ForofficeuseonlyTeamControlNumberForofficeuseonlyT152766F1T2F2T3ProblemChosenF3T4F42016MCM/ICMSummarySheetInordertopredictthewaterscarcityandoptimizetheconfigurationreasonably,weanalyzethesituationofwaterscarcitybyestablishingamathematicalmodel,andproposethefeasiblesuggestionsonoptimization.Alltheworkisbasedonthesufficientdatawecollect.Firstly,thelocalsituationofwaterscarcityisestimatedbyintroducingthewaterlackingrateindex.Secondly,thelocalwaterconsumptionispredictedfrompersonalliving,industry,agricultureandecology.Meanwhile,thelocalwaterconsumptionispredictedthroughestablishingacompoundmodelwhichbasedonanimprovedLogisticModelandthestatisticalregressionanalysis.Thirdly,theGrayPredictionMetabolismModelisusedforpredictingtheamountoflocalwatersupply.Atlast,wecomprehensivelyanalyzetheexperimentalresults,andpredicttheabilityofwatersupplyinthislocalarea.Toverifytheavailabilityofthemodel,wechoosetheNorthChinaastheobjectofstudy.Weconcludethatthisareaisseriouslyscarcebefore2010onthebasisofmassdata.Thewaterscarcitywillsteadilyremitandreachbalaneein2025.ThisisduetoChinahasfinishedtheSouth-to-NorthWaterDiversionandtheNorthChinagainslargewaterresourcesfromoutside.Theresultscallinsidewiththetruth,sothemodelisreliable.ThenwetrytooptimizethewatersupplyinganddemandingstructureintheNorthChina,sothatitcanrealizetheinternalself-sufficiency.Weuseanalytichierarchyprocess(AHP)toassessthefourschemesofwaterstorage,watertransfer,wastewatertreatmentanddesalinationfromfouraspectsoftimeliness,sustainability,economic,environmentalbenefits,soamorescientificwatersupplyingsystemisdeveloped.Finally,bymeansofadjustingtheindustrialstructure,optimizingthemodeofagriculturalirrigationandimprovingthewaterconservationawarenessofcitizens,weproposeawaterresourcesallocationmodeltooptimizethewatersupplysystemintheNorthChina.Inthisway,thewaterscarcityintheNorthChinacanbesolvedfiveyearsaheadoftheoriginalschedule.KeywordsWaterscarcity;waterlackingrateindex;improvedLogisticModel; GrayPredictionWaterscarcity;waterlackingrateindex;improvedLogisticModel; GrayPrediction166Waterscarcity;waterlackingrateindex;improvedLogisticModel; GrayPredictionWaterscarcity;waterlackingrateindex;improvedLogisticModel; GrayPrediction166MetabolismModel;statisticalregression;analytichierarchyprocess(AHP)ContentsINTRODUCTION&BACKGROUNDSPROBLEMANALYSIS2.1ProblemRestatement2.2ProblemsolvingASSUMPTIONSNOTATIONSBASICMODEL5.1Modelofthewaterconsumption5.1.1CompoundpopulationModelbasedonLogisticModel5.1.2ModelofIndustrialwaterconsumption5.1.3Modeloftotalwaterconsumptionofaregion109.5.2ModeloftheGrayMetabolismModelGM(1,1)10PrincipieofcommonGrayGM(1,1)Model PrincipleofGrayMetabolismModelGM(1,1) [2]Accuracytesting 1012125.3Modelofwatersupplycapacityofaregion■14.5.4Strengths&Weakness,1.5....CHOOSEAREGIONTOANALYZE166.1Briefintroduction1.6....6.2Physicalscarcity:,Economicalscarcity:1877PREDICTIONMODELFORTHENORTHCHINA 19AAPPENDIX 5677PREDICTIONMODELFORTHENORTHCHINA 19AAPPENDIX 567.1ModelofwaterconsumptioninNorthChina.207.2WatersupplymodelintheNorthChina27.7.3ThecomprehensiveevaluationtothefuturewaterresourcesintheNorthChinaStrengthsandWeaknesses32…8OPTIMIZATIONOFWATERRESOURCESALLOCATION338.1OptimizationofwatersupplyallocationConstructthemodelofhierarchicalstructure338.1.2Constructionofcomparisonmatrixoftarget-criterionlayer.348.1.3Constructionofcomparisonmatrixcriterion-targetlayer.378.1.4Totalsortsofhierarchyandconsistencycheck428.1.5Interpretationofresult438.2Optimizationofwaterconsumptionallocation478.2.1Constructionofwaterresourcesallocationmodel478.2.2Mainconstraintequations488.2.3ModelSolution50CONCLUSIONS53FURTHERDISCUSSIONS54REFERENCE55StrategyofConqueringThirstWatersupplymoduleismainiy composed ofsurfacewaterandWatersupplymoduleismainiy composed ofsurfacewaterandIntroduction&BackgroundsAneffectiveplanofsolvingthewaterscarcityproblemiscrucialtohumansociety.AccordingtotheUnitedNations,todaymorethanonebillion peoplelackaccesstosafe,cleandrinkingwater,andjust10countriesshare60percentoftheworld'snatural,renewablewaterresources;what'smore,waterusehasbeengrowingattwicetherateofpopulationoverthelastcentury.Amodelofwaterscarcityoftheworldshowstheserioussituation.