A Clustered, Decentralized Approach to Urban Water Management

Current models in design of urban water management systems and their corresponding infrastructure using centralized designs have commonly failed from the perspective of cost effectiveness and inability to adapt to the future changes. These challenges are driving cities towards using decentralized systems. While there is great consensus on the benefits of decentralization; currently no methods exist which guide decision-makers to define the optimal boundaries of decentralized water systems. A new clustering methodology and tool to decentralize water supply systems (WSS) into small and adaptable units is presented. The tool includes two major components: (i) minimization of the distance from source to consumer by assigning demand to the closest water source, and (ii) maximization of the intra-cluster homogeneity by defining the cluster boundaries such that the variation in population density, land use, socio-economic level, and topography within the cluster is minimized. The methodology and tool were applied to Arua Town in Uganda. Four random cluster scenarios and a centralized system were created and compared with the optimal clustered WSS. It was observed that the operational cost of the four cluster scenarios is up to 13.9 % higher than the optimal, and the centralized system is 26.6% higher than the optimal clustered WSS, consequently verifying the efficacy of the proposed method to determine an optimal cluster boundary for WSS. In addition, optimal homogeneous clusters improve efficiency by encouraging reuse of wastewater and stormwater within a cluster and by minimizing leakage through reduced pressure variations.

cluster boundaries such that the variation in population density, land use, socio-economic 23 level, and topography within the cluster is minimized. The methodology and tool are 24 applied to Arua Town in Uganda. Four random cluster scenarios and a centralized system 25 were created and compared with the optimal clustered WSS. It was observed that the 26 operational cost of the four cluster scenarios is up to 13.9 % higher than the optimal, and 27 the centralized system is 26.6% higher than the optimal clustered WSS, consequently 28 verifying the efficacy of the proposed method to determine an optimal cluster boundary 29 for WSS. In addition, optimal homogeneous clusters improve efficiency by encouraging 30 reuse of wastewater and stormwater within a cluster and by minimizing leakage through 31 reduced pressure variations. 32

Introduction 40
Human well-being and improvement are governed by the availability of water and 42 energy [1]. These resources are either becoming less abundant relative to demand or are 43 running the risk of critical scarcity in many places with recent crises occurring in Cape 44 Town, South Africa and Chennai, India [2, 3]. Despite long-and short-term shortages, the 45 conventional approach of designing centralized urban utility systems has been driven by 46 19 th century technological principles, applied during a time when resources were 47 abundant, demand was relatively small, and growth in urban areas was rapid [4]. This 48 approach has led to a highly complex, interconnected, and dysfunctional systems that are 49 a hindrance to efficient and sustainable resource management, particularly where growth 50 patterns were uncontrolled and chaotic. With increasing global change pressures 51 including population increases and climate change, there are increasing concerns about 52 whether conventional centralized water systems will be able to manage scarcer and less 53 reliable water resources in a cost efficient manner [5,6]. These systems also require a 54 huge management effort and small changes in one part of the system can cause change 55 propagation through the whole system. For example, the rationing of water in areas with 56 a scarce water supply is a complex problem. The problem is even greater in the case of 57 large systems and when network distribution system pressure variation is high, and the 58 treated water supply is intermittent. This can cause unacceptable variations in the 59 Besides efficient use and reuse of scarce and less reliable resources, there are additional 81 reasons that support the shift from conventional centralized water systems to decentralized 82 clustered water systems. Clustered systems could be adapted to future changes with low effort 83 and without affecting the performance of the entire system [13,14]. Their modular diversity 84 exponentially increases the number of possible configurations that can be achieved for urban 85 water systems from a given set of inputs. Decentralized/clustered water systems can be 86 implemented in an incremental fashion, which reduces investment costs and makes the 87 transition easier to manage [15][16][17]. In addition, decentralized water systems allow a staged 88 development that traces the urban growth trajectory more closely and can be implemented 89 more quickly than a conventional approach (as the planning and implementation process is 90 easier to manage). According to Wang et al. [16], the gradual stepwise development of 91 decentralized systems enables the expansion of urban water systems that follows the spatial 92 growth, and hence, embeds flexibility to water systems. In addition, clustered systems provide 93 a better capacity to reduce the risk associated with water-system contamination through 94 biological or chemical ingression as well as malicious attacks with chemical, biological and/or 95 radiological agents. This is because decentralized units are small and independent units where 96 the effect associated with water contamination and malicious attacks will be contained within a 97 cluster. However, in case of centralized urban water-supply systems any contaminant 98 ingression and malicious attack could propagate to the whole systems. Internal peak demand 99 storage of potable water, in the form of aquifer storage and recovery systems, can be 100 integrated into decentralized systems wherein the injection and recovery wells can be placed 101 cluster, various parameters such as the location of water sources (surface water and ground 124 water), topography (Digital elevation-DEM), spatial and temporal distribution of population, 125 land use characteristics, and the socio-economic status of the area are considered [19]. These 126 parameters are used to define source-demand distance, intra-cluster demand, and topographic 127 homogeneity of the study area [20]. 