Introductio.docx

Introductio.docx

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Introductio

1.Introduction

Withthepredictedincreaseinglobetemperature,thehumanfacemanydisastersincludingthenaturalecosystemsandthesocialeconomy.Inthenaturalecosystems,thereisthemeltingoftheglacier,morerisingsealevelandsoon.Inthesocialeconomy,thereistheproductionofmaincropsandanimalhusbandry,thewatersupply,theenergyresourcessupplyandsoon.Andtherearesomerelationswiththeaffects.Becausethereisverydifficulttoassessalltheaffects,weonlydiscussthemostimportanteffectinthispaper:

themeltingofthenorthpolaricecap.

2.RestatementClarificationoftheproblem

Asweknow,ifthenorthpolaricecaphasmelted,thehumanwillfacethehugedisaster.Soit’simportantandnecessarytostudytheproblem.Consideringtherearemanyeffects,weonlydiscussthefollowingeffects:

●Theriseofthesealevel;

●Theaggravationofthehurricane;

●Themigrationandmutationofthespecies;

●Theinternationaleconomicimpact.

Thenweestablishourmodelstoassesstheeffectsabove.WecalculatetheeffectsonthecoastofFloridaeverytenyearsforthenext50yearsduetothemelting.Inourmodels,theeffectsoflargemetropolitanareasattractourgreatattention.

Aftercalculatingtheeffects,wealsogivesomepreventivemeasurestoslowdowntheeffortsduetothemelting.

3.Assumption

Beforediscussingtheefforts,wewillneedthefollowingassumptions:

●TheicethickateverypointintheArcticisthesame

Infact,thereisimpossiblethat

4.Modeldesign

4.1Estimateoftheimpactoftheriseofthesealevel

4.1.1CalculatetheareaoftheArctic

Fromtheassumptionabove,allthemeltedicechangestothewater.

First,wedealwiththeArcticSeaIceConcentrations（AppendixA）[1].IntheArcticSeaIceConcentrations,theArcticisdigitizedonastandard1-degreegridandthetotalgridsare80*58.WecanobtaintheLatitudeandLongitudecoordinates（AppendixB）[1].AnalyzingthedataoftheLatitudeandLongitudecoordinates,wethinktheshapeofthegridisanirregularquadrilateral.Andwedividethequadrilater

-alintotwotriangles,andthevertexpointsofthetrianglesarethevertexpointsofthegrid.Theareaofthegridisthesumofthetwotriangleareas.WiththeLatitudeandLongitudecoordinates,wecalculatetheareaofonetriangle.Theapproachisasfollow:

●Onegridisdividedintotwotrianglesasfollow

●Onetriangleofthegridisasfollow（Figure2）:

Figure2Arandomtriangulargrid

（

arethetriangularsides）

●Calculatearandomsideofsometriangulargridbythefollowingformula:

Where,

=thedistancebetweenthepointAandthepointB（km）;

=theradiusoftheearth（=6371km）;

=thelongitudesofthepointsAandB,and;

=theLatitudesofthepointsAandB.

●Counttheareaofthetriangle

asfollow:

Where,

=

.

●Counttheareaoftheothertriangle.

Theapproachisthesameasthemethodwithwhichwecounttheareaofthetriangle

●Assesstheareaofthegrid.

Theareaofthegridisthesumofthetwotriangleareas.

4.1.2Buildthefunctiontheamountoftheareacoveredbyiceandthetime

After,wecompileaCprogramtodotheareaofeverytriangulargrid,andreceiveadatapacketreplacedbyDataA.ThesumoftheDataAistheareaoftheArctic（

）.WiththeArcticSeaIceConcentrations,wecanobtainthepercentageofeverygridsquareareacoveredbyiceeveryyearwithanotherCprogram,andreceivecorrespondingdatapacket（donateDataB）.DataAmultiplyDataB,andtheresultisdonatedDataC.DataCisanarray

.EitherdatumintheDataCindicatestheareacoveredbyiceinthegrid.Thesumoftherowofthearray

dividedbytheareaofArctic（excludingthefirstrow）istheamountoftheareacoveredbyiceintheArcticeveryyearandgenerateddatapacket（donateDataD）.DataDisanarray

.Thearray

columnsstatetheyearsfrom1901to1994.

ThenwecandrawanexpressionoftheamountoftheareacoveredbyiceintheArcticbythemethodofcurvefittingwithMatlab:

Where,

=theyearwewanttostudy（When

isequalto0,theyearis1990）;

=ThepercentageoftheareacoveredbyiceintheArcticforyear.

Whenfitting,weusetheleastsquaremethod.Whenthefunctionisquadric,theminimumvarianceestimationis0.0494.Whenthefunctioniscubic,thevalueis0.0472.Consideringonthenumericalaccuracyofthecomputer,weusethecubicfunctionandthefittingfigureisasfollow（Figure2）.

Figure2Thefittingcurve

Theringdenotestheactualdata

4.1.3Drawafunctiontocalculatethesea-iceamountforspecificmonth

Thesea-iceconcentrationsforthemonthsoftheclimatologicallyaremaximalinMarchandminimalinSeptemberfortheperiod1990to1999derivedfromSSM/Idata[].

