This study used the Integrated Massively Parallel Atmospheric Chemical Transport (IMPACT) model (Ito et al., 2020, and references therein). Simulations were performed for the year 2016, using a horizontal resolution of 2.0∘ × 2.5∘ for latitude by longitude and 47 vertical layers. The chemical transport model was driven by the Modern-Era Retrospective analysis for Research and Applications 2 (MERRA-2) reanalysis meteorological data from the National Aeronautics and Space Administration (NASA) Global Modeling and Assimilation Office (GMAO) (Gelaro et al., 2017). Thus, the radiative feedback of the dust aerosol on the climate was not considered in this study.

The model simulated the emissions, chemistry, transport, radiation, and deposition of major aerosol species, including mineral dust, black carbon (BC), particulate organic matter (POM), sulfate, nitrate, ammonium, and sea spray aerosols, and their precursor gases. Dust emissions were dynamically simulated using a physically based emission scheme (Kok et al., 2014; Ito and Kok, 2017) with the soil mineralogical map (Journet et al., 2014; Ito and Shi, 2016). Atmospheric processing of mineral dust aerosols, during transport, was projected for four distinct aerosol size bins (< 1.26, 1.26–2.5, 2.5–5, and 5–20 µm in diameter). In this version of the IMPACT model, two modes were used for sulfate aerosol (nuclei and accumulation mode), and two moments were predicted within each mode (sulfate aerosol number and mass concentration) (Liu et al., 2005). The surface coating of sulfate on dust aerosols occurred because of the condensation of sulfuric acid gas on their surfaces, coagulation with sulfate aerosol, and formation in aqueous reactions within cloudy regions of the atmosphere (Liu et al., 2005). The heterogeneous uptake of nitrate, ammonium, and water vapor by each aerosol for each size bin was interactively simulated in the model following a hybrid dynamical approach (Feng and Penner, 2007). Five types of aerosols (i.e., dust, nucleated sulfate, carbonaceous aerosols from fossil fuel combustion, carbonaceous aerosols from biomass burning, and sea salt) were assumed to be externally mixed in each size bin for the computation of spectral optical properties (Xu and Penner, 2012). To derive atmospheric concentration of mineral composition for dust aerosol, “tagged” tracer was used for each size-resolved mineral source. The direct emissions of dust were evenly distributed in mixing ratio throughout the planetary boundary layer. The global scaling factor of dust emission was determined from the comparison of the model results with ground-based AOD measurements near the dust source regions prior to the adjustment to the DustCOMM (Kok et al., 2014; Ito and Kok, 2017). In recent review papers, multi-model evaluations of aerosol iron concentrations and their solubilities have been comprehensively summarized on global and regional scales (Myriokefalitakis et al., 2018; Ito et al., 2021).

To improve the accuracy of our simulations of mineral dust, we made several upgrades to the online emission and gravitational settling schemes used in Ito et al. (2020). The dust emissions were extremely sensitive to soil moisture, and thus the bias was adjusted with satellite observations (Ito and Kok, 2017). However, the satellite measurements were only available every other day, depending on location. The Soil Moisture Active Passive (SMAP) Level-4 Soil Moisture data product addressed these limitations by merging the satellite observations into a numerical model of the land surface water and energy balance while considering the uncertainty of the observations and model estimates (Reichle et al., 2019). In this work, we utilized the 3-hourly data of soil moisture derived from the SMAP for barren and open shrublands separately (Reichle et al., 2018). To achieve this, we used the Moderate Resolution Imaging Spectroradiometer (MODIS) land cover map at 500 m resolution to calculate the fraction of barren and open shrublands in each grand surface layer (Friedl et al., 2019)

Compared to the assumption on spherical shapes of aerosols, the dust asphericity increased aerodynamic drag at a given volume and mass and thus increased gravitational settling lifetime by about 20 % (Huang et al., 2020). Here, we implemented a globally averaged asphericity factor of 0.87 (Huang et al., 2020) to the gravitational settling scheme for mineral dust. Nevertheless, the lifetime of the dust aerosol for the largest-size bin in the IMPACT model, even after accounting for asphericity (1.4 d for 5–20 µm in diameter), was significantly shorter than an ensemble of model results (2.1 ± 0.3 d for the mass mean diameter of 8.3 µm) (Kok et al., 2017). The impact of this underestimate of atmospheric lifetime is explored using the DustCOMM data set, as was summarized in Table 2 (E3 - E4).

