A unary linear regression is used to estimate the spatial distribution of particulate matter over the PRD, as expressed in Equation (1):

where

Y is the predicted variable,

X are the independent variables of the model,

a is a constant and

b is the coefficient of the variables. In our model,

X represents AOT values with high-resolution, and

Y is predicted PM concentrations. As

Figure 2 shows, PM

_{10} and AOT are highly linear-correlated, thus an observed set of values of station-measured PM

_{10} concentrations and satellite-derived AOT values at the same place in 2008 could be used to develop the linear model in

Figure 3. Then, through the established regression model, the unmeasured PM concentrations in non-station areas can be retrieved from 500 m-resolution aerosol optical thickness, for the satellite-derived AOT maps are spatially continuous, and show values both at station and non-station points.

**Figure 3.**
Correlation diagram between average aerosol optical thickness within 500 m radius of the monitoring station and station-measured PM_{10} concentrations.

Retrieval of 500 m-resolution AOT in this study is based on an improved dark dense vegetation (DDV) method, proposed by our previous study [

38]. Aerosol products of satellite remote-sensing provide an effective way to study air pollution, but have a conflict between resolution and signal-to-noise ratio (SNR). Our method, on a basis of MOD04-C005 algorithm, hopes to obtain Aerosol Optical Thickness (AOT) with a higher spatial resolution in the case of moderate decreases in SNR [

39]. The theory of the method is that in the case of low surface reflectance, the 2.1-μm channel is transparent to most aerosol types so that its apparent reflectance can be considered to be equal to the surface reflectance [

40,

41]. The relations among the surface reflectance in the blue, red and SWIR band are not a fixed ratio but depend on the scattering angle and NDVI

_{SWIR} derived from reflectance at 1.24 and 2.12 μm bands, taking into account the angular variability and surface type, since the Earth’s surface is not Lambertian and some surface types exhibit bidirectional reflectance functions (BRDF). Besides, before AOT retrieval, the MODIS cloud mask products (MOD35_L2) were applied to remove the cloud on MODIS L1B images. For the remaining potentially clear pixels, the selection of dark pixels by discarding brightest 50% and darkest 20% of reflectance at 0.66 μm, also reduce the cloud and surface contamination. Thus, the AOT can be retrieved from the surface reflectance due to the correlation between surface reflection in the blue (0.49 μm), red (0.66 μm), and 2.12 μm bands. Changing the movement pattern of the retrieval window, selecting a more suitable aerosol type, and storing the look-up table as a four-dimensional array, enhance the spatial resolution of AOT considerably relative to MODIS AOT products. The selection of effective dark pixels is conducted in a window of 20 × 20 pixels (10 km × 10 km), and the calculation of the surface reflectance at 0.47 and 0.66 μm are functions of the surface reflectance at 2.13 μm, NDVI and the scattering angle. We also adopted the aerosol type suitable for the study area proposed by Li [

21], rather than using the urban or continental aerosols in the 6S model. All of these factors would reduce the errors of AOT retrieval on the bright surfaces, especially in urban areas. The AOT maps by our algorithm are much smoother and show more extensive value ranges with fewer null values. We also validated the retrieval results with ground measurements and 10 km-resolution MODIS AOT products, both showing high precision. We will further validate our retrieval results of aerosol optical thickness in specific seasons and regions once we get ground observations of AOT and PM on a long time scale.

#### 4.1. Retrieval of the Instantaneous Particulate Distribution

Data involved in the retrieval include MODIS L1B data onboard the Terra satellite covering the whole Pearl River Delta, and PM

_{10} measurements at 10:00 to 11:00 a.m. at the 15 stations on 2, 3 and 5 January 2008, together with atmospheric boundary height and relative humidity were downloaded from NCEP CFSR on the same days. The MODIS instrument passes the entire Earth twice per day, with Terra in the morning and Aqua in the afternoon, while the PM data at the stations were recorded hourly. To reduce the effects of the difference in temporal resolution on the relationship between PM

_{10} and AOT, PM data recorded from 10:00 to 11:00 at the 15 point locations were used to match the Terra data in our study. After deriving the AOT from the MODIS images, the relationship between average AOT values within 500 m radius of the monitoring station and PM

_{10} from all sites was established as shown in

Figure 3. The accuracy of the relationship is affected by the imperfect match between the spatial-temporal resolutions of AOT-PM data, as the AOT was estimated at about 10:30 a.m. with a spatial resolution of 500 m, and the null values were excluded from the calculation. The PM data, on the other hand were recorded from 10:00 to 11:00 at the 15 point locations. In addition, the relative humidity and atmospheric boundary layer height have impacts on the correlation between column AOT and ground PM

_{10} concentrations. The spatial distribution maps of PM

_{10} on 2, 3 and 5 January using the linear model in

Figure 3 are shown in

Figure 4. The difference between the slope values of the models in

Figure 2 and

Figure 3 is possibly caused by the measuring instruments, and the PM concentrations from ground observations are a little higher than that from the monitoring stations.

