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中国研究生创新实践系列大䗙
"华为杯"第十八届中国研究生
China Graduate Students' Innovation and Practice Series Da䗙 "Huawei Cup" The 18th China Graduate School

数学建模竞赛 Mathematical modeling competition

题目 空气质量预报的二次建模及相关问题研究 Title Research on quadratic modeling and related issues for air quality forecasting

摘
要：
摘 To:

在大气环境污染对人体及生态环境有重要影响的今天，采取相应污染防治控制措施十分必要。通过建立空气质量预报模型，提前获知可能发生的大气污染过程并采取相应控制措施，是减少大气污染对人体健康造成的危害、提高环境空气质量的有效方法之一。我国目前常用的是 WRF-CMAQ 模拟体系对空气质量进行预报，但受制于模拟的气象场以及排放清单的不确定性，以及对包括臭氧在内的污染物生成机理的不完全明晰，大气物理化学机理分析还存在缺陷，使得首要污染物、空气质量等级命中率低，WRF-CMAQ 预报模型的结果并不理想。因此在 WRF-CMAQ 等一次预报模型模拟结果的基础上，结合更多的数据源进行再建模，以提高预报的准确性。
In today's world, where atmospheric pollution has a significant impact on the human body and the ecological environment, it is necessary to take appropriate pollution prevention and control measures. Through the establishment of air quality forecasting model, it is one of the effective ways to reduce the harm of air pollution to human health and improve the ambient air quality by knowing the possible air pollution process in advance and taking corresponding control measures. At present, the WRF-CMAQ simulation system is commonly used in China to forecast air quality, but due to the uncertainty of the simulated meteorological field and emission inventory, as well as the incomplete understanding of the generation mechanism of pollutants including ozone, there are still deficiencies in the analysis of atmospheric physicochemical mechanisms, which makes the hit rate of the primary pollutants and air quality levels low, and the results of the WRF-CMAQ forecasting model are not ideal. The results of the WRF-CMAQ forecasting model are not satisfactory. Therefore, based on the simulation results of primary forecasting models such as WRF-CMAQ, the modeling is combined with more data sources to improve the accuracy of forecasts.
对于问题1, 监测点 A 从 2020 年 8 月 25 日到 8 月 28 日逐日实测的数据中并无异常数据，可直接按照附录中的方法计算监测点 A从 2020 年 8 月 25 日到 8 月 28 日每天实测的 AQI 和首要污染物，结果如表 3-4,3-6 所示。
For question 1, there is no abnormal data in the daily measured data from August 25 to August 28, 2020 at monitoring point A. The daily measured AQI and the primary pollutant at monitoring point A from August 25 to August 28, 2020 can be calculated directly according to the method in the appendix, and the results are shown in Tables 3-4 and 3-6 below.
对于问题2，将附件1中的数据采集记录并针对记录进行数据预处理，主要是针对数据异常情形，采取如下处理方式：实测数据部分或全部缺失的情况：变量值缺失值取为前后时刻的平均值；受某些偶然因素的影响，实测数据在某个小时（某天）的数值偏离数据正常分布：若超出正常变量分布范围则取为对应的最小值或最大值；利用 3 σ 3 σ 3sigma3 \sigma 准则将异常数据剔除。基于数据预处理的变量值，根据公式计算每天对应的 AQI 值，根据其属性利用基于划分的聚类方法 k-means 聚类根据对污染物浓度的影响程度，对气象条件进行聚类，对聚类结果进行可视化；在 AQI 结果排序的基础上对气象条件进行合理分类，并阐述各类气象条件的特征；并对整体数据进行多次聚类，最终根据聚类结果，选择分为三类，聚类中心点如表 4-1 所示，阐述各类气象条件的特征。
For question 2, the data collection records in Annex 1 and data preprocessing for the records, mainly for data anomalies, the following processing methods are adopted: the case of partially or completely missing measured data: the missing value of the variable value is taken as the average of the moments before and after; due to the influence of some accidental factors, the value of the measured data at a certain hour (a certain day) deviates from the normal distribution of the data: if it is outside the range of the normal distribution of variables, it is taken as the corresponding minimum or maximum value; the 3 σ 3 σ 3sigma3 \sigma criterion is used to eliminate the abnormal data. If it is out of the normal distribution of the variable, it is taken as the corresponding minimum or maximum value; the 3 σ 3 σ 3sigma3 \sigma criterion is utilized to exclude the abnormal data. Based on the pre-processed variable values, calculate the corresponding AQI values for each day according to the formula, use k-means clustering based on its attributes to cluster the meteorological conditions according to the degree of influence on the concentration of pollutants, and visualize the results of the clustering; reasonably categorize the meteorological conditions on the basis of the sorting of the AQI results, and describe the characteristics of each type of meteorological conditions; and perform multiple clustering of the overall data, and ultimately, the data will be classified according to their characteristics. The data are clustered several times, and finally, according to the clustering results, three categories are selected, and the centers of clustering are shown in Table 4-1 to describe the characteristics of each type of meteorological conditions.
对于问题 3，根据前问气象条件对污染物浓度的影响篮选出来的具有代表性及独立性的气象条件，建立了基于 BP 神经网络预测框架。该模型搭建神经网络框架对一次预报数据及实时监测数据输入完成空气质量预报的预测，并在加入更新天气质量数据的过程中不断调整，该模型适用于数据更新的预测建模。经过一系列测试，二次预报数学模型同时适用于 A、B、C 三个监测点，并且建立的 BP 神经网络二次预报模型预测结果中 AQI 预报值比一次建模的预报值的误差更小，首要污染物预测准确度更高。此外，对空气质量预测的二次建模模型结果与真实值对比并于其他模型相比较验证了模型的有效性。并使用该模型预测监测点 A、B、C 在 2021 年 7 月 13 日至 7 月 15 日 6 种常规污染物的单日浓度值，给出相应的 AQI 和首要污染物的结果，如表 5-3所示。
For Problem 3, a BP neural network-based prediction framework was established based on the representative and independent meteorological conditions selected from the basket of effects of meteorological conditions on pollutant concentrations in the previous question. The model builds a neural network framework for primary forecast data and real-time monitoring data input to complete the prediction of air quality forecasts, and continuously adjusted in the process of adding updated weather quality data, the model is suitable for data updating prediction modeling. After a series of tests, the secondary forecasting mathematical model is applicable to the three monitoring points A, B and C at the same time, and the established BP neural network secondary forecasting model predicts the AQI forecast value with less error than the primary modeling forecast value, and the accuracy of the primary pollutant prediction is higher. In addition, the results of the quadratic modeling for air quality prediction were compared with the real values and other models to verify the validity of the model. The model was used to predict the single-day concentration values of six conventional pollutants at monitoring points A, B, and C from July 13 to July 15, 2021, and the corresponding AQI and top pollutant results were given, as shown in Table 5-3.
对于问题 4，根据问题 3 中建立的 BP 神经网络预测框架，加入考虑风向及监测点 A、 A1、A2、A3 之间的位置，改进模型构造协同预报模型，利用遗传算法采用实数编码、模拟二进制交叉和多项式变异，对 BP 神经网络预测模型进行行改进，对在测试集的使用上也进行更改，取相同时间段内四个不同监测点测试的污染物浓度和气象信息作为训练集，训练神经网络，结果如表 6-1所示。
For Problem 4, according to the BP neural network prediction framework established in Problem 3, adding the consideration of the wind direction and the location of monitoring points A, A1, A2 and A3, improving the model to construct a cooperative forecast model, using genetic algorithms to improve the BP neural network prediction model by using the real number coding, simulating the binary crossover and polynomial variance, and changing the use of the test set to take the pollutant concentration and meteorological information of the four different monitoring points tested in the same period as the training set to train the neural network, the results are shown in Table 6.1. The pollutant concentrations and meteorological information from four different monitoring points in the same time period were used as the training set to train the neural network, and the results are shown in Table 6-1.
关键词：空气质量预报，首要污染物，AQI，k-means 聚类，二次建模，BP 神经网络，遗传算法
Keywords: air quality forecasting, top pollutants, AQI, k-means clustering, quadratic modeling, BP neural network, genetic algorithm

