Morphogenesis of Urban Water Distribution Networks: a Spatiotemporal Planning Approach for Cost-Efﬁcient and Reliable Supply

entropy

Article Morphogenesis of Urban Water Distribution Networks: A Spatiotemporal Planning Approach for Cost-Efﬁcient and Reliable Supply

Jonatan Zischg * , Wolfgang Rauch and Robert Sitzenfrei

Unit of Environmental Engineering, University of Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria; [email protected] (W.R.); [email protected] (R.S.) * Correspondence: [email protected]; Tel.: +43-512-507-62160

Received: 26 July 2018; Accepted: 13 September 2018; Published: 14 September 2018

Abstract: Cities and their infrastructure networks are always in motion and permanently changing in structure and function. This paper presents a methodology for automatically creating future water distribution networks (WDNs) that are stressed step-by-step by disconnection and connection of WDN parts. The associated effects of demand shifting and flow rearrangements are simulated and assessed with hydraulic performances. With the methodology, it is possible to test various planning and adaptation options of the future WDN, where the unknown (future) network is approximated via the co-located and known (future) road network, and hence different topological characteristics (branched vs. strongly looped layout) can be investigated. The reliability of the planning options is evaluated with the flow entropy, a measure based on Shannon’s informational entropy. Uncertainties regarding future water consumption and water loss management are included in a scenario analysis. To avoid insufficient water supply to customers during the transition process from an initial to a final WDN state, an adaptation concept is proposed where critical WDN components are replaced over time. Finally, the method is applied to the drastic urban transition of Kiruna, Sweden. Results show that without adaptation measures severe performance drops will occur after the WDN state 2023, mainly caused by the disconnection of WDN parts. However, with low adaptation efforts that consider 2–3% pipe replacement, sufficient pressure performances are achieved. Furthermore, by using an entropy-cost comparison, the best planning options are determined.

Keywords: urban transition; EPANET 2; network disconnection; network growth; uncertainties; performance and adaptation; ﬂow entropy

1. Introduction Cities are highly dynamic structures that are experiencing demographic changes with large population growth in most regions of Asia and Africa, whereas a general population decline is taking place in Europe. The shrinking city phenomenon and abandonment of urban districts are gaining in importance worldwide. According to Oswalt and Rieniets [1] every fourth city in the world was shrinking between 1990 and 2000 with a rising trend. One of the most prominent examples is the city of Detroit, USA, where today about one third of the town area is abandoned or demolished due to deindustrialization [2]. Conversely, strong city growth and the expansion of neighborhoods with annual growth rates up to 5% are observed in the last years [3]. These urban transitions stress not only the above-ground infrastructure like streets or public transport, but also the underground water infrastructure due to the necessary modiﬁcations in the network’s structure and function. Water supply systems are one of the most important infrastructures in society and its well-functioning is essential. Shifting demand patterns, endeavors from centralized

Entropy 2018, 20, 708; doi:10.3390/e20090708 www.mdpi.com/journal/entropy Entropy 2018, 20, 708 2 of 21 to decentralized techniques [4], network expansions, or connectivity loss are only a few examples for transition processes which stress the ability to perform. Along with the long life span of several decades (in some cases even exceeding 100 years), the influence of a newly constructed pipe in the future system and the interaction with the existing system emphasize the importance of future oriented planning and management [5]. “Network transitioning” describes the pathway from an existing (source) network to a future (destination) network [6]. Usually transition processes of water infrastructure are relatively slow and take place over decades, where the network structure remains nearly constant (see e.g., Ref. [4]). Here we present a method and apply it to a case study to assess fast ongoing transitions, with severe impacts on the network’s structure. Changes of the network structure are densifications, expansions and/or disconnection of network parts caused by climate change, population changes, changes in land use, and shifts in water technology [7–9]. While new network parts must be designed for expected load conditions and spatial constraints, the existing network may need to be adapted to provide sufficient performances at all times of the transition process. In many cases, the detailed future network layout is largely unknown, because decisions on urban transitions are usually made without taking the water infrastructure into account. In summary, transitioning of urban infrastructure systems is characterized by real world complexity and high uncertainties, which is strongly dependent on the urban development. In the field of water distribution system analysis, it is widely accepted that measures for hydraulic capacity reliability and redundancy have to be considered in the design process to account for such uncertainties and unforeseeable events. Among many stochastic and reliability-based methods, flow entropy, based on Shannon’s informational entropy [10], is proven to be a consistent surrogate measure of reliability and failure tolerance [11,12]. High entropy values indicate equally important flow paths, i.e., the absence of dominant supply structures, whose failure could cause a severe system breakdown. Higher entropies are not only dependent on the number of supply sources and alternative flow paths, but also on their scale and spatial location. For example, a loop in the network structure with high flows (e.g., proximity to the supply source) is rated higher than a loop in secondary pipes with lower flows, where potential system failures have smaller impacts on the global performance. Compared to other criteria, this measure has the advantage that it is relatively easy to calculate, non-iterative, and that the data requirements are minimal [11,13]. Previous studies presented methods of designing and evaluating the long-term transition under deep uncertainties of water infrastructure (planning horizon of several decades), as for example shown by Marlow et al. [14], Eggimann et al. [15] and Urich and Rauch [16] whose work emphasized on urban drainage system transitions. Creaco et al. in Refs. [17,18] presented an optimization methodology for the optimal growth of water distribution networks (WDNs) with respect to costs and reliability, also considering demand uncertainties. In their work, they considered the step-by-step connection of pipes and concluded that solely designing one ideal “final state network” is not optimal, neglecting possible deficiencies of the WDN at intermediate states. However, disconnections and uncertainties of the network topology were not considered in their works. Existing studies of complex real world WDN transitions are limited and therefore further research is necessary also with regard to exploring case studies of unspecific methods [19,20]. A promising concept is the creation of many possible future network layouts, rather than assessing a fixed topology. The idea is to use the often available future road network (RN) from city planners as the basis for an automatic WDN planning approach. This concept of so-called “in-silico” or “semi-virtual” networks was already used for network reconstructions [21] or even the approximation of real water infrastructure networks where missing network information is approximated with known surrogate information, such as the co-located road network data [22,23]. In comparison with the work presented in Ref. [22], this study extends transition modeling by the interaction of the existing WDN data and future “in-silico” network data, also taking into account uncertain population developments that allow for future design under a probable range of uncertainties. Furthermore, the work presents a simple local adaptation concept of pipe replacement Entropy 2018, 20, 708 3 of 21 Entropy 2018, 20, x FOR PEER REVIEW 3 of 21 basedbased onon thethe least-least- “monetary”“monetary” costcost pathpath whichwhich isis appliedapplied toto thethe WDN,WDN, inin casecase aa defineddefined criticalcritical performanceperformance can no longer longer be be achieved achieved at at a acertain certain tr transitionansition state. state. After After sufficient sufficient performances performances are areachieved achieved for forall allWDN WDN states, states, we we perform perform a acost-r cost-reliabilityeliability comparison comparison of of different WDNWDN designdesign alternativesalternatives (layout(layout andand designdesign demand).demand). Entropy-costEntropy-cost ratiosratios helphelp decisiondecision makersmakers identifyidentify reliablereliable planningplanning optionsoptions thatthat workwork forfor aa broadbroad rangerange ofof futurefuture conditions,conditions, andand quantifyquantify necessarynecessary costscosts (WDN(WDN layoutlayout andand adaptationadaptation costs)costs) atat an an earlyearly state state of of the the transition. transition. TheThe noveltynovelty ofof thisthis workwork isis toto investigate many planning options with regard to WDN structure, andand toto provideprovide sufficientlysufficiently working,working, reliablereliable andand cost-efficientcost-efficient systemssystems overover time.time. SpecificSpecific problemproblem statesstates cancan bebe well-definedwell-defined andand optimized,optimized, butbut inin reality,reality, transitiontransition processesprocesses areare oftenoften drivendriven byby aa multitudemultitude ofof uncertain uncertain conditions. conditions. Therefore, Therefore, the the proposed proposed approach approach serves serves as aas screening a screening method method for decisionfor decision makers makers to realize to realize a masterplan a masterplan and givesand gives a holistic a holistic view view on network on network dynamics, dynamics, rather rather than focusingthan focusing on one on specific one spec problemific problem or state. or state.

2.2. MaterialsMaterials andand MethodsMethods 2.1. Model Development 2.1. Model Development This section presents the development of the model to assess WDN transitioning, on the basis This section presents the development of the model to assess WDN transitioning, on the basis of of the city masterplan, future network design alternatives and concepts for system adaptation. the city masterplan, future network design alternatives and concepts for system adaptation. Additionally, all planning options are assessed by a variety of scenarios (e.g., demand increase due to Additionally, all planning options are assessed by a variety of scenarios (e.g., demand increase due population growth) during the transition process. In Figure1 the model is shown in a ﬂow chart and to population growth) during the transition process. In Figure 1 the model is shown in a flow chart described in detail in the subsequent sections (see headed associated section numbers). and described in detail in the subsequent sections (see headed associated section numbers).

FigureFigure 1.1. DescriptionDescription ofof thethe modelmodel forfor waterwater distributiondistribution networknetwork (WDN)(WDN) transitioning.transitioning.

