Improving the Estimation of Daily Aerosol Optical Depth and Aerosol Radiative Effect Using an Optimized Artiﬁcial Neural Network

: Aerosols can absorb and scatter surface solar radiation (SSR), which is called the aerosol radiative forcing effect (ARF). Great efforts have been made for the estimation of the aerosol optical depth (AOD), SSR and ARF using meteorological measurements and satellite observations. However, the accuracy, and spatial and temporal resolutions of these existing AOD, SSR and ARF models should be improved to meet the application requirements, due to the uncertainties and gaps of input parameters. In this study, an optimized back propagation (BP) artiﬁcial neural network (Genetic_BP) was developed for improving the estimation of the AOD values. The retrieved AOD values using the Genetic_BP model and meteorological measurements at China Meteorological Administration (CMA) stations were used to calculate SSR and bottom of the atmosphere (BOA) ARF (ARFB) using Yang’s Hybrid model (YHM). The result show that the Genetic_BP could be used for estimating AOD values with high accuracy (R = 0.866 for CASNET (China Aerosol Remote Sensing Network) stations and R = 0.865 for AERONET (Aerosol Robotic Network) stations). The estimated SSR also showed a good agreement with SSR measurements at 96 CMA radiation stations, with RMSE, MAE, R and R 2 of 29.27%, 23.77%, 0.948, and 0.899, respectively. The estimated ARFB values are also highly correlated with the AERONET ARFB ones with RMSE, MAE, R and R 2 of − 35.47%, − 25.33%, 0.843, and 0.711, respectively. Finally, the spatial and temporal variations of AOD, SSR, and ARFB values over Mainland China were investigated. Both AOD and SSR values are generally higher in summer than in other seasons. The ARFB are generally stronger in spring and summer than in other seasons. The ranges for the monthly mean AOD, SSR and ARFB values over Mainland China are 0.183–0.333, 10.218–24.196 MJ m − 2 day − 1 and − 2.986 to − 1.244 MJ m − 2 day − 1 , respectively. The Qinghai-Tibetan Plateau has always been an area with the highest SSR, the lowest AOD and the weakest ARFB. In contrast, the Sichuan Basin has always been an area with low SSR, high AOD, and strong ARFB. The newly proposed AOD model may be of vital importance for improving the accuracy and computational efﬁciency of AOD, SSR and ARFB estimations for solar energy applications, ecological modeling, and energy policy.


Introduction
Solar radiation (SSR) is defined as the power per unit area received from the Sun in the form of electromagnetic radiation [1]. SSR is composed of direct and diffuse solar radiation, which controls the of AOD values. Xu et al. [65] reconstructed the AOD values during 1993-2012 throughout China using a broadband extinction model, which showed good agreement with AERONET AOD values with RMSE, MAE and R of 0.101, 0.029 and 0.848, respectively. Guo et al. [66] revealed the spatial and temporal characteristics of the AOD values during 1980-2008 over Mainland China using TOMS AOD  and MODIS AOD products (2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007)(2008). Meanwhile, many studies have been conducted at regional scale in China using meteorological measurements and satellite observations [67][68][69][70][71]. China is a big country with severe anthropogenic aerosol emissions, which has posed great uncertainties on the global climate change. Many studies have been conducted on the spatial and temporal variations of the aerosol radiative effect in China. These studies were mainly focused on the area with intensive population and air pollution, for example Central-East China [72], the Pearl River Delta [73], and the Yangtze River Delta [8]. However, few studies have been made for analyzing the AOD and ARF values in different climate zones and terrain features over Mainland China, due to the relative sparse AOD and SSR measurements in China. Further studies should be made on the spatial and temporal variations of AOD and the ARF on SSR over Mainland China.
This study attempted: (1) to explore a new simplified model (Genetic_BP) for improving the estimation of AOD, SSR and ARFB values, based on the Genetic algorithm, back propagation neural network (BP) and an SSR estimation model (hereafter, YHM) developed by Yang et al. [74]; (2) to evaluate the retrieved AOD values by the Genetic_BP model and the retrieved SSR and ARF values by YHM in various climate zones throughout China using daily AOD, SSR, ARF measurements; and (3) to reveal the spatial and temporal variations of AOD, SSR and ARFB values in different climate zones and terrains over Mainland China.