(SeeFigure1)Figure1:themapoftheworld'swaterscarcityAtthesametime,oursocietalandeconomicgrowthislargelydrivenbytheproductiveuseofwater.Actually,theworldtripleditswateruseinthelast50yearsalone.Ourworldpopulationisincreasing,yetwestillshareonewaterresource-andit'slimited.Ifwe'regoingtomeettheagricultural,industrialandresidential needsofthisgrowing world,wemustuseourwaterineffective,efficientways.ProblemAnalysisProblemRestatementDevelopamodelthatprovidesameasureoftheabilitythataregioncabprovidecleanwatertomeettheneedsofitspopulation.Doingallthisworkwithconsideringthedynamicnatureofthefactorsthataffectbothsupplyanddemand.Pickonecountryorregionwherewateriseitherheavilyormoderatelyoverloaded. Explainwhyandhowwaterisscarceinthatregion.Showwhatthewatersituationwillbein15years,andpredicthowthissituation impactthelivesofcitizens ofthisregion.Designanintervention plantakingallthedriversofwaterscarcityintoaccountaccordingtothesituation,tohelpwiththewaterscarcityandoptimizingthemodel.Estimatetheoptimizedmodelandpredicttheresults.ProblemsolvingWeaddresstheproblemofoptimizingwateruseofaregionthroughanalyzingthewatersituation,whichprovidesameasureoftheabilityofaregiontoprovidecleanwatertomeettheneedsofitspopulation.Themodelconsistsoftwobigmodules:watersupplyandwaterconsumption.groundwater,thedegreeofenvironmentaigovernance,storagecapacity.precipitation,etc.Watermoduleismainlycomposedofpersonallivingwater,agriculturalwater,industrialwaterandecologicalwateruse,etc.Finallywecomparethemodelofwatersupplywiththemodelofwaterconsumption, thentakeacertainevaluation indextomeasuretheregion'swatersupplycapacity.Next,sincetheregionofNorthChina(includeBeijing,Tianjin,Hebei,Shanxi,InnerMongolia)meetstherequirement ofbeingheavilyormoderatelyoverloadedonusingwater,wechoosetheNorthChinaastheresearchingregion.Weexplainthesocialandenvironmentalreasonsofthescarcityfromphysicalandeconomical sides,todissectwhatfactsimpactthewaterscarcity.Thenwemakequantitativeandqualitative analysisofthewatersupplyandconsumptioninthisregion,togetwhatthecharacteristicsofthesituationin15years.Atlast,accordingtothefourthandfifthquestion,weoptimizethemodelfromimprovingwatersupplyandreducingwaterconsumption,tosolvetheproblemofwatershortage.Weconsideraboutimprovingthewatersupplybytheconstruction ofreservoirs,waterdiversionworks,waterdesalination, wastewatertreatment,andpolitical,economicandsocialconsiderations. Ontheotherside,wereducethewaterconsumptionfromraisingawarenessaboutsavingwaterandimprovingagriculturalirrigationmethods,adjustingthestructureofindustrialwater,improvingecologicalaspectstoconsiderautonomyability.Thenundertheoptimizationofwatersupplyandwaterconsumption wesetupawaterallocationoptimizationmodel,whichisusedforexploitationandutilizationplanningofwaterresources,meanwhilepredictthesituationofwaterresourcesusinginthefuture.Assumptions☆gnoretheimpactsoftheextremedisasters.☆gnoretheimpactsofthemigrationofpopulation.☆ignoretheadministration costinlateperiodofwaterdiversionproject☆gnoretheeffectsoftheotherpollutingfactorsinthewastewaterwhenconsideraboutthepolluteddegree.☆gnorethetransportationcostofthewatersupplywhenconsiderabouttheseawaterdesalination.N(t)islargeenough.N(t)islargeenough.☆Weassumethatthereisnobigrevolutionintheconfigurationofwatersupply.Notations