目录 catalogs

  1. 问题重述 … 4 Restatement of issues 4
  2. 模型假设及关键性符号说明 … 6 Description of model assumptions and key symbols 6
  3. 问题一分析与求解 … 7 Problem 1 Analysis and Solution 7
    3.1 问题一分析 … 7 3.1 Analysis of Issue 1 7
  4. 2 问题一求解 … 7 2 Solving Problem 1 7
  5. 问题二分析与求解 … 9 Problem 2 Analysis and Solution 9
  6. 1 问题二分析 … 9 1 Analysis of question two 9
  7. 2 问题二求解 … 10 2 Solving Problem 2 10
  8. 2.1 数据预处理 … 10 2.1 Data pre-processing 10
    1. 2 模型原理及框架 … 12 2 Modeling Rationale and Framework 12
  10. 2.3 聚类结果 … 13 2.3 Clustering results 13
  11. 问题三分析与求解 … 15 Problem 3 Analysis and Solution 15
  12. 1 问题三分析. … 15 1 Analysis of question three ......................... ... 15
  13. 2 问题三求解 … 16 2 Solving Problem 3 16
    5.2.1模型原理及框架 … 16 5.2.1 Modeling Principles and Framework 16
    5.2.2 模型结果 … 18 5.2.2 Model results 18
  14. 问题四分析与求解 … 21 Problem 4 Analysis and Solution 21
  15. 1 问题四分析 … 21 1 Analysis of question four 21
  16. 2 问题四求解 … 21 2 Solving problem 4 21
  17. 2.1 模型原理及框架 … 21 2.1 Model Rationale and Framework 21
  18. 2.2 模型结果 … 23 2.2 Model results 23
  19. 结论与模型评价 … 24 Conclusions and Model Evaluation 24
    7.1 结论 … 24 7.1 Conclusion 24
  20. 2 模型评价 … 25 2 Evaluation of the model 25
  21. 2.1 模型优点 … 25 2.1 Advantages of the model 25
    7.2.2 模型缺点 … 25 7.2.2 Model shortcomings 25
    参考文献 … 27 References ... 27

