建筑排水构造

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandWaterDemandanditsApplicationinBeijing

LongxiaQian&HongruiWang&KeniZhang

Received:17October2012/Accepted:15April2014/Publishedonline:1September2014

#SpringerScience+BusinessMediaDordrecht2014

AbstractInChina,studiesonwatersupplyandwaterdemandbalancehavereceivedmuchattention,butriskbetweenwatersupplyandwaterdemandlacksthesamefocus.Thispaperpresentsevaluationcriteriaofriskbetweenwatersupplyandwaterdemand,whichincludesthreat,susceptibility,andvulnerability.Anewquantitativedefinitionofthreatisgivenbasedonfuzzyprobability;Susceptibilityisproposedforevaluatingtheinherentstateofthewaterresourcesystems;Vulnerabilityisqualitativelydefinedandcomputedintermsofeconomiclosses.Amodelforriskevaluationisdevelopedbasedonthemaximumentropyprincipleanddiscriminantanalysis.RisksinBeijing,usedasacasestudy,areevaluatedunderdifferentscenariosofinflow.Theresultsshowthatalltherisksin2020arefirstorsecondgrade.Afterusingreclaimedwaterandtransferredwater,thethirdgradeandfourthgraderiskaccountfor75%,with25%ofthefirstgradeandsecondgraderisk.Therefore,risksarestillhighinthesituationsoflowprecipitationperiods.

KeywordsThreat.Susceptibility.Vulnerability.Riskbetweenwatersupplyandwaterdemand.Fuzzyprobability.Maximumentropy.Discriminantanalysis

1Introduction

Riskisequaltothetwo-dimensionalcombinationofevents/consequencesandassoci-ateduncertainties(KaplanandGarrick1981;Aven2007;Haimes2009;Guetal.2012),andprobabilityisoftenusedasatooltoexpressanddescribeuncertaintiesinriskassessment(Suetal.2013;Arenaetal.2014;RosenbergandLund2009;MadaniMadanietal.2014;Tsakiris2007).Hashimotoetal.(1982)proposedthenotionofreliabilityas“thefrequencyorprobabilitythatasystemisinasatisfactorystate”forwaterresourcessystemperformanceevaluation.Manyresearchersappliedreliabilitytotheirstudies,suchaswatersupplyrisk,watershortagerisk,andwaterdistribution

L.Qian:H.Wang(*):K.Zhang

CollegeofWaterSciences,BeijingNormalUniversity,Beijing100875,Chinae-mail:henrywang@bnu.edu.cn

L.Qian

ResearchCenterofOceanEnvironmentNumericalSimulation,InstituteofMeteorologyandOceanography,PLAUniversityofScienceandTechnology,Nanjing211101,China

4434L.Qianetal.

network(Ruanetal.2005;Rajagopalanetal.2009;Sandoval-Solisetal.2011;Liserraetal.2014).However,thewaterresourcessystemisverycomplicated;itischaracterizedbyuncertaintiesduetorandomnessandfuzziness(Zuoetal.Zuoetal.2003;Mujumdaretal.MujumdarandSasikumar2002;Bardossyetal.BardossyandDisse1993).Therearelittlestudiesonwaterresourcesriskincludingbothrandom-nessandfuzziness.Threatisproposedforsimultaneoustreatmentofrandomnessandfuzzinessinthispaper.

AccordingtoHaimes(2006),riskarisesbecauseoftheinteractionsbetweennaturalorhuman-inducedhazardsandvulnerableconditionsofasystem.Haimes(2009)alsopointedoutthatitiscrucialtoconsidertheinherentstatesofthesystem(e.g.,physical,technical,organizational,andcultural)thatcanbesubjectedtoanaturalhazardorbeexploitedtoadverselyaffect(causeharmordamageto)thatsysteminriskanalysis.Hashimotoetal.(1982)proposedcriteria(reliability,vulnerabilityandresiliency)forevaluatingthepossibleperformanceofwaterresourcesystem,butnoneofthesecriteriareflecttheinherentstatesofwaterresourcesystemthatcanbeexploitedtocauseharmordamagetothesystem.AndsincethenmanyresearchersproposedcriteriaforwaterresourcesystemsriskbasedonthoseofHashimoto(Ruanetal.2005;Liuetal.2006;Sandoval-Solisetal.2011)withoutmanifestationoftheparticularstatesofthesystem.Thispaperpresentsanindicatortoevaluatetheinherentstatesofthewaterresourcesystemswhichiscalledsusceptibility.

