没有合适的资源?快使用搜索试试~ 我知道了~
2016美国大学生数学建模特等奖论文集(ICM,含赛题)E52831.pdf
1.该资源内容由用户上传,如若侵权请联系客服进行举报
2.虚拟产品一经售出概不退款(资源遇到问题,请及时私信上传者)
2.虚拟产品一经售出概不退款(资源遇到问题,请及时私信上传者)
版权申诉
0 下载量 126 浏览量
2024-03-17
21:57:46
上传
评论
收藏 772KB PDF 举报
温馨提示
![preview](https://dl-preview.csdnimg.cn/88982081/0001-f70bb7b10a934c008db73d7a1a876672_thumbnail.jpeg)
![preview-icon](https://csdnimg.cn/release/downloadcmsfe/public/img/scale.ab9e0183.png)
试读
18页
美国大学生数学竞赛获奖论文,历届,单项文件,内容丰富,大学生数学,数学竞赛,参考资料,极具参考价值
资源推荐
资源详情
资源评论
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![pdf](https://img-home.csdnimg.cn/images/20210720083512.png)
![doc](https://img-home.csdnimg.cn/images/20210720083327.png)
![](https://csdnimg.cn/release/download_crawler_static/88982081/bg1.jpg)
For office use only
T1
________________
T2
________________
T3
________________
T4
________________
Team Control Number
52831
Problem Chosen
E
For office use only
F1
________________
F2
________________
F3
________________
F4
________________
2016
MCM/ICM
Summary Sheet
(Your team's summary should be included as the first page of your electronic submission.)
Type a summary of your results on this page. Do not include the name of your school, advisor, or team members on this page.
Tackling Water Scarcity: Modeling Water Access in India Using Multiple Regression Analysis
“Water, water, every where,” lamented the Ancient Mariner, “Nor any drop to drink” [8]. Samuel
Taylor Coleridge might as well have been describing India’s water crisis. It is not an absolute lack of
water that threatens India’s water security, but a challenge of managing this critical resource. Our task
was to construct a mathematical model capable of measuring a country’s ability to provide clean water for
its population, to use this model to forecast India’s water security fifteen years into the future, to develop
an intervention policy to enhance water security, and to use our model to predict the policy’s success over
the same time frame.
We approached the problem by constructing a series of multiple linear regression models using
publicly available data in order to account for the wide variety of factors that influence water access. We
first used a simple two-predictor model that explained 43.7% of the variance in access to water. Using
this basic model as a foundation, we considered a variety of predictors for water security and used a
variable selection algorithm to develop a refined model that explained 71.6% of the variance in access to
water.
After testing the model’s applicability to India’s water supply by comparing model-generated
predictions of access to water against published statistics, we used an autoregressive multivariate model
to forecast the change of each water access predictor variable over the next fifteen years and the resulting
projections to predict changes to India’s water security through the year 2031. Our model did not directly
account for climate change, so we used published data on effects of climate change on water supply to
create a climate-corrected forecast model.
Finally, we developed a multidisciplinary intervention policy designed to increase the availability
of clean water in India. Using published data to determine appropriate alterations to the predictor values,
we simulated the changes in access to water fifteen years after implementation of our proposed policy
changes, resulting in a 3.78% increase in water access.
