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An Estimation Method for PM_{2.5} Based on Aerosol Optical Depth Obtained from Remote Sensing Image Processing and Meteorological Factors

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## Abstract

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_{2.5}) in size is important for controlling environmental pollution. Currently, ground measurement points of PM

_{2.5}in China are relatively discrete, thereby limiting spatial coverage. Aerosol optical depth (AOD) data obtained from satellite remote sensing provide insights into spatiotemporal distributions for regional pollution sources. In this study, data from the Multi-Angle Implementation of Atmospheric Correction (MAIAC) AOD (1 km resolution) product from Moderate Resolution Imaging Spectroradiometer (MODIS) and hourly PM

_{2.5}concentration ground measurements from 2015 to 2020 in Dalian, China were used. Although trends in PM

_{2.5}and AOD were consistent over time, there were seasonal differences. Spatial distributions of AOD and PM

_{2.5}were consistent (R

^{2}= 0.922), with higher PM

_{2.5}values in industrial areas. The method of cross-dividing the test set by year was adopted, with AOD and meteorological factors as the input variable and PM

_{2.5}as the output variable. A backpropagation neural network (BPNN) model of joint cross-validation was established; the stability of the model was evaluated. The trend in the predicted values of BPNN was consistent with the monitored values; the estimation result of the BPNN with the introduction of meteorological factors is better; coefficient of determination (R

^{2}) and RMSE standard deviation (SD) between the predicted values and the monitored values in the test set were 0.663–0.752 and 0.01–0.05 μg/m

^{3}, respectively. The BPNN was simpler and the training time was shorter compared with those of a regression model and support vector regression (SVR). This study demonstrated that BPNN could be effectively applied to the MAIAC AOD data to estimate PM

_{2.5}concentrations.

## 1. Introduction

_{2.5}, which encompasses a large variety of toxic and harmful substances. Environmental epidemiological studies have confirmed that long-term exposure to PM

_{2.5}increases the incidence of cardiovascular and respiratory diseases [1,2]. Recent studies have determined that air pollutants are closely related to mortality associated with diabetes and increased obesity risk [3,4]. Therefore, monitoring PM

_{2.5}mass concentrations and studying the causes of air pollution are important for safeguarding human health [5]. A time series of PM

_{2.5}mass concentrations can be obtained using data derived from ground measurements. However, recent studies have reported that the spatial distribution of PM

_{2.5}ground measurement points in China is limited [6,7]. With the growing development of satellite remote sensing technology, aerosol optical depth (AOD) obtained by remote sensing with a high spatial resolution and wide coverage has become an effective method to estimate PM

_{2.5}mass concentration [8,9]. AOD is a powerful parameter for describing aerosol extinction and can be used as a proxy for atmospheric turbidity in air pollution research [10]. AOD data can be obtained from different sensors such as the Advanced Very High-Resolution Radiometer (AVHRR), Visible Infrared Imaging Radiometer Suite (VIIRS), Advanced Along-Track Scanning Radiometer (AATSR), and Moderate Resolution Imaging Spectroradiometer (MODIS). Wei et al. (2019) compared 11 global monthly AOD products with Aerosol Robotic Network (AERONET) sites, including four products from the European Space Agency’s Climate Change Initiative (AATSR-ADV, AATSR-EN, AATSR-ORAC, and AATSR-SU) and AVHRR, Multi-angle Imaging Spectro Radiometer (MISR), Terra and Aqua MODIS, POLarization and Directionality of the Earth’s Reflectance (POLDER), Sea-viewing Wide Field-of-view Sensor (SeaWiFS), and VIIRS products. The MODIS products show the best performance with the best evaluation metrics in describing the temporal aerosol variations [11]. Currently, most studies have employed AOD data based on the Dark Target (DT) algorithm [12], the Deep Blue (DB) algorithm [13], or a combination of Dark Target and Deep Blue (DTB) algorithm [14]. The 10 km AOD products have been widely used in PM

_{2.5}estimation studies [15,16]; however, a 10 km resolution is not fine enough to resolve local variability [17,18,19]. Multi-angle implementation of atmospheric correction (MAIAC) is a new aerosol retrieval algorithm [20] that decouples aerosol and surface contributions using time series data. Jethva et al. (2019) verified and analyzed aerosols using the MAIAC algorithm on dark surfaces and showed that its accuracy was equal to or higher than that of the DT algorithm, and for bright surfaces, its accuracy was generally higher than that of the DB algorithm [21]. Li et al. (2020) found that compared with DT, DB, and DTB AOD products, the 1 km MAIAC AOD product obtained the best correspondence with AERONET measurements, with an overall coefficient of determination (R

^{2}) of 0.891 [22].

