2016年美国大学生数学建模E题英文版论文.doc

In this paper, a model is established to provide a measure of the ability of a region to provide clean water to meet the needs of its population, and find out the reason for the lack of water resources. Specific tasks are as follows:For Task 1: We establish a model. In the model, we think the supply of clean water depends on the amount of surface water, underground water and sewage purification. The water requirements are decided by the amount of life water, agricultural water and industrial water in the region. In water supply, surface water is affected by the annual average temperature, annual average precipitation and forest coverage rate. The groundwater is impacted by the annual average temperature, annual average precipitation. The agricultural water is affected by the population of the region and annual average precipitation. The GDP of the region influences the industrial water consumption. We use the principle of multivariate nonlinear regression to find out the regression coefficient. And then make sure its function. The ratio of water supply and water requirements is used as a measure of the ability of a region to provide clean water. We find that the ability of a region to provide clean water is good or not by comparing the ratio with 1.For Task 2: The model selects the Shandong Province of China as the testing region. We analyse the data of Chinas Shandong area between 2005 and 2014, and then crystallize the model through the thought of the function fitting and multivariate nonlinear regression. By the model, we think Shandong provinces ability to provide clean water is weak. And then from two aspects which physical shortage and shortage of economic, this paper analyses the causes of water shortage in Shandong Province, and thus test the applicability of the model.For Task 3: We select several factors affecting water supply and water demand badly, which is annual precipitation, annual average temperature, the forest coverage rate and population forecast. We analyse the data of Chinas Shandong area between 2005 and 2014, according which to predict the changes of those factors in 15 years. After that this paper uses the model to analyse the situation of Shandongs water in 15 years.For Task 4: According to the model in Task 1 and the analysis of the Task 2. We find the main factors influencing the ability to provide clean water in Chinas Shandong province. By these factors we make the intervention program. In view of the low average annual rainfall, increase the average annual rainfall by artificial rainfall. In view of the forest coverage rate, forest plantation and protect vegetation is came up with. For sewage purification capacity, putting forward to improve sewage treatment technology and improve the sewage conversion rate and increases daily sewage quantity. In view of the total population, we put forward the policy of family planning for water consumption per capita, putting forward to set the daily water consumption per person. And putting forward the industrial wastewater must reach the indexes of the rules, developing seawater desalination technology to increase the supply of clean water. Water has always been the hot spot in the world.The future is also not exceptional. Only finding out the problem, we can suit the remedy to the case.The model measure the ability of a region to provide clean water by analysing the cases which influence the supply and remand of water. Based on this, make a good intervention program. Offering helps to solve global water issues.1 Introduction41.1 Problem Statement41.2Problem Analysis41.2.1Task 1 Analysis41.2.2Task 2 Analysis41.2.3Task 3 Analysis51.2.4Task 4 Analysis51.2.5Task 4 and 5 Analysis52 Assumptions and Notations52.1 Assumptions52.2 Notations63 Model Establishment and Solution73.1 The effect of single factor on the water supply in a certain area73.1.1Effects of annual average temperature, annual average precipitation and forest coverage on surface water resources in a certain area73.1.2 Effects of annual average temperature and annual precipitation on groundwater resources in a certain area73.1.3 Influence of total population and per capita water consumption on daily water consumption in a certain area83.1.4 The influence of average annual rainfall and total population on agricultural water consumption in a certain area83.1.5 Effect of average annual rainfall and population in an area of agricultural water use93.2 Function Arrangement93.2.1 Water supply function93.2.2 Water demand function93.2.3 The ability of a region to provide clean water103.3 In order to test the accuracy and usability of the model, this model is selected as a test area in Shandong Province, China.103.3.1 Total surface water resources103.3.2 Total groundwater resources133.3.3 Total industrial water consumption function153.3.4 Total agricultural water consumption function163.3.5 Assessment of water supply capacity183.4.2 Remediation Measures193.5 Forecast for the next 15 years193.5.1 Forecast of average annual rainfall203.5.2 Prediction of annual temperature213.5.3 Prediction of forest cover213.5.4 Prediction of population223.6 Intervention Program233.6.1 Present ofthe Intervention Program233.6.2 Implement ofthe Intervention Program244 Advantages and Shortcoming of the model254.1Advantages：254.2 Shortcoming255 Improvement of model266 Reference267 Appendices277.1 Data used in task 2277.2 Matlab Source Code291 Introduction1.1 Problem StatementOn the earth, the water that human beings can use the water directly or indirectly, is an important part of natural resources. At present, the total amount of the earths water is about billion cubic meters, of which the ocean water is billion cubic meters, accounting for about 96.5% of the total global water. In the remaining water, the surface water accounts for 1.78%, 