1. 问题重述 1. Restatement of the problem

空气污染物排放的时空变化和相应的气象条件的变化能够对人体健康产生短期和长期影响，污染物浓度超标对居民健康有着巨大的危害，对生态、环境和交通等人类社会活动等产生巨大的影响。一个有效的空气质量预报系统有助于人类掌握污染物未来浓度信息，制定相应的防治策略，对空气中污染物的浓度水平提前给出精确的预报，使因污染物浓度超标所造成空气污染物排放的时空变化和相应的气象条件的变化能够对人体健康产生短期和长期影响，污染物浓度超标对居民健康有着巨大的危害，对生态、环境和交通等人类社会活动等产生巨大的影响 [ 2 ] [ 2 ] ^([2]){ }^{[2]} 。
Temporal and spatial changes in air pollutant emissions and corresponding changes in meteorological conditions can have both short- and long-term effects on human health, and exceeding pollutant concentrations can have a huge impact on the health of the population, as well as on the ecology, the environment, and transportation and other human social activities. An effective air quality forecasting system helps human beings to grasp the information of future concentration of pollutants, formulate corresponding prevention and control strategies, and give accurate forecasts of the concentration level of pollutants in the air in advance, so that the spatial and temporal changes in air pollutant emissions caused by exceeding pollutant concentrations and the corresponding changes in meteorological conditions can have a short- and long-term impact on human health, and exceeding pollutant concentrations have a huge impact on the health of the population. Exceeding the pollutant concentration has a great harm to the health of the residents and a great impact on the ecology, environment, transportation and other social activities of human beings [ 2 ] [ 2 ] ^([2]){ }^{[2]} .
目前常用 WRF-CMAQ 模拟体系（以下简称 WRF-CMAQ 模型）对空气质量进行预报。 WRF-CMAQ 模型主要包括 WRF 和 CMAQ 两部分：WRF 是一种中尺度数值天气预报系统，用于为 CMAQ 提供所需的气象场数据；CMAQ 是一种三维欧拉大气化学与传输模拟系统，其根据来自 WRF 的气象信息及场域内的污染排放清单，基于物理和化学反应原理模拟污染物等的变化过程，继而得到具体时间点或时间段的预报结果。WRF 和 CMAQ 的结构如图 1-1、图 1-2 所示:
Currently, the WRF-CMAQ modeling system (hereafter referred to as WRF-CMAQ model) is commonly used for air quality forecasting. The WRF-CMAQ model mainly consists of two parts: WRF is a mesoscale numerical weather prediction system, which is used to provide meteorological field data for CMAQ; CMAQ is a 3D Eulerian atmospheric chemistry and transport simulation system, which simulates the changes of pollutants and other processes based on the physical and chemical reaction principles according to the meteorological information from the WRF and the pollutant emission inventories in the field, and then obtains the forecast results at specific time points or time periods. CMAQ is a three-dimensional Eulerian atmospheric chemistry and transport simulation system, which simulates the changes of pollutants based on physical and chemical reactions based on the meteorological information from WRF and the pollution emission inventory in the field, and then obtains the forecast results at specific time points or time periods.
图 1-1 中尺度数值天气预报系统 WRF 结构 [ 1 ] [ 1 ] ^([1]){ }^{[1]}
Figure 1-1 Structure of WRF for Mesoscale Numerical Weather Forecasting System [ 1 ] [ 1 ] ^([1]){ }^{[1]}
图 1-2 空气质量预测与评估系统 CMAQ 结构
Figure 1-2 Structure of CMAQ, an air quality prediction and assessment system
但受制于模拟的气象场以及排放清单的不确定性，以及对包括臭氧在内的污染物生成机理的不完全明晰，WRF-CMAQ 预报模型的结果并不理想。故题目提出二次建模概念：即指在 WRF-CMAQ 等一次预报模型模拟结果的基础上，结合更多的数据源进行再建模，以提高预报的准确性。其中，由于实际气象条件对空气质量影响很大(例如湿度降低有利于臭氧的生成），且污染物浓度实测数据的变化情况对空气质量预报具有一定参考价值，故目前会参考空气质量监测点获得的气象与污染物数据进行二次建模，以优化预报模型。
However, the results of the WRF-CMAQ forecasting model are not satisfactory due to the uncertainty of the simulated meteorological fields and emission inventories, as well as the incomplete understanding of the generation mechanism of pollutants including ozone. Therefore, the topic proposes the concept of secondary modeling, which means that based on the simulation results of primary forecast models such as WRF-CMAQ, the modeling is combined with more data sources to improve the accuracy of the forecasts. In particular, since the actual meteorological conditions have a great influence on air quality (e.g., lower humidity is conducive to ozone production) and the changes in the measured pollutant concentration data have a certain reference value for air quality forecasting, the secondary modeling will be carried out with reference to the meteorological and pollutant data obtained from the air quality monitoring sites to optimize the forecasting model.
二次模型与 WRF-CMAQ 模型关系如图 1-3 所示。将 WRF-CMAQ 模型运行产生的数据简称为 “一次预报数据”，将空气质量监测站点实际监测得到的数据简称为 “实测数据”。一般来说，一次预报数据与实测数据相关性不高，但预报过程中常会使用实测数据对一次预报数据进行修正以达到更好的效果。
The relationship between the secondary model and the WRF-CMAQ model is shown in Figure 1-3. The data generated by the WRF-CMAQ model are referred to as the "primary forecast data", and the data obtained from the actual monitoring at the air quality monitoring stations are referred to as the "measured data". Generally speaking, the correlation between the primary forecast data and the measured data is not high, but the measured data are often used in the forecasting process to correct the primary forecast data to achieve better results.
图 1-3 二次模型优化的 WRF-CMAQ 空气质量预报过程
Figure 1-3 WRF-CMAQ air quality forecasting process with secondary model optimization
为进行二次建模以预测给定监测点未来三天的空气质量情况，题目提供了监测点长期空气质量预报基础数据，包括污染物浓度一次预报数据、气象一次预报数据、气象实测数据和污染物浓度实测数据，其中，所有一次预报数据的时间跨度为2020年7月23日到2021年 7 月 13 日，所有实测数据的时间跨度为 2019 年 4 月 16 日到 2021 年 7 月 13 日，数据总量在十万量级（详见附件 1 − 3 1 − 3 1-31-3 ）。
For secondary modeling to predict the air quality conditions at a given monitoring site for the next three days, the title provides the long-term air quality forecasting base data at the monitoring site, including the primary forecast data of pollutant concentrations, the meteorological primary forecast data, the meteorological measured data, and the pollutant concentration measured data, of which all the primary forecast data span from July 23, 2020 to July 13, 2021, and all the measured data span from April 16, 2019 to July 13, 2021, and the total amount of data is in the order of 100,000 (see Annex 1 − 3 1 − 3 1-31-3 for details).
需要注意的是：（1）每日预报的时间固定为早晨 7 点，此时可以获得当日 7 时及之前时刻的实测数据，以及运行日期在当日及之前日期的一次预报数据（预报时间范围截至第三日 23 时）。监测时间在当日 7 时以后的逐小时实测数据和运行日期在次日及以后的一次预报数据都是无法获得的，例如：在2021年7月13日晨间对7月13日至7月15日的空气质量进行预报过程中，可供参考的实测数据时间范围为（2019 年 4 月 16 日 00：00至2021年 7 月 13 日 7：00），模型运行日期范围为（2020年7月23日至2021年7月13日）。(2)受监测数据权限及相应监测设备功能等的限制，部分气象指标的实测数据无法获得。（3）由于一次预报对邻近日期的准确度较高，故理论上二次预报对邻近日期的准确度也较高。
It should be noted that: (1) The time of the daily forecast is fixed at 7:00 a.m., at which time the measured data of the current day at 7:00 a.m. and the hourly measured data of the current day and before, as well as the one-time forecast data of the operation date of the current day and the date before, are available (the time range of the forecast is up to 23:00 a.m. on the third day). Hour-by-hour measured data after 7:00 a.m. on the same day and one-time forecast data for the next day and beyond are not available. For example, during the morning forecast of air quality from July 13 to July 15 on July 13, 2021, the time range of the measured data available for reference is (April 16, 2019 at 00:00 to July 13, 2021 at 7:00), and the model run date range is (April 16, 2019 at 00:00 to July 13, 2021 at 7: 00), and the model run date range is (July 23, 2020 to July 13, 2021). (2) Due to limitations in monitoring data permissions and functions of corresponding monitoring equipment, etc., measured data of some meteorological indicators are not available. (3) Since the primary forecast is more accurate for the neighboring dates, the secondary forecast is theoretically more accurate for the neighboring dates as well.
