Where to Find Water Pipes and Sewers?—On the Correlation of Infrastructure Networks in the Urban Environment

Article Where to Find Water Pipes and Sewers?—On the Correlation of Infrastructure Networks in the Urban Environment

Michael Mair, Jonatan Zischg, Wolfgang Rauch and Robert Sitzenfrei * Unit of Environmental Engineering, University of Innsbruck, Technikerstr. 13, 6020 Innsbruck, Austria; [email protected] (M.M.); [email protected] (J.Z.); [email protected] (W.R.) * Correspondence: [email protected]; Tel.: +43-512-507-62195

Academic Editor: Andreas N. Angelakis Received: 14 December 2016; Accepted: 16 February 2017; Published: 21 February 2017 Abstract: Urban water infrastructure, i.e., water supply and sewer networks, are underground structures, implying that detailed information on their location and features is not directly accessible, frequently erroneous, or missing. For public use, data is also not made available due to security concerns. This lack of quality data, especially for research purposes, requires substantial effort when such data is sought for both statistical and model-based analyses. An alternative to gathering data from archives and observations is to extract the information from surrogate data sources (e.g., the street network). The key for such an undertaking is to identify the common characteristics of all urban infrastructure network types and to quantify them. In this work, the network correlations of the street, water supply, and sewer networks are systematically analyzed. The results showed a strong correlation between the street networks and urban water infrastructure networks, in general. For the investigated cases, on average, 50% of the street network length correlates with 80%–85% of the total water supply/sewer network. A correlation between street types and water infrastructure properties (e.g., pipe diameter) cannot be found. All analyses are quantiﬁed in the form of different geometric- and graph-based indicators. The obtained results improve the understanding of urban network infrastructure from an integrated point of view. Moreover, the method can be fundamental for different research purposes, such as data veriﬁcation, data completion, or even the entire generation of feasible datasets.

Keywords: integrated analysis; synergies in data; graph theory based indicators; geometric indicators; interlinked networks

1. Introduction In an urban system, a substantial number of public infrastructures can be represented in the form of a network, e.g., streets, subway systems, water supply pipes, and sewer pipes. The fundamental work of Strogatz [1], on the dynamics of complex networks, and Milo, et al. [2], on the design of network systems by motifs, allows an understanding and utilization of the advantages of such a structured approach. The application of complex network analysis procedures to urban street networks has been shown by several authors, e.g., Porta, et al. [3], Jiang and Claramunt [4] and Yin, et al. [5]. For sewer networks, Urich, et al. [6] suggested using a graph-theoretical approach, and Möderl, et al. [7] used graph theory to describe water supply networks. Additionally, Sitzenfrei, et al. [8] analyzed automatically generated water distribution system data based on GIS data. All of these investigations are speciﬁcally for one single network type. One of the key issues of urban water infrastructure is that the pipes and sewers are underground structures with direct and obvious spatial information on the location only given at the manholes.

Water 2017, 9, 146; doi:10.3390/w9020146 www.mdpi.com/journal/water Water 2017, 9, 146 2 of 15 Water 2017, 9, 146 2 of 15

TheThe sheersheer size size of of the the network network (the (the typical typical dimension dimension of the of the specific specific pipe pipe length length per person per person is 10 m)is 10 often m) resultsoften results in unclear, in unclear, wrong, wrong, and occasionally and occasionally missing missing data. Hence, data. theHence, required the required data for networkdata for network analysis (likewise,analysis (likewise, statistical- statistical and model-based)‐ and model is‐based) often not is often completely not completely available, available, not freely not accessible freely accessible (due to security(due to concerns),security concerns), or of poor or quality of poor (e.g., quality wrong (e.g., data wrong records data of infrastructurerecords of infrastructure element properties). element Therefore,properties). a substantialTherefore, amounta substantial of time amount is spent of in time data is collection spent in and data observation. collection However,and observation. even if dataHowever, is available, even if itdata is frequently is available, not it storedis frequently in a digitized not stored format in a neededdigitized for format further needed processing for further (e.g., ESRIprocessing Shapefile). (e.g., High-resolutionESRI Shapefile). spatialHigh‐resolution infrastructure spatial data infrastructure (e.g., consumption data (e.g., data consumption at the household data level)at the belong household to different level) belong authorities, to different complicating authorities, the exchange complicating and arbitrarily the exchange intersecting and arbitrarily the data inintersecting terms of legal the data aspects in terms even of more legal (e.g., aspects the even exchange more of (e.g., data the with exchange third parties of data is with often third forbidden parties andis often subject forbidden to legal and terms subject and to legal conditions terms and of operatingconditions companies).of operating companies). Thus, even Thus, though even datasets though exist,datasets legal exist, aspects legal aspects may counteract may counteract a successful a successful data exchange. data exchange. Considering Considering that that the the evolvement evolvement of waterof water infrastructure infrastructure networks networks began began several several decades decades ago [ago9], the [9], availability the availability of historical of historical data isdata even is worse.even worse. In this In case, this information case, information on the buildon the year build of networkyear of network components components is indispensable. is indispensable. Finding alternativeFinding alternative approaches approaches to generate to andgenerate extract and missing extract data missing out of data alternative out of alternative data sources data (surrogate sources data)(surrogate on infrastructure data) on infrastructure networks is, networks therefore, is, a therefore, relevant research a relevant topic—notably research topic—notably for the purpose for the of model-building,purpose of model especially‐building, for especially research for purpose. research purpose. Blumensaat,Blumensaat, et al. [[10]10] reportedreported anan algorithmalgorithm forfor creatingcreating hydrodynamichydrodynamic sewersewer modelsmodels withwith limitedlimited datadata using streetstreet network datadata downloaded fromfrom OpenStreetMapOpenStreetMap asas thethe input.input. This approach assumesassumes aa strongstrong correlationcorrelation betweenbetween thethe streetstreet andand sewersewer networknetwork (the(the authorsauthors estimateestimate thethe spatialspatial congruencecongruence toto bebe betweenbetween 30%30% andand 95%).95%). Following this idea, the questionquestion arises whetherwhether and how thethe streetstreet networknetwork data, data, which which is is easily easily accessible accessible at at a a high high quality, quality, can can assist assist in in gaining gaining knowledge knowledge of otherof other urban urban infrastructure, infrastructure, such such as wateras water networks. networks. WithWith anan algorithmalgorithm toto complementcomplement thethe missingmissing informationinformation onon thethe urbanurban waterwater infrastructureinfrastructure basedbased onon availableavailable andand easilyeasily accessibleaccessible data (e.g.,(e.g., streetstreet data),data), thethe hydraulichydraulic behaviorbehavior of thethe waterwater supplysupply andand sewersewer networksnetworks couldcould bebe assessed.assessed. Even when thethe entireentire waterwater networknetwork informationinformation isis missing,missing, possiblepossible water water networks networks can can easily easily be be created created without without a substantial a substantial effort, effort, and and these these data data can becan used be used in further in further evaluations. evaluations. Although Although the data the will data not will be exact,not be it exact, will resemble it will resemble a possible a networkpossible layout,network allowing layout, allowing for a realistic for a modeling realistic modeling endeavor endeavor in the scientific in the context.scientific context. FigureFigure1 1 shows shows the the overall overall vision vision of of this this work. work. In In a a first first step step the the geometricgeometric‐ andand graph-based graph‐based characteristicscharacteristics (Figure (Figure 1:1 analyses: analyses column) column) of different of different network network types typeson a multi on a‐utility multi-utility basis are basis identified are identified(e.g., road, (e.g., sewer, road, water sewer, supply water (Figure supply 1: data (Figure column)).1: data Based column)). on the identified Based on characteristics the identified we characteristicsassume to be able we assumeto reconstruct to be able missing to reconstruct data of sewer missing and data water of supply sewer and network water datasets supply networkwith the datasetshelp of surrogate with the helpdata of(e.g., surrogate road data) data (see (e.g., Figure road data)1: reconstructed (see Figure 1data: reconstructed column). data column).

