Analyzing the role of consumer behavior in coping with intermittent supply in water distribution systems

<jats:title>Abstract</jats:title>         <jats:p>In developing countries, most water distribution systems (WDS) are operated as intermittent water supply (IWS) systems. A significant share of them also delivers water to consumers in irregular and unreliable ways. To meet water demands under such inconsistent WDS operations, IWS consumers commonly adapt to flexible consumption behaviors characterized by storing the limited water available during shorter supply periods in intermediate storage facilities for subsequent usage during more extended non-supply periods. Towards accounting for this characteristic behavior in understanding the IWS behavior more realistically, this paper presented the development, functioning, and application of a novel open-source PYTHON-based simulation tool (EPyT-IWS) for WDS, virtually acting like an IWS modeling extension of EPANET 2.2. EPyT-IWS integrates EPANET 2.2 solver with an independent hydraulic solver to mimic the water withdrawal during supply periods, storage in intermediate storage facilities, and subsequent use. The applicability of the simulation tool was demonstrated by performing extended-period hydraulic simulations on a typical WDS with representative IWS attributes. The simulation outcomes showed that practicing the typical consumption behavior, involving storing water within underground tanks and later pumping it into overhead tanks, allows consumers to cope with the intermittent water availability and meet their demands very suitably. Besides the water supply duration, the clock time of water supply in IWS systems was predicted to influence consumers' ability to fill the intermediate storage tanks and meet water demands. This study's overall findings can advance the state-of-the-art for planning, designing, and operating WDS with IWS characteristics.</jats:p>

section_content: Water distribution systems (WDS) are designed to deliver consumers adequate drinking water, meeting necessary quality criteria. Although WDS of the developing regions of the globe is designed initially to provide water continuously per speci ed standards, most operate inconsistently. Speci cally, in South Asian countries, particularly India, most WDS provide water to consumers for less than 24 h a day (Charalambous and Laspidou 2017; Ghorpade et al. 2021 ). These systems are termed intermittent water supply (IWS) systems. Kumpel and Nelson (2016) estimated that an alarming (~ 370 million) population in India relies on IWS systems to meet their water demands. 

Several causes, such as population growth, urbanization, increased occurrence of extreme weather events, inadequate accessibility of freshwater, inadequate sizing of distribution network, and water losses, can be attributed to the IWS operation of WDS (Loubser et al. 2020 ). Ghorpade et al. (2021) reasoned that once any WDS falls into the 'vicious' trap of IWS operation, it might become challenging to climb up because of the intricate relationships between several drivers (design, operation, maintenance, institutional capacity, consumer satisfaction, revenue generation, etc. ) that govern its performance. 

Altogether, IWS systems can be divided into three categories -predictable (non-supply occurs within a predictable schedule), irregular (non-supply occurs at unknown intervals, generally for short periods, i. e., no more than a few days), and unreliable (uncertain supply time and long unknown periods of non-supply) (Galaitsi et al. 2016). Past studies suggest that WDS operations in Indian cities fall in irregular and unreliable intermittency (Asian Development Bank and Ministry of Urban Development Government of India 2007; Burt et al. 2018 ). To meet water demands under such erratic WDS operations, consumers generally practice exible consumption behaviors (Fig. 1 ) that involve withdrawing the available water during shorter supply periods and storing it in intermediate storage facilities (Mohan and Abhijith 2020). 

From a detailed inspection, consumer behavior in IWS (irregular and unreliable) systems is distinguishable into Types A and B. Suppose the expected static pressures at the consumer (ferrule) points are less, or the supply is essentially uncertain; the consumers tend to practice Type A behavior (Fig. 1a ) -store water within underground (sumps) storage tanks and later pump it into overhead (rooftop) tanks for use. On the contrary, if the static pressures at the consumer points are high enough to deliver the water to the rooftop tanks directly, the consumers practice Type B behavior (Fig. 1b ) -avoid sump storage and successive pumping. Intriguingly, against the common assumption that the demand satisfaction in residential areas is minimal under IWS, practicing either of these two types of behavior is anticipated to allow the consumers to cope with the non-continuous water availability and meet their demands more suitably (Andey and Kelkar 2009). 

Several attempts to couple the transient free-surface and pressurized ows in distribution pipes toward modeling the hydraulics within IWS systems (Liou and Hunt 1996; Bourdarias et al. 2008 Weston et al. 2022 ) can be seen in the literature. However, consumer behavior in IWS systems is surprisingly overlooked in most of them. Mohan and Abhijith (2020) attempted to address this limitation by representing the out ows (water withdrawal) at the consumer points of highly (unreliable) intermittent WDS as uncontrolled ori ce-based demand. They employed the uncontrolled-type head-discharge relationship suggested by Reddy and Elango (1989) and a non-iterative time-stepping method using backward differencing to analyze the hydraulic characteristics of a draining IWS system. However, Mohan and Abhijith (2020) did not emphasize the water storage constraints (volume of sumps and/or rooftop tanks) and inadvertently associated the consumer demands with the leakage losses. Furthermore, their model also showed limitations in conserving mass and momentum and accurately estimating the draining time (Meyer and Ahadzadeh 2021). 