根据《环境空气质量标准》（GB3095-2012），用于衡量空气质量的常规大气污染物共有六种，分别为二氧化硫 ( SO 2 ) SO 2 (SO_(2))\left(\mathrm{SO}_{2}\right) 、二氧化氮 ( NO 2 ) NO 2 (NO_(2))\left(\mathrm{NO}_{2}\right) 、粒径小于 10 μ m 10 μ m 10 mum10 \mu \mathrm{~m} 的颗粒物 ( PM 10 ) PM 10 (PM_(10))\left(\mathrm{PM}_{10}\right) 、粒径小于 2.5 μ m 2.5 μ m 2.5 mum2.5 \mu \mathrm{~m} 的颗粒物 ( PM 2.5 ) PM 2.5 (PM_(2.5))\left(\mathrm{PM}_{2.5}\right) 、臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 、一氧化碳 ( CO ) ( CO ) (CO)(\mathrm{CO}) 。其中，臭氧污染在全国多地区频发，对臭氧污染的预警与防治是环保部门的工作重点。臭氧浓度预报也是六项污染物预报中较难的一项，其原因在于：作为六项污染物中唯一的二次污染物，臭氧并非来自污染源的直接排放，而是在大气中经过一系列化学及光化学反应生成的（参考附录一种近地面臭氧污染形成机制部分），这导致用 WRF-CMAQ 模型精确预测臭氧浓度变化的难度很高；同时，国内外已有的研究工作尚未得出臭氧生成机理的一般结论 [ 2 ] [ 2 ] ^([2]){ }^{[2]} 。
According to the Ambient Air Quality Standards (GB3095-2012), there are six conventional air pollutants used to measure air quality, namely sulfur dioxide (SO2), nitrogen dioxide (NO2) ( NO 2 ) NO 2 (NO_(2))\left(\mathrm{NO}_{2}\right) , particulate matter (PM) ( PM 10 ) PM 10 (PM_(10))\left(\mathrm{PM}_{10}\right) with particle sizes 10 μ m 10 μ m 10 mum10 \mu \mathrm{~m} , PM 2.5 μ m 2.5 μ m 2.5 mum2.5 \mu \mathrm{~m} with particle sizes ( PM 2.5 ) PM 2.5 (PM_(2.5))\left(\mathrm{PM}_{2.5}\right) , ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) , carbon monoxide ( CO ) ( CO ) (CO)(\mathrm{CO}) , and ozone ( CO ) ( CO ) (CO)(\mathrm{CO}) . , particulate matter ( PM 10 ) PM 10 (PM_(10))\left(\mathrm{PM}_{10}\right), particulate matter smaller than 2.5 μ m 2.5 μ m 2.5 mum2.5 \mu \mathrm{~m} ( PM 2.5 ) PM 2.5 (PM_(2.5))\left(\mathrm{PM}_{2.5}\right) , ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) and carbon monoxide ( CO ) ( CO ) (CO)(\mathrm{CO}) . Among them, ozone pollution is frequent in many areas of the country, the warning and prevention of ozone pollution is the focus of the environmental protection department. Ozone concentration forecasting is also one of the more difficult of the six pollutants forecasting, the reason is: as the only secondary pollutant among the six pollutants, ozone is not directly emitted from the pollution sources, but is generated in the atmosphere through a series of chemical and photochemical reactions (refer to the Appendix, a part of the mechanism of the formation of near-surface ozone pollution), which results in the difficulty in accurately predicting the change of ozone concentration using the WRF-CMAQ model; at the same time, there are many international and domestic organizations that have been working on ozone pollution warning and prevention. This makes it difficult to accurately predict changes in ozone concentration using the WRF-CMAQ model; at the same time, general conclusions on the mechanism of ozone generation have not yet been drawn from the existing domestic and international research work [ 2 ] [ 2 ] ^([2]){ }^{[2]} .
综上所述，根据问题要求，基于一次预报数据及实测数据（见附件）进行空气质量预报二次数学建模，建立一个具有一定的鲁棒性的模型，完成以下四个问题。请注意，实际工作
In summary, according to the requirements of the problem, the secondary mathematical modeling of air quality forecasting based on the primary forecast data and the measured data (see annex) is carried out to build a model with certain robustness to complete the following four problems. Please note that the actual work
中会遇到数据为空值或异常值的情况（见附录），故要求建立的模型具有一定的鲁棒性。
In the case of null values or outliers (see Appendix), the model is required to be robust.
问题 1. 使用附件 1 中的数据，按照附录中的方法计算监测点 A 从 2020年8月25日到 8 月 28 日每天实测的 AQI 和首要污染物，按照附录 "AQI 计算结果表"的格式给出结果。
Question 1: Using the data in Annex 1, calculate the measured daily AQI and top pollutants for monitoring point A from August 25 to August 28, 2020 according to the methodology in the Appendix, and present the results in the format of the "AQI Calculation Results Table" in the Appendix.
问题 2. 在污染物排放情况不变的条件下，某一地区的气象条件有利于污染物扩散或沉降时，该地区的 AQI 会下降，反之会上升。使用附件 1 中的数据，根据对污染物浓度的影响程度，对气象条件进行合理分类，并阐述各类气象条件的特征。
Question 2: If the meteorological conditions in an area are conducive to the dispersion or deposition of pollutants, the AQI of the area will decrease, and vice versa, if the pollutant emissions remain unchanged. Using the data in Annex 1, rationalize the classification of meteorological conditions according to the degree of influence on pollutant concentrations and describe the characteristics of each type of meteorological condition.
问题 3. 使用附件 1、2 中的数据，建立一个同时适用于 A、B、C三个监测点（监测点两两间直线距离 > 100 km > 100 km > 100km>100 \mathrm{~km} ，忽略相互影响）的二次预报数学模型，用来预测未来三天 6 种常规污染物单日浓度值，要求二次预报模型预测结果中 AQI 预报值的最大相对误差应尽量小，且首要污染物预测准确度尽量高。并使用该模型预测监测点 A、B、C 在 2021 年 7 月 13日至 7 月 15 日 6 种常规污染物的单日浓度值，计算相应的 AQI 和首要污染物，依照附录 "污染物浓度及 AQI 预测结果表"的格式给出结果。
Question 3: Using the data in Annexes 1 and 2, establish a quadratic forecasting mathematical model applicable to three monitoring points A, B and C at the same time (with a straight line distance > 100 km > 100 km > 100km>100 \mathrm{~km} between the two monitoring points, ignoring the interaction) to predict the single-day concentration values of six conventional pollutants in the next three days, and require that the maximum relative error of the AQI prediction in the quadratic model should be as small as possible and that the accuracy of the top pollutant prediction should be as high as possible. The maximum relative error of the AQI forecasts in the secondary forecasting model should be as small as possible, and the accuracy of the primary pollutant forecasts should be as high as possible. The model is used to predict the single-day concentrations of the six conventional pollutants at monitoring points A, B, and C from July 13 to July 15, 2021, calculate the corresponding AQIs and the top pollutants, and give the results in the format of the "Table of Pollutant Concentrations and AQI Prediction Results" in the Appendix.
问题 4. 相邻区域的污染物浓度往往具有一定的相关性，区域协同预报可能会提升空气质量预报的准确度。如图 4，监测点 A 的临近区域内存在监测点 A1、A2、A3，使用附件 1、3 中的数据, 建立包含 A、A1、A2、A3 四个监测点的协同预报模型, 要求二次模型预测结果中 A Q I A Q I AQIA Q I 预报值的最大相对误差应尽量小，且首要污染物预测准确度尽量高。使用该模型预测监测点 A、A1、A2、A3 在 2021 年 7 月 13 日至 7 月 15 日 6 种常规污染物的单日浓度值，计算相应的 AQI 和首要污染物，依照附录 "污染物浓度及 AQI 预测结果表"的格式在文中给出结果。并讨论：与问题 3 的模型相比，协同预报模型能否提升针对监测点 A 的污染物浓度预报准确度？并说明原因。
Pollutant concentrations in neighboring areas are often correlated, and regional synergistic forecasting may improve the accuracy of air quality forecasting. As shown in Fig. 4, monitoring points A1, A2, and A3 exist in the neighboring area of monitoring point A. Using the data in Appendices 1 and 3, a synergistic prediction model is built with four monitoring points A, A1, A2, and A3, and it is required that the maximum relative error of the A Q I A Q I AQIA Q I forecast values in the quadratic model should be as small as possible, and that the prediction of the primary pollutants should have as high an accuracy as possible. The model is used to predict the single-day concentrations of six conventional pollutants at monitoring points A, A1, A2, and A3 from July 13 to July 15, 2021, and to calculate the corresponding AQIs and top pollutants, and the results are presented in the text according to the format of the "Pollutant Concentration and AQI Prediction Results Table" in the Appendix. Discuss whether the collaborative forecasting model can improve the accuracy of pollutant concentration prediction for monitoring point A compared with the model in Question 3. Explain the reasons.