_{2.5}mass concentrations using AOD data obtained from satellite-based remote sensing [23,24,25,26]. The spatiotemporal distributions of PM

_{2.5}are influenced by multiple factors such as meteorology [27], land use [28], and human activities [29]; changes in these factors can be estimated using satellite observations. Luo et al. (2021) analyzed the relationships between PM

_{2.5}concentration and meteorological factors in Harbin. The results showed that relative humidity was positively correlated to PM

_{2.5}concentration, while temperature, wind direction, and wind speed were negatively correlated to PM

_{2.5}mass concentration [30]. Li et al. (2015) studied the spatiotemporal variations in AOD and PM

_{2.5}mass concentrations in the USA and found that interannual changes in AOD and PM

_{2.5}were highly consistent [31]. Initial studies used the atmospheric chemical transport model to simulate the scale factor between AOD and PM

_{2.5}, thereby enabling an estimation of PM

_{2.5}mass concentrations from AOD [32]. Wang (2003) discussed the simple linear relationship between MODIS AOD on the Terra/Aqua satellites and hourly PM

_{2.5}in Alabama, USA. The correlation coefficient (R) between AOD and PM

_{2.5}was 0.70, while that for monthly comparisons was 0.91 and 0.95 for Terra and Aqua, respectively [33]. To improve model performance, meteorological parameters and land-use information were gradually incorporated into the model (R

^{2}= 0.59–0.84), including a multiple regression model [34], linear mixed effect model [35], and geographically weighted regression model [36,37]. Although these models were of key importance in air pollution estimates, most statistical methods were difficult to find and displayed complex nonlinear laws. In recent years, significant progress has been made in the remote sensing inversion of PM

_{2.5}based on machine learning, including support vector regression (SVR) [38], artificial neural network (ANN) model [39], and random forest model [40]. ANN is a nonlinear mapping model that can cope with systems that are difficult to describe using mathematical models and has the characteristics of parallel processing, self-adaptation, self-organization, associative memory, and approaching arbitrary nonlinearity. Gupta and Christopher (2009) used MODIS AOD data at 0.55 µm to estimate PM

_{2.5}over the southeastern USA, based on an ANN that reduced the uncertainty of PM2.5 estimations from satellite data [41]. Their study demonstrated the potential for using ANNs for operational air quality monitoring. Guo et al. (2013) (R = 0.4–0.83) and Ni et al. (2018) (R

^{2}= 0.54–0.68) established the backpropagation neural network (BPNN) to estimate PM2.5 using MODIS AOD, and the corresponding results showed that a PM

_{2.5}estimation model based on MODIS AOD products could be effectively applied to PM

_{2.5}monitoring under the framework of a BP network [42,43]. The structure of a BP neural network is divided into input layer, hidden layer, and output layer, and there are connection weights between neurons in adjacent layers. The hidden layer can be a single layer or a multi-layer, and the number of hidden layer nodes selected has an effect on the accuracy of BPNN. Although a BP neural network can realize any nonlinear fitting learning, BPNN also shows some drawbacks, such as the randomness of initial weights and thresholds. There is no systematic method for determining the number of hidden layer nodes at present [44]. Most studies, including those mentioned above, have ignored the randomness of the initial weight threshold. Without considering the extreme value of error, a single result is not sufficient to represent the final performance of the model. In addition, most studies determined the model parameters, including the number of neurons in the hidden layer, through a single and randomly divided verification set. Thus, there was no guarantee that the network parameters were optimal. Therefore, based on the analysis of the spatiotemporal correlation between AOD and PM