To improve the accuracy of our simulations of dust RE, we made upgrades to the radiative transfer calculations (Ito et al., 2018, and references therein). In this study, we integrated the Rapid Radiative Transfer Model for GCMs (RRTMG) online within the IMPACT model to calculate the radiative fluxes associated with atmospheric aerosols. RRTMG is a radiative transfer code that calculates the SW and LW atmospheric fluxes (Iacono et al., 2008). Given the size range of dust particles, scattering and absorption in the online model were described in terms of Mie theory. Assuming homogeneous spherical particles, the spectral optical properties such as the mass extinction coefficient, single scattering albedo, and asymmetry parameter were calculated using a lookup table as a function of refractive index and size parameter (Xu and Penner, 2012). The impact of this spherical assumption is explored using aspherical factor, as was summarized in Table 2 (E5 - E4).

The mineral dust particles were assumed to follow prescribed size distributions within each size bin (Liu et al., 2005). In applying the lookup table, the size spectrum for mineral dust was divided into 30 sub bins (Wang and Penner, 2009). As for the SW, the particle size increased with the uptake of sulfate, nitrate, ammonium, and water by the aerosols (Xu and Penner, 2012). These coating materials on aerosol cores were treated as internally mixed with each aerosol core in each size bin. Thus, the coating materials on dust only can reduce solar absorption of mineral dust. Subsequently, these optical properties were used by the RRTMG to calculate RE based on dust mixing ratio distributions in the IMPACT model. The dust RE was estimated as the difference in the calculated radiative fluxes with all aerosols and with all aerosols except the dust aerosols coated with sulfate, nitrate, ammonium, and water for each bin. As the LW scattering was not accounted for in the RRTMG, we multiplied the LW radiative fluxes by the adjustment factors of 1.18 ± 0.01 and 2.04 ± 0.18 for the dry particles at the surface and TOA (Dufresne et al., 2002), following Di Biagio et al. (2020). The larger adjustment factor at TOA reflects the fact that the upward LW radiation emitted from the ground surface can be trapped through scattering and absorption compared to the surface. The broadband direct and diffuse albedos for both the UV visible and visible IR were specified from the hourly MERRA-2. The surface emissivity was based on the hourly MERRA-2. Long-lived greenhouse gas concentrations were obtained from historical greenhouse gas concentrations for climate models (Meinshausen et al., 2017). Water vapor concentrations were specified according to the MERRA-2. Cloud optical properties were calculated based on the liquid and ice visible optical depths from the MERRA-2, prescribing effective radii of 10 µm for water droplets and 25 µm for ice particles, respectively (Gettelman et al., 2010; Heald et al., 2014).