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2.1.1.2.1.1. City City Masterplan Masterplan InIn urban urban planning, planning, the the citycity masterplanmasterplan comprisescomprises a description of of the the futu futurere city’s city’s spatial spatial and and temporaltemporal development, development, defines defines regulatory regulatory changes, changes, and and lays lays out aout strategic a strategic direction direction of future of future visions. Comprehensivevisions. Comprehensive objectives objectives regarding regarding urban landscape urban landscape and water and resource water resource development, development, national andnational public and interests public areinterests specified are specified from a municipality from a municipality perspective perspective and therefore and therefore a masterplan a masterplan is case studyis case specific study specific [24]. Such [24]. aSuch blueprint a blueprint for the for futurethe future is the is the basis basis for for the the successful successful realization realization ofof a transitiona transition process, process, out out of of which which various various planning planning alternatives alternatives cancan be derived for for further further testing testing and and optimization.optimization. Furthermore, Furthermore, it it decreasesdecreases thethe numbernumber of uncertainties and and makes makes the the modeling modeling process process lessless complex complex [25 ,26[25,26].]. The masterplanThe masterplan defines, defines, for example, for example, ambitions ambitions from centralized from tocentralized decentralized to waterdecentralized management water in management the future, the in the disconnection future, the disconnection of abandoned of city abandoned districts duecity todistricts water due quality to problems,water quality expected problems, city densifications expected city or densifications expanding neighborhoods, or expanding neighborhoods, which lead to network which lead growth. to Innetwork the cases growth. where In no the masterplan cases where is available, no masterplan stochastic is available, network stochastic growth models network such growth as random models or fitness-basedsuch as random attachment or fitness-based models canattachment be used model to anticipates can be network used to anticipate development network [27]. development [27]. 2.1.2. Source and Destination Networks 2.1.2. Source and Destination Networks The starting point of this modeling approach is an existing hydraulic model (e.g., EPANET 2 model)The of starting the WDN point (hereinafter of this modeling called sourceapproach network). is an existing It includes hydraulic all water model sources, (e.g., EPANET pipes and 2 junctionsmodel) of with the theirWDN attributes, (hereinafter control called devices source and netw allork). information It includes on spatiallyall water andsources, time pipes dependent and waterjunctions consumption with their andattributes, water control leakage. devices While an thed all source information network on spatially represents and an time existing dependent WDN, thewater future consumptionsystem may and be water fairly leakage. unknown While in terms the so ofurce a detailednetwork networkrepresents layout an existing and future WDN, water the demandfuture system (e.g., duemay tobe cityfairly expansions). unknown in terms Based of on a detailed a city masterplan, network layout a new and future future supplywater demand concept can(e.g., be developed,due to city considering,expansions). e.g.,Based various on a futurecity masterplan, network topologies. a new future In this supply process, concept many can future be systemsdeveloped, (destination considering, networks) e.g., various with different future network graph theoretical topologies. and In this hydraulic process, design many arefuture created systems (e.g., (destination networks) with different graph theoretical and hydraulic design are created (e.g., loop loop degree of the network, design demand and supply redundancy). To account for future demand degree of the network, design demand and supply redundancy). To account for future demand uncertainty in the design process, different pipe capacity factors (hereinafter called “safety factors”) uncertainty in the design process, different pipe capacity factors (hereinafter called “safety factors”) are used. Compared to the source network, the destination network differs in its topology, demand are used. Compared to the source network, the destination network differs in its topology, demand distribution, pipe diameter & roughness, position of water sources and water losses (see Figure2). distribution, pipe diameter & roughness, position of water sources and water losses (see Figure 2).

FigureFigure 2.2. ConceptualConceptual representation representation of an of urban an urban transi transitiontion affecting affecting the water the distribution: water distribution: Source Sourcenetwork network and possible and possible future futuredestination destination networks. networks.

GivenGiven a a deﬁned defined goal goal inin thethe citycity masterplan,masterplan, aa setset ofof destination networks is is created. created. Thereby Thereby partsparts of of the the source source network network and and the the newly newly designed designed “in-silico” “in-silico” WDN WDN parts parts are are combined. combined. The Theidea idea is tois use to use the the often often available available future future road road network network (RN) (RN) from from city city plannersplanners as the basis basis for for an an automatic automatic WDNWDN planning planning approach. approach. PreviousPrevious studies proved the high co-location co-location between between road road and and urban urban infrastructureinfrastructure networks, networks, where where aboutabout 80%80% ofof WDNsWDNs are located below below 50% 50% of of the the RN RN [28,29]. [28,29]. In In the the presented model, it is assumed that 100% of the WDN is co-located with the RN (WDN ⊆ RN). presented model, it is assumed that 100% of the WDN is co-located with the RN (WDN ⊆ RN). However, not all roads may contain pipes; this is mainly due to cost reasons. So there are the two However, not all roads may contain pipes; this is mainly due to cost reasons. So there are the two extreme cases of possible “in-silico” WDN topologies; (1) a branched network, representing the extreme cases of possible “in-silico” WDN topologies; (1) a branched network, representing the minimum spanning tree of the RN, and (2) a highly looped topology, where the WDN layout is minimum spanning tree of the RN, and (2) a highly looped topology, where the WDN layout is identical with the RN. Between these two cases, the loop degree can vary with the cycle index (CI).

Entropy 2018, 20, 708 5 of 21 identicalEntropy 2018 with, 20, thex FOR RN. PEER Between REVIEW these two cases, the loop degree can vary with the cycle index5 of (CI). 21 While a CI of 0 describes a branched layout, a CI > 0 indicates the availability of alternative ﬂow While a CI of 0 describes a branched layout, a CI > 0 indicates the availability of alternative flow paths paths (loops) in the WDN, which is also an indicator for reliability and redundancy. More detailed (loops) in the WDN, which is also an indicator for reliability and redundancy. More detailed information of the CI can be found in Mair et al. [29]. During the generation process of the future WDN information of the CI can be found in Mair et al. [29]. During the generation process of the future parts, different CIs are considered. Furthermore, the digital elevation model (DEM), the existing WDN, WDN parts, different CIs are considered. Furthermore, the digital elevation model (DEM), the (future) demand distribution, the position of (future) water sources and the (future) road network are existing WDN, (future) demand distribution, the position of (future) water sources and the (future) required for model input (see Figure3). The “in-silico” WDN parts can either represent missing data road network are required for model input (see Figure 3). The “in-silico” WDN parts can either of existing systems, or possible future network expansions/densiﬁcations. represent missing data of existing systems, or possible future network expansions/densifications.

FigureFigure 3. 3.Example Example of of an an existing existing WDN WDN layout layoutand and thethe approximationapproximation ofof unknownunknown WDN parts using spatialspatial road road network network data data as as surrogate. surrogate.

TheThe WDN WDN creation creation is is performed performed with with DynaMind, DynaMind, anan openopen sourcesource softwaresoftware writtenwritten inin C++C++ and and developeddeveloped at at the the Unit Unit for for Environmental Environmental Engineering Engineering ofof thethe UniversityUniversity ofof Innsbruck.Innsbruck. The software containscontains (1) (1) a a spanning spanning tree tree based based algorithm algorithm forfor designingdesigning aa minimalminimal operating new network network layout, layout, (2)(2) an an algorithm algorithm to to create create a a cyclic cyclic structure structure for for the the purposepurpose ofof networknetwork reliability and (3) an an automated automated pipe-sizingpipe-sizing algorithm algorithm to to create create WDN WDN based based on on geographic geographic information information system system (GIS) (GIS) data data as input as input [30]. To[30]. obtain To aobtain connected a connected network, network, the “in-silico” the “in-silico” parts are parts connected are connected to the closest to the junctionclosest junction of the existing of the WDN,existing unless WDN, other unless connection other connection points are points manually are deﬁned.manually The defined. software The uses software a pipe uses sizing a pipe algorithm sizing foralgorithm selected pipefor selected sets (e.g., pipe all sets unknown (e.g., all WDN unknow parts)n WDN based parts) on a deﬁned based on pressure a defined surface pressure inclination surface at inclination at hourly peak demand (Qh,max) as presented by Saldarriaga et al. [31]. Other WDN design hourly peak demand (Qh,max) as presented by Saldarriaga et al. [31]. Other WDN design optimization algorithmsoptimization might algorithms be more might suitable be more when suitable focusing when on focusing the detailed on the planning detailed planning of small of case small studies. case studies. However, the reasons for choosing this design algorithm are the low computational costs However, the reasons for choosing this design algorithm are the low computational costs and the good and the good approximation of optimal WDN design solutions, even for WDNs with several approximation of optimal WDN design solutions, even for WDNs with several thousands of nodes thousands of nodes and pipes. and pipes.

