完整版数模美赛08年A题.docx
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完整版数模美赛08年A题.docx
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完整版数模美赛08年A题
Abstract
Theglobaltemperatureisrisingrapidlytodaywhichhascausedanextensiveicemelt,sothestudyofpredictingrisingsealevelbecauseoficemeltinNorthPolarisessential.OurstudywilltrytopredicttheimpacttoFloridafrommeltingiceinNorthPolar.Ourstudieshavethreesteps:
●Predictthetemperature:
WedidthepredictionbyNeuralnetworkandgivethechangeoftemperaturein50years,basedonalargeamountofdatafromtheIntergovernmentalPanelonClimateChange(IPCC);
●Modelthemassoficemeltingandthesealevel:
ThesealevelmodelismainlybasedontheprincipleofThermodynamicsanditeration.Theresultsdemonstratethatthesealevelwillriseby10.8cmtotallyin50years.PredictionofourmodelcanbeprovedtobecrediblebyconsultingthedatafromIPCC.Weintroduceacorrectterm
tomodifyourmodel.Wecanchange
tosimulatesealevelriseindifferenttemperaturecondition.
●AnalyzetheimpactstoFlorida:
WemodeltheerosionofFlorida’sshorelinetomakeitclearthatwhensealevelrisetoacertainextentthatFloridawillfacemanyseriousproblemssuchasflooding,destructionofbiodiversity,(HealthCare),Lossofagricultureproduction(salinizationofsoil)andsoonoverthenext50years..Wefindthe17citiesorareasand15airportswhichareseverelyimpactedbytheriseofsealevel.
(Basedonourresults,)Withoutattachingmoreimportancetosolvingtheproblem,shorelineofseveralcoastalcitieslikeMiamiwillbeerodedseriously,andthelowestplace
KeyWestwillbedisappeared.Itwillcostahugefinancialloss,sofurtherprotectionshouldbeputintoplace.
Introduction
Background
GlobalWarmingandsealevelrise
“Airtemperaturesatthetopoftheworldcontinuetorisetwiceasfastastemperaturesinlowerlatitudes,causingsignificanticemeltonlandandsea”[Fears,December17,2014].Oneoftheseriousconsequencesisthatsealevelwillrise.Globalaveragesea-levelroseatanaveragerateofabout3.1[2.4to3.8]mmperyearfrom1993to2003[IPCC].Thisinformationsuggeststhatfrom1993to2003thesea-levelriseby3.1cmtotally.
Ourwork
Thequestionrequiresustopredictthenext50years’conditionoficemeltingandanalyzetheeffectsontheFlorida,especiallysomebigcities.Sowecanseparatethisquestionintotwoparts:
●Howmuchandhowfastwilltheseelevelrisewithin50years?
●WhataretheeffectsontheFloridabecauseoftheriseofsealevel,especiallysomebigcities?
Studyobject:
IcecapinGreenland
ArcticmainlyconsistsofGreenland,whichoccupiesabout9%glaciersallovertheworld.MeltinginArcticismainlyduetoGreenland,meltingoffloatingicecanbeignored.SowecanconsiderGreenlandasstudyobject.
Modelingthesealevel
Wedevelopamodelforsea-levelriseasthefunctionoftime.Thismodelcanpredictsea-levelriseinfuture.
AnalysisofFlorida
Afterhavingcalculatedtheincreasedsealevelwithinnext50years,weanalyzetheimpacttotheFlorida.
●Risingsealevelcanseriouslythreatenthedevelopmentofcities.Ithasbeenthreateningsomeislandsandcoastalcities.Overthenext18years,abouttwothirdsamong544Americantownswillbetwiceaslikelytofacefloods[Huang].Morefrequencyhurricanewillhappen.
●Seawaterwillcorrodeseacoast.
●Alargequantityofdrinkingwaterwillbepolluted.
Assumption
●SealevelriseisprimarilyduetothemeltingoficecapinGreenLand.WeignoretheotherfloatingiceintheNorthernPolar.
●Theincrementofseawaterfrommeltingwillflowovertheoceansuniformly
●Saltintheicewillnotaffectstheprocedureofmelting.
ModelⅠ:
TemperaturePrediction
GreyPredictionModel:
Theweaknessofthegreypredictionisthattheresultisincreasingallthetime.Inotherwords,itcannotshowthechangesindetail.
NeuralNetworkpredictionModel:
ModelⅡ:
Meltingiceandtheriseofsealevel
Modeltheriseofsealevel
Themainreasonofthesealevelrisingisthemeltingoficecapandthemassofmeltingiceisequaltothemassofseawatergeneratedfrommelting.So,basedonseveralphysicalprinciples,wemodeltheriseofsealevelbycalculatingthemassofmeltingice.Weassumethattheincrementofseawaterfrommeltingwillflowovertheworlduniformly,whichmeansthemeltingicewillcontributetotheriseofsealevel,dividedbytheareaoftheocean.
Theincrementofseawaterfrommeltingice
Thetotalvolumeofmeltingicecap
Thetotalvolumeofwatergeneratedfrommelting
Thesealevelrise
Theoveralloceanarea:
361745300km2,thisis71percentofearth’stotalsurfacearea(Wikipedia).