Figure 1. Proposed approach to use surrogate informationinformation forfor networknetwork (re-)construction.(re‐)construction.

The benefit of such a method would save significant time in data preparation. Virtual water networks could also potentially be automatically generated for benchmarking purposes of new designs and optimization algorithms [11].

Water 2017, 9, 146 3 of 15

The benefit of such a method would save significant time in data preparation. Virtual water networks could also potentially be automatically generated for benchmarking purposes of new designs and optimization algorithms [11]. The key to such an analysis, and a main focus of this work, is to identify the correlation of different infrastructure networks (i.e., streets and pipes). Likewise, identifying the potential characteristics, which may be used as a parameter for an algorithm to generate realistic water infrastructure models, is important. A first analysis has been performed in Mair, et al. [12], in which the main focus was to prepare easily accessible network data (the street network from OpenStreetMap) for the combined network analysis across street, sewer, and water supply networks. However, a detailed analysis containing the geometric and graph analytical indicators has not been previously performed. The aim of this paper is to close this gap by performing a detailed network analysis across the street, sewer, and water supply networks (on a multi-utility basis) to better understand the coherences in the design and layout and to identify important characteristics of the water infrastructure in urban areas. If such a spatial link can be identified, future work can focus on developing new approaches that complement missing data or even automatically generate the realistic and semi-artificial datasets of interlinked water infrastructure networks at a city scale. As accuracy of the surrogate data increases (e.g., the development data of streets), the use of this approach is not limited to the scientific community, but these sets may also be useful for stakeholders/planners for making decisions [13]. For example, it can be of interest for assessing future investments in infrastructure (e.g., assessing network structure uncertainties [14], spatial layout optimization [15], testing expansion strategies, or testing of rehabilitation strategies [16,17]). This work is, therefore, structured in two parts: (1) detailed statistical multi-utility analysis of three real-world test cases and identification of controlling parameters for network interdependencies; and (2) sensitivity analysis of the identified parameters.

2. Materials and Methods In the scope of this work, street, water supply, and sewer networks are compared from different perspectives. To perform a sound analysis on all three network types, complete and detailed datasets are required for each network. Detailed datasets for street networks are easily accessible (e.g., from Google Maps or OpenStreetMap) and are already at a sufficient quality for automatic processing. To assess which information on water infrastructure can be deducted from the street data, case studies have investigated sufficient information sources covering the water supply and urban drainage network for the comparison. Data covering urban water infrastructure networks are available from existing EPANET2 [18] and SWMM5 [19] models for water supply and sewer networks, respectively. These datasets include detailed information (e.g., pipe width diameter, roughness coefficient, and slope information) of all network components required for state-of-the-art hydraulic modeling. Each of the sets represents an infrastructure network system with a type-specific service within a defined service area. For a water supply network, the service is to supply water to specific locations, whereas in a sewer network, the service is to dispose storm and/or wastewater within the entire service area. The service areas of all three types of investigated networks may not be congruent and, therefore, the intersection of all service areas defines the area of interest on which the analyses are performed. Within this area, all required and detailed data must be available to develop a valid proposition about network similarities. Figure2 shows the service area of the street, sewer, and water supply networks of an alpine city (in this work, this case study is called CS1). The solid-shaped polygon is the intersection of all three service area polygons and defines the area of interest regarding the data analysis. A network correlation/similarity analysis can be performed in various ways. In this work, network layout and graph-based analyses are conducted. Under the scope of these two types, characteristics/indicators are identified to better understand the correlation of urban infrastructure. Water 2017, 9, 146 4 of 15 Water 2017, 9, 146 4 of 15

Sewer system service area

Area of interest

Water supply system service area

Figure 2. Area of interest defined by the service area intersection of all network types. Figure 2. Area of interest defined by the service area intersection of all network types. 2.1. Geometric Analysis and Parameter Sensitivity 2.1. Geometric Analysis and Parameter Sensitivity Following the approach from Mair, et al. [12], a detailed analysis is performed for geometric networkFollowing indicators the approach over different from network Mair, et types al. [12], (multi-utility a detailed basis). analysis The is analysis performed of different for geometric datasets networkincludes indicators a classification over ofdifferent the results network depending types on (multi the different‐utility basis). street types,The analysis pipe diameters, of different and datasetsconduit includes diameters. a classification Street network of the data results is easily depending accessible on the and different often of street good types, quality. pipe In diameters, this work, andstreet conduit network diameters. data are Street used andnetwork downloaded data is easily from accessible OpenStreetMap, and often including of good the quality. specific In this street work, type streetof each network element data within are used the dataset and downloaded (for five different from OpenStreetMap, types). including the specific street type of eachThe element exact within street widththe dataset and information(for five different about types). parking lots, pavements or additional lanes, for example,The exact are street not includedwidth and in information this data. To about compensate parking for lots, this pavements lack of information, or additional street lanes, widths for example,depending are on not the included street types in arethis assumed data. To (the compensate assumed width for this in Sectionlack of 3.2information,) and an additional street widths width dependingis included on in the the street analysis types resulting are assumed in a (the corrected assumed width width (the in Section sum of 3.2) the and assumed an additional and additional width is includedwidth). in For the sensitivity analysis resulting analysis, in the a corrected parameter width of the (the additional sum of the street assumed width and varies additional on both width). street Forsides sensitivity from 0.5 analysis, to 5 m, while the parameter the related of percentage the additional of that street which width contains varies the on infrastructureboth street sides network from 0.5is determinedto 5 m, while and analyzedthe related (see percentage Section 3.2 of). Analysesthat which based contains on this the assumption infrastructure consider network parallel is determinedpipes/conduits and belowanalyzed a street. (see OnceSection the 3.2). corrected Analyses street based areas on are this identified, assumption street-type consider non-specific parallel pipes/conduitsand specific geometric below a analysesstreet. Once can the be performedcorrected street by intersecting areas are identified, the geometric street data‐type of non the‐ differentspecific andnetwork specific types geometric (see Section analyses 3.3). can be performed by intersecting the geometric data of the different network types (see Section 3.3). 2.2. Graph Analysis 2.2. Graph Analysis The network layout of a water supply or sewer system can be interpreted as an undirected connectedThe network graph, layoutG, in which of a water all link supply elements or sewer (e.g., pipes, system pumps, can be conduits) interpreted are as the an edges undirected (E) and connectedall node elements graph, (e.g.,, in which junctions, all link outlet, elements tanks, (e.g., reservoirs) pipes, pumps, are the conduits) vertices ( Vare) of the a graphedges G(=) and(E, allV) . nodeThe weightelements of each(e.g., edgejunctions, is the outlet, function tanks,w : reservoirs)E → R, which are the maps vertices each edge() ofe a∈ graphE to a , value of R. .The The weightweight of of each each edge edge is is the equal function to the : length → of, thewhich corresponding maps each edge link element ∈ to a in value the real of infrastructure. The weight ofnetwork. each edge Based is equal on thisto the representation, length of the corresponding a graph-based link analysis element can in be the performed. real infrastructure Under thenetwork. scope Basedof this on work, this severalrepresentation, different a graph‐based indicators analysis are investigated:can be performed. (1) total Under indicators, the scope such of asthis the work, total severalnumber different of vertices graph (# indicatorsV) and the are total investigated: number of(1) edgestotal indicators, (#E); and such (2) relative as the total indicators, number of which vertices are (graph# ) and size the independent. total number Since of the edges latter ( # indicator); and type(2) relative is not as indicators, straightforward which to are compare graph to size the independent.total indicator Since type, the the latter following indicator definition type is is not based as straightforward on select informal to compare and basic to definitions the total indicator of graph type,theory. the The following two indicators definition that is arebased used on in select this work informal are thenand introduced.basic definitions of graph theory. The i two indicatorsA path P thatof a graphare usedG isin a this sequence work are of verticesthen introduced.(v1,..., v i) ∈ V in which each consecutive pair of verticesA path (v iof, v ia+ graph1) ∈ P is is connected a sequence by of an vertices edge e ∈E,…,. The∈ weight in whichw(P) of each a path consecutive is the sum pair of of all verticesedge weights , within ∈ theis connected path. A shortest by an edge path (SP) ∈ is. The a path weight connecting of two a path vertices is the within sum of a all graph edge in