128 topography, land uses, and associated demand characteristics. However, with the advent of 146 clustering, study of the behavior of smaller areas has become necessary to allow for the 147 creation of uniformity within the clusters. The population distribution, land use and socio-148 economic parameters are aggregated into a spatio-temporal demand distribution of the area. 149 Intra-cluster demand homogeneity is used as one of the parameters to minimize the effort 150 required to move water and wastewater. Intra-cluster homogeneity is the measure of the 151 similarities or dissimilarities between parcels of the same cluster. Clustering of large and small 152 demand areas together involves huge variations in consumption which can cause larger 153 pressure fluctuations than areas with similar demand distribution. This causes additional efforts 154 to supply and manage water and wastewater in the area. For example, areas with urban 155 agriculture have different demand patterns than industrial or residential areas. Thus, 156 maximizing the similarities by clustering residential and agricultural areas separately will 157 improve the required efforts as compared to if they were clustered together. The clustering of 158 different land uses into unique clusters will ensure multiple uses of water by cascading it from 159 higher to lower-quality needs and through reclamation treatments for a return to the supply 160 side of the other cluster. Water used by residential clusters can be re-used by industrial or 161 agricultural clusters. Demand based clustering also improves the ability to implement relevant 162 technology (i.e. water treatment and wastewater reuse recycling schemes) within a 163 homogeneous cluster. This also allows better control of small and homogeneous cluster units. 164 Topography is the other major factor which affects the flow of water and wastewater. Areas 165 with similar topographic characteristics (minimum differential relief) reduces cost associated 166 with infrastructure and pumping of water and wastewater in the area. However, large 167 variations in topography increases the effort required to collect and supply water, discharge 168 wastewater, and develop reuse systems. For example, water supply systems in areas with large 169 topographic variations cause large pressure fluctuations and require a large amount of energy 170 for pumping, as well as a large system capacity to satisfy the required level of service. Thus, 171 partitioning the urban area based on improved intra-cluster topographic homogeneity will 172 reduce the costs associated with water system investment and operation (energy). It allows for 173 improved resource efficiency by encouraging reuse and recycling of wastewater within the 174 cluster and by minimizing leakage (distribution system water loss) through reduced pressure 175

variations. 176
The methodology uses two major steps for clustering water-supply systems (WSS); 177 minimization of source-demand distance and maximization of intra-cluster homogeneity. The 178 details of the proposed steps are shown in Figure 1. The starting point of the proposed method 179 to cluster WSS is to consider all the input parameters of the study areas. This involves the 180 location of water sources (surface water, groundwater, and stormwater collection points), 181 topography, spatio-temporal population growth and associated demand, land use 182 characteristics and socio-economic status. Thus, the proposed clustering method minimizes the 183 source-demand distance by assigning demand to the source. The Euclidean norm minimization 184 approach is used to minimize source-demand distance. This method also maximizes the 185 homogeneity within the cluster so that source-demand distance, topography, and demand   greywater. This method involves grouping water sources and determining their group center 197 such that the effort required for collection is minimized. Then each demand parcel is assigned 198 to one source group center such that the distance between source and demand parcel (grid 199 cell) is minimized. Grid parcels are square cells characterized by attributes of spatial location (X 200 and Y coordinates), elevation, and demand. The source-demand distance for each parcel 201 depends on the specified source center locations. Euclidean norm minimization is used to 202 optimize the source-demand distance for all clusters. The formulation is done as a demand 203 assignment problem where each parcel is assigned to the nearest source. Then parcel 204 membership is determined from the minimization process. 205 The determination of the optimal number of source centers is not the focus of this paper. 206 The number of clusters for the area can be determined from the required size of a cluster. 207 According to Bieker et al. [8], the size of a cluster must be guided by the principle "as small as 208 possible, as big as necessary" to achieve the ecological, economic, and social interest. BMBF 209 [22] compared different scales for areas which range from 10,000 up to more than 200,000 210 people and proposed a recommended size ranging from 50,000 to 100,000 people as a suitable 211 scale for an integrated decentralized system for fast growing urban areas. Bieker et al. Once the groups of sources are identified, a simple source center calculation is carried out 227 to determine the centroid of the sources within the same group. Taking a similar approach as in 228 determining a mass center, the source center is calculated using Eq. (1). 229 Where Dc is source center, Qi and Di are the supply capacity of the source and the distance from 232 reference water source.