2. 模型假设及关键性符号说明 2. Model assumptions and description of key symbols

（1）假设空气质量检测站点实时监测所采集数据可以良好反映此时刻的空气质量情况；
(1) It is assumed that the data collected by the real-time monitoring of air quality detection stations can reflect the air quality situation at this moment in time well;
（2）假设设备检测过程中所采集的正常数据都是准确的;
(2) It is assumed that the normal data collected during the testing of the equipment are accurate; the
（3）假设通过数据找出的首要污染物浓度可以反映出空气质量等级；
(3) It is assumed that the concentrations of the top pollutants identified through the data reflect the air quality classes;
（4）假设每改变一次首要污染物的值，空气质量情况和情况都会相应及时的发生变化。
(4) It is assumed that for each change in the value of the primary pollutant, the air quality situation and condition will change accordingly and in a timely manner.
符号说明： Symbol Description:

符号 notation

AQI
C O 3 C O 3 C_(O_(3))\mathrm{C}_{\mathrm{O}_{3}}
IAQI P IAQI P IAQI_(P)\mathrm{IAQI}_{\mathrm{P}}
C P C P C_(P)\mathrm{C}_{\mathrm{P}}
BP Hi BP Hi BP_(Hi)\mathrm{BP}_{\mathrm{Hi}}
BP Lo BP Lo BP_(Lo)\mathrm{BP}_{\mathrm{Lo}}
IAQI Hi IAQI Hi IAQI_(Hi)\mathrm{IAQI}_{\mathrm{Hi}}
IAQI Lo IAQI Lo  IAQI_("Lo ")\mathrm{IAQI}_{\text {Lo }}

意义 significance

空气质量指数； Air Quality Index;
臭氧 ( O 3 ) O 3 (O_(3))\left(O_{3}\right) 最大 8 小时滑动平均；
Ozone ( O 3 ) O 3 (O_(3))\left(O_{3}\right) Maximum 8-hour sliding average;
污染物 P 的空气质量分指数，结果进位取整数； Air quality sub-index for pollutant P, with results rounded to the nearest whole number;
污染物 P 的质量浓度值； Mass concentration values for pollutant P;
与 C P C P C_(P)\mathrm{C}_{\mathrm{P}} 相近的污染物浓度限值的高位值；
Higher values of pollutant concentration limits that are similar to C P C P C_(P)\mathrm{C}_{\mathrm{P}} ;
与 C P C P C_(P)\mathrm{C}_{\mathrm{P}} 相近的污染物浓度限值的低位值；
Lower values of pollutant concentration limits that are similar to C P C P C_(P)\mathrm{C}_{\mathrm{P}} ;
与 BP Hi BP Hi BP_(Hi)\mathrm{BP}_{\mathrm{Hi}} 对应的空气质量分指数； The air quality sub-index corresponding to BP Hi BP Hi BP_(Hi)\mathrm{BP}_{\mathrm{Hi}} ;
与 BP Lo BP Lo BP_(Lo)\mathrm{BP}_{\mathrm{Lo}} 对应的空气质量分指数。 The air quality sub-index corresponding to BP Lo BP Lo BP_(Lo)\mathrm{BP}_{\mathrm{Lo}} .

3. 问题一分析与求解 3. Problem 1 analysis and solution

3.1 问题一分析 3.1 Analysis of question one

题目提供了监测点长期空气质量预报基础数据，包括污染物浓度一次预报数据、气象一次预报数据、气象实测数据和污染物浓度实测数据，其中，所有一次预报数据的时间跨度为2020年7月23日到2021年7月13日，所有实测数据的时间跨度为2019年4月16日到2021年7月13日，一次预报数据包括了近地 2 米温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) 、地表温度 ( K ) ( K ) (K)(\mathrm{K}) 、湿度 ( % ) ( % ) (%)(\%) 、近地 10 米风速 ( m / s ) ( m / s ) (m//s)(\mathrm{m} / \mathrm{s}) 、大气压 ( Kpa ) ( Kpa ) (Kpa)(\mathrm{Kpa}) 的相应气象参数共 15 个，及用于衡量空气质量的六种常规大气污染物的小时平均浓度，常规大气污染物分别为一氧化碳 ( CO ) ( CO ) (CO)(\mathrm{CO}) 、二氧化硫 ( SO 2 ) SO 2 (SO_(2))\left(\mathrm{SO}_{2}\right) 、氮氧化物 ( NOx ) ( NOx ) (NOx)(\mathrm{NOx}) 、臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 等气体污染物和可吸入颗粒物 ( PM 10 ) PM 10 (PM_(10))\left(\mathrm{PM}_{10}\right) 、细颗粒物 ( PM 2.5 ) PM 2.5 (PM_(2.5))\left(\mathrm{PM}_{2.5}\right) 等颗粒态污染物，这些大气污染物对公众生活具有潜在的负面影响，甚至会引发一系列健康问题 [1]。
The title provides basic data for long-term air quality forecasting at the monitoring sites, including primary forecast data of pollutant concentrations, meteorological primary forecast data, meteorological measured data, and pollutant concentration measured data, of which all primary forecast data span from July 23, 2020 to July 13, 2021, and all measured data span from April 16, 2019 to July 2021 On July 13, 2019, a total of 15 meteorological parameters corresponding to near-surface 2-meter temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) , surface temperature ( K ) ( K ) (K)(\mathrm{K}) , humidity ( % ) ( % ) (%)(\%) , near-surface 10-meter wind speed ( m / s ) ( m / s ) (m//s)(\mathrm{m} / \mathrm{s}) , and atmospheric pressure ( Kpa ) ( Kpa ) (Kpa)(\mathrm{Kpa}) are included in a single forecast, as are the hourly average concentrations of the six conventional air pollutants used to measure air quality. These are gaseous pollutants such as carbon monoxide (CO) ( CO ) ( CO ) (CO)(\mathrm{CO}) , sulfur dioxide (SO2) ( SO 2 ) SO 2 (SO_(2))\left(\mathrm{SO}_{2}\right) , nitrogen oxides (NOx) ( NOx ) ( NOx ) (NOx)(\mathrm{NOx}) , and ozone (Ozone) ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) , as well as particulate pollutants such as inhalable particulate matter (PM) ( PM 10 ) PM 10 (PM_(10))\left(\mathrm{PM}_{10}\right) and fine particulate matter (FPM) ( PM 2.5 ) PM 2.5 (PM_(2.5))\left(\mathrm{PM}_{2.5}\right) , which are potentially negatively affecting the lives of the public and may even cause a series of health problems [1]. These air pollutants have potential negative impacts on public life and may even cause a series of health problems [1].
其中，臭氧污染在全国多地区频发，对臭氧污染的预警与防治是环保部门的工作重点。臭氧浓度预报也是六项污染物预报中较难的一项，其原因在于：作为六项污染物中唯一的二次污染物，臭氧并非来自污染源的直接排放，而是在大气中经过一系列化学及光化学反应生成的 [ 3 ] [ 3 ] ^([3]){ }^{[3]} 。问题要求使用附件 1 中的数据，按照附录中的方法计算监测点 A 从 2020 年 8月25日到8月28日每天实测的 AQI 和首要污染物，并将结果按照附录"AQI 计算结果表"的格式放在正文中。根据观察发现，需要用到的参数在2020年8月25日到8月28日中不存在空值缺失等问题，因此问题 1 可以直接通过公式求出相应的结果。
Among them, ozone pollution occurs frequently in many areas of the country, and the early warning and prevention of ozone pollution is the focus of the work of the environmental protection department. Ozone concentration forecasting is also one of the more difficult of the six pollutants because, as the only secondary pollutant among the six pollutants, ozone is not directly emitted from pollution sources, but is generated through a series of chemical and photochemical reactions in the atmosphere [ 3 ] [ 3 ] ^([3]){ }^{[3]} . The question asked to use the data in Annex 1 to calculate the measured AQI and the top pollutants for each day from August 25 to August 28, 2020 at monitoring point A according to the methodology in the appendix, and to put the results in the body of the text in the format of the appendix "AQI Calculation Results Table". It is observed that there are no null values missing for the parameters used from August 25 to August 28, 2020, so the corresponding results for Question 1 can be obtained directly from the formula.

