Cluster Analysis of Urban Water Supply and Demand: Toward Large-Scale Comparative Sustainability Planning

(1)

Cluster Analysis of Urban Water Supply and Demand:

Toward Large-Scale Comparative Sustainability Planning

The MIT Faculty has made this article openly available.

Please share

how this access benefits you. Your story matters.

Citation

Noiva, Karen et al., "Cluster analysis of urban water supply and

demand: Toward large-scale comparative sustainability planning."

Sustainable Cities and Society 27 (November 2016): 484-96 doi.

10.1016/j.scs.2016.06.003 ©2016 Authors

As Published

https://dx.doi.org/10.1016/J.SCS.2016.06.003

Publisher

Elsevier BV

Version

Final published version

Citable link

https://hdl.handle.net/1721.1/128741

Terms of Use

Creative Commons Attribution-NonCommercial-NoDerivs License

(2)

ContentslistsavailableatScienceDirect

Sustainable

Cities

and

Society

j o u r n a l ho me p a g e :w w w . e l s e v i e r . c o m / l o c a t e / s c s

Cluster

analysis

of

urban

water

supply

and

demand:

Toward

large-scale

comparative

sustainability

planning

Karen

Noiva

∗

,

John

E. Fernández,

James

L. Wescoat

Jr.

DepartmentofArchitecture,MassachusettsInstituteofTechnology,77MassachusettsAve,Cambridge,MA02139,USA

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received29January2016

Receivedinrevisedform2June2016 Accepted4June2016

Availableonline7June2016 Keywords:

Clusteranalysis Comparativemethods Sustainableurbanwatersystems Waterbudget

Wateruse

a

b

s

t

r

a

c

t

Thesustainabilityofurbanwatersystemsisoftencomparedinsmallnumbersofcasesselectedasmuch fortheirfamiliarityasfortheirsimilaritiesanddifferences.Fewstudiesexaminelargeurbandatasets toconductcomparisonsthatidentifyunexpectedsimilaritiesanddifferencesamongurbanwater sys-temsandproblems.Thisresearchanalyzedadatasetof142citiesthatincludesannualpercapitawater use(m3_/yr/cap)_and_population._It_added_a_0.5◦_grid_annual_water_budget_value_(P-PET/yr)_as_an_index ofhydroclimaticwatersupply.Withtheseindicesofurbanwatersupplyanddemand,weconducted ahierarchicalclusteranalysistoidentifyrelativesimilaritiesamong,anddistancesbetween,the142 cases.Whilesomeexpectedgroupingsofclimaticallysimilarcitieswereidentified,unexpectedclusters werealsoidentified,e.g.,citiesthatusewateratgreaterratesthanlocalclimaticwaterbudgets pro-vide.Thosecitiesmustseekwaterfromgreaterdistancesandgreaterdepths.Theyfacegreaterwater andwastewatertreatmentcosts.Tobecomemoresustainabletheymustincreasewateruseefficiency, demandmanagement,reuse,andrecycling.Thesignificanceofthepopulationvariablesuggeststhat addingotherexplanatorysocio-economicvariables,aswellasmoreprecisewatersystemindices,are logicalnextstepsforcomparativeanalysisofurbanwatersustainability.

1. Introductionandconceptualframework

Comparativeurban water researchis importantfor drawing generalizationsaboutsustainabilityandforadaptinglessonsfrom one set of cities for consideration in others. The current sta-tusof comparativeurbanwaterresearchis limited(Mollinga& Gondhalekar,2014;Wescoat,2014).Many studiesexamine sin-glecasestudies(e.g.,Gandy,2014).Someselectcasesthatreﬂect theauthors’expertise(Novotny,Ahern,&Brown,2010;Wörlen etal.,2016).Othersgroupcasestudiesunderpredeﬁnedheadings, e.g.,arid,tropical,low-income,megacities,etc.(Fletcher&Deletic, 2008).Moststriveforgeneralizablemodelsandmethodsbut with-outanalyzingalargenumberofcases(Mollinga&Gondhalekar, 2014).Asaresult,comparisonsandtheconclusionsthatcanbe drawnfromthemtendtobelimitedandqualitative(Mollinga& Gondhalekar,2014;Wescoat,2009;Wescoat,2014).Thisstudylays afoundationforcomparativeresearchonurbanwater sustainabil-ityusingclusteranalysismethods.

Thesustainabilityframeworkemployedhereinvolvestwo sim-plemassbalancevariablesforurbanwatersystems.Theﬁrstisan

∗ Correspondingauthor.

E-mailaddresses:knoiva@mit.edu,knoiva@gmail.com(K.Noiva).

annualclimaticwaterbudgetforeachurbanarea,whichsubtracts potentialevaporationfromprecipitation(elaboratedinthe meth-odssectionbelow)(Willmott,Rowe,&Mintz,1985).Waterbalance analysisestimatesclimaticwater supply(P) anddemand(PET). Somecitieshaveanannualwaterbalancesurplusthatcanbestored ormanagedasrunoff,whileothershaveclimaticwaterdeﬁcitsthat mustbemanagedthroughrainwaterharvesting, wateruse efﬁ-ciency,recycling,reuseand,barringthosemethods,longdistance waterimports(Plappally&Lienhard,2012;Plappally&Lienhard, 2013).Thesecondmetricisgrossannualwaterusepercapitain eachcity.Thesetwovariablesprovideannualestimatesofclimatic watersupplyandgrosspercapitawaterdemand.Whileonewould expectsomecorrelationbetweensupplyanddemand,citieshave historicallysupplementedlocalwatersupplieswithlongdistance watertransfers,aquiferdepletion,andinsomecasesdesalination (McDonald,Weber, Padowski,Flörke,&Schneider,2014).These variablesareweaklycorrelatedandaretreatedhereasindependent variablestoclassifythesustainabilityofurbanwaterpatterns.

The water balance approach may be compared with other sustainabilityheuristicssuchaswater footprint analysis,which examinesdifferenttypesandamountsofwateruseina system (HoekstraandChapagain,2007;Hoff,Döll,Fader,Gerten,&Hauser, 2014).Herewe adaptthefootprintideainanurbanWaterUse and ClimateIndex (WUCIin m2_/cap)_(See _Section ₂_)._This_type

http://dx.doi.org/10.1016/j.scs.2016.06.003

(3)

of accountingis taken furtherin studies of virtualwater trade and sustainable supply chain analysis (e.g., Daniels, Lenzen, & Kenway,2011;Ercin,Aldaya,&Hoekstra,2011;Hoffetal.,2014; Konar,Dalin,Hanasaki,Rinaldo,&Rodriguez-Iturbe,2012;Suweis, Konar,Dalin,Hanasaki,&Rinaldo,2011).Explanatorysustainability heuristicssuchastheIPATequation(I=P*A*T)relate environmen-talimpacts(e.g.resourceuse)(I)topopulationsize(P),afﬂuence (A),andtechnology(T)(Rosa,York,&Dietz,2004).TheIPAT equa-tiontakesmultipleforms.OnepopularversionisI=P*F,whereFis impactpercapita(Chertow,2001).WhileIPATispresentedasan equation,itismoreofaheuristicofdrivingandameliorating fac-tors(Chertow,2001).Greateremphasisonexplanatoryanalysisof watersupplyanddemandpatternsisneededineachapproach,but aﬁrststeptowardthataimisidentifyingandcharacterizingurban waterpatterns,whichcanthenenablesystematicsubsamplingand comparison.

