Key variables required for aerosol direct radiative forcing estimates are aerosol optical thickness (AOT), Ångström Exponent (AE) and single scattering albedo (SSA), which are determined not only by aerosol amount but also by physical and optical parameters such as size distribution, hygroscopicity, mixing state of the particles, and refractive index especially of absorbing particles such as black carbon (BC) and dust. As the values of these parameters are often assumed in climate models, we investigate how the variations in these prescribed parameters can explain the differences in AOT, AE and SSA between the simulation by an aerosol global model and the ground-based remote sensing observation, AERONET. We conclude that the differences between our simulations and AERONET observations of AOT, AE and SSA are larger than sampling errors but can be generally explained by the uncertainty of the assumed parameters, although some simulations have clear biases that may be caused by errors in both emission and transport by the model. The uncertainty of sulfate sizes significantly dominates the uncertainty of AOT, AE and SSA, whereas the uncertainty of dust refractive indices and mixing states of organic carbon and BC is dominates the uncertainty of SSA.
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 Asia is one of the areas with the highest aerosol burdens [Ramanathan et al., 2008]. Atmospheric aerosols consist of sulfate, organic (OC), and black carbon (BC) particles, which effectively scatter and absorb solar radiation and so change the earth's radiation budget (this is called the aerosol direct effect). The radiative forcing by aerosols over Asia is very large and the aerosol direct radiative forcing at the surface can be much larger than the aerosol indirect and greenhouse gases radiative forcings [Ramanathan et al., 2008].
 To properly estimate aerosol direct radiative forcing in models, we need to estimate accurately aerosol optical properties such as aerosol optical thickness (AOT), Ångström Exponent (AE) and single scattering albedo (SSA), aerosol vertical distribution (including relative height between aerosols and clouds), and surface albedo. The aerosol optical properties are determined not only by aerosol amount but also by physical and optical parameters such as size distribution of aerosol, hygroscopicity, mixing state of particles, and refractive index (especially in absorbing particles such as BC and dust) [e.g., Forster et al., 2007]. Usually these parameters are assumed in most global and regional models [e.g., Textor et al., 2007; Carmichael et al., 2008], although their values are poorly constrained.
 Mode radii and width of size distributions in the fine particle comprising of both sulfate and OC aerosols show large ranges of values according to observations by aerosol mass spectrometers (AMS) [e.g., McFiggans et al., 2005] and retrievals of AERONET [e.g., Omar et al., 2005]. The mixing state of aerosol is also an important factor in the estimation of aerosol optical properties [Ramanathan and Carmichael, 2008]. In particular, the mixing state of BC is an important issue, because internal mixing with non-absorbing species can increase the particle's absorbability of solar radiation [e.g., Bond et al., 2006]. Several observations suggest that BC in outflow regions is often internally mixed with other species and has a core/shell structure [e.g., Shiraiwa et al., 2008]. But most global aerosol models treat BC particles as external mixtures or, at best, internal mixtures under the complete melting assumption [e.g., Koch et al., 2009]. The difference in the treatment of the BC mixing state in simulations and in real life is probably one of the main reasons for the difference in BC mass concentrations between simulation and observation [Koch et al., 2009]. Furthermore, the refractive index (especially imaginary part) for BC is still largely uncertain [Bond and Bergstrom, 2006]. Hygroscopicity, another key factor in estimating aerosol optical properties, is uncertain due to mixing states, which is especially a problem for OC because of its complex chemical composition that includes humic-like substances (HULIS) [Kanakidou et al., 2005, and references therein]. For dust particles, estimates of the imaginary part of refractive index differ within factor of ten [e.g., Nakajima et al., 2007]. Based on this discussion, we have developed our sensitivity analysis, which will be discussed in more detail in the next section.
 In summary, we identify various uncertainties in the estimation of aerosol optical properties that can cause significant differences in AOT, AE and SSA, although emission and removal processes of aerosols and their precursors are also still uncertain in modeling studies [e.g., Textor et al., 2007]. Therefore, in this study, we investigate how variations in these assumed parameters for a constant aerosol concentration can explain differences in AOT, AE, and SSA between simulations by a global three-dimensional aerosol transport-radiation model, SPRINTARS [Takemura et al., 2005], and observations by AERONET. As far as we know, a comparison among different uncertainties has not been done before, so that this study should be very meaningful for the proper understanding of uncertainty of current global model simulations.
2. Methodology: Model Description and AERONET Measurements
 SPRINTARS has been implemented in an atmospheric general circulation model, MIROC [K-1 Model Developers, 2004, hereinafter MIROC AGCM], and uses the radiation scheme MSTRN-8, [Nakajima et al., 2000] and developed by Takemura et al. [2000, 2002, 2005], Goto et al. [2008, 2011b] and Goto et al. (Radiative impacts of ammonium-sulfate-nitrate components by aerosol direct and indirect effects in a global aerosol model, submitted to Journal of Geophysical Research, 2011). In this study, we run this model with a T42 horizontal resolution (approximately 2.8° by 2.8° in latitude and longitude) and 20 layers in the vertical with a time step of 20 min. The model calculates the mass mixing ratios of the main tropospheric aerosols, i.e., carbonaceous aerosol (BC and organic carbon), sulfate, ammonium, nitrate, soil dust, sea salt, the precursor gases of sulfate, i.e., sulfur dioxide (SO2) and dimethylsulfide, and the precursor gas of ammonium, i.e., ammonia. The aerosol transport processes include emission, advection, diffusion, sulfur chemistry, sulfate-ammonium-nitrate thermodynamic equilibrium, wet deposition, dry deposition and gravitational settling.