Vulnerabilityisatermusedbydifferentresearcherswithdifferentmeanings(Haimes2006;Preziosietal.2013;Wuetal.2014;Wangetal.2012;Safavietal.2014).Oneofthemostcommonnotionsisthatvulnerabilityisperceivedasadirectconsequencesoftheexposuretoagivenhazard,e.g.Alexander(2000)definedvulnerabilityas“thepotentialforcasualty,destruction,damage,disruptionorotherformsoflosswithrespecttoaparticularelement.”Dilleyetal.(2005)proposedvulnerabilityas“theapparentweaknessofthephysicalandsocialsystemstoparticularhazards”andmadethenumericalestimationofvulnerabilityintermsoffatalitiesoreconomiclosses.AlthoughHashimotoetal.(1982)proposedaquantitativedefinitionforoverallsystemvulnerabilityexpresssedintermsofexpectedmaximumseverity,theexpectedvaluehassomeshortcomings(Aven2010).Intheresearch,vulnerabilityisqualitativelydefinedandexpressedintermsofeconomiclosses.

InChina,balancebetweenwatersupplyandwaterdemandhasreceivedmuchattention,whilethequantitativestudiesonrelationshipsbetweenwatersupplyandwaterdemandarefarmoresufficient(Gao1997;Shenetal.2006).Thereexistuncertaintiesinwatersupplyandwaterdemandbecauseofuncertaintiesinprecipitation,runoff,andwateruse(Zuoetal.Zuoetal.2003;Bardossyetal.BardossyandDisse1993).Therefore,thereexistsriskbetweenwatersupplyandwaterdemand.

Motivatedbytheabovediscussion,thispaperaimstopresentevaluationcriteriaforriskbetweenwatersupplyandwaterdemandthatmakesitpossibletodescribetheinherentnatureofriskinaqualitativeway.Thesemeasuresdescribethelikelyhoodthatasystemisinaunsatisfactorystateincludingbothrandomnessandfuzziness(threat),theinherentstatesofthewaterresourcesystems(susceptibility),andadirectconsequenceoftheexposuretoagivenhazardexpressedintermsofeconomiclosses(vulnerability).Moreover,amodelisdesignedforevaluatingriskbetweenwatersupplyandwaterdemand.

Thepaperisorganizedasthefollowing:first,evaluationcriteriaforriskbetweenwatersupplyandwaterdemandaredescribedanddefined;second,amodelforevaluatingriskbetweenwatersupplyandwaterdemandisdeveloped;third,theuncertaintyofinflow,riskevaluationunderdifferentscenariosinBeijingareconsidered.finally,discussionandconclu-sionsarepresented.

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4435

2EvaluationCriteriaforRiskBetweenWaterSupplyandWaterDemand

AccordingtoMileti(1999)andDilleyetal.(2005),theevaluationcriteriafornaturaldisasterriskareprobability,exposureandvulnerability.Tsakiris(2014)believesthatriskistherealthreattoasystemgivenitsvulnerablestatestowardsthephenomenon.Basedonthediscussionintheintroduction,weconcludethatriskisduetothefollowingcombinedeffects:threatofnaturalorhuman-inducedeventsandsuscepti-bilityofasystemtobeaffectedbytheexternalevent.Vulnerabilityisamanifestationoftheconsequenceofrisk.Threatreferstotheprobabilityofsomethingundesirablehappeninginthegiventime.Susceptibilityisreferredtoastheinherentstatesofthesystemorthesetofconditionsresultingfromphysical,social,andeconomicfactorsthatareexploitedtoadverselyaffectthesystem.Vulnerabilityisdefinedaspotentiallossesduetoaparticularhazardforagivenareaandreferenceperiod.Threatandvulnerabilitywillbequantitativelydefinedfromanewviewpoint.2.1Threat(T)