2.1.3.2.1.3. Intermediate Intermediate State State Networks Networks InIn most most cases, cases, changes changes from from an an existing existing system system toto thethe ﬁnalfinal systemsystem are long term processes processes which which cannotcannot be be directly directly implemented implemented at at one one speciﬁcspecific timetime step,step, butbut havehave toto bebe successivelysuccessively introduced in in different phases, making the modeling of intermediate transition states unavoidable [18]. During different phases, making the modeling of intermediate transition states unavoidable [18]. During such a transition process the network’s structure and function changes progressively. Parts of the such a transition process the network’s structure and function changes progressively. Parts of the existing system may be taken out of service, while other parts are connected to the existing system or existing system may be taken out of service, while other parts are connected to the existing system the demand pattern changes, e.g., due to changing land use. At the same time, the total water or the demand pattern changes, e.g., due to changing land use. At the same time, the total water consumption and its spatial distribution can change over time. Such stresses can cause a system consumption and its spatial distribution can change over time. Such stresses can cause a system breakdown, where required performance levels cannot be guaranteed anymore. In our analysis breakdown, where required performance levels cannot be guaranteed anymore. In our analysis several transition state models, which represent specific time steps during the investigation period, are automatically created (see Figure 4).

Entropy 2018, 20, 708 6 of 21 several transition state models, which represent speciﬁc time steps during the investigation period, are automatically created (see Figure4). Entropy 2018, 20, x FOR PEER REVIEW 6 of 21

FigureFigure 4. 4.Automatic Automatic creation creation ofof intermediateintermediate WDN on basis of of the the source source and and destination destination WDN WDN and and thethe city city masterplan. masterplan.

TheThe basis basis forfor thethe intermediateintermediate statestate modelmodel configurationsconfigurations is is the the source source and and the the destination destination networksnetworks and and the the masterplan, masterplan, whichwhich describesdescribes the spatiotemporal development development of of the the city, city, and and as as wellwell as theas WDN.the WDN. By disconnecting By disconnecting spatially spatia definedlly pipesdefined from pipes the WDN from (“intended the WDN disconnection”), (“intended thedisconnection”), network may bethe splitnetwork into may sub-networks be split into which sub-networks are not connected which are to not the connected water source to the anymore. water Thissource is the anymore. case when This is a the pipe case coincides when a pipe with coincides a bride with or cut-edge a bride or of cut-edge the network, of the network, whose deletionwhose increasesdeletion increases the number the number of connected of connected components compon [32ents]. Resulting[32]. Resulting “unintended” “unintended” disconnections disconnections are are determined through a network connectivity analysis. Unconnected parts are either additionally determined through a network connectivity analysis. Unconnected parts are either additionally removed, or reconnected to the main network, depending on the unintended and intended pipe removed, or reconnected to the main network, depending on the unintended and intended pipe disconnection ratio. Newly connected pipes have the attributes (location, connection points, disconnection ratio. Newly connected pipes have the attributes (location, connection points, diameter) diameter) of the destination network and their year of connection is defined in the masterplan. The of the destination network and their year of connection is defined in the masterplan. The disconnected disconnected nodal demand is shifted to the newly connected parts, and the distribution is assumed nodal demand is shifted to the newly connected parts, and the distribution is assumed to coincide to coincide to the final WDN, while the total demand is scenario dependent (see Section 2.1.4). By the to the final WDN, while the total demand is scenario dependent (see Section 2.1.4). By the fact that fact that in a first step the intermediate WDN state are not individually designed, a “single state in a first step the intermediate WDN state are not individually designed, a “single state design” is design” is followed. With this strategy critical WDN states are identified in space and time. In a followed. With this strategy critical WDN states are identified in space and time. In a second step a second step a WDN re-design based on the least- “monetary” cost path is considered in case a WDNspecified re-design performance based on cannot the least- be assured “monetary” (see Section cost path 2.1.6). is considered in case a specified performance cannot be assured (see Section 2.1.6). 2.1.4. Scenario Analysis 2.1.4. Scenario Analysis Future water demands and their geospatial distributions are highly uncertain [33]. They depend Future water demands and their geospatial distributions are highly uncertain [33]. They depend on multiple factors, including changes in population and consumption behavior, alterations in land onuse, multiple and tourism factors, [34]. including Water loss changes reduction in population is a main challenge and consumption in WDN operation behavior, and alterations management, in land use,saving and valuable tourism [resources34]. Water and loss providing reduction isadditional a main challenge flow capacities in WDN [35]. operation Furthermore, and management, the water savingdemand valuable fraction, resources which is and supplied providing via the additional central distribution flow capacities system, [35 depends]. Furthermore, on the degree the water of demanddecentral fraction, supply which(e.g., rainwater is supplied harvesting) via the centralor the provision distribution of sufficient system, fire depends flow [36]. on theIn this degree work of decentralwe investigate supply possible (e.g., rainwater future developments harvesting) orof thethe provisioncity’s total ofwater sufficient demand fire by flow a scenario [36]. In analysis, this work wewhere investigate the base possible demand future is multiplied developments by time ofdependent the city’s factors total water [37]. demand by a scenario analysis, where the base demand is multiplied by time dependent factors [37]. 2.1.5. Simulation and Performance Assessment 2.1.5. Simulation and Performance Assessment The presented model has an interface to the hydraulic solver EPANET 2 [38] by which every networkThe presented state is simulated model hasfor peak an interface demand toand the a pe hydraulicriod of low solver water EPANET usage. Different 2 [38] by daily which patterns every networkfor domestic state isand simulated industrial for demands peak demand as well and as for a period water losses of low are water applied usage. [39]. Different With the daily simulation patterns forresult, domestic global and performance industrial demands indicators as are well calculated as for water to assess losses arethe appliedhydraulic [39 condition,]. With the the simulation water result,quality global and performancethe reliability indicatorsof the WDN. are calculatedThe follow toing assess performance the hydraulic indicators condition, are calculated: the water Nodal quality andpressure the reliability head at ofpeak the demand, WDN. The maximum following water performance age during indicators a low demand are calculated: period, flow Nodal entropy pressure at headhourly at peak peak demand, demand, maximumand the number water of age elem duringentary a low loops demand of the created period, WDN flow entropy layouts. at hourly peak demand,The and principles the number of global of elementary performance loops indicators of the created (PIs) are WDN briefly layouts. outlined. We use normalized performance indices, where each node i of the WDN is associated with a performance value from 0 (requirements not fulfilled) to 1 (requirements fulfilled), based on predefined threshold limits [40]. Equation (1) shows the calculation of the local nodal performance PIi with the upper and lower threshold values Tu and Tl. The factor α (0 or 1) depends on the performance criterion (minimum pressure or maximum water age), and xi is the performance variable (e.g., nodal pressure). In

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The principles of global performance indicators (PIs) are briefly outlined. We use normalized performance indices, where each node i of the WDN is associated with a performance value from 0 (requirements not fulfilled) to 1 (requirements fulfilled), based on predefined threshold limits [40]. Equation (1) shows the calculation of the local nodal performance PIi with the upper and lower threshold values Tu and Tl. The factor α (0 or 1) depends on the performance criterion (minimum pressure or maximum water age), and xi is the performance variable (e.g., nodal pressure). In addition, a weight wi (e.g., nodal demand) is assigned to the local performances PIi and aggregated to one global representative value PI, where N is the total number of nodes (see Equation (2)).

 |0 − α|, x ≤ T  i l PI = |1 − α|, xi ≥ Tu (1) i  xi−Tl  − α , x > T ∧ x < Tu Tu−Tl i l i

∑N w × PI = i=0 i i PI N (2) ∑i=0 wi For the WDN reliability assessment the informational ﬂow entropy E is calculated. The concept is based on Shannon’s entropy function nn S = − ∑ pl ln pl (3) l=1 where S is the entropy; pl is the probability of the l-th outcome; and nn is the number of outcomes [10]. S is zero, if one event is certain and the probabilities of the other events are zero. Tanyimboh and Templeman [41] developed a method to account for entropy in WDNs (Equation (4)).

s N ! Q Q d d Qij Qij E = − ∑ 0k ln 0k − ∑ i ln i + ∑ ln (4) T T T Ti T Ti k=1 i=1 ij∈NDi | {z } | {z } E-supply E-node(s) source(s)

In WDN analysis, E describes the uncertainty of all possible flow paths from the source to every demand node [11,42]. Usually, the number of sources is limited to one or a few supply nodes, confronting many demand nodes and, therefore, inhomogeneity in the flow distribution that exists. Also, the node degree (i.e., connected pipes to a junction) is limited through space [43], which influences entropy maximization. High entropy values indicate that a demand node is connected by many equally important flow paths, which characterizes highly reliable and redundant systems that can cope best with failures, such as pipe breaks [44]. Hence, in terms of WDN design, a high entropy value is sought. The value increases when the system is supplied by more sources of equal importance and when the flow paths have similar flows (absence of a “main” path). E consists of two terms, one describes the entropy related to the supply sources, and the other is related to the nodes. N is the total number of nodes, s denotes the number of sources, T is the total demand (=ˆ total inflow to the WDN), di is the demand at node i, Ti is the total inflow at node i, Qij is the outflow at node i to each successor node j (ij ∈ NDi, the pipe set of successors at node i) and Q0k is the inflow from supply source k [13]. When, e.g., considering only one supply source, the first term in Equation (4) is zero. Moreover, the number of elementary loops in the network is assessed by Γ = E − N + 1, where E is the number of edges (pipes, valves, pumps) and N the number of nodes (junctions, tanks, reservoirs) of the WDN [43]. The various WDN design alternatives are assessed with a simple cost function which depends on the length and diameter of the pipes [13]. This allows for a cost-reliability comparison of different transition strategies, to support decision makers in choosing a reliable layout and design for the new WDN. Any other hydraulic modeling [13], network graph [32], or energy [45] based performance indicators can easily be implemented in the model. Entropy 2018, 20, 708 8 of 21