Figure3Meansea-iceconcentration（1990-1999）fromSSM/Idatafor（a）Marchand（b）September[].

Wecanconcludethatthesea-iceconcentrationforMarchismuchbiggerthanthesea-iceconcentrationforSeptemberfromtheFigure3.Andifweusetheaveragesea-iceconcentrationperyeartoweightthemeansea-iceconcentrationforMarchorSeptember,theresultwemakeisunreal.It’snecessarytodrawaexpressiontoestimatethesea-iceamountforMarchandForSeptember.

March

Theapproachweuseisverysimilartotheapproachwithwhichweobtaintheaverageamountoftheareabyiceeveryyear.WiththeArcticSeaIceConcentrations,weassessthepercentageofeverygridsquareareacoveredbyiceforMarch.Withthecurvefitting,wedrawaexpressionasfollow:

Where,

=ThepercentageoftheareacoveredbyiceintheArcticforMarch.

Andthecurveisasfollow（Figure4）:

Figure4ThefittingcurveforMonth

September

Theapproachisasbefore.Andthefunctionandthecurveareasfollow（Figure5）:

Where,

=thepercentageoftheareacoveredbyiceforSeptember.

Figure5ThefittingcurveforSeptember

4.1.4Therelationbetweentheriseofthesealevelandthetime

Infact,therearemanyfactorscausingtheriseofthesealevel.However,themostimportantfactorisadecreaseofthedensityofseawater,andtheicemeltedisasecondaryfactor[].Thevalueinuseofthemeasureddataisverysmall.Wemustcalculatetheriseofthesealevelandthetimeunitistenyears.

Becausethegrossmassisinvariablewhentheicemelts,wecandesigntheexpressionasfollowtogettheriseofthesealevel:

Where,

=theamountoficemeltedfortenyears;

=thesurfaceareaoftheSea（

）;and

=theriseofthesealevelfortenyears.

Inordertogetthevaluefor

weshouldknowthevalueof

.Wehaveassessedtheareacoveredbyiceandthedensityofice（

）.Ifweneedtogainthevalueofthe

theicethicknessateverypointoftheArcticisnecessary.However,thereisnopersontoinvestigatethedatauntil2007[]andit’simpossibleforustoseekthedata.Sowethinktheicethicknessateveryplaceisinvariable.Andweassumethatthetotalmeltingicethicknessfortenyearsisonemeter.Themeltingiceareafortenyearsisobtained:

Where,

=theareacoveredbyiceforthespecialyear;

=theareacoveredbyicefortheyearthedistancebetweenwhichandthespecialyearistenyears,and;

=themeltingiceareafortenyears.

Before,wehavebuiltthefunctionbetweenthepercentagecoveredbyiceandthetime.Sothevalueof

canbegivenwiththepercentagemultiplyingtheareaoftheArctic（

）,andwecanalsogainthevalueof

bythesamemethod.Withfitting,therelationbetweentheriseofthesealevelfortenyearsandthetimeisbuilt.Thenwepredicttheriseofthesealevelinthenext50yearspertenyears.

4.2Therelationbetweentheamountoficemeltedandoceansurfacetemperature

Inthefollowingmodels,weusethepercentagecoveredbyiceasatokenoftheamountoficemelted.Inordertofindthepertinencebetweenthepercentagecoveredbyiceandoceansurfacetemperature,weshouldinquireoceansurfacetemperatureeveryyear.Oceansurfacetemperaturedatapacket（AppendixA）isdenotedbyDataE[].Withthesecondcolumnofthearray

and

wedrawaconclusionthattherelationbetweenthepercentagecoveredbyiceandoceansurfacetemperatureisnegativecorrelationwithMATLAB.Andthedegreesofthecorrelationis0.6017.

4.3Therelationbetweenthepercentagecoveredbyiceandthehurricane

Thistheory,asNaturepointsout,isthatthehurricanehasplayedanimportantroleintheriseofoceansurfacetemperature.Thehumanhasconfirmedtherelationbetweenthehurricaneandtheriseofoceansurfacetemperaturefromquantityforthefirsttime.ThescholarsfromUniversityofLondonstudytherelation,andtheNaturepublishestheresult.TheNaturepointsoutthatifoceansurfacetemperatureincreases

℃,thehurricanefrequencywillhaveaincreaseof50%.Thefollowingfigure（Figure6）showstherelationbetweenthehurricaneandtheriseofoceansurfacetemperature.

Figure6Therelationbetweenthehurricaneandtheriseofoceansurfacetemperature

Withthemodel4.2,wemakeaconclusionthattherelationbetweenthepercentagecoveredbyiceandoceansurfacetemperatureisnegativecorrelation.Withthismodel,weknowthattherearesomerelationsbetweenthehurricaneandtheriseofoceansurfacetemperature.Whenicemelts,oceansurfacetemperaturewillincrease.Ifthetemperatureincreases,itwillhaveaneffectonthehurricane.Sotherearesomerelationsbetweenthepercentagecoveredbyiceandthehurricane.Inthemass,whenicemelting,thehumanwillsuffermorehurricanedisaster.

4.4Therelationbetweenthepercentagecoveredbyiceandtheprecipitation

A