Corresponding author: I. B. Ocko, Program in Atmospheric and Oceanic Sciences, Princeton University, 201 Forrestal Rd., Princeton, NJ 08540, USA. (firstname.lastname@example.org)
 The direct radiative forcing of the climate system includes effects due to scattering and absorbing aerosols. This study explores how important physical climate characteristics contribute to the magnitudes of the direct radiative forcings (DRF) from anthropogenic sulfate, black carbon, and organic carbon. For this purpose, we employ the GFDL CM2.1 global climate model, which has reasonable aerosol concentrations and reconstruction of twentieth-century climate change. Sulfate and carbonaceous aerosols constitute the most important anthropogenic aerosol perturbations to the climate system and provide striking contrasts between primarily scattering (sulfate and organic carbon) and primarily absorbing (black carbon) species. The quantitative roles of cloud coverage, surface albedo, and relative humidity in governing the sign and magnitude of all-sky top-of-atmosphere (TOA) forcings are examined. Clouds reduce the global mean sulfate TOA DRF by almost 50%, reduce the global mean organic carbon TOA DRF by more than 30%, and increase the global mean black carbon TOA DRF by almost 80%. Sulfate forcing is increased by over 50% as a result of hygroscopic growth, while high-albedo surfaces are found to have only a minor (less than 10%) impact on all global mean forcings. Although the radiative forcing magnitudes are subject to uncertainties in the state of mixing of the aerosol species, it is clear that fundamental physical climate characteristics play a large role in governing aerosol direct radiative forcing magnitudes.
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 It has been established over the past decade that aerosols exert a significant negative (cooling) radiative forcing on the climate system, partially offsetting the positive (warming) forcing induced by greenhouse gases [Intergovernmental Panel on Climate Change (IPCC), 2007]. Individually, however, not all aerosol species contribute to a cooling tendency. Whereas every aerosol decreases the amount of solar radiation reaching the surface, some aerosols scatter solar radiation and enhance the planetary albedo, while others absorb solar radiation and trap energy in the climate system. There are a number of factors that impact the negativity and positivity of direct radiative forcing (DRF) by aerosols, such as emissions, concentrations, removal processes, atmospheric transport, optical properties, and physical climate characteristics. This study focuses on how physical climate factors—in particular, cloud cover, surface albedo, and relative humidity, which vary spatially and temporally—impact the individual magnitudes of aerosol radiative forcings. Although aerosols remain one of the largest uncertainties in our understanding of the climate system, current climate models continue to provide important insights into the sensitivity of scattering and absorbing aerosols.
 In order to address the problem, we have chosen to focus on three anthropogenic aerosol species that exert the strongest magnitudes of DRF on the climate system. Sulfate, the oxidation product of sulfur dioxide emitted from natural and anthropogenic sources, is identified as the dominant scattering aerosol responsible for masking global warming [Charlson et al., 1991]. Black carbon is recognized as a primarily absorbing carbonaceous aerosol, and is a significant contributor to global warming tendency through absorption of solar radiation in the atmosphere [e.g., Jacobson, 2000, 2001b; Sato et al., 2003; Forster et al., 2007; Ramanathan and Carmichael, 2008] and when deposited on snow and ice [Hansen and Nazarenko, 2004]. Organic carbon—coemitted with black carbon—also contributes to the anthropogenic aerosol net radiative forcing. Properties and forcings of sulfate and black carbon, however, are better understood than that of organic carbon and represent two well-known extreme cases of an anthropogenic strong scatterer and strong absorber. Additional aerosols that provide radiative forcings much smaller in magnitude on a global average are nitrate and anthropogenic dust [Forster et al., 2007].
 Sources of sulfate include precursor emissions from fossil fuel combustion, volcanic eruptions, and biological ocean activity. Carbonaceous aerosols also have natural and anthropogenic sources, with the anthropogenic sources comprising of contained and incomplete combustion of fossil fuels and biofuels, and uncontained biomass burning. Organic carbon is further emitted from plants and debris, and also produced secondarily in the atmosphere by gaseous compounds. Concentrations of all three aerosols have risen considerably since preindustrial times, exerting a significant present-day radiative forcing on the climate [Forster et al., 2007]. Escalating sulfate, black carbon, and organic carbon concentrations since the preindustrial era are attributed to anthropogenic sources, such as contained and uncontained combustion.
 Direct radiative forcings of aerosols are difficult to quantify because species are short-lived with large spatial and temporal variability, and measurements are not prevalent globally [Ramaswamy et al., 2001]. Estimates of global mean sulfate top-of-atmosphere (TOA) DRF range from −0.21 W/m2 [Takemura et al., 2005] to −1.3 W/m2 [Charlson et al., 1992]. Global mean black carbon TOA DRF estimates range from +0.25 W/m2 [Schulz et al., 2006] to +0.98 W/m2 [Sato et al., 2003]. Organic carbon TOA DRF estimates range from −0.06 W/m2 [Jacobson, 2001b] to −0.41 W/m2 [Hansen et al., 1998]. The IPCC Fourth Assessment Report (AR4) estimates −0.4 ± 0.2 W/m2 sulfate DRF, +0.34 ± 0.25 W/m2 black carbon DRF, and −0.19 ± 0.2 W/m2 organic carbon DRF [Forster et al., 2007]. Estimates of organic carbon forcings are therefore smaller in magnitude than sulfate and black carbon per the IPCC assessments, and are also more uncertain.
