Retrieval of Aerosol Fine-mode Fraction over China from Satellite Multiangle Polarized Observations: Validation and Application

The aerosol fine-mode fraction (FMF) is an important optical parameter of aerosols, and the FMF is difficult to accurately retrieve by traditional satellite remote sensing methods. In this study, FMF retrieval was carried out based on the multiangle polarization data of Polarization and Anisotropy of Reflectances for Atmospheric Science coupled with Observations from Lidar (PARASOL), which overcame the shortcomings of the FMF retrieval algorithm in our previous research. In this research, FMF retrieval was carried out in China and compared with the AErosol RObotic NETwork 15 (AERONET) ground-based observation results, Moderate Resolution Imaging Spectroradiometer (MODIS) FMF products, and Generalized Retrieval of Aerosol and Surface Properties (GRASP) FMF results. In addition, application of the FMF retrieval algorithm was carried out, a new FMF dataset was produced, and the annual and quarterly average results of FMF from 2006 to 2013 were obtained in all of China. The research results show that the FMF retrieval results of this study are comparable with the AERONET ground-based observation results in China, with correlation coefficient (r), mean absolute 20 error (MAE), root mean square error (RMSE), and the proportion of results that fall with the expected error (Within EE) are 0.770, 0.143, 0.170, and 60.96%, respectively. Compared with the MODIS FMF products, the FMF results of this study are closer to the AERONET ground-based observations. Compared with the FMF results of GRASP, the FMF results of this study are closer to the spatial variation in the ratio of PM2.5 to PM10 near the ground. The analysis of the annual and seasonal average FMF of China from 2006 to 2013 shows that the FMF high value area in China is mainly maintained in the area east of the 25 "Hu Line", with the highest FMF year being 2013, and the highest FMF season is winter.

observations (Zhang et al., 2016), mainly based on multiangle scalar observations to obtain total aerosol optical depth (AODt), and multiangle polarization observations to obtain AODf. The ratio of the two is FMF. Compared with the existing MOIDS FMF products, the accuracy of the FMF results obtained by this method is significantly improved, which shows the feasibility of the method. However, there are still some problems that need to be solved if this method is to be applied in large spaces.
For example, the empirical parameters of surface reflectance estimation during scalar retrieval vary greatly with region, and 70 high-precision AODt retrieval results can only be obtained in specific regions. In polarization retrieval, there is a problem of low retrieval value for high aerosol loading (Chen et al., 2015;Zhang et al., 2018). In response to these problems, we have also carried out follow-up research work, made certain improvements to the above problems and have achieved more accurate AODt and AODf in a large space (Zhang et al., 2017;Zhang et al., 2018). Then, in theory, it is possible to achieve the goal of FMF in a large space. Although Yan et al. achieved high-precision FMF retrieval based on the LUT-SDA method (Yan et al.,75 For the retrieval of AODt, we introduced the empirical orthogonal function (EOF) to estimate the surface reflection contribution under multiangle observations to solve the regional limitation of the semiempirical parameters of the surface in the original method. Subsequently, this is combined with the retrieval lookup table and substituted into the forward model for simulation 100 calculation, and finally, AODt can be obtained through the cost function. The correlation coefficient (r) and root mean square error (RMSE) between the obtained AODt and AERONET ground-based observations are 0.891 and 0.097, respectively. For more details about the EOF method, please refer to our 2017 study (Zhang et al., 2017).
For the retrieval of AODf, our research and other scholars have shown that the AODf results obtained by using the official LOA algorithm have a certain deviation compared with ground-based observations. To improve the retrieval accuracy of AODf, 105 we proposed the Grouped Residual Error Sorting (GRES) method in 2018 to solve the problem of an inaccurate evaluation function caused by error accumulation under multiangle observation. Based on this method, combined with a bidirectional polarized surface reflectance (BPDF) model to estimate the polarized surface reflectance (Nadal and Bré on, 1999), we have obtained higher-precision AODf results in eastern China, and the r and RMSE between the results and the AERONET groundbased observations are 0.931 and 0.042, respectively. More method details can be found in our research published in 2018 110 (Zhang et al., 2018).
Based on the new retrieval method, we have obtained higher-precision AODt and AODf retrieval results on a large spatial scale, which also provides the possibility of obtaining accurate FMF results on a large spatial scale. Next, we will obtain FMF based on the AODt and AODf retrieved by the new method, validate the FMF retrieval results based on the AERONET ground-based observation results and further obtain the FMF temporal and spatial distribution results over terrestrial China. Note that since 115 the EOFs during the AODt retrieval need to be constructed with the observation results of the POLDER 3*3 window, the resolution of the final FMF retrieval result is also the size of the POLDER 3*3 window (approximately 18 km).