2.1.6. Critical Performance and Adaptation Existing WDNs can tolerate a certain amount of deviations from the optimum planning state to deal with uncertainties (e.g., demand increase, connectivity loss), whilst still guaranteeing sufficient performance requirements (e.g., sufficient pressure). In case the WDN cannot satisfy all requirements local adaptation measures (e.g., pipe replacement) must be considered to improve the performance to a sufficient level. For cost benefits, an effort is made to leave existing components of the WDN unchangedEntropy 2018 as, 20 much, x FOR asPEER possible. REVIEW Therefore, we focus on the redesign and replacements of the weakest8 of 21 components by a diameter increase and roughness decrease, in case the minimum pressure threshold valuecomponentspcrit is not by met.a diameter To find increase the weak and networkroughness components, decrease, in case pipes the with minimum unusual pressure high friction threshold loss value pcrit is not met. To find the weak network components, pipes with unusual high friction loss (user-defined threshold hcrit) are identified and redesigned on a least- “monetary” cost path from the (user-defined threshold hcrit) are identified and redesigned on a least- “monetary” cost path from the critical node to the supply source. The concept is shown in Figure5 and subsequently described. critical node to the supply source. The concept is shown in Figure 5 and subsequently described. The The WDN can be mathematically represented as weighted graph G(V, E(W)), which consists of a node WDN can be mathematically represented as weighted graph G(V, E(W)), which consists of a node set set V, an edge set E and a set of values W mapped. Dijkstra’s algorithm [46] is used to identify the V, an edge set E and a set of values W mapped. Dijkstra’s algorithm [46] is used to identify the shortest shortest path L in the network from a critical node (e.g., minimum pressure pmin) to a given root node path L in the network from a critical node (e.g., minimum pressure pmin) to a given root node (e.g., (e.g., water source S). water source S).

FigureFigure 5. 5.Local Local adaptation adaptation concept concept basedbased onon the redesign of critical critical pipes pipes along along the the least- least- “monetary” “monetary” costcost path. path.

AllAll edges edgesE Eof of the the graph graphG Gare are thereby thereby weighted weighted withwith thethe monetarymonetary costscosts wij(e(eijij),), wherewhere eeij ijisis the the edgeedge between between node nodei andi andj andj andw wijij> > 0.0. Along the shortest path, path, the the pipes pipes with with unusual unusual high high unit unit head head loss (ho,i,j > crithcrit) are identified and successively redesigned in an iterative process based on Equation loss (ho,i,j > h ) are identiﬁed and successively redesigned in an iterative process based on Equation (5), (5), where new and old pipe diameters are denoted with dn,i,j and do,i,j, hn and ho,i,j are the new and old where new and old pipe diameters are denoted with dn,i,j and do,i,j, hn and ho,i,j are the new and old ® unitunit head head loss, loss, respectively respectively [ 47[47].]. The The followingfollowing algorithmalgorithm waswas implemented in in MATLAB MATLAB R2016b R2016b®. .

𝑑s,,ℎ5 ,, 𝑑,, = 5 do,i,jho ,i,j (5) dn,i,j = ℎ (5) hn The procedure is described as follows: The procedure is described as follows: 1. Start with the n × n adjacency matrix Aij from the finite graph WDN: n nodes; eij edge from node 1. Starti to node with thej; E nall× edges.n adjacency matrix Aij from the ﬁnite graph WDN: n nodes; eij edge from node 2. i toWeight node eachj; E all edge edges. eij with its diameter dependent monetary value wij: pipe length [m] × unit cost 2. Weightvalue [€/m]. each edge eij with its diameter dependent monetary value wij: pipe length [m] × unit cost 3. valueIdentify[€/m]. the junction J with minimum pressure head pmin, violating pcrit. 3. 4. IdentifyCalculate the the junction weightedJ with shortest minimum path pressure L between head sourcepmin, violating S and junctionpcrit. J using Dijkstra’s 4. Calculatealgorithm. the weighted shortest path L between source S and junction J using Dijkstra’s algorithm. 5. Determine unit head losses hij of all edges in E. 5. Determine unit head losses hij of all edges in E. 6. Choose pipes from the shortest path C ⊆ L, which overstep the head loss threshold hcrit. 6. Choose pipes from the shortest path C ⊆ L, which overstep the head loss threshold hcrit. 7. If the no pipe oversteps hcrit, reduce hcrit by 10% and go back to step 6. 7. If the no pipe oversteps hcrit, reduce hcrit by 10% and go back to step 6. 8. Design new diameter dn,i,j for each element in C with new unit head loss hn according Equation 8. Design(5). new diameter dn,i,j for each element in C with new unit head loss hn according Equation (5). 9.9. RoundRoundd dn,i.jn,i.j toto nearest nearest discrete discrete diameter diameter class class and and set setpipe pipe roughness roughness to standard to standard value valuefor new for newpipes. pipes. 10. Replace all redesigned pipes in the WDN. 11. Run hydraulic simulation. 12. Update weights wij in the adjacency matrix A. 13. Repeat step 3 to 10 until sufficient performance pmin ≥ pcrit is reached in all nodes or the predefined number of maximum iterations is exceeded. 14. Determine (adaptation) costs. This WDN redesign concept using the least cost path algorithm allows for a simple cost-effective pipe replacement of the weakest components of the WDN. This measure improves the pressure

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10. Replace all redesigned pipes in the WDN. 11. Run hydraulic simulation.

12. Update weights wij in the adjacency matrix A. 13. Repeat step 3 to 10 until sufﬁcient performance pmin ≥ pcrit is reached in all nodes or the predeﬁned number of maximum iterations is exceeded. 14. Determine (adaptation) costs.

EntropyThis 2018 WDN, 20, x FOR redesign PEER REVIEW concept using the least cost path algorithm allows for a simple cost-effective9 of 21 pipe replacement of the weakest components of the WDN. This measure improves the pressure performances, but raises additional costs. All All redesign redesign and pipe replacement works are thereafter referred to as network adaptations.

2.2. Case Study Reliable demonstration casescases for for city city transition transition are are rare. rare. We We apply apply the the presented presented methodology methodology to toa real a real world world WDN WDN transition, transition, where where a huge a huge urban urban transition transition occurs occurs within within the nextthe next decades. decades.The caseThe casestudy study is the is Swedish the Swedish city of city Kiruna, of Kiruna, where substantial where substantial parts of theparts town of havethe town to be have displaced to be about displaced 4 km abouteastwards. 4 km The eastwards. reason for The that reason is the expansionfor that is of th mininge expansion activities of belowmining ground, activities which below threatens ground, all whichinfrastructure threatens by all creating infrastructure underground by creating settlements underground and cracks. settlements Nevertheless, and cracks. mining Nevertheless, activities will miningcontinue. activities This rapid will ongoing continue. city This transition rapid ongoing is captured city in transition the masterplan is captured and isin therefore the masterplan well-suited and isto presenttherefore the developedwell-suited method. to present Although the thedeveloped above-ground method. infrastructure Although transition the above-ground is precisely infrastructuredeﬁned, the underground transition is precisely infrastructure defined, is largely the underground unknown. infrastructure In Zischg et al. is [largely48] the unknown. transition Inmodeling Zischg et of al. the [48] urban the drainage transition system modeling was presented.of the urban drainage system was presented.

2.2.1. City Masterplan For the city transition of Kiruna, a detailed detailed mast masterplanerplan for future future city city development development was provided by decision makers. It It includes includes the the planned planned road road network network and and the the building building blocks blocks of of the the new new center, center, which isis located located at at the the eastern eastern part part of the of current the current town. Thetown. construction The construction and deconstruction and deconstruction processes processesare deﬁned are by defined six phases. by six People phases. living People in deﬁned living restrictedin defined areas restricted haveto areas be relocated have to be to therelocated new city to thecenter new on city a step-by-step center on a step-by-step basis by the endbasis of by the the century end of (see the Figurecentury6). (see Figure 6).

Figure 6. CityCity masterplanmasterplan of of Kiruna Kiruna deﬁning defining the the spatiotemporal spatiotemporal urban urban transition: transition: Restricted Restricted areas areas and andnewly newly planned planned city centercity center with with the futurethe future road road network. network.

2.2.2. Source and Destination Networks The existing WDN of the year 2012 represents the source network and contains all necessary modeling parameters parameters (see (see Figure Figure 7a).7a). For For security security reasons, reasons, the the detailed detailed layout layout cannot cannot be shown be shown here; nevertheless the quantitative results are presented. The WDN is set as the EPANET 2 input file and comprises 5845 junctions, 6069 pipes and three demand patterns for domestic and industrial consumption, as well as water losses. Water losses in the existing WDN are crucial, accounting for approximately 18% of the hourly peak demand (Qh,max). Despite their unknown distribution, they are integrated as additional nodal demand with the weighting of pipe length (linear) and nodal pressure (non-linear) according to Maskit and Ostfeld [49].