Applicationofstatisticaldata-miningtechniquessuchascluster analysistourbansocio-economicclassificationiswell-established (Astel,Tsakovski,Barbieri,&Simeonov,2007;Bettencourt,2013; Kim,1997; Batty,Axhausen,Giannotti,Pozdnoukhov,&Bazzani, 2012; MacCannell,1957; Kennedy, 2011). Applicationto water issueswithincitiesisamorerecentdevelopment(Yuetal.,2013; Diao,Farmani, Fu,Astaraie-Imani,&Ward,2014), as is classifi-cation of urban water systems within a particular country(Yu &Chen,2010;Rahill-Marier &Lall,2013;Rao&Srinivas,2008a, Chapter 3; Rao &Srinivas, 2008b,Chapter 3).In reviewing the waterresourcesliterature,Mollingaand Gondhalekarsuggested anapproachforassessing‘small-N’and‘medium-N’casestudies (Mollinga&Gondhalekar,2014).Forexample,clusteringhasbeen appliedtotheproblemofforecasting short-termwaterdemand withinasinglecityormunicipalwatersystem,whichfallsunderthe categoryofasmall-Nanalysis(Garg,2007;Candelieri&Archetti, 2014;Wu,Lv,Dong,Wang,&Xu,2012).Otherclusteringstudies fallintothemedium-Ncategoryofcomparativeanalysis,including onethatincludesak-meansclusteringofcitiesbasedonwater foot-print,energyconsumption,andmunicipalwastewithintheUnited Kingdom(Khamis,2012).AstudybyMayeretal.usedcluster anal-ysistoclassifywatershedsintheGreatLakesbasinaccordingto socialandenvironmentalattributes(Mayer,Winkler,&Fry,2014). Andalarge-NstudybytheColumbiaUniversityWaterCenterused hierarchicalclusteringtoanalyzeutilityratesintheUnitedStates withregardstofinancialsustainability(Rahill-Marier&Lall,2013). Thispaperusesclusteringalgorithmstoanalyzewatersupply anddemandfor142citiesaroundtheworldtodevelopan interna-tionalclassificationofurbanwatersustainabilitysituations.Ituses theMITUrbanMetabolismdatabase(Fig.1),whichwascreated todevelopanurbansustainabilitytypologybasedonfour predic-torvariables(population,populationdensity,affluence[GDPper capita],andclimate[Köppenclassification]); andeightresponse variables(percapitaconsumptionofconstructionminerals, indus-trialminerals,biomass,water,totalenergy,totalmaterials,fossil fuels, and electricity) (Saldivar-Sali, 2010; Ferrão & Fernández, 2013,Chapter 4).Our analysisuses the same set of cities and expandsthelarge-Nanalysisofurbanwaterissuesaselaboratedin thenextsection.

2. Dataandmethods

TheUrbanMetabolismdatasetincludes142citiesdistributed acrossmajorcontinentsandclimates.Wefocusedparsimoniously ontwovariablesintheUrbMetdatabase,addedawaterbudget variable,andthenusedthemtoconstructaWaterUseandClimate Index(WUCI).Thesevariableswere:

1.Percapita water consumption (CONS), toassess thescale of urbanwateruse.

2.Population(POP),toassessthepotentialsigniﬁcanceofcitysize. 3.Netannualclimaticwaterbudget(DIFF),toassesshydroclimatic

watersupplies.

4.WaterUseandClimateIndex(WUCI),toprovideameasureof urbanwaterusepercapitaindexedtoannualprecipitation.

Themain watervariableintheUrbMetdatasetis percapita wateruseincubicmetersperyear(m3_/cap/year)₍_Table₁_)._This valuewasdrawninmostcasesfromtheWorldBank-supported International Benchmarking Network (IBNET)supplemented by city-speciﬁcdatawhennotavailableinIBNET(Saldivar-Sali,2010; IBNET,2015).ThedeﬁnitionofpercapitawateruseinIBNETis grossannualwaterproduction bya utilitydividedbythe num-berofpeopleintheservicearea.Percapitawateruserangedfrom 14m3_/cap/year_(Yangon)_to₃₅₅_m3_/cap/year _(Cairo)._We_did_not disaggregatepercapitauseintoresidentialandcommercial sub-sectors,thoughthatwouldbeavaluableextensionofthisresearch. Climaticwaterbalanceanalysiswasemployedtoestimategross annual water supplies, usingthe University of Delaware’s 0.5◦ gridWebWIMP1_tool₍_Willmott_et_al.,₁₉₈₅_)._The_annual_Difference

(DIFF)betweenPrecipitationandPotentialEvapotranspiration,in meters peryear (m/yr),for each of the 142cities wasscraped fromthedatabase.The 0.5◦ resolution wascoarse,butdeemed appropriateforindexingthewaterbalanceofmajorurbanareas, whichgenerallyoccupyanddrawuponlargercatchmentareas out-side theiradministrativeboundaries. Citiesinthedatabasehad DIFFvaluesrangingfrom−1.446m/yr(AbuDhabi)to+3.833m/yr (Anchorage).

City population data (POP) from the UrbMet database was includedtoassessthepotentialdifferencethatcitysizemakesfor classifyingpatternsofurbanwatersupplyanddemand.Population sizerangesfrom270,000(BandarSeriBegawan)to14.34million (Shanghai).Thesepopulationestimatesfromtheearly2000sare conservativelybasedoncityboundariesvis-à-vislarger metropoli-tanregions.

The aforementioned WebWIMP tool also provided average annualprecipitationdata(PREC)inmetersperyearforeachcity. PREC2_was_used_to_calculate_Water_Use_and_Climate_Index_(WUCI),

whichhadunitsofm2_/capita: WUCI =CONS/PREC

WUCIwasnotincludedasametricintheclusteranalysis,butwas usedinvisualizingtheresults.

Severalmethodswereusedtovisualizeindividualurbanwater variables andrelationshipsamongthem.Priortoclustering,we exploredthedatausingqq-normalplots,histograms,and scatter-plots.Weﬁrstplotteddataforeachmetriconabarchartwherethe citiesaresortedaccordingtotheirvalueforthatmetric(Fig.2a–c). Fig.2aandbhaveasimilardistributionofpositivevalues,witha longertailofsmallercitiesinFig.2aandamoreevenprogression ofwaterconsumptionvaluesinFig.2b.Incontrast,Fig.2cincludes negativeaswellasescalatingpositivevaluesfornetannualwater balance(Fig.3).