_{2.5}, this study aimed to solve the problems existing in BPNN by fine-tuning the dataset according to the annual cross-division; the model parameters were determined through joint cross-validation and evaluating the stability of the model. The BPNN was compared using a regression model and SVR to verify the performance advantages.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, Dalian spreads from a latitude of 38°43′N to 40°10′N and a longitude of 120°58′E to 123°31′E. As shown in Figure 1a, Dalian is a city with three sides surrounded by sea, located at the southernmost point of Northeast China and the juncture where the Yellow Sea and the Bohai Sea meet. It is characterized by a semihumid temperate continental monsoon climate with characteristics of a marine climate. As shown in Figure 1b, Dalian has a high altitude in its center where it gradually extends lower to the east and west. Dalian is one of the most important central cities among the coastal areas of Northern China, with a population of almost 7.45 million residents. With the rapid development of industries, human activities are the main contributing factors to air pollution. Cai and Shao studied the relationship between PM

_{2.5}and the outpatient volume of the respiratory, cardiology, and neurology departments. The results show that with the increase in PM

_{2.5}in the air, the outpatient volume of these departments also tended to increase [45]. Meanwhile, the Dalian Center for Disease Control and Prevention center registration showed that the incidence rate of cancer in Dalian was mainly in the respiratory system and digestive system, and the incidence rate of lung cancer was the highest. Therefore, the estimation of PM

_{2.5}with Dalian as the study area is of great significance to health and air pollution control. Figure 1b, region (Ⅰ) shows the main urban areas of Dalian; Figure 1b, region (Ⅱ) shows the urban–rural integration or rural areas which have relatively sparse populations and high degrees of vegetation coverage.

#### 2.2. Data Sources

#### 2.2.1. PM_{2.5}

_{2.5}data provided by the National PM

_{2.5}Real-time Monitoring Network (http://www.pm25china.net, accessed on 10 January 2022). The distributions of the 10 monitoring ground measurement points in Dalian are shown in Figure 1c. The types of major air pollutants at each ground measurement points vary; for example, the polluted Dalian Industrial Zone is represented by points 1 and 6, and the polluted main traffic line is represented by point 10 [46]. In this study, the hourly data were averaged to obtain daily data using measurement points from 2015 to 2020, and the daily data of each monitoring station were averaged to obtain the overall daily data of Dalian.

#### 2.2.2. AOD

#### 2.2.3. Meteorological Factors

_{2.5}particles [48]. According to the pattern exhibited by the monsoon, the aerosol solubility will be effectively diluted. The bottom-left half of Table 1 show correlation coefficient, the top-right half show p-values. There is a strong correlation between PM

_{2.5}and AOD from Table 1. PM

_{2.5}is positively correlated with temperature and humidity, and negatively correlated with wind speed and precipitation. In addition, the positive correlation between AOD and temperature and humidity is more significant.

#### 2.3. Methods

#### 2.3.1. Data Preprocessing

_{2.5}hourly mass concentration data were considered invalid if they met one of two conditions: (1) the hourly mass concentration was maintained for more than 12 h; (2) the hourly mass concentration was more than three times the standard deviation of the 24 h mass concentration [49]. The larger the aerosol AOD value, the stronger the extinction effect of aerosol on the light propagation path. The range of AOD was 0–2 (>99.4%) in this study area. According to the daily PM

_{2.5}mass concentration and AOD data of Dalian, outliers of 8% and 9% were excluded from the box plots, respectively. The spatiotemporal distributions of annual PM

_{2.5}concentrations were obtained through interpolation using the inverse distance weight algorithm in ArcGIS (ESRI, Redlands, CA, USA). The spatiotemporal distributions of the annual AOD data were obtained by taking the average values of daily AOD data based on ENVI.

_{2.5}were fused on the temporal–spatial scale. AOD pixels were consistent with PM

_{2.5}measurement locations, and the AOD daily data corresponded to the PM

_{2.5}daily data. When the AOD or PM

_{2.5}mass concentration data were invalid for a given day, it was considered that no effective data points existed for that day. Different data fusion methods can have a great impact on correlation [50,51]. Some studies have selected typical regions to replace the whole or have used the method of taking the mean value of each region for data fusion. This study used the time series method to observe the change in the trend of AOD, meteorological factors, and PM

_{2.5}and performed data fusion through the time series curve. AOD–meteorological factors–PM

_{2.5}fusion data are shown in Table 2.

