Method for quantifying influence of fireworks and crackers on fine particulate matter level
By establishing a meteorological factor and PM2.5 concentration data analysis method based on the XGBoost model, the problem of the increase in CO concentration during the fireworks and firecrackers causing high PM2.5 regression results were solved, and the accurate quantification of the impact of fireworks and firecrackers on PM2.5 concentration was achieved.
Patent Information
- Application Number
- CN202510025306.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-08
- Publication Date
- 2025-05-13
- Estimated Expiration
- 2045-01-08
AI Technical Summary
The CO concentration generated during the fireworks and firecrackers is increased, resulting in a high return result for PM2.5, which underestimates the impact of fireworks and firecrackers on PM2.5.
By obtaining local meteorological factors and PM2.5 concentration data, processing them into training sets and verification sets, an XGBoost model was established, PM2.5 concentration data was simulated when fireworks were not set off, and the concentration difference was calculated to intuitively quantify the impact of fireworks on PM2.5 concentration after setting off fireworks.
This method can directly quantify the PM2.5 concentration reconstruction value data. The calculation process is simple, does not require a lot of computing power, does not rely on the three-dimensional transmission model, and the calculation results are fast and efficient, ensuring the accuracy of the data that fireworks affect the level of fine particulate matter.
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Figure CN119993307A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of atmospheric pollutant assessment, and in particular to a method for quantifying the impact of fireworks and firecrackers on the level of fine particulate matter. Background Art
[0002] The main chemical components of fireworks and firecrackers include oxidants, combustibles, flame colorants and other special effects drugs. Under the high temperature and high pressure conditions after being triggered, the substances in fireworks and firecrackers undergo a series of chemical reactions, releasing a large amount of sulfur dioxide, nitrogen oxides, heavy metals and organic matter, and producing a large amount of particulate matter, which causes a significant deterioration in air quality.
[0003] Currently, the most widely used method to evaluate the impact of fireworks and firecrackers on PM 2.5 The method of affecting particulate matter (particles with a diameter of 2.5 microns or less) is based on PM 2.5 / CO ratio method. The effect of fireworks on PM 2.5 、PM 10 , SO2 and NO2 concentrations, but less impact on CO concentration. Therefore, CO can be used as the reference standard pollutant concentration. 2.5 Analysis of the effect of fireworks and firecrackers on PM 2.5 Contribution of PM 2.5 The assumption of the / CO method is that the CO concentration is stable. However, due to incomplete combustion, a certain amount of CO will be produced during the burning of fireworks, which will increase the CO concentration and make the PM 2.5 The concentration was too high, and the impact of fireworks on PM was underestimated. 2.5 impact. Summary of the invention
[0004] The purpose of the present invention is to provide a method for quantifying the impact of fireworks on the level of fine particulate matter, so as to solve the problem that the burning process of fireworks will produce a certain amount of CO, which will increase the concentration of CO and thus make the PM 2.5 High concentration problem.
[0005] To achieve the above object, the present invention provides the following technical solutions:
[0006] A method to quantify the impact of fireworks on fine particulate matter levels includes: obtaining local meteorological factors and local PM 2.5 concentration data; the meteorological factors and PM 2.5 The concentration data were processed into training set and validation set. The relationship between meteorological factors and PM 2.5 XGBoost model for concentration data; the meteorological factors in the validation set are input into the XGBoost model, and the XGBoost model outputs PM according to the meteorological factors in the validation set.2.5 Concentration reconstruction value data, among which PM 2.5 The concentration reconstruction value data is the data when the XGBoost model simulates the fireworks without setting off fireworks; the PM 2.5 Concentration data and PM 2.5 The concentration reconstruction value data is subtracted to obtain the quantitative concentration difference, which can intuitively quantify the PM after setting off fireworks. 2.5 The influence of concentration.
