2016美国大学生数学建模比赛H奖

For office use only T1 _ T2 _ T3 _ T4 _ Team Control Number 5367453674 Problem Chosen E E For office use only F1 _ F2 _ F3 _ F4 _ 2016 MCM/ICM Summary Sheet Analyzing the Water Scarcity Bsaed on the Water Footprint Theory Abstract Our aim is to establish a model to evaluate a regions ability of providing available water for the peoples lives and production, select a region from the UN water scarcity map, and then use the relevant indicators to evaluate the regions water supply condition. For task one, a dynamic evaluation model is established by using the theory of virtual water and the water footprint to evaluate the water supply ability of a region. We consider agricultural water consumption, industrial water consumption, ecological and environmental water, domestic water consumption, and the import and export of virtual water in our dynamic evaluation module. We establish five main evaluation indexes to analyze the situation of water supply ability and the water resources in a region. For task two, we take Qingdao as an example. Qingdao is a serious water scarcity city, located in the eastern part of Shandong Province, China. We put the relevant data of Qingdao city in 2014 into the evaluation model we built in task one, and then get the conclusions: Qingdao is in a condition of water scarcity, the water resources are not enough to meet the needs of its population. In addition, the economic benefit of unit water consumption is not large, the waste rate of water resource is high, and the utilization rate of water resource is low. For task three, we use the grey prediction model to predict agricultural production water, industrial water, domestic water, ecological water, exports of virtual water, imports of virtual water, and available water resources quantity of Qingdao in 15 years. By using the evaluation model we get the conclusions: In 2030, Qingdao city is still in a condition of water scarcity, and need to obtain water from the surrounding area. But the economic benefits of per unit water are large, and the utilization ratio is large, as well. For task four, we design intervention plans from the perspectives of the virtual water trade, the economic performance of water footprint, the physical water footprint, and the source of water. Then we analyze the effects of these plans on the ecosystem and the surrounding areas of Qingdao. For task five, we analyze from the perspective of the source of the available water, and project the water availability of Qingdao on the basis of intervention plans. Team # 53674 Page 1 of 20 1 Problem statement In recent years, with the increasing of population, the water scarcity has garnered increased attention. There is a great relationship between water scarcity and environmental factors or social factors, and our main task is to make a reasonable analysis and model the problem of water scarcity. The first problem to be solved is to determine the reasonable criteria to determine whether a regions water resources can meet the needs of the population. Then select a region from the United Nations map of water shortage, and analyze the reason of water scarcity from the perspective of society and environment. Next, we analyze the water resources in 15 years in the selected countries and the intervention plan was made, and the influence of the plan on the surrounding areas and ecosystems was discussed. Finally, apply the model and the plan to predict the capacity of water available in the future and analyze whether there will be a shortage of water resources in the selected country. 2 Problem analysis In order to build a model to measure the clean water supply capacity in a region, We introduce the concept of virtual water 1 and water footprint 2 to build the model. The water footprint can be used to measure the direct and indirect water consumption in the process of production. It also can be used to measure the real demand and occupation status of the water resources in a region from the point of view of consumption. We calculate the agricultural production water, industrial production water, residents living water, and ecological environment water by using the virtual water theory. We set up three overall evaluation indexes to evaluate the condition of water resources in a region. These indexes can analyze problems from the points of physical and economic scarcity. According to the UN water scarcity map, the water in Qingdao in China is heavily overloaded, so we select the Qingdao in China to study. We put the relevant data into the model and get the evaluation conclusion of water resources condition in Qingdao. In process of predicting the status of water resources in Qingdao city in 15 years, we can evaluate the status of water resources in Qingdao city after 15 years by using the evaluation model established as long as we predict the evaluation indexes in future. Therefore, we focus on the establishment of the forecasting model. We use the grey forecasting model to forecast the change of other variables. We get the conclusion by putting the results into the evaluation model. In the process of making the intervention plan, we comprehensively considered the factors which affect the water shortage and put forward the intervention plan. In addition, we analyze the impact of the intervention plan on the local area and the surrounding areas. Then, under the premise of the intervention plan, we use the evaluation model and the forecasting model to project water availability of Qingdao city into the future. 