Observation Data
Daily AOD (550 nm) records during 2002-2014 at CARSNET and AERONET stations throughout China were used for the estimation and validation of AOD values. Then, these AOD retrievals together with daily meteorological measurements including air temperature (T), relative humidity (RH), surface pressure (P), and sunshine duration (SH) at 839 CMA stations were used to retrieve SSR and ARFB over Mainland China using the YHM model. Finally, daily SSR measurements at 96 CMA stations (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) and the aerosol radiative effect (bottom of atmosphere) data at AERONET observations (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014) were used for validating the accuracy of the SSR and ARFB retrievals by the YHM model, respectively. Figure 1 shows the spatial distribution of these CARSNET stations, AERONET stations, SSR stations, CMA meteorological stations and AERONET stations. Table 1 shows the statistical indicators representing the geographical and climate patterns of these CARSNET, AERONET, SSR and CMA stations. These stations cover most areas of China with various and complicated geomorphology and terrain features. Figure 2 shows the monthly variations of T, RH, P, and SH for CARSNET, AERONET, SSR and CMA stations. T was generally higher in summer and lower in winter. The highest monthly mean T for CARSNET, AERONET, SSR and CMA were 24.91 • C, 26.08 • C, 24.43 • C and 23.72 • C in July, respectively. The lowest monthly mean T for CARSNET, AERONET, SSR and CMA were −4.78 • C, −3.52 • C, −3.27 • C and −3.41 • C in January, respectively. The P for CARSNET, AERONET, SSR, and CMA were generally higher in winter and lower in summer. The highest monthly mean P for CARSNET (930.91 hPa), AERONET (930.91 hPa), SSR (926.62 hPa), and CMA (918.26 hPa) were in January; and the lowest monthly mean P for CARSNET (913.91hPa), AERONET (913.91 hPa), SSR (911.04 hPa), and CMA (903.99 hPa) were in July. The highest monthly mean RH for CARSNET (65.51%), AERONET (67.51%), SSR (67.47%) and CMA (69.40%) were in September; and the lowest monthly mean RH for CARSNET (45.99%), AERONET (40.55%), SSR (52.78%) and CMA (55.65%) were in April. The SH were generally higher in spring and summer and lower in winter. The longest Remote Sens. 2018, 10, 1022 5 of 25 monthly mean SH for CARSNET (7.94 h), AERONET (10.25 h), SSR (7.27 h) and CMA (7.04 h) were in June, May, May, and August, respectively; and the shortest monthly mean SH for CARSNET (5.36 h), AERONET (6.89 h), SSR (5.13 h) and CMA (5.15 h) were in February, December, January and January, respectively.  Figure 2 shows the monthly variations of T, RH, P, and SH for CARSNET, AERONET, SSR and CMA stations. T was generally higher in summer and lower in winter. The highest monthly mean T for CARSNET, AERONET, SSR and CMA were 24.91 °C, 26.08 °C, 24.43 °C and 23.72 °C in July, respectively. The lowest monthly mean T for CARSNET, AERONET, SSR and CMA were −4.78 °C, −3.52 °C, −3.27 °C and −3.41 °C in January, respectively. The P for CARSNET, AERONET, SSR, and CMA were generally higher in winter and lower in summer. The highest monthly mean P for CARSNET (930.91 hPa), AERONET (930.91 hPa), SSR (926.62 hPa), and CMA (918.26 hPa) were in January; and the lowest monthly mean P for CARSNET (913.91hPa), AERONET (913.91 hPa), SSR (911.04 hPa), and CMA (903.99 hPa) were in July. The highest monthly mean RH for CARSNET (65.51%), AERONET (67.51%), SSR (67.47%) and CMA (69.40%) were in September; and the lowest monthly mean RH for CARSNET (45.99%), AERONET (40.55%), SSR (52.78%) and CMA (55.65%) were in April. The SH were generally higher in spring and summer and lower in winter. The longest monthly mean SH for CARSNET (7.94 h), AERONET (10.25 h), SSR (7.27 h) and CMA (7.04 h) were in June, May, May, and August, respectively; and the shortest monthly mean SH for CARSNET (5.36 h), AERONET (6.89 h), SSR (5.13 h) and CMA (5.15 h) were in February, December, January and January, respectively.   Lat is latitude, Lon is longitude, A is altitude above sea level, P is surface pressure, RH is relative humidity (100%), SH is sunshine duration, T is air temperature.