Dust Constraints from joint Observational-Modelling-experiMental analysis (DustCOMM) is a data set of three-dimensional (3-D) dust properties obtained by combining observational, experimental, and modeling constraints on dust properties. While details can be found in Adebiyi et al. (2020) and Adebiyi and Kok (2020), we provide a brief overview here. First, DustCOMM's constraint on the 3-D dust size distribution combines dozens of previously published in situ measurements of dust size distributions taken during several field campaigns, with an ensemble of climate model simulations. The framework used those in situ measurements first to constrain the globally averaged size distribution (Adebiyi and Kok, 2020), which is used subsequently to adjust the bias in an ensemble of six global model simulations (Adebiyi et al., 2020). The constraints on dust size distribution range from 0.2 to 20 µm in diameter, where a generalized analytical function describes the sub-bin distribution based on brittle fragmentation theory (Kok, 2011). The second DustCOMM product – atmospheric dust mass loading – combines the constraints on dust size distribution with constraints on dust extinction efficiency and dust aerosol optical depth (Adebiyi et al., 2020). The constraints on dust extinction efficiency used the single-scattering database of Meng et al. (2010) and leveraged measurements of the dust index of refraction as well as account for the non-spherical shape of dust particles (Kok et al., 2017). For this, we approximate dust as tri-axial ellipsoidal particles described by the globally representative values of measured dust aspect ratio (the length-to-width ratio) and the height-to-width ratio (HWR) obtained from Huang et al. (2020). Furthermore, the dust aerosol optical depth used to obtain the dust mass loading combines the semi-observationally based data set from Ridley et al. (2016) with information from four reanalysis products. This includes the MERRA-2, Navy Aerosol Analysis and Prediction System (NAAPS), Japanese Reanalysis for Aerosol (JRAero), and Copernicus Atmosphere Monitoring Service interim reanalysis (CAMSiRA) (Adebiyi et al., 2020). The aerosol RE of mineral dust strongly depends on both the magnitude of dust load and the dust size distribution (Tegen and Lacis, 1996; Liao and Seinfeld, 1998). The DustCOMM data set contains total column loading (X,Y) and concentration of mineral dust resolved by season (T) and particle size (S) (Adebiyi et al., 2020). To correct the bias in the seasonally averaged size-resolved dust emission in the IMPACT model, EIMPACT(X,Y,T,S), the sum of bin 1, bin 2, and bin 3 dust emission flux was scaled by the seasonal mean of the ratio of the sum of bin 1, bin 2, and bin 3 dust column loading between the model, LIMPACT(X,Y,T,S), and DustCOMM, LDustCOMM(X,Y,T,S), at each 2-D grid box. The bias correction factor, Lbias(X,Y,T), between the IMPACT model and DustCOMM data set is given by 1Lbias(X,Y,T)=∑S=13LDustCOMM(X,Y,T,S)/∑S=13LIMPACT(X,Y,T,S). When the source function was used for high-latitude dust in the Northern Hemisphere, this led to substantially high emissions and thus RE over there, likely due to the influences from long-range-transported dust. Therefore, the direct emissions of dust from the nine major source regions only (Kok et al., 2021) were adjusted using the DustCOMM data (Fig. 1). To adjust the size bias in dust emissions, the mass fraction of emitted dust for each bin was prescribed according to the size-resolved total column loading of DustCOMM at each 2-D grid box. The mass fraction for each size bin, SDustCOMM(X,Y,T,S), is given by 2SDustCOMM(X,Y,T,S)=LDustCOMM(X,Y,T,S)/∑S=14LDustCOMM(X,Y,T,S). Thus, the dust emission flux after the adjustment, EDustCOMM(X,Y,T,S), is given by 3EDustCOMM(X,Y,T,S)=Lbias(X,Y,T)×SDustCOMM(X,Y,T,S)×EIMPACT(X,Y,T). Overall, the IMPACT-simulated lifetime of the dust aerosol for the second-size bin (7.8 d, 1.26–2.5 µm in diameter) was in good agreement with the ensemble of model results (8.5 ± 1.1 d for the mass mean diameter of 1.8 µm) (Kok et al., 2017). To correct the bias in the seasonally averaged 3-D dust size distribution after the transport, the mass fraction of dust concentration for each bin between 0.2 and 20.0 µm in diameter was scaled at each 3-D grid box prior to calculating the radiative fluxes using the RRTMG by the ratio of mass concentration of PM2.5 (i.e., the sum of bin 1 and bin 2) to each bin (Table 3).

To account for the dust asphericity, an adjustment factor was applied to the spherical optical properties at each dust size parameter and refractive index. The adjustment factors for the spectral optical properties of non-spherical particles were calculated after Huang et al. (2021). The atmospheric aging of mineral dust can form a uniform coating around the mineral core and therefore decrease particle asphericity during transport. This is implicitly considered in the globally averaged shape distribution of dust (Huang et al., 2019). Specifically, Huang et al. (2021) combined globally representative dust shape distributions (Huang et al., 2020) with a shape-resolved single-scattering database (Meng et al., 2010). This database combines four computational methods (Mie theory, T-matrix method, discrete dipole approximation, and an improved geometric optics method) to compute the single-scattering properties of non-spherical dust for a wide range of shape descriptors. Huang et al. (2021) provided the lookup table containing optical properties of non-spherical dust as functions of size parameter and refractive index.

The approximation of particles to spheres is evaluated by applying aspherical factors to the optical properties of the mass extinction coefficient, single scattering albedo, and asymmetry parameter for SW, as well as absorption fraction of extinction for the LW. At the same time, we maintained the consideration of asphericity on the gravitational velocity and kept the dust concentrations unaltered between the spherical (denoted as “Sphere”) and aspherical (denoted as “Asphere”) cases.

