ uence the impact of pressure on meter accuracy. The most sensitive parameter in the model was the meter age. Metering accuracy was relatively constant after a period of 5 years. The least sensitive parameter was the working pressure which caused a slight change to the annual billed volume. The ability of the model to accurately predict the meter registration degenerated with an increasing annual billed volume. Model 2 meters were the best performing and probably the most suitable meters in the KWDS.

INTRODUCTION developing world (Mutikanga et al. a, b). In service, water meters can be tested in the laboratory for a range of flow rates to develop metering error curves fundamental to the understanding of precise consumption levels (Fontanazza et al. ; Arregui et al. ). However, the guidelines followed in these evaluations recommend that measurements are taken under steady-state flow conditions. As part of the meter management process, data are collected and stored on a regular basis (monthly) by water authorities each time meters are read to aid in the issuance of water bills. In a study, Mbabazi et al. () used this billing information to develop meter degradation profiles from which the most suitable meters were identified to navigate hindrances associated with the accurate determination of water meter accuracy. Unmetered water volumes from degradation rates were also calculated. However, the adoption of this approach to a large extent has proved difficult for flawed historical databases and the lack of technical competence to validate data (Sempewo & Kyokaali ).
To address the aforesaid limitations, simple deterministic models are suggested from the analysis of data collected over a 4-year period (2010-2014) on a routine basis by a water authority to predict water meter accuracy.
The data used in this study have been the basis of generating monthly water bills and ensuring a reliable water service connection to users. Multivariate regression models for both volumetric and velocity-type meters are developed to assess the impact of working pressure on water meter accuracy. Degradation rates across three-meter models are compared from which the most suitable meters in the Kampala Water Distribution System (KWDS) are determined.
To account for the probabilistic nature of water meter registration, a sensitivity analysis involving both the working pressure and meter age against the annual totalized volume is provided. This simple technique addresses differences in methodological competence that affects knowledge transfer from academia to stakeholders in the water industry. To the best of our knowledge, no work has been done previously to relate pressure and billing information at the same time to metering accuracy without the need to conduct laboratory experiments. The results from this study provide an understanding of the effect of working pressure on water meter accuracy across various meter models and encourage players in the water industry to continuously collect and keep metering information for future use.

Data sets used in the stud
In this study, data from an existing water utility meter management program were availed to the authors. This information comprised two data sets used for monitoring and the assessment of domestic meters in the KWDS: (1) billing data set containing anonymous customer billing information with variables such as water meter types, meter serial numbers, field installation date, date of last meter reading and totalized volume (m 3 ), and (2) pressure data set containing readings from working pressure tests conducted over a short period (less than 24 h) at anonymous customer premises. While the apparent loss from domestic meters might be small compared to large meters for industrial users, the cumulative effect from the numerous domestic meters can be significant (Mantilla-Peña et al. ). Some of the billing data included an estimate of readings based on previous user consumption trends for two reasons: (1) customer premises are closed during the day making it difficult for personnel to access readings from an installed meter and (2) the irregular update to the GIS database renders the tracing of installed meters in the KWDS impossible (Mutikanga et al. a, b).
The sole purpose for conducting working pressure tests was not to provide data for this study but rather to analyze the actual hydraulic conditions in the network to ensure (1) that newly connected water meters were not subjected to premature wear and tear because of unfavorable hydraulic overload conditions, (2) that users received an appropriate water flow at both low and peak demand times, and (3) smooth meter separation (NWSC personal communication).
However, there is uncertainty on whether the provided values in the database guaranteed adequacy and reliability to all consumers in the network since the pressure monitoring tests were conducted for a limited time.
Customer property numbers in the pressure data set were matched with customer reference numbers in the billing data set. This resulted into a small data set comprising 724 meters from eight different manufacturers. The variability in meter models reduced the risk of using a single meter model to generalize meter failure. Investigations on the pressure data revealed property referencesan indicator of the actual network block maps showed that meters were captured from different parts of the KWDS hence creating a homogenous population to justify a smaller sample size population for the analysis (Mutikanga et al. a, b). The pressure readings assessed were also conducted during meter separation procedures which are special circumstances less likely to generate enough data.
Finally, the data availed by the water authority were not readily usable in its current form which imposed the need for improved data management. Nonetheless, there was a fair representation of the meter types, the frequency of usage of the meters based on KWDS characteristics.
A selection of three-meter models (Models 1-3) constituting 80% of the data was carried out. Of these, 91 (15.7%) were Model 1, 137 (23.4%) were Model 2 and 351 (60.6%) were Model 3. The data had the following variables: the customer reference numbers, property reference numbers, average working pressure, meter type, installation date, date of last meter reading and totalized volume.