 In all experiments, monthly averaged global distributions for sea surface temperature and sea ice are used as provided by the Hadley Centre, UK Met Office. During the model simulations meteorological fields are nudged to NCAR/NCEP reanalysis (wind, water vapor, and temperature). Emission inventories for 2000 for aerosols and its precursors are those described by Takemura et al. , Goto et al. [2011a] and Goto et al. (submitted manuscript, 2011).
 In this study, we calculate AOT, AE and SSA in the same way as Takemura et al.  with modifications as proposed by Schutgens et al. . The aerosol compounds considered here are four categories: dust (10 bins ranging from 0.13 to 8.2 μm), sea salt (4 bins ranging from 0.174 to 5.62 μm), carbon (7 species consisting of five different OC/BC mixture, pure BC and biogenic secondary OC, each with their own dry mode radius of 0.1 μm), ammonium-sulfate-nitrate (1 species with one dry mode radius of 0.0695 μm, and hereafter we call the ammonium-sulfate-nitrate aerosol just sulfate). Each category is treated as an external mixture. Hygroscopic growth is considered for sulfate, OC, and seasalt [d'Almeida et al., 1991; Tang and Munkelwitz, 1994]. The optical calculation is based on the Mie theory using refractive indices for mixed particles that are calculated by volume-weighted refractive indices under the assumption of complete internal mixture. In sensitivity experiments, we modify size distributions of OC and sulfate, hygroscopicity of OC, mixing state of the OC/BC particles, and refractive index of dust and BC components. The mixing state is assumed to be a core-shell structure for the BC and OC mixture). These experimental conditions are listed in Table 1.
The values are in geometric-mean number radii of one modal distribution.
The sizes are within AMS-observed ones ranging about 400–600 nm in vacuum aerodynamic diameter with broad and high variations, that is, about 200 nm of the geometric-mean number radius [e.g., McFiggans et al., 2005].
The growth factor, Gf, is an empirical function of RH, defined as Gf = (1 − RH)−γ with γ of 0.125, that means the Gf at 90% RH is 1.333, corresponding to levoglucosan [Koehler et al., 2006, and references therein].
The Gf is also an empirical γ-model with γ of 0.045, that means the Gf at 90% RH is 1.108, corresponding to most SOA and HULIS compounds [Kanakidou et al., 2005, and references therein].
 AERONET is the largest network in the world to monitor aerosol optical properties from the ground-based remote sensing using sun/sky photometers and has been developed and maintained at NASA Goddard Space Flight Center [Holben et al., 1998]. In this study, we compare simulated AOT, AE and SSA with AERONET retrieved values at six Asian stations (see Figure 1; Kanpur (80°E, 26°N), Xianghe (116°E, 39°N), and Bac Giang (106°E, 21°N), and outflow regions including Gosan (126°E, 33°N), NCU Taiwan (121°E, 24°N), and Shirahama (135°E, 33°N)), see http://aeronet.gsfc.nasa.gov.
 In this study, we compare 5 year-averages of optical values from simulations under clear sky conditions and AERONET-retrieved values, which themselves are derived from monthly averaged values of both simulation and AERONET results during years (2001 to 2005). Therefore we consider at most sixty samples at each site and calculate statistical parameters. Numerical experiments are run for six years (2000–2005) with the first year used for spin up. We use AERONET-retrieved AOT at 550 nm and AE at 440 and 870 nm, and calculate AERONET-retrieved SSA at 550 nm by interpolating AOT and absorption AOT at both 440 and 675 nm.
 Our simulated results of AOT, AE and SSA in the standard experiment generally reproduce the AERONET-retrieved values well (Figure 1). The averaged AOT for the six Asian sites ranges from 0.20 to 0.65 with negative biases in aerosol source regions (Xianghe, Kanpur, and Bac Giang) and positive biases in outflow regions (Gosan and Shirahama). The AOT values in the Asian aerosol source regions are larger than those in similar sites in North America and Europe [e.g., Remer et al., 2005]. In Kanpur, the variability of simulated AOT is very large because simulated AOT due to dust from the Middle East region is large in India during summer as confirmed by Goto et al. [2011a]. We also find a tendency of underestimates of the simulated AOT over aerosol source regions and its overestimates over outflow regions. This implies that emissions of aerosols can be underestimated and removal processes of aerosols can be underestimated in our model. The averaged AE for the six Asian sites ranges from 1 to 1.4 with the largest bias of −0.2 at NCU Taiwan. The AE values for the Asian regions are smaller than those for similar sites in North America and Europe possibly because of dust presence in Asia [e.g., Remer et al., 2005]. In averaged SSA in the six Asian sites, the values range from 0.90 to 0.95, except Kanpur (the value is 0.86), with absolute biases of about 0.04 in Kanpur and Xianghe and less than 0.02 in other sites.