Assignment of Demand Parcel to the Nearest Source 235
Source allocation is a demand assignment problem where demand parcels are assigned to 237 the nearest source center. The method employs a minimization of the sum of Euclidean norms 238 within the cluster. Some researchers have proposed minimizing the sum of Euclidean distance 239 for shortest-path optimization [23]. The theories and algorithms for minimizing Euclidean 240 distance can be applied to many optimization problems. In this study, the sum of Euclidean 241 norms is used to determine the membership of parcels based on the shortest distance to the 242 water source centers. The same membership is given to the parcels that are assigned to the 243 same source center. This increases the compactness [21] and reduces the cost of pipe networks 244 and the energy needed for pumping long distances. Compacted networks with closer proximity 245 also increase resource efficiency by reducing leakage that would be higher in large centralized 246 systems. Given a set of parcels (representing the study area) with dimension vector P = {P1, 247 P2,…,Pn}, ∈ ℝ Euclidean norm defines, ‖ ‖ = ( * ) 1 2 , = 1 ℎ ‖ ‖ = | |, the 248 absolute value of P. ‖ ‖ is the Euclidean norm of P that is used to measure the distance 249 between points [24]. For example, suppose = ( , ) ∈ ℝ 2 and the source centers are 250 defined by = ( 1 , 1 ) ∈ ℝ 2 . Then the shortest distance from the source to the parcel is 251 determined using Eq. (2). 252 253 ‖ ‖ = √( 1 − ) 2 + ( 1 − ) 2 (2) Given the Euclidean norm of each parcel (from each source center), distance minimization is 255 performed using Eq. (3). Then each parcel will have membership (to the source center) based 256 on the minimization of Euclidean norms. The membership defines grouping of similar parcels 257 which are assigned to the same source center. The Euclidean norm minimization algorithm is 258 shown in Figure 3. 259 Where ( , ) is the Euclidean norm from the source centers, ‖ ‖ is the minimum 261 Euclidian norm of each parcel from source centers, is an attribute which is described by 262 parameters where the variation needs to be minimized (i.e location and elevation parameters). 263 The movement of water is based on an absolute distance which depends on the link (pipe) 264 layout and pressure distribution; this requires hydraulic simulation of the whole network. 265 However, to simplify the clustering process, in this study the minimization of the Euclidean 266 norm is employed by using the relative distance based on the coordinate of demand parcels 267 and supply centers. Once the parcels are assigned to the source center by the minimizing 268 Euclidean norm principle, the membership values are used in the maximization of cluster 269 homogeneity. 270

Maximization Intra-cluster Homogeneity and Connectivity 275
Traditionally, the design of WSS has been performed for large spatial extent areas which 277 involve a variety of topography, population distribution, land use, socio-economic, and 278 associated demands. However, with the advent of decentralization, the study of the behavior of 279 smaller areas has become a necessity so as to allow for uniformity within the clusters. In this 280 section, clustering involving the maximization of intra-cluster homogeneity and connectivity 281 analysis is used. Intra-cluster homogeneity is used to measure the similarity or dissimilarity 282 between parcels of the same cluster. Maximization of intra-cluster homogeneity allows 283 clustering the parcels so that parcel attributes within a cluster are closely related to one 284 another [20]. Three major parameters are considered in the clustering process. These are 285 membership (determined by Euclidean norm minimization), topography (elevation of the 286 parcels), and spatio-temporal demand distribution (determined from the population 287 Minimizing Euclidean norm algorithm (1) For the given C source centers, the Euclidean norm of a parcel is determined with respect to their parameter P = {P1, P2,…, Pn}, yielding the distances d(p, pc).
(2) Given the set of Euclidean norms {d1, d2,….dc} for each parcel, the total cluster Euclidean norm is minimized by assigning a parcel to the nearest source center.