3. 2 问题一求解 3.2 Problem solving

首先要计算臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 最大 8 小时滑动平均，因为当臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 最大 8 小时滑动平均浓度值高于 800 μ g / m 3 800 μ g / m 3 800 mug//m^(3)800 \mu \mathrm{~g} / \mathrm{m}^{3} 时，或其余污染物浓度高于 IAQI = 500 IAQI = 500 IAQI=500\mathrm{IAQI}=500 对应限值时，不再进行其空气质量分指数计算。
The first step is to calculate the maximum 8-hour sliding average of ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) because when the maximum 8-hour sliding average of ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) is higher than 800 μ g / m 3 800 μ g / m 3 800 mug//m^(3)800 \mu \mathrm{~g} / \mathrm{m}^{3} , or when the concentration of the remaining pollutants is higher than the corresponding limit value of IAQI = 500 IAQI = 500 IAQI=500\mathrm{IAQI}=500 , the calculation of their AQ sub-indexes is no longer carried out.
臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 最大 8 小时滑动平均是指一个自然日内 8 时至 24 时的所有 8 小时滑动平均浓度中的最大值，其中 8 小时滑动平均值指连续 8 小时平均浓度的算术平均值。其计算公式如下:
The maximum 8-hour sliding average of ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) is the maximum of all 8-hour sliding average concentrations from 8:00 a.m. to 24:00 a.m. on a natural day, where the 8-hour sliding average is the arithmetic mean of the concentrations averaged over 8 consecutive hours. The formula is as follows.
C O 3 = max t = 8 , 9 , … , 24 { 1 8 ∑ i = t − 7 t c i } C O 3 = max t = 8 , 9 , … , 24   1 8 ∑ i = t − 7 t   c i C_(O_(3))=max_(t=8,9,dots,24){(1)/(8)sum_(i=t-7)^(t)c_(i)}\mathrm{C}_{\mathrm{O}_{3}}=\max _{\mathrm{t}=8,9, \ldots, 24}\left\{\frac{1}{8} \sum_{\mathrm{i}=\mathrm{t}-7}^{\mathrm{t}} \mathrm{c}_{\mathrm{i}}\right\}
其中 c i c i c_(i)c_{i} 为臭氧在某日 t − 1 t − 1 t-1t-1 时至 t t tt 时的平均污染物浓度。
where c i c i c_(i)c_{i} is the average pollutant concentration of ozone from t − 1 t − 1 t-1t-1 to t t tt on a given day.
各项污染物的空气质量分指数(IAQI), 其计算公式如下:
Air quality sub-index (IAQI) for each pollutant, calculated as follows.
IAQI P = IAQI H − IAQI Lo BP Hi − BP Lo ⋅ ( C P − BP Lo ) + IAQI Lo IAQI P = IAQI H − IAQI Lo BP Hi − BP Lo ⋅ C P − BP Lo + IAQI Lo IAQI_(P)=(IAQI_(H)-IAQI_(Lo))/(BP_(Hi)-BP_(Lo))*(C_(P)-BP_(Lo))+IAQI_(Lo)\mathrm{IAQI}_{\mathrm{P}}=\frac{\mathrm{IAQI}_{\mathrm{H}}-\mathrm{IAQI}_{\mathrm{Lo}}}{\mathrm{BP}_{\mathrm{Hi}}-\mathrm{BP}_{\mathrm{Lo}}} \cdot\left(\mathrm{C}_{\mathrm{P}}-\mathrm{BP}_{\mathrm{Lo}}\right)+\mathrm{IAQI}_{\mathrm{Lo}}
各项污染物项目浓度限值及对应的空气质量分指数级别见表 3-1。
The concentration limits for each pollutant and the corresponding AQSIQ levels are shown in Table 3-1.
表 3-1 空气质量分指数（IAQI）及对应的污染物项目浓度限值
Table 3-1 Air Quality Index (IAQI) and Corresponding Concentration Limits for Pollutant Items
序 号  序   号  {:[" 序 "],[" 号 "]:}\begin{aligned} & \text { 序 } \\ & \text { 号 } \end{aligned}序号 指数或污染物项目 Index or pollutant item 空气质量分指数及对应污染物浓度限值 Air quality sub-indices and corresponding pollutant concentration limits 单位 unit (of measure)
0 空气质量分指数(IAQI) Air quality sub-index (IAQI) 0 50 100 150 200 300 400 500 -
" 序 号 " 指数或污染物项目 空气质量分指数及对应污染物浓度限值 单位 0 空气质量分指数(IAQI) 0 50 100 150 200 300 400 500 -| $\begin{aligned} & \text { 序 } \\ & \text { 号 } \end{aligned}$ | 指数或污染物项目 | 空气质量分指数及对应污染物浓度限值 | | | | | | | | 单位 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 0 | 空气质量分指数(IAQI) | 0 | 50 | 100 | 150 | 200 | 300 | 400 | 500 | - |
1 一氧化碳(CO)24 小时平均 Carbon monoxide (CO) 24-hour average 0 2 4 14 24 36 48 60 mg/ m3
2 二氧化硫 ( SO 2 ) 24 SO 2 24 (SO_(2))24\left(\mathrm{SO}_{2}\right) 24 小时平均 Sulfur dioxide ( SO 2 ) 24 SO 2 24 (SO_(2))24\left(\mathrm{SO}_{2}\right) 24 Hourly average 0 50 150 475 800 1600 2100 2620 μ g / m 3 μ g / m 3 mug//m^(3)\mu \mathrm{g} / \mathrm{m}^{3}