[0007] As a further solution of the present invention: the acquisition of historical local meteorological factors and local PM 2.5 Concentration data, including: the meteorological factors include local temperature, humidity, precipitation, wind volume, wind speed and ground pressure, where temperature, humidity, precipitation, wind volume, wind speed and ground pressure come from local meteorological monitoring data and environmental monitoring data. Beneficial effect: This method uses multiple meteorological data to input the trained XGBoost model, calculates multiple factors through the XGBoost model, and simulates the current PM 2.5 The concentration reconstruction value data is more accurate.
[0008] As a further solution of the present invention: the wind volume vector is decomposed into u component and v component; the u component = wind speed * sin ((wind direction - 180) × π / 180); the v component = wind speed * cos ((wind direction - 180) × π / 180); wherein the wind speed and wind direction data are from local meteorological monitoring data. Beneficial effect: the wind volume is vector decomposed into u component and v component, after the meteorological monitoring equipment detects the wind speed and wind direction data, the u component and the v component are calculated, and then the wind volume is calculated by synthesis, the wind volume calculation is fast and convenient, the calculation is accurate, and the operation is convenient.
[0009] As a further solution of the present invention: 2.5 The concentration data is processed into a training set and a validation set, including: the local meteorological factors and the local PM 2.5 The extracted part of the concentration data is the training set; the local meteorological factors and the local PM 2.5 The remaining part of the concentration data is the validation set; the training set is the corresponding data monitored during the period when fireworks are not set off; and the validation set includes the corresponding data monitored during the period when fireworks are set off.
[0010] As a further solution of the present invention: the data volume of the training set is greater than the data volume of the validation set.
[0011] As a further solution of the present invention: the method of establishing the relationship between meteorological factors and PM according to the training set 2.5The XGBoost model for concentration data includes: the XGBoost model has several hyperparameters; the hyperparameters include the number of trees, the learning rate, the maximum depth of the tree, the minimum loss function reduction required for each tree training and the splitting of the tree; the number of trees is used to represent the number of iterations; the learning rate is used to control the contribution of each tree to the final prediction; the maximum depth of the tree is used to control the complexity of the tree; the proportion of samples randomly selected when each tree is trained; the minimum loss function reduction required for the splitting of the tree is used to control the tree generation process.
[0012] As a further solution of the present invention: the XGBoost model is established by using Yes optimization to select optimized hyperparameters to establish an optimized XGBoost model; the optimized XGBoost model fits multiple prediction PMs according to the data in the training set. 2.5 Concentration data, based on multiple predicted PM 2.5 Concentration data and PM corresponding to the local area in the training set 2.5 The coefficient of determination R was calculated from the concentration data. 2 (linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv, the determination coefficient R 2 (Linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv are used to reflect the stability and accuracy of the optimized XGBoost model.
[0013] As a further solution of the present invention: it also includes: obtaining PM 2.5 PM / CO ratio method was used to calculate PM during non-fire periods. 2.5 The concentration data and CO concentration data are used to calculate the ratio between the two, and the ratio is multiplied by the CO concentration data during the discharge period to obtain the PM concentration during the discharge period. 2.5 Regression data, PM during the fireworks period 2.5 The measured concentration data minus PM 2.5 Regression data, get the ratio concentration difference, to get the effect of fireworks on PM 2.5 ; compare the quantified concentration difference with the ratio concentration difference.
[0014] Compared with the prior art, the present invention has the following beneficial effects:
[0015] 1. In the present invention, by using local meteorological factors and local PM 2.5 The training set processed from the concentration data is used to train the XGBoost model. After the XGBoost model training is completed, when it is necessary to calculate the effect of fireworks on PM 2.5 When the concentration affects the contribution, after inputting the data related to the meteorological factors, the PM 2.5 The concentration reconstruction value data is then converted into the actual monitored PM2.5 Concentration data and PM 2.5 By subtracting the concentration reconstruction value data, we can directly obtain the effect of fireworks on PM 2.5 The concentration affects the value of the contribution, and this method can directly quantify the PM 2.5 Concentration reconstruction value data, in the calculation of PM 2.5 The numerical process of the concentration effect contribution is simple, does not require a lot of computing power, does not rely on a three-dimensional transport model, and the calculation results are fast and efficient.
