Historical satellite remote sensing of AOD has been recorded going back to the 1980s. Despite limitations in accuracy (Chu et al., 2002), the satellite-measured AOD has global distributions with relative long-time coverage that makes it suitable for evaluating model simulation performance (Roy et al., 2007; Liu et al., 2010; Wang et al., 2010, 2011) and for understanding the evolution of atmospheric aerosols (Chin et al., 2014). To minimize the influences from uncertainties of a single satellite product, we conducted our analysis based on all available satellite retrievals (or averages) with more robust estimates (e.g., the level-3 data set). The Advanced Very High Resolution Radiometer (AVHRR) provides the longest-running global satellite observations, starting in 1981. Long-term AVHRR-retrieved AOD over the oceans (AVHRR retrievals are unavailable over land due to relatively large uncertainties associated with surface reflectance over the land surface) has been produced by the NOAA Climate Data Record (CDR) project (Chan et al., 2013; Zhao et al., 2013). Five satellite retrieval products that cover both land and ocean are also used in this study (Table 1). The Total Ozone Mapping Spectrometer (TOMS) is one of the earliest satellites providing AOD measurement products with data from 1979 to 2001 (Torres et al., 1998, 2002). However, it is not specifically designed to measure aerosols and thus has limited accuracy (Chin et al., 2014). Both the TOMS product and AVHRR product are only used here for trend analysis. The other four data sources are more recent satellite products, i.e., the Seaviewing Wide Field-of-view Sensor (SeaWiFS) (McClain et al., 1998; Hsu et al., 2012; Sayer et al., 2012), the Multiangle Imaging Spectroradiometer (MISR) (Kahn et al., 2005; 2010) and the Moderate Resolution Imaging and Spectroradiometer (MODIS) on both NASA's Earth Observing System (EOS)-Terra and EOS-Aqua satellites (Kaufman et al., 1997; Remer et al., 2005, 2008; Levy et al., 2010) that have improved accuracy mostly covering the period of the 2000s. The bright desert surfaces that are missing in the “dark target” retrieval (ver. 5.1) in the MODIS AOD product are filled by the “deep blue” retrieval that uses the 412 nm channel of MODIS to enable the retrieval of AOD over bright surfaces over land (Hsu et al., 2004). An exception to this is for MODIS-Terra data after 2007 when there is no deep-blue retrieval available.

In conducting the modeled–observed comparisons, the satellite data sets are interpolated to the 108 km × 108 km grid of the CMAQ northern hemispheric domain as shown in Fig. 1. The grid matching was conducted by using the simple inverse distance weighting method. To be consistent with the specific time that the satellite crosses the Equator, especially for the four more recent satellites, i.e., MISR (10:30 local time), SeaWiFS (noon local time), MODIS-Terra (10:30 local time) and MODIS-Aqua (13:30 local time), we chose to extract the AOD from model outputs at 11:00 (local time).

Model-simulated AOD is also compared with measurements from the worldwide ground-based Aerosol Robotic Network (AERONET) that has been widely used for satellite product validation and model evaluations because of its direct measurements and unified high standard for instrument calibration (Holben et al., 2001; Chin et al., 2014). We select eleven sites from the AERONET with relatively long-term historical records to enable comparison of AOD trends, as additional evidence demonstrating the decadal changes in the tropospheric aerosol burden. For the purpose of comparison with the model, all the AERONET AOD observations were converted to the 533 nm band based on the equation of the Ångström exponent.

Since this study focuses on the aerosol direct radiative effect, the clear-sky SWR product is examined in this analysis. The Clouds and the Earth's Radiant Energy System (CERES) instruments were developed for NASA's EOS report observations starting from 1997 (Wielicki et al., 1996, 1998). The CERES Energy Balanced and Filled (EBAF) data set provides satellite-derived clear-sky shortwave radiation at TOA over the globe on a monthly averaged basis starting from 2000 (Loeb et al., 2009, 2012). Such observation-derived clear-sky SWR at TOA with global coverage is suitable for comparison with model simulations (Satheesh and Ramanathan, 2000; Rajeev and Ramanathan, 2001; Anantharaj et al., 2010) and estimation of the DRE (Yu et al., 2006; Patadia et al., 2008) at a regional scale.