Heatfromriseoftemperature:
Accordingtotheprincipleofthermaltransmission,heatwillalwaysbetransmittedfromhightemperaturetolowtemperature.So,thefinalstateofstuffinthethermalcyclingsystemwillreachtoasametemperature.So,weassumethatthetemperatureofthewholeicecapwillincreaseby
whentheworldtemperatureriseby
However,ittakestimefortheicecaptotransmittheheatfromtherisetemperature.Weusethe
everymonthtocalculatetheincreaseofmeltingiceineachmonthandgetthetotalincrementbyaccumulation,whichmeanspartsoftheheatfromtemperaturewillbeabsorbedandusedtomeltice.So,definingacoefficient
andwewillhavetheheatwhichicecapabsorbsfromtherisingtemperatureinthen-thmonth:
Theheatcomesfromrisesoftemperatureinthen-thmonth
Thecoefficientofcapacityofabsorbingheatinonemonth
Thespecificheatcapacityofice
Themassofthewholeicecap
Themassofmeltingiceinthen-thmonth
Thechangeoftemperatureinthen-thmonth
Wetrytofindthe
bycalculatingthemassofmeltingiceinknownyears.“RecentlyreportedGrISmassbalancevariesfromnear-balancetomodestmasslosses[47to97gigatons(Gt)year−1]inthe1990s,increasingtoamasslossof267±38Gtyear−1in2007”(Michiel).
Massofmeltingice:
Themassofmeltingiceinthismonthwilldependsonnotonlytherisingtemperature,butalsothemassofmeltingiceinthelastmonth.Wedividetheheatabsorbedbytheicebythemeltingenthalpyoffusionforwatertoobtainthemassofextrameltingiceresultedfromtheriseoftemperatureinthismonth.
Themassofmeltingiceinthen-thmonth
△fusHθm:
Themeltingenthalpy
Thetotalmassofmeltingiceinthenextkyears
Moreover,“Since2006,highsummermeltrateshaveincreasedGreenlandicesheetmasslossto273gigatonsperyear”(PartitioningRecentMassLoss).Andtheinitialmassofmeltingiceinthefirstmonthwillbecalculatedasfollows:
:
Themassofmeltingiceintheinitialyear.
Thetotalriseofsealevelinthenextkyears
DesignofAlgorithms:
Sincewehavethefunction
weareabletocalculatethemassofmeltingiceinthenextnmonthsusingcomputerprogramwiththedataoftemperaturesandtheinitialamountofmeltingiceinthefirstmonth.
Thisiseasytoachieveusingtwolineararrays
and
inMATLAB.Runasimpleforloopfrom2tonandcalculate
duringeachpasssothatthewhole
arraycanbefound.
Sothatthetotalamountofmeltingiceatn-thmonthisthesummationfrom
to
.Alsothetotalriseofsealevelcanbeeasilyfound.
ModelResults:
Sealevelwillelevateby10centimetersin50years
Thesolutionswerecodedusingmatlab:
Figure1:
Themassofmeltingiceinthenext50years
Figure2:
Theriseofsealevelinthenext50years
Thepredictionaboutriseofsealeveleverydecadeinnext50years:
Validationofourmodel:
Theresultsshowthatthesealevelwillelevatebyapproximately10centimeterstotallyand2millimeters/yr,whichaccordwiththepredictioninRelativeMeanSeaLeveltrendsfromNOAA.
Moreover,ifwecalculatedtheriseofsealevelwithoutconsideringtheincreaseoftemperature,whichmeanssealevelriseattheratetodayinthenext50years,theorderofmagnitudesismatchupwithourresult.So,basedontheanalysisabove,theresultsofourmodel
ModelⅢAnalysis:
TheeffectstowardsFlorida
Basedonourresults,thesealevelwillrise10centimetersinthefollowing50years,whichthreatenFloridainthefutureandresultintremendousimpacts.“Some2.4millionpeopleand1.3millionhomes,nearlyhalftherisknationwide,sitwithin4feetofthelocalhightideline.SealevelriseismorethandoublingtheriskofastormsurgeatthislevelinSouthFlorida.”(Floridaandrisingsea)
Figure3thealtitudesofFlorida()
Aswecanseefromthispicture,mostcitiesorcountiesinthesouthernFloridaliebesidesthecoast.Statisticsuggeststhat17countieswithaltitudessmallerthan3feetwillbethreatenedbytheriseofsealevelin50years.Thecountiesandairportswhichwillbeinvolvedarelistedasfollows:
Cities:
Miami,Homestead,FortLauderdale,WestPalmBeach,Titusville,StAugustine,Clearwater,StPetersburg,Tampa,Brandon,Bradenton,PortCharlotte,CapeCoral,BonitaSprings,Naples,MarcoIsland,andGrandIsle.
Airports:
MiamiInternationalAirport,FortLauderdaleInternationalAirport,CentralFloridaRegionalAirport,CedarKnollFlyingRanch,DaytonaBeachRegionalAirport,CraigMunicipalAirport,JacksonvilleInternationalAirport,StGeorgeIslandAirport.
MajorCitiesAnalysis
Wechoose4metropoliseswhichwillbeseverelyimpactedtodosomefurtheranalysis.
Miami
MiamiisthebiggestcityinFloridawiththeaverageelevationof3feet(0.9144m)[ikipedia].Also,itisacoastalcity.Soaccordingtowhatwepredictthatsealevelwillrise10.8037cmwithin50years,wecandrawaconclusionthatthisc
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