Water 2017, 9, 146 5 of 15 which the total weight is minimal. A cycle of a graph is a path in which the first and the last vertices are equal. A minimum spanning tree (MST) of a graph G is a connected graph without cycles, which connects all vertices MST = (Esub, V) ⊆ (E, V) = G and the sum of all edge weights is minimal. With the help of these basic definitions, the two indicators can be defined as the cycle (CI) and leaf indicator (LI). The authors of this work are aware of the immense diversity of graph measures and metrics in graph theory; however, in this work a new, innovative, and simple graph-based indicator is introduced with the focus on analyzing water infrastructure graphs.

2.2.1. Cycle Indicator (CI) This indicator describes characteristics of the cycles (loops) within an infrastructure network and is often implemented for reliability purposes. Water supply and sewer networks are mostly realized with the aim of minimum construction cost. Crucial for the total construction cost of an infrastructure network is the total length of the network. If we disregard the aspect of reliability, the infrastructure network has a tree-like structure with minimum construction cost and service level. This is equivalent to a minimal working network structure (following called MWG). In a mathematical sense, this network is a generalized minimum Steiner tree [20] connecting all relevant nodes (these nodes are also known as Steiner terminals) in a given graph (e.g., street network graph) with a minimal network length, to guarantee the service offered by the water infrastructure network. The relevant vertices/nodes in a water supply network are all junctions with a demand greater than zero, and in a sewer network, all inlet nodes. Due to the high complexity (NP-complete) and, therefore, high computational runtime for ﬁnding such a tree, the following approximation with a time complexity of O(|E| log(|V|) + |V|2) is used for generating an MWG (|E| and |V| are the number of edges and vertices). Based on the MWG the cycle indicator (CI) can be evaluated. The overall runtime complexity of the MWG algorithm (Steiner tree approximation) is the sum of the MST algorithm complexity O(|E| log(|V|)) (Using Kruskal’s algorithm [21]) and TRIM algorithm complexity O(|V|2) (check each vertex if it is part of one unique edge and, if yes, deleting it). Additionally, more accurate, but also more computationally intense, approximations have been established [22]. In this work all analyses regarding the CI indicator are performed on datasets of water supply and sewer network graphs. Based on these graphs the generalized minimum Steiner tree is equivalent to a minimum spanning tree minus all non-terminal leafs. Hence, the choice of the approximation function has no impact on the results of CI. The layout of a minimal working infrastructure network (Figure3: MWG) is assumed to be equivalent to an MST of the graph (Figure3: MST(G)) in which all leaves are removed that are not mandatory for the network service. All other edges are for redundant capacity, reliability, and part of a cycle (Figure3: reliability graph). An MST of a graph does not necessarily need to be unique (e.g., graph G in Figure3 has two different MSTs). By comparing the path length of the path connecting two vertices within the MWG with the alternative shortest path length between the identical vertices in the reliability graph (RG), the fraction of the path length for building a cycle can be obtained. Equation (1) presents this comparison where a and b are two vertices of the graph G, MWG(G) is a minimum spanning tree without leaves which are not relevant for the network service, and Pa,b and SPa,b are a path and the shortest path of the graph MWG and RG connecting vertices a and b, respectively.

w(SPa,b(RG)) CIa,b := (−) (1) w(Pa,b(MWG(G)))

By performing these steps for all possible tuple-combinations of vertices of graph G, all cycles/loops within an infrastructure network can be analyzed. Water 2017, 9, 146 6 of 15 Water 2017, 9, 146 6 of 15