MODIS Products and MERRA2 Datasets
The AOD values derived from MODIS level-2 products (MOD04/MYD04) and level-3 products (MOD08/MYD08) during 2002-2014 were validated at CARSNET and AERONET stations in this study. Meanwhile, the daily mean AOD values derived from MERRA2 (The Modern Era Retrospective-Analysis for Research and Applications) during 1980-2015 were also evaluated using AOD measurements from CARNET and AERONET stations. Lat is latitude, Lon is longitude, A is altitude above sea level, P is surface pressure, RH is relative humidity (100%), SH is sunshine duration, T is air temperature.

MODIS Products and MERRA2 Datasets
The AOD values derived from MODIS level-2 products (MOD04/MYD04) and level-3 products (MOD08/MYD08) during 2002-2014 were validated at CARSNET and AERONET stations in this study. Meanwhile, the daily mean AOD values derived from MERRA2 (The Modern Era Retrospective-Analysis for Research and Applications) during 1980-2015 were also evaluated using AOD measurements from CARNET and AERONET stations.

Climatic Zones and Terrain Features
The Shuttle Radar Topography Mission (SRTM) 90m digital elevation model (DEM) data were used to derive surface elevation (http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp). The climate and terrain regionalization data were provided by Resource and environment science data center of the Chinese Academy of Sciences (http://www.resdc.cn). Figure 3 shows the terrain features in China. There are 50 topographic zones over Mainland China.

Climatic Zones and Terrain Features
The Shuttle Radar Topography Mission (SRTM) 90m digital elevation model (DEM) data were used to derive surface elevation (http://srtm.csi.cgiar.org/SELECTION/inputCoord.asp). The climate and terrain regionalization data were provided by Resource and environment science data center of the Chinese Academy of Sciences (http://www.resdc.cn). Figure 3 shows the terrain features in China. There are 50 topographic zones over Mainland China.

Optimized Back Propagation Neural Network Based on Genetic Algorithm
The back propagation (BP) neural network is the most widely used AI models for numerical fitting problems with strong learning ability and high accuracy [75]. The basic idea of BP is to find a function that best maps a set of input parameters to the correct output values using gradient descent optimization algorithm, which minimizes the mean square error between the network's actual output

