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Team#17696Page30of31ForofficeuseonlyT1________________T2________________T3________________T4________________TeamControlNumber17696ProblemChosenBForofficeuseonlyF1________________F2________________F3________________F4________________2013MathematicalContestinModeling(MCM/ICM)SummarySheetSummaryFreshwateristhelimitingconstraintfordevelopmentinmuchoftheworld.TakeChinaintoconsideration,thenation’sfreshwatersuppliescannolongerquenchitsthirst.WebuildModelOneandModelTwotopredictthefreshwaterneededandavailablein2025,fromwhichwecangetavisualizedconclusionofwatershortageinfutureChina.BasedontheconclusionwesetupModelThreeandModelFourtoputforwardstrategiestosolvetheproblemofsavingwaterindifferentfieldsandincreasethesourcesoffreshwater.Inordertofindthebeststrategies,ModelFivewassetuptoevaluatethedifferentstrategiesbasedontheindexesofcostandwatersaving.Finallywecameupthebeststrategyaccordingtoourmodels.Thefirstmodelpredictsthefreshwateravailablein2025basedontheassumptionthatthemainsourcesoffreshwaterarestableintheshortperiod.ModelTwoassumesthatsweepingreformswillnotbeimplementedintermsofindustry,agricultureandsocietyandpredictstheamountoffreshwaterneededbasedontheusageofdifferentfieldsandareasinordertomakethepredictionmoreconvincing.Basedonthethoughtof“strategicsourcinginitiative”,thethirdmodelisbuilttocutthewaterexpenditure.RegressionModelandAnalyticHierarchyProcessareemployedtosolvetheproblemofsavingfreshwaterinindustry,agricultureanddomestic.ModelFourisemployedtosolvetheproblemofincreasingthesourceoffreshwaterthroughdesalinizationandsewagerecycling.Theevaluationofdifferentstrategiestakescostandgoalintoconsideration.PrincipalComponentAnalysisisemployedtoevaluatethestrategies.Wedividedthestrategiesinto“Businessasusual,Governance,StrongandAtallCosts”,andthestrongscoreshighestinthecomprehensiveevaluationofallstrategies.Weproposedourwaterstrategybasedontheanalysisandevaluationabove.Inanutshell,wepredictedthefreshwatershortageroundlyandputforwardastrategybasedonthecomprehensiveevaluationindistinctivethoughts.Keywords:mathematicmodels,Chinesewaterstrategy,waterresource Team#17696Page30of31ContentWater,Water,EverywhereMathematicModelsofChinaWaterStrategy1.Introduction32.Assumptions43.KeyTerminologyandSymbols44.Predictionsoffreshwater54.1HowmuchfreshwaterisavailableinChinain2025?64.2HowmuchfreshwaterwillbeneededinChinain2025?74.3.1Predictionsbasedondifferentfields84.3.2Predictionsbasedondifferentareas94.3Conclusion115.SolutionstotheProblem115.1Savefreshwater115.1.1Savefreshwaterusedinindustry125.1.2Savefreshwaterusedinagriculture135.1.3Savefreshwaterindomesticuse165.2Increasethesourcesoffreshwater185.2.1Seawaterdesalination185.2.2Turnsewagetofreshwater185.3Adjustthedistributionofwaterbothintimeandarea205.3.1Watertransfers205.3.2Conservation216.EvaluationofWaterStrategies216.1Principalcomponentanalysis(PCA)model216.2EvaluationofstrategiesbasedonPCAmodel226.3Whichstrategyisthebest?28 Team#17696Page30of317.StrengthsandWeaknesses287.1Strengths287.2Weaknesses298.Reference29 Team#17696Page30of311.IntroductionFreshwateristhelimitingconstraintfordevelopmentinmuchoftheworld.TakeChinaintoconsideration,thewaterresourcesofChinaareaffectedbybothseverewaterquantityshortagesandseverewaterqualitypollution.Agrowingpopulationandrapideconomicdevelopmentaswellaslaxenvironmentaloversighthaveincreasedwaterdemandandpollution[1]http://en.wikipedia.org/wiki/Water_resources_of_the_People's_Republic_of_China.RainfallSurfacewaterIndustryDomesticUndergroundwaterSeawaterdesalinationSewagetreatmentAgricultureFreshwaterEcologicalwaterutilizationUnevenlydistributedinareaandtimeSourceConsumeAcrossChina,thenation’sfreshwatersuppliescannolongerquenchitsthirst.Chineseexpertswarnedoffutureorcurrentwatershortages.Waterresourceusagewasexpectedtopeakin2025whenthepopulationpeaks.Belowisthefigureoftheanalysisofthesupplyandcostoffreshwater.Figure1SourceandconsumeofthefreshwaterWhatevertheuseoffreshwater(industry,agriculture,domesticuse),hugesavingofwaterandimprovingofwatermanagementispossible.Legislativeactionsshouldbesoughttogetmunicipalitiestousewaterinarational,planned,orderlyway.Inadditiontowaterandconservationstorage/movement,desalinizationtechnologythatremoveexcesssaltandothermineralsfromwaterholdspromisetoconvertsaltwaterintofreshwatersuitableforhumanconsumptionorirrigation.Duetothewaterproblems,aswellasforfutureexports,Chinaisbuildingupitsdesalinationtechnologicalabilitiesandplanstocreateanindigenousindustry.Some