Figure 3. CI evaluation. Figure 3. CI evaluation. 2.2.2. Leaf Indicator (LI) 2.2.2. Leaf Indicator (LI) A leaf of a graph is a path that is not part of any cycle. In urban water infrastructure networks, theseA leaf paths of a correspond graph is a to path household that is connections, not part of anypipes cycle. coming In from urban the water water infrastructuresource, and conduits networks, theseleading paths to correspond the waste‐water to household treatment connections,plant. Equation pipes (2) shows coming the method from the employed water source, for determining and conduits leadingthis toindicator. the waste-water is the treatmentsubset of all plant. edges Equation which are (2)not shows part of theany methodcycle. The employed fraction (LI) for of determining leaves is equal to the total weight of all leaves divided by the total network weight. this indicator. Esub is the subset of all edges which are not part of any cycle. The fraction (LI) of leaves # is equal to the total weight of all leaves divided∑ by the total network weight. ∶ # (2) ∑ #E ∑ sub w(e ) = i=0 i (−) LI : #E (2) 2.3. Description of Case Studies (CS) ∑i=0 w(ei) In this paper, we investigate three case studies in an alpine region with different network sizes, 2.3. Description of Case Studies (CS) denoted as CS1 to CS3. For all case studies, information of the water supply (e.g., pipe diameter and length)In this and paper, sewer we (e.g., investigate conduit cross three section, case roughness, studies in and an alpineslope) systems region are with derived different from networkhydraulic sizes, denotedand hydrodynamic as CS1 to CS3. models, For all respectively. case studies, Street information network ofdata the is waterdownloaded supply from (e.g., OpenStreetMap pipe diameter and length)for andthe area sewer of interest (e.g., conduit (intersecting cross section,the service roughness, area of the and water slope) supply systems and sewer are derived network). from Due hydraulic to security concerns, we are not allowed to publish the exact layout of all case studies in this work. and hydrodynamic models, respectively. Street network data is downloaded from OpenStreetMap Therefore, all case studies are described by quantifying several characteristics. for the area of interest (intersecting the service area of the water supply and sewer network). Due Table 1 shows initial properties of all three case studies. When using the population value as an to securityindicator concerns, for the size we of are a service not allowed area, CS1 to is publish the largest the case exact study layout (resembling of all case a medium studies‐sized in thiscity) work. Therefore,and CS2 all and case CS3 studies are nearly are described of equal size by quantifying(resembling a several small city/large characteristics. village). All listed values shouldTable1 be shows seen as initial properties properties of the ofinitial all threeinput datasets. case studies. The presented When using data reveals the population that, for all value three as an indicatorhydraulic for thecase size studies, of a the service level of area, detail CS1 (of the is the models) largest is approximately case study (resembling identical (e.g., a the medium-sized smallest pipe city) anddiameters CS2 and CS3range are between nearly 25 of mm equal and 31 size mm). (resembling Further, the a water small supply city/large network village). in the city All (CS1) listed has values shouldonly be a seenslightly as higher properties length of than the the initial sewer input network datasets. (7.43%). The This presented difference data is higher reveals for that, the villages for all three hydraulic(CS2 and case CS3; studies, 53.59% the and level 31.42%, of detail respectively). (of the models) Within the is approximately city pipe/conduit identical length per (e.g., inhabitant the smallest is much smaller in the city (for CS1, 2 m) compared to the villages (for CS2 and CS3, up to 6 m). pipe diameters range between 25 mm and 31 mm). Further, the water supply network in the city (CS1) has only a slightly higher length thanTable the 1. sewer Case study network properties. (7.43%). This difference is higher for the villages (CS2 and CS3; 53.59% and 31.42%, respectively). Within the city pipe/conduit length per inhabitant is much smaller in the city (for CS1, 2 m) comparedRow CS1 to the villagesCS2 (forCS3 CS2 and CS3, up to Population (‐) 1 120,000 13,000 11,000 6 m). Widest pipe diameter (mm) 2 600 500 250 Widest conduit diameter (mm) 3 2444 2130 1800 Table 1. Case study properties. Lowest pipe diameter (mm) 4 25 31 30 Lowest conduit diameter (mm) 5 150 100 150 Row CS1 CS2 CS3 Total water supply network length (km) 6 217.67 64.2 61.9 PopulationPipe length/inhabitant (-) (m) 17 120,0001.81 4.93 13,000 5.63 11,000 WidestTotal pipe Sewer diameter network (mm) length (km) 28 202.88 600 41.8 500 47.1 250 WidestConduit conduit length/inhabitant diameter (mm) (m) 39 1.69 2444 3.22 2130 4.28 1800 Lowest pipe diameter (mm) 4 25 31 30 Lowest conduit diameter (mm) 5 150 100 150 Total water supply network length (km) 6 217.67 64.2 61.9 Pipe length/inhabitant (m) 7 1.81 4.93 5.63 Total Sewer network length (km) 8 202.88 41.8 47.1 Conduit length/inhabitant (m) 9 1.69 3.22 4.28 Water 2017, 9, 146 7 of 15

3. Results and Discussion Geometric and graph-based analyses are performed for all three case studies and presented below with an interpretation. Similar to the structure of the described methods, the calculations of the area of interest are presented ﬁrst. Next, the results of the detailed geometric analysis (evaluation based on street types and diameters of pipes and conduits) are shown, followed by graph-based analysis containing the indicators CI and LI.

3.1. Area of Interest As described in the methods section, the area of interest is calculated by intersecting the service areas of the water supply and sewer network. This intersection is used for clipping the street network data. Table2 shows the identical properties of the input datasets, after clipping, according to the calculated area of interest. Using the area of interest as an indicator for describing the size of the systems, CS1 has the largest area with 25 km2. CS2 and CS3 have nearly identical sizes resulting in close population densities when comparing these values with the population values in Table1. Due to clipping the water supply and sewer network data to a common area of interest, some data is not regarded. The amount of clipped data is shown by comparing the total network length of the original input dataset (Table1: rows 6 and 8) with that of the clipped data (Table2: rows 7 and 9). Disregarded data of sewer networks is marginal for all three case studies. Neglected data of the water supply networks for the CS1 is also marginal. CS2 and CS3 show a higher deviation, with 24% and 15% of the data being clipped, respectively. This clipping results from the lower service area of the sewer networks. These clipped network zones are usually those parts of the sewer network in which not all inhabitants are connected to the sewer system, or in which long main trunks occur in the water supply network. Comparing the widest diameter of pipes occurring within the clipped (Table2: row 3) and original (Table1: row 2) water supply dataset, CS2 shows that many portions of the main trunks are not considered in this case. This is because of missing information of the sewer network in the identical area and long main trunks from the reservoir to the valley within the water supply network. Generally speaking, the service area of water supply systems is more likely to be larger when compared to the service area of the sewer system within the identical case study. After clipping the street network datasets to the area of interest, Table2 (row 11) shows that the obtained street network length is nearly twice as long as the sewer or water supply network within the identical case studies.

Table 2. Area of interest properties for all case studies.

Row CS1 CS2 CS3 Area of interest—AI (km2) 1 25.14 5.88 5.35 Population density (Pop/ km2) 2 4774 2210 2056 Widest pipe diameter (mm) 3 600 305 250 Widest conduit diameter (mm) 4 2,440 2130 1800 Lowest pipe diameter (mm) 5 25 31 30 Lowest conduit diameter (mm) 6 150 100 150 Total water supply network length (km) 7 216.75 48.7 52.20 Pipe length/inhabitant (m) 8 1.81 3.74 4.75 Total sewer network length (km) 9 201.93 41.4 46.82 Conduit length/inhabitant (m) 10 1.68 3.19 4.26 Total street network length (km) 11 419.48 78.1 67.87

For the geometric analysis, all clipped datasets are used, and for the graph-based analysis, the original datasets are used for investigations. Water 2017, 9, 146 8 of 15