Forawatersupplysystem,awatersupplyisafailureifWsislessthanWd,makingthewatersupplysystembeastateofshortage.WdandWsdenotetheamountofwaterdemandandwatersupplyrespectively.Werefertothreatastheprobabilityofthewatersupplysystembeinginthestateofwatershortage.Inordertodefinethreat,twoimportantconceptsareintroducedinthispaper,thefirstoneisrelatedtoviewingthewatersupplysystembeinginthestateofshortageasafuzzyevent;thesecondoneisrelatedtofuzzyprobabilitywhichcanincludebothrandomnessandfuzziness.Zadeh(Zadeh1968)definedfuzzyprobabilityasfollows:

ZÀÁeAf¼μAfðyÞfðyÞdyð1ÞP

Rn

WhereμAfðyÞisthemembershipfunctionofthefuzzyeventAfandf(y)istheprobability

densityfunctionoftherandomvariableY.

Wedefinethreatbasedonthedefinitionoffuzzyprobabilityas:

Zx

TðxÞ¼μðtÞfðtÞdtð2Þ

0A

WhereArepresentsfuzzyevent(thewatersupplysystembeingthestateofshortage),xis

amountofwatershortage,i.e.x=Wd−Ws.f(t)istheprobabilitydensityfunctionofwatershortage,andμAðtÞisthemembershipfunctionofwatershortage.Asaresultofuncertaintiesofinflowintheplanningyear,theamountofwatershortagexisavariable,sotheintegralintervaloftheEq.(2)is[0,x]andthreatisafunctionofx.

f(t)willbedeterminedthroughthemaximumentropyprincipleandμAðtÞcanbeexpressedasfollows:

80;><󰀄t−W󰀅p

a

μðtÞ¼;

>A:Wm−Wa

1;

0≤t≤WaWa≺t≺Wmt≥Wm

ð3Þ

WhereWadenotesanacceptablevalueofwatershortage,Wmdenotesthemaximumvalueofwatershortage,andpisapositiveintegerwhichiscomputedbyfitting.

4436L.Qianetal.

2.2Susceptibility(S)

Susceptibilityisreferredtoastheinherentstates(e.g.physical,social,andecolog-ical)ofthewaterresourcessystemthatcausethesystemtobesubjecttowatershortage,includingthreeevaluationindicators:precipitation(P),satisfactoryrateofwaterdemand(Sr)andutilizationrateofwaterresources(Ur).Precipitationisthemainreplenishmentsourceofwaterresources,thatnotonlydeterminessurfacerunoffandsurfacewater,butalsoinfluencesreplenishmentandavailablegroundwateramount.Sristhereflectionofsatisfactiondegreeofwaterdemand.Uristhemanifestationofexploitationdegreeofwaterresources.WedefineSrandUras:

Sr¼

WasWtd

ð4Þ

WhereWasdenotestheavailablewatersupply,andWtddenotestotalwaterdemand.

Ur¼

WssþWgs

Wt

ð5Þ

WhereWssdenotestheavailablesurfacewatersupply,WgsdenotestheavailablegroundwatersupplyandWtdenotestotalwaterresources.2.3Vulnerability(V)

Vulnerabilityreferstopotentialeconomiclossduetowatershortage,anditsunitisbillionrmb(ChineseYuan).Wedefinevulnerabilityas:

80>3X0ð6Þwiei>:E¼

i¼1

Wherexiswatershortage,E′istheutilizationbenefitofwaterresourcespercube(m3),

wi(i=1,2,3)denotethemassesofei(i=1,2,3),andei(i=1,2,3)denotethebenefitcoefficientsofagriculturalwateruse,industrialwateruseanddomesticwateruserespectively.