Table1:NotationsandDescriptionsNotationsDescriptionsttimeunitN(t)Grosspopulationoftime tN(t0)Grosspopulationoftimet0MAllowedmaxpopulationinaregionaNaturalpopulationgrowthrateP(t)tPopulationnetgrowthrateoftimePCoefficientoflifeSRelativestandarddeviationWWaterconsumptionpercapitaA(t)GrossofthepersonalwaterconsumptionuWaterlackingrateU()UpstreamcollectionofobjectsXZTLSewagewaterbacktotheremainingamountXRSVReservoircapacityofthesurfacewaterPZBC1Agriculturalproductionfunctioncoefficient

XZGOLateralgroundwaterrunoffPZGUGroundwaterminingupperlimitPRSFInflowPCSDChannelofwaterproportionPZWERiverecologicalwaterrequirementPNSFAttheendoftheriverchannelcontrolinflowXZGOLateralgroundwaterrunoffPZGUGroundwaterminingupperlimitPRSFInflowPCSDChannelofwaterproportionPZWERiverecologicalwaterrequirementPNSFAttheendoftheriverchannelcontrolinflowXCSOThedodger'sriverwateramountXCSOBasicmodelModelofthewaterconsumptionThewaterconsumption ofoneregionmainlyconsistsofpersonalconsumption,agriculturalconsumption,industrialconsumptionecologicalconsumption andetc.Andtheagricultural consumptionindustrial consumption changeswiththeenvironment changing,populationincreasing,andeconomicsdeveloping.Thereforeweneedtodevelopmathematicalmodelforthefourfactstoresearch.Personalconsumptionreferstoasinglepersonusewatertodrink,Modelbasedonbathandsoonfordailylife.ModelbasedonCompound populationLogisticModel

LogisticModelfitsforcontinuouspopulationgrowth,butalsocanappearnegativegrowthinsomecountries.Weestablishacompoundpopulation modelbasedonLogisticModel,thenbuildthemodelofpopulationnetgrowthrateinone-placelinear,byresearchingthelawofpopulationgrowth.AccordingtoLogisticModel,themodelofthepopulation growthratecanexpressastheinitialvalueproblemofdifferentialequationdN(t)N(t0)N。N(t)N(t)(1)PostulateN(t) P(t)LogisticModelfitsforcontinuouspopulationgrowth,butalsocanappearnegativegrowthinsomecountries.Weestablishacompoundpopulation modelbasedonLogisticModel,thenbuildthemodelofpopulationnetgrowthrateinone-placelinear,byresearchingthelawofpopulationgrowth.AccordingtoLogisticModel,themodelofthepopulation growthratecanexpressastheinitialvalueproblemofdifferentialequationdN(t)N(t0)N。N(t)N(t)(1)PostulateN(t) P(t),and P(t)denotesthepopulation netgrowthrate,denotesthenatural populationgrowthrate,denotesthecoefficientoflife,N(t)denotesthegrosspopulation,N(t0)denotesthegrosspopulationofinitialtime.Formula(1)representsaninitialvalueproblemsofBernoulliequation,and.Thusevenifandwecanobtainthesolution.However,duetothelimiteddatainformation,wecannotconfirmtheparameterswehaveobtainedthesolutions,itmadenocontributiontopredictthegrossofpopulation.Thereforeweassumethatthepopulationnetgrowthratehaslinearrelationshipwithtime;thatisthemodelofthepopulationnetgrowthrate:and.ThusevenifPtatba,bareuncertainconstant.Theresultsofamultiply bislessthan