Team#17696Page30of31citieshaveintroducedextensivewaterconservationandrecyclingprogramsandtechnologies[2]MICHAELWINES,ChinaTakesaLosstoGetAheadintheBusinessofFreshWater,October25,2011,.Onefocusofdesalinizationistodevelopcost-effectivewaysofprovidingfreshwaterforhumanuseinregionswheretheavailabilityoffreshwaterislimited.Large-scaledesalinizationtypicallyusesextremelylargeamountsofenergyaswellasspecialized,expensiveinfrastructure,makingitverycostlycomparedwiththeuseoffreshwaterfromriversorgroundwater.2.AssumptionslTherewillbenowarandnaturaldisastersinChinaduringthisperiod.lThestateswechooseformodelingwillnotexperiencemassmigrationsofpopulation.Thewateruseatthestateleveliscloselyrelatedtothestatepopulation.Ourwateruseestimationmodeldoestakepopulationchangeintoconsideration,whilethechangefollowsthecurrentdemographictrends.lSweepingreformswillnotbeimplementedintermsofindustry,society,economy,policy,cultureandenvironment.Ourestimationmodelprefersthatthefuturedevelopmentintermsofindustry,society,economy,policy,cultureandecosystemcankeepasteadypacethrough2013to2025.lTheunitcostofdesalinationisthesameindifferentareas.lTheunitcostofwatertransferisthesameindifferentareas.lTheresident’swaterconsumptionisthesameinsamearea.lTheincreaseinfreshwaterstoragefromthethawofglacierscausedbyclimatechangeandglobalwarmingisnotconsidered.Climatechangeandglobalwarmingaremajorobstacleshumanbeingsarefacing.Manyaresearchhasbeendoneonthistopic.Weexpectthateffectivemeasurescanbetakenandthethawofglacierswillbeceasedonedaybefore2025.Andsuchincreaseiswhatwedonothopefor.3.KeyTerminologyandSymbols3.1GrayModel(GM)GrayModelissuchamodelthatitestablishesagraydifferentialpredictionmodelthroughasmallamountofincompleteinformation,andmakesafuzzylong-termdescriptionofthedevelopmentoftheobject. Team#17696Page30of313.1ExponentialSmoothingForecastingMethod(ESFM)ExponentialSmoothingForecastingMethodreferstoamethodthatintroducesasimplifiedweightedfactorthatusessomeindicatorsofcurrentactualnumberandcurrentforecastnumberasthefoundation,namelysmoothingcoefficient,toachieveanaverageindexsmoothforecastmethod.Itisachangeofweightedmovingaveragepredictionmethod.3.2RegressionModel(RM)RegressionModelissuchamodelthatthroughtheestablishmentofthemathematicalmodelbetweenthenumbersthathaverelatedrelationshipsaccordingtothestatisticaldatainthepastyears,conductsanaturalregressionmodelingtoanalyzethechangelawbetweenthedifferentquantities.3.3AnalyticHierarchyProcess(AHP)AnalyticHierarchyProcessisadecision-makingmethodthatdecomposestheelementsthatarealwaysrelatedintogoals,standardsandschemelevelwhicharebasedontoanalyzethequalitativeandquantitativerelations.3.4SymbolstTimesVarianceCharacteristicvalueThefirstprincipalcomponentThesecondaryprincipalcomponentThethirdprincipalcomponent4.PredictionsofFreshWaterChina'swaterresourcesinclude2711.5cubickilometersofmeanannualrun-offinitsriversand828.8cubickilometersofgroundwaterrecharge.Aspumpingwaterdrawswaterfromnearbyrivers,thetotalavailableresourceislessthanthesumofsurfaceandgroundwater,andthusisonly2821.4cubickilometers.80%oftheseresourcesareintheSouthofChina[3]TheComprehensiveReportofChina’sSustainableDevelopmentofWaterResourceStrategyResearch.2008.Inthispart,weemployedGrayModeltopredicttheamountoffreshwaterthatisneededandavailablein2025. Team#17696Page30of314.1HowmuchfreshwaterisavailableinChinain2025?Figure2TheamountoffreshwaterinChinaWedrewafigureofthetotalamountofwaterresourcesinChinafrom2003to2011.Byobservingthefigureabove,wecanfindthatthetotalamountoffreshwaterinChinamovedinsteadycycles,andtheaverageamountisaround2700cubickilometers.Analogously,thesurfacewaterandundergroundwaterinChinacanberegardedasunchangeduntil2025.Figure3TheaverageannualprecipitationindifferentregionsofChinaMostoftherainChinaexperiencesduringtheyearoccursduringthesummermonths.WesearchedthedataofrainfallinChina,andrainfalldiffersfromdifferentregions.ThepictureabovesuggeststhattheannualrainfallinChinaisnearlystable