数模美赛08年A题

1、AbstractThe global temperature is rising rapidly today which has caused an exte nsive ice melt, so the study of p redict ing rising sea level because of ice melt in North Polar is essential. Our study will try to predict the impact to Florida from melt ing ice in North Po lar .Our studies have three

2、 ste ps:P redict the temp erature:and give the change ofWe did the p redicti on by Neural n etworktemperaturein 50 years, based on a largeamount of datafromthe IntergovernmentalPanel on ClimateCha nge (IP CC);Model the massof icemeltingand the sea level: The sea levelmodel is mainiybasedon the princ

3、iple of Thermodynamicsanditerati on. The results dem on strate that the sea level will rise by 10.8cm totally in 50 years. P redict ion of our model can be p roved to bea to simulate sea levelcredible by consultingthe data from IPCC. We introduce a correctterm a to modify our model. We can changeris

4、e in differe nt temp erature con diti on.An alyze the imp acts to Florida:We model the erosi on of Floridashoreli ne to make it clear that whe n sea level rise to a certa in exte ntthat Florida will face many serious problemssuch as flooding.destructi on of biodiversity, (Health Care), Loss of agric

5、ulturep roducti on (sali ni zati on of soil) and so on over the n ext 50 years. Wefind the 17 cities or areas and 15 air ports which are severely imp actedby the rise of sea level.(Based on our results,) Without attachi ng more imp orta nee to sol vingthe problem,shoreline of several coastal cities

6、like Miami will beeroded seriously, and the lowest pl ace - Key West will be disa pp eared.It will cost a huge finan cial loss, so further p rotecti on should be putinto p lace.ContentIn troduct ionBackgro undOur workStudy object : Ice cap in Gree niandModeli ng the sea levelAn alysis of FloridaAssu

7、 mp ti onModel I :Temperature PredictionGrey P redictio n Model:Neural Network p redict ion Model:6Model n :Melting ice and the rise of sea levelModel the rise of sea levelHeat from rise of temp erature:Mass of melt ing ice:Desig n of Algorithms:Model Results: Sea level will elevate by 10 cen timete

8、rs in 50 years10Validatio n of our model:1.1Model 川 Analysis: The effects towards FloridaMajor Cities An alysis.14Miami1.4Tampa15Cape Coral15Key West16Other Imp acts in Florida:1.6Recomme ndati ons to coastal Florida:18Judgme nts1.8Stren gths1.8Weak nesses1.9Refere nee20In troductio nBackgroundGloba

9、l Warmi ng and sea level rise“Air temp eratures at the top of the world continue to rise twice as fast as temp eratures in lower latitudes, caus ing sig nifica nt ice melt on land and sea ” Fears, December 17, 2014. One of the serious consequences is that sea level will rise. Global average sea-leve

10、l rose at an average rate of about 3.1 2.4 to 3.8 mm per year from 1993 to 2003lPCC. This in formatio n suggests that from 1993 to 2003 the sea-level rise by 3.1cm totally.con diti on of iceOur workThe questi on requires us to p redict the n ext 50 years melt ing and an alyze the effects on the Flor

11、ida, esp ecially some big cities.So we can sep arate this questi on into two p arts:How much and how fast will the see level rise within 50 years?What are the effects on the Florida because of the rise of sea level,esp ecially some big cities?Study object : Ice cap in Gree niandArctic main ly con si

12、sts of Gree niand, which occ upies about 9% glaciers all over the world. Melt ing in Arctic is mai niy due to Gree niand, melt ing of floating ice can be ignored. So we can consider Greeniand as study object.Modeli ng the sea levelWe devel op a model for sea-level rise as the fun ctio n of time. Thi

13、s model can p redict sea-level rise in future.An alysis of FloridaAfter hav ing calculated the in creased sea level within n ext 50 years, we an alyze the impact to the Florida.Risi ng sea level can seriously threate n the devel opment of cities. Ithas bee n threate ning some isla nds and coastal ci

14、ties. Over the next18 years, about two thirds among 544 America n tow ns will be twiceas likely to face floods Huang. More frequencyhurricane willhappen.Sea water will corrode seacoast.A large qua ntity of drinking water will be p olluted.Assum pti onSea level rise is p rimarily due to the melt ing

15、of ice cap in Gree n Land.We ignore the other floati ng ice in the Norther n Po lar.The in creme nt of sea water from melt ing will flow over the ocea nsuni formlySalt in the ice will not affects the p rocedure of melt ing.Model I :Temperature PredictionGrey P rediction Model:The weak ness of the gr

16、ey p redicti on is that the result is in creas ing all the time. In other words, it cannot show the cha nges in detail.ItsNeural Network p redicti on Model:in丰十rr沁HIH 二- :Modeljoir 100 wo EDO巾 wizM wmiwo swdn :Melting ice and the rise of sealevelModel the rise of sea levelThe main reas on of the sea