Water 20173.2. ,Parameter9, 146 Sensitivity 8 of 15 The street network data used from OpenStreetMap does not contain information about parking 3.2. Parameterlots, pavements, Sensitivity additional lanes, or roadside ditches. To compensate for this lack of information, the actual street width is increased by an additional street width. This is investigated in order to consider Thestreet street parallel network pipelines, data which used would from not OpenStreetMap be identified with does the not initially contain‐assumed information street width about from parking lots, pavements,the literature (the additional assumed lanes, width or in roadsideTable 3). ditches. To compensate for this lack of information, the actualFigure street 4 widthshows the is increasedresults of a sensitivity by an additional analysis where street the width. correlation This of is additional investigated street in width order to considerand streetcovered parallel network pipelines, length is investigated which would for notthe three be identiﬁed alpine case with studies. the initially-assumedBy adding additional street street width fromwidth the literature starting (thefrom assumed 0.5 m, the width total water in Table supply/sewer3). network length situated below the road Figureincreases4 shows in a non the‐linear results manner. of a sensitivity This increase analysis results where from the the number correlation of pipes of additional or conduits, street which width are parallel to a street e.g., below a parking area. When all parallel elements (pipes or conduits) are and covered network length is investigated for the three alpine case studies. By adding additional within the corrected street width (assumed width + two times the additional street width), a re‐ streetincrease width starting of the street from width 0.5 m, results the total in watera near‐ supply/sewerlinear increase networkof the total length water situated supply belowand sewer the road increasesnetwork in a lengths non-linear below manner. a street This(Figure increase 4—starting results from from 3.5 the m of number additional of pipes street orwidth). conduits, This linear which are parallelincrease to a street represents e.g., belowpipes/conduits a parking crossing area. Whenstreets. all These parallel pipes elements should not (pipes be included or conduits) in successive are within the correctedanalyses. streetTherefore, width the (assumed determined width value + for two the times additional the additional street width street is the width), point at a which re-increase the of the streetcurve width changes results from ina non a near-linear‐linear increase increase to a oflinear the increase total water (Figure supply 4—3.5 and m sewerof additional network street lengths belowwidth). a street (Figure4—starting from 3.5 m of additional street width). This linear increase represents pipes/conduitsThe outcome crossing is similar streets. for These all case pipes studies should and not reveals be included that a representative in successive additional analyses. street Therefore, width of around 3.5 m on both roadsides (in total 7 m) includes only parallel water infrastructure (for the determined value for the additional street width is the point at which the curve changes from a comparison see Figure 4). Based on this parameter, a corrected street width for each street type is non-linear increase to a linear increase (Figure4—3.5 m of additional street width). determined.

Figure 4. Sensitivity analysis of additional street width and covered network length below the streets Figure 4. Sensitivity analysis of additional street width and covered network length below the streets for three alpine case studies. for three alpine case studies. Table 3 shows the different street types with the assumed and corrected street widths. The latter Theincludes outcome an additional is similar width for of all 3.5 case m on studies each street and side, reveals determined that a from representative the previous additionalanalysis. The street widthstreet of around type “Other” 3.5 m includes on both streets roadsides with the (in street total types 7 m) “service”, includes “residential”, only parallel and water “unclassified”. infrastructure These types have nearly identical widths; therefore, these types are merged into one category. For (for comparison see Figure4). Based on this parameter, a corrected street width for each street type further analysis, the corrected street widths are used. is determined. Table3 shows the differentTable street3. Assumed types street with width the depending assumed on and street corrected types. street widths. The latter includes an additional width of 3.5 m on each street side, determined from the previous analysis. Type Motorway Primary Secondary Tertiary Other The street type “Other” includes streets with the street types “service”, “residential”, and “unclassiﬁed”. Assumed width (m) 21 14 14 13 2 These types have nearly identical widths; therefore, these types are merged into one category. Corrected width (m) 28 21 21 20 9 For further analysis, the corrected street widths are used.

Table 3. Assumed street width depending on street types.

Type Motorway Primary Secondary Tertiary Other Assumed width (m) 21 14 14 13 2 Corrected width (m) 28 21 21 20 9 Water 2017, 9, 146 9 of 15 Water 2017, 9, 146 9 of 15

3.3. Geometric Analysis Figure 55 shows shows selected selected general general geometricgeometric resultsresults fromfrom all all three three case case studies. studies. ComparedCompared toto the the geometric analysis performed in Mair et al. [12], [12], in which a pipe or conduit is identified identiﬁed to be below a street independently of the length, in this work, the results depend on on the pipe or or conduit length. length. The average values show that approximately 50% of the street network contains 78% of the water supply or sewer network. Due to the the limited limited area area for for water water supply supply and and sewer sewer systems systems in in high high-density‐density areas, this value is increasing, demonstrated byby CS1CS1 withwith aa valuevalue exceedingexceeding 90%.90%.

Streets containing water supply pipes (%) Streets containing sewer pipes (%) Water supply pipes below the street (%) Sewer pipes below the street (%) 93 92 85 83 78 78 74 67 54 51 50 50 48 48 44 44

CS1 CS2 CS3 AVERAGE

Figure 5. Street type independent geometric results of various street types.

Table4 4 shows shows the the fraction fraction of of different different street street types types within within the the street street networks networks (clipped (clipped byby thethe areaarea of interest). Only between 10% 10% and and 20% of the total street network length are motorways, primary, secondary, or tertiary streets. The remaining streets streets are categorized as others and include service, residential, and unclassiﬁedunclassified streetsstreets withwith thethe samesame geometricgeometric characteristics.characteristics.

Table 4. Fraction of street types in a street network. Case Study Motorway Primary Secondary Tertiary Other Case Study Motorway Primary Secondary Tertiary Other CS1 6.12 7.67 2.60 7.81 75.80 CS1 6.12 7.67 2.60 7.81 75.80 CS2 0.35 6.89 2.62 8.37 81.77 CS2 0.35 6.89 2.62 8.37 81.77 CS3CS3 2.972.97 5.485.48 7.887.88 3.78 3.78 79.88 79.88

Investigations into the fraction of pipe diameters and type of the street are presented in Figure 6. Investigations into the fraction of pipe diameters and type of the street are presented in Figure6. Following Trifunovic [23], pipes are classified according to their diameter ( in mm) and usage, i.e., into Following Trifunovic [23], pipes are classified according to their diameter (d in mm) and usage, i.e., trunk mains ( 400 ), secondary mains (200 400), distribution mains (80 200), and into trunk mains (d ≥ 400 ), secondary mains (200 ≤ d < 400), distribution mains (80 ≤ d < 200), and service pipes ( 80). service pipes (d < 80). The columns “All pipes” in Figure 6 and columns “d > 0” in Figure 7 show the fraction of the The columns “All pipes” in Figure6 and columns “ d > 0” in Figure7 show the fraction of the pipe and conduit classification within a water supply and sewer network independent of the street pipe and conduit classification within a water supply and sewer network independent of the street types, respectively. By contrast, all other columns show the fraction of pipes and conduits of the entire types, respectively. By contrast, all other columns show the fraction of pipes and conduits of the entire network length in correlation with the five different street types (Figures 6 and 7). These results are network length in correlation with the five different street types (Figures6 and7). These results are also presented in form of a table in Appendix A. also presented in form of a table in AppendixA. Below a motorway, only one percent of all pipes of a water supply system are placed. These pipes Below a motorway, only one percent of all pipes of a water supply system are placed. These pipes are mostly only crossing the motorway. Independent of the diameter, between 49% and 72% of a water are mostly only crossing the motorway. Independent of the diameter, between 49% and 72% of a water supply network are found below the street type “Other”. Approximately 50% of the diameters in this supply network are found below the street type “Other”. Approximately 50% of the diameters in category display a diameter between 80 mm and 200 mm, accounting for the class “distribution this category display a diameter between 80 mm and 200 mm, accounting for the class “distribution mains”. Generally speaking, approximately 60% of water supply network pipes are distribution mains”. Generally speaking, approximately 60% of water supply network pipes are distribution mains. mains. The fraction of service pipes is a sign of the level of detail of the network data (household The fraction of service pipes is a sign of the level of detail of the network data (household connection connection included or not). included or not). Similar to the classification of pipes according to usage in water supply systems, a classification Similar to the classification of pipes according to usage in water supply systems, a classification for conduits (three different classes on the basis of Gujer [24]) within sewer systems is performed. for conduits (three different classes on the basis of Gujer [24]) within sewer systems is performed. Figure 7 shows the fraction of conduit diameters according to specific street types. The major portion (between 62% and 85%) of a sewer network is below a street of type “Other”, less than 10% is below primary/secondary streets, and less than 1% is below motorways.