Priortoclustering,thesevariables weretransformedusinga base-10logarithmictransformation(log10),whichreduced skew-nessandimprovedthesymmetryoftheirdistribution(Fig.4aand

1_WebWIMP_is_short_for_the_{“Web-based,}_{Water-Budget,}_Interactive,_Modeling

Program”andisavailablethroughtheUniversityofDelawareat:http://climate. geog.udel.edu/∼wimp/.

2_PREC_was_used_instead_of_DIFF_in_calculating_WUCI,_since_DIFF_had_values_close

tozeroandthereforecouldnotbeusedinthedenominator.However,PRECwas highlycorrelatedtoDIFF.

(4)

Fig.1.Worldmapofthe142citiesintheUrbMetdatabase.

Table1

DescriptivestatisticsforCONS,DIFF,POP,andWUCIfortheUrbMetdatabase.

Metric Unit QuartileBreak

0% 25% 50% 75% 100% Mean St.Dev.

CONS m3_/cap/year _14.0 _57.3 _86.5 _148.5 _355.0 _110.8 _75.2

DIFF m./year −1.446 −0.241 0.089 0.447 3.833 0.124 0.752

POP millions 0.0273 0.647 1.649 3.764 14.350 2.883 3.182

WUCI m2_/cap _5.717 _49.04 _117.9 _189.1 _14200.0 _303.7 _1223.0

b).Aconstant,a,wasaddedtoDIFFpriortothetransformsuchthat a=1−DIFFmin(whereDIFFminwastheminimumvalueofDIFF).

Whileitmightbeexpectedtofindcorrelationbetweenthesize ofthe populationorwater consumption and local water avail-ability(i.e.,DIFF),thecorrelationwasfoundtobelow.Asseenin Table2,thervalueforlog10(CONS)vs.log10(DIFF+a)wasfound tobe0.02withasignificancelevelofp=0.8373,whilethervalue for log10(POP) vs. log10(DIFF+a) wasfound tobe 0.01 with a p=0.9261.Inotherwords,thelog10transformsofCONSandDIFF werefoundtobeindependent,aswerethelog10transformsof DIFFandPOP.Asmallnegativecorrelationofr=−0.12wasfound betweenlog10(CONS) vs. log10(POP),but the significance level wasonly0.1684.Inotherwords,thesethreevariablesseemtobe independentofeachother,justifyinganexploratorydata-mining approachtothedata.

2.1. Clusteranalysismethods

Clusteranalysisis usedin exploratorydataminingtogroup objects in a dataset in such a way that those within a group aremoresimilartoeach otherthantoobjectsin othergroups. Commonclusteringapproachesincludehierarchicalclustering, k-meansclustering, and model-based clustering. For purposes of

exploringthesedata,hierarchicalclusteringwaschosen.Weused t-DistributedStochastic Neighbor Embeddingto reduce dimen-sionalityinthedataforvisualizationandclustering(vanderMaaten &Hinton,2008).Afterthelog10transformationeachmetricwas scaledtounity.Adistancematrixwasthencalculatedusingthedist functionfromthestatslibraryinRandtheEuclideandistance for-mulainwhich||a−b||2=SQRT(SUM(ai−bi)2).ThebasicEuclidean distanceformulawasusedastherewerenotheoreticalreasonsto preferamorecomplexformula,andotherformulasdidnotproduce substantiallydifferentormoreinterestingresults.These visualiza-tionmethodsarebrieﬂydescribedbelowanddisplayedasFigs.6–8 intheresultssection.

2.1.1. t-DistributedStochasticNeighborEmbeddingin scatterplots

The t-SNE method for reducing dimensionality enhances visualization in scatterplots by iterativelyassigning each high-dimensionalobject to a point in a two-dimensional space.The pointsareassignedsuchthatneighborsaremoresimilartoeach otherthantodistantobjects.Inatwo-dimensionalvariablespace, thehumaneyecantosomeextentdistinguishclusteredgroups of observations fromone another. As dimensionalityincreases, thetaskbecomessubstantiallymoredifﬁcultandlessintuitive.In

(5)

Fig.2. Population(millions),percapitawaterconsumption(cu.m./cap/year),andannualdifference(calculatedasthedifference(DIFF)betweenprecipitationandpotential evapotranspirationinm/year).

reducingdimensionality,thet-SNEapproachenablesobservations tobevisualizedinawaythatismoreintuitivetothehumaneye.

Thedistancematrixproducedbydistwasusedasthe dissimilar-itymatrixgivenastheargumenttot-SNE(t-DistributedStochastic NeighborEmbedding).t-SNEproducedtwo vectorscontainingthe

coordinatesembeddingeach citywithinthet-SNEspace.These vectorswerethen scaledtounityandaseconddistancematrix wasconstructedfromthesedata.Thisseconddistancematrixwas thenpassedasanargumenttothehierarchicalclusteringalgorithm hclust,whichtakesanagglomerativeapproachtohierarchical

(6)

clus-Fig.3. Wateruseandclimateindexinm2_/capita_(WUCI₌_CONS/PREC).

Table2

Pearson’scorrelationcoefﬁcientandsigniﬁcanceofbase-10logarithmic transfor-mationsofaverageannualpercapitawaterconsumption(CONS),averageannual difference(DIFF),andpopulation(POP).

Metric log10(CONS) log10(DIFF+a) log10(POP) log10(CONS) 1.00 0.02,p=0.8373 −0.12,p=0.1684

log10(DIFF+a) 1.00 0.01,p=0.9261

log10(POP) 1.00

tering. Each observation starts in its own cluster, and pairs of clustersarejoinedateachiterativestep.Ateachiterativestep,the

hclustgroupsarecomparedbasedonalinkagecriterion.Several commonlinkagecriteriaexist.WeusedWard’sminimumvariance method,whichminimizesthesquaredEuclideandistance.This cri-terionledtoadecreaseinvariancefortheclusterbeingmerged:at eachstep,thepairofclustersmergedisbasedontheoptimalvalue oftheerrorsumofsquares(d_ij=d({Xi},{Xj})=||Xi−Xj||2).

2.1.2. Dendrograms

Theresultsofhierarchicalclusteringwerealsovisualizedusinga tree-likestructureknownasadendrogram,whichrepresents rela-tionshipsofsimilarityamongsttheobservations.Thedendrogram ofclusterresultsshowsthestep-wisepairingofexisting subclus-ters.Eachbranchiscalleda“clade”andeachterminalnodeisa “leaf”.Thehorizontaldistanceofeachbranchindicatesameasure ofthedistancebetweenclades.Thedendrogramis“cut”toadesired heightornumberofclusterstodeterminethemembershipofeach leaf(i.e.,city).