17、 level rising is the melt ing of ice cap and the mass of melt ing ice is equal to the mass of sea water gen erated from melting. So, based on several physical principles, we model the rise of sea level by calculating the mass of melting ice. We assume that the in creme nt of sea water from melt ing

18、will flow over the world uni formly,which mea ns the melt ingice will con tributeto the rise of sea divided by the area of the ocea n.p ? = p ?= m?L? L?x =-? The in creme nt of sea water from melt ing ice ?The total volume of melt ing ice cap ? The total volume of water gen erated from melt ing ?x T

19、he sea level riseThe overall ocean area: 361745300km2, this is 71 perce nt of earth total surface area (Wik ip edia).Heat from rise of temp erature:Accord ing to the principle of thermal tran smissi on, heat will always betransmittedfrom high temperatureto low temperature.So, thelevel,finalstate of

20、stuff in the thermalcyclingsystem will reach to a same temp erature. So, we assume that the temp erature of the whole ice capwill in crease by?T whe n the world temp erature rise by?T.However, it takes time for the ice cap to tran smit the heat from the risetemp erature.We use the ?T every month to

21、calculate the in crease ofmelt ing ice in each month and get the total in creme nt by accumulati on.which mea ns p arts of the heat from temp erature will be absorbed andused to melt ice. So, defi ning a coefficie nt(?) and we will have the heatwhich ice cap absorbs from the risi ng temp erature in

22、the n-th month:Q?= ?m ?- ?m ?(?-1)?T ?Q?The heat comes from rises of temp erature in the n-th month?The coefficie nt of cap acity of absorb ing heat in one monthc?The sp ecific heat cap acity of icem? The mass of the whole ice cap 2.45 X1016 ?m?The mass of melti ng ice in the n-th month?T? The chang

23、e of temperature in the n-th monthWe try to find the ? by calculating the mass of melting ice in knownyears. “ Rece ntly rep orted GrIS mass bala neevaries from n ear-bala neeto modest mass losses 47 to97 gigatons (Gt) year-1 in the 1990s,in creas ing to a mass loss of 267± 38 Gt year -1 in 200

24、7 ” (Michiel).?=5.6735 X 10-3Mass of melt ing ice:WeThe mass of melt ing ice in this month will depends on not only the rising temp erature, but also the mass of melt ing ice in the last month.divide the heat absorbed by the ice by the melt ing en tha Ipy of fusi on for water to obtai n the mass of

25、extra melt ing ice resulted from the rise of temp erature in this mon th.Q?m?= ?m?(?-i)+ fusH 0m12?m?(?)=刀?m ?=i?m?The mass of melti ng ice in the n-th monthusH 0m: The melting enthalpy3.36 x 105J/kg m?) The total mass of melting ice in the next k years” (P artiti oningMoreover, “ Since 2006, high s

26、ummer melt rates have in creasedGree niand ice sheet mass loss to 273 gigat ons per yearRece nt Mass Loss). And the in itial mass of melt ing ice in the first month will be calculated as follows:2.73 xi014?/122.73 x 1014?m?:?-1) = ?=12 ?m?)?x(k)=石=? p ?The mass of melt ing ice in the in itial year.?

27、x(k) The total rise of sea level in the next k yearsDesig n of Algorithms:Si nee we have the fun cti on?min = f(?m i(n-i),?Tn) , we are able to calculate the mass of melt ing ice in the n ext n mon ths using computerp rogram with the data of temp eratures and the in itial amount of melt ingice in th

28、e first mon th.This is easy to achieve using two lin ear arrays?mi and ?T in MATLAB.Run a simp le for loop from 2 to n and calculate?m in during each pass sothat the whole ?m i array can be found.for j¥Tn rn rnll mnrftM =/（咖T TlSo that the total amount of melt ing ice at n-th month is the summa

29、ti onfrom ?mi1 to ?min. Also the total rise of sea level can be easily found.Model Results: Sea level will elevate by 10 cen timeters in 50yearsThe soluti ons were coded using matlab:Figure 1: The mass of melt ing ice in the n ext 50 yearsFigure 2: The rise of sea level in the n ext 50 yearsThe p re

30、dict ion about rise of sea level every decade in n ext 50 years:?x(10)=0.9874 cm?x(20)=2.5125 cm?x(30)=4.6222 ?x(40)=7.3674 ?x(50)=10.8037 ?Validati on of our model:The results show that the sea level will elevate by approximately10 cen timeters totally and 2 millimeters/yr, which accord with the p

31、redicti on in Relative Mean Sea Level trends from NOAA.Moreover, if we calculated the rise of sea level without con sideri ng the in crease of temp erature, which mea ns sea level rise at the rate today in the n ext 50 years, the order of magn itudes is match up with our result. So, based on the an