The aerosol RE of mineral dust depends on mineralogical composition. For the sensitivity simulation to the SW and LW refractive indices, we used the global mean of laboratory measurements of the refractive index from 19 natural soils from various source regions around the world in Di Biagio et al. (2019) (denoted as “DB19”) and in Di Biagio et al. (2017) (denoted as “DB17”), respectively. To illustrate the regional heterogeneity of refractive index, the refractive index obtained from 19 samples was aggregated into nine main source regions, and the arithmetic mean was calculated for each source region (Di Biagio et al., 2017, 2019). The regionally averaged imaginary parts of the refractive indices at the wavelength of 0.52 and 9.7 µm showed large differences in SW and LW absorptivity, respectively, between different samples collected at various geographical locations (Fig. 1).

The optical properties from the measurements for dust samples generated from 19 natural soils suggested a considerable role of Fe oxides in determining the SW absorption (Di Biagio et al., 2019). The refractive indices for mineral components were used for hematite, goethite (Bedidi and Cervelle, 1993), silicate particle group, quarts, gypsum (CaSO4) (Stegmann and Yang, 2017), and calcite (CaCO3) (Long et al., 1993) in the simulations denoted as “Mineral”. The hematite and goethite were treated separately according to the mineralogical map (Journet et al., 2014). Consequently, hematite mass content averaged in the dust at emission (0.79 % for fine and 0.50 % for coarse from the IMPACT simulation) was lower than goethite content (1.8 % and 1.3 %, respectively) on a global scale. In addition to the primary emission of gypsum, CaSO4 is secondarily formed due to the dissolution/precipitation of CaCO3 in thermodynamic equilibrium condition (Ito and Feng, 2010). To illustrate the difference in refractive index, the global mean of the mineral composition was used for the comparison with DB19 (Fig. 1). The imaginary parts of the refractive indices from mineralogical map were higher than DB19, resulting in a stronger absorption over the SW spectrum.

The mineral dust LW refractive index also depends on its mineralogical composition (Sokolik et al., 1998; Di Biagio et al., 2017). The LW refractive index of Volz (1983) has been widely used in climate models and satellite remote sensing algorithms and thus was examined here (denoted as “V83”) (Song et al., 2018). The imaginary parts of the refractive indices from V83 were higher than DB17, resulting in a stronger absorption over most of the LW spectrum. To analyze the dependence of the results on less (more) absorptive SW and less (more) absorptive LW refractive indices, we made further sensitivity simulations by varying the values of imaginary parts of the refractive index within the range of values from Di Biagio et al. (2017, 2019) (10th or 90th percentiles for SW or LW, respectively) (denoted as “Less” or “More”). The associated real parts with 10th or 90th percentile imaginary parts for LW were calculated to account for the Kramers–Kronig relation (Lucarini et al., 2005).

To estimate dust radiative effect efficiency, aerosol and radiation remote sensing products were used with various methods (Table 4) (Zhang and Christopher, 2003; Li et al., 2004; Christopher and Jones, 2007; Brindley and Russell, 2009; Yang et al., 2009; Di Biagio et al., 2010; Hansell et al., 2010, 2012; Song et al., 2018).

The instantaneous SW radiative effect efficiency at TOA is obtained from the linear regression of TOA radiation flux versus AOD observations, although the values in low-dust periods can be substantially influenced by other types of aerosols such as biomass burning (Li et al., 2004). This radiative effect efficiency corresponds to the instantaneous value derived under the limited condition at the measurements (e.g., solar position, atmospheric condition). From the extrapolation of the instantaneous value, the diurnal mean dust SW radiative effect efficiency at the surface and TOA can be derived based on model calculations.

The LW radiative effect efficiency at TOA can be obtained from the linear regression of TOA radiation flux versus AOD observations over the source regions (Brindley and Russell, 2009). However, the observed outgoing LW radiation is not only dependent on DAOD but also on other factors such as dust layer height, water vapor content, and other types of aerosols. Thus, the LW radiative effect efficiency is estimated from the difference between observed outgoing LW radiation and the dust-free outgoing LW radiation, which can be estimated using the radiative transfer model (Song et al., 2018).