Entropy 2018, 20, 708 10 of 21 here; nevertheless the quantitative results are presented. The WDN is set as the EPANET 2 input ﬁle and comprises 5845 junctions, 6069 pipes and three demand patterns for domestic and industrial consumption, as well as water losses. Water losses in the existing WDN are crucial, accounting for approximately 18% of the hourly peak demand (Qh,max). Despite their unknown distribution, they are integrated as additional nodal demand with the weighting of pipe length (linear) and nodal pressure (non-linear) according to Maskit and Ostfeld [49]. Entropy 2018, 20, x FOR PEER REVIEW 10 of 21

FigureFigure 7. 7.WDN WDN states: states: ( a(a)) source source network,network, andand (b) one possible possible destination destination network-design network-design alternative alternative 1 (see1 (see Table Table1). 1).

FigureTable 1.7bDefinition shows one of designpossible alternatives destination considering network different at year cycle 2100. indices The andnew safety network factors. parts are created based on the road network. The new systems are independently designed with a pipe sizing Safety Factor f Cycle Index CI (-) algorithm [31] and different future design demands (𝑓×𝑄,). Comparing existing and future systems, the latter(-) becomes denser max * (total 0 ** networks 0.1 0.2length 0.3 reduction 0.4 of 0.5 about 0.6 25%) 0.7 and a 0.8 new position of the water storage1 tank has to 1 be considered. 2 3 Due 4 to the 5 “unintended” 6 7 disconnection 8 9 10 of the north- western part of the1.3 network at 11year 2100, 12 a new 13 conn 14ection 15 to the 16 source 17 has 18 to be 19 established. 20 Based on *the WDN expansion layout is identicaltarget of to the road system network a future (RN); **safety WDN factor layout representsf has to be the chosen. minimum Itspanning provides tree additional (MST) of the RN. pipe capacity to deal with possible future demand increases and structural changes and to cope with other unexpected developments. The distribution of the demand nodes is identical for every design alternativeFigure7 b(DA). shows In oneTable possible 1 the different destination design network alternatives at year of 2100. the future The newWDN network are defined parts and are createditemized based from on 1 to the 20. road The network.variation of The the newCI define systemss the aredegree independently of loops (alter designednative flow with paths) a pipe of sizingthe new algorithm WDN parts. [31] and different future design demands ( f × Qh,max). Comparing existing and future systems, the latter becomes denser (total networks length reduction of about 25%) and a new position ofTable the water1. Definition storage of design tank has alternatives to be considered. considering Due different to the cycle “unintended” indices and safety disconnection factors. of the north-western part of the network at year 2100, a new connection to the source has to be established. Safety Factor f Cycle Index CI (-) Based on the expansion target of the system a future safety factor f has to be chosen. It provides (-) max * 0 ** 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 additional pipe capacity to deal with possible future demand increases and structural changes and to 1 1 2 3 4 5 6 7 8 9 10 cope with other unexpected developments. The distribution of the demand nodes is identical for every 1.3 11 12 13 14 15 16 17 18 19 20 design alternative (DA). In Table1 the different design alternatives of the future WDN are defined and * WDN layout is identical to the road network (RN); ** WDN layout represents the minimum itemized from 1 to 20. The variation of the CI defines the degree of loops (alternative flow paths) of the spanning tree (MST) of the RN. new WDN parts. 2.2.3. Scenario Analysis 2.2.3. Scenario Analysis The network transition analysis includes the investigation of three simple scenarios describing The network transition analysis includes the investigation of three simple scenarios describing the total future water demand development, excluding water losses (see Figure 8a). the total future water demand development, excluding water losses (see Figure8a). • Stagnation (Scenario 1): The basic assumption for the first scenario is that the total demand • Stagnationremains constant (Scenario within 1): Thethe period basic assumption of investigation. for the This first describes scenario no ispopulation that the totalchange demand over remainstime, but constant a change within of its thelocation. period of investigation. This describes no population change over • time,Growth but a(Scenario change of2): its The location. second scenario implies an increase of water usage up to 30% until the end of the century, which represents a population or demand per capita growth within the new city center [50]. • Decay (Scenario 3): The third scenario considers a gradual decrease of water usage up to 30% until the end of the century. This represents, a population decline, a demand per capita reduction, or an increased decentral water supply. For this case study, this scenario could also describe the effects of an economic collapse related to a falling market price of iron ore [50]. Along with the future water consumption, the water loss is another important factor to be

considered. In the existing system the total water loss accounts for 42 l/s (≙0.18×𝑄,), which are

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to be significantly decreased in the future. Until 2100 the total water loss is expected to be reduced by • 60% Growthdue to (Scenarioa newly 2):constructed The second WDN scenario of better implies quality an increase (approximately of water usage 50–60% up toof 30% total until future the networkend oflength) the century, and the which concurrent represents deconstruction a population of old, or demand leaking persystem capita parts growth (see Figure within 8b). the newThis watercity loss center reduction [50]. of approximately 25 l/s corresponds to the mean domestic demand equivalent •of aboutDecay 10,000 (Scenario people 3): (half The thirdthe population scenario considers in 2010), awhich gradual shows decrease the importance of water usage of considering up to 30% wateruntil leakage the end in the of theexisting century. system This and represents, reducing a it population in the future. decline, A leakage a demand increase per capitaof existing reduction, WDN partsor over an increased time and decentralleakage reductions water supply. due Forto year thisly case pipe study, rehabilitations, this scenario are could beyond also describethe scope the of our model.effects of an economic collapse related to a falling market price of iron ore [50].

FigureFigure 8. Water8. Water demand demand scenarios scenarios over over time: time: (a) Future (a) Future water consumption,water consumption, and (b) and water (b loss) water reduction. loss reduction. Along with the future water consumption, the water loss is another important factor to be considered.2.2.4. Performance In the existing Assessment system and the Adaptation total water loss accounts for 42 l/s (0.18 × Qh,max), which are to be significantlyThe minimum decreased pressure in theand future. entropy Until are 2100investig theated total at water maximum loss is hourly expected water to be consumption, reduced by 60% due to a newly constructed WDN of better quality (approximately 50–60% of total future network while water age is assessed for low demand periods. The user-defined threshold values Tu and Tl for length)the performance and the concurrent assessments deconstruction of minimum of pressure old, leaking and system water age parts are (see listed Figure in 8Tableb). This 2. The water critical loss reductionperformance of approximatelyis defined by the 25 mi l/snimum corresponds pressure to thehead mean of 15 domestic m at a demand demand node equivalent at the maximum of about 10,000hourly people peak load. (half theIn case population this threshold in 2010), is which not fulf showsilled, the the importance adaptation of concept considering is applied. water leakage In this inprocess, the existing the critical system pipes and (see reducing Section it in2.1.6) the future.with an A exceeding leakage increase unit head of existingloss of 25 WDN m/km parts (hcrit over) are time and leakage reductions due to yearly pipe rehabilitations, are beyond the scope of our model. redesigned using a new target unit head loss (hn) of 8 m/km. 2.2.4. Performance Assessment and Adaptation Table 2. User-defined threshold values for performance analysis. The minimum pressure and entropy are investigated at maximum hourly water consumption, Performance Threshold Tu Tl α while water age is assessed for low demand periods. The user-defined threshold values Tu and T for Minimum pressure (m) 40 0 0 l the performance assessments of minimum pressure and water age are listed in Table2. The critical Maximum water age (h) 120 24 1 performance is defined by the minimum pressure head of 15 m at a demand node at the maximum hourly peak load. In case this threshold is not fulfilled, the adaptation concept is applied. In this The diameter classes and unit costs used for the WDN design and adaptation for this case study process, the critical pipes (see Section 2.1.6) with an exceeding unit head loss of 25 m/km (hcrit) are application are adjusted from Ref. [13] and reported in Table 3. redesigned using a new target unit head loss (hn) of 8 m/km. Table 3. Pipe diameters D and unit costs, adopted for the design phase. Table 2. User-defined threshold values for performance analysis. D (mm) Costs (€/m) D (mm) Costs (€/m) D (mm) Costs (€/m) Performance Threshold T T α 50 190 125 250u l 300 360 80 227Minimum pressure150 (m)272 40 0350 0 399 Maximum water age (h) 120 24 1 90 229 160 275 400 420 100 231 200 299 450 450 The diameter110 classes and235 unit costs used250 for the WDN328 design500 and adaptation480 for this case study application are adjusted from Ref. [13] and reported in Table3.

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Table 3. Pipe diameters D and unit costs, adopted for the design phase.