Forster et al.  does not provide details concerning the spatial distribution and governing factors of aerosol radiative forcings. Ramaswamy et al.  (IPCC TAR) provides an insight into spatial details of the forcings but uses earlier estimates of aerosol emissions and concentrations. Aerosol DRF magnitudes vary geographically, and investigations indicate that this fundamentally can have interesting and important implications for the climate response [e.g., Ramaswamy and Chen, 1997; Erlick et al., 2006]. This study explores the sensitivity of scattering and absorbing aerosol direct radiative forcing to physical climate characteristics both globally and regionally, in an effort to advance our understanding of the sensitivity of aerosol direct forcings. The individual roles of clouds, surface albedo and relative humidity are investigated, and the similarity/dissimilarity of the roles for the scattering and absorbing species are discussed. Alongside top-of-atmosphere (TOA) forcings, this work also studies the surface forcings. Insection 4, we address sensitivities of aerosol indirect radiative forcings.
 In order to constrain uncertainties and perform independent sensitivity studies to assess the influence of physical factors on the magnitudes of DRF, aerosol concentrations are prescribed (i.e., no interaction with the climate system) and are assumed to be externally mixed. It is to be noted that aerosols have been observed to exist in a variety of internal mixtures [Jacobson, 2000], although how pervasive this is globally and seasonally, or how to best represent such internal mixtures in climate models, has not yet been definitively ascertained [e.g., Jacobson, 2001b]. Several earlier studies [see IPCC, 2007] have employed the external mixture assumption, and climate responses associated with the aerosol offset of anthropogenic greenhouse gas effects have been primarily evaluated assuming external mixtures [e.g., IPCC, 2007; Levy et al., 2008]. We focus on how physical factors impact DRFs using the external mixture framework; later, we estimate how the forcings would change by assuming internal mixing between sulfate and black carbon (section 3.2.4).
2. Model Description
 We employ a global climate model to assess how physical climate characteristics govern the sign and magnitude of individual aerosol DRFs. The NOAA Geophysical Fluid Dynamics Laboratory (GFDL) CM2.1 model was chosen because of its notably successful simulation of Earth's climate conditions, particularly compared with temperature reconstructions over the twentieth century [Delworth et al., 2006; Knutson et al., 2006]. The simulations demonstrate the powerful influences of the offset between the long-lived greenhouse gases (LLGHGs) and aerosol effects on key climate variables, e.g., surface temperature, ocean heat content, ocean circulation, etc. [Delworth and Dixon, 2006; Delworth et al., 2005]. The aerosol distributions used in CM2.1 [Horowitz, 2006] generally match observed global and regional surface concentrations to within a factor of two [Ginoux et al., 2006]. The largest discrepancies with observations are overestimates of sulfate optical depth, overestimates of black carbon concentrations over some source regions, and underestimates of organic carbon optical depth in biomass burning regions. These inconsistencies are likely due to excessive hygroscopic growth at high relative humidity, excess emissions, and treatment of specific extinction and hygroscopic growth, respectively.
 Black carbon vertical profiles in CM2.1 have been compared to available observations from several field campaigns by Koch et al. . Although the concentrations fall within the realm of other modeling studies, all models overestimate the amount of black carbon at higher elevations and our model falls at the higher end of the range. However, thorough validation is impractical as there are no globally observed vertical profiles, and measurements are only available from a few locations and field campaigns. In addition to aerosol distributions, CM2.1's clear- and all-sky surface fluxes have been compared and assessed against observations [Freidenreich and Ramaswamy, 2011].
 An additional motivation for using the CM2.1 model as the basis for our study is that as deduced from a climate metrics examination [Reichler and Kim, 2008], CM2.1 has been adjudged to be in the top tier of the world's climate models. Therefore, an additional gain from this study is that the anthropogenic aerosol forcings are examined in the same IPCC AR4-class model that also produced the twentieth-century responses. Furthermore, aerosol forcings used in climate model integrations have been examined and reported in only a limited number of the IPCC AR4 models in concert with climate response analysis.
 A standalone version of the CM2.1 radiation code is implemented to determine the individual solar and thermal-infrared radiative forcings, using the shortwave radiation algorithm adapted fromFreidenreich and Ramaswamy  and the longwave radiation algorithm from Schwarzkopf and Ramaswamy . The shortwave algorithm includes 18 bands in the solar spectrum, and the longwave algorithm includes eight bands. Aerosol optical depth, single scattering albedo, and asymmetry parameter are calculated from optical properties derived from Mie theory [Haywood and Ramaswamy, 1998] and the concentrations interpolated from MOZART, and, for sulfate, as a function of hygroscopic growth. The aerosol sizes assume a lognormal distribution and species are assumed to be externally mixed. As studies have indicated that aerosols may often be internally mixed [e.g., Jacobson, 2001b], we conduct additional simulations with internal mixtures of sulfate and black carbon to assess the effect of aerosol mixing state on our results.