[0016] 2. In the present invention, there is no need to detect CO concentration data, and the change in CO concentration caused by setting off fireworks will not affect the PM after the subsequent setting off of fireworks. 2.5 The contribution value of concentration is affected, ensuring the accuracy of the data on the impact of fireworks and firecrackers on the level of fine particulate matter, and the effect of use is good. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] Figure 1 The figure is a schematic diagram of the process steps of the method of the present invention. DETAILED DESCRIPTION
[0018] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0019] Example:
[0020] like Figure 1 The figure shows the schematic diagram of the method flow of the present invention. In this embodiment, a method for quantifying the impact of fireworks and firecrackers on the level of fine particulate matter includes:
[0021] S1: Obtain local meteorological factors and local PM 2.5 Concentration data;
[0022] S2: Combine meteorological factors and PM 2.5 The concentration data were processed into training set and validation set;
[0023] S3: Establish information about meteorological factors and PM based on the training set 2.5 XGBoost model for concentration data;
[0024] S4: The meteorological factors in the validation set are input into the XGBoost model, and the XGBoost model outputs PM according to the meteorological factors in the validation set. 2.5 Concentration reconstruction value data, among which PM 2.5The concentration reconstruction value data is the data when the XGBoost model simulates the fireworks without setting off;
[0025] S5: The PM in the validation set 2.5 Concentration data and PM 2.5 The concentration reconstruction value data is subtracted to obtain the quantitative concentration difference, which can intuitively quantify the PM after setting off fireworks. 2.5 The influence of concentration.
[0026] In the present invention, the local meteorological factors and the local PM 2.5 The training set processed from the concentration data is used to train the XGBoost model. After the XGBoost model training is completed, when it is necessary to calculate the effect of fireworks on PM 2.5 When the concentration affects the contribution, after inputting the data related to the meteorological factors, the PM 2.5 The concentration reconstruction value data is then converted into the actual monitored PM 2.5 Concentration data and PM 2.5 By subtracting the concentration reconstruction value data, we can directly obtain the effect of fireworks on PM 2.5 The concentration affects the value of the contribution, and this method can directly quantify the PM 2.5 Concentration reconstruction value data, in the calculation of PM 2.5 The numerical process of the concentration contribution is simple, does not require a lot of computing power, does not rely on a three-dimensional transmission model, and the calculation results are fast and efficient, which is beneficial to the subsequent air control.
[0027] The present invention does not require the detection of CO concentration data, and thus the change in CO concentration caused by setting off fireworks will not affect the subsequent PM after setting off fireworks. 2.5 The contribution value of concentration is affected, ensuring the accuracy of the data on the impact of fireworks and firecrackers on the level of fine particulate matter, and the effect of use is good.
[0028] Furthermore, local meteorological factors and local PM 2.5 The relevant data in the concentration data are all collected continuously with hours as the time unit, and can also be collected continuously with days as the time unit.
[0029] Furthermore, Extreme Gradient Boosting Decision Tree (XGBoost) is an algorithm or engineering implementation based on the gradient boosting decision tree (GBDT). The basic idea of XGBoost is the same as GBDT, but some optimizations have been made, such as using the second-order derivative in the formula derivation to make the loss function more accurate; adding the tree model complexity as a regular term to the optimization target to avoid overfitting; sorting the data in advance through parallel calculations, and then saving it as a block structure, which is repeatedly used in subsequent iterations to greatly reduce the amount of calculation; and being able to automatically learn the strategy for handling missing values.
[0030] In this embodiment, historical local meteorological factors and local PM 2.5 Concentration data, including: Meteorological factors include local temperature, humidity, precipitation, wind volume, wind speed and ground pressure, among which temperature, humidity, precipitation, wind volume, wind speed and ground pressure come from local meteorological monitoring data and environmental monitoring data. The temperature, humidity, precipitation, wind volume, wind speed and ground pressure data detected by local meteorological monitoring equipment are input into the XGBoost model, and multiple data are calculated through the XGBoost model to simulate the current PM 2.5 Concentration reconstruction value data, this method uses multiple meteorological data to input the trained XGBoost model, calculates multiple factors through the XGBoost model, and simulates the current PM 2.5 The concentration reconstruction value data is more accurate.