Efforts have also been made to establish records of observation-derived clear-sky shortwave radiation at the surface, for the purpose of reducing the uncertainties in the fluxes at the surface, which are significantly larger than those at the TOA (Wild et al., 2006). For surface observations with high frequency such as the World Climate Research Programs Baseline Surface Radiation Network (WCRP-BSRN), it is possible to process a stratification of records into cloudy and clear-sky periods on the basis of an advanced clear-sky detection algorithm (Long and Ackerman, 2000; Wild et al., 2005) and to validate the model (Wild et al., 2006; Freidenreich and Ramaswamy, 2011). Unlike those at the TOA, the surface fluxes cannot be directly measured by satellites. However, the CERES mission estimates a global clear-sky surface SWR through radiative transfer calculations using satellite-retrieved surface, cloud, and aerosol properties as input (Kato et al., 2013), which agrees with the surface observations on a global mean level (Wild et al., 2013). The satellite-derived surface product has also been used in recent analyses (Hakuba et al., 2014).

For comparison with model simulations on a regional scale, we used the CERES-derived clear-sky shortwave radiations at both TOA and the surface. In addition, we used clear-sky SWR at seven sites of the Surface Radiation Budget Network (SURFRAD, a component of the BSRN network) processed by Gan et al. (2014). These seven sites are grouped into the eastern US (including Bondville, IL; Goodwin Creek, MS; Penn State, PA; and Southern Great Plains, OK) and the western US (including Table Mountain, CO; Desert Rock, NV; and Fort Peck, MT) for comparison with simulations.

In consideration of the limited length of the record, as in our previous study (Xing et al., 2015), this study only focuses on linear trends. The linear least square fit method was employed, and significance of trends was examined with a Student's t test at the 80, 90 and 95  % confidence levels (p=0.2, 0.1 and 0.05). To be consistent with the available period of satellite products mostly covering the period of the 2000s, the two decades were separated into two time periods spanning, i.e., the 1990s (1990–2000) and 2000s (2000–2010) for analysis.

Due to discrepancies in the sensitivities and retrieval algorithms of the various sensors, satellite-retrieved AODs from the different platforms are not necessarily consistent with each other. Figure 2 displays the spatial distribution of JJA-averaged AOD from multiple-platform satellite retrieval data sets as well as from the model simulation. The “polluted half-circle” that starts from the Sahara Desert to East Asia is evident in MISR, MODIS-Terra and MODIS-Aqua. Missing data are found in large areas of China and India in both TOMS- and SeaWiFS-retrieved AOD. Inconsistencies among satellite retrievals are also noticeable in the North Pacific Ocean as well as in the southwestern United States, where higher AOD is shown in MODIS-Terra and MODIS-Aqua but low or no value in other satellite retrievals. In general, the model captures the spatial pattern of AOD but underestimates the AOD levels in dust areas including the Sahara Desert, the Arabian Desert, the Indo-Gangetic basin in northern India that is affected by dust storms coming from the west during summer (Prasad and Singh, 2007) as well as the Gobi Desert in western China. Such underestimations as well as unexpected high AOD estimates in Hawaii might be associated with the uncertainty of the wind-blown dust module in which parameters related to the calculation of “threshold friction velocity” need future investigation (Fu et al., 2014). Ridley et al. (2014) found similar underestimation of summer AOD over the Sahel in their modeling study, suggesting that such biases might be associated with the Haboobs-driven dust emission, which is not well represented in the current dust module (Marsham et al., 2011). However, the model captures the moderate AOD level in the eastern US (EUS) and Europe (EUR) in early years and the high AOD level in eastern China (ECH) where anthropogenic aerosols are the dominant contributors. Slight underestimation in ECH and EUS might be associated with underestimation of fine particles (Xing et al., 2015), and poor representation of secondary organic aerosol formation is also more evident in summer (see Fig. 3a, b, c).

