mcm1999C Ground Pollution 大地污染美国数学建模 - matlab数学建模

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标题：mcm1999C Ground Pollution 大地污染美国数学建模
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所属分类: 数学建模资源类型：文档文件大小: 5.89 KB 上传时间: 2019-08-19 20:56:32 下载次数: 66 资源积分：1分提供者: jiqiren mcm1999C Ground Pollution 大地污染

内容：
(MCM 1999C)

Background:

Several practically important but theoretically difficult mathematical problems pertain to the assessment of pollution. One such problem consists in deriving accurate estimates of the location and amount of pollutants seeping inaccessibly underground, and the location of their source, on the basis of very few measurements taken only around, but not necessarily directly in, the suspected polluted region.

Example

The data set (an Excel file at http://www.comap.com/mcm/procdata.xls, downloadable into most spreadsheets) shows measurements of pollutants in underground water from 10 monitoring wells (MW) from 1990 to 1997. The units are micrograms per liter (μg/l). The location and elevation for eight wells are known and given in Table 1. The first two numbers are the coordinates of the location of the well on a Cartesian grid on a map. The third number is the altitude in feet above Mean Sea Level of the water level in the well.

Table 1.

Well # x-Coordinate(ft) y-Coordinate(ft) Elevation(ft)

MW-1 4187.5 6375.0 1482.23

MW-3 9062.5 4375.0 1387.92

MW-7 7625.0 5812.5 1400.19

MW-9 9125.0 4000.0 1384.53

MW-11 9062.5 5187.5 1394.26

MW-12 9062.5 4562.5 1388.94

MW-13 9062.5 5000.0 1394.25

MW-14 4750.0 2562.5 1412.00

The locations and elevations of the other two wells in the data set (MW-27 and MW-33) are not known. In the data set, you will also see the letter T, M, or B after the well number, indicating that the measurements were taken at the Top,. Middle, or Bottom of the aquifer in the well. Thus, MW-7B and MW-7M are from the same well, but from the bottom and from the middle. Also, other measurements indicate that water tends to flow toward well MW-9in this area.

Problem One

Build a mathematical model to determine whether any new pollution has begun during this time period in the area represented by the data set. If so, identify the new pollutants and estimate the location and time of their source.

Problem Two

Before the collection of any data, the question arises whether the intended type of data and model can yield the desired assessment of the location and amount of pollutants. Liquid chemicals may have leaked from one of the storage tanks among many similar tanks in a storage facility built over a homogeneous soil. Because probing under the many large tanks would be prohibitively expensive and dangerous, measuring only near the periphery of the storage facility or on the surface of the terrain seems preferable. Determine what type and number of measurements, taken only outside the boundary or on the surface of the entire storage facility, can be used in a mathematical model to determine whether a leak has occurred, when it occurred, where (from which tank) it occurred, and how much liquid has leaked.

大地污染(美国竞赛1999年C题)

背景

若干实践中重要但理论上困难的数学问题与污染的评估有关。这种问题之一就是根据只是在被怀疑为已污染地区的周围而不必直接在该地区中测得的很少的测量数据来导出不易进入的地下的渗漏污染物的位置和数量、以及污染源的精确估计。

例子

数据可通过http://www.comap.com/mcm.prodata.xls找到。该数据集（一种电子表格文件an Excel file），它能卸载到大多数电子数据表（spreadsheets）展示了从1990到1997在10个监测井处地下水中污染物的数量数据。单位是微克（mg/l）。8个测井的位置和高度是已知的并在下表给出。头两个数是在一张地图的直角格点上井的位置的坐标。第三个数是井中水面高出平均海平面的高度（以英尺计）。数据集中另两个井（MW-27和MW-33）的位置和高度不同。在该数据集中你还会看到数字后面的字母T(Top),M(Middle)或B(Bottom)，它们分别表示测量是在井的含水层的顶部、中部和底部进行的。因此，MW-7B和MW-7M是来自同一个井，但分别是底部和中部的测量。此外，其它的测量数据表明水有流向该区域中的MW-9号井的趋势。

问题一

试建立一个数学模型来决定在由该数据集来表示的区域和时间里是否由任何新的污染物产生。若有，试识别新的污染物并估计它们的污染源的位置和时间。

问题二

在收集任何数据之前，会提出下列问题：是否拟议中的数据类型和模型能给出关于污染物所在的位置和数量的我们想要的估计。液态的化学物质会从埋置在均匀的土壤的储藏中的一个储藏罐中渗漏。因为若要在许多大罐的下面去探测的费用会过分昂贵而且危险，所以只能在储藏设备的边缘地区附近或在看来更合适的地区的表面进行测量。试决定只是在整个储藏罐的边界的外面或表面进行什么样类型的测量以及测量数目可以用于一个数学模型以决定上楼是否发生，何时发生，何处（从哪个罐）发生，以及渗漏多少液体。

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mcm1999C Ground Pollution 大地污染 .doc