AccordingtothestudyofYuan(Yuanetal.2002)ontheefficiencyofwateruse,thedefinitionsofei(i=1,2,3)are:

1Xbi

e1¼

mi¼1Mi

m

ð7Þ

Wheremisthecategoryofthemaincrops,biisthenetirrigationbenefitofthejthkindofcropperacreage,andMiisthewaterconsumptionnormofthejthkindofcrop.

e2¼

10000

Âg2Âf2D2

ð8Þ

WhereD2iswaterconsumptionamountpertenthousandRMB(ChineseYuan)product,g2istheallocationcoefficient,i.e.therateofbenefitbroughtbywateruse,andf2istheratioofnetindustrialbenefittoproduct.

Becausedomesticwaterbenefitisdifficulttoquantifyandthewatersupplysystemofindustrialwateristhesameasthatofdomesticwater,thecoefficientofdomesticwaterbenefit(i.e.e3)isassumedtobeequaltothatofindustrialwaterbenefitinthepaper.

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4437

3ModelDevelopmentforRiskBetweenWaterSupplyandWaterDemand3.1SimulationofProbabilityDistributionofWaterShortageSequence

ClausiusRpresentedentropyforthefirsttimein1865.ShannonCEproposedinformationentropyin1948andhethoughtentropyisareflectionoftheuncertaintydegreeoftheinformationsource.Jaynes(1957)putforwardthemaximumentropyprincipleonthebasisofinformationsource.Inviewofrandomnessofwaterresourcessystem,wesimulatetheprobabilitydistributionofwatershortagesequencebythemaximumentropyprinciple.Thearithmeticofsimulatingprobabilitydensityfunctionthroughthemaximumentropyprincipleisasfollows(Diaoetal.Diaoetal.2007):

Zb

fðxÞlnfðxÞdxmaxS¼−

Zba

s:t:fðxÞdx¼1

ð9Þ

Zb

a

a

xnfðxÞdx¼μn

n¼1;2;⋯;N

Whereμnisthenthorderoforiginmoment,Nistheorderoforiginmoment.First,

Lagrangianmultipliers(l0+1)andln(n=1,2,⋯,N)areintroducedandthesolutionoftheprobabilitydensityfunctioncanbetransformedintoaproblemofconditionalfunctionalextremum.Andthentheprobabilitydensityfunctioncanbeobtainedthroughvariationandderivation:

!NX

ð10ÞλnxnfðxÞ¼expλ0þ

n¼1

Whereλn(n=0,1,⋯,N)areundeterminedparameters,theycanbeobtainedbymathemat-icalcalculation.3.2ClusterAnalysis

Clusteranalysis,amethodofMultivariateStatistics,isoftenusedforclassifyingsampleor

variable.Accordingtothetheoryofdiscriminantanalysis,riskrankofthetrainingsampleisdeterminedinadvance.Inthispaper,clusteranalysisisusedtoclassifythesequencesofthreat,susceptibilityandvulnerability.Therearethreemethodsofclusters,includingTwoStepCluster,K-MeansClusterandHierarchicalCluster.Inthispaper,HierarchicalClusterisappliedforriskclassification.TheprincipleofHierarchicalCluster(Liuetal.LiuandGu2007)is:nobservationsareregardedasnkinds,andtwokindswhosedistanceisclosesttoeachotherareincorporatedintoonekind,andthentwokindswhosequalityisclosesttoeachotherarefoundfromthe(n-1)kinds.Byanalogy,theclusteringprocessdoesn’tstopuntilallobservationsareincorporatedintoonekind.3.3DiscriminantAnalysis

Inthispaper,thepurposeofriskevaluationistojudgetheriskrankintheplanningyearintermsofthesequencesofthreat,susceptibilityandvulnerability.Discriminantanalysis(Lu

4438L.Qianetal.