Team#17696Page30of31duringashortperiod,anditisdifferentfromdifferentregions.Basedontheseconclusionsandcombiningwithotherdocuments,wecancalculatethefreshwaterthatisavailablein2025:Equation1RelationshipbetweentheamountoftotalfreshwaterandavailablefreshwaterWhere:thevolumeofavailablefreshwater;:thevolumeoftotalfreshwater;:thepercentagethattheavailablefreshwatertakeinthetotalfreshwater.Afterthesubstitutionofnumericalvalues,wecanfigureoutthevolumeofavailablefreshwaterin2025:cubickilometers4.2HowmuchfreshwaterwillbeneededinChinain2025?Totalwaterwithdrawalswereestimatedat554cubickilometersin2005,orabout20%ofrenewableresources.Demandisfromthefollowingsectors:·65%agriculture·23%industry·12%domesticFigure4theamountoffreshwatersupplyIn2006,626000squarekilometerswereirrigated[4]FAOAquastat.ChinaProfile,Version2010. Team#17696Page30of31AccordingtothedatapublishedbytheNationalBureauofStatisticsofChina,wedrewafigureoftheamountofthewatersupplyinChinafrom2003to2011(waterwassuppliedforindustry,agriculture,anddomestic).ByobservingthefigureaboveandanalyzingthedatafromChinesegovernment,wecanfindthatthesupplyoffreshwaterincreasedeveryyear,namelytheneedoffreshwaterisincreasedovertime.Chineseexpertswarnedoffutureorcurrentwatershortages.Waterresourceusagewasexpectedtopeakin2030whenthepopulationpeaks.Consideringthatthetrendofincreasingwillnotexperiencelargefluctuations,wechoseGrayModeltopredicttheneedoffreshwaterin2025,sinceGMcansolvestabletimeseriesproblems.4.2.1PredictionsbasedondifferentfieldsUseGrayModeltopredictthefreshwaterdemandin2025lClass-compareverificationWecountedthetotalwaterresourceyearsfrom2003to2011asfollows：(4-1)uCalculatetheclass-compareToensurethefeasibilityofGraymodel,wefirstlyperformeddataexamination:(4-2)uClass-comparejudgmentPutthecalculatedclass-comparetosubstitute(4-3)Sinceall，k=2,3…,9,sowecanusetomakeacontentGM(1,1)model.lBuildGM（1,1）modeluOne-accumulatesequenceoftheoriginaldata Team#17696Page30of31(4-4)uBuilddataofmatrixBandvectorYuCalculatethevalueof(4-5)uBuildmodel(4-6)Sothatequationhasresponseparticularsolution(4-7)Figure5thecomparisonbetweensimulationandrealdata Team#17696Page30of31Table1ModeltestlGM(1.1)ModelerrortestSeriesYearTheoriginaldataSimulationvalueResidualerrorRelatederror1200353205320002200455475684-37.180.00673200556335657-24.910.0044420065794573261.370.010652007581858089.6820.0017620085909588523.990.004172009596559622.2850.00048201060216041-20.440.00349201161076121-14.210.0023Theaverageofrelatederroris0.0042Table2CommonAccuracyClassrankingLevel1Level2Level3Level4Theaverageofrelatederror0.010.050.100.20Bythecomparisonoferrortestvalueandthecommonaccuracyclass,wecanseethattherankofthemodelislevel1,whichmeansthemodelhashighaccuracyandcanbeusedforprediction.ResultTheresultisthatthefreshwaterindemandin2025willbe745.2cubickilometers.4.2.2PredictionsbasedondifferentareaslTheinformationofsixstrictinChinauNorth:Beijing,Tianjin,Hebei,Shanxi,InnerMongoliauNortheast:Liaoning,Jilin,HeilongjianguEast:Shanghai,Jiangsu,Zhejiang,Anhui,Fujian,JiangxiuSouth:Henan,Hubei,Hunan,Guangdong,Hainan,GuangxiuSouthwest:Chongqing，Sichuan，Guizhou,Yunnan，TibetuNorthwest:Shaanxi，Gansu，Qinghai，NingxiaXinjiang Team#17696Page30of31lWeemployedGM(1.1)topredictthewaterneededindifferentregionsin2025.Table3Freshwaterneededindifferentregionsin2025DistrictWaterdemandin2025(cubickilometer)North54.2Northeast101.7East244.9South186.5Southwest72.4Northwest93.3Total753.0Fromthetablewecanseethetotalamountoffreshwaterneededin2025is753.0cubickilometers,comparingtothepredictionbasedondifferentfieldswhichis745.2cubickilometers,weconcludethattheresultiscorrect.4.3ConclusionAccordingtotheresultsofpredictingtheamountoftheavailablefreshwaterandfreshwaterneededin2025,wedrewsomeconclusionsasfollow:lInChina,theamountoffreshwaterneededin2025almoststretchestothelimitofthewateravailable,sincetheformerisabout745cubickilometersandthelatterisabout746cubickilometers.SotakestepstosavefreshwaterisnecessaryforthegovernmentofChina,andadoptanappropriatewaterstrategyiscrucialforthedevelopment.lInChina,freshwaterisunevenlydistributedinbothareaandtime,makingwatertransferandconservationnecessaryandimportant.5.SolutionstotheProblemFromtheconclusionabovewehaveknownthattakenecessarystepstosavefreshwaterisveryimportantinChina.Accordingtotheproblemsintheconclusion,weputforwardsolutionsfromthreeaspects,namelysavingfreshwater,increasingthesourceoffreshwaterandadjustingthedistributionofwaterintimeandspace.5.1SavefreshwaterFreshwaterdemandismainlyfromindustry,agricultureanddomestic,sothatthemeasurestosavefreshwaterwillbeadoptedinthreeaspects. Team#17696Page30of315.1.1SavefreshwaterusedinindustryTheindustrycanbedividedintohighwaterconsumptionandlowwaterconsumptionindustry,readjustingtheindustrialstructurecanremarkablysavefreshwaterconsumption.Bydecreasingthepercentagethathighwaterconsumedenterprisestakeinthewholeindustryandatthesametimeincreasingthepercentageoflowwaterconsumedenterprises,thefreshwatercanbesavedyetthecostofindustrialrestructuringwillincrease.Weaccessedrelevantinformationandsummeduparelationshipamongthereductionhighwaterconsumptionindustry,freshwatersavingandtheincreasingofcost.WeemployedExponentialSmoothingForecastingMethod(ESFM)topredicttheamountofcostandwatersaving.Themathematicalexpressionoftherelationshipbetweenthepercentageofhighwaterconsumptionindustryreductionandthecostis:(5-1)Inordertochooseanappropriatevalueof,wecalculatedthestandarddeviationofdifferentforecastingbasedondifferent.Table4StandarddeviationSofdifferentforecastingStandarddeviationofdifferentforecasting0.20.50.836.206524.294217.7608Fromthetablewecanfindthatthewhen=0.8,theSgotminimumvalue17.7608,sowechoose=0.8.Themathematicalexpressionis:(5-2)UsingRegressionModel,wesummedupthemathematicalexpressionoftherelationshipbetweenthepercentageofhighwaterconsumptionindustryreductionandthepercentageoffreshwatersaving:(5-3)Where:regressioncoefficient,:randomerror. Team#17696Page30of31Wecanfigureoutthevalueof,and,sotheultimatemathematicexpressionis:(5-4)Thecoefficientofdetermination0.8985,itshowsthattheregressioneffectisprettygood.Finspectionwasusedtoconductsignificanceanalysis,andthevalueofPis0.000,thelevelofsignificanceisacceptable.Byaccessingrelevantinformationandthebuildingmathematicmodelsabove,wesummeduparelationshipamongthereductionhighwaterconsumptionindustry,freshwatersavingandtheincreasingofcost.Table5Therelationamongthewatersaving,industryadjustmentandthecostThepercentageofhighwaterconsumptionindustryreduction(%)Theincreaseofthepercentageinfreshwatersaving(%)Theincreaseofcost(100million)10.41.3515.5101.713.5152.424.5203.537.6254.655.8305.476.7356.2102.2Thetablesuggeststhatthepercentageoffreshwaterreductionandcostwillbothincreasewiththepercentageofhighwaterconsumptionindustryreductionincreasing.5.1.2SavefreshwaterusedinagricultureAgriculturalwaterreferstowaterusedforirrigationandruralcattlewater,andwaterusedforirrigationaccountsforabout91.1%[5]http://www.gsdkj.net/pro/view.php?id=22928.Soimprovingwaterefficiencyinirrigationiscrucialtosaveagriculturewater.Oncethequantitativeandtemporalcharacteristicsofoptimalwaterdemandhavebeendetermined,amethodthatcanmakesuchwateravailableinthemosteffectivewayshouldbeselected.Therearethreemainirrigationmethods,namely:Surface(orgravity)irrigation,Sprinklerirrigation,Dripirrigation.lAnalysisofthreeirrigationmethodsAsweknowthatSurfaceirrigationinvolvestheapplicationofwaterbygravityflowtothesurfaceofthefield.Surfaceirrigationistheeasiestandtheleastcost Team#17696Page30of31methodyetconsumesmostofthewater.Sprinklerirrigationsystemsimitatenaturalrainfall.Thesesystemsaremoreefficientthansurfaceirrigation,however,theyaremorecostlytoinstallandoperatebecauseoftheneedforpressurizedwater.Thismethodcanachieveefficienciesashighas95%andwatersavingsofup70%.Figure6SprinklerirrigationDripirrigationdeliverswaterthroughtheuseofpressurizedpipesanddrippersthatrunclosetotheplantsandthatcanbeplacedonthesoilsurfaceorbelowground.Dripirrigationisreportedtohelpachieveyieldgainsupto100%,watersavingsupto80%.Figure7DripirrigationlImprovingirrigationmethodstosavewaterInordertosavefreshwaterusedinagricultureandincreasetheefficiencyofirrigation,wesuggestthegovernmenttopopularizetheSprinklerandDripirrigationmethods.Themorethepercentageofsprinkleranddripaccountsforinirrigationmethodsincreases,themorefreshwaterwillbesavedandinthesamewaythecostincreases.WebuildRegressionmodelstoanalyzethequantitativerelationshipbetweenthepercentageofsprinkler/dripirrigationandwatersavingaswellastherelationshipbetweenthepercentageofbetterirrigationmethodsandcost.lRegressionmodel Team#17696Page30of31Figure8TherelationshipbetweentheindustryadjustmentandthewatersavingFigure9TherelationshipbetweentheindustryadjustmentandthecostAccordingtothedataofpast,wedrewafigureoftherelationshipbetweenthepercentageofSprinkler/Dripirrigationmethod,andanotherfigureisofthepercentageofbetterirrigationmethodandthecost.Fromthepicturewecanseethattheindependentvariablehasgoodlinearrelationswithtodependentvariables.Theregressionmodelis:(5-5)Where:regressioncoefficient,:randomerror.Whenprocessingdata,weconducteddeviationanalysisandpickoutoutliers.Figure10deviationanalysis1Figure11deviationanalysis2Thepicturessuggestthatthereisoneabnormalpointinpicture1andtwo