#### 2.3.2. Establishment of BPNN

_{1}, x

_{2}, …, x

_{n}are the input of BPNN; y

_{1}, y

_{2}, …, y

_{m}are the output of BPNN. In the training process of BPNN, firstly, the network should initialize the weights ω

_{ij}and ω

_{jk}, initialize the thresholds a

_{j}of the hidden layer and b

_{k}of the output layer, and then calculate the hidden layer output H.

_{jk}, and b

_{k}, BPNN prediction output O is calculated.

_{ij}, ω′

_{jk}are the new weights; a′

_{j}, b′

_{k}are the new threshold, and η is the learning rate.

_{2.5}was used as the output value to establish a BPNN.

#### 2.3.3. Model Comparison

#### 2.3.4. Correlation Evaluation Indexes

^{2}), the root mean square error (RMSE), and the prediction accuracy (Acc). The Acc formula was (9) [61]:

_{i}was the real value data sequence, P

_{i}was the estimated value data sequence, and n was the number of samples. MAPE was mean absolute percentage error.

_{RMSE}, the more stable the model.

## 3. Results and Discussion

#### 3.1. Temporal Distributions of AOD and PM_{2.5}

_{2.5}from 2015 to 2020 are shown in Figure 5 (after eliminating outliers). The trends in AOD and PM

_{2.5}are generally consistent, exhibiting a strong time correlation. However, there are seasonal differences: AOD was higher in summer and lower in winter, whereas the PM

_{2.5}mass concentrations were lower in summer and autumn and higher in spring and winter.

_{2.5}in summer and autumn from 2015 to 2020 were 23.9 μg/m

^{3}and 23.5 μg/m

^{3}, respectively, while those in the spring and winter were 30.7 μg/m

^{3}and 31.3 μg/m

^{3}, respectively. The height of the shallow boundary layer makes PM

_{2.5}accumulate continuously in winter, resulting in higher PM

_{2.5}concentration.

#### 3.2. Spatial Distributions of AOD and PM_{2.5}

_{2.5}and AOD concentrations in the southwest of Dalian, wherein smoke and dust are produced by industrial processes and exhaust fumes are emitted by vehicles. The average concentrations of PM

_{2.5}in monitoring points 1 and 6 were 37.06 and 33.69 μg/m

^{3}, respectively. The PM

_{2.5}concentrations of the coastal areas were relatively low, with monitoring points 2, 4, 9, and 10 showing average PM

_{2.5}concentrations of 26.42, 27.33, 25.76, and 28.62 μg/m

^{3}, respectively. The average AOD values in monitoring points 1 and 6 were 0.32 and 0.29, respectively. Monitoring points 2, 4, 9, and 10 had a relatively low AOD, with mean AOD values of 0.21, 0.24, 0.22, and 0.22, respectively. From the perspective of the whole region of Dalian, northeastern Dalian had a low average AOD of 0.24, and the average AOD in the main urban area was 0.33. The spatiotemporal distribution of AOD and PM

_{2.5}demonstrated good correlation as their extreme points were consistent (R

^{2}= 0.922) with the high values in the main urban area and low values in the northern urban–rural area.

_{2.5}and AOD had high values in areas with a high population density, and low values in Zhuanghe City, North Dalian, where the population density was relatively low. Jinzhou District and Pulandian District in central Dalian had a moderate population density, and PM

_{2.5}and AOD were also widely distributed in this area. There is a core and two wings in the spatial structure of Dalian, which takes the city center as the core and takes the developments along the Bohai Sea and the Yellow Sea. Seven sub-center cities of Dalian are connected with industrial groups. Wafangdian City is in the northwest geographically, where there are three industrial nodes. AOD values are high, the same as the eastern seaboard. Therefore, population density, industrial layout, and urban planning have a certain impact on the distribution of PM

_{2.5}and AOD.

#### 3.3. BPNN

^{3}–6.82 μg/m

^{3}and 6.38 μg/m

^{3}–7.23 μg/m

^{3}, respectively. When the number of iterations and learning rate were 3000 and 0.1, respectively, the RMSE was the smallest.