 To investigate both the uncertainty of AOT, AE and SSA among our sensitivity experiments and the reason for the discrepancy in these optical variables between simulations and observations, we calculate a relative bias (RB), defined as (Si-Oi)/Oi, in units of percentage. The Si represents AOT, AE or SSA in the standard and the sensitivity experiments and the Oi represents those in AERONET retrieval for sites i. The results for AOT, AE and SSA are shown in Figure 2. For AOT, the range in the RB due to the sulfate size is clearly the largest with values ranging from 15% at Kanpur to 35% at both Xianghe and Gosan. The second most important factors in AOT uncertainty at all sites are related to the BC refractive indices and the OC sizes, with RB magnitudes of 4–11%. Their magnitudes in Bac Giang and Kanpur are larger than those in other Asian sites possibly because concentrations of carbonaceous aerosols are larger. However, the AOT uncertainty due to the core/shell mixing of OC and BC, OC hygroscopicity and the dust refractive indices are small with magnitudes of 3–7%, 1–3%, and almost 0%, respectively.
 The largest factors in the range of the RB for AE are parameters related to sulfate sizes with the magnitudes ranging from 36% at Kanpur to 54% at Xianghe. The OC aerosol sizes, the BC refractive indices and the mixing states of OC and BC also cause relatively large variation at Kanpur and Bac Giang but smaller variation at other sites because of the differences in carbonaceous aerosols concentrations. The OC hygroscopicity, however, is not large at any sites. The dust refractive indices have also small impacts on the AE uncertainty as well as the AOT uncertainty at Asian sites.
 For SSA, magnitude of its RB due to dust refractive indices is the largest with the value ranging from 2% at Bac Giang to 5% at Kanpur, Xianghe and Gosan. The 5% RB variation at these sites means that the difference in SSA between simulation and AERONET is approximately 0.04. The range of the RB for SSA due to the mixing state of OC and BC and the sulfate sizes are calculated to be 2–4% and 1–4%, respectively. However, the other factors, like the BC refractive indices and the OC hygroscopicity, have only a small impact on the SSA uncertainty with RB differences of less than 1%.
 Finally, we calculate an aerosol radiative forcing for shortwave (SW ARF) under clear-sky conditions using both results obtained above numerical experiments and an approximation proposed by Nakajima et al.  with the assumption that surface albedo and asymmetry factor is fixed at 0.2 and 0.65, respectively. As a result, the differences in mean SW ARF among the experiments for the sulfate size is the largest with values of 15.4 W m−2 (at the top of atmosphere, TOA) and 20.0 W m−2 (at the surface, SFC) at Xianghe, which is the largest values of SW ARF among the sites. These are strongly caused by the difference in AOT shown in Figure 2a. The variations of the dust refractive indices, which cause largest differences in SSA, could cause some differences in the SW ARF with the values of 4.7 W m−2 (TOA) and 6.1 W m−2 (SFC) at Xianghe, which is the most sensitive site to the variations of the dust absorption among the sites.
 We try to understand to what extent the uncertainty in AOT, AE, and SSA due to particle model assumptions can explain differences in these optical properties between simulations and observations. Most of the variations of the differences between our simulations and the AERONET results in the sites include zero values, which means the differences between our simulations and the AERONET in AOT, AE and SSA are larger than sampling errors but can be generally explained due to the uncertainty of the assumed parameters. The sulfate size (69.5–200 nm in radius) has the largest impact on AOT (the magnitude of the variations is 0.08–0.24), AE (the magnitude of the variations is 0.36–0.73), and SSA (the magnitude of the variations is 0.01–0.04) for these six Asian sites. However, this study assumes one modal distribution of sulfate although its distribution can be two or three modal distributions according to observations [e.g., McFiggans et al., 2005]. Therefore, the uncertainty caused by the sulfate particle distribution can become large. The smallest impact on AOT, AE, and SSA is caused by OC hygroscopicity uncertainty. The mixing state of OC and BC particles and the dust refractive indices have only large impacts on SSA with the values of the variations ranging 0.01–0.04. The OC sizes and the BC refractive indices also have relatively large impacts on AOT, AE, and SSA at Kanpur and Bac Giang, whereas they have small impacts in other sites. However, some results, i.e., AOT in Kanpur, have clear biases, and this means that also emission and transport errors exist in the model and are quite large.
 We acknowledge relevant researchers and staffs for the AERONET sites, the NCAR/NCEP reanalysis data, HadISST data, MIROC model, and SPRINTARS model. T. Diehl and AeroCom project are also thanked for providing emission data sets. Some of the authors were supported by projects from JAXA/EarthCARE, MEXT/VL for Climate System Diagnostics, MOE/Global Environment Research Fund A-1101, NIES/GOSAT, MEXT/RECCA/SALSA and NIES/CGER (NEC SX-8R).
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.