Optimized Back Propagation Neural Network Based on Genetic Algorithm
The back propagation (BP) neural network is the most widely used AI models for numerical fitting problems with strong learning ability and high accuracy [75]. The basic idea of BP is to find a function that best maps a set of input parameters to the correct output values using gradient descent optimization algorithm, which minimizes the mean square error between the network's actual output value and the expected output value [76]. In this study, nine parameters (RH, T, P, SD, A, day number (D), visibility (VIS) and cloud fraction (TCP), and MERRA2 AOD) that were closely correlated with AOD values were set as input parameters for the BP model; daily AOD measurements at the CARSNET and AERONET stations were set as the model output parameter for the BP model. A total of 70% of the databases during the whole study period were used to train the BP model, and 30% of them were used for testing the model. The AOD values could be calculated using the following equation: where F g is the estimated AOD; Z (w, x, b) means the hidden transfer function; w i (t) is the weight; x i (t) is the input parameter indiscrete time space; and b is the neuronal bias. The basic schematic architecture of the BP neural network in this study is illustrated in Figure 4.  Then, the Genetic algorithm was introduced to optimize the weights and the thresholds of the BP neural network for the estimation of AOD values. It is a meta-heuristic algorithm proposed by Holland [37]inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms, which is commonly used to generate high-quality solutions to optimization and search problems. The Genetic_BP model for improving the estimation of AOD values could be conducted as the following steps ( Figure 5): (1) Initialize random population. The basic structure of the BP neural network in this study is 9-10-1 (Figure4) with 9 input layers, 10 hidden layers and 1 output layer. Thus, the number of weights is 9×10+10×1 = 100; the number of thresholds is 10+1 = 11. Thus, the encoding length is 100+11 = 111. (2) Selection operation. The new individuals with high fitness values would be selected from old individuals using roulette selection method. The selection probability for individuals was calculated as following equation: Then, the Genetic algorithm was introduced to optimize the weights and the thresholds of the BP neural network for the estimation of AOD values. It is a meta-heuristic algorithm proposed by Holland [37] inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms, which is commonly used to generate high-quality solutions to optimization and search problems. The Genetic_BP model for improving the estimation of AOD values could be conducted as the following steps ( Figure 5): (1) Initialize random population. The basic structure of the BP neural network in this study is 9-10-1 ( Figure 4) with 9 input layers, 10 hidden layers and 1 output layer. Thus, the number of weights is 9 × 10 + 10 × 1 = 100; the number of thresholds is 10 + 1 = 11. Thus, the encoding length is 100 + 11 = 111. (2) Selection operation. The new individuals with high fitness values would be selected from old individuals using roulette selection method. The selection probability for individuals was calculated as following equation: where P i is the selection probability; and g i is the fitness value, which could be calculated as follows:  (4) where N is the number of the input layers of BP neural network (6); y i is the i-th expected output value; o i is the i-th predicted output values; and b is a constant value. (3) Crossover operation. The crossover operation was conducted using arithmetic crossover algorithm: where a cj and a dj are the c-th and d-th chromosome at j position; and b is a constant within 0-1.
(4) Mutation operation. The mutation operation was conducted using following equations: where a max and a min are the maximum and minimum value for a ij ; r is a random number [0-1]; r 2 is also random number; g is the number of iterations; and Gmax is maximum evolution times. Detailed information about the Genetic_BP model can be found in [77].  Then, the Genetic algorithm was introduced to optimize the weights and the thresholds of the BP neural network for the estimation of AOD values. It is a meta-heuristic algorithm proposed by Holland [37]inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms, which is commonly used to generate high-quality solutions to optimization and search problems. The Genetic_BP model for improving the estimation of AOD values could be conducted as the following steps ( Figure 5): (1) Initialize random population. The basic structure of the BP neural network in this study is 9-10-1 (Figure4) with 9 input layers, 10 hidden layers and 1 output layer. Thus, the number of weights is 9×10+10×1 = 100; the number of thresholds is 10+1 = 11. Thus, the encoding length is 100+11 = 111. (2) Selection operation. The new individuals with high fitness values would be selected from old individuals using roulette selection method. The selection probability for individuals was calculated as following equation: where is the selection probability; and is the fitness value, which could be calculated as follows:

Yang's Hybrid Model
Yang's Hybrid model (YHM) is a physically-based broadband model for estimating solar radiation, taking into account of five main radiation-damping processes, including Rayleigh scattering, aerosol extinction, ozone absorption, water vapor absorption and gas absorption. YHM was first developed by Yang et al. [78], then improved by Yang and Koike [79] for hydrological applications, and further improved by Yang et al. [74] by importing global data sets. YHM is recognized as one of the best SSR models [80,81], which could be expressed as follows: where H all means the daily surface solar radiation (MJ m −2 day −1 ) for all-sky conditions. The cloud effect on daily SSR is corrected using a cloud transmittance parameter τ c , which is a function of the actual sunshine durations (SH) and the maximum possible sunshine durations (N). Detail description on Yang's Hybrid model could be found in Appendix A.

Aerosol Radiative Forcing Effect on SSR
The ARF is defined here as [82]: where SSR WA is the estimated SSR without the presence of aerosols in the atmosphere; and SSR N A denotes the estimated SSR with aerosols in the atmosphere.