zero.Puttingequation (2)intoequation(1),wecangetthemodelthatreflectsthegrossofthepopulation.詈(atb)N(t)N(to)NoBysolvingtheinitialvalueofthedifferentialequationproblem,wecangetthecompositemodelofpopulationgrowth:N(t)N。expbto01 expbtN(t)N。0 22Inthisdifferentialequation,guessing蛭atb

dtNt,becauseNtisgreaterthanzero,tb一becomestheonlystablepointofafunction Nt,thenwedrawbtheconclusion thatwhent-,Ntagetsthemaximumabsolutevaluepoint.Inthisdifferentialequation,guessing蛭atb

dtNt,becauseNtisgreaterthanzero,tb一becomestheonlystablepointofafunction Nt,thenwedrawbtheconclusion thatwhent-,Ntagetsthemaximumabsolutevaluepoint.Whenconstantaislessthanzero,andconstant bisgreaterthanzero,wegetNtisamonotonicincreasing functionin0上,andaamonotonicdecreasing functionbin——asoachievesthemaximumvalueN—whenaNtisabNtisat—;Whenaisgreaterthanzero,andbislessthanzero,amonotonicdecreasingfunctionin0,丄,andamonotonicincreasingai1 i1i1 i1i1 i1i1 i1function inbfunction in,soNtachievestheminimumvalueN——abwhent 一aSincethegrossofpersonalwaterconsumptionSincethegrossofpersonalwaterconsumptionA(t)W*N(t),thenofthegrossofpersonalwaterweput(4)intoit,wegettheequationconsumption:ofthegrossofpersonalwaterAtWNqexp bt0述expbtof225.1.2ModelofIndustrialwaterconsumptionAccordingtothenationalindustrial waterconsumptionstatisticsfromvariouscountries,thevaluepresentsalineartrend.WedeterminetheindustrialwaterconsumptionB(t)throughlinearfitting.Weuseleastsquaremethodforfitting.Themethodmakesparametert2Qinfunction QYabXireachestheminimumvalue.aandi1barecalledtheLeastsquaresestimators.Duetothenecessaryconditionoftheextremuminthecalculus,weobtainaandb:dQ

daabXidQ

dbt2 Yii1bXiXi0XiXiXYi1t—2XiXXiXYKi1b1 t 一2Xi XaYbXB(t).B(t).fittheindustrialwaterconsumption5.1.3Modeloftotalwaterconsumptionofa5.1.3ModeloftotalwaterconsumptionofaregionSinceitisthesamefortheagriculturalconsumptionC(t)andecological consumptionD(t)tocalculateasitdoesinindustrialconsumption B(t)SinceitisthesamefortheagriculturalconsumptionC(t)andecological consumptionD(t)tocalculateasitdoesinindustrialconsumption B(t),wecandeterminethemodeloftotalwaterconsumption. Basedonthemodelofpersonalconsumption, industrialE(t)consumption,agriculturalconsumption,andecologicalconsumption,wecandeterminethemodeloftotalwaterconsumptionofaregionasfollows:E(t)t2 t2E(t)W*N0E(t)W*N0*exp[(bt。5.2ModeloftheGrayMetabolismModel5.2ModeloftheGrayMetabolismModelGM(1,1)Principleofcommon