AERONET data
At present, aerosol ground-based products of AERONET have been developed to version V3, and the data of version V2 are no longer available for download. Among these products, there are two products that can be used to validate the results of 120 satellite FMF retrieval: one is the FMF product based on the spectral deconvolution (SDA) method (O'Neill et al., 2001a;O'Neill et al., 2001b;O'Neill et al., 2003), and the other is based on the size distribution (SD) retrieval product (Dubovik and King, 2000). Generally, SDA products can provide more FMF ground-based results. At present, most base stations in China provide SDA products with level 2.0 data quality. Therefore, SDA products are the first choice for FMF comparison in this study. However, it is worth pointing out that the Beijing site lacks the SDA product with level 2.0 data quality, so we used 125 the SD product instead. Finally, this study selected the level 2.0 products of 16 AERONET sites in China during 2006-2013 (POLDER on-orbit time) to validate the FMF retrieval results of this study. The specific spatial locations of AERONET sites are shown in Figure 2, and the specific site information is shown in Table 1. However, note that not all AERONET sites have long-term observational data. The sites with long-term observational data are the Beijing, Xianghe, Taihu, and Hong_Kong_PolyU sites.
The FMF retrieved in this study is the FMF at 550 nm. Neither the SDA product nor the SD product directly provides the FMF result at this wavelength. Therefore, the AERONET FMF needs to be wavelength converted. For SDA products, the products include AODt, AODf at 500 nm and the corresponding Angstrom Exponent (AE), so the FMF of SDA products can be (1) 135 where 550, is the FMF of the SDA product at 550 nm after conversion, 500 is the AODf at 500 nm, 500 is the AODt at 500 nm, is the fine-mode AE, and is the coarse and fine-mode AE.
The SD products provide AODt and AODf at 440 nm and 675 nm, respectively. Eq.

Validation method 145
In this study, the average value of ground-based observation results within ±30 min of the satellite's transit was used for comparison with the satellite retrieval results. The satellite retrieval result used for comparison is the effective retrieval result https://doi.org/10.5194/amt-2020-374 Preprint. Discussion started: 9 October 2020 c Author(s) 2020. CC BY 4.0 License.
where Cov() represents the covariance, D() represents the variance, represents the FMF retrieval value, 155 represents the value of AERONET FMF, and n is the number of validation points. We have counted the FMF validation results of different surface types, and the specific information is shown in Table 2. The 170 r, MAE, and RMSE at all sites in this study are 0.770, 0.143, and 0.170, respectively, and Within EE is 60.96%, again indicating that the FMF satellite retrieval results of this study are comparable with the ground-based observation results. All the validation results of this study cover six surface types: urban, barren, grasslands, wetlands, croplands, and forests. Overall, since the validation data of the barren type mainly come from the QOMS_CAS site, the validation results at this surface type are poor.

Introduction to the FMF retrieval method
Although the r at the other five surface types has a certain change, it is 0.508 (barren)-0.831 (forests)), but in terms of the three 175 indicators of MAE, RMSE and Within EE, the differences in the five surface types are relatively small, especially Within EE, which is concentrated at approximately 60%, similar to the site-by-site results. The errors of the FMF retrieval results in this study are relatively stable at these five surface types.
We further counted the error distribution of the FMF retrieval results, and the statistical results are shown in Figure 4. The figure shows that the FMF error of this research is mainly distributed between -0.3 and 0.3. This part of the data accounts for 180 approximately 86%, but the part less than the AERONET ground-based FMF observation value accounts for approximately 75%, indicating that the retrieval result of this study is lower than that of the ground-based observations. The specific reason needs to be analysed from the FMF retrieval method of this study. The FMF in this study is obtained from the ratio of AODf to AODt, and the retrieval accuracy of the two parameters directly determines the retrieval accuracy of FMF. Therefore, we https://doi.org/10.5194/amt-2020-374 Preprint. Discussion started: 9 October 2020 c Author(s) 2020. CC BY 4.0 License. compared the retrieved AODs with those of the ground-based data in 2013, and the statistical results are shown in Table 3. 185 The table shows that the mean errors between the AODf and AODt of our retrieval and the ground-based results are -0.039 and 0.043, respectively, indicating that the AODf retrieval result has a negative offset, and the AODt retrieval result has a positive offset, that is, the numerator is small and the denominator is large, eventually leading to a small FMF.  somewhat similar to this study, while the Yangtze River Delta is a low-value area.