Model Performance
The following statistical indicators including the correlation coefficient (R), the determination coefficient (R 2 ), the mean absolute bias error (MAE, %), the root mean square error (RMSE, %), and the root mean square error value (RMSEE, MJ m −2 day −1 ) were used to evaluate the model accuracy for the Genetic_BP model and the YHM solar radiation model: where n means the number of data points; G est,i and G obs,i are the estimated and observed AOD/ARF/SSR, respectively; G est,i and G obs,i represent the mean of the estimated AOD/ARF/SSR and observed AOD/ARF/SSR, respectively; and M means the mean of the observed AOD/ARF/SSR values.

Validation of Estimated AOD
The AOD values retrieved by the Genetic_BP model were directly compared with measured AOD values at the CARSNET and AERONET stations. Figure 6a shows the scatter plot of AOD values from the CARSNET stations and AOD values calculated by Genetic_BP. Figure 6b Figure 7 shows the monthly variations of the statistical indicators representing the model accuracy of the Genetic_BP models at the CARSNET stations and AERONET stations, respectively. The results show that the model deviations for Genetic_BP model were relatively large in summer than that in spring and winter, due to the effect of cloudy and rainy weather in summer on the ground meteorological measurements. The largest RMSE (45.56%) and MAE (29.94%) for the estimated AOD values at CARSNET stations were found in September; the smallest RMSE (34.74%) and MAE (24.49%) were found in December; the smallest R (0.847) and R 2 (0.718) were in December; and the largest R (0.887) and R 2 (0.787) in September. The largest RMSE (59.76%) and MAE (39.66%) for the estimated AOD values at the AERONET stations were found in July; the smallest RMSE (44.80%) and MAE (29.82%) were found in October; the smallest R (0.801) and R 2 (0.642) were in May; and the largest R (0.875) and R 2 (0.766) were in December.  The AOD retrievals by the Genetic_BP model were also compared with the AOD observations and estimations from MODIS and MERRA2 atthe CARSNET stations. Figure 8   The AOD retrievals by the Genetic_BP model were also compared with the AOD observations and estimations from MODIS and MERRA2 atthe CARSNET stations. Figure 8

Validation of the Estimated SSR
Daily AOD values retrieved by the Genetic_BP model and meteorological measurements at 96 CMA radiation stations over Mainland China were used for the estimation of SSR using YHM. Figure  9 shows the validation result of the estimated SSR values by YHM at 96 CMA radiation stations. The results show that the YHM can estimate the SSR values with high accuracy, with RMSE, MAE, R and R 2 of 29.27%, 23.77%, 0.948 and 0.899, respectively. Figure 10 illustrates the spatial distributions of RMSE and MAE for YHM throughout China, respectively. It is clear that the YHM shows comparable performance over Mainland China, especially in the Plateau zones due to its strict theoretical basis on the radiation dumping processes in the atmosphere; for example, the RMSE for Ganzi, Germu, Gangcha and Lhasa were8.36%, 8.51%, 9.63% and 9.65%, respectively; and the MAE were6.74%, 7.00%, 7.66% and 7.88%, respectively. The model accuracy in northern China is generally higher than