Recently, Suribabu et al. (2022) proposed a straightforward method to simulate the out ow to the household storage tanks and analyzed the performance of IWS systems by applying the modeling environment of EPANET 2. 2 (Rossman et al. 2020 ). However, their approach was limited to understanding the direct effects of lling the underground sump tanks (via uncontrolled withdrawal of water) on the emptying of the source tank. The impact of actual water consumption (meeting of demands) and subsequent emptying and lling (via pumping) of rooftop tanks on governing the water withdrawal at the consumer points and the overall behavior of a WDS during the IWS practice was not examined. Furthermore, the approach by Suribabu et al. (2022) was limited only to Type A consumer behavior. This paper presents a pressure-dependent volume-driven approach and a novel simulation tool (named EPyT-IWS) to overcome the above-speci ed limitations of the existing state-of-the-art. The proposed tool allows us to simulate consumer behavior in IWS systems realistically and comprehend whether this enables the consumers to cope with the restricted water availability. The suitability of EPyT-IWS for conducting extended-period analysis was demonstrated by applying it to a typical WDS, delivering water to 2,650 consumers (530 households) initially proposed by Suribabu et al. (2022), with the essential characteristics of a representative IWS system. The results corroborate the ability of the proposed tool to mimic the domestic consumer response to intermittency closest to reality and to perceive the knowledge of how far away the WDS is from an equitable operation.
section_name: Introduction

section_name: Development And Functioning Of Epyt-iws

section_content: EPyT-IWS is designed as an open-source PYTHON-based extension of EPANET 2. 2, employing the EPANET-PYTHON toolkit developed initially by the KIOS Research and Innovation Center of Excellence, University of Cyprus. It integrates the modeling environment of EPANET with an independent hydraulic solver. At each time step, the EPANET solver is applied to solve the part of the hydraulic model initialized as input data les for EPANET (in. inp format), and the independent hydraulic solver is employed to solve the remaining part, auto-generated by the EPyT-IWS algorithm. The functioning of EPyT-IWS is conceptualized in Fig. 2. 

The foremost task in simulating irregular and unreliable intermittent WDS operation using EPyT-IWS is conceptualizing and developing the hydraulic model. EPyT-IWS de nes WDS as graphs, with the links representing the pipes and the nodes representing connections between pipes, consumers, hydraulic control elements (pumps, valves, regulators), and water sources (reservoirs and tanks). The base demand value is kept at zero at every consumer node, and an arti cial string is connected (Fig. 3 ) to simulate consumer behavior associated with IWS operation. For consumer behavior Type A, an imaginary string gets additionally connected to every arti cial string (Fig. 3a ), but for Type B, such an imaginary string would be redundant (Fig. 3b ). The imaginary string is auto-generated by the EPyT-IWS algorithm, and its components are not de ned in the EPANET input data le. 

The arti cial string comprises a tank, three nodes, three pipes, and a ow control valve (FCV), and the imaginary string constitutes a tank, a node, and a connecting pipe. Speci c nodes and pipes of the arti cial strings are dummies. Dummy nodes have zero base demand and the same elevation as the consumer node, except arti cial node-3, which has the same elevation as the household. All dummy pipes have negligible length. The constituents of the arti cial and imaginary strings for Type A and Type B consumer behavior are detailed in Table 1.
section_name: Conceptual overview

section_content: In typical (irregular and unreliable) IWS systems, the house connection constitutes a minimum of three 90° Elbows, a stop valve, and a pipe that discharges freely into a storage tank, all connected in series (Suribabu et al. 2022 ). The minor head losses within the house connection would be signi cant, and the minor loss coe cient ( ) would add up to ~ 5. 90 (Bhave 1991). Therefore, the ow rate through the house connection pipe at every consumer node would be directed by the static pressure head at the ferrule point and the friction losses within the house connection arrangement. 

An approximate technique is applied in EPyT-IWS to determine the ow rate (Fig. 4 ). 

For every consumer node, the major ( ) and minor head loss ( ) functions are estimated using Eqs. 1 and 2, respectively. Assuming number of house connections are aggregated at any consumer point, the value of can be estimated using Eq. (3). At each time step ( ), based on the piezometric head ( in m) available at the source node( ) delivering water to the consumer node, the ow rate value for the house connection pipe can be approximated using Eq. 4-5. Based on the estimated value, the major, minor, and total head losses can be estimated using Eq. 6-8. Based on value estimated, the effective pressure head ( in m) can be estimated with Eq. ( 9 ) to verify whether the value is high enough to permit a ow rate of within the house connection pipe. 9

If comes out as a positive value, the estimated value can be considered the withdrawal at node ( in m 3. s - 1 ). If is a negative value, Eq. ( 10 ) can be applied to determine the value. 