The model successfully captured AOD trends after 2000 in three non-dust land regions (i.e., ECH, EUS and EUR). The spatial distribution of the AOD trend (yr-1) and time series of region-averaged AOD are provided in Figs. 2 and 3, respectively. In ECH, a significant increase in the AOD level is suggested from satellite retrievals, with growth rates of +0.001 to +0.004 (+0.3 to +1.7 %) yr-1. Such an increase in AOD has also been simulated by the model, though with a faster growth of +0.014 (+5.3 %) yr-1 (see Table 2). The overestimation of the AOD trend in ECH is caused by the discrepancy between the simulated and observed AOD trend over the southern part of eastern China, which can be strongly influenced by biomass burning in Southeast Asia (Deng et al., 2008; Fu et al., 2012). As displayed in Fig. 2, the model failed to capture the negative trend of the satellite-retrieved AODs in Southeast Asia. Variations of biomass burning activity in Southeast Asia are difficult to capture in the model without an accurate temporally resolved biomass emission inventory, currently not available. The declining trends shown in observed AOD might also be associated with the recession since late 2008 (Lin et al., 2010) that may be not well represented in the emission inventory. The SeaWiFS retrieved AOD presents a more significant (at the p=0.1 level) increasing trend compared to other satellite products, though the growth rate (+0.004 yr-1) is still lower than that of the simulated AOD trend (+0.014 yr-1). The simulated declining trends of -0.004 (-2.7 %) yr-1 in EUS and -0.003 (-2.1 %) yr-1 in EUR are very close to the observed trends of -0.003 to -0.008 (-1.5 to -4.4 %) yr-1 and -0.002 to -0.007 (-1.0 to -3.8 %) yr-1, respectively. Additionally, declining trends in both observed and simulated AODs in EUS and EUR are significant (at least at the p=0.2 level). For the period before 2000, the simulated AOD in ECH also shows an increasing trend of +0.002 (+1.0 %) yr-1, which is smaller in magnitude than that after 2000. The opposite trend (though not significant at the p=0.2 level) estimated from both AVHRR and TOMS might be explained by the limited number of grid values available for calculation (refer to Fig. 3). Both simulation and satellite retrievals (except TOMS in EUR, which has no trend) show declining trends in EUS and EUR before 2000, with magnitudes comparable to those for the period post 2000, and the declining trend in EUR is significant (at the p=0.2 level) in both simulated and AVHRR-retrieved AOD.

The model captures the decreasing trends in the North Atlantic (NAT) for both the before-2000 and after-2000 periods (as seen in Table 2 and Fig. 3f). Such declining trends are attributable to decreases in both EUS and EUR. The AOD trends in the North Pacific (NPA) before 2000 could possibly be associated with a declining trend in global background AOD from biomass burning in Southeast Asia, dust variations in the Sahara Desert and anthropogenic emission reduction in Japan, Europe and North America. For the period before 2000, both simulated and satellite-retrieved AOD in NPA exhibit declining trends of -0.003 (-2.08 %) yr-1 and -0.001 to -0.002 (-0.5 to -0.6 %) yr-1, respectively. However, after 2000, the increase in transport from ECH results in an increasing trend shown in both simulated and most satellite-retrieved AOD (significant at the p=0.2 level for SeaWiFS and MISR) in NPA of +0.003 (+2 %) yr-1 and +0.001 to +0.002 (+0.3 to +1.7 %) yr-1, respectively, except in AVHRR-retrieved AOD, which exhibits the opposite trend.