GrayGM(1,1)ModelGraySystemtheoryholdstheviewthatalltherandomquantitiesaregrayvariablesandprocesswithincertainrangeandtimeinterval.Themodelisestablishedafterprocessingthesedataincertainwaysandrankingintoregulartimeseries.,itisfitforpredictionGraySystemPredictionModelGM(1,1)rankingintoregulartimeseries.,itisfitforpredictiontothedevelopmentofsystematicbehavioreigenvalue. GraySystemPredictionModelGM(1,1)producesrandomnumberandtransformsthemintoordereddata,andthenestablishesdifferentialequation,later.itseeksfortheregulation ofproducingthedataandthenrestoretheoperatingresults.Thespecificstepsarefollowing:Weaccumulatethevariablex(0) {x(0)(1),x(0)(2),L,x(0)(N)}togetx(1){X⑴(1),x⑴(2),L,x(1)(N)}hereinto,wegetX⑴(t)tx(0)(i)X⑴(t1),(t 1,2,...,n).iSowecanestablishadifferentialequationintheformofanalbinoasfellow:dxiax(1)udtThebleaching solution ofdifferentialequation areasfollows(disperseresponse):x(1)(t) [x(0)(1)u]ea(ta1)uaParameterkdenotestimeseries,canbeyear,seasonormonth.aMarkparametersequencesas U,UbWeobtainUfromtheseequations:Ub? (BTB)1BTyWhileBrepresentsdatamatrix,ydenotesdatacolumn.x(0)(2)y X(0)(3)Mx(0)x(0)(2)y X(0)(3)Mx(0)(N)GMModelisforonce,anditisthepredictedvaluewhen t{n1,n2,...},wemustrestoretheobtaineddata ?(1)(t1)(or小⑴)to曲(t1)(or?(0)(t))through repeatedlyminuswithdetermining(I—AGO):t爐(i)i101)(t)x(1)(k)；[x⑴(2)X⑴⑴]12[x(1)(3)0(2)] 1M 11[x⑴(N)X⑴(N1)]1Becausewegetcumulativeamountby0(1)爐0(1)爐"“(t0,1,2,...).,itSince0)(t1) X(0)(i),weget0)(t1)5.2.2Principleof GrayMetabolismModelGM(1,1)[2]Aftermakingagraypredictionandgettingthelatestinformationaddsthisinformationintotheoriginaldataseriesandwipesofftheoldestinformationatthesametime. Then,usingthenewoneasoriginalseries,itrepeatstheabovestep1.1tosetupGM(1,1)Model,soonandsoforth,untilthefulfillmentofallthepredictionobjectives,andthatistheGrayMetabolismModel wewanted。Accuracytesting

Relativeerrorandposterior differeneeratioCaretwomostcommonlyusedwaytotestthemodel,anditsbasicprocessisfollowing:x(0)isoriginalseries,?(0)istheseriessimulatedbyGMModelandisresidualsequenee。Withinitis(t)x(0)(t)?(0)(t),therelativeerrorsequeneeisp1 ,andthusthetotalwaterresourceamountinyearn)couldbeobtained. Hereintowehaveandtisthesimulatedrelativeerrorofthepoint,andkistheaverageyearn)couldbeobtained. Hereintowehaveandtisthesimulatedrelativeerrorofthepoint,andkistheaveragerelativeerror.p1isdefinedasthepredictionaccuracy,whichisdisplayedinpercentage.S1S2J(xS2J(x(0)(t)X(0))2一(0)xx(0)(k)n；S；S2isthemeanvarianeeTable2:WhereS1isthemeanvarianeeofresidualoforiginalseries;Cistheposteriordiffereneeratio.Hereisarefereneetableattachedthatillustratesthemodelaccuracyclassificationindetails:TheaccuracyofthemodelAccuracyofmodelRelativeerror/%AveragerelativeValueofCaccuracy(p,%)Firstclass1950.35Secondclass580p950.35C0.5Thirdclass1070p800.5C0.65disqualification20700.65Thus,themethodofpredictingwaterresourceamountinoneplaceandcheckingtheaccuracycouldbegained.Modelofwatersupplycapacity ofaModelofwatersupplycapacity ofaregionWedefinewaterscarcityF(t)regionWedefinewaterscarcityF(t)as:FtYtWN0expat2FtYtWN0expat2bt0—- exp2bt手BtCtDt[3][3],weleadinvariableInordertoestimatethesituationoftheregionwaterlackingrateu:uM*100%E(t)Formeasuringthedegreeofwaterlackinginthisregion,weset4thlevelevaluationonthebasisofwatershortagerateuthestandardseetable3:Table3:TheclassificatorystandardScarceshortageMainproblemssituationrate