Comparison with GRASP products
In our previous research, the accuracy of FMF calculated from the GRASP product was validated (Wei et al., 2020). The results of comparison with 8 SONET (Sun-sky radiometer Observation NETwork) sites show that the r between GRASP FMF and ground-based observations is 0.77, and Within EE is 62.35%, which is similar to the results of this study in Section 3.1.
However, by comparing the spatial distribution results of the two, we found some differences. We processed the latest V2.06 220 version of GRASP aerosol products. Figure 8 shows the annual averaged FMF spatial distribution of GRASP in 2013 (also normalized). Compared with Figure 6, we can see certain differences. The relatively high value area of GRASP results is mainly in southern China. We subtracted the results of this study from the average GRASP FMF results and obtained the numerical difference between the two, as shown in Figure 9. The figure shows that the difference between the two in the North China Plain and the southern Xinjiang region is relatively small. The largest differences are mainly concentrated in the southern 225 and northeastern China and Qinghai-Tibet Plateau regions. The GRASP results in these areas are greater than our results, and a small number of pixels can be larger than 0.3. However, these areas lacked publicly available sunphotometer observations in 2013 and before. The PARASOL ended its exploration mission in October 2013, and it is impossible to compare the subsequent time periods, so it is difficult to directly compare with ground-based observations to illustrate the correctness of the spatial distribution of the two. 230 In this study, the ground PM2.5 and PM10 in situ results were compared with the ground-based FMF results. It is expected that the ratio of PM2.5 to PM10 can be used to analyse the correctness of this study, as well as the GRASP FMF results in the spatial distribution trend. We selected the 2015 Beijing Olympic Sports Center monitoring site (116.407°E, 40.003°N, straightline distance of less than 4 km), which was the closest to the AERONET Beijing site, and compared the hourly averaged results of the ratio of PM2.5 to PM10 with the FMF results. Although the definitions of the two are quite different, the ratio of PM2.5 to 235 PM10 is actually a parameter of particulate matter near the ground, while FMF is actually a parameter of the atmospheric column of aerosols, but the comparison results of the two ( Figure 10) show that there is a correlation between the ratio of PM2.5 to PM10 and FMF, and the r is 0.709. This result may be because aerosols are mainly distributed near the ground, and PM2.5 and PM10 can represent different particle modes. In the end, the actual difference between the two parameters is smaller. Since the ratio of PM2.5 to PM10 is comparable to the ground-based FMF results, if there are more in situ data, it can indirectly verify 240 the spatial distribution trend of this study and the GRASP results.
Due to the lack of in situ data for particulate matter in China in 2013, this study can only be based on the 2013 environmental protection key city air in the China Statistical Yearbook (http://www.stats.gov.cn/tjsj/ndsj/). The annual average value of air quality is used for limited analysis. We extracted the FMF retrieval results and GRASP results of the corresponding 47 cities in the statistical yearbook and calculated the annual average FMF of each city for comparison with the ratio of the annual 245 average PM2.5 to PM10 of each city. The spatial distribution of the administrative regions of these 47 cities is shown in Figure   11. These cities cover most of China's provinces and have a wider spatial distribution range than the AERONET sites in Figure   2. The comparison results in Figure 12 show that although the annual average FMF results of this study in each city are lower https://doi.org/10.5194/amt-2020-374 Preprint. Discussion started: 9 October 2020 c Author(s) 2020. CC BY 4.0 License. than the annual average results of the ratio of PM2.5 to PM10, the change trend of the FMF results of this study is better than the results of GRASP FMF. The r between the FMF of this study and the ratio of PM2.5 to PM10 is 0.778, while GRASP is 250 0.472, which can provide evidence for the correctness of the FMF results of this study in the spatial distribution. The low FMF results in this study are related to the calculation methods of the annual average values of PM2.5 and PM10 in each city. Generally, most of the in situ monitoring sites for particulate matter in each city are distributed in urban areas, and the number of sites distributed in rural areas is small (for example, 9 of the 12 state-controlled sites in Beijing are in urban areas). When calculating the average FMF of a city, one pixel may contain the results of multiple monitoring stations in place, which makes it difficult 255 to achieve accurate spatial location matching. To facilitate data processing, all pixels within the urban administrative boundary are directly used to calculate the average value, and the large number of FMFs in rural areas is generally lower than that in cities, which ultimately leads to a lower FMF average result.
Based on the validation and comparison results in Sections 3.1 to 3.3, this research has obtained FMF satellite retrieval results with good accuracy in China, which proves the reliability and stability of the retrieval method. Compared with the MODIS 260 FMF products, the r, MAE, RMSE and Within EE of the results of this study are all higher than the results of MODIS.
Compared with the GRASP FMF, the results of this study are closer to the results of the ratio of PM2.5 to PM10 in terms of the spatial distribution of the entire region of China. The above results all illustrate the effectiveness and advantages of the FMF retrieval method used in this study. Compared with our original FMF retrieval method, which can only be used at the urban area scale, this research has achieved FMF retrieval in a large space. Therefore, we will carry out the practical application of 265 FMF satellite remote sensing retrieval based on the new method.      from March to May, summer is from June to August, autumn is from September to November, and winter is from December to February. As seen from the figure, for the east area of the "Hu Line", the overall FMF reached its highest value in winter, mainly concentrated in the range of 0.7-0.8; the FMF of southern China still has a relatively high value in the spring, and the 335 overall value is approximately 0.6, while in North China, the plain area is lower, generally between 0.4-0.5; the North China Plain in summer is similar to that in spring, but there is a significant decline in southern China, the value is generally between 0.3-0.5; in autumn, the overall value begins to rise, the value is approximately 0.6. The Sichuan-Chongqing economic zone maintains a relatively high value in all four seasons, and the value in some areas in winter is close to 0.8; the three northeastern provinces also have high values in winter, and the overall value is between 0.4-0.7. For the area west of the "Hu line", the 340 northern Xinjiang area is higher in autumn and winter, and it can reach 0.7 in some areas in winter, and the southern Xinjiang area also shows a significant increase in winter, with some high values close to 0.6; the Qinghai-Tibet Plateau maintains a low value in all seasons, and the value is mainly concentrated between 0.1-0.3. https://doi.org/10.5194/amt-2020-374 Preprint. Discussion started: 9 October 2020 c Author(s) 2020. CC BY 4.0 License.