Consequently, the semi-observationally based estimates of the dust radiative effect efficiency could be biased, in part, due to large uncertainties associated with the estimation method, the selection of cloud-free and dust-dominant data, and dust physicochemical properties. To understand the sensitivity of the dust radiative effect efficiency to the particle size distribution, asphericity, and refractive index of dust, radiative transfer computations have been carried out in previous studies (Li et al., 2004; Song et al., 2018). Song et al. (2018) found that the combination of the coarser dust particle size distribution and the more absorptive LW refractive index (V83) yielded the best simulation of the dust LW radiative effect in comparison with the satellite flux observations (i.e., Clouds and the Earth's Radiant Energy System, CERES), compared to the less absorptive LW refractive index (DB17).

We compared our model estimates of DAOD550 against semi-observationally based data in box plots and Taylor diagrams (Taylor, 2001) for the evaluation of the various model experiments against semi-observationally based estimates (Ridley et al., 2016; Adebiyi et al., 2020) to provide a concise statistical summary of the bias, correlation coefficient, root-mean-square errors, and the ratio of standard deviation (Fig. 2, Tables S1 and S2 in the Supplement). IMPACT-Sphere-Mineral-V83 (E1) simulations resulted in a significant underestimation of the global and annual mean of DAOD550 (0.023) (Fig. 2 and Table 3). After considering the dust asphericity for spectral optical properties, we adjusted IMPACT-simulated dust loads against the constraints on dust load from the DustCOMM data set. This adjustment led the simulated total dust load to increase from 25 Tg (E1) to 32 Tg (E2), which addressed the issue of coarse dust underestimation and fine dust overestimation by the model (Fig. 3, Table 3). Consequently, the global and annual mean of DAOD550 from DustCOMM-Asphere-DB19-V83 (E2) simulation (0.029) fell within the range in the semi-observationally based estimate (0.030 ± 0.005) (Ridley et al., 2016) (Table 3). We found that the agreement in the median with the semi-observationally based estimate (0.127) was improved from IMPACT-Sphere-Mineral-DB17 (0.049) to DustCOMM-Asphere-DB19-V83 (0.117) (solid line within the box in Fig. 2d). We also found higher DAOD550 from E2 than E1 over East Asia and Bodélé/Sudan in winter (Fig. 2, Table S2). The better agreement suggested that DustCOMM-Asphere-DB19-V83 (E2) simulation was reasonably constrained by the DAOD550 (Ridley et al., 2016; Adebiyi et al., 2020).

Modeled estimates of clear-sky dust SW radiative effect efficiencies (W m-2 DAOD550-1) at the surface (Table S3) and TOA (Table S4) were compared with estimates reported by regional studies based on satellite observations over North Africa and the North Atlantic (Fig. 4). Sensitivity simulations demonstrated that the radiative effect efficiency strongly depended on the particle size, refractive index, and particle shape (Fig. 4). The adjustment of size-resolved dust concentration and shape with the same refractive index led to overestimates of the SW radiative effect efficiencies against semi-observationally based data at TOA (from E1 to E6 in Fig. 4h), because coarser dust absorbs SW radiation more efficiently than finer particles. Subsequently, the use of less absorptive SW refractive index with DustCOMM-Asphere-DB19-V83 (E2) simulations led to a better agreement (from E6 to E2 in Fig. 4). On the other hand, the use of much less (10th percentile) absorptive SW refractive index from DustCOMM-Asphere-Less-More (E7) simulation deteriorated the agreement due to the underestimate of cooling at the surface (Fig. 4g). In contrast, the use of a more absorptive SW refractive index from DustCOMM-Asphere-Mineral-V83 (E6) improved the agreement at the surface. However, the semi-observationally based estimates of diurnally averaged radiative effect efficiency at the surface were derived from extrapolation of the instantaneous values, which would affect the comparison due to differences in the methodologies between dust models (Sect. 2.6). The differences in the model-based estimates of radiative effect efficiency might arise from different data sets of the refractive index, size distribution, and particle shape (Song et al., 2018).