Validation of the Estimated SSR
Daily AOD values retrieved by the Genetic_BP model and meteorological measurements at 96 CMA radiation stations over Mainland China were used for the estimation of SSR using YHM. Figure 9 shows the validation result of the estimated SSR values by YHM at 96 CMA radiation stations. The results show that the YHM can estimate the SSR values with high accuracy, with RMSE, MAE, R and R 2 of 29.27%, 23.77%, 0.948 and 0.899, respectively. Figure 10 illustrates the spatial distributions of RMSE and MAE for YHM throughout China, respectively. It is clear that the YHM shows comparable performance over Mainland China, especially in the Plateau zones due to its strict theoretical basis on the radiation dumping processes in the atmosphere; for example, the RMSE for Ganzi, Germu, Gangcha and Lhasa were 8.36%, 8.51%, 9.63% and 9.65%, respectively; and the MAE were 6.74%, 7.00%, 7.66% and 7.88%, respectively. The model accuracy in northern China is generally higher than that in southern China, due to the dry air conditions there; for example, the RMSE for Erenhot, Ejinaqi and Urat in Inner Mongolia were 8.90%, 9.18% and 9.88%, respectively; and the MAE were 5.91%, 6.45% and 6.88%, respectively. Relatively larger estimation errors mainly distributed in southern China, owing to the abundant precipitable water vapor, changing weather and frequent cloud occurrence there; for example, the RMSE for Jishou in Hunan province, Ganzhou in Jinagxi province and Changsha in Hunan province were 30.55%, 29.25% and 27.52%, respectively; the MAE are 25.36%, 23.25% and 23.18%, respectively. The largest estimation errors were found in Chongqing in the Sichuan Basin, with RMSE and MAE of 35.95% and 30.11%, respectively, while the smallest estimation errors were found in Gaer in the Tibetan Plateau, with RMSE and MAE of 6.87% and 5.16%, respectively.    Figure 11 shows the monthly variation of the RMSE, MAE, R and R 2 for YHM over Mainland China. The results show that the YHM performs superior in autumn and winter than that in summer and spring, owing to the relatively larger estimation error of the AOD retrievals in spring and the frequent cloudy and rainy days and changing weather in summer. The largest RMSE (29.02%) and MAE (25.13%) for YHM are found in September and August, respectively, while the smallest RMSE     Figure 11 shows the monthly variation of the RMSE, MAE, R and R 2 for YHM over Mainland China. The results show that the YHM performs superior in autumn and winter than that in summer and spring, owing to the relatively larger estimation error of the AOD retrievals in spring and the frequent cloudy and rainy days and changing weather in summer. The largest RMSE (29.02%) and MAE (25.13%) for YHM are found in September and August, respectively, while the smallest RMSE     [84] evaluated the accuracy of three SSR products including ISCCP-FD, GEWEX-SRB, and GLASS products over Mainland China. The results indicated that the SSR retrievals by YHM were more accurate than those from the ISCCP-FD, GEWEX-SRB, and GLASS products. The RMSEE for ISCCP-FD, GEWEX-SRB, and GLASS were 2.40 MJm −2 day −1 , 3.09 MJm −2 day −1 , 2.95 MJm −2 day −1 , and 2.95 MJm −2 day −1 , respectively; the R for ISCCP-FD, GEWEX-SRB, and GLASS was 0.94, 0.91, 0.93, and 0.93, respectively. Overall, YHM using the estimated AOD values by Genetic model could be used for the estimation of SSR with high accuracy and robustness.

Validation of Estimated ARFB
Daily AOD values retrieved by the Genetic_BP model and daily meteorological measurements at the CMA stations were used for estimating SSR values (with or without aerosols) using YHM. Then, the ARFB values at 27 AERONET stations were calculated using formula (14). Finally, the estimated ARFB values were validated at 27 AERONET stations. Figure 12 shows the scatter plot between the estimated ARFB values and AERONET ARFB ones. It is obvious that the estimated ARFB values are in good agreement with AERONET ARFB values with RMSE, MAE, R and R 2 of −35.47%, −25.33%, 0.843, and 0.711, respectively. Figure 13 illustrates the monthly variations of the statistical indicators representing the model accuracy of the estimated ARFB values at AERONET stations. The results indicate that relatively larger model deviations are observed in summer than in spring and winter, due to the strong effect of cloudy and rainy weather at the sites of the meteorological stations, and high human activity in summer. The largest RMSE (45.08%) and MAE (29.16%) for the estimated ARFB values at AERONET stations were found in August, whilethe smallest RMSE (34.55%) and

Validation of Estimated ARFB
Daily AOD values retrieved by the Genetic_BP model and daily meteorological measurements at the CMA stations were used for estimating SSR values (with or without aerosols) using YHM. Then, the ARFB values at 27 AERONET stations were calculated using formula (14). Finally, the estimated ARFB values were validated at 27 AERONET stations. Figure 12 shows the scatter plot between the estimated ARFB values and AERONET ARFB ones. It is obvious that the estimated ARFB values are in good agreement with AERONET ARFB values with RMSE, MAE, R and R 2 of −35.47%, −25.33%, 0.843, and 0.711, respectively. Figure 13

Annual Variation of AOD-SSR-ARFB in China
Daily meteorological measurements at 716 CMA stations were used to calculate the daily and monthly mean AOD values over Mainland China using the Genetic_BP model. Then, the daily and monthly mean SSR and ARFB throughout China were calculated using YHM and formula (14). Figure  14 shows the annual mean values of AOD, SSR and ARFB during 1980-2015 over Mainland China. It was obvious that AOD, SSR and ARFB are closely correlated. The R between the annual mean AOD and SSR values was0.715; the R between the annual mean AOD and ARFB values was−0.919; and the R between the annual mean AOD and SSR values was−0.793.