Team#17696Page30of31abnormalpointsinpicture2,aftereliminatingthepointswebuildaregressionmodelagain.Andtheultimaterelationbetweentheincreasingpercentageofsprinkle/dripirrigationmethodandfreshwatersaveis:(5-6)Thecoefficientofdetermination0.9234Usingthesamemodel,onlychangethedependentvariable,wecanobtaintherelationbetweentheincreasingpercentageofsprinkle/dripirrigationmethodandthetotalcost:(5-7)Thecoefficientofdetermination0.8943Assumethegovernmentwillafford10%ofthetotalcost,theultimatecostwillbeexpressedasfollow:(5-8)lResultByaccessingrelevantinformationandthebuildingmathematicmodelsabove,wesummeduparelationshipamongtheincreaseofsprinkle/dripirrigationinagriculture,freshwatersavingandtheincreasingofcost.Table6Therelationamongagricultureimprovement,watersavingandcostTheincreaseofSprinkle/DripirrigationandpercentageinAgriculture（%）Theincreaseofthepercentageinfreshwatersaving（%）Theincreaseofcost（100million）12250056480010115200151565102018780025258900303095003534109625.1.3SavefreshwaterindomesticuseFreshwaterusedinhouseholdscanbeaffectedwithseveralfactorssuchaswaterprice,consciousnessofsavingwaterandtheapplyingofwater-savingdevice.WeemployedAnalyticHierarchyProcess(AHP)modeltofindtherelationsamongthecost,freshwatersavingandthefactorsthataffectdomesticwateruseand Team#17696Page30of31calculatetheweightsofeachfactor.lFirst,ajudgmentmatrixwasconstructed(5-9)ØThematrixconstructedisprettysubjective,soviabilitytestisnecessary.Solvingmatrixeigenvaluesandchoosethelargestoneasoneofthemedianofnextstep,theotheroneisthesizeofthematrix.ØDefineainconformitydegreeindex，toshowthejudgmentmatrixisrealistic.(5-10)Tothisproblem,thesizeofthematrixnis3.lSecond,defineaRandomConsistencyIndex，whichisonlyrelatedtothesizeofthejudgmentmatrix.Table7MeanofrandomconsistencyindexRIRandomconsistencyindexRIn234567891000.520.891.121.261.361.411.461.49Inthisproblem,0.52lThird,calculatetheproportionoftherandomconsistency.(5-11)Inthisproblem，CR=0.07718Thewayofjudgmentis:ifCR<0.1,thenthejudgmentmatrixissatisfactory,otherwisethejudgmentmatrixisunsatisfactory.DuetotheresultofCR,wecanseethejudgmentmatrixisacceptable.lFourth,calculatetheeigenvectorofthemaximizedeigenvalue.Standardizingtheeigenvectorandmakethesumofitscomponentsis1.Theultimatestandardizedeigenvectoriscalledweightvector: Team#17696Page30of31(6-12)Byaccessingrelevantinformationandthebuildingmathematicmodelsabove,wesummeduparelationshipamongthefactorsofdomesticwateruse,freshwatersavingandthecost.Table8Relationshipsofthefactorsofdomesticwateruse,freshwatersavingandcost.Thepercentageofwaterpricerising(%)Savingwaterconsciousness(%)Risingpercentofapplyingwater-savingdevice(%)Freshwatersaving(%)Cost(100million)Weight0.6874Weight0.1123Weight0.20031110,50.75551,63.31010102.75.41515153.37.62020203.510.32525254,212.43030305.015.63535355.617.3Thecostequationis:Cost=0.1123(savingwaterconscious)+0.2003(Risingpercentofapplyingwater-savingdevice)-0.6874(waterpricerising);Thefreshwatersavingequationis:Freshwatersaving=0.1123(savingwaterconscious)+0.2003(Risingpercentofapplyingwater-savingdevice)-0.6874(waterpricerising);5.2Increasethesourceoffreshwater5.2.1SeawaterdesalinationSeawaterdesalinationisaneffectivewaytoincreasethequantityofwatersource,anditisalsoastrategicchoicetosolvethelackoffreshwaterresources.ThelengthofChinesemainlandcoastlineismorethan18000kilometers,therearemorethan150coastalcitiesand6500islandsofwhichtheareasismorethan500squaremeters.ThisistheadvantagesofdevelopingseawaterdesalinationinChina[6]Desalinationtechnologydevelopment"12thFive-YearPlan".DuringChina's"Eleventhfiveyearsplan"period,thegrowthrateoftheannualcapacityofseawaterdesalinationismorethan60%,bytheendof2010,Chinabuilt Team#17696Page30of31morethan70setsofdesalinationdevices,thedesigningcapacityofdesalinationis600,000cubicmeters/day[7]"Thedevelopmentofdesalinationindustry"12thFive-YearPlan".Accordingtothedataabove,wepredictedthatthecapacityofdesalinationinChinawillincreaseby900%in2025,namely1.971cubickilometersfreshwaterwillbeproducedin2025.5.2.2TurnsewagetofreshwaterTherearemanywaystocleanuppollutedwater,butatpresentmostofthewaystodealwithsewageaimatdischargeinsteadofrecycling.Accordingtothedataoftheamountofsewageprocess,weassumedtheproportionofwatercanbeusedagain,sotheincreasingvolumeoffreshwatercanbepredictedinthefuture.Table9TherelationofsewageprocessingandcostandwaterpurificationinpastThepaperanalysisdataofpastandbuildDoubleExponentialSmoothingModel(DESM)topredicttheamountofwatercanbeusedagainfromsewage.YearsSeriesThecapacityofdailysewageprocessingincity（cubickilometers）Theincreasepercentageofwaterpurification%Thetotalofcost(100million）200310.66260.4200420.7387100.5200530.79897.50.5200640.973417.90.6200751.03365.80.7200861.11737.50.8200971.21848.30.9201081.339390.7201191.41419.20.82012101.56309.50.8Basedonthedataabove,weusedDESMtopredictthewateramount.