Preliminary data analysis
Recent studies have shown the significance of considering water consumption patterns when determining water meter accuracy (Arregui et al. ; Karadirek ). The percentage of consumption taking place at specified flow rates can be used to estimate the weighted error, thus directly impacting degradation rates. Consumption patterns also affect the average starting flow, an aid in the understanding of meter under-registration or non-registration over time. However, the problem with using the billing database in this study was that clear water consumption patterns for the different users, meter types and sizes could not easily be established. Therefore, determining individual water consumption patterns required visiting customer properties but given the cost and time implication of this task, this option was not viable. Also, it is common for water authorities to reserve the right to keep consumer information confidential even if it is available. An average daily consumption for this research was assumed to be 0.78 m 3 /day based on findings from a demand profiling study in Kampala that found single-family users with a storage tank accounting for 80% of the total water consumption (Mutikanga ). This consumption pattern also aligns well with low flows experienced in the developing world (Fourie et al. ).
The age of the meters was based on the frequency of use. Water meters, in particular volumetric-type meters constituting 76% of the total installed meters in the KWDS, have been found to fail less than 5 months after installation due to water quality problems (Mutikanga ). Also, there were numerous date inconsistencies that could have resulted into a significant loss of data.
The water meter size was assumed to be DN 15 mm because the data were obtained from a distribution network studied in prior investigations (Mutikanga et al. a, b; Mbabazi et al. ). The water volume registered by a meter each year (hereafter, annual billed volume) was calculated from two variables, i.e., last reading of the totalized volume (m 3 ) and age as shown in the following equation: Incomplete records of 193 meters related to: no registered volume (zero current reading) assumed to be newly installed meters and nonfunctional (stuck) or abandoned meters were excluded from the analysis. Additionally, water meters with meter misreadings (negative totalized volume) and abnormal spikes or dips in consumption (abnormally high or low volumes) caused by poor data handling from capturing data to the customer billing database were also excluded. Figure 1 shows the distribution of the meter models that met the inclusion criteria and considered for further statistical analysis.

Development of multivariate linear regression models
The annual billed volumes for Models 1-3, along with the information about select operating conditions for each meter model, were used to develop regression models to predict the annual billed volume in RStudio (R Core Team ). The meter age and working pressure were considered predictor variables, while the annual billed volume was the response variable. A linear relationship was assumed between the response and predictor variables which took the general form in the following equation: where y is the annual billed volume (m 3 =year), β 1 and β 2 are coefficients for the meter age and working pressure, respectively, x 1 and x 2 are meter age (years) and average working pressure variables, respectively, and ε is the error term accounting for other factors not included in the model.