At each time step, the EPyT-IWS algorithm computes the value for every consumer node, and updates the ow setting of the arti cial FCV within the arti cial string. The ow rate through the arti cial pipe-1 and arti cial pipe-2 will equal the FCV setting if the arti cial tank level is less than its depth. Else, the ow rates would be zero. The value would govern the in ow to the arti cial tank connected to every consumer node. For Type B consumer behavior, the out ow from the arti cial tank would be administered entirely by the time-series demand value of arti cial node-3. However, for Type A consumer behavior, the imaginary string components need to be accounted for in estimating the arti cial tank out ow.
section_name: Simulating withdrawal at consumer nodes

section_content: Typically, under Type A consumer behavior in IWS systems, pumps are operated to ll the rooftop tanks and to meet water demands. EPyT-IWS avoids physically adding the pumps to the hydraulic model but indirectly simulates the pump operation using the in-built hydraulic solver. The hydraulic solver takes an adequate pumping rate ( ) for every consumer node to simulate the imaginary tank lling and arti cial tank emptying. EPyT-IWS algorithm assumes that the demands at consumer nodes are met at any time step if the water level within the imaginary tank is above a certain value (minimum required water depth, in m). Similarly, the algorithm assumes no pumping occurs until the water level within the imaginary tank is below a speci c depth (threshold depth for pump activation, in m). 

The algorithm considers that even when the imaginary tank level is below the value for pump activation, the pump cannot operate until the water level within the arti cial tank is above a critical value (critical water depth, in m). Once the pump switches on, the arti cial tank emptying, and the imaginary tank lling would continue until either of two conditions occurs -the arti cial tank level dropping below value or the imaginary tank reaching full.
section_name: Simulating storage tank(s) dynamics

section_content: For performing the extended-period hydraulic simulation using EPyT-IWS, appropriate hydraulic time step ( in s) and simulation time duration ( in days) values need to be speci ed as input. Besides, the initial state of the components of the arti cial strings and imaginary strings attached to the system nodes of the WDS needs to be indicated. By default, EPyT-IWS takes the initial water level within the arti cial and imaginary tanks as 0 and 0. 5 m, respectively. Also, the default value at every consumer node is selected as ve times its base demand value. The values for,, and are set as 0. 1 m, 0. 2 m, and 0. 5 m by default.
section_name: Extended-period analysis of WDS operation

section_name: Application Of Epyt-iws

section_content: The rural WDS (Fig. 5 ), initially proposed by Suribabu et al. (2022), was slightly modi ed by introducing a pumping arrangement and was selected as the test network to demonstrate the applicability of EPyT-IWS. The rural WDS serves 530 houses distributed along the pipes. However, the house supply connections were aggregated to nodes for modeling purposes. Each consumer node was presumed to consist of half the number of house supply connections along the pipes connecting them. Each house was assumed to have ve inhabitants, and the total number of consumers for the rural WDS was worked out as 2,650. The per capita water consumption was selected as 55 LPCD (CPHEEO 1999). The elements of the test network include a reservoir (a proxy for a water treatment plant), a pump, an elevated storage tank, 22 nodes, and 22 pipes. The reservoir was assumed to have an elevation of 95 m and was located far from the storage tank. The pumping operation to ll the storage tank was assumed to occur at a xed pumping rate of 150 LPM. The storage tank has an elevation of 107. 5 m, and all consumer nodes have 100 m elevation values. The Hazen-Williams roughness coe cient value for all 22 pipes was assumed as 130. The storage tank outlet was always assumed to be open, causing the tank lling due to pump operation and its draining due to withdrawal at consumer points to happen concurrently. The details regarding the number of house supply connections corresponding to each consumer node, its average daily demand, and the length and diameter of pipes are speci ed in Table 2.
section_name: Test network

section_content: Different test cases (Table 3 ) were selected by varying the pump operating schedule to simulate the consumer behavior in IWS systems. For all test cases, the time window was kept at 120 days to evaluate the ability of consumers to cope with the restricted and uncertain water supply practices over the long run of an IWS system. For 9 (out of 11) cases, except Case 5a and 7a (Table 3 ), the consumer behavior in every system node was assumed as Type A. Cases 1-3 correspond to consistent operation of pumps for only 1 (from 6 AM to 7 AM), 3 (from 6 AM to 9 AM), and 6 h (from 6 AM to 12 PM) every day, respectively. Cases 4-7 correspond to unreliable intermittency. For all these four cases, the water supply practice for the rst 60 (out of 120) days was kept alike: 3 h pumping (from 6 AM to 9 AM) for the rst 30 days; no pumping and no water supply during 31 to 45 days; and restarting of pumping on the 46th day and only 1 h pumping (from 6 AM to 7 AM) for the next 15 days. For the subsequent 60 days, 3 h pumping was adopted for the four cases by varying the clock time of pumping (Table 3 ). Cases 5a and 7a correspond to the case with the consumers of the most upstream node (Node 1) adopting Type B consumer behavior and the remaining consumers aggregated in the rest of the nodes continuing with Type A behavior. The diurnal variations in the household water consumption at every node under all the cases analyzed were represented using a demand pattern (Table 4 ) that was evolved from scrutinizing the time-series water demand data generated by Jethoo and Poonia (2011) for an Indian city (Jaipur) based on the socioeconomic data. The consequence of alternate water sources such as groundwater, tankers, bottled water, and community water lters was entirely ignored for modeling purposes.
section_name: Test cases for analysis