_{2.5}normalized value. The R

^{2}value between the estimated values and the monitored value of the training set (a)–(f) were about 0.660. However, there is a positive offset and a small slope, which means that there is underestimation for high value or overestimation for low value in the forecast time series. Therefore, any of the cases selected in Figure 8 were introduced with the meteorological factors for the training set, respectively, with set (a) as an example, and the prediction results are shown in Figure 9. The specific R

^{2}values increasing were, respectively, 0.024, 0.023, 0.01, and 0.008, corresponding to TEMP, RH, PRE, and WS, and the positive offsets were also improved.

^{2}value in each case was increased about 0.055, and the maximum value was increased by 0.111. In addition, the positive offset was improved significantly. Meteorological factors can improve the estimation accuracy of the model and have an important impact on the estimation of PM

_{2.5}.

^{2}and RMSE of the estimated PM

_{2.5}values and the monitored value were calculated and are shown in Table 6. The range of R

^{2}values were 0.663–0.752 and the range of RMSE values were 6.23–6.45 μg/m

^{3}. The R

^{2}value in each case was increased by about 0.032, and the maximum value was increased by 0.046. Temperature had the greatest impact on model accuracy among meteorological factors. In addition, the RMSE SD values were 0.01–0.05 μg/m

^{3}. These findings indicate that the model has a strong generalization ability and stability, which is close to the simulation effect of the training set; hence, there was no overfitting.

_{2.5}BPNN. However, it can be seen from Figure 11d that the model has not yet reached the estimation of PM

_{2.5}for lower concentrations. That is to say, the BPNN model can be used to estimate the trend of interannual PM

_{2.5}and needs to be improved for estimating the daily extreme value of PM

_{2.5}in the future.

#### 3.4. Comparison of BPNN with Regression Analysis and SVR

^{2}values of all models were all above 0.650, and the precision of meteorological factors–BPNN was the highest, with an R

^{2}of 0.757 and an RMSE of 6.11 μg/m

^{3}. Compared with the LR, NLR, MLR, and SVR methods, the R

^{2}and RMSE of BPNN were improved; however, the improvement degree was not significant. According to the comparison results, the regression equation obtained by the regression analysis model is relatively intuitive. Under the influence of structure, BPNN cannot directly showcase the direct correlation between output and input, but the neural network stores information in the connection weight. When the error between the expected and output reaches the requirement, the corresponding relationship of input and output can be obtained. LR, MLR, and NLR curves can only describe the approximate relationship between variables; the complicated regression cannot reflect the relationship among all regression data. The optimal nonlinear model obtained in this study was a univariate cubic model, but it was not determined whether it described the essential relationship between variables. BPNN approaches the objective function by learning, and a single hidden layer can be used to fit complex and continuous functions; hence, the computational sophistication of BPNN is reduced. The results showed that the accuracy of BPNN was similar to that of SVR, but SVR ran for a long time. Therefore, BPNN is superior to other models used in this study in terms of the PM

_{2.5}concentration estimate.

#### 3.5. Discussion

#### 3.5.1. Research Findings

_{2.5}inversions based on satellite remote sensing data. Statistical models (e.g., linear mixed models, geographically weighted regressions, and geographically and temporally weighted regressions) are commonly used for this purpose, all delivering high R

^{2}values (0.64–0.86) [63,64,65]. We analyzed the spatiotemporal correlation between AOD and PM

_{2.5}and performed simple regression fitting. We determined that a simple linear relationship between AOD and PM

_{2.5}did not exist, which made it difficult to accurately model using traditional regression methods. In this case, we established a BPNN with a strong nonlinear description ability. Mathematically, it was proven that the three-layer neural network could approach any nonlinear continuous function with arbitrary precision, which was further confirmed by the research results of the current study. Regarding the overfitting, underfitting, and sample dependence problems of BPNN, we made improvements in three aspects, namely, dataset division, model parameter determination, and model evaluation, which compensated for the deficiencies of the BPNN. The space–time extra trees (STET) were about 0.8, which were higher than those of BPNN (R

^{2}= 0.66–0.75) in recent studies [66,67], and the R

^{2}of MLR was reduced to 0.54 in some time or regions. Both of them had poor stability. The BPNN prediction model had great temporal and spatial consistency and was more suitable for universal prediction. Significantly, the RMSE (6.36 μg/m

^{3}) mean of the BPNN was much lower than MLR (7.18 μg/m

^{3}, 13.4 μg/m

^{3}) and STET (14.60 μg/m

^{3}), which proved that BPNN was advantageous in estimating the AOD of PM

_{2.5}. Prior studies focused on the correlation between PM

_{2.5}and AOD spatiotemporal distribution or established a model to estimate PM

_{2.5}[68,69,70]. This study analyzed the correlation between MAIAC AOD and PM

_{2.5}in terms of seasonal scale, spatial scale, and annual scale, as well as established an estimation model to provide a theoretical reference for variations in the characteristics of AOD and PM

_{2.5}.