2006)canjudgewhatkindtheobjectbelongstoonthebasisofsomeobservedormeasuredvariables,makingtheerrorprobabilitysmallest.Therefore,discriminantanalysisisusedforjudgingriskrankintheresearch.Discriminantanalysiscanalsochoosethevariablesthatcontainmoreinformationfrommanyindependentvariablesreflectingfeaturesoftheobject.Thegeneraldescriptionoflineardiscriminantfunctiontakestheform:

y¼a1x1þa2x2þ…þanxn

ð11Þ

Whereyisthediscriminantvalue,x1,x2,…,xnarevariablesthatarereflectionsoffeaturesoftheobject,anda1,a2,…,anarediscriminantcoefficients.

ThemodelforevaluatingriskbetweenwatersupplyandwaterdemandisshowninFig.1.

4CaseStudy

Inthissection,riskbetweenwatersupplyandwaterdemandin2020forBeijingisevaluatedandanalyzedbyusingtheproposedmodel.

TheanalysismodelforriskbetweensupplyanddemandofwaterresourcesSusceptibilityThreatVulnerabilityProbabilitydistributionmodelbasedonmaximumentropyContstructionofmembershiofunctionFuzzyprobabilityClassifyingtheseriesbyhierarchicalclusterConstructionoffourdiscriminantfunctionsAnalysisforsupplyanddemandbalanceofwaterresourcesEvaluationofriskbetweensupplyanddemandofwaterresourcesunderdifferentscenariosintheplanningyearFig.1Arithmeticprocessofanalysismodelforriskbetweensupplyanddemandofwaterresources

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4439

4.1FeaturesofWaterResourcesofBeijing

Beijing,locatedintheHaiheBasin,consistsoffivewatersystemsfromtheeasttowest(Fig.2).Theaverageprecipitationis585mmannualy.Asaresultofinfluencesofmonsoon,precipitationischaracterizedbyasymmetryintemporalandspatialdistribution,aswellasalternationofdryandwetperiods.Thefloodseason(JunetoSeptember)hascentralizedabout85%ofthesumofall-yearprecipitation,whichoftenresultsinflooddisaster.However,watershortageoccursintheremaindermonthsduetolowprecipitationandlargewateruse.Beijingisaninternationalmetropoliswithmorethan16millionpeople,anditisalsoacitywithseriouswatershortage.Theamountofwaterresourcespercapitaisabout200m3inBeijing,whichis1/8ofthatinChinaand1/30ofthatintheworld.WatershortagehasbecomethemaincauseofhinderingtheeconomicandsocialdevelopmentofBeijing(Wangetal.WangandLiu2001;Wangetal.WangandWang2009;Hanetal.HanandRuan2007).

4.2ModelforEvaluatingRiskBetweenWaterSupplyandWaterDemand

Watershortagesequence(1956–1978)isusedtoconstructthethreatfunction,sequencesofthreat,susceptibility,andvulnerability(1979–2008).Theyareappliedtoconstructthemodelofdiscriminantanalysis.

Fig.2DistributionofwatersystemofBeijing

4440L.Qianetal.

4.2.1ConstructionoftheThreatFunction

Accordingtothearithmeticofsimulatingprobabilitydensityfunctionthroughthemaximumentropyprinciple,theprobabilitydensityfunctionofwatershortagecanbeobtained.Itisexpressedasfollows:

󰀆󰀇

fðxÞ¼exp−0:9021−0:002ðx−11:2213Þ−0:0519ðx−11:22Þ2þ0:0007ðx−11:22Þ3ðx>0Þð12ÞSubstitutingtheEq.(3)andEq.(12)intotheEq.(2)andthenintegratingover[0,x],the

functionofthreatcanbeobtained.However,theanalyticfunctionexpressionofthreatcannotbeobtainedduetocomplexityofintegratedfunction.Thethreatfunctioncanbedrawnbymeansofnumericalintegral(Fig.3)andthevaluesofthreat(1979–2008)canbecomputed.InFig.3,thehorizontalcoordinatexdenoteswatershortagewiththeunitofbillionm3.FromFig.3,it’sconcludedthatthreatincreaseswiththeincreaseofwatershortage.4.2.2ComputationofSusceptibilityandVulnerability