1.69% of the groundwater. The fresh water that human mainly use of is about billion cubic meters, accounting for only 2.53% in the global total water storage. Few of them is distributed in lakes, rivers, soil and underground water, and most of them are stored in the form of glaciers, permafrost and permafrost, The glacier water storage of about billion cubic meters, accounting for 69% of the worlds total water, mostly stored in the Antarctic and Greenland, the available clean water in the dwindlingwith time going by.In order to assess the ability to provide clean water of an area, we set up an assessment model.1.2Problem Analysis1.2.1Task 1 AnalysisTask 1 requires establishing a model to measure the ability of a region to provide clean water. At the same time,we also need to provide a measure standard.This paper make the ratio of water supply and water requirements of a region as the measure standard, by which to measure the ability of a region to provide clean water.A regions main source of water is groundwater, surface water and sewage purification.The model assumes the volume of groundwater in a region is mainly affected by average annual temperature, annual precipitation;Thevolume of surface water is mainly affected by the average annual temperature, annual precipitation, the forest coverage rate.These factors decide water supply of an area.The waterdemand of an area mainly includes living water, agriculture water and industrial water. We assume living water is affected by the population and per capita consumption decision;Agricultural waterdepends an annual precipitation and population decision;Industrial water is mainly decided by a gross regional product.The above factors decide the water demand in a certain area.1.2.2Task 2 AnalysisAccording to the information provided in the map, in Asia, Chinas Shandong Province is the region meeting the requirements.Through the data collection of Shandong Province, we can find the annual temperature, annual precipitation, the forest coverage rate, groundwater, surface water, sewage treatment capacity, water, agricultural water, industrial water, population,per capita consumption and GDP data.And then according to the model of Task 1,we analyze the ratio by using multivariate nonlinear regression to make sure that Shandong province is a water-deficient area.After proving that Shandon province is short of water through the model, we analyze the reasons for lack of water from two aspects: physical shortage and economic shortage.1.2.3Task 3 AnalysisBecause we already have the relevant data, we can function to fit the relationship between the variables and the year.Thus it is possible to predict in Shandong Provinces data in the 15 years, then input the data into the model to achieve the purpose of prediction.In addition, it can be combined with the actual situation and the selected areas of the corresponding policy to analysis which factors will have a great change in the 15 years.We still can analyze from two aspects of society and the environment.Social aspects includes the promotion of water conservation, population growth;Environmental aspects includes policy changes to the environment, sewage purification capacity enhancement and so on.1.2.4Task 4 AnalysisFormulating plans for intervention mainly start from the perspective of the main model. According to the content of the model, we can still divide all of factors into two types: the social and environmental factors. The intervention programs can be developed based on two types of factors that affect the supply of water, reducing as much as possible the negative impact of the factors that control factors and intensifying the development of a positive impact. In addition, because Shandong Province is beside the sea, desalination and other measures can be developed to increase clean water supply sources.1.2.5Task 4 and 5 AnalysisTask 4 intervention programs indirectly impact the water supply and demand water through a direct impact on GDP model of forest cover, annual precipitation, annual temperature, water emissions, sewage treatment capacity, population growth and the region.2 Assumptions and Notations2.1 Assumptionsl The water resources in a region are derived from the purification of surface water, groundwater and sewage, and the demand of water resources comes from domestic water, industrial water and agricultural water.l The surface water supply in a certain area is affected only by the average annual temperature, annual precipitation and forest coverage. The groundwater supply is affected by the annual average temperature and annual precipitation.l The regions water consumption of a certain region depends on the population and per capita water consumption; Agricultural water consumption is affected by the average annual precipitation and the numberof people. Industrial water is mainly determined by a regional GDP.l A certain region will not suddenly increase or decrease the population largely.l There will not be a serious natural disasters in a region in the next period of time.2.2 NotationsSurface water volume in a region or countryUnderground water in a region or countryIndustrial water consumption in a region or countryAgricultural water consumption in a region or countryDaily water consumption in a region or countryWater demand in a region or countryAverage annual rainfallAnnual average temperatureforest coverageforest coverageTotal populationThe amount of water in a region or countryCoefficient of determination of the regression equationStatistic valueProbability valueregression coefficientPer capita water consumptionSewage treatment capacityA region to provide clean water capacity3 Model Establishment and SolutionThe model established here is a use of a regions water supply and water demand ratio to determine whether the water shortage in the