The model also captures declining trends in regions influenced mostly by natural mineral dust aerosol, i.e., SHR, CAT and NIN for the period before 2000. Such declining trends might result from a reduction in surface winds over dust source regions in Africa (Ridley et al., 2014). The AOD in CAT also shows a declining trend in most satellite retrievals for the period after 2000; however, the magnitude, i.e., up to -0.006 (-1.6 %) yr-1, is much smaller than that for the period before 2000, which is up to -0.011 (-2.8 %) yr-1. Simulations show a similar transition from stronger declining trends of -0.005 (-1.9 %) yr-1 before 2000 to smaller declining trends of 0.000 (-0.02 %) yr-1 after 2000. However, the model fails to capture the increasing trends in the Arabian Desert as well as its downwind ocean area NIN that can be observed from satellite-retrieved AOD (see Figs. 2, 3h). Additionally, the simulated increasing trend in SHR has a smaller magnitude of +0.001 (+0.33 %) than satellite-retrieved AOD trends of +0.002 to +0.15 (+0.5 to +2.3 %), except for MODIS-Terra. This discrepancy might be caused by the poor representation of dust emissions over the Arabian Desert.

The spatial location of the 693 AERONET sites can be seen in Fig. 4a, which shows the averaged summer AOD of all available records for each site. The corresponding simulated AOD averaged from the same selected periods that were used to average the observations at each site is given in Fig. 4b for comparison. Generally, the spatial gradients of AOD shown in the model are consistent with that from observations. However, the model tends to underestimate AOD both over regions where anthropogenic aerosols are dominant (ECH, EUS and EUR) as well as over regions where natural aerosols are dominant (SHR, CAT and NIN). Such a discrepancy is consistent with the comparisons against satellite retrievals in the previous section.

Eleven AERONET sites that have relatively long-term records were selected for trend analysis and are marked by red boxes in Fig. 4a. The simulated AOD as well as the satellite-retrieved AOD is chosen from the corresponding grid cell for each site based on its spatial location. A site-by-site comparison is presented in Fig. 5.

At the Beijing site (Fig. 5a), which is in northeastern China, the model agrees with satellite retrievals that show a continual increasing trend from 1990 to 2010. However, the AOD level from AERONET is much higher than both simulated and satellite-retrieved AOD, and shows an opposite trend. Such a discrepancy was also found in our previous analysis when comparing concentrations of precursors against surface observations (Xing et al., 2015). Extremely high AOD levels from AERONET also indicate that the coarse spatial resolution might limit the model's ability to represent the pollution distribution at a finer scale. Another site within the ECH area is Chen-Kung University (Fig. 5b) in Taiwan. Simulated and satellite-retrieved AOD trends show opposite directions, possibly because the model fails to capture the variations in biomass burning activities in Southeast Asia as discussed in the previous section. However, the correlation coefficient is relatively high (R=0.44) and the bias is relatively small (NMB = -5 %). The AOD measured by AERONET shows a similar increasing trend as the simulation, but the correlation is poor.

Simulated, surface-observed and satellite-retrieved AODs are found to be consistent with each other in the other two land areas where anthropogenic aerosols are dominant, i.e., EUS and EUR. At the GSFC site (Fig. 5c) in EUS, all AODs show declining trends of -0.007 to -0.013 yr-1, which is slightly higher than that of the region-averaged trend of -0.003 to -0.008 yr-1. The correlation coefficient between the simulated and observed AOD ranges between 0.42 and 0.57, but the underestimation is > 40 % due to the underestimation of fine particles (Xing et al., 2015). At the Lille site (Fig. 5d) in EUR, simulated, surface-observed and satellite-retrieved AODs show consistent decreasing trends of -0.003 to -0.007 yr-1, which are comparable with the region-averaged level. The correlation between the simulated and observed AOD ranges between 0.17 and 0.19 and the smaller NMB of < ±15 % compared to the EUS region likely is attributable to a better simulation of fine particle concentrations (Xing et al., 2015).