Substitutingavailablewatersupply,wateruse,waterconsumptionnormofmaincropsandindustrialproducts(1979–2008)intoEq.(4),Eq.(5),Eq.(6),Eq.(7)andEq.(8),satisfactoryrateofwaterdemand,utilizationrateofwaterresourcesandvulnerabilityfrom1979to2008canbeobtained.4.2.3RiskClassification

Accordingtothesequencesofthreat,vulnerabilityandsusceptibility(1979–2008),risksofBeijingareclassifiedbymeansofhierarchicalcluster(Fig.4).InFig.4,thehorizontalcoordinatedenotesthreat,theverticalcoordinatedenotesvulnerability,andthemarkerdenotesriskrank.RiskfeaturesofallranksareshowninTable1.4.2.4ConstructionofModelofDiscriminantAnalysis

Thesequencesofthreat,precipitation,andsatisfactoryrateofwaterdemand,aswellasutilizationrateofwaterresources,vulnerability,andriskclassification(1979–2008)are

3.532.52Threat1.510.50−0.5051015202530x

Fig.3Threatfunctionofwatershortage

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4441

Fig.4RiskclassificationofBeijing(1979–2008)

regardedasatrainingsampleofdiscriminantanalysis.Weusestepwisemethod.TheresultsareshowninTable2andTable3.

Table2isasummaryofstepwisediscriminantanalysis.ThefirstStatisticisusedtoselectthevariablewhichcanenterdiscriminantfunctionineachstep.ThesecondStatisticisusedtodecidewhethertheselectedvariablecanretainineachstep.Theresltshowstheselectedthreevariables(i.e.threat,vulnerabilityandsatisfactorydegreeofwaterresources)havesignificantcontributionsfordiscriminant.

Table3representsthecoefficientsofFisher’slineardiscriminantfunction.AccordingtotheresultsofTable3,fourdiscriminantfunctionscanbeexpressedasfollows:

F1F2F3F4

¼10:530T¼25:858T¼16:431T¼22:230T

þ14:410Vþ767:468Sr−340:355þ14:270Vþ806:928Sr−390:498þ14:336Vþ857:291Sr−421:674þ18:773Vþ869:911Sr−480:321

ð13Þ

Table1RiskfeaturesofallranksRiskRankRiskoffirstgradeRiskofsecondgradeRiskofthirdgradedRiskoffourthgrade

Feature

WatersupplyisseriouslyscarceandthelossisverygreatWatersupplyisscarceandthelossisgreat

WaterdeficiencyamountislittleandthelossissmallWatersupplyisenoughwithoutloss

4442

Table2Variablesentered/removedStep

Entered

Wilks’LamberStatistic

df1df2

df3

ExactFStatistic

123

Threat(T)

Vulnerability(V)

Satisfactoryrateofwaterdemand(Sr)

0.1160.0540.03

123

333

26.00026.00026.000

66.12127.57420.817

L.Qianetal.

df1df2369

26.00050.00058.560

Sig.0.0000.0000.000

4.3RiskEvaluationin2020inBeijing

4.3.1AnalysisonWaterSupplyandWaterDemandBalance

Calculationoflongseriesmonthbymonthisappliedtoanalyzewatersupplyandwaterdemandbalance.Thewatersupplysequenceisinflowamountsfrom1956to2007(52yearsinall)andthewaterdemandsequenceispredicatedvaluesofwaterusein2020.Weobtainwatershortagesequenceunder52kindsofinflowin2020.

4.3.2RiskEvaluation(WithoutConsiderationofUsingTransferredWaterandReclaimedWater)

Sequencesofthreat,vulnerabilityandsatisfactoryrateofwaterdemandunder52kindsofinflowin2020areobtainedaccordingtothethreatfunction(Fig.4)andEq.(4)and(6),showninFig.5.