section_content: Two performance metrics were used to evaluate the EPyT-IWS outcomes and to compare the ability of the considered IWS operations and the water consumption behavior to meet the water demands. The rst metric is de ned as the demand satisfaction ratio ( ), which symbolizes the capacity to meet the water demands of the household consumers in any node over a speci c time. is speci ed using an index called demand de cit, de ned using Eq. ( 11 ).
section_name: Performance metrics

section_content: where, = demand de cit in consumer node at time (%); = actual water demand in node at time (LPM); and = water demand satis ed in node at time (LPM). For every consumer node, the node denotes its equivalent imaginary node or arti cial node-3 under Type A and Type B consumer behavior, respectively. 

The rst performance metric ( ) can be estimated using Eq. ( 12 ) based on value. 

12 where, = value for consumer node over the time window and = initial time. 

= 1 signi es that the consumers in node can meet their entire demand over the time. 

The second performance metric is relative withdrawal ( ) and is de ned using Eq. ( 13 ). For every consumer node, a desirable value ( ) can be evolved by associating the number of house supply connections aggregated at the node with the total number of house supply connections served by the WDS. For example, for Node 1, the desirable value would be 0. 047 (i. e., 25/ 530). If the value for every consumer node is equal to, then the IWS practice adopted can be deemed equitable over time.
section_name: 11

section_content: The extended-period hydraulic analysis of the test network under varying cases (Table 3 ) was conducted using EPyT-IWS by selecting the as 60 s and as 120 days. The default values were selected for initial water depth within the arti cial and imaginary tanks and for. The other input parameter values selected are detailed in Table 5. The simulations were run using a desktop computer with Intel® Core™ i7-6700 CPU @ 3. 40 GHz processor, 16. 0 GB installed memory, and a 64-bit operating system.
section_name: Input parameters for hydraulic simulation

section_name: Results And Discussion

section_content: The outcomes of the hydraulic analysis of the test network under Cases 1-3 using EPyT-IWS shed light on the effects of pumping duration on the dynamics of water level within the storage tanks and subsequent demand satisfaction of the consumers. Six nodes (Nodes 1, 3, 6, 13, 16, and 22) of the test network were selected (Fig. 5 ) to illustrate and explain the results. Node 1 is the upstream node nearest the storage tank, and Nodes 6, 16, and 22 are downstream dead-end nodes. Nodes 3 and 13 can be de ned as intermediate nodes. The variations in the underground sump tank level in the six nodes mentioned above over the simulation time under Cases 1-3 are portrayed in Fig. 6. Likewise, the predicted water level dynamics within the rooftop tanks are depicted in Fig. 7. Figure 8 schematically illustrates the variations in the demand de cit values under the three cases over the simulation period. 

The values of the performance metrics ( and ) for the 22 nodes over 120 days estimated for Cases 1-3 are shown in Fig. 9. The variations of the two metrics over the entire simulation period are also detailed in Fig. 9.
section_name: Effects of pumping duration

section_content: Although all six nodes were at the same elevation, the lling and emptying dynamics of the underground sump tanks were found to be entirely distinct for them under the three cases, apparently due to the differences in their speci c positions relative to the storage tank. Under Case 1, EPyT-IWS predicted that the water level within the underground sump tank in Node 1 would reach a maximum within ~ 50 minutes. However, during the same time, the water levels within the sump tank in Node 3 were predicted to be only 0. 63 m, and the same in Node 6, only 0. 04 m. The water level pro les under Case 1 predicted for Nodes 1 and 3 differed distinctly from that for Nodes 6, 13, 16, and 22 (Fig. 6a ). The tank water level was found to attain a pseudo-equilibrium around the value for these four nodes. This is because the EPyT-IWS algorithm envisages the consumers to start the water pumping as soon as the tank level rises above the limit to overcome the water shortage caused by the emptying of rooftop tanks (Fig. 7 ). Intriguingly, the underground sump tank level in Node 1 was never predicted to reach the value, while the same in Node 3 oscillated between 0. 6 and 0. 5 m during the pumping hours (Fig. 6a ). 