Sufficient<5AchievesthebalaneebetweensupplyanddemandofwaterresourcesLight5~10Normalyearsinbalanee,butintheaverageyear,thewatersupplymayoccur.Middle10~20Notonlyindesignlevelyearofwatershortageoccurs,alsoinnormaltimesHeavy>20Watersupplygapisextremelyserious.WadingactivitiesareseverelyrestrictedStrengths&WeaknessStrengths☆Itovercomesthetraditional methodontheforecastingwatersupply,facingtheproblems oftheshortageofsamples,difficultimpiementationandhighrequirement.☆Inthepredictionprocess,wecanweedouttheolddataandaddnewdataconstantly,maintainingthehigherpredictionprecision.☆ItmakesupthesituationofLogisticpopulationgrowsnegatively.☆Themodelisfitformanyareas.☆themodelsofindustry,agriculture,ecologicalwaterconsumptionareconcludedfromthechangerules,aresufficientinscientificnature.Weakness☆Without considering theuncertaintyofsocialdevelopment,themodelnotalwaysreflectsthefuturewaterresourcescondition.☆Themodelcanonlybeusedoveraperiodoftimeforprediction.Itislimitedforextremeconditions.☆themodelsofthesubsystemmaynotformalinearrelationshipinvariouscountries,uniessthesituationisclosetoChina.ChoosearegiontoanalyzeInadditiontothemodel,wealsochoosetheregionofNorthChinatoanalyze.BriefintroductionTheNorthChinaisanimportantpartoftheGreatPlainsintheeastofChina,whichlocatedatnorthlatitude32°?40°andintheeastIongitude114 °T21〔NorthChina'sborderisverylarge.TheborderofnorthisthesouthofYanMountains.ThesouthernborderisonthenorthsideoftheDabieMountains.ThewesternboundaryinTaihangtotheFuniuMountainAdjacenttotheEastistheBohaiSeaandtheYellowSea,alsowithatotalareaof300thousandsquarekilometers.Plainhastoo

muchadvantagesuchasflatterrain,manyrivers,convenienttransportationandadvaneedeconomy.Fromancienttimestothepresent.NorthChinaisthecenterofChinaintheeconomy,politicsandculture(seearea.Andalso,Beijing,thecapitalofChina,isinitsnorthernpart.(seeFigure2)Figure2:theregioninredcurveisthechosenarea.NorthChinaisoneofthemostwater-lackingareaofthenation,withonly6%gross、11%percapitaoftheaveragelevel.Whyitisscarceinwater,andhow?Weconclude thereasonsfromthephysicalandeconomicaspects,includingsocialandenvironmentalobjects.Physicalscarcity:Theamountsofthewaterresourcesispoor.Theregionisalluvialplain,andlackedofriversandlakes.What'smore,thevegetationcoverageisnotenough,therainfallflowsawaywiththesolid.Thusthewaterconservationispoor.Formanyyears,Waterresourcespercapitaaveragevolumeis335cubicmeters,reachesnearly15%ofthenationalpercapita.Waterresourcesareunevendistributedoftimeandspace.Annually,itmainlyperformsintheeventofawetyearanddryyearphenomenon;withinoneyear,mainIyinsummerandautumn,theprecipitationandwaterresourcesquantityismore,whilelessrainfallinwinterandspring.Theunevendistributionofwaterresourcesinspacemainiyreflectthatthewaterresourcesquantitychangewithzonalandsurfaceevaporationisunevendistribution.Thisregionbelongstomonsoonclimateofmediumlatitudes,therainfalliscomparativelyscarce.Theseaboveareenvironmentalcauses.Thehugepopulationandgiantconsumptions.Theplainpopulationaccountsforabout20%ofthetotalpopulation,withonly6%gross15%percapitaoftheaveragelevel.Theurbanizationanddevelopingeconomicsincreasethedemandofwaterinunitarea.Andthisobviouslystressthewatersupplying.Theseabovearesocialcauses.6.3Economicalscarcity:Seriouspollution andwaste,wastewater treatment rateislow.Industrialdevelopmentandpopularizationofvariouskindsofagriculturalchemicalsleadstoseriouspollution. SetanexampleDeterioration ofwaterqualityisanimportantfactofwatershortageinnorthChina.SuchastheYongdingRiverupstreamoftheGuanTingreservoirinBeijing.becauseoftheseriouspollutionofwaterupstreamreservoirhaslostthefunctionofwatersupply,addingtothewatershortagesituationinBeijing.What'smore,sewagetreatmentcapacityintheregionisnotdifferent,BeijingandTianjinmunicipalwastewatertreatmentrateishigher,whileotherurbanwastewatertreatmentrateislow.Humanactivities.Ontheonehand,thedevelopmentandutilizationofwaterresources,andontheotherhand,ischaracterizedbytheinflueneeoflanduse.Duetotheshortageofwaterresourcesandtheyhavetoexcessiveexploitationofgroundwater.Theregionexploit54.78%oftheamountofthegroundwaterinChina.Urbanizationcausedrainfallinfiltration togroundwaterrecharge,andexpandingagriculturalirrigationarea,increasethewaterevaporationconsumption.Thequantityofsurfacewaterandgroundwaterinthenaturalsystemgreatlyreduced—thisformsaviciouscircleinobtainingwater.PredictionmodelfortheNorthChina