(3) Steps i and ii are repeated until all parcels are assigned to the closest source center (then a membership will be assigned to each parcel based on the source center to which they belong).
distribution, land use, and socio-economic parameters). The clustering process involves the 288 grouping of similar parcels. An inter-cluster homogeneity is used as a measure of similarity 289 between parcels and a K-means optimization technique is employed to maximize intra-cluster 290 homogeneity by minimizing the total cluster variance with respect to the mean value. In 291 addition, a connectivity analysis is proposed to ensure the linkage of parcels within clusters. The 292 details of the proposed steps are discussed in the subsections. used as a measure of homogeneity. A K-means algorithm is a commonly employed method that 302 converges to a local optimum value for clustering. It is very popular because it is 303 computationally fast and memory efficient. A K-means algorithm is used herein to cluster the 304 WSS based on the principle of minimizing the dissimilarity of the three parameters: source-305 demand distance, topography, and demand within the cluster. Unlike topography and demand, 306 the distance parameter is dependent on the source centers; thus, distance related membership 307 value (discussed earlier) is used to identify to which source center each parcel is assigned.
Given a set of parcels p representing the study area {X1, X2,…, Xp}, where each parcel 309 has n-dimensions (i.e. topography, elevation), K-means clustering aims to partition the parcels 310 (p) into K clusters (K≤p) within an assigned data-set S {S1, S2,…,Sk}. For the given cluster 311 assignment A that involves K groups, the total cluster variance is minimized through 312 minimization of the sum of the squares of Euclidean norm for all clusters using Eq. (4). (4) Where A is cluster assignment, K is the number of clusters, Ni is the number data-set assigned 316 to Si, µi is mean of parcels in cluster Si and is calculated using Eq. (5) [26]. 317 A K-means algorithm achieves optimal clustering assigning parcels so that the difference 318 between parameters of the parcels and their centroids are as small as possible. Maximizing 319 intra-cluster homogeneity for WSS involves several steps (as shown in Figure 1). Firstly, the 320 optimizer selects initial cluster centroids (means) randomly. Secondly, an initial cluster 321 boundary is defined by assigning demand parcels to the initial cluster centroids. Thirdly, the K-322 means optimization evaluates the difference between parameters of the parcels and their 323 centroids (this is used as a measure of homogeneity). Fourthly, the optimization uses the 324 homogeneity as a termination criterion. It uses an iteration based evolutionary optimization 325 which involves the assignment of parcels to the closest mean and calculating a new mean until 326 the assignment no longer changes (means no improvement in homogeneity). Thus, the 327 simulation stops. Otherwise the above steps repeat until there is no change in parcel 328 assignment between subsequent simulations. Figure 4  (2) Given an initial set of K means, the algorithm assigns parcels to the closest mean so that the total variance is minimized with respect to the mean (3) Calculate a new mean to be the centroid of the cluster (4) Repeat steps (1) and (3) until the assignments do not change

Intra-cluster Parcels Connectivity 343
Intra-cluster parcel connectivity, defined as the linkage of a parcel within a cluster, is used 345 to check whether a parcel of one cluster is located in another cluster. Given the membership of 346 parcel "P" defined as P(m,n) and neighbor parcels as P(n±1,m±1), if parcel P(m,n) of one cluster 347 neighbors two or more parcels from another cluster, and has only one neighbor from its own 348 cluster, the evaluation of the minimum Euclidean norm of the parcel P(m,n) is performed with 349 respect to the neighboring cluster centroid and is re-assigned to the closest one. In addition, 350 the periphery parcels, which do not have many neighbors, are merged to the nearest cluster 351 group in case they belong to another cluster. This connectivity analysis alone does not 352 guarantee the existence of cluster members in another spatial location. One can use the 353 smallest recommended size of cluster and/or the smallest demand that a cluster should supply 354 to decide on merging isolated parcels to the neighboring cluster. An isolated parcel group will 355 be kept as an independent cluster if the demand it supplies is greater than the required 356 minimum size/demand within the cluster. However, a parcel group that does not satisfy the 357 mentioned condition will be merged to the neighbor cluster. The decision of which cluster to predicted spatial extent of Arua in 2032 is shown in Figure 6. 374 The town of Arua is experiencing a critical shortage of water because it depends on only a 380 small river (Enyau River) for its supply [28]. With population growth and increasing wealth it is 381 predicted that the water demand will likewise rise to 17,217 m 3 /d in the year 2032, which would worsen the water shortage. This predicted future demand takes into consideration the 383 different population density and socio-economic status of each of the parish areas. 384 The current approach to water management in Arua is based on a conventional centralized 385 approach where water is collected upstream, used, and discharged downstream and does not 386 encourage the use of local sources such as groundwater, stormwater harvesting, or wastewater 387 reuse and recycling. It has become obvious that the current practices of urban water 388 management are not sustainable to meet the future challenges in Arua. However, the rapid 389 urban growth in emerging areas coupled with the fact that those emerging areas do not have 390 mature infrastructure and urban planning for the area has not yet occurred means that there 391 are real opportunities to implement a clustered urban water system management system in 392 Arua. 393 394