By increasing the pumping hours from 1 to 3 h, the minimum depth to which the water level drops within the sump tank in Node 1 increased from 0. 96 to 1. 22 m, and the highest level reached within Node 3 raised from 0. 88 to 1. 55 m. An entirely contracting sump tank level pro le compared to Case 1 with a mean value of 1. 01 m was predicted for Node 3. For the other four nodes, an escalation of the slopes of the initial rising part of the pro le curves was virtually evident (Fig. 6b ). For instance, concerning the sump tank in Node 22, the time required to attain the pseudo-equilibrium decreased from 24. 3 days under Case 1 to 9. 4 days under Case 2. Similar impacts as Case 2 were also predicted for Case 3 with 6 h regular pumping (Fig. 6c ). The minimum depth to which the water level drops within the sump tank in Node 1 increased further to 1. 66 m and the tank in Node 3 was predicted to get full. From a vague look, the sump tank pro les in Node 3 and Node 13 under Case 3 resembled those predicted in Node 1 and Node 3, respectively, under Case 1 (Figs. 6a and 6c ). Concerning Node 22, the time to attain pseudoequilibrium decreased further to 4. 4 days. An increase in the slopes of the early rising portion of the pro le curves corresponding to Nodes 6, 13, 16, and 22 was also predicted under Case 3 compared to Case 1. 

Concurrently analyzing the EPyT-IWS predictions of rooftop tank levels (Fig. 7 ) and demand de cit values (Fig. 8 ) under the three different pumping operation cases delivers a perfect picture of the ability of Type A consumer behavior to cope with the IWS practices. As seen in Fig. 7, even under Case 1 with only 1 h daily pumping, the household consumers aggregated in Node 1 were predicted to meet their water demands continually without any demand de cit. However, the consumers aggregated in none of the other nodes could meet their demands without de cit under Case 1 (Fig. 7a ). Like what was predicted for overhead tanks (Fig. 6 ), the rooftop tank water levels in Nodes 6, 13, 16, and 22 under Case 1 attained a pseudo-equilibrium around the value. 

Signi cant changes in the demand de cit plots became apparent with increased pumping duration (Fig. 8 ). The 3 h pumping practice under Case 2 was found adequate to meet the water demands of all 29 households aggregated in Node 3 incessantly. While the 6 h pumping practice (Case 3) was insu cient to satisfy the water demands of consumers aggregated in every node, the results signi ed that the Type A

behavior can facilitate the consumers to lessen the demand de cits by a signi cant degree (Fig. 8c ). The mean demand de cit values for Nodes 6 and 13 decreased from 99. 2 and 97. 5% to 70. 2 and 30. 9%, respectively, after changing the pumping duration from 1 to 6 h. Nonetheless, a similar impact was not predicted for Nodes 16 and 22. The mean de cit values for these nodes over 120 days decreased to 98. 3 and 97. 9% from a shared value of 99. 4%. These disparities, over again, emphasize the importance of the consumer positions relative to the water source in coping with the IWS practices. 

The performance metric values estimated under the three cases also verify the previous inferences. As seen in Fig. 9a, the = 1 estimated for Node 1 over 120 days under the three cases considered suggests that the household consumers in Node 1 can meet their water demands like that in a continuous WDS by adopting the Type A behavior. However, under Case 1, the value estimated for all other nodes, including Node 2, the second-most upstream node, was found to be less than one. The value of 0. 446 estimated for Node 2 implied that the 47 households aggregated in this node could fully meet the water demands only ~ 45% of the time considered. The increment in the pumping hours induced uneven impacts in the values estimated for the 22 nodes. Although a pumping duration of 6 h was found appropriate in fully meeting the demands in ve nodes (Nodes 1, 2, 3, 7, and 10) and in meeting water demands for > 90% of the time considered in four nodes (Nodes 4, 5, 8, and 11), it was still not enough for consumers in 44 households, mainly aggregated in the three downstream nodes (Nodes 16, 21, and 22), to ful ll demands for > 0. 05% of the total analyzed time. Furthermore, the variations in the estimated values over the 120 days window (Fig. 9c ) disclosed that even though the typical (Type A) consumer behavior facilitates an improved demand satisfaction, it cannot entirely avoid the unreliability in water availability associated with IWS practices. 

The values estimated under the three cases revealed more speci cs of equity concerning the IWS operation practices. Under Case 1, in ve out of 22 nodes (Nodes 1, 2, 3, 7, and 10), the values over the 120 days were more signi cant than the corresponding desirable values (Fig. 9b ). This signi es that the consumers of 154 households aggregated in these ve nodes draw more water from the WDS during the supply hours than the remaining 376 households. However, surprisingly, although ~ 36% of the total water supplied over the 120 days (four times the desirable) was predicted to be drawn by the households aggregated in Node 2, the value was estimated to be only 0. 446. Interestingly, by drawing only ~ 21% of the total water supplied over the 120 days under Case 2, the consumers in Node 2 were predicted to be able to ful ll their water demands. This signi es that the value only gives a certain sense of the relative distribution of the delivered water among the different nodes and sheds no light on the delivered water volume. As well, looking speci cally at Node 1, under Case 1, the 25 aggregated households fully met their demands by drawing ~ 13% less than that drawn by consumers of Node 2. 