At the HJAndrews site (Fig. 5e) on the western coast of the US where fewer emission reductions occurred than in the EUS, the simulated AOD shows a slightly increasing trend of +0.001 yr-1 that is also found in surface-observed and satellite-retrieved AOD. Such increasing trends might be associated with the increased AOD level in NPA after 2000. At Bonanza Creek (Fig. 5f), the model fails to capture the abnormal high AOD level observed by both AERONET and satellites for the years of 2004 and 2009, when large forest fires occurred in Alaska (National Interagency Fire Center, http://www.nifc.gov/fireInfo/fireInfo_stats_lgFires.html), resulting in a significantly enhanced PM burden. At Mauna Loa (Fig. 5g) located in the Hawaiian Islands, the model overestimates the AOD level compared to both AERONET and satellite observations, resulting from the uncertainties of wind-blown dust emissions. The AERONET-monitored AOD is even lower than the satellite retrievals, which might be explained by the high elevation (3400 m) of this AERONET site.

However, the model tends to underestimate AOD by 30–60 % in areas where mineral dust aerosols are dominant. At the Banizoumbou site (Fig. 5h) in the Sahel, south of the Sahara Desert, increasing trends of +0.004 to +0.017 yr-1 shown in both surface-observed and satellite-retrieved AOD are successfully captured by the model, which shows a similar increasing trend of +0.010 yr-1. Also, the correlation between the simulated and observed AOD is fairly good (R > 0.5). At the Cape Verde site (Fig. 5i) in CAT where most satellites show continual decreasing trends, AOD observed by AERONET shows a slight increasing trend of +0.005 yr-1. A similar increasing trend is also evident in the simulated AOD, i.e., +0.002 yr-1. Another site where the model agrees with AERONET better than satellites is Sede Boker (Fig. 5j) in Israel, between the Sahara Desert and the Arabian Desert. The small declining trend of AOD observed by AERONET is captured by the model, with better correlation and smaller bias than compared with satellite-retrieved AOD. However, at Solar Village (Fig. 5k) in the Arabian Desert, the model fails to capture increasing trends of AOD observed in both AERONET and satellites, which is consistent with the finding we discussed in the previous section.

The upwelling clear-sky SWR at TOA represents the solar radiation reflected back to space by surface albedo as well as atmospheric aerosols. If surface albedo changes are negligible, its variation is indicative of the changes in top of the atmosphere cooling effects due to aerosols. The spatial distributions of observed and simulated clear-sky SWR at TOA are presented in Fig. 6 for 2000 and 2010. Higher values are shown in the areas with highly reflective surfaces, i.e., ice-covered and desert land areas where ground-surface albedo is higher. Because the aerosol radiative effect has been considered in the feedback case, the simulated TOA SWR is higher than that in the non-feedback case, particularly in regions with high AOD levels such as ECH and SHR, and also compares better with the CERES data relative to the simulation without aerosol feedback effects. However, simulated clear-sky TOA SWRs over desert areas, EUS, EUR and southern Asia are still lower than those derived by CERES due to the underestimation of natural and anthropogenic aerosols.

The spatial distribution of land-use types in the model is kept unchanged for the 21-year period. Therefore, there is no clear trend of SWR in the non-feedback case over the entire domain, except over the Arctic Ocean where simulated ice cover is melting, leading to a significant declining trend of TOA SWR. This is also evident in the CERES data. The TOA SWR trend in the feedback case that also represents the trend of DRE shows a similar spatial pattern as the AOD trend shown in Fig. 2. A comparison of the time series of the TOA SWR anomaly (anomaly in the average of 2000–2010, as seen in Fig. 7) also suggests better agreement with observations for the feedback simulation in which the correlation with observations is higher than that in the no-feedback case.