D (mm) Costs (€/m) D (mm) Costs (€/m) D (mm) Costs (€/m) 50 190 125 250 300 360 80 227 150 272 350 399 90 229 160 275 400 420 100 231 200 299 450 450 110 235 250 328 500 480

Entropy 2018, 20, x FOR PEER REVIEW 12 of 21 3. Results 3. Results 3.1. Model Application 3.1.In Model the following Application sections the previously introduced model is applied to the urban transition of Kiruna.In Altogether, the following for thesections case studythe previously application introduc 1440 WDNed model configurations is applied to are the created urban andtransition simulated, of containingKiruna. Altogether, 20 generated for designthe case alternatives study application (different 1440 CIs WDN and safety configurations factors), eachare evaluatedcreated and for sixsimulated, temporal containing states (from 20 2013 generated to 2100), design under alternatives two hydraulic (different load conditionsCIs and safety (high factors), and low each daily demand),evaluated three for futuresix temporal demand states scenarios, (from 2013 with to and 210 without0), under adaptation. two hydraulic After load the conditions performance (high analysis and andlow the daily application demand), of thethree adaptation future demand concept, scenar a comparisonios, with ofand the without 20 planning adaptation. options After is made the by analyzingperformance the costs analysis and and reliability the application indicators. of the adaptation concept, a comparison of the 20 planning options is made by analyzing the costs and reliability indicators. 3.1.1. Possible Destination Networks 3.1.1. Possible Destination Networks Figure9 presents two example future WDN layouts. In Figure9a a branched realization of the WDN toFigure connect 9 presents all demand two example nodes (CI future = 0) WDN is shown, layouts. which In Figure represents 9a a thebranched minimum realization spanning of the tree (MST)WDN of to the connect co-located all demand road network nodes (CI (WDN = 0) is= ˆshowMST(RN)).n, which Conversely,represents the Figure minimum9b presents spanning a highly tree looped(MST) WDN of the layout, co-located which road is identicalnetwork to(WDN the co-located ≙ MST(RN)). road Conversely, network and, Figure thus, 9b has presents morealternative a highly flowlooped possibilities WDN layout, to connect which theis identical demand to nodesthe co-loc (WDNated =roadˆ RN). network The nodal and, thus, demand has more is taken alternative from the expectedflow possibilities population to connect density the map demand defined nodes in the (WDN master ≙ RN). plan. The Water nodal losses demand of newlyis taken constructed from the WDNexpected parts population are accounted density with map 10% ofdefined the average in the demandmaster plan. (referred Water to losses scenario of 1).newly The constructed position and settingWDN of parts the pressureare accounted reducing with valve10% of (PRV) the average are determined demand (referred manually to onscenario the basis 1). The of the position topological and characteristicssetting of the pressure of the road reducing network valve and (PRV) the are topographic determined boundary manually conditions on the basis to of ensure the topological adequate pressurecharacteristics ranges ofof approximatelythe road network 50 mand in thethe newtopogr cityaphic center. boundary The attributes conditions of the to PRVensure are adequate unaltered pressure ranges of approximately 50 m in the new city center. The attributes of the PRV are unaltered for every design alternative. The new WDN parts are designed with a pipe sizing algorithm (see for every design alternative. The new WDN parts are designed with a pipe sizing algorithm (see Section 2.1.2) and thus have sufficient performances. However, this does not necessarily mean that Section 2.1.2) and thus have sufficient performances. However, this does not necessarily mean that high performances are established across the entire system, due to integrated older WDN parts and high performances are established across the entire system, due to integrated older WDN parts and different future demand scenarios. These interactions and possible weak points are investigated in the different future demand scenarios. These interactions and possible weak points are investigated in performance analysis, where intermediate WDN states are also considered. the performance analysis, where intermediate WDN states are also considered.

FigureFigure 9. 9.Example Example design design alternatives alternatives consideringconsidering different future WDN WDN structures: structures: (a ()a )branched branched layout,layout, and and (b ()b strongly) strongly looped looped layout. layout.

3.1.2. Intermediate State Networks The intermediate WDN states are defined by the years 2013, 2018, 2023, 2033 and 2050. During the transition process some parts of the existing WDN (source network) are disconnected, while new parts are connected at the same time. Simultaneously, a demand shift takes place from the disconnected parts to the new parts. “Unintended” network disconnections caused by the “intended” disconnections (i.e., pipes inside the restricted area) are of minor importance and therefore additionally removed. The demand of those parts is also shifted to the new WDN. Figure 10 shows two example intermediate state networks. Existing WDN parts cannot be fully shown for data protection and security reasons.

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3.1.2. Intermediate State Networks The intermediate WDN states are deﬁned by the years 2013, 2018, 2023, 2033 and 2050. During the transition process some parts of the existing WDN (source network) are disconnected, while new parts are connected at the same time. Simultaneously, a demand shift takes place from the disconnected parts to the new parts. “Unintended” network disconnections caused by the “intended” disconnections (i.e., pipes inside the restricted area) are of minor importance and therefore additionally removed.

TheEntropy demand 2018,of 20, those x FOR partsPEER REVIEW is also shifted to the new WDN. Figure 10 shows two example intermediate13 of 21 state networks. Existing WDN parts cannot be fully shown for data protection and security reasons.

FigureFigure 10. 10.Example Example of of two two generated generated transition transition state state WDNs WDNs for for the the KirunaKiruna casecase study:study: ( a) WDN WDN 2023, 2023, and (b) WDN 2050. and (b) WDN 2050.

3.1.3.3.1.3. Performance Performance Assessment, Assessment, Critical Critical Performance Performance and and Local Local Adaptation Adaptation HereHere we we present present the the results results of of the the performance performance assessment, assessment, wherewhere thethe WDNWDN efficienciesefficiencies are determineddetermined with with global global indices indices (see (see Section Section 2.1.5 2.1.5)) during during the the transition transition process.process. InIn the firstfirst analysis nono adaptation adaptation concept concept is is considered, considered, to to identify identify transition transition states states fromfrom whichwhich supplysupply problems are to bebe expected, expected, through through the the step-by-step step-by-step stressing stressing of of the the WDN. WDN.In Inthe the secondsecond analysisanalysis thethe adaptation concept,concept, including including the the critical critical performance performance assessment assessment andand pipepipe redesign,redesign, isis appliedapplied to provide sufficientsufficient performances performances and and determine determine the the necessary necessary pipe pipe replacement replacement rates rates (see (see SectionSection 2.1.62.1.6).). FigureFigure 11 11illustrates illustrates the the performance performance trends trends of of the the maximum maximum waterwater ageage andand minimumminimum pressure fromfrom the the initial initial state state in in 2012 2012 to to the the final final state state in in 2100. 2100. The The PI PI minimumminimum pressurepressure for the source source network network is 0.986. This means that the pressure head at approximately 99% of the demand nodes is greater or is 0.986. This means that the pressure head at approximately 99% of the demand nodes is greater or equal to 40 m for hourly peak demand (Qh,max). equal to 40 m for hourly peak demand (Qh,max). In particular Figure 11a shows the trend of water age performance, where slight drops at the In particular Figure 11a shows the trend of water age performance, where slight drops at the intermediate states are observed, even for the stagnation scenario of constant total demand. The intermediate states are observed, even for the stagnation scenario of constant total demand. The reason reason for that are excess capacities at intermediate states, due to faster connection than disconnection for that are excess capacities at intermediate states, due to faster connection than disconnection process process (shifted demand from the restricted areas is lower than the design capacities of the newly (shifted demand from the restricted areas is lower than the design capacities of the newly connected connected pipes). We also observe a strong dependency on the future water consumption, where the pipes). We also observe a strong dependency on the future water consumption, where the water age is water age is lower (desired) for a demand increase. The effect of the design alternative of the new lowercenter (desired) on the forwater a demand age reveals increase. less influence. The effect We of do the not design see a alternativecorrelation between of the new the center CI variation on the waterand agethe revealswater age, less however influence. using We dohigher not seesafety a correlation margins (f between= 1.3) for the increased CI variation waterand consumption the water age,reveals however lower using water higher age performances safety margins due ( fto= lower 1.3) for flow increased velocities. water consumption reveals lower water ageFigure performances 11b presents due the to lower minimum flow velocities.pressure performances with (highlighted) and without (shaded)Figure 11applicationb presents of the the minimum adaptation pressure concept. performances It can be withseen (highlighted)that until state and 2023 without the WDN (shaded) is applicationrelativelyof robust the adaptation when facing concept. connectivity It can be losses seen and that changed until state flow 2023 patterns. the WDN However, is relatively after robust state when2023, facing the first connectivity weak points losses occur and where changed the flowsystem patterns. breaks However, down due after to overused state 2023, pipe the capacities, first weak pointswhich occur are wheremainly the caused system by breaks the disconnection down due to overusedof pipes. pipeThis capacities,is noted by which the arerelatively mainly similar caused byperformance the disconnection drops, of regardless pipes. This of isthe noted demand by thescen relativelyario. With similar application performance of the adaptation drops, regardless concept of theand demandthe redesign scenario. of the Withweakest application pipes, the of minimu the adaptationm pressure concept performances and the redesignsignificantly of the improve weakest to guarantee sufficient hydraulic conditions at peak demand. At final state, higher variations of the PI minimum pressure can be observed, caused by greater demand variations, different WDN topologies and pipe replacement rates (see Figure 12). Owing to the fact the main problems occur in the existing WDN parts, there are also no clear distinctions here between the design alternatives that can be made.