#### 3.5.2. Limitations

_{2.5}based on AOD has research merit, this approach also has certain limitations.

- (1)
- Here, the limited number of ground measurement points impeded the analysis of the spatiotemporal correlations between AOD and PM
_{2.5}. - (2)
- Seasonal differences in AOD and PM
_{2.5}were not incorporated into the establishment of BPNN. - (3)
- The BPNN model can be used to estimate the trend of interannual PM
_{2.5}and needs to be improved for estimating the daily extreme value of PM_{2.5}in the future.

_{2.5}and AOD historical data, data on daily to hourly timescales, and investigation of spatiotemporal characteristics. At the same time, future research should expand the scope of model comparison and explore the advantages of machine learning.

## 4. Conclusions

_{2.5}is the most important pollutant in the atmosphere, and it not only affects the ecological environment, but also endangers human health. AOD is an important index to evaluate the change in atmospheric environment. In this study, AOD was used to estimate the mass concentration of PM

_{2.5}in order to realize the full space coverage of PM

_{2.5}, which is crucial for air quality monitoring and human health research. Therefore, based on the analysis of spatiotemporal correlation, a BPNN model with joint cross-validation was established to accurately estimate the daily concentration of PM

_{2.5}in Dalian, China. MAIAC AOD and PM

_{2.5}exhibited strong spatiotemporal correlations. Temporally, AOD was higher in summer and lower in winter, whereas PM

_{2.5}mass concentrations were lower in summer and autumn and higher in spring and winter. On the annual scale, the AOD of Dalian showed a decreasing trend, year by year. Spatially, the spatiotemporal distribution of AOD and PM

_{2.5}demonstrated a good correlation (R

^{2}= 0.922), and this result was consistent with the distribution of population density. In this study, each year from 2015 to 2020 was used as the test set, and other years were used as the training set. Using AOD and meteorological factors (TEMP, WS, RH, PRE) as the input of the model, six BPNN models were established. The results showed that the estimation result of the BPNN with the introduction of meteorological factors is better than that of the AOD–PM

_{2.5}BPNN. The range of R

^{2}values were 0.663–0.752 and the range of RMSE values were 6.23–6.45 μg/m

^{3}. The R

^{2}value in each case was increased by about 0.032. Temperature had the greatest impact on model accuracy among meteorological factors. The difference caused by the randomness of the initial weight and threshold of BPNN to the operation results of the model was considered. We further compared the performance of BPNN with regression models and SVR. The results demonstrated that BPNN was advantageous over the LR, NLR, MLR, and SVR methods in terms of the model sophistication and training time. Therefore, BPNN with a generalization ability and stability can be considered as the best candidate technology for PM

_{2.5}concentration estimation, providing scientific basis for macroscopic and long-term monitoring of air pollution.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

_{2.5}Real-time Monitoring Network (http://www.pm25china.net, accessed on 10 January 2022), Level-1 and the Atmosphere Archive and Distribution System Distributed Active Archive Center (https://ladsweb.modaps.eosdis.nasa.gov/, accessed on 10 January 2022) and China Meteorological network (http://data.cma.cn, accessed on 10 January 2022).

## Conflicts of Interest

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**Figure 1.**Map of (

**a**) China. Elevation map of (

**b**) Dalian and (

**c**) main urban areas of Dalian. (

**b**) Dalian main urban region and urban–rural region. (

**c**) Spatial distributions of PM

_{2.5}point in Dalian.

**Figure 9.**Estimated results of AOD + meteorological factors–PM

_{2.5}BPNN of training set (

**a**), (

**a**) AOD + TEMP–PM

_{2.5}BPNN, (

**b**) AOD + RH–PM

_{2.5}BPNN, (

**c**) AOD + PRE–PM

_{2.5}BPNN, (

**d**) AOD + WS–PM

_{2.5}BPNN.