For the period of 2000–2010, the simulated TOA SWR from the feedback case exhibits a significant increasing trend of +0.301 W m-2 (+42 %) yr-1 in ECH, a decreasing trend of -0.095 W m-2 (-0.14 %) yr-1 in EUS and a decreasing trend of -0.106 W m-2 (-0.15 %) yr-1 in EUR (as seen in Fig. 7a–c and Table 3). Similar trends are evident in the CERES-derived TOA SWR, which shows a relatively smaller increasing trend of +0.103 W m-2 (+14 %) in ECH, but fairly comparable decreasing trends of -0.099 W m-2 (-0.14 %) and -0.116 W m-2 (-0.17 %) yr-1 in EUS and EUR, respectively. No observed satellite-derived TOA SWR is available back to the 1990s; however, the signs of the simulated TOA SWR trends agree well with the corresponding sign of the simulated and observed AOD trends in each region (Table 3).

The simulated TOA SWR in NPA (Fig. 7e) shows a declining trend of -0.092 W m-2 (-0.17 %) yr-1 before 2000 and an increasing trend of +0.107 W m-2 (+0.20 %) yr-1 after 2000, which are consistent with the AOD trends for each period. The increasing trend in TOA SWR after 2000 is noticeable in CERES data as well, with a relatively smaller increasing trend of +0.057 W m-2 (+0.13 %) yr-1. In NAT (Fig. 7f), the simulated TOA SWR is decreasing for the whole period, with a stronger declining trend of -0.136 W m-2 (-0.25 %) yr-1 from 1990 to 2000 compared to the trend of -0.039 W m-2 (-0.07 %) yr-1 for the period after 2000. The decrease in TOA SWR in this region is associated with the corresponding reduction in AOD that also shows more significant decreasing for the period before 2000. However, the declining trend from the model for 2000–2010 is too weak to be observed in CERES data, which show a small increasing trend of +0.023 W m-2 (+0.05 %) yr-1.

The decreasing AOD in the Sahara Desert leads to a decreasing TOA SWR trend in the downwind ocean region CAT that is noticeable in both simulation and CERES data. More evidence of a decreasing trend in TOA SWR is shown in the simulation for the period before 2000 than that for the period after 2000 because the reduction of AOD in CAT is greater before 2000 than after. The model also captured the increasing TOA SWR trend in the Sahel that is also evident in CERES.

The significant declining trend in SHR for the period of 1990–2000 simulated by the model is associated with the corresponding decreases in AOD. However, the model fails to capture the slightly increasing trend observed by CERES over the Arabian Desert (as seen in Fig. 6a), also resulting in a failure to capture the increasing trend in NIN for the period of 2000–2010 (Figs. 6a, 7h). This discrepancy is consistent with those noted in the AOD comparison, i.e., that simulated AOD in NIN shows a decreasing trend but observed AOD is increasing.

Higher surface SWR is shown in the mid-latitude regions where the solar zenith angle is high during June–August. The surface SWR is also influenced by the water vapor in the atmosphere; therefore, the desert areas (and downwind ocean regions) with relative dry air show higher surface SWR compared to other areas located at the same latitude (see Fig. 6b). Due to aerosol direct radiative effects, the simulated surface SWR decreases in the feedback case compared to the no-feedback case and is more comparable to the surface SWR derived from CERES. The surface SWR in ECH and EUS shows a noticeable reduction from the no-feedback to the feedback case, but is still overestimated compared to that derived by CERES. A more pronounced reduction in surface SWR caused by aerosol direct radiative effects is shown in regions dominated by natural dust aerosols, because the reduction of surface SWR in dust areas (and downwind ocean regions) is also caused by the decrease in near-ground albedo due to decreases in wind-blown dust emissions stemming from the lower wind speed, which is one of the climate responses to the aerosol radiative effects.