2.1.3. Violinplots/boxplots

Theclusterresultswerealsoplottedasviolinplotswithboxplots superimposedoverthem.Theviolinplotisessentiallyaboxplot witharotatedkerneldensityplottedinsteadofabox.The box-plot(orbox-and-whiskerplot)depictsthemedianvalueofeach clusterasabandwithinthebox.Thetopandbottomofeachbox (the“hinges”)representtheﬁrstandthirdquartiles.Boxplotsmay include“whiskers”—verticallinesextendingfromthetopsand bot-tomsoftheboxes.Thelengthofthewhiskersisdeterminedbythe inter-quartilerange(IQR),whereIQR=Q3−Q1:i.e.,thedifference betweenthethirdandﬁrstquartiles.Thewhiskersextendfrom eachhingetothevaluethatiswithin1.5*IQRofthehinge.Any valuebeyondthewhiskersisanoutlierandisplottedasapoint.

3. Clusteranalysisresults

Theclusteranalysisyieldedinterestingresultsatseverallevels ofdivisionandgrouping.Weexaminedtheresultsfromtwotoeight clusters,andfoundthatsixclustersyieldedthemostvariedyetstill legibledifferenceswitheachofthefourvisualizationmethods.The typologygeneratedbythesixclustersispresentedanddiscussed here.TheworldmapinFig.5displayshowthesetypesappear spa-tially.Ithassomeclearpatterns,suchasEastAsian,SouthAsian, CentralAfricancities,andothermixed/gradientpatternsinEurope andNorthAmerica.However,ithastoomuchcomplexityto char-acterizefromvisualinspectionalone.

ThedendrograminFig.6depictsthepositionsofthe142cities acrossthefullrangeofclusters(i.e.,from1to142);citiesare col-oredbytheselectedsixcluster-typology.ThescatterplotinFig.7 depictsthecitiesinthetwo-dimensionalspaceproducedusing t-SNE,whichconveysmoreclearlytherelativesimilaritybetween citiesandclusters.

However,thesixclustersare mostreadilyinterpretedusing theviolinboxplotsshowninFig.8.Thesegraphicvisualizations madeitpossibletodiscernthesixurbanclustersinqualitativeand quantitativeterms.Table3usedtheseﬁgurestodeﬁnethegeneral

(7)

Fig.4. Histogramsforaverageannualpercapitawaterconsumption(CONS)(Fig.4a);andaverageannualdifference(DIFF)+a(aconstant)transformedbyabase-10logarithm (Fig.4b).

(8)

Fig.6. Dendrogramofclusterresults,withcitiescoloredbyclustermembership.

characteristicsofeachclusterandlistseveralrepresentativecities. Wenowrecasttheseresultsasaworkingtypologyofurbanwater sustainabilitysituations.Thedescriptionofeach “type”usesthe

terms“low”,“medium”,and“high”inquantitativeaswellas quali-tativeterms,astheyarebasedonthequartilebreaksandthresholds betweenclusters.

(9)

Fig.7. Scatterplotofcities,plottedinthetwo-dimensionalspaceproducedbyt-SNE.

3.1. Type1:largecitieswithverylowpercapitawater consumption

These cities representa range of climateand supply condi-tions, buttheirnetwater balancesare predominantlynegative. ThemedianvalueofPOPforType1citiesliesinthe3rdquartile. Type1citiesfallpredominantlybelowthemedianvalueforCONS, withamedianvalueof45.0m3_/cap/year,_which_is_within_the_ﬁrst quartile.3_The_median_value_for_DIFF_for_Type₁_also_lies_within_the

1stquartile,andtheboxforType1onDIFFlieswithinthe1stand 2ndquartiles.Inotherwords,Type1citiestendtohavenegative valuesforDIFF.Tosummarize,Type1citiestendtohavelarge

pop-3_The_WHO_recommends_around₁₀₀_L/cap/day_per_person_(36.5_m3_/cap/year).

ulations,lownatural wateravailability,andverylow percapita waterconsumption,whichraisesconcernsabouttheir sustainabil-ityinhydroclimaticandsocio-economicterms.Type1citiesare mostdissimilarfromcitiesofType3and6,whicharesmallerand wetter.TheyshowsomeoverlapwithType2andType4cities.

3.2. Type2:medium-sizedcitieswithmedium-lowwater consumptionandanetwaterbalanceofaroundzero

Type2citieshavevaluesforPOPthatfallpredominantlyinthe 2ndquartile,withamedianvalueof1.188million;Type2cities tendtobemedium-lowtomedium-sized.Thesecitieshave the second-lowestmedianvalueforCONS,afterthoseofType1.Type 2citiesalsohavelowtomoderatewaterbalancesthat(DIFF).In summary,Type2citiestendtobemid-sizecitieswithanetwater

(10)

Fig.8. Violin-andbox-plotsforPOP,CONS,DIFF,andWUCI.

Table3

DescriptiveattributesofeachurbanwatersystemType.Thedesignations‘high’,‘medium’,and‘low’aremadewithreferencetothestatisticalquartiles(shownontheviolin plotsindashedlines)andtothethresholdsbetweentypes.

Type DIFF CONS POP WUCI RepresentativeCities

1 Rangefromlowtohighbut predominantlyverylowto low(negative).

Verylow Rangefrom

medium-lowtovery large

Rangefromlowto medium,but predominantlylow

Casablanca,Jakarta, Kinshasa,Lagos,Mumbai

2 Medium-low/Medium Medium-low Medium-sized Rangefromlowto

medium,but predominantlylow

Barcelona,Hamburg, Prague,Ulaanbaatar, Vienna

3 Rangefrommediumto high(positive)

Medium Generallysmaller Rangefromlowto

medium,but predominantlylow

Bern,Boston,Copenhagen, Geneva,Hanover 4 Rangefromlowtohigh;

predominantlymedium andpositive

Rangefrommedium-hightohigh Rangefrom medium-hightohigh; predominantlyhigh

Rangefromlowto medium,but predominantly medium

London,Montreal,New York,Singapore,Sydney

5 Verylow Veryhigh Rangefromverysmall

toverylarge

Rangefromlowto medium,but predominantly medium

Cairo,Doha,Dubai,Kuwait City,Phoenix

6 Medium;generallypositive Veryhigh Lowtomedium-low High Amsterdam,Denver,Kuala Lumpur,Milan,Stockholm

(11)

balanceclosetozero(i.e.,moderatewaterresources)and medium-lowwateruse,whicharecharacteristicsthatmaybesustainable. 3.3. Type3:smallcitieswithmediumlevelsofwater

consumptionandpositivenetwaterbalances

Thesecitiestendtobesmallrelativetotheothercitiesinthe dataset;theirmedianvalueisthelowestofanyofthesixcitytypes at494,700.NearlyallType3citiesfallwithinthe1stquartilefor POP.TheyhaveamedianvalueforCONSof84m3_/cap/day._Type₃

citieshavethehighestmedianvalueforDIFFofanyoftheother types,at0.417m/year,andmostType3citieshavevaluesforDIFF inthe3rdand4thquartiles.Inotherwords,Type3citiestendtobe small,withrelativelyhighnaturallyavailablewaterresourcesand mediumlevelsofwaterconsumption.Thesecitieshavethelowest WaterUseandConservationIndex(WUCI),andmightthereforebe deemedthemostsustainableintermsofuse(thoughnotinterms ofriskwhichisnotconsideredinthisanalysis).Type3citiesshow similaritieswithType2andType6;andtheyaremostdissimilar fromTypes1,4,and5.