Though the values for both Nodes 1 and 2 were more than four times their respective values, the consumers aggregated in Node 2 could not ll their underground sump tanks, and the tank level was predicted to oscillate between 0. 75 and 0. 5 m. Due to this, they could not pump water from the underground sump tank to the rooftop tanks most of the time. Thus, it can be implied that the discontinuity of water availability can impede consumers' capacity to ful ll their demands. As expected, increasing the pumping hours has positively impacted reducing the disparities between the calculated and expected values (Fig. 9b ). However, the effects were pronounced only at the nodes closer to the storage tank, and at downstream nodes, particularly in Nodes 16, 21, and 22, the impacts were relatively nominal. For instance, between Cases 1 and 3, the value calculated for Node 22 only increased from 0. 002 to 0. 003, while the same for Node 1 decreased from 0. 231 and almost reached the desirable value. The 120 days variations in the values also verify the above inference (Fig. 9d ). Altogether, the EPyT-IWS outcomes corresponding to Cases 1-3 imply the importance of simultaneously examining the performance metrics ( and ) in arriving at the optimal pumping schedule for any IWS system.
section_name: DSR RW

section_content: The EPyT-IWS outcomes of Test network analysis under Cases 4-7 revealed a picture of consumer response against irregular and unreliable IWS practices in WDS. The results also highlighted the effects of the clock time of pumping on the dynamics of water withdrawal at the consumer points and subsequent demand satisfaction of the consumers. The values of and over 120 days estimated for Cases 4-7 are depicted in Fig. 10. The variations of these two metrics in Nodes 1, 3, 6, 13, 16, and 22 over the entire simulation period are also illustrated in Fig. 10. It may be recalled that there is no difference in the total pumping duration between Cases 4, 5, and 6, and the total period for which the pump operates and supplies water to the storage tank is 285 h over 120 days. The only difference between Cases 4-6 is the clock time of pump operation over the last 60 days of the total time considered (Table 3 ). Nonetheless, under Case 7, unlike Cases 4-6, the pump operates from 11 AM till 12 AM for an additional 600 h over the last 60 days. 

Interestingly, substantial disparities were evident in the values estimated for the 22 nodes over 120 days under Cases 4-7 (Fig. 10a ). Although such differences for the under Case 7 from the rest were foreseeable, the apparent dissimilarities between the values estimated under Cases 4-6 were unexpected. For Node 1, as anticipated, the value estimated (0. 931) was the same under all four cases of irregular pumping. However, the value was less than the maximum estimated under Cases 1-3 (Fig. 9a ). This signi es that the amount of water that can be stored within the underground sump tank is insu cient to prevail over the non-availability of water caused by the shutting down of pumps for 15 days (Fig. 10c ). For Nodes 2 and 3, the values were almost equal under Cases 4-6. However, from a closer look, the values under Case 4 were slightly higher than the other two and were equal to that estimated under Case 7 for Nodes 2 and 3 (0. 828 and 0. 794, respectively). Between the values estimated under Cases 5 and 6, the values under Case 5 were marginally high. 

However, for the remaining 13 nodes, the demand satisfaction of consumers under Case 5 was higher than that under Cases 4 and 7. These differences were predicted to be more profound in the downstream nodes. Speci cally, looking at Nodes 6, 16, and 22 (Figs. 8a and 8c ), operating the pump from 9 PM to 12 AM for the last 60 days (Case 5) induced a substantial rise in the ability of consumers to ful ll their demands compared to operating the pumps from 11 AM to 2 PM (Case 4) and 4 PM to 7 PM (Case 6). 

The estimated values for these three nodes were 0. 266, 0. 157, and 0. 185 under Case 5, while the same under Cases 4 and 7 were signi cantly lower (0. 033, 0. 009, and 0. 010 and 0. 039, 0. 009, and 0. 011, respectively). The reason for the same can be attributed to the diurnal variations in water demand. Under Case 5, the pump was operated during the period when the water demands of the consumers were relatively minimal (Table 4 ). Due to this reason, the consumers aggregated in the upstream nodes (mainly Nodes 1, 2, and 3), who experience a somewhat uninterrupted demand satisfaction, seldom operate their pumps during the late-night pumping hours. Hence, out ows to the underground sump tanks of households aggregated in the upstream nodes were predicted not to occur for extended periods under Case 5 compared to Cases 4 and 7. This led to more volume of delivered water becoming available to withdraw for the underground sump tanks aggregated in the downstream parts of the WDS, eventually enabling them to ll up their rooftop tanks more frequently and ful ll their demands. Under Case 7, by increasing the pumping hours from 3 to 13 h for the last 60 days, the values for all the nodes of the test network were predicted to attain the maximum value of 1 (Fig. 10c ). This implies that adopting the typical Type A behavior enables the consumers to enjoy uninterrupted demand satisfaction even under the IWS operation of WDS if the water supply is reasonably prolonged and regular (predictable intermittency). 