[0031] In this embodiment, the wind volume vector is decomposed into u component and v component; u component = wind speed * sin ((wind direction - 180) × π / 180); v component = wind speed * cos ((wind direction - 180) × π / 180); wherein the wind speed and wind direction data are from local meteorological monitoring data. The wind volume is vector decomposed into u component and v component. After the meteorological monitoring equipment detects the wind speed and wind direction data, the u component and the v component are calculated, and then the wind volume is calculated by synthesis. The wind volume calculation is fast and convenient, the calculation is accurate, and the operation is convenient.
[0032] In this embodiment, meteorological factors and PM 2.5 The concentration data is processed into training sets and validation sets, including: local meteorological factors and local PM 2.5 The extracted part of the concentration data is used as the training set; the local meteorological factors and local PM 2.5 The remaining part of the concentration data is the validation set; the training set is the corresponding data monitored during the period when fireworks are not set off; the validation set contains the corresponding data monitored during the period when fireworks are set off. 2.5The training set formed by the concentration data is used to train the XGBoost model, which then forms the meteorological factors and PM 2.5 The relationship between the concentration data and the simulated PM during the period without fireworks can be directly quantified by inputting meteorological factors. 2.5 Concentration reconstruction value data, when quantitative verification is needed for the concentration of fireworks during the explosion period, 2.5 When the meteorological factors of the validation set are input into the XGBoost model, PM 2.5 The concentration reconstruction value data is then used to reconstruct the PM 2.5 Concentration data and PM 2.5 The concentration reconstruction value data is subtracted to obtain the quantitative concentration difference, and the numerical value of the quantitative concentration difference is used to intuitively quantify the PM after setting off fireworks. 2.5 The influence of concentration.
[0033] In this embodiment, the amount of data in the training set is greater than the amount of data in the validation set. A larger amount of data in the training set can make the XGBoost model training more stable and accurate.
[0034] Furthermore, the training set accounts for meteorological factors and PM 2.5 80% of the total concentration data, and the remaining data is the validation set. The training set of 80% of the total data makes the XGBoost model more stable and accurate, and the training effect is good.
[0035] In this embodiment, the relationship between meteorological factors and PM is established based on the training set. 2.5The XGBoost model for concentration data includes: the XGBoost model has several hyperparameters; the hyperparameters include the number of trees, the learning rate, the maximum depth of the tree, the minimum loss function reduction required for each tree training and the splitting of the tree; the number of trees is used to represent the number of iterations; the learning rate is used to control the contribution of each tree to the final prediction; the maximum depth of the tree is used to control the complexity of the tree; the proportion of samples randomly selected when training each tree; the minimum loss function reduction required for the splitting of the tree is used to control the tree generation process. Specifically, XGBoost has multiple hyperparameters, among which the number of trees (n_estimators) indicates the number of iterations. More trees will improve the fitting ability of the model, but it is also easy to cause overfitting; the learning rate (learning_rate or eta) controls the contribution of each tree to the final prediction. A smaller learning rate usually requires more trees to converge, but may improve the generalization ability of the model; the maximum depth of the tree (max_depth) controls the complexity of the tree. A tree that is too deep is prone to overfitting, and a tree that is too shallow may not capture the complexity of the data; the proportion of randomly selected samples when training each tree (subsample), usually set to between 0.5 and 1.0, a value that is too small may lead to underfitting, and a value that is too large may lead to overfitting; the minimum loss function required for tree splitting is reduced (gamma), which is used to control the tree generation process.
[0036] In this embodiment, the XGBoost model is established by using the YES optimization to select the optimization hyperparameters to establish the optimized XGBoost model; the optimized XGBoost model fits multiple prediction PMs according to the data in the training set. 2.5 Concentration data, based on multiple predicted PM 2.5 Concentration data and PM corresponding to the local area in the training set 2.5 The coefficient of determination R was calculated from the concentration data. 2 (linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv, determination coefficient R 2 (Linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv are used to reflect the stability and accuracy of the optimized XGBoost model.