FromFig.5,wecanconcludethat:boththreatandvulnerabilityaregreaterinthesituationsoflowprecipitationperiods;themaximumvaluesofthemappearinthesituationoftheprecipitationof448mm;threatandvulnerabilityvarywithprecipitationandthevariationtrendsofthemaresimilar;andsatisfactoryrateofwaterdemand(Sr)islessinthesituationsoflowprecipitationperiodsandtheminimumvalueappearsinthesituationoftheprecipitationof499mm.

Risksunder52kindsofinflowin2020areevaluatedbasedonthediscriminantanalysismodel(Eq.13),showninFig.6.Theresultshowsthat:inthesituationofdifferentprecipi-tationperiods(1956–2007),thefirstgraderiskaccountsfor32.7%andtheremainderissecondgrade.Thereby,thesituationofwatersupplyandwaterdemandin2020inBeijingisextremelydangerous.Somemeasuresmustbetakentoreducerisk.

Table3Classificationfunctioncoefficients(Fisher’slineardiscriminantfunction)VariableFunction

Satisfactorydegreeofwaterresources(Sr)Threat(S)Vulnerability(V)(Constant)

1767.46810.53014.410−340.355

2806.92825.85814.270−390.498

3857.29116.43114.336−421.674

4869.91122.23018.773−480.321

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4443

(a)

2.652.62.559.49.298.88.68.4Threat2.52.452.42.352.32.252.2(b)

Satisfactory rate of water demand0.580.570.560.550.540.530.520.51Fig.5Valuesofthreatandvulnerability(a)andsatisfactoryrateofwaterdemand(b)under52kindsofinflow

4.3.3EvaluationofInfluencesofSouth-to-NorthWaterTransferandReclaimedWaterUseAsforBeijing,middlerouteprojectofSouth-to-NorthWaterTransfer,whichwillstartoperatingin2014,isanimportantmeasureofmitigatingwaterdeficiencyfromthepointofresources.Atpresent,Beijing-ShijiazhuangsectionofmiddlerouteprojectofSouth-to-NorthWaterTransferhasopened,withTransferredwaterof3billionm3everyyear.AccordingtotheplanningofSouth-to-NorthWaterTransferProject,waterof14billionm3wouldbetransferredtoBeijingin2020.Moreover,reclaimedwaterusehasbeenincreasinganditmayachieve10billionm3in2020.

Valuesofthreat,vulnerabilityandsatisfactoryrateofwaterdemandafterusingtransferredwaterandreclaimedwaterin2020areobtainedaccordingtothethreatfunction(Fig.3)andEq.(4)and(6).

Risksunder52kindsofinflowafterusingtransferredwaterandreclaimedwaterin2020areevaluatedbasedonthediscriminantanalysismodel(Eq.13),showninFig.7.Theresultshowsthatrisksofthirdgradeandfourthgradeaccountfor75%.ItindicatesthatSouth-to-NorthWaterTransferandreclaimedwaterareessentialtoreduceriskbetweenwatersupply

3.2508469.1797.9585.7479.1572.3433.1596631.4668387.3585.1442.1560.3594.7662.4500727.7669.4687.4446.13539445753.85046.1797.9585.7479.1572.3433.1596361.4663887.3585.1442.1560.3594.7662.4507207.7669.4687.4446.13539448.53753.2Precipitation [mm]ThreatvulnerabilityPrecipitaion [mm]Vulnerability [billion RMB]2.79.444L.Qianetal.

Fig.6Riskevaluationunder52kindsofinflowwithouttakinganymeasures

andwaterdemandinBeijing.However,theproportionofrisksoffirstgradeandsecondgradeisstillhigh(around25%,Fig.7).ShowninFig.7,risksoffirstgradeandsecondgradeappearinthesituationofprecipitationof350mmto400mm.Itindicatesthat:eveniftransferredwaterandreclaimedwaterareusedsimultaneously,riskisstillhighinthesituationoflowprecipitationperiods.Therefore,othermeasuresshouldbetakentoreducerisk.