3.4. Type4:verylargecitieswithhighpercapitawater consumptionandapositivenetwaterbalance

Type4citieshavelargepopulationswithamedianvalueof4.45 million.Type4citiesalsohavehighpercapitawateruse(CONS, withamedianvalueof154.5m3_/cap/year,_which_falls_in_the_4th

quartile).AlmostallType4citiesareinthe3rdand4thquartiles forCONSandDIFF.Theyareverylargecitieswithlargenatural watersuppliesandhighdemand,andtheythushavethepotential tobesustainable.

3.5. Type5:citiesofvariedsizewithveryhighpercapitawater consumptionlocatedinhighlyaridenvironments

Thesecitieshavethesecond-highestmedianvalueforCONS,at 209.0m3_/cap/year;_almost_all_of_these_cities_have_CONS_that_falls

withinthe4thquartile.However,Type5hasthelowestDIFFofany ofthetypes,withamedianvalueof−1.36m/yearandamaximum valueof_−0.916m/year.ThePOPofType5citiesrangesfromthe smallesttothelargest:from32,400to6.759million.Tosummarize, Type5citieshaveawiderangeofpopulationsize,andtheyare characterizedbyhighwateruseandverylowwaterbudgets.This patternraisesseriousconcernsabouttheirsustainability.

3.6. Type6:medium-sizedcitieswithveryhighpercapitawater consumptionandlowpositivewaterbalance

Thesecitiestendtobemedium-sizedcities,withhighpercapita waterconsumptionandlow,positivewaterbalances.Theyareone ofthemostrapidlygrowingformsofurbanizationindeveloping countries,andthispatternraisesconcernsabouttheir sustainabil-ity.Type6citiesaremostsimilartoType1,Type2,andType3cities. TheyaremostdissimilarfromType1andType5cities,especially intermsofDIFF.

4. Discussion

4.1. Discussionoftypes

4.1.1. Thelargecities:verylowvs.highCONS(Types1&4)

Thelargestcities,withfewexceptions,appear inType1and Type4.ThemaindistinctionbetweenType1andType4isthatType 1citieshaveverylowCONSwhileType4citieshavehighCONS.As wouldbeexpected,Type1citieshaveaWUCIthatismuchlower thanthatofType4cities.However,Type1citiestendtohavealow

DIFF,andthismeansthattheWUCIofType1citiesismoresimilar tothatofType2andType3citiesthanitwouldbeotherwise.

Thehighpercapitawater consumption exhibitedbyType4 citiessuggeststhatthesecitiescurrentlyhavesufficientwater sup-plyandurbanwaterinfrastructure.Type4citiesalsotendtobe locatedinareaswithhighernaturalwateravailabilitythanseveral othercitytypes,suchasType1.However,becausethe popula-tionofType4citiestendstobesolargeandconsumptionisso high,thesecitieslikelyfacemanychallengesinsecuringsufficient watersupplynowandinthefuture.Thisisindeedwhatwefind. Evencitieswithabundantnaturalresources,suchasSingaporeand NewYork,haverecentlymadesubstantialinvestmentsin promot-ingwaterconservationandininnovativewaterinfrastructure(e.g., desalinationandreclamation).

BothType1andType4citiesarelikelytohavechallengesin obtainingsufﬁcientwaterresourcesfortheirlargeurban popula-tions.However,differencesexistbetweenthesetwotypes.Many Type1 cities arelocated indeveloping countries and undergo-ingrapidurbanization.Theirwaterresourceschallengesmaybe heightenedbylownaturalwateravailability,rapidurbanization, andlowaccesstoﬁnancialresources.Thelowwaterconsumption inthesecitiesmayalsobeassociatedwithrelativelylowlevelsof infrastructure.EventhoughType1citiescurrentlyconsumeless waterthanType4cities,itwouldnotnecessarilybeappropriateto saytheyare“moresustainable”thanType4cities.IfType4cities areabletomanageresourceswithintheirwatershedareas prop-erly,theymaybeassustainablerelativetotheirwatersupplyas Type1cities.AsType1citiescontinuetogrowanddevelop,sotoo willthesizeoftheircatchmentareas;Type1citiesmayeventually becomeType4cities.

Type1citieshavetheopportunitytoimplementnewtypesof technologiesand pioneeringwater managementpractices, such asmoredecentralized,neighborhoodlevelwater treatmentand reuse,ratherthantryingtocopythedevelopmentofwatersupplies inType4cities.ThiswouldbeanexcellentopportunityforType1 citiestocollaboratewithType4citiesforknowledgeexchange. 4.1.2. Thesmall,wetcities(Type3)

Type3citiesarecharacterizedbylowpopulationsthathave low-tomedium-levelsofpercapitawaterconsumptionand medium-tohigh-naturalwatersupply.Thesecitiesarelikelytohavethe fewestissueswithsustainablewatersupplyofanyofthetypes. WatersupplystressesmaybelessacuteforType3cities.However, inspiteofrelativelylowCONSandabundantwaterresources,many ofthecitiesinType3stillfacechallengeswithsustainableurban watermanagement.Thesemayincludechangesinwaterquality duetourbanization,aginginfrastructure,andﬂooding.

4.1.3. Themedium-sizedcities:mediumvs.highCONS(Types2& 6)

Withafewexceptions,medium-sizedcities(thoseinthe2nd and3rdquartilesofPOP)tendtofallintoTypes2and6.Type6 citieshavehighernaturallyavailablewaterresources.Another dis-tinctionbetweenthetwotypesisthatType6citieshaveveryhigh CONS,whichraisesconcernsabouttheirsustainability,whilethose ofType2havemedium-lowCONS.