， Team#17696Page30of31,(5-13)Whent=9,wecancalculatethevalueofaandb:a=13447,b=694.5906Thelineartrendequationis:(5-14)Inordertocalculatetheamountofwaterpurificationofeveryyear,weletTequalto1.(5-15)Usethisequationwefiguredouttheamountofannualsewagepurificationfrom2013to2025.Consideringthecostofthesewagewilldecreaseby3%eachyear,sotheequationis:（1+thepercentageofwaterpurification）(6-15)Table10ThepredictionoftheamountofannualsewagepurificationandcostYearsSeriesThecapacityofdailysewageprocessingincity（cubickilometers）Theincreasepercentageofpurification(%)Thetotalofcost（100million）2013111.783610.31.12014121.86124.40.32015132.098611.20.72016142.27468.31.02017152.33566.61.32018162.55675.21.42019172.67455.81.52020182.89026.01.62021193.10056.61.82022203.36786.01.92023213.65787.02.02024223.90007.42.12025234.26788.62.3Byaccessingrelevantinformationandbuildingmathematicmodelsabove,weknowthat6%ofthesewagetreatmentcanbeturnedintofreshwater.Accordingto Team#17696Page30of31China’s12thfive-yearplanandthedatapredictedbyourmodel,theamountofwaterturnedfromsewageis4.26780.25=1.0669cubickilometers.5.3Adjustthedistributionofwaterbothintimeandarea5.3.1WatertransfersLarge-scalewatertransfershavelongbeenadvocatedbyChineseplannersasasolutiontothecountry'swaterwoes.TheSouth-NorthWaterTransferProjectisbeingdevelopedprimarilytodivertwaterfromtheYangtzeRivertotheYellowRiverandBeijing.TheSouth–NorthWaterTransferProjectisamulti-decadeinfrastructureprojectofthePeople'sRepublicofChinatobetterutilizewaterresourcesavailabletoChina.ThisisbecauseheavilyindustrializedNorthernChinahasamuchlowerrainfallanditsriversarerunningdry.TheprojectincludesaWestern,aCentralandEasternroute.AllthreeroutesaimtodivertwaterfromtheYangtzeRivertotheYellowRiverandHaiRiver.TheeasternrouteusesthecourseoftheGrandCanal;thecentralrouteisfromtheupperreachesoftheHanRiver(atributaryofYangtzeRiver)toBeijingandTianjin;andthewesternrouteisinthewesternheadwatersoftheriverswheretheYangtzeRiverandtheYellowRiverareclosesttooneanother.Thisprojectwilldivert44.8billioncubicmeters/yearofwaterfromSouthtoNorth.TheideafortheSouth–NorthWaterTransferProjectoriginatedfromMaoZedongwhosaid,"Southernwaterisplentiful,northernwaterscarce.Ifatallpossible,borrowingsomewaterwouldbegood."Thecompleteprojectisexpectedtocost$62bn–morethantwiceasmuchastheThreeGorgesDam[8]"Thedevelopmentofdesalinationindustry"12thFive-YearPlan".Constructioncostsoftheeasternandcentralrouteswereestimatedtobe$37.44bnin2008.Thegovernmenthadbudgetedonly$7.9bn,lessthanaquarterofthetotalcost,atthattime,including26bnfromthecentralgovernmentandspecialaccounts,8bnfromlocalgovernmentsandalmost20bninloans.Asof2008,around30bnRMBhadbeenspentfortheconstructionoftheeastern(5.66bnRMB)andcentralroutes(24.82bnRMB).Costsoftheprojectshavesignificantlyincreased[9]"Waterconservation«Defra".defra.gov.uk.2013[lastupdate]..RetrievedJanuary24,2013.5.3.2ConservationWaterconservationencompassesthepolicies,strategiesandactivitiestomanagefreshwaterasasustainableresourcetoprotectthewaterenvironmentandtomeetcurrentandfuturehumandemand.Population,householdsizeandgrowthandaffluenceallaffecthowmuchwaterisused.Factorssuchasclimatechangewillincreasepressuresonnaturalwaterresourcesespeciallyinmanufacturingandagriculturalirrigation. Team#17696Page30of31Inimplementingwaterconservationprinciplesthereareanumberofkeyactivitiesthatmaybebeneficial.1.Anybeneficialreductioninwaterloss,useorwaste2.Avoidinganydamagetowaterquality.3.Improvingwatermanagementpracticesthatreduceorenhancethebeneficialuseofwater6.Evaluationofwaterstrategies6.1Principalcomponentanalysis(PCA)modelPrincipalcomponentanalysismodelisakindofmultivariatestatisticalanalysismethod,whichaimsatturningmultiplevariablesintolessnumberofthemainvariablesbythelineartransformation.Inanactualproject,inordertocomprehensivelyanalyzetheproblem,weoftenputforwardalotofrelatedvariables(orfactors),sinceeachvariablecanreflectsomeinformationofthesubjectindifferentextent.However,toomanyvariableswillincreasethecomplexityofthesubjectintoresearchingthemultivariatetopics.Peoplenaturallywanttogetmoreinformationfromlessvariablenumber.Inmanycases,thereisarelationshipbetweenvariables.Oncethereisacertaincorrelationbetweentwovariables,itcouldberegardedthatthetwovariableshascertainoverlapinreflectingtheinformationofthesubject.Principalcomponentanalysisisamethodthatestablishesnewvariablesasfewaspossibleofalloriginalvariables,andeachtwoofthenewvariableisnotrelatedtoeachother.Thesenewvariablesarerequiredtoreflecttheinformationofthetopicasmuchaspossible.6.2EvaluationofstrategiesbasedonPCAmodelAccordingtothebasictheoryofPCAmodel,weusedPCAmethodtochoosetheappropriatewaterstrategy.Afterselectingprincipalcomponent,summingupthescoreofprincipalcomponentbasedonitsvariancecontribution,weobtainedthecomprehensiveevaluationindexofdifferentstrategies,thenwecanchoosethemostappropriate(thebest)strategy.lDatastandardizationInordertoeliminatetheilleffectofdifferentofdimension,weneedtostandardizethedata.Assumingthatthenumberofsamplesintestingdataisn,thenumberofindexisp,namely.weorderthejindexvalueofsampleIis,when