Application of the Proposed Clustering Method and Results 395 396
One of the major initiatives of the Arua municipality is to degazette (repurpose) the forest 397 area (called Barifa) in a 5-year time period and incorporate it into the central business district of 398 the town. Since the forest area has a predefined boundary, the clustering processes in this 399 study can isolate this area and consider it to be a pre-clustered unit. Additionally, prior to the 400 clustering process, a decoupling of the existing central WSS from the emerging areas was 401 performed by identifying the existing municipality boundary (Figure 6). Then the proposed WSS 402 clustering technique which minimizes the source-demand distance and maximizes intra-cluster 403 homogeneity was applied. 404

Source-Demand Distance minimization 406
In this case study, 10 groundwater sources and 4 potential surface-water abstraction 408 locations were identified (Figure 7). Once the capacity and locations of available sources were 409 identified, the water sources were merged into groups such that the distance between grouped However, the determination of the number of groups required is not the focus of this paper. 417 Thus, the minimum cluster size with a population of 10,000 was used in decentralizing the 418 emerging area as suggested by Webster [5] to determine the number of source centers for 419 grouping. The evaluation of the distance between sources was preformed using Eq. (2). The 420 output of source-group identification process is shown in Figure 7(a) and (b). Once the groups 421 were identified the X, Y coordinate and supply capacity Qs were used to calculate source-422 centers. The source and source-center information is summarized in Table 1. prior to the clustering process. Eq. (2) is applied to each parcel of the emerging areas to 437 determine the Euclidean norm from the 7 source centers in the emerging area. Given the performed using Eq. (3). Then, each parcel was assigned a membership value. Figure 8(a, b)  440 shows the output of parcels assigned to the nearest source and the membership respectively 441 using Euclidian norm minimization. The membership defines groupings of similar parcels which 442 are apportioned to the same source center. 443 The above clustering shown in Figure 8 is purely based on distance and does not include 449 demand and topographic parameters. The next stage incorporates these parameters in addition 450 to a membership value using intra-cluster homogeneity maximization.

Maximizing Homogeneity and Connectivity Analysis 453
Homogeneity maximization was applied to determine the final cluster boundaries for the 455 study area. The distance-based membership value (determined in the distance minimization 456 stage), topographic, and demand information were used as input parameters. The study area 457 topography ranges from 1,160 m to 1,240 m asl, and the determination of demand was 458 performed using the population, socio-economic status, and land use information. The input 459 elevation and demand information are plotted for the case study area and shown in Figure 9 Given the input parameters, a K-means algorithm was applied to maximize the intra-cluster 466 homogeneity. Multiple runs of the K-means simulation were performed to avoid the problem 467 associated with initialization, and the algorithm showed similar clusters. The final output of the 468 clusters is shown in Figure 10 a parcel group which is in another cluster, the size was used to decide whether to keep the 481 group as a new independent cluster or to merge it with the nearest cluster. A group merging 482 was performed if a cluster/group was too small. Groups with a size less than 20% of the 483 maximum cluster size were distributed to the neighboring cluster to avoid large variation in 484 cluster size. However, a recommended cluster size and/or the smallest demand that a cluster 485 should supply were used to decide whether to merge isolated parcels. Figure 11(a) shows the 486 final cluster boundaries after isolated neighboring parcels were re-distributed, and the final 487 cluster boundary for the case study area is shown in Figure 11 cluster. This was necessary to create an acceptable sample size for the analysis. To generate 516 randomly assigned clusters, the cluster boundaries for each scenario were rotated 517 approximately 10° counter-clockwise from the previous scenario. This includes scenario-1 518 through Scenario-4. In addition, a typical centralized WSS was used as a benchmark for 519 comparison. Since the design of WDS is not the focus of this paper, a parcel-based power 520 footprint calculation was used for comparison between the scenarios. The power requirements 521 of the four decentralized WSS boundaries were compared with the proposed decentralized 522 WSS. Operational cost can be visualized by analysis of the power requirements for the various 523 scenarios. Cost is directly proportional to power, therefore the cluster which demands the least 524 power will be most cost efficient. The power provided by a pump is determined using Eq. (6). 