4.1.4. Thearidcities:lowDIFF(Type5)

Type5citieswerelocatedinhighlyaridenvironments:these cities had negative values of DIFF, which means that there is muchlessrainfallthanpotentialevapotranspiration.Yet surpris-inglythesecitieswerealsodistinguishedbytheirhighlevelsof waterconsumption(CONS).Thesecitiesarethereforelikelytorely extensivelyonwatertransfersorwaterimportsforwatersupply, eitherasriversorcanals(e.g.,CairoandPhoenix),conversionof saltwatertofreshwater(e.g.,DubaiandAbuDhabi),andminingof

(12)

fossilaquifers.Transportingwateroverlargedistances, desalina-tion,andreclamationareallassociatedwithrelativelylargecosts and issues of ﬁnancialsustainability and management capacity (Plappally&Lienhard,2012;Plappally&Lienhard,2013).Thewater resourcesforcitiesinType5areparticularlyvulnerableto eco-nomicshocks,energyshortages,andpoliticalchanges(sincethey maybeobtainingwaterfromoutsidetheirjurisdiction).Cost recov-eryandconservationmayhelpType5citiesincreasetheresilience oftheirurbanwatersystemstoclimatechangeandexternal pres-suresonwatersupplies.

4.2. Discussionofthresholds

ThethresholdsforDIFFsuggestthatcitiesinregionswith nat-urallyabundantwaterresourcesmaybefundamentallydifferent fromthoseinmorearidcontexts.Types3,4,and6predominantly havevaluesforDIFFgreaterthanzero,whichsuggeststhat,allother thingsbeingequal,thesecitiesmayhaverelativelymoreeaseat obtainingwaterresourcesthantheothertypes.

ThethresholdsforPOPraiseintriguingquestions.Arethere sig-niﬁcantdifferencesinprovidingurbanwaterresourcesforcities largerthan1million?Types1and4tendtobethelargestcitiesin thedatabase,butthesetwotypesdifferinCONSandDIFF.Cities ofType1haveverylowCONSandlowDIFF,whilethoseofType4 havehighCONSandapositiveDIFF.Thissuggeststhatcitysizeis notdeterministicallyrelatedtoclimateorconsumption.

4.3. Discussionofoutliersandoverlaps

Itisimportanttorememberthatthesetypesarebasedonthe statisticalclusteringofcontinuousvariables.Citieswithinatypeare mostlikelytobemoresimilartoeachotherthantoothercities,and distinctfromothertypesinsomestatisticallysigniﬁcantway.The differenttypesofcitiesidentiﬁedintheclusteringwererelatively distinctononeortwovariablesbutmayhaveotherwiseoverlapped withanothertypeonanother.Becauseofthis,citieswith differ-entmembershipmayhavesimilarmetricsandthereforefacesome commonsustainabilitychallenges.Forinstance,CairoandParisare membersofType5andType2,respectively,andduetotheir rela-tivesizesarelikelytosharesimilarchallengeswithcitiesofType1 andType4,respectively.

TheseoverlapsanddistinctionscanbeunderstoodfromFig.7, thescatterplotofthet-SNEresults,inwhichthecitiesthatfallclose tooneanotheraremostsimilar,whilethosethatarefurtherapart aremostdissimilar.Twocitiesthatlieinatransitionzonebetween adjacenttypesmaybehavedifferenttypologicalmembershipbut bestatisticallysimilartoeach other. Withinthe variablespace showninFig.7,itisalsopossibletovisuallyidentifysub-groupings. AsubgroupingofDenver,Tbilisi,Vladivostock,Victoria,Stockholm, Dublin,Ottowa,andKathmanducanalsobeidentiﬁedinthe den-drogram.Withinthissubgroupingtherearenon-intuitivepairings intheterminalleafnodes,suchasKathmanduwithDublinand VladivostockwithDenver,whichmayidentifyunexpected simi-larities.

4.4. Discussionofintuitiveandunexpectedresults

Someof these results are surprising while others are more expected.Forinstance,itisnotmuchofasurprisethatcitiesinvery aridclimatesweregroupedtogether.However,priorto applica-tionoftheclusteringalgorithmthiswasnotaforegoneconclusion, andtheresultsdistinguishedsigniﬁcantdifferencesinwater con-sumptionofaridcities.Thishighlightstheabilityoftheapproach toyieldmeaningfulresults.Itisperhapsalsonotmuchofa sur-prisethatthelargestcitiesweregroupedtogether,astheywerein Type1andinType4.Atthesametime,somemayﬁndit

surpris-ingtoseeLondon,LosAngeles,Singapore,Sydney,andNewYork togetherinaclusterinlightoftheirclimaticdifferences.However, examinationofcontemporarywaterissuesinthesecitiessupports thisgrouping.Allofthesecitieshavereachedasizewherewater isimportedfromlongdistancesanddesalinationhasbeenatleast consideredifnotimplemented;allofthesecitieshaveissueswith waterqualityandstormwaterrunoff.Watersustainabilityplans forthesecitiesmaythusbeexpectedtohavesomesimilarities. It mightalsohave beenexpectedthat large, rapidlyurbanizing citiesindevelopingcountrieswouldbegroupedtogether,asthey wereinType1.Forinstance,itmighthavebeenpossibletoidentify SãoPauloandMumbaiashavingsimilarchallengesinmeetingthe demandsoftheirburgeoningpopulations,butwearenotawareof previousresearchthathascomparedtheseurbanwatersystems.It isnotablethatthismeaningfulpairing,andothers,wereidentiﬁed througharelativelysimplecombinationofmetrics,withrelatively widelyavailabledata,usingaveryscalablemethod.

Theresultsalsoidentifiedmoresurprisinginternational group-ings.ConsiderthesubgroupingofHanover,Durban,Copenhagen, Vilnius,andSanSalvadorinType3.Whileitisperhapsless sur-prisingthat Copenhagen,Hanover,and Vilniusare similar,it is surprisingtoincludeDurbanandevenmoresoSanSalvadorwith those three.Yetupon examiningthescatterplots ofthese mid-rangevaluesonmostvariables,itmakessensewhythesecities were clustered. The identification of such sub-groups demon-stratestheutilityofapplyingquantitativedata-miningalgorithms touncoversignificantandintriguingpatternsofcitiesaroundthe world.

5. Conclusionsandfuturework

Ourresultsprovideaninitialanswertothequestion—how sim-ilarandhowdifferentarecitiesintermsoftheirwaterresource supplyand usagepatterns?One ofthemainaimsof thisstudy wastousesimplemetricsforwatersupplyanddemandto iden-tifygroupsofsimilaranddifferentcities.Usingstatisticalclustering identifiedsixmeaningfulclustersofurbanwatersustainability con-ditions.Werecasttheseclustersasatypology,andindicatedhow ourresultscanbeusedforstratifiedsamplingofsmallernumbers ofcasesformorefine-grainedcontextualandcomparative inter-nationalwaterresearch.