Although differences in the values estimated under Cases 4-6 for the 22 nodes are not as signi cant as that for, noticeable disparities become apparent from a thorough look (Fig. 10b ). 

Like what we have observed under Cases 1-3, the values estimated under Cases 4-6 in the upstream nodes were larger, and the values corresponding to the downstream nodes were signi cantly lower than the respective desirable values (Figs. 9b and 10b ). Although from the values, Case 5 can be deemed the most effective pumping schedule among the three irregular pumping cases (Cases 4-6), it is challenging to make such a clear-cut inference based on the values. 

However, based on the results, it is hard to disregard the growth in the equity of the water supply introduced by the increase in the pumping hours (Figs. 10b and 10d ). For Nodes 1, 3, 6, 13, 16, and 22, with desirable values of 0. 047, 0. 055, 0. 034, 0. 060, 0. 028, and 0. 043, respectively, the average values corresponding to the nal 60 days under Case 5 were 0. 071, 0. 160, 0. 009, 0. 029, 0. 002, and 0. 005. 

By increasing the water supply duration, the average values over the nal 60 days improved to 0. 040, 0. 073, 0. 035, 0. 066, 0. 026, and 0. 039, respectively, and became very close to the desirable values (Fig. 10d ). Thus, it can be implied that Type A consumer behavior stimulates a virtually equitable water distribution among consumers under a predictable and regular water supply routine.
section_name: Effects of clock time of pumping

section_content: From the previous results (Figs. 7 and 8 ), it became apparent that by adopting the Type A consumer behavior, the consumers aggregated in the most upstream node (Node 1) could meet virtually their entire water demands compared to those aggregated in other locations of the test network. Naturally, it becomes appealing to comprehend how this could vary if those consumers switch over to the more economical Type B behavior, avoiding constructing underground sump tanks and operating pumps. In this regard, Cases 5a and 7a were analyzed using EPyT-IWS. The values of and thus calculated are illustrated in Fig. 11. (connecting ferrule point and storage tank), and the household pumping rate ( ) was performed to ascertain the impacts of the selected input parameter values (Table 5 ) on the EPyT-IWS predictions. The maximum capacity of the underground sump tank was varied from the default value of 2 m 3 to 1. 5 (chosen minimum) and 2. 5 m 3 (chosen maximum). The same for the rooftop tank was varied from the default value of 1 m 3 to 0. 5 and 1. 5 m 3. From the default values of 2. 5 m and 2 m, respectively, for the maximum depth of the underground sump and overhead rooftop tanks, the values were altered to 2 and 3 m and 1. 5 and 2. 5 m, respectively. The diameter value of the house connection pipe varied from the default value of 19. 05 mm to 12. 69 and 25. 40 mm. From the default value of ve times the base demand value at every node, the value was varied as three and seven times the base demand value. All the simulations were performed by selecting the consistent pumping routine speci ed in Case 1 and using the same (60 s) and (120 days) values as those for the earlier simulations. The results obtained, in terms of and values, are described in Fig. 12. 

The results specify that out of the six parameters, the EPyT-IWS outcomes are most sensitive to the diameter value selected for the house connection pipes. Notable differences between the and over 120 days were evident in all 22 nodes from varying the house connection pipe diameter, contrasting that distinguishable and value variations were apparent only in the upstream node, primarily Nodes 1 and 2, for the rest ve parameters (Fig. 12 ). The high impact of the diameter value of the house connection pipe in controlling the EPyT-IWS outcomes is attributed to the implication of and values on the pressure-dependent value estimation for every consumer node (based on Eq. 5

or Eq. 10). The second-most arti cial string component parameter that is most in uential to the EPyT-IWS outcomes was the capacity of the underground sump tanks. This value varies the total volume of water that the consumers can collect during water supply hours for subsequent pumping and usage, in uencing the demand satisfaction and the total withdrawal volume at the consumer points. The household pumping rate was found to be the imaginary string component parameter that signi cantly controls the and estimations because of its in uence on governing the emptying and lling dynamics of the sump tank and rooftop tanks, respectively. The other three parameters, such as sump tank depth, rooftop tank capacity, and rooftop tank depth, were not quite prominent in administering EPyT-IWS outcomes under the IWS operation scenario speci ed as Case 1.
section_name: Effects of altering consumer behavior

section_content: Consumers of IWS systems generally practice exible consumption behaviors (de ned as Type A and Type B) to cope with the non-continuous water availability and meet their demands more appropriately. 