32、alysis above, the results of our modelModeln Analysis:The effects towardsFloridaBased on our results, the sea level will rise 10 cen timeters in thefollowi ng 50 years, which threate n Florida in the future and result intreme ndous imp acts.“Some 2.4 milli on people and 1.3 milli on homes,n early ha

33、lf the risk n ati on wide, sit withi n 4 feet of the local high tide line.Sea level rise is more tha n doubli ng the risk of a storm surge at this levelin South Florida. ” (Florida and rising sea)浑二工 Jk .砂脾ar- . , T. . I_；=；lilM Sf '上/- ，# / - _'广一7 * A -:产.广 y />曲 W2ifc:2* :-宀r-,.；七:绵L&#

34、39;.二叮-1令.一丄匚/才护:做 _ 吟超广入打土 "宀；宀今E YhJ .". k .丿 J £“ 工-宀，囂广文-I-“丸:RSTT：¥ Y = _ 疣Sb/$ - 2/ n. - .1 « - - - . . -i k L十:=f 汕么丿- *< ;尸 W八;1 *. ,. 7Ti说二汀曙肛-i ffu rif(,C'uFigure 3 the altitudes of Florida ()As we can see from this pi cture, most cities or coun ties in the

35、souther nFlorida lie besides the coast. Statistic suggests that 17 coun ties with altitudes smaller tha n 3 feet will be threate ned by the rise of sea level in 50 years. The coun ties and air ports which will be invo Ived are listed as follows:Cities: Miami, Homestead, Fort Lauderdale, West P alm B

36、each, Titusville,St August ine, Clearwater, St P etersburg, Tampa, Brandon, Brade nton,Port Charlotte , Cape Coral, Bon ita Sprin gs, Nap les, Marco Isla nd, andGrand Isle.Air ports: Miami Intern ati onal Air port, Fort Lauderdale Intern ati onalAirport, Cen tral Florida Regi onal Airport, Cedar Kn

37、oil Flyi ng Ranch,Dayt ona Beach Regi onal Air port, Craig Mun ici pal Airport, Jacks on villeIntern ati onal Air port, St George Isla nd Air port.Major Cities AnalysisWe choose 4 metr op olises which will be severely imp acted to do some further an alysis.MiamiMiami is the biggest city in Florida w

38、ith the average elevati on of 3 feet(0.9144m) 15ik ip edia. Also, it is a coastal city. So accordi ng to what wep redict that sea level will rise 10.8037cm within 50 years, we can draw acon clusi on that this city would be greatly in flue need.The po ssibility of flood ing would grow while the frequ

39、e ncy of hurrica newill in crease. It is a big challe nge to sewer system of Miami. Accord ing toour simulati on, sea level ris ing would also threate n Miami Intern ati onalAir port.Ano ther p roblem is that the sea water would gnaw at theshoreli ne. Many coastal man-made build ings are too closed

40、to the seawhich they would face a serious problem of being eroded. Aside fromthreate ning of los ing habitat, local drinking water would be p olluted.TampaTampa is a city located on the west coast of Florida. It is the third largestcity in Florida. It is famous because of tourism. Although thehighes

41、tpoint in the city is only 48 feet (15 m) wiki pedia, risi ng sea level will doharm to its natural disaster. Tampa is special because it hasthe OldTampa Bay and Hillsborough Bay which is easy to be attacked by stormsurge. Sea level rising would produce much more violent stormsurge.The boun dary of T

42、ampa would also be lost. What's more, Traffic facilitiessuch as Tampa Intern ati onalAir portwere un derthreate ningofdisa pp eari ng.Cape CoralThis city is famous because of its far-stretchi ng beach and ani mated quay.Besides, it has more tha n 30 garde ns and golf courses which attractmany to

43、urists. A variety of animals also promotes this city ' s tourism.However, sea level rising would erode shoreli ne of Cape Coral. It woulddestroy n atural en vir onment of this area, and the n damages biodiversity.And still worse, Pine Island would mostly disappear. So, the economicdamage there w

44、ill be hardly assessed.Key WestIt is an isla nd of Florida, which have the lowest altitude. So if sea levelrises to some exte nt, it would be the first to be un der water.Other Imp acts in Florida:Biodiversity:Wild life and rare ani mals in Florida will be imp acted by lossof habitat and food. Moreo

45、ver, it is hard for plants and ani mals in Floridato adapt the newclimatic con diti onsand the in crease of relative airhumidity.Architecture:Sealevel rise will cause salinization,which will impact thearchitectural p roduct ion.Economy P ressure: More money will be put into the drain age systemsand

46、dam p roject,which mea ns less city con struct ionand bus in essdevel opment.Health Care: Higher sea level will in crease the risk of some disease like malaria.Recomme ndati ons to coastal Florida:Build higher dams:In this way can cities hold back the rising floodwaters.Prepare for flood ing:Comp lete sup ervisory con