Ourworkalsoprovidesacontextforassessingwater manage-mentchallengesand policyalternativesina meaningfulway.It identiﬁedbothexpectedandsurprisingpairingsandgroupingsof citiesthatcanbeexploredthroughfurthercomparativeanalysis insmall-Normedium-Nstudies.Forinstance,thetypology identi-ﬁedunanticipatedsimilarities,mostnotablyamongcasesofcities thatconsumedfarmorethantheirlocalsupply,evenwhenthose suppliesvariedfromaridtohumid.

Our results primarily demonstrate the utility of statistical clusteringof a small number of metricsto supportmeaningful internationalcomparisonofcities.Therelevanceofthistypology toagenda-settingandpolicy-makingforsustainabilitydependson theassertionthatcitiesaremorelikelytosharesimilar sustain-abilitychallengeswithothercitiesthathavesimilarsupplyand demandmetrics.Whilewebelievethatcitieswithinatype,or adja-centtoeachotherinFig.7,aremorelikelytosharesimilarissuesin urbanwaterresourcemanagement,therelativeproximityor dis-similarityoftwocitiesalonecannotdeterminewhetherthemost pressingwaterresourceandmanagementchallengesthesecities faceare,infact,similar.Furtherworkthatlinkssmall-N,medium-N, andlarge-Nscalesofcomparativeanalysismustbedonetouncover morenuancedpredictiverelationshipsbetweenwatersupplyand demandmetricsandsustainabilityissues.

(13)

Thethresholdsinourresultsprovideabasisforposingquestions withtestablehypotheses.ThethresholdsforPOP,CONS,andDIFF areintriguing,butwhethertheyareinfactmeaningfulrequires furtherstudy.Forinstance,thelevelsforthesethresholdsor typo-logicalmembershipofparticularcitiesmaychangeifthedatabase ofcitiesisexpandedoriftheclusteringisrepeatedonthesameset ofcitiesatadifferentpointintime.Hopefully,astimeprogresses wemightseetheemergenceofnewtypes,suchasthatoflarge, afﬂuentcitieswithlowwateruse.

Anextstep in thisanalysis wouldbetoexamine the sensi-tivityoftheclusteringtotheunderlyingdataset.Thereareother opportunitiesfornextstepsintheanalysis.High-priority exten-sionsofthisanalysisareexpandingthesetofcitiesandintegrating additionalmetrics,suchasawater qualityvariable,partitioning waterconsumptionintomunicipalandindustrialcomponents,and addingmetricsassociated withmore socio-economicaspectsof watermanagement,includingGDPorhouseholdincome. Includ-ingdataontheﬁnancial,energy,material,andlanduseintensity ofurbanwatersupplycouldprovideinsightintotheurban water-land-energynexus.Thedatasetcouldalsobeaugmentedbythe inclusionofperformanceindicatorssuchasleakageratesandcost recoveryratesincludedindatabases suchasIBNET. Thiswould allowforamorereﬁnedapproachtoidentifyingtypesofwater sys-temsandtargetareastoenhancethesustainabilityofurbanwater management.

Anotherattractivestepwouldbetoincludespatialand tem-poralvariationsintheunderlyingdata.Forinstance,theclimate metric couldbedisaggregated toamonthly waterbudget.This wouldallowfordistinctionstobemadeamongcitieswithlarge intra-annualvariationintheirwaterbudgets,sincethisvariation canhaveimportantimplicationsforwaterstorage,management, andreuse.Expandingthedatasettoincludemultipleyearsofdata forcitiesmightallowforidentiﬁcationoftypesbasedonvariability andtrends—forinstance,citiesthathaveincreasingordecreasing percapitawateruse(CONS).

Insummary,weappliedstatisticaldata-miningtechniquesto develop aninitialurbanwater typology basedoncity size,per capitawater consumption, and netannual water balance.This typologyisanimportantfirststepincharacterizingurbanwater supply and demand patterns around theworld and will facili-tatetransferofknowledgeandmeaningfulcasestudyresearchto furtherourunderstandingofsustainableurbanwaterresources management. We demonstrated that statistical clustering is a useful method for developing a quantitative basis for small-N and large-N comparative urban water management case study research.Thetypology presentedhereis asignificant contribu-tiontothiseffort,butitisonlyastart.Itwillbenefitfromfuture casestudyresearch,standardizationofdata,expansionofmetrics toconsidertemporalandspatialvariation,disaggregationofwater consumptionandnetannualwaterbalancedata,andtheinclusion ofmorecities.

Acknowledgements

Thisresearchwasmadepossiblewithgenerousfundingfrom the Rambøll Foundation and Liveable Cities Lab for a research projectonEnhancing Blue-GreenInfrastructureand Social Per-formanceinHighDensityUrbanEnvironments(2014–2016).We thankRicharddeNeufville,anonymousreviewers,andtheeditors forhelpfulfeedback.

AppendixA. Supplementarydata

Supplementarydataassociatedwiththisarticlecanbefound,in theonlineversion,athttp://dx.doi.org/10.1016/j.scs.2016.06.003.

References

Astel,A.,Tsakovski,S.,Barbieri,P.,&Simeonov,V.(2007).Comparisonof self-organizingmapsclassiﬁcationapproachwithclusterandprincipal componentsanalysisforlargeenvironmentaldatasets.WaterResearch,41(19), 4566–4578.

Batty,M.,Axhausen,K.W.,Giannotti,F.,Pozdnoukhov,A.,Bazzani,A.,Wachowicz, M.,etal.(2012).Smartcitiesofthefuture.TheEuropeanPhysicalJournal: SpecialTopics,214(1),481–518.

Bettencourt,L.(2013).Theoriginsofscalingincities.Science,340(6139), 1438–1441.

Candelieri,A.,&Archetti,F.(2014).Identifyingtypicalurbanwaterdemand patternsforareliableshort-termforecasting—theICeWaterprojectapproach, 16thConferenceonWaterDistributionSystemAnalysis.ProcediaEngineering, 89,1004–1012.

Chertow,M.R.(2001).TheIPATequationanditsvariants.JournalofIndustrial Ecology,4(4),13–29.

Daniels,P.L.,Lenzen,M.,&Kenway,S.J.(2011).Theinsandoutsofwateruse—a reviewofmulti-regioninput-outputanalysisandwaterfootprintsforregional sustainabilityanalysisandpolicy.EconomicSystemsResearch,23(4),353–370.

Diao,K.,Farmani,R.,Fu,G.,Astaraie-Imani,M.,Ward,S.,&Butler,D.(2014).

Clusteringanalysisofwaterdistributionsystems:identifyingcritical componentsandcommunityimpacts.WaterScience&Technology,70(11), 1764–1773.

Ercin,A.E.,Aldaya,M.M.,&Hoekstra,A.Y.(2011).Corporatewaterfootprint accountingandimpactassessment:thecaseofthewaterfootprintofa sugar-containingcarbonatedbeverage.WaterResourcesManagement,24, 721–741.

