数模美赛08年A题.doc

AbstractThe global temperature is rising rapidly today which has caused an extensive ice melt, so the study of predicting rising sea level because of ice melt in North Polar is essential. Our study will try to predict the impact to Florida from melting ice in North Polar .Our studies have three steps:l Predict the temperature: We did the prediction by Neural network and give the change of temperature in 50 years, based on a large amount of data from the Intergovernmental Panel on Climate Change (IPCC);l Model the mass of ice melting and the sea level: The sea level model is mainly based on the principle of Thermodynamics and iteration. The results demonstrate that the sea level will rise by 10.8 cm totally in 50 years. Prediction of our model can be proved to be credible by consulting the data from IPCC. We introduce a correct term to modify our model. We can change to simulate sea level rise in different temperature condition.l Analyze the impacts to Florida: We model the erosion of Floridas shoreline to make it clear that when sea level rise to a certain extent that Florida will face many serious problems such as flooding, destruction of biodiversity, (Health Care), Loss of agriculture production (salinization of soil) and so on over the next 50 years. We find the 17 cities or areas and 15 airports which are severely impacted by the rise of sea level.(Based on our results,) Without attaching more importance to solving the problem, shoreline of several coastal cities like Miami will be eroded seriously, and the lowest place-Key West will be disappeared. It will cost a huge financial loss, so further protection should be put into place.ContentIntroduction3Background3Our work3Study object: Ice cap in Greenland3Modeling the sea level3Analysis of Florida3Assumption4Model :Temperature Prediction4Grey Prediction Model:4Neural Network prediction Model:4Model :Melting ice and the rise of sea level5Model the rise of sea level5Heat from rise of temperature:5Mass of melting ice:6Design of Algorithms:7Model Results: Sea level will elevate by 10 centimeters in 50 years7Validation of our model:8Model Analysis: The effects towards Florida10Major Cities Analysis11Miami11Tampa11Cape Coral12Key West12Other Impacts in Florida:12Recommendations to coastal Florida:13Judgments13Strengths13Weaknesses13Reference14IntroductionBackground Global Warming and sea level rise“Air temperatures at the top of the world continue to rise twice as fast as temperatures in lower latitudes, causing significant ice melt on land and sea” Fears, December 17, 2014. One of the serious consequences is that sea level will rise. Global average sea-level rose at an average rate of about 3.1 2.4 to 3.8 mm per year from 1993 to 2003IPCC. This information suggests that from 1993 to 2003 the sea-level rise by 3.1cm totally. Our work The question requires us to predict the next 50 years condition of ice melting and analyze the effects on the Florida, especially some big cities. So we can separate this question into two parts:l How much and how fast will the see level rise within 50 years?l What are the effects on the Florida because of the rise of sea level, especially some big cities?Study object: Ice cap in Greenland Arctic mainly consists of Greenland, which occupies about 9% glaciers all over the world. Melting in Arctic is mainly due to Greenland, melting of floating ice can be ignored. So we can consider Greenland as study object. Modeling the sea levelWe develop a model for sea-level rise as the function of time. This model can predict sea-level rise in future. Analysis of FloridaAfter having calculated the increased sea level within next 50 years, we analyze the impact to the Florida.l Rising sea level can seriously threaten the development of cities. It has been threatening some islands and coastal cities. Over the next 18 years, about two thirds among 544 American towns will be twice as likely to face floods Huang. More frequency hurricane will happen. l Sea water will corrode seacoast. l A large quantity of drinking water will be polluted.Assumptionl Sea level rise is primarily due to the melting of ice cap in Green Land. We ignore the other floating ice in the Northern Polar.l The increment of sea water from melting will flow over the oceans uniformlyl Salt in the ice will not affects the procedure of melting.Model :Temperature Prediction Grey Prediction Model:The weakness of the grey prediction is that the result is increasing all the time. In other words, it cannot show the changes in detail. Neural Network prediction Model:Model :Melting ice and the rise of sea levelModel the rise of sea level The main reason of the sea level rising is the melting of ice cap and the mass of melting ice is equal to the mass of sea water generated 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 increment of sea water from melting will flow over the world uniformly, which means the melting ice will contribute to the rise of sea level, divided by the area of the ocean. wVw= iVi= mix=VwSoVw The increment of sea water from melting iceVi The total volume of melting ice capVm The total volume of water generated from meltingx The sea level riseSo The overall ocean area: 361745300km2, this is 71 percent of earths total surface area (Wikipedia).Heat from rise of temperature:According to the principle of thermal transmission, heat will always be transmitted from high temperature to low temperature. So, the final state of stuff in the thermal cycling system will reach to a same temperature. So, we assume that the temperature of the whole ice cap will increase by T when the world temperature rise by T.However, it takes time for the ice cap to transmit the heat from the rise temperature. We use the T every month to calculate the increase of melting ice in each month and get the total increment by accumulation, which means parts of the heat from temperature will be absorbed and used to melt ice. So, defining a coefficient() and we will have the heat which ice cap absorbs from the rising temperature in the n-th month:Qn=ci(mc-mi(n-1)TnQn The heat comes from rises of temperature in the n-th month The coefficient of capacity of absorbing heat in one monthci The specific heat capacity of icemc The mass of the whole ice cap 2.451016kgmin The mass of melting ice in the n-th monthTn The change of temperature in the n-th monthWe try to find the by calculating the mass of melting ice in known years. “Recently reported GrIS mass balance varies from near-balance to modest mass losses 47 to 97 gigatons (Gt) year1 in the 1990s, increasing to a mass loss of 267 38 Gt year1 in 2007”(Michiel).