2023 Tianfu Cup National Undergraduate Mathematical Contest in Modeling
Question B Governance of China's Environmental Issues
Reproduction of the original title:
Problem background:
With the rapid economic development and the continuous growth of population, China's environmental problems have become an important problem that needs to be solved urgently. These environmental problems have not only had a huge impact on people's health and quality of life, but also caused great damage to the ecosystem and ecological balance. In recent years, the Chinese government has actively promoted the development of environmental protection, and achieved certain results by adopting a series of policies and measures. However, the problem of environmental pollution is still very serious, and further measures need to be taken to solve it.
Among them, air pollution is one of the most prominent environmental problems in China. Due to the acceleration of urbanization and the development of industrialization, harmful substances such as PM2.5 in the air of many cities exceed the standard, posing a serious threat to people's health. Therefore, establishing a mathematical model between the air quality index (AQI) and the concentration of different pollutants can help the government and the public better understand the situation of air quality and take corresponding measures to improve air quality.
In addition, water pollution is also an important aspect of China's environmental problems. With the acceleration of urbanization and the development of industrialization, the water environment in many areas has been seriously polluted, and water quality issues have become the focus of public attention. Therefore, it is of great significance for the government and the public to understand the seriousness of water environment problems and promote water environment governance to construct a comprehensive evaluation index of water environment quality to reflect the pollution degree and treatment effect of the water environment.
In addition, urban noise pollution is also a long-standing environmental problem. Due to the increase of traffic density and building density in cities, as well as changes in people's lifestyles, urban noise pollution has become a widespread problem. In order to better monitor and control urban noise pollution, it is imperative to optimize the monitoring network of urban noise pollution to minimize the number of monitoring points while ensuring the accuracy and comprehensiveness of monitoring results. Against the above background, ask you and your team to address the following questions. Please solve:
Problem 1: Air pollution has become one of the most prominent environmental problems in China. How to establish a mathematical model between the air quality index (AQI) and the concentration of different pollutants to better understand the situation of air quality and take corresponding measures to improve air quality? Please give the top 10 cities with the best air quality in every city in the country.
Question 2: With the acceleration of urbanization and the development of industrialization, the water environment in many areas has been seriously polluted, and water quality issues have become the focus of public attention. How to construct a comprehensive evaluation index of water environment quality to reflect the pollution degree and treatment effect of the water environment? Please give the top 10 cities with the best water environment in various cities across the country.
Question 3: Due to the increase of traffic density and building density in cities, as well as changes in people's lifestyles, urban noise pollution has become a widespread problem. Select a city and collect the required data to determine how to optimize the urban noise pollution monitoring network to minimize the number of monitoring points while ensuring the accuracy and comprehensiveness of the monitoring results.
Solving process
This question is a common topic, environmental protection, and one of the important evaluation criteria for environmental protection is air quality. The first question is how to establish a mathematical model between the air quality index (AQI) and the concentration of different pollutants to better understand Understand the situation of air quality and take corresponding measures to improve air quality? Please give the top 10 cities with the best air quality in every city in the country.
First of all, the air quality index and the concentration of different pollutants. What do you need to find out about the concentrations of different pollutants? If you have experience, you will know the "two dust and four air", PM2.5, PM10, CO, NO2, SO2, O3, these six indicators can accurately measure the air quality of a certain place, and then take corresponding measures against pollution sources. But this data collection is very annoying, but fortunately I have it. The first question is to build a multiple linear regression model based on the impact of different pollutants on air quality; and then perform a visual comparison of the overall air quality and a ring chart or pie chart comparison between multiple factors. The first question is very Simple. Let me make a sample, how to do the visual chart?
Then the second question about water pollution is the same, but it is slightly different. I will not evaluate the difficulty of the whole question. I will not write wasteful exercises such as question restatement, question background, model assumptions, and references. If you want to build and solve the entire model, please see below "Only modeling QQ business cards" Click on the QQ business card.