Ferrão,P.,&Fernández,J.(2013).Urbantypologies:prospectsandindicators.In SustainableUrbanMetabolism.Cambridge,MA:TheMITPress(Chapter7)

Fletcher,T.,&Deletic,A.(Eds.).(2008).Datarequirementsforintegratedurbanwater management:urbanwaterseries-UNESCO-IHP(Vol.1).Paris,France:CRCPress.

Gandy,M.(2014).Thefabricofspace:water,modernity,andtheurbanimagination. Cambridge,MA:TheMITPress.

Garg,V.(2007).Forecastingthewaterdemandusingregressionandclusteranalysis forSaltLakeCity.Mastersthesis.UtahStateUniversity.

Hoekstra,A.Y.,&Chapagain,A.K.(2007).Waterfootprintsofnations:wateruseby peopleasafunctionoftheirconsumptionpattern.WaterResources

Management,21(1),35–48.

Hoff,H.,Döll,P.,Fader,M.,Gerten,D.,Hauser,S.,&Siebert,S.(2014).Water footprintsofcitiesöindicatorsforsustainableconsumptionandproduction. HydrologyandEarthSystemSciences,18,213–226.

IBNET.(2015).IB-NETDatabase.https://database.ib-net.org/Accessed28.01.16 Kennedy,E.H.(2011).Reclaimingconsumption:sustainability,socialnetworks,and

urbancontext.Doctoraldissertation.RuralSociology,UniversityofAlberta.

Khamis,A.(2012).Developingatypologyofurbanresourceconsumption.In1st CivilandEnvironmentalEngineeringStudentConference.

Kim,J.-S.(1997).ThedifferentiationofSouthKoreancities:amultivariateanalysis. Master’sthesis.DepartmentofGeography,TheUniversityofCalgary.

Konar,M.,Dalin,C.,Hanasaki,N.,Rinaldo,A.,&Rodriguez-Iturbe,I.(2012).

Temporaldynamicsofblueandgreenvirtualwatertradenetworks.Water ResourcesResearch,48,W07509.

MacCannell,E.H.(1957).Anapplicationofurbantypologybyclusteranalysistothe ecologyoftenAmericancities.Doctoraldissertation.UniversityofWashington.

Mayer,A.,Winkler,R.,&Fry,L.(2014).Classiﬁcationofwatershedsintointegrated socialandbiophysicalindicatorswithclusteringanalysis.EcologicalIndicators, 45,340–349.

McDonald,R.I.,Weber,K.,Padowski,J.,Flörke,M.,Schneider,C.,Green,P.A.,etal. (2014).Wateronanurbanplanet:urbanizationandthereachofurbanwater infrastructure.GlobalEnvironmentalChange,27(2014),96–105.

Mollinga,P.,&Gondhalekar,D.(2014).Findingstructureindiversity:astepwise small-N/medium-Nqualitativecomparativeanalysisapproachforwater resourcesmanagementresearch.WaterAlternatives,7(1),178–198.

Novotny,V.,Ahern,J.,&Brown,P.(2010).Watercentricsustainablecommunities: planning,retroﬁttingandbuildingthenexturbanenvironment.NewYork,NY: Wiley.

Plappally,A.K.,&Lienhard,J.H.(2012).Energyrequirementsforwaterproduction, treatment,enduse,reclamation,anddisposal.RenewableandSustainable EnergyReviews,16,4818–4848.

Plappally,A.K.,&Lienhard,J.H.(2013).Costsforwatersupply,treatment,end-use andreclamation.DesalinationandWaterTreatment,41(1–3),200–232.

Rahill-Marier,B.,&Lall,U.(2013).America’swater:anexploratoryanalysisof municipalwatersurveydata.Whitepaper.NewYork:ColumbiaWaterCenter, EarthInstitute,ColumbiaUniversity.http://water.columbia.edu/2013/10/16/ americas-water-an-exploratory-analysis-of-municipal-water-survey-data/

Accessed14.12.15

Rao,A.R.,&Srinivas,V.V.(2008a).Regionalizationbyhybridclusteranalysis.In RegionalizationofWatersheds.pp.17–55.Dordrecht,Netherlands:Springer (Chapter2).

Rao,A.R.,&Srinivas,V.V.(2008b).Regionalizationbyfuzzyclusteranalysis.In RegionalizationofWatersheds.pp.57–111.Dordrecht,Netherlands:Springer (Chapter3).

Rosa,E.A.,York,R.,&Dietz,T.(2004).Trackingtheanthropogenicdriversof ecologicalimpact.Ambio,33(8),509–512.

Saldivar-Sali,A.N.D.(2010).Aglobaltypologyofcities:classiﬁcationtreeanalysisof urbanresourceconsumption.Master’sthesis.DepartmentofArchitecture,MIT.

(14)

Suweis,S.,Konar,M.,Dalin,C.,Hanasaki,N.,Rinaldo,A.,&Rodriguez-Iturbe,I. (2011).Structureandcontrolsoftheglobalvirtualwatertradenetwork. GeophysicalResearchLetters,38,L10403.

vanderMaaten,L.J.P.,&Hinton,G.E.(2008).Visualizinghigh-dimensionaldata usingt-SNE.JournalofMachineLearningResearch,9,2579–2605.

Wörlen,M.,Wanschura,B.,Dreiseitl,H.,Noiva,K.,Wescoat,J.,&Moldaschl,M. (Eds.).(2016).Enhancingblue-greeninfrastructureandsocialperformancein highdensityurbanenvironments:summarydocument.Uberlingen,Germany: RambollLiveableCitiesLab.

Wescoat,J.L.(2009).Comparativeinternationalwaterresearch.Journalof ContemporaryWaterResearch&Education,142,61–66.

Wescoat,J.L.(2014).Searchingforcomparativeinternationalwaterresearch: urbanandruralwaterconservationresearchinIndiaandtheUnitedStates. WaterAlternatives,7(1),199–219.

Willmott,C.J.,Rowe,C.M.,&Mintz,Y.(1985).Climatologyoftheterrestrial seasonalwatercycle?InternationalJournalofClimatology,5(6),589–606.

Wu,S.,Lv,M.,Dong,S.,Wang,J.,&Xu,H.(2012).Classiﬁcationcalculationonwater consumptionofurbanwatersupplynetworkbasedonclustering.In2012 WorldAutomatonCongress(pp.1–4).

Yu,N.,&Chen,R.(2010).Researchonthedevelopmentofurbaninfrastructurein Chinabasedonclusteranalysis.In2010InternationalConferenceon ManagementandServiceScience(pp.1–5).PublishedbyIEEE.

Yu,Y.,etal.(2013).ClusteranalysisforcharacterizationofrainfallsandCSO behavioursinanurbandrainageareaofTokyo.WaterScience&Technology, 68(3),544–551.