Entropy 2018, 20, 708 14 of 21 pipes, the minimum pressure performances significantly improve to guarantee sufficient hydraulic conditions at peak demand. At final state, higher variations of the PI minimum pressure can be observed, caused by greater demand variations, different WDN topologies and pipe replacement rates (see Figure 12). Owing to the fact the main problems occur in the existing WDN parts, there are also no clear distinctions here between the design alternatives that can be made. Entropy 2018, 20, x FOR PEER REVIEW 14 of 21

FigureFigure 11. Investigation 11. Investigation of performanceof performance trends trends considering: considering: ( (aa) )The The maximum maximum water water age ageduring during a low a low demand period, and (b) minimum pressure heads at hourly peak demand. demand period, and (b) minimum pressure heads at hourly peak demand. We then take a closer look on the results of the critical performance analysis and the local system We then take a closer look on the results of the critical performance analysis and the local system adaptation (according to Section 2.1.6). Figure 12a exemplarily presents the local minimum pressure adaptation (according to Section 2.1.6). Figure 12a exemplarily presents the local minimum pressure head at the most unfavorable demand node before (shaded) and after system adaptation head(highlighted), at the most unfavorable whereas in Figure demand 11 global node indices before were (shaded) shown. and The after threshold system value adaptation pcrit for the (highlighted), critical crit whereasperformance in Figure analysis11 global is indicesshown by were the shown. bold dotted The thresholdline in Figure value 11.p Thefor adaptation the critical concept performance is crit analysisperformed is shown when by thepcrit boldis violated dotted at line hourly in Figure peak demand. 11. The adaptationThe minimum concept pressure is performed head in the when sourcep is violatednetwork at hourly is approximately peak demand. 17 Them. The minimum performance pressure pathways head inare the similar source to network the global is approximatelyminimum 17 m.pressure The performance indicator, with pathways the highest are similar variation to theat th globale final state. minimum Corresponding pressure indicator,pipe replacement with the rates highest variationare demonstrated at the final state.in Figure Corresponding 12b, differentiated pipe by replacement the demand scenario. rates are For demonstrated the growth scenario in Figure the 12b, differentiatedhighest replacement by the demand rates (2.7%) scenario. are necessary, For the growthwhereas scenariothey are lowest the highest for the decay replacement scenario rates(2.2%). (2.7%) However, pipe replacement is necessary for all tested pathways and the differences between the are necessary, whereas they are lowest for the decay scenario (2.2%). However, pipe replacement is scenarios are relatively low, which indicates that the pipe disconnections represent the main cause of necessary for all tested pathways and the differences between the scenarios are relatively low, which stress for the WDN, especially after the year 2023. One reason for the relatively low adaptation rates indicatesis the that step-by-step the pipe reduction disconnections of water losses represent (see Figure the main 8b), which cause provides of stress additional for the WDN, capacities especially for after thedomestic year 2023.and industrial One reason water for demand. the relatively Performed low pipe adaptation replacements rates isat thestate step-by-step t, influence reductionthe next of waterfuture losses state (see t+1. Figure This8 explains,b), which for provides example, additional why for the capacities growth scenario for domestic in 2023 andno pipe industrial upgrades water demand.are performed, Performed as pipe they replacementshave already been at state completedt, influence at an theearlier next state. future By using state t+1.this adaptationThis explains, for example,concept, whythe latest for the possible growth times scenario for inpipe 2023 replacement no pipe upgradesare chosen are to performed, maintain sufficient as they have alreadyperformances. been completed The accumulated at an earlier adaptation state. By rates using be thistween adaptation 2–3% (corresponds concept, theon average latest possible to 0.03% times for pipeper replacementyear) of the total are chosennetwork to length maintain are low sufficient compared performances. to the necessary The accumulatedpipe rehabilitation adaptation of approximately 1–2% per year [51]. The obtained information about the locations of the weakest WDN rates between 2–3% (corresponds on average to 0.03% per year) of the total network length are low parts (not shown here for security reasons), the amount, and the latest possible time for necessary compared to the necessary pipe rehabilitation of approximately 1–2% per year [51]. The obtained pipe replacements, can support decision makers in planning necessary rehabilitation works. information about the locations of the weakest WDN parts (not shown here for security reasons), the amount, and the latest possible time for necessary pipe replacements, can support decision makers in planning necessary rehabilitation works.

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Entropy 2018, 20, x FOR PEER REVIEW 15 of 21 Entropy 2018, 20, x FOR PEER REVIEW 15 of 21

Figure 12. Adaptation concept: (a) Performance analysis based on minimum pressure head criterion, FigureFigure 12. Adaptation 12. Adaptation concept: concept: (a ()a Performance) Performance analysis based based on on mi minimumnimum pressure pressure head head criterion, criterion, and (b) the necessary pipe replacement to achieve a sufficient performance level. and (andb) the (b) necessarythe necessary pipe pipe replacement replacement to to achieve achieve a sufficient sufficient performance performance level. level. 3.1.4. Cost-Reliability Comparison of the Design Alternatives 3.1.4.3.1.4. Cost-Reliability Cost-Reliability Comparison Comparison of of the the Design Design Alternatives The last planning objective is to identify a reliable and cost-efficient future WDN layout. From The lastThe planninglast planning objective objective is tois identifyto identify a reliablea reliable and and cost-efficient cost-efficient futurefuture WDN layout. layout. From From the the results presented in the previous section, no conclusions about the reliability of the different resultsthe presented results presented in theprevious in the previous section, section, no conclusions no conclusions about about the reliabilitythe reliability of theof the different different design design alternatives could be made. The design alternatives differ in total network length, pipe alternativesdesign alternatives could be made. could Thebe made. design The alternatives design alternatives differ in differ total in network total network length, length, pipe diameterspipe diameters and required adaptation works, which all can be associated with costs. For WDN reliability diameters and required adaptation works, which all can be associated with costs. For WDN reliability and requiredand robustness adaptation assessment, works, the which elementary all can number be associated of loops and with the costs.flow entropies For WDN are reliabilitycalculated. and and robustness assessment, the elementary number of loops and the flow entropies are calculated. robustnessFigure assessment, 13 shows example the elementary WDN alternatives number for of Kiruna loops and’s new the city flow center. entropies Road network are calculated. (Figure Figure13a), 13 Figure 13 shows example WDN alternatives for Kiruna’s new city center. Road network (Figure 13a), showsdemand example distribution WDN alternatives (Figure 13b), for an Kiruna’sd four design new alternatives city center. (DAs) Road with network varying (Figure network 13 topologya), demand demand distribution (Figure 13b), and four design alternatives (DAs) with varying network topology distributionand flow (Figure distribution 13b), are and illustrated. four design Darker alternatives links indicate (DAs) high with flows, varying while brighter network links topology have lower and flow and flow distribution are illustrated. Darker links indicate high flows, while brighter links have lower flows. distributionflows. are illustrated. Darker links indicate high flows, while brighter links have lower flows.

Figure 13. Chosen design alternatives (DAs) and flow patterns at final state 2100 for Kiruna’s new city Figure 13. Chosen design alternatives (DAs) and flow patterns at final state 2100 for Kiruna’s new city Figurecenter. 13. Chosen (a) Road design network, alternatives (b) demand (DAs) distribution, and flow and patterns (c–f) four at finaldesign state alternatives 2100 for (DAs) Kiruna’s with new center. (a) Road network, (b) demand distribution, and (c–f) four design alternatives (DAs) with city center.varying (a network) Road network,topology and (b) demandflow distribution. distribution, and (c–f) four design alternatives (DAs) with varying network topology and flow distribution. varying network topology and flow distribution.

Figure 14a compares the associated costs for the newly built WDN (referred as “layout costs”) and the adaptation costs (associated with the necessary pipe replacement for sufﬁcient hydraulic Entropy 2018, 20, x FOR PEER REVIEW 16 of 21

Figure 14a compares the associated costs for the newly built WDN (referred as “layout costs”) and the adaptation costs (associated with the necessary pipe replacement for sufficient hydraulic performance) for the 20 design alternatives. Their loop degree (measured with the CI) increases from left to right on the abscissa. The “layout costs” are defined as the additional costs compared to the cheapest layout option, which represents the branched WDN with zero elementary cycles (see Figure 13c) and no additional safety capacities (DA 2). The strongly looped WDN, which is identical to the RN layout with an additional safety margin of 30% for future demand increase, is the most expensive planning option (DA 11). The reason for that is the highest total network length and high flow capacities. Furthermore, it can be observed that the adaptation costs are slightly higher for lower loop degree, but it is remarkable that the relative layout costs are dominating the adaptation costs for this case study. Figure 14b illustrates the calculated flow entropy values for the 20 design alternatives under three future demand scenarios at the final WDN state. It can be seen that branched networks with no alternative flow paths (CI = 0) are the most cost-effective options, but reveal the lowest entropy values. When the WDN layout is identical to the RN, the entropies are highest, but also the costs strongly increase. Moreover, it can be noted that bigger pipe diameters (due to higher safety factors), Entropygenerally2018 ,cannot20, 708 be associated with higher entropies. Take, for example, the diameter increase16 ofof 21 a main pipe. This would consequently attract more flow, cause higher flow inhomogeneity, and thus reduce the entropy. Furthermore, it can be observed that, the higher the loop degree, the higher is the performance)entropy variation for for the the 20 different design alternatives. demand scenarios. Their loopThe reason degree for (measured this increased with variability the CI) increases is flow fromrearrangements, left to right which on the alter abscissa. the flow The distributions. “layout costs” For are most deﬁned design as the alternatives additional the costs growth compared scenario to thereveals cheapest the highest layout entropies, option, which except represents for the design the branched alternatives WDN 2, 12, with 14, zero8, 9 and elementary 10. cycles (see FigureWhen 13c) comparing and no additional the (normalized) safety capacities entropy-cost (DA 2). re Thelation strongly in Figure looped 14c,WDN, a strong which correlation is identical can tobe theobserved RN layout for the with final an state additional WDNs, safety for which margin th ofe systems 30% for are future designed demand for. increase, At earlier is states the most no expensiveentropy-cost planning relation option is found, (DA due 11). to The the reasondomina fornce that of existing is the highest WDN totalparts network(“unchanged length topology”) and high ﬂowand only capacities. minor Furthermore,newly constructed it can beparts observed (“changing that thetopology”). adaptation Highest costs are entropy-cost slightly higher ratios for at lower final loopstate, degree, and thus but itthe is remarkablemost suitable that WDN the relative option layouts for costsKiruna’s are dominating new city thecenter, adaptation are the costs design for thisalternatives case study. 5, 19 and 1, with 44, 48 and 111 elementary loops, respectively (see Figure 13d–f).