**Figure 11.**(

**a**–

**f**) Simulation diagram of PM

_{2.5}estimated and monitored values of test set. (

**a**) 2015 as the test set. (

**b**) 2016 as the test set. (

**c**) 2017 as the test set. (

**d**) 2018 as the test set. (

**e**) 2019 as the test set. (

**f**) 2020 as the test set.

R/p-Values | PM_{2.5} | AOD | TEMP | RH | WS | PRE |
---|---|---|---|---|---|---|

PM_{2.5} | - | <0.001 | <0.001 | <0.001 | <0.001 | 0.300 |

AOD | 0.800 | - | <0.001 | <0.001 | <0.001 | 0.420 |

TEMP | 0.244 | 0.351 | - | <0.001 | <0.001 | 0.009 |

RH | 0.385 | 0.463 | 0.384 | - | <0.001 | <0.001 |

WS | −0.186 | −0.176 | −0.310 | −0.233 | - | 0.973 |

PRE | −0.040 | 0.031 | 0.101 | 0.214 | −0.001 | - |

Variable | Min | Max | Avg | SD |
---|---|---|---|---|

PM_{2.5} (μg/m^{3}) | 10.750 | 76.493 | 26.808 | 10.862 |

AOD | 0.025 | 1.776 | 0.289 | 0.249 |

TEMP (°C) | −11.500 | 32.300 | 10.235 | 10.533 |

RH (%) | 93.000 | 16.000 | 50.739 | 15.248 |

WS (m/s) | 3.038 | 8.600 | 3.038 | 1.269 |

PRE (mm) | 0.000 | 22.600 | 0.291 | 1.766 |

Data Set | Training Set (Year) | Test Set (Year) |
---|---|---|

1 | a (2016, 2017, 2018, 2019, 2020) | 2015 |

2 | b (2015, 2017, 2018, 2019, 2020) | 2016 |

3 | c (2015, 2016, 2018, 2019, 2020) | 2017 |

4 | d (2015, 2016, 2017, 2019, 2020) | 2018 |

5 | e (2015, 2016, 2017, 2018, 2020) | 2019 |

6 | f (2015, 2016, 2017, 2018, 2019) | 2020 |

Hidden Layer Activation Function | Output Layer Activation Function | Training Function | Target Error | Number of Iterations | Learning Rate |
---|---|---|---|---|---|

tansig | purelin | trainlm | 10^{−5} | 3000 | 0.1 |

Hidden Layer Neurons | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

RMSEa | 10.64 | 6.41 | 6.42 | 11.66 | 11.18 | 58.40 | 13.59 | 33.73 | 12.03 | 10.34 | 13.71 |

RMSEb | 6.44 | 6.45 | 6.48 | 7.50 | 6.76 | 6.83 | 6.80 | 6.96 | 7.18 | 7.23 | 7.97 |

RMSEc | 6.48 | 6.77 | 6.82 | 7.32 | 10.07 | 8.25 | 7.43 | 10.87 | 14.66 | 13.42 | 12.48 |

RMSEd | 6.47 | 15.74 | 10.48 | 44.45 | 44.40 | 11.42 | 10.77 | 26.51 | 10.57 | 21.53 | 18.61 |

RMSEe | 6.39 | 6.37 | 6.50 | 10.06 | 6.80 | 6.46 | 6.47 | 6.83 | 8.08 | 8.58 | 6.82 |

RMSEf | 6.49 | 6.95 | 6.67 | 61.71 | 52.15 | 36.39 | 38.52 | 53.71 | 32.86 | 32.26 | 18.18 |

Input Variable | Test Set (Year) | ||||||||
---|---|---|---|---|---|---|---|---|---|