= 5.673510-3Mass of melting ice:The mass of melting ice in this month will depends on not only the rising temperature, but also the mass of melting ice in the last month. We divide the heat absorbed by the ice by the melting enthalpy of fusion for water to obtain the mass of extra melting ice resulted from the rise of temperature in this month.min=mi(n-1)+QnfusHmmi(k)=n=112kminmin The mass of melting ice in the n-th monthfusHm: The melting enthalpy3.36105J/kgmi(k) The total mass of melting ice in the next k yearsMoreover, “Since 2006, high summer melt rates have increased Greenland ice sheet mass loss to 273 gigatons per year” (Partitioning Recent Mass Loss). And the initial mass of melting ice in the first month will be calculated as follows:2.731014kg/12mi-1= mii=2.73101412kgx(k)=VwSo=mi(k)wSo mii : The mass of melting ice in the initial year. x(k) The total rise of sea level in the next k yearsDesign of Algorithms:Since we have the function min=f(min-1,Tn), we are able to calculate the mass of melting ice in the next n months using computer program with the data of temperatures and the initial amount of melting ice in the first month. This is easy to achieve using two linear arrays mi and T in MATLAB. Run a simple for loop from 2 to n and calculate min during each pass so that the whole mi array can be found.So that the total amount of melting ice at n-th month is the summation from mi1 to min. Also the total rise of sea level can be easily found.Model Results: Sea level will elevate by 10 centimeters in 50 yearsThe solutions were coded using matlab:Figure 1: The mass of melting ice in the next 50 yearsFigure 2: The rise of sea level in the next 50 yearsThe prediction about rise of sea level every decade in next 50 years:x10=0.9874 cm x20=2.5125 cm x30=4.6222 cmx40=7.3674 cmx50= 10.8037 cmValidation of our model:The results show that the sea level will elevate by approximately 10 centimeters totally and 2 millimeters/yr, which accord with the prediction in Relative Mean Sea Level trends from NOAA. Moreover, if we calculated the rise of sea level without considering the increase of temperature, which means sea level rise at the rate today in the next 50 years, the order of magnitudes is match up with our result. So, based on the analysis above, the results of our model Model Analysis: The effects towards FloridaBased on our results, the sea level will rise 10 centimeters in the following 50 years, which threaten Florida in the future and result in tremendous impacts. “Some 2.4 million people and 1.3 million homes, nearly half the risk nationwide, sit within 4 feet of the local high tide line. Sea level rise is more than doubling the risk of a storm surge at this level in South Florida.” (Florida and rising sea) Figure 3 the altitudes of Florida ()As we can see from this picture, most cities or counties in the southern Florida lie besides the coast. Statistic suggests that 17 counties with altitudes smaller than 3 feet will be threatened by the rise of sea level in 50 years. The counties and airports which will be involved are listed as follows:Cities: Miami, Homestead, Fort Lauderdale, West Palm Beach, Titusville, St Augustine, Clearwater, St Petersburg, Tampa, Brandon, Bradenton, Port Charlotte， Cape Coral, Bonita Springs, Naples, Marco Island, and Grand Isle.Airports: Miami International Airport, Fort Lauderdale International Airport, Central Florida Regional Airport, Cedar Knoll Flying Ranch, Daytona Beach Regional Airport, Craig Municipal Airport, Jacksonville International Airport, St George Island Airport.Major Cities AnalysisWe choose 4 metropolises which will be severely impacted to do some further analysis.MiamiMiami is the biggest city in Florida with the average elevation of 3 feet (0.9144m) 11ikipedia. Also, it is a coastal city. So according to what we predict that sea level will rise 10.8037cm within 50 years, we can draw a conclusion that this city would be greatly influenced. The possibility of flooding would grow while the frequency of hurricane will increase. It is a big challenge to sewer system of Miami. According to our simulation, sea level rising would also threaten Miami International Airport. Another problem is that the sea water would gnaw at the shoreline. Many coastal man-made buildings are too closed to the sea which they would face a serious problem of being eroded. Aside from threatening of losing habitat, local drinking water would be polluted. TampaTampa is a city located on the west coast of Florida. It is the third largest city in Florida. It is famous because of tourism. Although the highest point in the city is only 48 feet (15 m) wikipedia, rising sea level will do harm to its natural disaster. Tampa is special because it has the Old Tampa Bay and Hillsborough Bay which is easy to be attacked by storm surge. Sea level rising would produce much more violent storm surge. The boundary of Tampa would also be lost. Whats more, Traffic facilities such as Tampa International Airport were under threatening of disappearing. Cape CoralThis city is famous because of its far-stretching beach and animated quay. Besides, it has more than 30 gardens and golf courses which attract many tourists. A variety of animals also promotes this citys tourism. However, sea level rising would erode shoreline of Cape Coral. It would destroy natural environment of this area, and then damages biodiversity. And still worse, Pine Island would mostly disappear. So, the economic damage there will be hardly assessed. Key WestIt is an island of Florida, which have the lowest altitude. So if sea level rises to some extent, it would be the first to be under water. Other Impacts in Florida:Biodiversity: Wild life and rare animals in Florida will be impacted by loss of habitat and food. Moreover, it is hard for plants and animals in Florida to adapt the new climatic conditions and the increase of relative air humidity. Architecture: Sea level rise will cause salinization, which will impact the architectural production.Economy Pressure：More money will be put into the drainage systems and dam project, which means less city construction and business development.Health Care: Higher sea level will increase the risk of some disease like malaria.Recommendations to coastal Florida:l Build higher dams: In this way can cities hold back the rising flood waters.l Prepare for flooding: Complete supervisory control system. Guarantee that citizen ca