3 Assumptions When predict the conditions of water resources in a region, we assume that there wont be major natural disasters, such as the long time catastrophic flood or rainstorm. Therefore, the water contents of the lakes wont change a lot and the local water resources system wont be damaged a lot. In addition, the flood cannot be used by people, and there is no meaning to analyze this factor. When consider the water consumptions of agricultural productions, because most of them have been absorbed by crops and the loss affected by many factors is small, Team # 53674 Page 2 of 20 therefore, it is not easy to calculate. In order to simplify the problem, we assume that the waste water in the process of agricultural irrigation wont affect the results. A regions water resources mainly come from the surface water, the groundwater, the regenerated water and other aspects of water resource that are too difficult to evaluate. Therefore, we assume that the other factors wont have great influences. 4 Dynamic evaluation model of water supply capacity based on the water footprint theory The water footprint theory was proposed by Hoekstra in 2002, which is a new method to reflect the utilization condition of water resources based on consumption. The water footprint theory is proposed based on the virtual water. The water footprint is the water inside all products and services which a country, an area or a person consumes in a certain period of time. That is to say, the footprints are formed by the water in the process of production and consumption. We use the water footprint to measures the real demand and occupation status of the water resources in a region from the perspective of consuming. 4.1 Establishing evaluation indexes We use the water footprint theory to establish model. Then, we set up a series of evaluation indexes to evaluate the condition of water resources in the area.We use the virtual water represents water consumed by agriculture, industry, residents, and ecological environment. When considering import and export trade, we also use the virtual water represents water included in the goods. We comprehensively consider the flow of water footprint and get the following formula4. + exportimport TVWAVWIVWDVWEVWVWVW（1） where TVW is the total water footprint of the region; theAVW is the water consumption of agricultural production; The IVWis the water consumption of industrial production; The DVWis the water consumption of the residents living; The EVWis the water consumption of the ecological environment; The emport VWis the amount of virtual water exported; The import VWis the total amount of the virtual water imported from other regions. Therefore, we get the flow chart of water footprint as follows. Team # 53674 Page 3 of 20 Figure 1: The flow chart of water footprint. By considering the physical scarcity and economic scarcity, we construct a series of evaluation indexes to evaluate the water supply capacity in a region by using the water footprint theory. In order to establish the dynamic model, we need to consider many dynamic factors, such as the change of population, the change of the annual virtual water imported and exported, GDP, and the trade volume. (1) Water supply capacity index (WSC): It is the ratio of the total water footprint of the region and the total amount of water resources availability in this region. The formula is as follows. WSC=(2) TVW WZ where WZ represents the total amount of water resources availability that can be utilized in this region. This indicator can represent the degree of water resources in a region supplying local peoples living. When1WSC , it indicates that the water footprint required for production is greater than the amount of available water resources, which means that the water resource condition of this region is heavily overloaded. Therefore, we obtain the water resources pressure index standard table as follows. Table 1 Water pressure 4 Water pressure 1WSC 1WSC 1WSC water resources are overload water resources reaches the maximum carrying capacity water resources in the range of capacity Team # 53674 Page 4 of 20 By putting theWSCinto the table1, we can get the pressure degree of water resources in the area. (2) Economic benefit of water footprint: It is the ratio of GDP and the total water footprint of the region. The formula is as follows3. (3) GDP EBW TVW This index represents the economic benefit level of the water footprint consumption. If the index value is high, it indicates that the economic benefit is big by consuming per unit amount of water Benefit is greater, the utilization of water resources is high. (3)The degree of effecting on the surrounding area: It is the ratio of the virtual water exported and the virtual water imported from other regions. The formula is as follows. export import VW Effect VW （4） This indicator represents the degree of impacting on other areas. If it is high, it indicates that the local water resource has a huge impact and contribution rate on other regions. (4)The water resource utility ratio index: 1(5) SVW WUR TVW where SVWis the scrap water. This indicator represents the water resource utility ratio. If it is high, it indicates that the amount of water which is scraped is less. (5) Average per capita water resources index: (6) WZ AVR popultion The average per capita water resources index is important in evaluating the condition of water resource. By compare it to the average per capita water resources in the world, we can obtain the conclusion. At this point, the dynamic evaluation model of the water supply capacity has been established. In the process of modeling, we consider a number of dynamic Team # 53674 Page 5 of 20 factors. The final evaluation system includes five evaluation indexes in table 3.We first need to obtain water footprints as shown in table 2 according to data. Then, we put