Annual Variation of AOD-SSR-ARFB in China
Daily meteorological measurements at 716 CMA stations were used to calculate the daily and monthly mean AOD values over Mainland China using the Genetic_BP model. Then, the daily and monthly mean SSR and ARFB throughout China were calculated using YHM and formula (14). Figure  14 shows the annual mean values of AOD, SSR and ARFB during 1980-2015 over Mainland China. It was obvious that AOD, SSR and ARFB are closely correlated. The R between the annual mean AOD and SSR values was0.715; the R between the annual mean AOD and ARFB values was−0.919; and the R between the annual mean AOD and SSR values was−0.793.

Annual Variation of AOD-SSR-ARFB in China
Daily meteorological measurements at 716 CMA stations were used to calculate the daily and monthly mean AOD values over Mainland China using the Genetic_BP model. Then, the daily and monthly mean SSR and ARFB throughout China were calculated using YHM and formula (14). Figure 14 shows the annual mean values of AOD, SSR and ARFB during 1980-2015 over Mainland China. It was obvious that AOD, SSR and ARFB are closely correlated. The R between the annual mean AOD and SSR values was0.715; the R between the annual mean AOD and ARFB values was−0.919; and the R between the annual mean AOD and SSR values was−0.793.
In the beginning of the 1980s, the annual mean AOD values over Mainland China were relatively lower than those in other periods during 1980-2015, due to low anthropogenic aerosol emissions in the beginning of the 1980s. Thus, the ARFB and SSR values in that period were higher than those in other periods. However  In contrast, northwestern China has always been an area with low AOD values, due to relatively lower human activity and clear air conditions, for example the ranges for the monthly mean AOD values in Alashan and Hexi Corridor, the western Inner Mongolia high plain, and the eastern Inner Mongolia high plains were 0.151-0.312, 0.149-0.298, and 0.133-0.298, respectively. The Qinghai Tibetan Plateau has always been an area with the lowest annual mean AOD values and monthly mean AOD values, due to the clear atmosphere there, for example, the ranges of the monthly mean AOD values in the Nagqu Plateau and the Ali mountains were 0.0120-0.082 and 0.044-0.106, respectively. 0.317, 0.407, 0.451, 0.411, 0.334, 0.372 and 0.335, respectively. In contrast, northwestern China has always been an area with low AOD values, due to relatively lower human activity and clear air conditions, for example the ranges for the monthly mean AOD values in Alashan and Hexi Corridor, the western Inner Mongolia high plain, and the eastern Inner Mongolia high plains were0.151-0.312, 0.149-0.298, and 0.133-0.298, respectively. The Qinghai Tibetan Plateau has always been an area with the lowest annual mean AOD values and monthly mean AOD values, due to the clear atmosphere there, for example, the ranges of the monthly mean AOD values in the Nagqu Plateau and the Ali mountainswere0.0120-0.082 and 0.044-0.106, respectively.   Daily meteorological measurements including surface pressure, surface temperature, relative humidity and sunshine duration at 716 CMA meteorological stations and retrieved AOD values using Genetic_BP model were used to reveal the spatial and temporal variations of SSR over Mainland China. Figures 17 and 18 illustrate these variations. The results show that the monthly mean SSR values gradually increased from January to May and decreased from June to December, owing to the variations of the annual cycle of solar zenith and the maximum sunshine duration in China. The monthly mean SSR for January, February, March, April, May, June, July, August, September, October, November, and December were10.604, 13.349, 17.221, 21.420, 23.998, 24.196, 24.580, 23.250, 19.674, 15.843, 12.207 and 10.218 MJ m −2 day −1 , respectively. The Qinghai Tibetan Plateau has always been an area with the highest SSR values, because of the weaker radiation extinction processes and clear sky conditions; for example, the annual mean SSR for the Zangnan mountain area, the Qiangtang Plateau Lake Basin, the Qaidam Basin and the Southern Qinghai Plateau Gully were22.714, 22.256, 20.175, 20.796 MJ m −2 day −1 , respectively. In contrast, the Sichuan Basin has always been an area with the lowest SSR values, owing to the relatively abundant precipitable water vapor and strong aerosol radiative effect. The annual mean SSR values for Sichuan Basin was 11.721 MJ m −2 day −1 . Northeastern China was also an area with low SSR values, owing to the short sunshine duration in winter and the relatively abundant precipitable water vapor in summer; for example, the annual mean SSR values for Greater Khingan Range was13.624 MJ m −2 day −1 . The SSR values are generally higher in northern China than in southern China in spring and summer, due to the relatively longer sunshine durations and drier air conditions in northern China than that in southern China. However, the SSR values are generally lower in northern China than in southern China in autumn and winter, owing to the relatively shorter sunshine duration in northern China than those in southern China.