Team#17696Page30of31standardizingthedataitistransformedinto（j=1,2,3....,.p）(7-1)Thenwegotthestandardizeddamatrix:(7-2)Where，.(7-3)lCorrelationcoefficientmatrixInordertoeliminatetheilleffectofdifferentofdimension,weneedtostandardizethedata.Basedonthestandardizeddatamatrix:Wecancalculatethecorrelationcoefficientmatrixoforiginaldataindex.Where（i=1,2....n;j=1,2.....p）(7-4)lCalculatetheeigenvaluesofcorrelationcoefficientmatrixWecalculatedtheeigenvaluesofcorrelationcoefficientmatrixandsortthemfromhightolow,namely.Thencalculatedthecorrespondingorthonormalunitfeaturevector.,thentheprincipalcomponenticanbeexpressedasthelinearcombinationofeachindexes.。(7-5)lDeterminethenumberofprincipalcomponentsBeforethedeterminationofprincipalcomponentsnumber,weneedtogiveacontrolvalue Team#17696Page30of31Accordingtotheequation(7-6)Theminimumvalueofqthatsatisfiestheequationaboveisthereservednumbermofprincipalcomponents.Inthisproblem,wechoose=5%.lCalculatethecomprehensivescoreFirstlycalculatethescoreofthenumberkprincipalcomponentofthenumberisample，(7-7)Thenusethevariancecontributionsofthemprincipalcomponentsasweights,calculatethecomprehensivescoreofthenumberisample.(7-8)lSortDoasortofdifferentstrategiesaccordingtothecomprehensivescoreofeachsample,anddeterminethebestoption.Employthefunction“princomp”:[pc.score.latent,tsquare]=princomp(ingredients)Wheretheingredientsrepresenthestandardizedsampleindexmatrix,pcrepresentsthelinearcombinationcoefficientmatrixofeachprincipalcomponent,latentrepresentstheeigenvalueofvariance,tsquarerepresentsthestatisticalmagnitude.lApplyingthemodeltoourproblemuThestatisticalresultsamountofwatersavingareasfollows.Table11ThestatisticalresultoftheamountoffreshwatersavingIndexadjustmentrange(%)Watersavinginindustry(%)Watersavinginagriculture(%)Watersavinginhousehold(%)Watersavinginpurification(%)10.420,55.25161,65.8101.7112.76.0152.4153.36.6203.5183.56.0254.6254,27.0305.4305.07.4 Team#17696Page30of31356.2345.68.6uAfterdatastandardization,theresultsareasfollows.Table12ThestatisticalresultoftheamountoffreshwatersavingIndexadjustmentrange(%)Watersavinginindustry(%)Watersavinginagriculture(%)Watersavinginhousehold(%)Watersavinginpurification(%)10.06450.05880.08930.604650.16120.17640.28570.6744100.27410.32350.48210.6977150.38710.44120.58930.7674200.56450.52940.62500.6977250.74190.73530.75000.8139300.87090.88240.89290.8604351111uCorrelationcoefficientmatrixuDeterminethenumberofprincipalcomponentTable13PrincipalcomponentcontributionCharacteristicvalueContributionCalculationcontributionThefirstprincipalcomponent4.312164.84%64.84%Thesecondaryprincipalcomponent1.173917.65%82.49%Thethirdprincipalcomponent0.943114.18%96.67%Theforthprincipalcomponent0.22143.3%100%Fromthetablewecanseethecontributionoffirstthreeprincipalcomponentsis96.67%,thecontrolparameter.Sowechoosethefirstthreecomponentstoevaluatethedifferentstrategy.Accordingtothenormalizedunitfeaturedvectorcorrespondingwiththe Team#17696Page30of31eigenvalueofmatrixR,thelinearcombinationofthefirstthreeprincipalcomponentstoindexis:(7-9)Accordingtothelinearexpressionofcoefficientandsymbols，wecandrawconclusionbelow.ØThefirstprincipalcomponent：hasnegativecorrelationwith,andhaspositivecorrelationwithØThesecondprincipalcomponent:hasnegativecorrelationwith,,andhaspositivecorrelationwith.ØThethirdprincipalcomponent：hasnegativecorrelationwith,,,andhaspositivecorrelationwithuCalculatethecomprehensivescoreUsethevariancecontributionsofthemprincipalcomponentsasweights,andcalculatethecomprehensivescoreofdifferentdegrees.(7-10)Sincetherearetwofactorsinevaluatingthestrategies,sowebuildtwocomprehensiveevaluationmodels.Theresultsofevaluationofcostarelistedinthetable.