these water footprints into model to calculate and get the evaluation indexes as shown in table 3. Finally, we use these three indicators to evaluate the water supply capacity of the region for peoples lives. Table 2: Water footprint and water resources of Qingdao City Water footprint The agricultural water consumption ( 3 /AWU m) Industrial water consumption ( 3 /IWW m) The domestic water consumption ( 3 /DVW m) The ecological water consumption ( 3 /EVW m) The virtual water of exportation ( 3 exp / ort VWEm) The virtual water of import( 3 / import VWm) The total water footprint of the region( 3 /TVW m) The regional available water resources ( 3 /WZ m) Table 3: The evaluation indexes The water Footprint Evaluation Indexes The water supply capacity index(WSC) The economic benefit of water footprint ()EBW The degree of effecting on the surrounding area()Effect The water resource utility ratio index ()WUR The average per capita water resources index ()AVR 4.2Analysis on the present situation of water resources shortage in Qingdao of China According to the UN water scarcity map 7, we know that the Qingdao city in China is in the heavily overloaded. Therefore, we select the Qingdao city in China to study. The Qingdao is located in the Shandong Peninsula in southern China and its east longitude is11930121 00 and north latitude is 35353709. The East and South of Qingdao are on the verge of the Yellow Sea, and the northeast of Qingdao is adjacent to Yantai city. The total area of Qingdao is 11282 square kilometers. The urban area consists of six district: the south of the city, the north of the city, Licang, Laoshan, Huangdao, and Yangcheng district. By looking up the Qingdao statistical yearbook and the water resources bulletin5, we get the data of industrial water, agricultural water and peoples living water of Qingdao(see Appendix 2). After that, we use the estimated average value of virtual water of China put forward by Hoekstra and Chapagain through studying more than 100 countries in the world 6. Finally, the consumption of virtual water in industry, agriculture and life of Qingdao city is obtained. Team # 53674 Page 6 of 20 By putting the data into the dynamic evaluation model of the water supply capacity in 4.1, we get the results in 2013 and 2014 as follows. Table 4: Water footprint and water resources of Qingdao City Water footprint 2013 2014 The agricultural water consumption ( 3 /AWU m) 9 6.21 10 9 5.65 10 Industrial water consumption ( 3 /IWW m) 8 3.88 10 8 3.44 10 The domestic water consumption ( 3 /DVW m) 8 4.87 10 8 4.34 10 The ecological water consumption ( 3 /EVW m) 8 2.36 10 8 2.28 10 The virtual water of exportation ( 3 exp / ort VWEm) 9 5.92 10 9 5.06 10 The virtual water of import( 3 / import VWm) 9 2.11 10 9 2.52 10 The total water footprint of the region( 3 /TVW m) 9 4.21 10 9 3.98 10 The regional available water resources ( 3 /WZ m) 9 3.42 10 9 4.11 10 Table 5: Composition diagram of water footprint of Qingdao in 2013 and 2014 The water Footprint Evaluation Indexes 2013 2014 The water supply capacity index(WSC)/% 307.27 217.35 The economic benefit of water footprint ()EBW 3 /(/)yuan m 90.34 111.14 The degree of effecting on the surrounding area ()Effect/% 2.01 2.45 The water resource utility ratio index ()/%WUR 63.25 74.31 The average per capita water resources index ()AVR/ 3 m 247 235 Conclusions: In 2013 and 2014, the water supply capacity index of Qingdao was 307.27%. The water supply capacity index (WSC)is greater than 1, which indicates that the water resources of Qingdao has been heavily overloaded according to table 1. The result is consistent with the UN water scarcity map and it shows the correctness of our model. We conclude that the water resources cannot meet the needs of agricultural, industry, ecological environment, and peoples lives of Qingdao City. To be sure, the rain water are not included in available water resources, which is the another reason of making the water supply capacity index is high. From the point of view of the city itself, Qingdao city is lack of water resources seriously and the annual rainfall is less. Average rainfall is 688.2 mm per year and the total amount of local water resources is 2.21billion cubic meters. The average per capita water resources is 235 which only takes 12% of the average level of China in Team # 53674 Page 7 of 20 2014. It is far less than the standard of 500 cubic meters per capita in the world. The resources of Qingdao cannot meet the needs of peoples production and life. In addition, from table 3, we conclude that the proportion of industrial water footprint is very small, which is mainly due to the large number of exportation of industrial products. The economic benefit of water footprint is high, which shows that water resources of Qingdao have great economic benefit in the national economy. The degree of effecting on the surrounding area is high and the water resource utility ratio index is low, which indicates that a lot of water is wasted. Therefore, Qingdao needs to further improve the technology of water treatment to increase water use efficiency. 4.3 The forecasting model of water resources of Qingdao City based in Grey Forcasting Theory As time goes by, a number of factors will change, such as the amount of the population, the total amount of economic production, the amount of water resources in a region, climate, and production structure. These changes will affect the five indicators involved in the water resources evaluation model in 4.1. Therefore, when we predict the condition of water resources in Qingdao City in 15 years, the key is to obtain the three indicators in 15 years and then analyze the status of water resources of Qi