region, the main variables involved.3.1 The effect of single factor on the water supply in a certain area3.1.1Effects of annual average temperature, annual average precipitation and forest coverage on surface water resources in a certain areaDue to the average annual temperature, annual precipitation, the forest coverage rate and surface water of linear or nonlinear relationship exists, so first in order to determine the average annual temperature, annual precipitation, the forest coverage rate and surface water, and then the nonlinear multiple regression analysis method to determine the functional relationship between the three factors and surface water.The surface water content is, Average annual precipitation, annual average temperature and forest coverage rate are , Using nonlinear regression statistical methods, the use of MATLAB fitting toolbox were identified , of the highest regression power(MATLAB fitting toolbox of the highest fitting function is the 9 power, greater than the 9 power function is too complex, not much research value), According to the decision coefficient R2 of the regression equation, the corresponding probability value of the statistic P, the regression coefficients, get the regression equation:3.1.2 Effects of annual average temperature and annual precipitation on groundwater resources in a certain areaThere is a linear or nonlinear relationship between the average annual temperature, average annual rainfall and the supply of groundwater, according to the idea of 5.1.1, the relationship between the average annual amount of groundwater supply, the average annual precipitation and the supply of groundwater is calculated. And the regression coefficient is determined, and the function relationship between the average annual temperature, average annual precipitation and the supply of groundwater is based on the regression coefficient:Design of underground water for , with an average annual precipitation, annual average air temperature respectively, using nonlinear regression statistical methods, according to the regression equation with coefficient of determination R2, F statistic corresponds to the probability value p, to determine the regression coefficients , got the regression equation: （2）3.1.3 Influence of total population and per capita water consumption on daily water consumption in a certain areaThe total population of a region and the amount of water consumption per capita and the daily use of the product of the relationship between the amount of water = total amount Water usage per person consumption.Set daily water consumption is , the total population, per capita water consumption were , , , the function of the relationship between the:（3）3.1.4 The influence of average annual rainfall and total population on agricultural water consumption in a certain areaDue to the annual precipitation and the total population and the area of agriculture of area of a water there is a linear or nonlinear relationship, according to the thought of multivariate nonlinear regression can be calculated average annual precipitation and the total population and the area of agriculture with the function relationship between water and to determine the regression coefficient and regression coefficient write GDP and industrial functional relationship between Gross domestic product GDP and industrial water consumption.Let industrial water consumption of , gross production set , using statistical nonlinear regression, regression equation based on the coefficient of determination, statistical probability valuecorresponding to the amount determined regression coefficients, the regression equation:（4）3.1.5 Effect of average annual rainfall and population in an area of agricultural water useAgricultural water consumption of , design with an average annual rainfall of , , using statistical nonlinear regression, regression equation based on the coefficient of determination, statistical probability valuecorresponding to the amount determined regression coefficients, the regression equation:（5）3.2 Function Arrangement3.2.1 Water supply functionThe model takes into account a regions water supply from three aspects: surface water resources, groundwater resources and the amount of sewage treatment. The function relation between surface water resources, groundwater resources, sewage treatment and water supply is the function, that is, the amount of water supply = surface water resources + groundwater resources.The amount of water supply is , and the sewage treatment capacity is , by(2) (1):（6）3.2.2 Water demand functionThe model takes into account the need for a region from three aspects: daily water consumption, industrial water consumption and agricultural water consumption. Daily water consumption, industrial water and agricultural water consumption and water demand is a function of the relationship between the function and the function, that is: water demand = daily water consumption + industrial water + agricultural water consumption.A demand for , by (3) (4) (5) to:（7）3.2.3 The ability of a region to provide clean waterA region to provide clean water and the area of water supply and water demand about, if water supply is greater than demand, the region provide clean water ability strong; on the contrary, the region provide clean water ability is weak. This model provides that a region to provide clean water capacity by the area of water supply and water demand ratio determined by (6) (7) available:(1) : the regions ability to provide clean water;(2) : the area provides a warning of the ability to provide clean water;(3) : the ability of the region to provide clean water is weak;3.3 In order to test the accuracy and usability of the model, this model is selected as a test area in Shandong Province, China.Provide the capacity of water resources in Chinas Shandong P