[0037] Different hyperparameter combinations have a significant impact on the performance of the model. 2.5 Concentration data and PM corresponding to the local area in the training set 2.5 Concentration data, calculation of determination coefficient R 2 , root mean square error RMSE, correlation coefficient R, and coefficient of variation cv are used to evaluate the model performance. The above parameters are used to intuitively evaluate the XGBoost model and continuously optimize the XGBoost model to achieve the purpose of stability and accuracy of the optimized XGBoost model;
[0038] Furthermore, when building the XGBoost model, the Bayesian optimization method is used to select the optimal hyperparameters and build the optimal XGBoost model. The determination coefficient R of the XGBoost model is 2 is 0.80, the root mean square error RMSE is 28.69, the correlation coefficient R is 0.90, and the coefficient of variation cv is 0.62;
[0039] The specific definition of the Bayesian optimization objective function is as follows:
[0040]
[0041]
[0042] Substituting the hourly data of meteorological factors into the model, the reconstructed value function of PM2.5 concentration unaffected by the setting off of fireworks and firecrackers is as follows:
[0043] Use the best model to predict
[0044] y_pred=pd.Series(best model.predict(X nofire),index=Xnofire.index)
[0045] # Create result data frame
[0046] result_df = pd.DataFrame({
[0047] Real network value':y_nofire,
[0048] Reconstructed value':y pred,
[0049] Fireworks and firecrackers impact':y_nofire-y_pred
[0050] })
[0051] 24-hour PM 2.5 The reconstructed concentration values are averaged to obtain the daily average value, which is then compared with the daily average actual monitored PM 2.5 By subtracting the concentration data, the average daily impact of fireworks on PM 2.5 The influence of concentration.
[0052] In this embodiment, it also includes: obtaining PM 2.5 PM / CO ratio method was used to calculate PM during non-fire periods. 2.5 The concentration data and CO concentration data are used to calculate the ratio between the two, and the ratio is multiplied by the CO concentration data during the discharge period to obtain the PM concentration during the discharge period. 2.5 Regression data, PM during the fireworks period 2.5The measured concentration data minus PM 2.5 Regression data, get the ratio concentration difference, to get the effect of fireworks on PM 2.5 ; compare the quantified concentration difference with the ratio concentration difference.
[0053] The main chemical components of fireworks and firecrackers include oxidants, combustibles, flame coloring agents and other special effect drugs.
[0054] Under the high temperature and high pressure conditions after being triggered, the substances in fireworks and firecrackers undergo a series of chemical reactions, releasing large amounts of sulfur dioxide, nitrogen oxides, heavy metals and organic matter, and producing a large amount of particulate matter, causing a significant deterioration in air quality.
[0055] Currently, the most widely used method to evaluate the impact of fireworks and firecrackers on PM 2.5 The impact method is based on PM 2.5 / CO ratio method. The effect of fireworks on PM 2.5 、PM 10 , SO2 and NO2 concentrations, but less impact on CO concentration. Therefore, CO can be used as the reference standard pollutant concentration. 2.5 Analysis of the effect of fireworks and firecrackers on PM 2.5 Contributions:
[0056]
[0057] PM 2.5 f =PM 2.5 -PM 2.5 r
[0058] Where: The average PM during the non-fire period 2.5 The ratio of concentration to average CO concentration, CO, PM 2.5 r are the hourly CO concentration and the hourly PM obtained by regression. 2.5 Concentration, PM 2.5 PM hourly 2.5 Concentration, PM 2.5 f is the ratio concentration difference, which shows the effect of fireworks on PM 2.5 The hourly contribution of .
[0059] Get PM 2.5 The ratio concentration difference obtained by the CO / CO ratio relationship method is compared with the quantitative concentration difference calculated by this method, and then the two detection methods can be used to verify each other, further improving the accuracy of the simulation calculation results.