**Figure 4.**
Spatial distribution of PM_{10} derived from 500 m-rsolution AOT in PRD on 2, 3 and 5 January 2008 (unit: μg/m^{3}).

**Figure 4.**
Spatial distribution of PM_{10} derived from 500 m-rsolution AOT in PRD on 2, 3 and 5 January 2008 (unit: μg/m^{3}).

Variations in local meteorological conditions and occurrence of multiple aerosol layers play important roles in the relationship between AOT and PM

_{10}. To estimate the PM concentrations directly from AOT may be somewhat tenuous, and the vertical distribution of aerosols and the relative humidity, related to atmospheric profiles, ambient condition, the size distributions and chemical compositions of aerosols, are especially important. As AOT reflects the aerosol optical properties of the total column whereas particle matter concentrations are usually recorded at 5 feet above the ground, the relation between them is greatly influenced by the vertical distribution of aerosols. As we know, AOT is the integral of the extinction coefficient

k_{a} at all altitudes along the vertical orientation, and is expressed as:

where

${\tau}_{\text{a}}(\text{\lambda})$ is the total atmospheric optical thickness, and

${k}_{\text{a}}(\text{\lambda},z)$ is the extinction coefficient at the altitude of

z and the wavelength of λ. Additionally, the vertical distribution of

${k}_{\text{a}}(\text{\lambda},z)$ could be described as the negative exponent form as:

where

${k}_{\text{a},0}(\text{\lambda})$ is the extinction coefficient at the wavelength of λ near the surface, and

H_{A} is the scale height of aerosol, approximately represented by the atmospheric boundary layer height (ABL) [

42,

43]. Combining Equations (2) and (3), we calculate

${\tau}_{\text{a}}(\text{\lambda})$ as:

On the other hand, the hygroscopic growth of particles has effects on the refraction and extinction index, as well as other optical properties of aerosols [

44]. The correlation between extinction coefficient

k_{a} and PM

_{10} is also affected by the chemical components of particles and relative humidity of the air, since the PM

_{10} concentrations measured by the instruments are almost the dry mass of the particles with aerodynamic diameter less than 10 μm. Thus,

f (

RH) is used to define the hygroscopic growing factor as [

36,

45]:

where g is an empirical fie coefficient and set as 1 in our study. The dry

${k}_{\text{a},0}(\text{\lambda})$ is obtained from

Hence, we could calculate the aerosol extinction coefficient in the dry air near the surface

${k}_{\text{a},\text{DRY}}(\text{\lambda})$ from Equation (1) to Equation (5), and express it as

Wang

et al. [

24] once described the relationship between

k_{a} and PM concentration on the basis of the Mie theory as

where Q

_{ext} is the size distribution integrated extinction efficiency, r

_{eff} is the effective radius, being approximately constant, and PMx is the mass concentration of PM. Therefore, it is possible to develop a linear correlation between

${k}_{\text{a},\text{DRY}}(\text{\lambda})$ and PM

_{10} concentrations, like

Furthermore, the vertical and relative humidity corrections on AOT could enhance the relationship and increase the robustness of the estimate.

Spatial distributions of ABL height and relative humidity on 2 and 3 January are displayed in

Figure 5. The comparison of measurements at the weather stations and forecast of relative humidity is shown in

Figure 6, with a correlation coefficient of 0.816. The deviation of the correlation is caused by the different temporal resolutions of these two datasets. Data from NCEP CFSR was at 6-hourly intervals while the station observations are hourly averaged.

**Figure 5.**
Spatial distribution of atmospheric boundary layer (ABL) height (unit: meter) on the left and relative humidity (unit: %) on the right in PRD at 6:00 UTC on 2, 3 and 5 January 2008, provided by NCEP CFSR, with a resolution of 0.5 degree.