525 Where P is the power to supply the fluid, ρ is the density of the fluid in kg/m 3 , g is the 526 gravitational acceleration in m/s 2 , Q is the flow rate in m 3 /s, and hp is the total head in meters. 527 The total head is the summation of the velocity head (ℎ ), friction head (ℎ ), and elevation 528 head (ℎ ) are found in Eq. (7). The velocity head was calculated using In this equation, is the imperial unit weight of the fluid and D is the distance from the 544 source center to the parcel. In some cases, the source center elevation is greater than the 545 parcel being supplied with water, causing the elevation head to be negative. When this arises, 546 the summation of the heads will most likely be negative; it is assumed that the power cannot 547 be negative. This ensures only positive power requirements are considered for the total cluster. 548 The last calculation is converting the power requirements to a yearly operational cost. The 549 following formula can be used to estimate the cost. Where the cost is in USD per year, P is the power in Watts, R is the current conversion factor for 553 Ugandan Shilling (UGX) to USD, C is the current price per kWh for Uganda in shs/kWh. This 554 calculation was completed for each scenario in the power usage scenario analysis. 555 The design of water distribution network and optimization of capital cost is not the focus of 559 this paper. Thus, to conduct a comparative analysis on the case study in Arua, a few 560 assumptions had to be made and used for each scenario in a similar manner. Every cluster 561 scenario of the WSS considered to have similar 15.24 cm (6-inch) schedule 80 distribution main 562 with a length halfway to the farthest distance from the source center to the cluster boundary. 563 In addition, a 2.54 cm (1-inch) schedule 80 pipe is to be used for all distribution from the main 564 to customer networks, having a coefficient of retardation of 150 and an inner diameter of 2.43 565 cm (0.957 in) (used in Eq. (8)). This assumption is made so that each random WSS scenario is 566 compared with optimized cluster using parcel-based energy usage. A few characteristics will 567 change for each parcel of different scenarios, such as length, elevation and flow rate; the 568 length, elevation and flow rate are taken from Figures 9(a, b). The same assumptions are 569 applied to the centralized WSS scenario where the source center is located at the existing water 570 source C9. 571 When performing the power usage analysis, all equations and concepts discussed in the 572 methodology section were applied to each parcel within the enclosed area, excluding parcels in 573 the existing municipality, forest area and outside the predicted town extent (Figure 6). This was 574 done for each of the five scenarios to produce an adequate sample for the power usage 575 analysis. Table 2 shows the power requirements of each cluster within every scenario, the total 576 power required by each scenario, the additional power usage each scenario has compared to 577 the proposed WSS, and the operational cost per year for each scenario was claculated. It is also 578 important to note that this is a comparative analysis as opposed to an absolute O&M cost 579 estimate of an optimal WDS. The total and excess power usage from Table 2 is represented in 580 Figure 12 with two separate axes. 581 The yearly operational cost for each scenario was estimated using Eq. (10). To use this 582 equation, the current conversion rate for UGX to USD and the price per kWh must be known; as 583 of November 2018, the conversion rate was $0.00027 USD/UGX (retrieved from Google 584 Finance) and the price was $0.185247 USD/kWh [30].  Figure 12. The bar graph represents the total power requirements per cluster. The line graph 594 represents the excess power of the WSS scenarios compared to the proposed WSS 595 same cluster. Maximization of intra-cluster homogeneity allows clustering the parcels so that 616 parcel attributes within a cluster are closely related to one another. Three major parameters 617 considered in the clustering process, include membership (determined from Euclidean norm 618 minimization), topography (elevation of the parcels), and spatio-temporal demand distribution 619 (determined from the population distribution, land use, and socio-economic parameters). A K-620 means optimization technique were applied to maximize intra-cluster homogeneity to reduce 621 the costs associated with water system investment and operation (energy and leakage) and to 622 improve resource efficiency (recycling). The efficacy of the developed clustering method was 623 tested in a real case study of Arua, Uganda. The WSS in Arua was divided into nine clusters, 624 thereby reducing the effort required to move water and wastewater, as well as developing 625 systems that offer opportunity to adapt to future changes. The case study demonstrated that it 626 is possible to apply the developed methodology to delineate clusters based on minimizing 627 distance between source and use and maximizing the intra-cluster homogeneity. An analysis 628 using calculated power requirements showed that the clustered approach did provide lower 629 cost and more efficiency.