Sensitivity analysis and model validation
The Model 1: sqrt(y) ¼ 21:19 À 1:38 (x 1 ) þ 0:02 (x 2 ) Model 2: sqrt(y) ¼ 17:88 À 0:94 Á sqrt (x 1 ) þ 0:04 Á (x 2 ) Model 3: sqrt(y) ¼ 27:74 À 1:89 Á sqrt (x 1 ) þ 0:02 Á (x 2 )    Model 2 had the lowest coefficient with respect to meter age (Equation (4)) and was subjected to the greatest median working pressure (Figure 3). This implies that higher working pressure has no effect on meter age, i.e., meters did not degrade faster when subjected to high working pressure as expected. The time over which pressure readings were taken was rather small and may not have been representative of the pressure fluctuations experienced during the service time of the meters probably explains this disparity.
Therefore, the need to monitor pressure for longer times may address this uncertainty.
The regression coefficients for Models 1-3 associated with working pressure were generally positive (Equations (3)- (5)). This shows that working pressure has a positive influence on the volume registered by both old (Models 1 and 2) and new (Model 3) meters. However, this was not significant for all the meter models (p > 0.05). Therefore, age did not influence the effect of pressure on water meter registration. This observation differs from a study finding by  (3)). Model 2 with a closely related registration mechanism to Model 1 (both positive displacement meters) was subjected to a slightly higher median pressure but had the greatest coefficient with respect to working pressure (Equation (4) which directly translates to metering accuracy was linear, the influence of meter age was exponential. Additionally, the age and totalized volume have been determined to have a logarithmic relationship to metering accuracy (Moahloli et al. ). Therefore, the relationship of both working pressure and age on meter registration (annual billed volume) may not be fully described linearly, hence the need to investigate for non-linearity. However, the latter approach may require a large skill, not readily available in the developing world. A linear assumption was preferred because of the less technical skill required to complete the analysis and simplicity in interpreting the results.
In Figure 6, Model 2 had the lowest change in accuracy (1.85% per year) with respect to meter age and the greatest change in accuracy (8.4%) when the pressure was increased from 10 to 50 m than Models 1 and 3. Therefore, Model 2 is the best meters in the model. This differs from findings in a study by Mbabazi et al. () which showed that Model 3 meters had the lowest meter accuracy degradation rates.
The difference could be attributed to variability in the However, the impact on meter accuracy caused by particulates was not modeled in this study and may require further investigation.
Water storage tanks at the customers' facilities affect the sizing of meters, and starting flow found to have significant impacts on metering errors (Fontanazza et al. ). Unreliable water supply has caused 80% of the customers to install private storage tanks which induce low flows and hinder the capacity of meters to accurately measure consumption (Mutikanga et al. a, b). When the water supply is

Sensitivity analysis and model validation
The sensitivity of the model output (annual billed volume) to the working pressure and meter age was assessed using Spearman's rank correlation coefficients after 10,000 Monte Carlo simulations. Table 2 provides a summary of the correlation coefficients. The most sensitive parameter in the model is the meter age, while the least sensitive parameter is the working pressure.
The meter age had a high negative correlation to the annual billed volume, implying that a capability of water meter registration decreases over time, i.e., new meters are more likely to have lower metering errors than older meters.
In Figure 7, the change in the annual billed volume is minimal and can be assumed to remain relatively constant after 5 years. This finding shows that meters may need to be replaced when the totalized volume is equivalent to a 5-year usage period. This will reduce the average life cost replacement of a water meter too early due to fixed initial The calculated annual billed volume was not always equal to the predicted annual billed volume. However, the model was better at predicting small volumes (<500 m 3 / year) more than higher volumes (>1,000 m 3 /year) ( Figure 3).
Therefore, the ability of the model to accurately predict the

CONCLUSIONS AND RECOMMENDATIONS
An assessment of the impact of working pressure on water meter accuracy was performed with multivariate regression models for both volumetric-(Models 1 and 2) and velocitytype (Model 3) meters. Working pressure showed a positive effect on meter accuracy for both old (Models 1 and 2) and new (Model 3) meters, implying that age has no influence on the effect of pressure on water meter accuracy. Model 2 had the lowest change in accuracy (1.85% per year) with respect to meter age and the greatest change in accuracy (8.4%) when the pressure was increased from 10 50 m than Models 1 and 3. Therefore, Model 2 is the best meters in the model. From the sensitivity analysis, the most sensitive parameter was the meter age. Metering accuracy was relatively constant after a period of 5 years. The least sensitive parameter was the working pressure and did not result into a noticeable change in the annual billed volume. The ability of the model to accurately predict the meter registration degenerated with an increasing annual billed volume.
A study designed where both consumption and pressure readings are taken at the same time can check the legitimacy of the model. Otherwise, results from this study show that meter accuracy can be determined from data collected on a regular basis by water authorities. The data used in the study were specific to Kampala; however, the methodology is applicable for use by water utilities which emphasize data collection and storage but lack the financial resources to carry out laboratory tests on individual meters. This study provides vital information to water utility managers that only replace meters after vandalism, theft and meter failure. In addition, this study will improve meter replacement programs and prepare more accurate cost-based calculations of the water value as it relates to meter models and meter registration, which are both important components in water utility charge structures.

DATA AVAILABILITY STATEMENT
All relevant data are included in the paper or its Supplementary Information.