![](https://csdnimg.cn/release/download_crawler_static/88982081/bg2.jpg)
Team # 52831 Page 1
Tackling Water Scarcity: Modeling Water Access in India Using
Multiple Regression Analysis
Contents
INTRODUCTION....................................................................................................................................... 2
DEFINITIONS.............................................................................................................................................. 2
ASSUMPTIONS ........................................................................................................................................... 3
Basic Model Assumptions..................................................................................................................... 3
Refined Model Assumptions ................................................................................................................. 3
MODELS OF THE WATER SCARCITY CRISIS ................................................................................. 4
THE BASIC MODEL.................................................................................................................................... 4
Description of the Model ...................................................................................................................... 4
Results................................................................................................................................................... 4
Discussion............................................................................................................................................. 4
REFINED MODEL ....................................................................................................................................... 5
Description of refinements ................................................................................................................... 5
Results................................................................................................................................................... 7
Discussion............................................................................................................................................. 7
APPLICATION OF THE REFINED MODEL TO INDIA..................................................................................... 7
Background on the Indian Water Crisis............................................................................................... 7
Testing the Model’s Applicability to India ........................................................................................... 8
Forecast to 2031................................................................................................................................... 8
Forecast accounting for climate change .............................................................................................. 9
Discussion............................................................................................................................................. 9
INTERVENTION PLAN.......................................................................................................................... 10
OVERVIEW AND JUSTIFICATION OF INTERVENTIONS .............................................................................. 10
Interventions for water supply............................................................................................................ 10
Interventions for sanitation ................................................................................................................ 11
Interventions for population growth................................................................................................... 11
Interventions for GDP ........................................................................................................................ 11
Interventions for pollution and technology ........................................................................................ 11
MATHEMATICAL DESCRIPTION OF THE INTERVENTION PLAN................................................................. 12
ANALYSIS OF INTERVENTION PLAN ........................................................................................................ 13
DISCUSSION............................................................................................................................................. 13
CONCLUSIONS........................................................................................................................................ 14
FUTURE WORK ...................................................................................................................................... 14
REFERENCES.......................................................................................................................................... 15
![](https://csdnimg.cn/release/download_crawler_static/88982081/bg3.jpg)
Team # 52831 Page 2
Introduction
Human life depends on access to clean water. While the world possesses an abundance of water, many
populations lack access to the clean freshwater essential for life. The world’s population is currently
estimated to have exceeded 7.3 billion people and is projected to reach 8.5 billion by 2030 [20]. Ensuring
all these people have access to clean water is a challenge that must be addressed on multiple fronts.
Though water is a renewable resource, groundwater and surface freshwater available for drinking or
agriculture accounts for only 1% of the world’s total water supply (the vast majority of the rest being
ocean water) [14]. Human populations are generally established in regions near water, with only 10% of
the world’s population living more than 10 km from a surface freshwater body [12]. However, presence
of a freshwater body alone does not guarantee access to safe and clean water. Despite improvements
through technology and education, some regions still practice open defecation or lack sanitation facilities,
resulting in contaminated water supplies [26].
Numerous factors, ranging from the physical and ecological to the political and socioeconomic, affect
whether a country or region experiences water scarcity. Among these are population growth, agriculture
and food production, climate, climate change, land use, water quality or water pollution, demand for
water, economic status, professional capacity (including education and working conditions), political
issues, social issues [3], and catastrophic events such as droughts or floods. As of 2007, an estimated 1.2
billion people experience physical scarcity and an additional 1.6 billion experience economic scarcity
[21].
In India, attempts by the government and other organizations have had some success in developing
municipal water supplies [11], but have failed to solve the problem for many Indians, in part due to the
country’s large and growing population, which is expected to exceed 1.5 billion people by 2030 [20].
In this paper, we address the challenge of modeling (and designing intervention policies against) water
scarcity by developing a series of regression models of increasing complexity. We apply these models,
combined with projections of future events such as population growth and climate change, to develop a
forecast of future water scarcity in India absent any intervention plan. Finally, we use our model to
propose a possible policy for addressing water scarcity in India and suggest the likely outcome of its
implementation.
Definitions
Because water scarcity is a complicated interdisciplinary problem, it is important to exercise care in
operationally defining one’s terms. Toward that end, in the interest of clarity, we use the following
definitions in this paper:
• Access to electricity is the percentage of a country’s population with access to electricity
according to data from “industry, national surveys, and international sources” [28].
• Access to water is the percentage of a country’s population actively using an improved water
source [38].
• Air pollution, expressed in micrograms per cubic meter, is “the average level of exposure of a
nation’s population to concentrations of suspended particles measuring less than 2.5 microns in
aerodynamic diameter, which are capable of penetrating deep into the respiratory tract and
causing severe health damage” [39].
• Clean water is freshwater that meets the criteria of an improved water source.
• Freshwater is defined as water that is not ocean water or other salt water.
• GDP per capita is a country’s gross domestic product divided by that same country’s midyear
population and is reported in current US dollars [34].