Summary
In this study, the multiangle polarization data of PARASOL were used to perform FMF retrieval, and the retrieval results were 345 compared with the AERONET ground-based observations, MODIS results, and GRASP results. Based on the FMF retrieval method, the retrieval of air pollution cases in China was carried out, and the results of the FMF temporal and spatial distribution in China from 2006 to 2013 were also obtained. Based on the above work content, the conclusions of this research are described as follows: (1) There is good agreement between the FMF results obtained in this study and the AERONET ground-based observation 350 results. The overall r, MAE, RMSE, and Within EE between the two are 0.770, 0.143, 0.170, and 60.96%, respectively.
(2) The FMF results obtained in this study were more practical than the MODIS FMF products. The r, MAE, RMSE, and Within EE between the FMF results and the ground-based observations are 0.812 versus 0.302, 0.072 versus 0.512, 0.102 versus 0.574, 79.72% versus 12.59%, respectively.
(3) Compared with the GRASP FMF, the FMF results obtained in this study are closer to the ratio of PM2.5 to PM10 in terms 355 of the spatial distribution trend. Compared with the annual average ratio of PM2.5 to PM10 in 47 Chinese cities in 2013, the r of this study is 0.778, and GRASP is 0.472. The FMF retrieval method in this study has significance for the development of aerosol polarization satellite remote sensing algorithms, and the FMF results obtained in China also have good practical value for application research in the field of atmospheric environments. China has launched the Gaofen-5 (GF-5) satellite equipped with a new multiangle polarization 365 sensor. With the release of GF-5 satellite data in the future, the results of this study can also provide algorithmic support for the application of its multiangle polarization sensor in the field of atmospheric environmental monitoring and are expected to produce subsequent FMF datasets. However, there are some shortcomings in this research. For example, the retrieval of FMF still depends on the accuracy of the two parameters AODf and AODt. In our previous research, although higher-precision results of AODf and AODt have been obtained, the FMF error is related to the error of the two retrieval parameters. The 370 transmission of the error will eventually amplify the retrieval error of FMF. Compared with the individual retrieval of AODf and AODt, the retrieval of FMF is still difficult. In the future, it is still necessary to further improve the retrieval accuracy of AODf and AODt. In addition, due to the limitation of the validation data, we are temporarily unable to further discuss the correctness of the spatial distribution trend of the FMF in this study and GRASP, and only the results of the ratio of PM2.5 to PM10 were used for indirect comparison. In the future, we can try to perform FMF retrieval in other regions with many ground-375 based observations around the world to further compare the findings of the two results.