However, this characteristic behavior in IWS systems has not been adequately accounted for in the existing state-of-the-art hydraulic models for IWS systems. Towards this limitation, this paper presented the development, functioning, and application of a pressure-dependent volume-driven hydraulic analysis
section_name: Conclusions

section_content: Funding This research was supported by a grant from the Ministry of Science & Technology of the State of Israel and Federal Ministry of Education and Research (BMBF), Germany.

section_name: Sensitivity Of Epyt-iws Outputs To Input Parameter Values

section_content: By switching from Type A behavior to Type B, the value for the consumers aggregated in Node 1 declined substantially from 0. 931 (Fig. 10a ) to 0. 007 (Fig. 11a ). This speci ed the ineptness to move to Type B behavior if the pumping operation continues the irregular and unreliable routine speci ed as Case 5. The results from EPyT-IWS simulations showed that the storage tank, acting as the source to the consumers of the test network, is prevented from becoming full under Case 5a due to the constant out ows to the underground sump tanks during the periods of water availability. Therefore, the static pressure at the ferrule point(s) of Node 1 never reaches the needed value to deliver water directly to the rooftop tanks located at a higher elevation (7 m above the ferrule point). The rooftop tank in Node 1 was predicted to ll for only 35 minutes (from 0 to 1. 05 m) from the start of the simulation, concurrently with the storage tank emptying (from the initial level of 2. 85 m). As a result, the consumers aggregated in this node could only satisfy their demands for ~ 21 h (over 120 days) by withdrawing water from the rooftop tank till it fell to the level corresponding to (Fig. 11c ). A noticeable decrease in the values for Node 1 (from 0. 126 under Case 5 to 0. 013 under Case 5a) also indicated that adopting Type B behavior by the consumers aggregated in Node 1 is not worthwhile under the IWS practice considered (Figs. 10b and 11b ). 

The inability of households in Node 1 to satisfy demands brought upon by switching over to Type B behavior did not re ect considerably on the remaining 505 households aggregated in the rest 21 nodes (Figs. 10a and 11a ). No noticeable change in the values under Case 5a compared to that under Case 5 was predicted in the downstream nodes (Figs. 10c and 11c ). At the same time, a visible increase was evident in two intermediate nodes -Nodes 7 and 10. The values in these two nodes increased to 0. 693 and 0. 677 from 0. 621 and 0. 610, respectively. Unlike the values, the values predicted for the intermediate nodes -speci cally Nodes 4, 7, 8, 10, 11, 13, 15, 17, and 18 -displayed an obvious rise between Cases 5 and 5a. The values for the above nine nodes increased from 0. 063, 0. 056, 0. 053, 0. 143, 0. 043, 0. 028, 0. 016, 0. 034, and 0. 019 to 0. 074, 0. 070, 0. 064, 0. 169, 0. 053, 0. 034, 0. 020, 0. 043, and 0. 022, respectively (Figs. 10b and 11b ). 

Switching from Type A to Type B behavior for Node 1 was predicted to be more viable if the IWS practice followed the pumping routine speci ed by Case 7. The predicted increase in the average values for Node 1 over the last 60 days (from 0 under case 5a to 0. 748 under case 7a) veri es the above statement (Fig. 11c ). The viability of switching from Type A to Type B was also re ected in the values (Figs. 11b and 11d ). However, switching to Type B consumer behavior in Node 1 impeded the consumers from achieving complete demand satisfaction (Fig. 11 ). Besides, as predicted (Fig. 10 ), complete demand satisfaction and virtually equitable water distribution can likely be attained by adopting Type A behavior in every node. Considering the above facts, altering the consumer behavior in Node 1 was deemed unreasonable for the test network under the cases analyzed.

section_content: Sensitivity analysis by individually varying the values of the maximum capacity and maximum depth of the underground sump and overhead rooftop tanks, the diameter values of the house connection pipe The positioning of consumers relative to the source tank is an essential factor in controlling their ability to withdraw water from WDS to their respective storage tanks. 

Type A behavior facilitates the consumers aggregated in locations closer to the source tank to relish uninterrupted water availability even under irregular and unreliable IWS operations. 

Barring the water supply duration, the clock time of water availability in IWS systems can signi cantly in uence consumers' ability to ll their storage tanks and meet water demands. 

Switching from Type A to Type B behavior (storing water directly in overhead rooftop tanks for use) can only be practical for consumers of IWS systems if reasonably prolonged and regular water supply practices are adopted. 

The sensitivity analysis results established the inevitability of careful selection of the parameter values concerning the additional arti cial and imaginary string connected to every node in the hydraulic model on the reliability of EPyT-IWS predictions. Altogether, the ndings corroborate the potential of the EPyT-IWS tool to induce signi cant contributions toward planning, designing, and operating WDS with IWS characteristics. The future directions involve advancing EPyT-IWS towards simulating transient freesurface and pressurized ows and modeling leakage losses.
section_name: Sensitivity Of Epyt-iws Outputs To Input Parameter Values

section_content: The authors have no competing interests to declare.
section_name: Declarations Competing Interests

section_content: All authors contributed to the study conception and design. Model development and analysis were performed by GRA. The rst draft of the manuscript was written by GRA, and all authors commented on previous versions of the manuscript. All authors read and approved the nal manuscript. Sensitivity analysis results obtained. The black dotted line signi es the difference between (a) DSR and (b)RW values estimated using minimum and maximum selected values of the parameters.
section_name: Author Contributions

section_name: References