Water 2017, 9, 146 10 of 15

Figure7 shows the fraction of conduit diameters according to speciﬁc street types. The major portion

Water(between 2017, 9 62%, 146 and 85%) of a sewer network is below a street of type “Other”, less than 10% is10 below of 15 Waterprimary/secondary 2017, 9, 146 streets, and less than 1% is below motorways. 10 of 15

CS1 CS2 CS3 80 CS1 CS2 CS3 80 70

[%] 70

[%]

60 60 50 50 40 correlation 40 correlation 30 type

30 type 20 20

street 10

street 10 0 0

Pipe types [‐] Pipe types [‐] Motorway Primary Secondary Tertiary Other Motorway Primary Secondary Tertiary Other

FigureFigure 6. 6. PipePipe types types in in correlation correlation with with street street types. types. Figure 6. Pipe types in correlation with street types.

CS1 CS2 CS3 90 CS1 CS2 CS3 90 80 [%] 80 [%] 70 70 60 60 50 50 correlation 40 correlation 40 30 type 30 type

20 20 10 street 10

street 0 0

Conduit diameter [cm] Conduit diameter [cm]

Motorway Primary Secondary Tertiary Other Motorway Primary Secondary Tertiary Other Figure 7. Conduit diameter in correlation with street types. Figure 7. Conduit diameter in correlation with street types. Figure 7. Conduit diameter in correlation with street types. TheThe results results of of this this analysis analysis reveal reveal a strong a strong correlation correlation between between street street network network data and data urban and water urban The results of this analysis reveal a strong correlation between street network data and urban water infrastructurewater infrastructure networks. networks. Furthermore, Furthermore, the presented the presented results can results be used can for be usedcomplementing for complementing missing infrastructure networks. Furthermore, the presented results can be used for complementing missing spatialmissing network spatial networkinformation information (missing (missingpipes) when pipes) datasets when datasetsare of poor are quality. of poor Further, quality. Further,the results the spatial network information (missing pipes) when datasets are of poor quality. Further, the results canresults be used can be for used developing for developing and validating and validating complementary complementary approaches approaches or orgeneration generation procedures procedures can be used for developing and validating complementary approaches or generation procedures using street network data as the input and generating entire sets of semi‐artificial water infrastructure using street network data as the input and generating entire sets of semi‐artificial water infrastructure networks. In developing countries, water network information might even be missing. In this case, a networks. In developing countries, water network information might even be missing. In this case, a possible water infrastructure layout can be created with such a generation procedure. possible water infrastructure layout can be created with such a generation procedure. A correlation between street network types and conduit/pipe diameter could not be found in A correlation between street network types and conduit/pipe diameter could not be found in this analysis. Due to the missing construction year information in the street network dataset, this analysis. Due to the missing construction year information in the street network dataset,

Water 2017, 9, 146 11 of 15 using street network data as the input and generating entire sets of semi-artiﬁcial water infrastructure networks. In developing countries, water network information might even be missing. In this case, a possible water infrastructure layout can be created with such a generation procedure. A correlation between street network types and conduit/pipe diameter could not be found in this analysis. Due to the missing construction year information in the street network dataset, information about pipe/conduit construction year and roughness cannot be extracted. However, planning rehabilitation measures for water infrastructure, information of the construction age is an important parameter [25]. Such historic network information is harder to gather than the actual state of a system. The results of this study can potentially also contribute to close this information gap by using historic street network information (derived from historical orthophotos) as the basis for network reconstruction of historical network states.

3.4. Graph Analysis Tables5 and6 show the results of all absolute and relative graph theory based analyses for water supply and sewer systems, respectively. These analyses are performed on the original dataset for the water supply and sewer network, in which no clipping according to the area of interest was performed. The reason for not clipping the data is that only the graph structure of the system should be analyzed with no geometric effects of other infrastructure network graphs.

Table 5. Results of the graph analysis for water supply networks.

CS1 CS2 CS3 Average #Nodes (-) 7128 790 452 #Edges (-) 7600 878 602 85% percentile of CI (%) 49.84 58.53 60.67 56.35 LI (%) 11.18 12.81 11.89 11.96

Table 6. Results of the graph analysis for sewer networks.

CS1 CS2 CS3 Average #Nodes (-) 5395 1232 1700 #Edges (-) 5756 1248 1710 85% percentile of CI (%) 34.98 19.25 29.29 27.84 LI (%) 28.62 80.83 64.68 58.04

The results show that the leaf indicator (LI) within a water supply network is approximately 12% of the total network length (Table5: LI). All other parts of the network are a part of one or more loops. Independent of the case study size, nearly the identical fraction can be identiﬁed. The fact that 88% of a water supply network is looped reﬂects the constraints on a water distribution system: not to fail in any circumstances. Evaluating the cycle indicator (Table5: CI) shows that 85% of all loops within a water supply network are constructed by including an alternative path between two service nodes, which is only up to 60% of the original path length in the MWG. In short, pipes for reliability are shortcuts for up to 40% of the distance between two service nodes compared to the path within the MWG. The plot of the empirical cumulative distribution function (CDF) of this indicator (Figure8: left) shows that in CS1, the gradient is much steeper when compared to CS2 and CS3. This steeper gradient results from the high degree of looping and urbanization in CS1, in which 93% of all pipes are below a street. The identical analysis was performed for sewer systems (Table6). Results indicate that the leaf indicator (LI) within a sewer network is between approximately 30% and 80%, with a mean value of 58%. These values show that the investigated sewer systems have fewer loops when compared to the water supply systems (Figure8: right—note, only a few data points are available for CS2 and Water 2017, 9, 146 12 of 15

CS3). These low values result from the higher tolerance of system failures for sewer systems. CS1 has a leaf indicator of 29%, which results from the higher population density and a higher meshed network layoutWater 2017 when, 9, 146 compared to CS2 and CS3. Moreover, CS1 has a combined sewer system with the12 main of 15 aim of preventing flooding of the system within highly urbanized areas during heavy rain events and to(closing treat polluted loops) to surface better runoff distribute at the local wastewater storm water treatment runoff. plant By contrast, during most CS2 rain and events. CS3 have In addition a lower topopulation the construction density; in of the additional urban areas, storage therefore, volumes more in pervious combination areas with are available combined for sewer the construction overflows withinof infiltration such systems, sites. The this piped combined sewer systemsystem canis, therefore, be maintained not highly by constructing stressed during alternative heavy rain flow events paths (closingand the system loops) toredundancy better distribute (loops) local can be storm limited. water runoff. By contrast, CS2 and CS3 have a lower populationHowever, density; when in theloops urban in such areas, systems therefore, occur, more more pervious than areas 85% are of availableall loops forare the constructed construction to ofinclude infiltration an alternative sites. The path piped between sewer two system service is, therefore, nodes for not which highly the stressed length is during up to 30% heavy of the rain original events andpath the length system (Table redundancy 6: CI and (loops)Figure can8: right). be limited.