2015 | 2016 | 2017 | |||||||

R^{2} | RMSE | Acc | R^{2} | RMSE | Acc | R^{2} | RMSE | Acc | |

AOD | 0.640 | 6.66 | 80.7% | 0.656 | 6.56 | 81.4% | 0.723 | 6.27 | 82.9% |

AOD + TEMP | 0.661 | 6.47 | 82.0% | 0.672 | 6.48 | 82.0% | 0.731 | 6.23 | 83.2% |

AOD + RH | 0.656 | 6.58 | 81.9% | 0.661 | 6.50 | 81.2% | 0.729 | 6.23 | 83.1% |

AOD + PRE | 0.648 | 6.60 | 81.8% | 0.658 | 6.55 | 81.9% | 0.719 | 6.25 | 83.0% |

AOD + WS | 0.645 | 6.65 | 81.7% | 0.658 | 6.62 | 81.8% | 0.711 | 6.26 | 82.9% |

AOD + All Features | 0.676 | 6.45 | 82.2% | 0.691 | 6.34 | 82.7% | 0.752 | 6.23 | 83.4% |

Input Variable | Test Set (Year) | ||||||||

2018 | 2019 | 2020 | |||||||

R^{2} | RMSE | Acc | R^{2} | RMSE | Acc | R^{2} | RMSE | Acc | |

AOD | 0.656 | 6.33 | 82.0% | 0.640 | 6.81 | 79.9% | 0.640 | 6.34 | 81.9% |

AOD + TEMP | 0.679 | 6.29 | 82.7% | 0.671 | 6.74 | 80.4% | 0.661 | 6.20 | 82.6% |

AOD + RH | 0.672 | 6.31 | 82.5% | 0.654 | 6.77 | 80.1% | 0.651 | 6.22 | 82.6% |

AOD + PRE | 0.671 | 6.33 | 82.2% | 0.643 | 6.78 | 80.0% | 0.653 | 6.31 | 82.3% |

AOD + WS | 0.667 | 6.33 | 82.2% | 0.642 | 6.80 | 79.9% | 0.650 | 6.34 | 82.0% |

AOD + All Features | 0.677 | 6.30 | 82.8% | 0.686 | 6.54 | 82.0% | 0.663 | 6.32 | 82.4% |

Model | Model Parameter | Model Expression | |||||||
---|---|---|---|---|---|---|---|---|---|

Hidden Neurons | C | g | R^{2} | RMSE/μg/m^{3} | RMSE SD/μg/m^{3} | Acc | Time | ||

BPNN | 2 | - | - | 0.723 | 6.35 | 0.26 | 82.4% | 2″00 | - |

SVR | - | 4 | 0.06 | 0.672 | 6.37 | 0.27 | 82.2% | 13″12 | - |

LR | - | - | - | 0.656 | 6.42 | 0.22 | 82.0% | - | PM_{2.5} = 34.28AOD + 17.00 |

NLR | - | - | - | 0.672 | 6.37 | 0.23 | 82.2% | - | PM_{2.5} = 14.87 + 47.09AOD − 14.16AOD^{2} + 3.15AOD^{3} |

MLR | - | - | - | 0.689 | 6.20 | 0.26 | 83.4% | - | PM_{2.5} = 0.80AOD + 0.07TEMP + 0.04RH − 0.05WS − 0.06PRE |

Meteorological factors–SVR | - | 2 | 1 | 0.689 | 6.25 | 0.28 | 83.3% | 11″29 | - |

Meteorological factors–BPNN | 2 | - | - | 0.757 | 6.11 | 0.26 | 84.4% | 2″00 | - |

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**MDPI and ACS Style**

Gu, J.; Wang, Y.; Ma, J.; Lu, Y.; Wang, S.; Li, X.
An Estimation Method for PM_{2.5} Based on Aerosol Optical Depth Obtained from Remote Sensing Image Processing and Meteorological Factors. *Remote Sens.* **2022**, *14*, 1617.
https://doi.org/10.3390/rs14071617

**AMA Style**

Gu J, Wang Y, Ma J, Lu Y, Wang S, Li X.
An Estimation Method for PM_{2.5} Based on Aerosol Optical Depth Obtained from Remote Sensing Image Processing and Meteorological Factors. *Remote Sensing*. 2022; 14(7):1617.
https://doi.org/10.3390/rs14071617

**Chicago/Turabian Style**

Gu, Jilin, Yiwei Wang, Ji Ma, Yaoqi Lu, Shaohua Wang, and Xueming Li.
2022. "An Estimation Method for PM_{2.5} Based on Aerosol Optical Depth Obtained from Remote Sensing Image Processing and Meteorological Factors" *Remote Sensing* 14, no. 7: 1617.
https://doi.org/10.3390/rs14071617