For the period of 2000–2010, the surface SWR simulated in the feedback case exhibits a decreasing trend of -0.56 W m-2 (-0.17 %) yr-1 in ECH (Fig. 7a) and an increasing trend of +0.097 W m-2 (+0.03 %) yr-1 and +0.141 W m-2 (+0.04 %) yr-1 in EUS (Fig. 7b) and EUR (Fig. 7c), respectively, with fairly good agreement with those derived from CERES (R > 0.5, which is much better than that calculated from the no-feedback case). Note that the simulated surface SWR trends in both EUS and EUR are considerably lower than CERES.

Similar to TOA SWR, the surface SWR trend in NPA also shows opposite directions for the periods before and after 2000 (Fig. 7e): an increasing surface SWR trend of +0.129 W m-2 (+0.04 %) yr-1 before 2000 but decreasing by -0.106 W m-2 (-0.03 %) yr-1 after 2000. Good agreement (R=0.45) is found with CERES-derived surface SWR, which also exhibits a significantly declining trend of -0.334 W m-2 (-0.10 %) yr-1 from 2000 to 2010. The simulated increasing trend in NAT (Fig. 7f) is stronger before 2000 than for the period after 2000, whereas CERES-derived surface SWR shows a small trend in the opposite direction, which is consistent with the discrepancy found in TOA SWR.

The model fails to capture the increasing trend in surface SWR shown in most parts of SHR (Fig. 6b). However, the simulation has a good agreement with that derived from CERES (R=0.49) from the series comparison of the surface SWR anomaly, suggesting that the variation of dust is too large to present a clear trend within a relatively short time period. Such a discrepancy might contribute to the bias in reproducing surface SWR in the downwind CAT region where the simulated and observed surface SWR trends present opposite directions for the period of 2000–2010. However, for the period of 1990–2000 when the reduction of dust aerosol in SHR is significant, the surface SWR in both SHR and CAT as expected presents increasing trends. In NIN (Fig. 7h), the decreasing trend from 2000 to 2010 shown in CERES-derived surface SWR is associated with the increase in dust aerosol from the Arabian Desert where the model fails to reproduce the observed AOD trend. The simulated surface SWR has a good correlation (R=0.57) with CERES data, though shows a slight trend in the opposite direction. The increasing trend of surface SWR as well as the decreasing trend of TOA SWR in NIN for the period of 1990–2010 is associated with the decreasing trend of AOD for the same period.

To further investigate the model's ability to reproduce the historical clear-sky SWR at the surface, we compared results from simulations of feedback and no-feedback cases with observations at SURFRAD sites. The simulation data are selected from grid cells corresponding to the spatial locations of each SURFRAD site at the time of the measurement, and then grouped to a regional level, i.e., the eastern and western US. The CERES data are also selected for each corresponding site for comparison, but not necessarily for the same time periods, since CERES data are monthly mean including all hours.

In general, the simulated clear-sky surface SWR agrees better with SURFRAD than with CERES, with higher correlation coefficients (Fig. 8). The increasing trend in the eastern US simulated by the model in the feedback case of +0.31 W m-2 yr-1 is more comparable with that observed by SURFRAD (+0.52 W m-2 yr-1) than CERES (+1.37 W m-2 yr-1), even though the CERES data are a monthly mean of 24 h, which is lower than daytime averages from both SURFRAD and the simulations. However, the model fails to reproduce some of the yearly variations (e.g., the sharp decrease during 1998–2000) that are evident in SURFRAD, suggesting the need for simulations conducted on a finer spatial scale with more accurate spatially resolved emissions.

The clear increasing trend of +0.62 W m-2 yr-1 shown in SURFRAD in the western US is associated with the increasing clear-sky diffuse radiation that might be influenced by factors other than aerosols (e.g., air traffic activities) (Gan et al., 2014). The model shows no trends because most reductions in aerosols occurred in EUS. CERES even shows a declining trend of -0.93 W m-2 yr-1 in the western US. The discrepancy in the two observation-derived trends suggests that there is a need to further improve the accuracy of observed surface SWR data as well.