**Figure 5.**
Spatial distribution of atmospheric boundary layer (ABL) height (unit: meter) on the left and relative humidity (unit: %) on the right in PRD at 6:00 UTC on 2, 3 and 5 January 2008, provided by NCEP CFSR, with a resolution of 0.5 degree.

**Figure 6.**
The scatter plot of measurements at the weather stations and forecast of relative humidity from NCEP CFSR.

**Figure 6.**
The scatter plot of measurements at the weather stations and forecast of relative humidity from NCEP CFSR.

ABL height and relative humidity data at 6:00 UTC (14:00 pm local time), which are the closest datasets to the overpassing time of satellite, were applied to the vertical and humidity correction on MODIS Terra images to reduce the errors from temporal scale. The correlation between average corrected

${k}_{\text{AOT},\text{DRY}}(\text{\lambda})$ and PM

_{10} is shown in

Figure 7. Comparison between

Figure 3 and

Figure 7 indicates that the correlation (R

^{2} = 0.55) is slightly higher after this correction but not significant, mainly because of the low spatial resolution of meteorological data. The final retrieved PM

_{10} images over the Pearl River Delta on 2, 3 and 5 January are displayed in

Figure 8.

**Figure 7.**
Correlation between extinction coefficient and surface-level PM_{10} after vertical and humidity correction using meteorologic data form NCEP CFSR.

**Figure 7.**
Correlation between extinction coefficient and surface-level PM_{10} after vertical and humidity correction using meteorologic data form NCEP CFSR.

**Figure 8.**
Spatial distribution of PM_{10} in PRD on 2, 3 and 5 January 2008 after vertical and humidity correction (unit: μg/m^{3}).

**Figure 8.**
Spatial distribution of PM_{10} in PRD on 2, 3 and 5 January 2008 after vertical and humidity correction (unit: μg/m^{3}).

The coarse spatial resolution of meteorological data leads to apparent grids in the images in

Figure 8. We therefore averaged the values of ABL height and relative humidity from NECP CFSR over the PRD to smooth and refine the maps. To do so, we took H

_{A} and RH in Equation (2) to be single valued rather than maps with 0.5° resolution. The relationship between corrected AOT and PM

_{10} is shown in

Figure 9 with a coefficient of 0.531. It indicates that the correlation can be enhanced by vertical and humidity corrections, but the degree of improvement depends on the accuracy of the meteorological data. The retrieved PM

_{10} images over the Pearl River Delta on 2, 3 and 5 January are displayed in

Figure 10.

**Figure 9.**
Correlation between extinction coefficient corrected by average value of atmospheric boundary layer height and relative humidity, and the surface-level PM_{10}.

**Figure 9.**
Correlation between extinction coefficient corrected by average value of atmospheric boundary layer height and relative humidity, and the surface-level PM_{10}.

**Figure 10.**
Spatial distribution of derived PM_{10} in PRD on 2, 3 and 5 January 2008 after correction (unit: μg/m^{3}).

**Figure 10.**
Spatial distribution of derived PM_{10} in PRD on 2, 3 and 5 January 2008 after correction (unit: μg/m^{3}).

#### 4.2. Retrieval of Yearly Average PM_{10} Distributions

We used all cloud-free MODIS data in 2008 to derive the corresponding AOT using the dark dense vegetation method. Averaging the results leads to an estimate of the yearly aerosol optical thickness over the PRD

Figure 11. However, in summer the common occurrence of clouds makes AOT rarely observable, thus only a few MODIS images were studied. The average results would be a little lower since AOT values in summer are higher than these in winter [

46]. Additionally we estimated the PM concentrations in non-site areas from our regression model. According to the station measurements provided by Guangdong Environmental Protection Bureau, the days of PM

_{10} exceeding the standard threshold 150 µg/m

^{3} in 2008 were 5 in Tianhu, 11 in Luhu Park, 46 in Xiapu, 20 in Chenzhong, 37 in Hangang School, 63 in Huijingcheng, 1 in Jinguowan, 27 in Jinjuzui, 43 in Wanqinsha, 23 in Donghu, 5 in Liyuan, 35 in Zimaling Park, 2 in Tamen, 1 in Quanwan and 0 in Tangjia, respectively. Linear regression of these data is shown in

Figure 12 with a correlation coefficient of 0.582. The slope coefficient in the linear regression model of yearly average AOT and PM

_{10} is relatively low, probably because of the average calculation on AOT and fewer sample points. The correlation between yearly mean AOT and observed PM