• Improved water sources are defined as “piped water on premises” or “other improved drinking
water sources” including “public taps or standpipes, tube wells or boreholes, protected dug wells,
protected springs, [and] rainwater collection” [27].
![](https://csdnimg.cn/release/download_crawler_static/88982081/bg4.jpg)
Team # 52831 Page 3
• Improved sanitation facilities are defined as “likely to ensure hygienic separation of human
excreta from human contact” and include systems that flush to a sewer, septic tank, or pit latrine,
pit latrines with slab, and composting toilets [27].
• Intervention, in the context of this paper, refers to any measure or measures implemented by
governments or organizations to directly or indirectly increase a population’s access to clean
water.
• Pollution is any contaminant introduced into an otherwise safe water supply and which renders
the water supply unfit (or less fit) for drinking or use in agriculture.
• Population growth is the annual increase in a country’s population counting all permanently
settled residents, defined in our models as “the exponential rate of growth of midyear population
from year t - 1 to t, expressed as a percentage” [41].
• Sanitation is the percentage of a country’s population using improved sanitation facilities [37].
• Scarcity of water is a relative measure of the supply of water available to a region against the
region’s demand for water; specifically in this case, scarcity of water refers to scarcity of clean
water, and is operationally defined as lack of access to water.
• Water security is a measure of the ability of a population to ensure supply of clean water meets
or exceeds demand; in this paper, we operationally define water security as access to water.
• Water supply, expressed in cubic meters, is defined as “renewable internal freshwater resources
per capita” [43]
Assumptions
Water scarcity is a complex interdisciplinary issue with international significance. Contained within the
problem are variables pertaining to politics, economics, culture, human biology, ecology, climatology,
geology, and many other disciplines. It is impossible to fully model every possible relevant factor. As
such, we made several assumptions and simplifications.
First, in all cases, we assume that the data we used in our models were both complete and accurate.
Inherent in our use of linear regression for the construction of our model, we must assume that all
variables included are linearly related to access to clean water, that none of our predictor variables are
correlated, the data are normally distributed, and the errors from the regression are normally distributed
with mean zero and constant variance. In all models, we assume that percent of population with access to
clean water is a direct (inverse) proxy for water scarcity. Because our model incorporates a forecast, we
assume that the relationships between variables will remain consistent for at least the next fifteen years.
Finally, due to availability of data, we model 2012 as the “current” year.
In addition, each of the particular models we constructed have their own sets of assumptions.
Basic Model Assumptions
The basic model is our simplest model, so the assumptions we made are few and far-reaching.
Specifically, we assume that population growth is a direct proxy for clean water demand and that GDP
per capita is a direct proxy for a country’s ability to meet that demand.
Refined Model Assumptions
For the refined model, the same assumptions apply, with the following additions and modifications:
• GDP per capita is a direct proxy for economic ability to promote water security,
• A country’s continent and latitude together provide a direct proxy for geographic
variance and climate,
• Access to electricity is a direct proxy for a country’s technological ability to promote
water security,
• Air pollution is a direct proxy for industrial and agricultural water pollution.
剩余17页未读,继续阅读
资源评论
![avatar-default](https://csdnimg.cn/release/downloadcmsfe/public/img/lazyLogo2.1882d7f4.png)
![avatar](https://profile-avatar.csdnimg.cn/fcd62adb0120465d9af280215b0ff722_snowtshan.jpg!1)
阿拉伯梳子
- 粉丝: 1674
- 资源: 5736
上传资源 快速赚钱
我的内容管理 展开
我的资源 快来上传第一个资源
我的收益
登录查看自己的收益我的积分 登录查看自己的积分
我的C币 登录后查看C币余额
我的收藏
我的下载
下载帮助
![voice](https://csdnimg.cn/release/downloadcmsfe/public/img/voice.245cc511.png)
![center-task](https://csdnimg.cn/release/downloadcmsfe/public/img/center-task.c2eda91a.png)
安全验证
文档复制为VIP权益,开通VIP直接复制
![dialog-icon](https://csdnimg.cn/release/downloadcmsfe/public/img/green-success.6a4acb44.png)