3 二氧化氮 ( NO 2 ) 24 NO 2 24 (NO_(2))24\left(\mathrm{NO}_{2}\right) 24 小时平均 Nitrogen dioxide ( NO 2 ) 24 NO 2 24 (NO_(2))24\left(\mathrm{NO}_{2}\right) 24 Hourly average 0 40 80 180 280 565 750 940
4 臭氧 ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) 最大 8 小时滑动平均
Ozone ( O 3 ) O 3 (O_(3))\left(\mathrm{O}_{3}\right) Maximum 8-hour sliding average		 0 100 160 215 265 800 - -
5 粒径小于等于 10 μ m 10 μ m 10 mum10 \mu \mathrm{~m} 颗粒物 ( PM 10 ) 24 PM 10 24 (PM_(10))24\left(\mathrm{PM}_{10}\right) 24 小时平均
Particle size less than or equal to 10 μ m 10 μ m 10 mum10 \mu \mathrm{~m} Particulate matter ( PM 10 ) 24 PM 10 24 (PM_(10))24\left(\mathrm{PM}_{10}\right) 24 Hourly Average		 0 50 150 250 350 420 500 600
6 粒径小于等于 2.5 μ m 2.5 μ m 2.5 mum2.5 \mu \mathrm{~m} 颗粒物（ PM 2.5 PM 2.5 PM_(2.5)\mathrm{PM}_{2.5} ）24 小时平均
Particle size less than or equal to 2.5 μ m 2.5 μ m 2.5 mum2.5 \mu \mathrm{~m} ( PM 2.5 PM 2.5 PM_(2.5)\mathrm{PM}_{2.5} ) 24-hour average		 0 35 75 115 150 250 350 500
1 一氧化碳(CO)24 小时平均 0 2 4 14 24 36 48 60 mg/ m3 2 二氧化硫 (SO_(2))24 小时平均 0 50 150 475 800 1600 2100 2620 mug//m^(3) 3 二氧化氮 (NO_(2))24 小时平均 0 40 80 180 280 565 750 940 4 臭氧 (O_(3)) 最大 8 小时滑动平均 0 100 160 215 265 800 - - 5 粒径小于等于 10 mum 颗粒物 (PM_(10))24 小时平均 0 50 150 250 350 420 500 600 6 粒径小于等于 2.5 mum 颗粒物（ PM_(2.5) ）24 小时平均 0 35 75 115 150 250 350 500 | 1 | 一氧化碳(CO)24 小时平均 | 0 | 2 | 4 | 14 | 24 | 36 | 48 | 60 | mg/ m3 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 2 | 二氧化硫 $\left(\mathrm{SO}_{2}\right) 24$ 小时平均 | 0 | 50 | 150 | 475 | 800 | 1600 | 2100 | 2620 | $\mu \mathrm{g} / \mathrm{m}^{3}$ | | 3 | 二氧化氮 $\left(\mathrm{NO}_{2}\right) 24$ 小时平均 | 0 | 40 | 80 | 180 | 280 | 565 | 750 | 940 | | | 4 | 臭氧 $\left(\mathrm{O}_{3}\right)$ 最大 8 小时滑动平均 | 0 | 100 | 160 | 215 | 265 | 800 | - | - | | | 5 | 粒径小于等于 $10 \mu \mathrm{~m}$ 颗粒物 $\left(\mathrm{PM}_{10}\right) 24$ 小时平均 | 0 | 50 | 150 | 250 | 350 | 420 | 500 | 600 | | | 6 | 粒径小于等于 $2.5 \mu \mathrm{~m}$ 颗粒物（ $\mathrm{PM}_{2.5}$ ）24 小时平均 | 0 | 35 | 75 | 115 | 150 | 250 | 350 | 500 | |
空气质量指数(AQI)取各分指数中的最大值，即 The Air Quality Index (AQI) takes the maximum value of each sub-index, i.e.
AQI = max { IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n } AQI = max IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n AQI=max{IAQI_(1),IAQI_(2),IAQI_(3),dots,IAQI_(n)}\mathrm{AQI}=\max \left\{\mathrm{IAQI}_{1}, \mathrm{IAQI}_{2}, \mathrm{IAQI}_{3}, \ldots, \mathrm{IAQI}_{\mathrm{n}}\right\}
式中, IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n IAQI_(1),IAQI_(2),IAQI_(3),dots,IAQI_(n)\mathrm{IAQI}_{1}, \mathrm{IAQI}_{2}, \mathrm{IAQI}_{3}, \ldots, \mathrm{IAQI}_{\mathrm{n}} 为各污染物项目的分指数。在问题中, 对于 AQI 的计算仅涉及表1提供的六种污染物，因此计算公式如下：
where IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n IAQI 1 , IAQI 2 , IAQI 3 , … , IAQI n IAQI_(1),IAQI_(2),IAQI_(3),dots,IAQI_(n)\mathrm{IAQI}_{1}, \mathrm{IAQI}_{2}, \mathrm{IAQI}_{3}, \ldots, \mathrm{IAQI}_{\mathrm{n}} is the sub-index for each pollutant item. In the problem, the calculation of AQI involves only the six pollutants provided in Table 1, so the formula is as follows:
AQI = max { IAQI SO 2 , IAQI NO 2 , IAQI PM 10 , IAQI PM 2.5 , IAQI O 3 , IAQI CO } AQI = max IAQI SO 2 , IAQI NO 2 , IAQI PM 10 , IAQI PM 2.5 , IAQI O 3 , IAQI CO AQI=max{IAQI_(SO_(2)),IAQI_(NO_(2)),IAQI_(PM_(10)),IAQI_(PM_(2.5)),IAQI_(O_(3)),IAQI_(CO)}\mathrm{AQI}=\max \left\{\mathrm{IAQI}_{\mathrm{SO}_{2}}, \mathrm{IAQI}_{\mathrm{NO}_{2}}, \mathrm{IAQI}_{\mathrm{PM}_{10}}, \mathrm{IAQI}_{\mathrm{PM}_{2.5}}, \mathrm{IAQI}_{\mathrm{O}_{3}}, \mathrm{IAQI}_{\mathrm{CO}}\right\}
空气质量等级范围根据 AQI 数值划分，等级对应的 AQI 范围见表 3-2。
The air quality class ranges are based on AQI values, and the corresponding AQI ranges for the classes are shown in Table 3-2.