5Discussion

Since1999,Beijinghasbeenaridintensuccessiveyears,whichhasstronglyaffectedwaterresourcesofBeijing.Themeanannualprecipitationandavailablewaterresourcesare469mmand26billionm3respectively,farlowerthanthoseofmulti-annualmean(585mmand37.4billionm3).Asaresultoflargerdecreaseinsurfacewater,groundwaterhasbecometheprimarysourceofwatersupply,withaproportionof70%to80%.However,thegroundwaterisinastateofsevereover-exploitationandthelevelofgroundwaterisdecreasingyearbyyear.Since1960s,thestorageofgroundwaterhasdecreasedby100billionm3,withseveredecreaseof60billionm3intenofthelasttwelveyears(2000–2011).Ontheotherhand,themeanannualwateruseisabout42billionm3(since1970s).Since1999,themeanannualwaterusehasdecreasedto35billionm3bycuttingdownwateruseduetodrought.Withoutspreadofcityscopeandrapidincreaseinpopulation,industrialanddomesticwaterusewillincreasetoacertainextent.Watershortagewillbeseriousinthefuture.AccordingtoFig.6,riskbetweenwatersupplyandwaterdemandwillbehigh.Somemeasuresmustbetakensuchasreclaimedwateruseandtransferredwateruse.

In2008,thereclaimedwateruseaccountsfor17%ofthetotalwateruse,exceedingsurfacewateruseforthefirsttime.ThereclaimedwaterwillplayamoreandmoreimportantpartinwaterresourcesallocationofBeijing.IftheprojectofSouth-to-NorthWaterTransfercan

EvaluationCriteriaandModelforRiskBetweenWaterSupplyandDemand4445

Fig.7Riskevaluationunder52kindsofinflowafterusingtransferredwaterandreclaimedwater

provide14billionm3in2020,riskbetweensupplyanddemandwillbereducedgreatly.However,WaterstorageofBeijinghasbeenusedupduetodurativedrought,andthewatersupplysystemisveryfragile.Iflowprecipitationeventswilloccurin2020,riskbetweenwatersupplyandwaterdemandmaybestillhigh.Besidesreclaimedwateruseandtransferredwateruse,othermeasuresmaybetakensuchasvirtualwateruse.

6Conclusions

Inthispaper,wefirstlyproposeevaluationcriteriaforriskbetweenwatersupplyandwaterdemand,i.e.threat,susceptibilityandvulnerability.Anewquantitativedefinitionofthreatisgivenbasedonfuzzyprobability;susceptibilityisproposedforevaluatingtheinherentstateofthewaterresourcesystems;vulnerabilityisqualitativelydefinedandcomputedintermsofeconomiclosses.Webelievethattheproposedcriteriaareareflectionoftheinherentfeaturesofrisk.Furthermore,amodelforevaluatingriskbetweenwatersupplyandwaterdemandisdevelopedbasedonthemaximumentropyprincipleanddiscriminantanalysis.RisksinBeijing,usedasacasestudy,areevaluatedunderdifferentscenariosofinflow(1956–2007)byusingthemodel.Theresultindicatesthatthefirstgraderiskaccountsfor32.7%andtheremainderissecondgrade.Afterusingtransferredwaterandreclaimedwater,risksarereducedinthemostcircumstancesofinflow.Nevertheless,riskisstillhighinthesituationoflowprecipitationperiodswithaproportionoffirstgradeandsecondgraderiskof25%.

AcknowledgmentsThestudyissupportedbytheNationalNaturalScienceFoundationofChina(GrantNo.51279006),(GrantNo.41375002)andtheChineseNationalNaturalScienceFund(BK2011123)ofJiangsuProvince.TheauthorswouldliketothanktheAssociateEditorandalltheanonymousreviewersfortheirvaluablecommentsandconstructivesuggestions,whichleadtotheimprovementofthepresentationofthispaper.

4446L.Qianetal.

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