Modeled estimates of clear-sky dust LW (Fig. 5) radiative effect efficiencies (W m-2 DAOD550-1) at the surface (Table S5) and TOA (Table S6) were compared with estimates reported by regional studies based on satellite observations over North Africa and the North Atlantic. Sensitivity simulations demonstrated that the radiative effect efficiency strongly depended on the particle size, refractive index, and particle shape (Fig. 5). Both the IMPACT-Sphere-Mineral-V83 (E1) and DustCOMM-Asphere-DB19-V83 (E2) simulations yielded better agreement with semi-observationally based data at the surface and TOA, compared to the less absorptive LW dust refractive indices (E3, E4, E5, and E7) (Fig. 5). The relatively high LW radiative effect efficiencies over western Africa were also consistent with the semi-observationally based data. On the other hand, the relatively low LW radiative effect efficiencies were found over eastern Africa. Moving toward the northeastern side of the region, however, the associated uncertainties in the semi-observationally based values increased (Brindley and Russell, 2009). The dust LW radiative effect efficiency depends strongly on the vertical profile of dust concentration, temperature, and water vapor, which would affect the comparison due to a high variability in these factors (Sect. 2.6).

The Saharan dust cools the ground surface by reducing the solar radiation reaching the surface and warms the atmosphere by absorbing solar radiation (Fig. 6). On the other hand, thermal emission by dust warms the surface and cools the atmosphere (Fig. 7). Our sensitivity simulations showed that the annually averaged net instantaneous radiative effect due to mineral aerosol (NET) ranged from -0.48 (DustCOMM-Asphere-Less-Less) to +0.25 (DustCOMM-Asphere-Mineral-V83) W m-2 at TOA (Table 5). The net RE from both the IMPACT-Sphere-Mineral-V83 (-0.00 W m-2) and DustCOMM-Asphere-DB19-V83 (-0.08 W m-2) simulations resulted within the 98 % confidence interval of the DustCOMM data set (-0.27 to 0.14 W m-2).

The SW RE by dust outweighs the LW warming effect at the surface in the IMPACT-Sphere-Mineral-V83 (E1) simulation (Fig. 8). Consequently, the highly absorbing dust could play an important role in the aerosol radiative forcing for the climate models to alter the West African monsoon, with the radiative heating concentrated in the dust layer (Miller et al., 2004b; Lau et al., 2009). Our model results of dust RE from the DustCOMM-Asphere-DB19-V83 (E2) simulation, however, suggested that the surface warming was substantially enhanced near the strong dust source regions (-0.23 W m-2 on a global scale) (Fig. 8), compared to the IMPACT-Sphere-Mineral-V83 simulation (-0.60 W m-2 on a global scale). Thus, our results demonstrated that the atmospheric radiative heating by mineral dust was substantially reduced for DustCOMM-Asphere-DB19-V83 (E2) simulation (0.15 W m-2), compared to the IMPACT-Sphere-Mineral-V83 (E1) simulation (0.59 W m-2).

To elucidate the differences in dust radiative effects between the IMPACT-Sphere-Mineral-V83 (E1) and DustCOMM-Asphere-DB19-V83 (E2) simulations and to explore the variability in different previous model estimates (Fig. 9), the differences in annually averaged radiative effects of mineral dust from DustCOMM-Asphere-DB19-DB17 (E4) simulation are shown in Fig. 10. A slope of one in Fig. 10 represents an identical change in both the surface and TOA and thus corresponds to no change in radiative heating within the atmosphere. The distances from the DustCOMM-Asphere-DB19-DB17 (E4) simulation demonstrated that large uncertainties existed for the size distribution and spectral optical properties. Our sensitivity simulations revealed that the DustCOMM-Asphere-DB19-V83 (E2) simulation led to a similar net RE at TOA compared to the IMPACT-Sphere-Mineral-V83 (E1) simulation but resulted in less cooling at the surface (Fig. 9). This revision can be divided into (1) the size-resolved abundance (black hexagons, E3 - E4, in Fig. 10), (2) SW refractive index (red diamonds, E6 - E4, in Fig. 10), and (3) particle shape (red circles, E5 - E4, in Fig. 10). Additionally, we show the sensitivity of dust RE to LW refractive index (DB17), which was used by both Di Biagio et al. (2020) and Balkanski et al. (2021).