(Thedatawerestandardizedby.Table14TherelationbetweendifferentindexesandcostSerialnumberIndexadjustmentrange(%)IncreasingcostinindustryIncreasingcostinagricultureIncreasingcostinhouseholdIncreasingcostinpurification110.0120.2280.0400.608250.0540.4370.1910.6523100.1320.4740.3120.695 Team#17696Page30of314150.2400.5940.4390.7835200.3670.7120.5930.8266250.5450.8120.7170.8697300.7500.8670.9020.913Table15Thecostofcomprehensiveevaluationranking8351111Indexadjustmentrange(%)ThefirstprincipalcomponentThesecondaryprincipalcomponentThethirdprincipalcomponentComprehensiveScoreComprehensiveranking10.2715-0.0307-0.54600.1005850.2832-0.1515-0.62710.06387100.3217-0.2886-0.68750.05566150.3435-0.4557-0.81910.02075200.3464-0.6627-0.9184-0.02874250.3135-0.8672-1.0444-0.10483300.3178-1.1242--1.1619-0.16482350.2468-1.3430-1.3727-0.28071Thehigherscoremeansthemorecost,sotherankingislower.Table16TheamountofsavingwatercomprehensiverankingUsethesamemethod,webuildthecomprehensiveevaluationmodeloffreshwatersaving.Indexadjustmentrange(%)ThefirstprincipalcomponentThesecondprincipalcomponentThethirdPrincipalcomponentComprehensiveScoreComprehensiveranking10.33180.0024-0.51760.1421150.3885-0.2181-0.61530.12622100.4006-0.4628-0.69100.08013150.3995-0.6196-0.81380.03434200.2596-0.7224-0.8620-0.09025250.2300-0.9870-1.0732-0.17736300.2172-1.1921-1.1858-0.23777350.2468-1.3430-1.3727-0.27178Thehigherscoremeansthemorewatersaving,sotherankingishigher.Basedonthemodelaboveweobtainedacomprehensivescoreoffreshwatersavingandcosts,theweightoffreshwatersavingis60%andtheweightofcostis40%,andtheequationis:Thefinalscore=-0.4thescoreofcost+0.6thescoreofsaving Team#17696Page30of31Thefinalscoreofdifferentstrategiesislistedinthetable.Table17thefinalscoreofdifferentstrategiesIndexadjustmentrange(%)ThescoreofcostThescoreofsavingThefinalscoreThefinalofrank10.10050.14210.0450250.06380.12620.05021100.05560.08010.02583150.02070.03430.0123420-0.0287-0.0902-0.065725-0.1048-0.1773-0.064630-0.1648-0.2377-0.076835-0.2807-0.2717-0.05056.3Whichstrategyisthebest?Wedividedthewaterstrategiesinto“Businessasusual,Governance,Strong,Atallcosts”.Accordingtotheresultofthecomprehensiveevaluationofdifferentstrategies,wecanseethatwhenthedegreeofadjustmentinindustrywhichincreasesthepercentoflowwaterconsumptionenterprisesthroughindustrialrestructureis20%,thestrategyscoreshighest;inthesameway,thebestpercentofadjustmentinagricultureis30%,thebestadjustmentdegreeindomesticis15%.Consideringallofthedegreesoftheadjustmentsindifferentfields,wechoosethe“Strong”strategywhichcanbesummedas:lTakestrongstepstoconductindustrialrestructure,decreasethehighfreshwaterconsumptionenterprisesby20%andatthesametimeincreasethelowfreshwaterenterpriseby25%whichcansavefreshwaterbyabout13.5%lImprovethemethodofirrigationinagriculture,andincreasetheuseofsprinkleranddripirrigationby30%before2015,whichcansavefreshwaterby25%.lIncreasethewaterpriceatanaverageby3%eachyear.lPromotethedesalinationtoincreasethesourcesoffreshwater.lPromotethesewagerecyclingindustry.lContinuedevelopingtheSouth-NorthWaterTransferProjecttoimprovethesituationoffreshwaterdistributeunevenlyinspace.lMaintaintheexistingreservoirstoimprovethewaterstorageandmovement. Team#17696Page30of31lPutemphasisonwaterconservationtomanagefreshwaterasasustainableresourcetoprotectthewaterenvironmentandtomeetcurrentandfuturehumandemand.7.StrengthsandWeaknesses7.1StrengthslBytheanalysisofthecurrentandformerfreshwateruseinChina,GrayModelwasemployedtopredictthedemandforfreshwaterin2025,whichisrelativelyprecise.Thepredictionsarebasedonbothareasandfields,whichismorecomprehensive.lManymathematicalmodelsandmethodshavebeenusedintheprocessofsolvingfreshwatershortageproblems,makingourwaterstrategymorerigorous.Manyfactorswhichhaveimpactonthefreshwaterhavebeentakenintoconsideration,suchasrainfall,storageandmovement,de-salinization,conservationandsoon,makingtheconsequenceoftheanalysismoreauthenticandthestrategymorefeasible.lThestrategychoicegivenwastheresultofroundlyconsiderationofthecostandefficiencybasedonPCA(PrincipalComponentAnalysis)model.Andtheevaluationofthemodelcangiveguidanceforadjustingandimprovingthewaterstrategy.7.2WeaknesseslWhenapplyingtheIndexsmoothingforecastingmethodtosolvetheproblemofsavingfreshwaterindifferentfields,themodelonlytakesCostastheKeyConstrainsFactoroftheimprovementapproachinfreshwatersaving,whichcanevaluatethefeasibilityofthestrategyinoneaspectbutcannothelpthegovernmenttoconsiderotherfactors.lDuringtheprocessofbuildingmodeltoevaluatethestrategiesandpredictthefreshwaterinfuture,somedataarenotavailable,soweBuildHypothesisbasedonsomecommonsense,whichmayaffecttheaccuracyofevaluatingandpredicting.8.Reference