Accordingtothemodeloftask1andthedatastatistics,whichusedtoexpresswatersupplyinNorthChina,intask2.Respectively.Themodelofwaterconsumptionandwatersupplywerecalculated.7.1ModelofwaterconsumptioninNorthChina.Table4:thetotalpopulationfrom2008to2014intheNorthChina⑷(unit:thousand)SequenceYearPopulationIncreaseGrowthrateperannum120081334702200913549020200.0151344873201014029048000.0354269694201114208017900.0127592845201214381017300.0121762396201314550016900.0117516177201414701015100.010378007

Figure3: annualaveragegrowthratescatteredpointsFigure3: annualaveragegrowthratescatteredpointsFromFigure3onecanseethattheaveragepopulationgrowthrateislinearwithtime,italsoverifiestheaveragepopulationgrowthrateislinearwithtimeinthetask1.Butin2010therewasanoutlierpoint,whichmayberelatedtothepolicy,economicandsocial.Wecouldexcludethepointwithoutaffectingtheoveralltrendofpopulation.Bythetask1,weknowtheaverageannualgrowthratemodelPtatb(t1,2 .14),whichmeanswhentequals1,itrepresentsyear2008.AccordingtothecensusofNorthChina,wecouldbederivedfromthepopulationaverageannualgrowthrateofcloseto1.Modelfitswell.UsingthesoftwareMatlab,weget0.000734,b0.017604.Thereforetheaverageannualgrowthrateof population is:Pt0.000734t0.017604UsingthesoftwareMatlab,weget0.000734,b0.017604.Thereforetheaverageannualgrowthrateof population is:Pt0.000734t0.017604Theapproximatecoefficient is0.9729whichThefittingresultsareshowninFigure4.

2呂4t/yearBT62呂4t/yearBT6G43Ti----Figure4:AnnualaveragegrowthrateofpopulationThefittingresultscouldgiveusthefactthattheannualaveragegrowthrateofpopulationPresentedanegativecorrelationwithtime,ontheotherhand,thegrowthofthepopulationinNorthChinawillbemoreslower,eventhereiszerogrowthatsometime.ThishasagreatrelationshipwiththelongtermfamilyplanninginChina.Puta0.000734,b0.017604intothecomplexmodel(4),wegetthemodelofpopulationgrowthintheNorthChina.N(t)N。exp 0.017604。 ^00073'。 exp0.017604 0.000734t-2Choosetheinitialcondition N(17)147010,therefore20.000734t2N(t)147010exp(1.043)exp0.017604t 2Sincea0.000734 0,b 0.017604 0,weobtainthemaxvalueofbN(t)whent-24.Thisrepresentsthatthepopulationofthe