First, at TOA, the SW RE was more sensitive to the size-resolved abundance (-0.17 W m-2 at the vertical axis of black hexagon in Fig. 10a), compared to LW (0.00 W m-2 at the vertical axis of black hexagon in Fig. 10b). Second, this smaller SW cooling effect with coarser dust (E3 - E4) was partially compensated for by more SW cooling with the use of the less absorptive SW refractive index (E4: -0.32 W m-2) than E6 (0.02 W m-2). Thirdly, the sensitivity of SW RE to dust asphericity was rather minor (0.04 W m-2 at the vertical axis of the red circle in Fig. 10a), partly because the lower DAOD was compensated for by the lower asymmetry parameter of spherical dust, which enhanced the amount of radiation scattered backward to space (Räisänen et al., 2013; Colarco et al., 2014). The partial compensation led to a small enhancement of SW RE for the IMPACT-Sphere-Mineral-V83 (E1) simulation and thus the resulting similar net RE compared to DustCOMM-Asphere-DB19-V83 (E2) at TOA (Fig. 9).

In contrast, at the surface, our sensitivity simulations demonstrated substantially different responses in the RE, mostly because of LW warming effects (Fig. 9). The enhanced LW warming by coarser dust (-0.08 W m-2 at the horizontal axis of black hexagon in Fig. 10b) was accompanied by the asphericity (-0.15 W m-2 at the horizontal axis of the red circle in Fig. 10b), because the enhancement of the absorption fraction of extinction due to asphericity was larger at coarser size. The enhanced LW warming effects of each as well as the synergy were further amplified using the more absorptive LW dust refractive index (Volz, 1983) (at the horizontal axis of the red diamond in Fig. 10b). As a result, our sensitivity simulations revealed that substantially less dust absorption at LW due to the underestimation of the coarse dust load and the assumption of the spherical shape (IMPACT-Sphere-Mineral-V83) contributed to the less surface warming, compared to DustCOMM-Asphere-DB19-V83 (Fig. 9).

A relatively good agreement of net RE by dust at TOA with both Di Biagio et al. (2020) (-0.06 W m-2) and Balkanski et al. (2021) (-0.02 W m-2) could be obtained from both the IMPACT-Sphere-Mineral-V83 (E1: -0.00 W m-2) and DustCOMM-Asphere-DB19-V83 (E2: -0.08 W m-2) simulations (Fig. 9 and Table 5). On the other hand, our modeled dust net RE at the surface from DustCOMM-Asphere-DB19-V83 (E2: -0.23 W m-2) indicated much less cooling than Di Biagio et al. (2020) (-0.63 W m-2), Balkanski et al. (2021) (-1.01 W m-2), and IMPACT-Sphere-Mineral-V83 (E1: -0.60 W m-2). The synergy of coarser size and aspherical dust could contribute to the less surface cooling of the DustCOMM-Asphere-DB19-V83 (E2), because of enhanced LW warming. At the same time, both Di Biagio et al. (2020) and Balkanski et al. (2021) used DB17 and considered dust with diameters more than 20 µm. Thus, the more absorptive LW dust refractive index (V83, E6 for LW: 1.00 W m-2) than DB17 (E4 for LW: 0.58 W m-2) (E6 - E4 for LW: 0.42 W m-2 at the horizontal axis of the red diamond in Fig. 10b) could also contribute to the less surface cooling, which might be partially compensated for in our model by the omission of dust with diameters more than 20 µm. Consequently, our estimate of atmospheric radiative heating by dust from DustCOMM-Asphere-DB19-V83 (E2: 0.15 W m-2) was lower than Di Biagio et al. (2020) (0.63 W m-2), Balkanski et al. (2021) (0.98 W m-2), and IMPACT-Sphere-Mineral-V83 (E1: 0.59 W m-2). Additionally, the hot and dry climate over brighter desert surface exaggerates differences in RE at the surface between the models (Miller et al., 2014). The low humidity allows dust particles to absorb LW radiation with reduced competition from water vapor, while high temperatures within the boundary layer increase downward thermal emission by dust (Liao and Seinfeld, 1998). The reduction of fine dust load after the adjustment leads to underestimates of the SW cooling at TOA. To improve agreement against semi-observationally based estimate of the radiative effect efficiency at TOA, the less absorptive SW dust refractive index is required for coarser aspherical dust. Thus, uncertainties in the size-resolved dust concentration, particle shape, and refractive index contribute to the diversity in the simulated dust RE at the surface.