Figure 8. CDF plots of CIs of water supply and sewer networks.

3.5. Applications of the Results Obtained from the Graph and Geometric Analyses However, when loops in such systems occur, more than 85% of all loops are constructed to include an alternativeThe analyses path of between this work two are service performed nodes in for order which to better the length understand is up to the 30% correlation of the original of different path lengthurban infrastructures (Table6: CI and and Figure to 8identify: right). potential surrogate data sources (Does the street network data help to better understand and describe the water infrastructure or does knowledge on, e.g., the water 3.5.supply Applications network support of the Results improving Obtained drainage from the data?). Graph The and obtained Geometric results Analyses also improve the understanding of urbanThe analyses network of infrastructure this work are performedfrom an integrated in order to point better of understand view and the can correlation be fundamental of different for urbandifferent infrastructures research purposes, and to identify like data potential verification, surrogate data data completion, sources (Does or even the streetthe entire network generation data help of tofeasible better datasets. understand For and data describe complementation the water infrastructure for deterioration or does modelling knowledge and on, e.g.,data the verification water supply the networkbenefits of support a multi improving‐utility approach drainage were data?). shown The obtainedin [25]. Additionally, results also improve for systematically the understanding testing of urbanalternatives network for infrastructure future water from infrastructure an integrated planning point of based view andon land can be‐use fundamental master plans for different[26], the researchobtained purposes,results of this like work data verification,can be essential. data completion, or even the entire generation of feasible datasets.Another For data application complementation of the obtained for deterioration results is modelling the enhancement and data verificationof existing thewater benefits network of a multi-utilitygeneration algorithms approach to were create shown so‐called in [25 virtual]. Additionally, or semi‐virtual for systematically networks. In this testing regard of alternativesthe results from for futurethis work water enable infrastructure identifying planning and quantifying based on potential land-use parameters master plans and [ showing26], the obtained the applicability results of of this the workforeseen can methods be essential. for network generation. Further investigations on developing, testing, and validating suchAnother an algorithm application are previously of the obtained successfully results applied is the and enhancement presented of[14]. existing In that water work, network design generationcriteria and algorithms hydraulic performances to create so-called of the virtual virtual or systems semi-virtual are also networks. compared In to this those regard of the the assumed results fromunknown this work real enablesystem. identifying It is shown and that, quantifying with the potentialstochastic parameters generation and process, showing hydraulic the applicability pressure ofdifferences the foreseen in water methods supply for networkmodels lower generation. that ±4 Further m compared investigations to the real on system developing, could testing,be achieved and validatingfor design loads. such an algorithm are previously successfully applied and presented [14]. In that work,

Water 2017, 9, 146 13 of 15 design criteria and hydraulic performances of the virtual systems are also compared to those of the assumed unknown real system. It is shown that, with the stochastic generation process, hydraulic pressure differences in water supply models lower that ±4 m compared to the real system could be achieved for design loads.

4. Summary, Conclusions, and Outlook In this manuscript, correlations in the urban infrastructure networks in the field of urban water management are analyzed in order to better understand the correlation of different urban infrastructures and to identify potential sources for surrogate data. The investigation is split into two main parts: a geometric analysis and a graph-based analysis. All calculations were performed on three case studies with different sizes in which complete and detailed datasets of street, water supply, and sewer networks are available. The first case study has 120,000 inhabitants, and the other two case studies have approximately 13,000 and 11,000 inhabitants. To strengthen the validity of the obtained results, future work will also focus on including more, and international, case studies. The results of geometric-based analyses showed a strong correlation between street networks and the urban water infrastructure (water supply/sewer network). On average, 50% of the street network length correlates with 80%–85% of the total water supply/sewer network. Urban water infrastructure networks are developed and constructed similar to a street network layout when using all streets of type “Others” (analyzed with OpenStreetMap data). A correlation between the pipe/conduit diameter and street type was not found. Due to the missing construction year information in the street network dataset, information covering the material and age of the pipes/conduits cannot be extracted. The graph-based analysis showed that up to 12% and 80% of a water supply and sewer system, respectively, are not part of any loops. The other parts of the network are completely looped. In total, 85% of all loops within a water supply and sewer system are constructed by finding an alternative path between two service nodes for which the path length is up to approximately 56% and 28% when compared to the original path, respectively. The focus was on identifying and quantifying significant network indicators, which are potentially useful as parameters for further applications. Potential application of the findings (e.g., deterioration modelling, future infrastructure planning, data complementation, or virtual network generators) were also identified and outlined. Especially for network generation algorithms, we investigated and evaluated graph-based indicators (leaf indicator and cycle indicator), which are fundamental for the development of such approaches. We observed that graph-based indicators are more useful as input parameters for such algorithms, whereas the geometric indicators are more suitable for validation. Statistically quantifying these indicators enables the development and validation of infrastructure networks (semi-virtual sewer and water supply network datasets) and the generation of algorithms for further use (e.g., a benchmark set to optimize algorithms and new hydraulic solver implementations). Such algorithms will consist of two parts: (1) network layout algorithms that can be seen as a reverse function of the cycle indicator; and (2) fulfilling hydraulic properties, which is an engineering design/optimization problem.

Acknowledgments: This work is part of 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 number 839743). Author Contributions: Michael Mair designed the study and in a first step developed the geometric and graph based analyses. Jonatan Zischg was responsible for data gathering and performing geometric analysis with the help of geographic information systems. Wolfgang Rauch and Robert Sitzenfrei conceived the study, supervised the work and partly wrote this paper. Conflicts of Interest: The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results. Water 2017, 9, 146 14 of 15

Appendix

Table A1. Pipe types in correlation with street types.

Pipe Type According to Pipes below Different Street Types (%) Case Study Motorway Primary Secondary Tertiary Other All CS1: service pipes 0.00 0.01 0.00 0.00 0.44 0.43 CS1: distribution mains 0.40 5.29 1.31 8.37 49.37 57.79 CS1: secondary mains 0.12 3.54 1.51 7.87 16.66 25.38 CS1: trunk mains 0.25 1.35 1.08 2.16 6.42 9.67 CS1: All 0.77 10.19 3.90 18.39 72.89 CS2: service pipes 0.00 0.00 0.00 0.04 1.70 1.73 CS2: distribution mains 0.00 3.21 1.18 8.82 47.59 56.93 CS2: secondary mains 0.00 1.91 2.61 0.62 12.01 15.74 CS2: trunk mains 0.00 0.00 0.00 0.00 0.00 0.00 CS2: All 0.00 5.12 3.78 9.48 61.31 CS3: service pipes 0.00 0.00 0.00 0.02 0.19 0.20 CS3: distribution mains 0.08 7.91 5.73 5.45 44.27 59.84 CS3: secondary mains 0.08 0.09 2.75 0.17 4.67 6.82 CS3: trunk mains 0.00 0.00 0.00 0.00 0.01 0.02 CS3: All 0.16 8.00 8.49 5.65 49.14

Table A2. Conduit diameter in correlation with street types.