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The ARFB were generally stronger in spring and summer than that in other seasons, due to the high

Conclusions
The applicability of a new AOD retrieval algorithm (Genetic_BP) for estimating daily AOD values over Mainland China was investigated. The estimated AOD values were validated at the CARSNET and AERONET stations. Then, the retrieved AOD values by the Genetic_BP model were used for improving the estimation of SSR and ARFB based on Yang's hybrid model. The estimated SSR values and ARFB values were evaluated using SSR (CMA) and ARFB (AERONET) measurements. Finally, the spatial and temporal variations of AOD, SSR and ARFB over Mainland China were investigated.
The results show that the Genetic_BP model could be used for estimating AOD values over Mainland China with comparable accuracy. The RMSE, MAE, R and R 2 for the estimated AOD values at the CARSNET stations were 41.46%, 27.51%, 0.866 and 0.749, respectively. The RMSE, MAE, R and R 2 for the estimated AOD values at the AERONET stations were 44.98%, 29.23%, 0.865 and 0.747, respectively. The validation results of the estimated SSR and ARFB values also showed good agreement with SSR and ARFB measurements. The RMSE, MAE, R and R 2 for the estimated SSR values at the CMA stations were 29.27%, 23. The AOD values were higher in spring than that in other seasons. The largest monthly mean AOD value (0.229) was found in March, while the smallest monthly mean AOD value (0.183) was in December. Relatively larger AOD values were mainly observed in the Sichuan Basin, while smaller AOD values were mainly observed in the Qinghai Tibetan Plateau. The SSR values were generally higher in summer than in other seasons, because of the relatively higher solar zenith and the greater sunshine duration in summer than in other seasons. The SSR values gradually increased from January (6.697 MJ m −2 day −1 ) to June (14.028 MJ m −2 day −1 ) and decreased from July (13.601 MJ m −2 day −1 ) to December (6.140 MJ m −2 day −1 ). The Qinghai Tibetan Plateau has always been an area with the highest SSR values, while the Sichuan Basin has always been an area with the lowest SSR values. The ARFB values were closely correlated with AOD and SSR values. The monthly mean ARFB values gradually decreased from January (−1.353 MJ m −2 day −1 ) to June (−2.750 MJ m −2 day −1 ) and increased from July (−2.636 MJ m −2 day −1 ) to December (−1.244 MJ m −2 day −1 ), owing the relatively higher AOD values and SSR values in summer than that in other seasons. Eastern China has always been an area with strong aerosol radiative effect, because of the strong human activity and anthropogenic aerosol emissions. The Tarim and Turpan Basin are also areas with strong ARF, owing to the dusty air conditions and high AOD values. In contrast, the Qinghai Tibetan Plateau has always been an area with weak ARF, due to the relatively lower AOD values than in other climate zones.
Certainly, this new approach for improving the estimation of AOD, SSR and ARFB should be further applied and validated in other climatic zones and ecosystems around the world. More attention should be paid to the quantitative correlations among AOD, SSR and ARFB in different climatic zones and ecosystems.