_{10} is slightly higher than that between the instantaneous values, mainly because averaging tends to eliminate outliers. The instantaneous AOT is influenced by many factors that show frequent fluctuations, such as temperature, monsoon, and precipitation, as well as human activities, such as fossil fuel burning. Retrieved AOT maps cannot reflect the true air quality when there appears to be a low or high value anomaly of these factors. Occurrence of clouds also makes aerosols sometimes rarely observable, accompanied by null values of AOT. Outliers and missing data may introduce bias or affect the representativeness of the results. The yearly average AOT can remove the occasional effects and eliminate the outliers of AOT by replacing them with the average values of the pixel. Thus, the larger the time scales, the higher the correlation between aerosol optical thickness and PM

_{10} concentration. The yearly average PM

_{10} is then retrieved through the regression equation (

Figure 13).

**Figure 11.**
A 500 m-resolution yearly average aerosol optical thickness in 2008 over the Pearl River Delta region retrieved from all cloud-free MODIS L1B data by using an improved Dark Dense Vegetation method.

**Figure 11.**
A 500 m-resolution yearly average aerosol optical thickness in 2008 over the Pearl River Delta region retrieved from all cloud-free MODIS L1B data by using an improved Dark Dense Vegetation method.

Table 5 lists the yearly average values of AOT, measured PM

_{10} and regressive PM

_{10} of the 15 monitoring stations in PRD, 2008. The predicted PM

_{10} was derived from the model shown in

Figure 12, by putting in the yearly average AOT values at each monitoring station. The deviations between the actually-measured and predicted PM

_{10} concentrations were calculated to indicate the stability of the model. The root mean square error (RMSE) between station measured PM

_{10} and the predicted PM

_{10} was calculated from the deviations to be ±10 µg/m

^{3}, indicative of the reliability of the retrieved results while the relative errors of the predicted results are from 1.75% to 27.12%, showing the limitations of the applicability of the model. Air quality at most sites is poor according to the standards of both yearly average PM

_{10} (70 µg/m

^{3}) laid down in the ambient air quality standards.

Figure 13 show that areas with the worst air pollution are located in Foshan city, at the border of Shunde and Zhongshan, west of Gongguan, and northwest of Shenzhen.

**Figure 12.**
Regression analysis between the yearly averaged retrieved AOT and ground-measured PM_{10} of the 15 monitoring stations in the PRD, 2008.

**Figure 12.**
Regression analysis between the yearly averaged retrieved AOT and ground-measured PM_{10} of the 15 monitoring stations in the PRD, 2008.

**Figure 13.**
Spatial distribution of retrieved yearly average PM_{10} concentrations in the PRD, 2008 (unit: μg/m^{3}).

**Figure 13.**
Spatial distribution of retrieved yearly average PM_{10} concentrations in the PRD, 2008 (unit: μg/m^{3}).

**Table 5.**
Yearly average values of AOT, measured PM_{10} and Predicted PM_{10} of the 15 monitoring stations in the PRD, 2008.

**Table 5.**
Yearly average values of AOT, measured PM_{10} and Predicted PM_{10} of the 15 monitoring stations in the PRD, 2008.
Sites | AOT | Measured PM_{10} (µg/m^{3}) | Predicted PM_{10} (µg/m^{3}) | Deviation (µg/m^{3}) | Relative Errors (%) |
---|

Tianhu | 0.238 | 62 | 54 | −8 | −12.90 |

Luhu Park | 0.575 | 65 | 77 | 12 | 18.46 |

Haogang school | 0.701 | 90 | 86 | −4 | −4.44 |

Xiapu | 0.506 | 91 | 72 | −19 | −20.88 |

Jinguowan | 0.274 | 45 | 56 | 11 | 24.44 |

Liyuan | 0.544 | 59 | 75 | 16 | 27.12 |

Tamen | 0.3 | 57 | 58 | 1 | 1.75 |

Quanwan | 0.202 | 57 | 51 | −6 | −10.53 |

Tangjia | 0.35 | 50 | 61 | 11 | 22.00 |

Zimaling Park | 0.677 | 82 | 84 | 2 | 2.44 |

Wanqinsha | 0.566 | 93 | 76 | −17 | −18.28 |

Donghu | 0.68 | 75 | 84 | 9 | 12.00 |

Jinjuzui | 0.669 | 80 | 84 | 4 | 5.00 |

Huijingcheng | 0.734 | 103 | 88 | −15 | −14.56 |

Chengzhong | 0.533 | 66 | 74 | −8 | −12.12 |