表 3-2 空气质量等级及对应空气质量指数(AQI)范围
Table 3-2 Air Quality Levels and Corresponding Air Quality Index (AQI) Ranges
空气质量等级 air quality rating 优 良 轻度污染 light pollution 中度污染 moderate pollution 重度污染 heavy pollution
 Serious contamination
严重污
染
严重污 染| 严重污 | | :---: | | 染 |
空气质量指数（AQI）范围 Air Quality Index (AQI) Range [ 0 , 50 ] [ 0 , 50 ] [0,50][0,50] [ 51 , 100 ] [ 51 , 100 ] [51,100][51,100] [ 101 , 150 ] [ 101 , 150 ] [101,150][101,150] [ 151 , 200 ] [ 151 , 200 ] [151,200][151,200] [ 201 , 300 ] [ 201 , 300 ] [201,300][201,300] [ 301 , + ∞ ) [ 301 , + ∞ ) [301,+oo)[301,+\infty)
空气质量等级 优 良 轻度污染 中度污染 重度污染 "严重污 染" 空气质量指数（AQI）范围 [0,50] [51,100] [101,150] [151,200] [201,300] [301,+oo)| 空气质量等级 | 优 | 良 | 轻度污染 | 中度污染 | 重度污染 | 严重污 <br> 染 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 空气质量指数（AQI）范围 | $[0,50]$ | $[51,100]$ | $[101,150]$ | $[151,200]$ | $[201,300]$ | $[301,+\infty)$ |
当 AQI 小于或等于 50 （即空气质量评价为 “优”）时，称当天无首要污染物；当 AQI大于 50 时，IAQI 最大的污染物为首要污染物，若 IAQI 最大的污染物为两项或两项以上时，并列为首要污染物；IAQI 大于 100 的污染物为超标污染物。
When the AQI is less than or equal to 50 (i.e., the air quality is evaluated as "excellent"), it is said that there is no primary pollutant on that day; when the AQI is greater than 50, the pollutant with the largest IAQI is the primary pollutant, and if the pollutant with the largest IAQI is two or more pollutants, they are classified together as the primary pollutant; and the pollutant with an IAQI greater than 100 is the exceedance pollutant.
通过 Matlab 编程，监测点 A 从 2020 年 8 月 25 日到 8 月 28 日根据逐日实测数据计算出的各项污染物的 IAQI 如表 3-3 所示，
The IAQIs for each pollutant at monitoring point A, calculated from day-by-day measured data from August 25 to August 28, 2020, using Matlab programming, are shown in Table 3-3.
表 3-3 监测点 A 从 2020 年 8 月 25 日到 8 月 28 日每天实测的 IAQI 和空气质量等级(逐日实测数据计算)
Table 3-3 Measured IAQI and Air Quality Levels at Monitoring Site A for Each Day from August 25 to August 28, 2020 (Calculated from Daily Measured Data)
监测日期 Date of monitoring 地点 spot IAQI 计算 IAQI calculation 空气质量等级 air quality rating
IAQI CO IAQI CO IAQI_(CO)\mathrm{IAQI}_{\mathrm{CO}} IAQI SO 2 IAQI SO 2 IAQI_(SO_(2))\mathrm{IAQI}_{\mathrm{SO}_{2}} IAQI NO 2 IAQI NO 2 IAQI_(NO_(2))\mathrm{IAQI}_{\mathrm{NO}_{2}} IAQI 0 3 IAQI 0 3 IAQI_(0_(3))\mathrm{IAQI}_{0_{3}} IAQI PM 10 IAQI PM 10 IAQI_(PM_(10))\mathrm{IAQI}_{\mathrm{PM}_{10}} IAQI PM 2.5 IAQI PM 2.5 IAQI_(PM_(2.5))\mathrm{IAQI}_{\mathrm{PM}_{2.5}}
2020/8/25 监测点 A Monitoring point A 13 8 15 60 27 16 良
2020/8/26 监测点 A Monitoring point A 13 7 20 46 24 15 优
2020/8/27 监测点 A Monitoring point A 15 7 39 109 37 33 轻度污染 light pollution
2020/8/28 监测点 A Monitoring point A 18 8 38 138 47 48 轻度污染 light pollution
监测日期 地点 IAQI 计算 空气质量等级 IAQI_(CO) IAQI_(SO_(2)) IAQI_(NO_(2)) IAQI_(0_(3)) IAQI_(PM_(10)) IAQI_(PM_(2.5)) 2020/8/25 监测点 A 13 8 15 60 27 16 良 2020/8/26 监测点 A 13 7 20 46 24 15 优 2020/8/27 监测点 A 15 7 39 109 37 33 轻度污染 2020/8/28 监测点 A 18 8 38 138 47 48 轻度污染| 监测日期 | 地点 | IAQI 计算 | | | | | | 空气质量等级 | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | | | $\mathrm{IAQI}_{\mathrm{CO}}$ | $\mathrm{IAQI}_{\mathrm{SO}_{2}}$ | $\mathrm{IAQI}_{\mathrm{NO}_{2}}$ | $\mathrm{IAQI}_{0_{3}}$ | $\mathrm{IAQI}_{\mathrm{PM}_{10}}$ | $\mathrm{IAQI}_{\mathrm{PM}_{2.5}}$ | | | 2020/8/25 | 监测点 A | 13 | 8 | 15 | 60 | 27 | 16 | 良 | | 2020/8/26 | 监测点 A | 13 | 7 | 20 | 46 | 24 | 15 | 优 | | 2020/8/27 | 监测点 A | 15 | 7 | 39 | 109 | 37 | 33 | 轻度污染 | | 2020/8/28 | 监测点 A | 18 | 8 | 38 | 138 | 47 | 48 | 轻度污染 |
则监测点 A 从 2020 年 8 月 25 日到 8 月 28 日根据逐日实测数据计算出的 AQI 和首要污染物，结果如表 3-4所示。
The AQI and the primary pollutant calculated from the day-by-day measured data from August 25 to August 28, 2020 at Monitoring Point A are shown in Table 3-4.