[0060] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.
Claims
1. A method for quantifying the impact of fireworks and firecrackers on fine particulate matter levels, characterized in that: include: Get local meteorological factors and local PM 2.5 Concentration data; The meteorological factors and PM 2.5 The concentration data were processed into training set and validation set; According to the training set, the relationship between meteorological factors and PM 2.5 XGBoost model for concentration data; The meteorological factors in the validation set are input into the XGBoost model, and the XGBoost model outputs PM according to the meteorological factors in the validation set. 2.5 Concentration reconstruction value data, among which PM 2.5 The concentration reconstruction value data is the data when the XGBoost model simulates the fireworks without setting off; The PM in the validation set 2.5 Concentration data and PM 2.5 The concentration reconstruction value data is subtracted to obtain the quantitative concentration difference, which can intuitively quantify the PM after setting off fireworks. 2.5 The influence of concentration.
2. The method for quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 1, characterized in that: The acquisition of historical local meteorological factors and local PM 2.5 Concentration data, including: The meteorological factors include local temperature, humidity, precipitation, wind volume, wind speed and ground pressure, wherein the temperature, humidity, precipitation, wind volume, wind speed and ground pressure come from local meteorological monitoring data and environmental monitoring data.
3. The method for quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 2, characterized in that: The wind volume vector is decomposed into a u component and a v component; The u component = wind speed*sin((wind direction-180)×π / 180); The v component = wind speed*cos((wind direction-180)×π / 180); Among them, wind speed and wind direction data come from local meteorological monitoring data.
4. The method for quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 3, characterized in that: The meteorological factors and PM 2.5 The concentration data is processed into training set and validation set, including: The local meteorological factors and local PM 2.5 The extracted part of the concentration data is the training set; The local meteorological factors and local PM 2.5 The rest of the concentration data is the validation set; The training set is the corresponding data monitored during the period when fireworks are not set off; The validation set includes corresponding data monitored during the fireworks and firecrackers setting off period.
5. The method for quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 4, characterized in that: The data volume of the training set is larger than that of the validation set.
6. The method of quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 1, characterized in that: The method of establishing the relationship between meteorological factors and PM 2.5 XGBoost models for concentration data, including: The XGBoost model has several hyperparameters; The hyperparameters include the number of trees, the learning rate, the maximum depth of the tree, the minimum loss function reduction required for each tree training time and the tree split; The number of trees is used to represent the number of iterations; The learning rate is used to control the contribution of each tree to the final prediction; The maximum depth of the tree is used to control the complexity of the tree; The proportion of samples randomly selected during training of each tree; The minimum loss function required for splitting the tree is reduced to control the tree generation process.
7. The method of quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 6, characterized in that: The XGBoost model is established by using Yesian optimization to select optimized hyperparameters to establish an optimized XGBoost model; The optimized XGBoost model fits multiple prediction PMs based on the data in the training set. 2.5 Concentration data, based on multiple predicted PM 2.5 Concentration data and PM corresponding to the local area in the training set 2.5 The coefficient of determination R was calculated from the concentration data. 2 (linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv, the determination coefficient R 2 (Linear regression fit), root mean square error RMSE, correlation coefficient R and coefficient of variation cv are used to reflect the stability and accuracy of the optimized XGBoost model.
8. The method of quantifying the impact of fireworks and firecrackers on fine particulate matter levels according to claim 1, characterized in that: Also includes: Get PM 2.5 PM / CO ratio method was used to calculate PM during non-fire periods. 2.5 The concentration data and CO concentration data are used to calculate the ratio between the two, and the ratio is multiplied by the CO concentration data during the discharge period to obtain the PM concentration during the discharge period. 2.5 Regression data, PM during the fireworks period 2.5 The measured concentration data minus PM 2.5 Regression data, get the ratio concentration difference, to get the effect of fireworks on PM 2.5 The impact of Compare the quantified concentration difference with the ratio concentration difference.
Citation Information
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