Figure 14. Comparison between between ( (aa)) WDN WDN costs, costs, and and ( (b)) flow ﬂow entropy at ﬁnalfinal state; (c) shows the temporal scale of the entropy-costentropy-cost relationrelation forfor 66 WDNWDN states.states.

Figure 14b illustrates the calculated flow entropy values for the 20 design alternatives under three future demand scenarios at the final WDN state. It can be seen that branched networks with no alternative flow paths (CI = 0) are the most cost-effective options, but reveal the lowest entropy values. When the WDN layout is identical to the RN, the entropies are highest, but also the costs strongly increase. Moreover, it can be noted that bigger pipe diameters (due to higher safety factors), generally cannot be associated with higher entropies. Take, for example, the diameter increase of a main pipe. This would consequently attract more flow, cause higher flow inhomogeneity, and thus reduce the entropy. Furthermore, it can be observed that, the higher the loop degree, the higher is the entropy variation for the different demand scenarios. The reason for this increased variability is flow rearrangements, which alter the flow distributions. For most design alternatives the growth scenario reveals the highest entropies, except for the design alternatives 2, 12, 14, 8, 9 and 10. When comparing the (normalized) entropy-cost relation in Figure 14c, a strong correlation can be observed for the final state WDNs, for which the systems are designed for. At earlier states no entropy-cost relation is found, due to the dominance of existing WDN parts (“unchanged topology”) and only minor newly constructed parts (“changing topology”). Highest entropy-cost ratios at final Entropy 2018, 20, 708 17 of 21 state, and thus the most suitable WDN options for Kiruna’s new city center, are the design alternatives 5, 19 and 1, with 44, 48 and 111 elementary loops, respectively (see Figure 13d–f).

4. Discussion In the following we discuss the implications and limitations of the presented work, and address possible future directions.

• Flow entropy as a reliability measure: For every flow configuration one specific entropy value exist and therefore depends on the source and demand node distribution and the network topology. Most studies on entropy maximization considered the redistribution of demand loads, whereas the topology and flow direction were assumed to be fixed. When considering the temporal scales of WDN (e.g., transitioning) this is not probable. We considered variations in the network topology and total demand of a real case study and found correlations between the loop degree and entropy. We think that further studies of spatial and topological network characteristics are necessary (e.g., the existence of loops in high capacity pipes or the spatial distribution of demand nodes with the source nodes) to better understand the entropy scaling of complex real-world systems. • “In-silico” networks: Unknown WDN parts are approximated with surrogate network data (e.g., roads) and complement known/existing data. This method has great potential in data reconstruction, network disaggregation, and network growth processes, such as network densification and/or expansion. Furthermore, certain links of the co-located network might be excluded in the generation process, so that critical components do not overlay in space (e.g., main pipe underneath main road). Those topics will be part of further investigations. • WDN design: After the WDN layout was set, the fast pipe design algorithm proposed by [31] was used. However, any other WDN optimization algorithms could be integrated if feasible in terms of computational costs. The distribution of demand nodes was fixed for every generated WDN layout, only their weights were changed for the WDN design and the scenario assessment. • Urban transition: We demonstrated the method for a very drastic city transition, where approximately half of the network will change in the future. However, the method works also for slower transitions (including network densification or network shrinking). Here, the urban development and therefore the network change is defined in a masterplan. In cases where no masterplan is available, stochastic models to predict the network development (e.g., preferential or other fitness-based attachment models) can be applied. In future work different case study applications could be tested. • Performance assessment: We mainly focused on the minimum pressure and the maximum water age as performance indices. The reliability was assessed with the flow entropy. The maximum pressure, flow velocities and modified resilience [13] were also considered, but not shown in this paper because no additional insight was gained. Additional topological, energy or hydraulic indices could easily be integrated without changing the proposed method. From a sustainability perspective, advanced pressure management, e.g., to reduce pipe leakage [52] and the use of pump as turbines instead of PRVs [53], could also be of great interest for WDN transitioning. However, these investigations were not subject of this work. • Local adaptation concept: When the critical performance (i.e., minimum pressure) cannot be fulfilled during the transition, specific pipes are redesigned and replaced. Pipe replacement is only one of many possible adaptation measures to provide sufficient performances. Often described as a “hard” measure, it raises additional costs. From the authors point of view this approach is especially useful when the necessary pipe replacement can (partly) coincide with yearly necessary rehabilitation works, i.e., the pipe must be replaced anyway. When the age of the pipes is known, the consideration of installing parallel pipes could be a suitable alternative option to increase capacity. Alternatively, “soft” measures, like peak demand reduction or decentral solutions of rainwater harvesting, might be more beneficial from a sustainability point of view. Entropy 2018, 20, 708 18 of 21

• Least cost path for pipe redesign: In branched networks there is one deﬁned path from a demand node (e.g., critical node with the worst performance) to the water source. In looped networks more than one path exists. By calculating the least- “monetary” cost path, short connections with small diameter are candidate pipes for the redesign. Depending on data availability of the source network, the least cost paths could be calculated by using alternative edge weights (e.g., pipe age, roughness or material). The presented algorithm requires a sufﬁcient geodetic head difference between water source and demand node, since only the head losses are reduced and no pumps are considered.

5. Summary and Conclusions In this work, a novel model was presented to assess complex urban transitions and their effects on the water distribution system under a variety of uncertainties. In contrast to the work presented in Zischg et al. [22], here the interaction of existing WDN and approximated “in-silico” networks are addressed over time while also taking into account uncertain population developments. Informational ﬂow entropy and other metrics are calculated on the pathway from an initial to a possible future WDN state to assess the temporal variability and the suitability of future planning options. Accompanying effects of external stresses, such as simultaneous connectivity loss, network expansion, and demand changes were considered. In the following the main points of the research are summarized:

• Unknown future WDN parts were generated based on the co-located known road network. In this process several network layouts (ranging from the minimum spanning tree to strongly looped networks) were created and connected with the existing WDN. These WDN parts were designed with a simple and fast pipe-sizing algorithm using a defined pressure surface inclination at hourly peak demand. • A city masterplan that defines the urban transition was used to change the WDN. Step-by-step WDN parts were disconnected, while other parts were connected to the existing (source) network. The functional changes assessed with hydraulic, water quality and reliability performance indices and reveal critical WDN configurations where problems are to be expected. For the case study application, it was shown that after the year 2023 pressure deficits will occur when appropriate transition planning is neglected. • A local adaptation concept was successfully applied in which critical pipes on the least- “monetary” cost path was redesigned, if the required minimum pressure head could no longer be guaranteed by the stressed system. With this targeted pipe replacement, the minimum pressure requirements were established across all transition states with overall replacement rates of approximately 3%. • Best suited WDN design alternatives were identified with a temporal cost-reliability (measured with the flow entropy) comparison. Generally, higher flow entropy values were achieved for costly planning options, where additional and equally important flow paths were provided especially for high capacity pipes. Highest entropy-cost ratios were obtained for network layouts with different loop degree.

The implications of the results are performance trends for various possible WDN planning options during a transition process from an initial to a desired future state. As a result, decisionmakers can be supported at an early phase of the project to plan necessary rehabilitation works by knowing the hydraulic deﬁciencies in space and time, in order to construct a cost-efﬁcient and reliable future water supply system.

Author Contributions: All authors substantially contributed in conceiving and designing the model and realizing this manuscript. Conceptualization, J.Z., W.R. and R.S.; Funding acquisition, W.R.; Investigation, J.Z.; Methodology, R.S.; Project administration, R.S.; Software, J.Z. and R.S.; Supervision, W.R. and R.S.; Visualization, J.Z.; Writing—original draft, J.Z.; Writing—review & editing, W.R. and R.S. All authors have read and approved the ﬁnal manuscript. Entropy 2018, 20, 708 19 of 21

Funding: This research is partly funded by the Joint Programming Initiative Urban Europe on behalf of the Austrian Ministry for Transport, Innovation and Technology (BMVIT) in the project Green/Blue Infrastructure for Sustainable, Attractive Cities [project NO. 839743] and by the Austrian Research Promotion Agency (FFG) within the research project ORONET [project NO. 858557]. Acknowledgments: The authors thank the “Tekniska Verken i Kiruna” for the provision of water distribution network data. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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