Conduit Diameter d (cm) Conduits below Different Street Types (%) According to Case Study Motorway Primary Secondary Tertiary Other All CS1: d < 25 (%) 0.04 0.06 0.01 0.12 2.97 2.88 CS1: 25 ≤ d < 100 (%) 0.24 5.42 2.37 8.75 62.16 65.60 CS1: d ≥ 100 (%) 0.13 4.17 1.25 6.84 19.58 23.90 CS1: d ≥ 0 (%) 0.41 9.64 3.63 15.70 84.71 CS2: d < 25 (%) 0.00 0.12 0.16 0.92 14.11 14.35 CS2: 25 ≤ d < 100 (%) 0.00 2.79 3.90 8.57 50.43 60.74 CS2: d ≥ 1000 (%) 0.00 1.30 0.33 0.12 7.23 8.21 CS2: d ≥ 0 (%) 0.00 4.20 4.39 9.62 71.76 CS3: d < 25 (%) 0.00 0.01 0.77 0.41 8.43 9.24 CS3: 25 ≤ d < 100 (%) 0.09 4.91 5.96 5.48 51.25 63.39 CS3: d ≥ 100 (%) 0.00 0.11 3.03 0.53 2.72 5.81 CS3: d ≥ 0 (%) 0.09 5.03 9.75 6.41 62.40

References

1. Strogatz, S.H. Exploring complex networks. Nature 2001, 410, 268–276. [CrossRef][PubMed] 2. Milo, R.; Shen-Orr, S.; Itzkovitz, S.; Kashtan, N.; Chklovskii, D.; Alon, U. Network motifs: Simple building blocks of complex networks. Science 2002, 298, 824–827. [CrossRef][PubMed] 3. Porta, S.; Crucitti, P.; Latora, V. The network analysis of urban streets: A dual approach. Phys. A Stat. Mech. Its Appl. 2006, 369, 853–866. [CrossRef] 4. Jiang, B.; Claramunt, C. A structural approach to the model generalization of an urban street network. Geoinformatica 2004, 8, 157–171. [CrossRef] 5. Yin, Z.-Y.; Walcott, S.; Kaplan, B.; Cao, J.; Lin, W.; Chen, M.; Liu, D.; Ning, Y. An analysis of the relationship between spatial patterns of water quality and urban development in Shanghai, China. Comput. Environ. Urban Syst. 2005, 29, 197–221. [CrossRef] 6. Urich, C.; Sitzenfrei, R.; Möderl, M.; Rauch, W. An agent-based approach for generating virtual sewer systems. Water Sci. Technol. 2010, 62, 1090–1097. [CrossRef] 7. Möderl, M.; Fetz, T.; Rauch, W. Stochastic approach for performance evaluation regarding water distribution systems. Water Sci. Technol. 2007, 56, 29–36. [CrossRef][PubMed] Water 2017, 9, 146 15 of 15

8. Sitzenfrei, R.; Möderl, M.; Rauch, W. Automatic generation of water distribution systems based on gis data. Environ. Model. Softw. 2013, 47, 138–147. [CrossRef][PubMed] 9. Sitzenfrei, R.; Möderl, M.; Rauch, W. Assessing the impact of transitions from centralised to decentralised water solutions on existing infrastructures—Integrated city-scale analysis with vibe. Water Res. 2013, 47, 7251–7263. [CrossRef][PubMed] 10. Blumensaat, F.; Wolfram, M.; Krebs, P. Sewer model development under minimum data requirements. Environ. Earth Sci. 2012, 65, 1427–1437. [CrossRef] 11. Möderl, M.; Sitzenfrei, R.; Rauch, W. Achilles approach to identify vulnerabilities in urban water infrastructure for operation and emergency management. In Proceedings of the IWA World Water Congress and Exhibition, Montreal, QC, Canada, 19–24 September 2010. 12. Mair, M.; Sitzenfrei, R.; Möderl, M.; Rauch, W. Identifying multi utility network similarities. In Proceedings of the World Environmental and Water Resources Congress, Albuquerque, NM, USA, 20–24 May 2012; pp. 3147–3153. 13. Kabir, G.; Sadiq, R.; Tesfamariam, S. A review of multi-criteria decision-making methods for infrastructure management. Struct. Infrastruct. Eng. 2013, 10, 1176–1210. [CrossRef] 14. Sitzenfrei, R.; Mair, M.; Diao, K.; Rauch, W. Assessing model structure uncertainties in water distribution models. In World Environmental and Water Resources Congress 2014: Water without Borders; Wayne, H.C., Ed.; American Society of Civil Engineering (ASCE): Reston, VA, USA, 2014; pp. 515–524. 15. Caparros-Midwood, D.; Barr, S.; Dawson, R. Optimised spatial planning to meet long term urban sustainability objectives. Comput. Environ. Urban Syst. 2015, 54, 154–164. [CrossRef] 16. Ammar, M.A.; Moselhi, O.; Zayed, T.M. Decision support model for selection of rehabilitation methods of water mains. Struct. Infrastruct. Eng. 2010, 8, 847–855. [CrossRef] 17. Kleidorfer, M.; Möderl, M.; Tscheikner-Gratl, F.; Hammerer, M.; Kinzel, H.; Rauch, W. Integrated planning of rehabilitation strategies for sewers. Water Sci. Technol. 2013, 68, 176–183. [CrossRef][PubMed] 18. Rossman, L.A. Epanet 2: Users Manual; National Risk Management Research Laboratory, U.S. Environmental Protection Agency: Cincinnati, OH, USA, 2000. 19. Rossman, L.A. Storm Water Management Model User’s Manual; version 5.0; National Risk Management Research Laboratory, Ofﬁce of Research and Development, US Environmental Protection Agency: Cincinnati, OH, USA, 2004. 20. Hwang, F.K.; Richards, D.S.; Winter, P. The Steiner Tree Problem; Elsevier: Amsterdam, The Netherlands, 1992. 21. Kruskal, J.B., Jr. On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 1956, 7, 48–50. [CrossRef] 22. Robins, G.; Zelikovsky, A. Improved steiner tree approximation in graphs. In Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms; Society for Industrial and Applied Mathematics: San Francisco, CA, USA, 2000; pp. 770–779. 23. Trifunovic, N. Introduction to Urban Water Distribution: UNESCO-IHE Lecture Note Series; Taylor & Francis: London, UK, 2006. 24. Gujer, W. Siedlungswasserwirtschaft—3.Auﬂage; Springer: Berlin, Germany, 2006. 25. Tscheikner-Gratl, F.; Sitzenfrei, R.; Rauch, W.; Kleidorfer, M. Enhancement of limited water supply network data for deterioration modelling and determination of rehabilitation rate. Struct. Infrastruct. Eng. 2016, 12, 366–380. [CrossRef] 26. Zischg, J.; Mair, M.; Rauch, W.; Sitzenfrei, R. Stochastic performance assessment and optimization strategies of the water supply network transtion of kiruna during city relocation. In Proceedings of the World Environmental and Water Resources Congress, Austin, TX, USA, 17–21 May 2015.

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