 The effective mass radii for sulfate, black carbon, and organic carbon are 0.166, 0.039, and 0.087 μm, respectively [Haywood and Ramaswamy, 1998; Ginoux et al., 2006]. Sulfate is treated optically as ammonium sulfate, and its inorganic and highly soluble composition accounts for its hydrophilic properties [Haywood and Ramaswamy, 1998]. Sulfate exists in a variety of other solid and liquid compounds as well, with a dependence on altitude [Jacobson, 2001a]. However, Nemesure et al.  found that sulfate radiative forcings were relatively insensitive to composition as opposed to other factors. While sulfate is purely scattering at short wavelengths, there is a small absorbing effect in the near infrared.
 Modeling aspects of organic carbon, in particular, are highly uncertain, and properties are less well-known than for sulfate and black carbon. Substantial uncertainties exist regarding its sources, emissions, emission factors, distributions, functional groups, hygroscopicity, optical properties, and secondary atmospheric production [Ming et al., 2005]. Furthermore, several studies also point to a significant absorption component of organic carbon [e.g., Kirchstetter et al., 2004; Alexander et al., 2008] in addition to its traditionally presumed scattering component. Chemical processing of organic carbon can also convert it to more hydrophilic forms. Here we assume organic carbon is nonabsorbing and nonsoluble, however we elaborate later about the effects if it were absorbing (section 3.3) and hygroscopic (section 3.2.3). The organic carbon distributions in CM2.1 correspond to that of organic matter, and we address the associated uncertainties in concentrations (as pointed out by Ginoux et al. ) in section 3.3.
 We calculate aerosol TOA DRFs and surface forcings from preindustrial (model year “1860”) to present day (model year “2000”) using simulated meteorological conditions. The radiative forcing calculations are computed off-line with the CM2.1 standalone radiation code, with a radiation time step of 3 h. The DRF definition used here followsIPCC , and is the instantaneous change in the net radiative flux at the tropopause between preindustrial and present-day aerosol concentrations with suppressed climate responses. DRFs are calculated for the entire climate system (top-of-atmosphere) since it has been shown that there is negligible difference between aerosol DRFs calculated at the tropopause and top-of-atmosphere (TOA) [e.g.,Haywood and Shine, 1997]. In addition, the surface radiative forcing [Forster et al., 2007] viz., the instantaneous change in the net radiative flux at the surface, is also computed. Although the shortwave and longwave forcings are calculated, a strong majority of the aerosol forcing occurs in the shortwave.
 To assess the sensitivity of the forcings to cloud cover, surface albedo, and relative humidity, DRFs are calculated for three independently perturbed cases—clear-sky conditions, constant 0.1 surface albedo (viz., a surface albedo comparable to that of the ocean for an annual mean solar zenith angle at the low latitudes), and dry sulfate (relative humidity is held constant at 30% such that sulfate hygroscopic growth is suppressed)—for present-day and preindustrial conditions. The forcings from the perturbed cases are then compared to the control case (model simulated cloud cover (all-sky), model-simulated surface albedo, and sulfate hygroscopic growth as a function of relative humidity). In addition, we employ a globally pervasive sulfate-black carbon internal mixing assumption to assess how the mixing state could alter radiative forcings computed in the control case. Only forcings are discussed in this study. No attempt is made to connect the forcings to climate responses due to the specific aerosol species or LLGHGs.
3. Results and Discussion
 The DRF calculations use preindustrial (PI) conditions as a reference case, against which the perturbed cases of present-day (PD) concentrations of isolated forcing agents are compared. Climate conditions for the “control” case include geographical distributions of cloud cover, surface albedo and relative humidity, and incorporate the annual cycle of insolation. These characteristics are the same for the PI and PD states, and were taken from PD simulations using CM2.1. To assess the sensitivity of aerosol magnitudes to physical climate factors (cloud cover, high-albedo surfaces, and high relative humidity) we compare the “perturbed” cases to the control case.
3.1. Control Case
 The TOA DRFs vary regionally, as seen in the upper panel of Figure 1, and are well-correlated with atmospheric burdens (not shown). Since the atmospheric lifetimes of aerosols are relatively short—on the order of one week, due to fast removal processes—sulfate, black carbon, and organic carbon have spatially inhomogeneous distributions over the globe, and this correspondingly influences the spatial pattern of radiative forcings. Global mean values are computed as −1.12 W/m2 for sulfate, +0.86 W/m2 for black carbon and −0.27 W/m2 for organic carbon, and can be contrasted with the global mean LLGHG TOA forcing of +2.46 W/m2 [Forster et al., 2007].
 Sulfate and organic carbon TOA DRFs are always negative (because organic carbon is treated as nonabsorbing), and black carbon TOA DRFs are always positive. The majority of the aerosol burdens are located between 30°S and 90°N, so it is expected that the strongest forcings fall within this range as well. The largest forcings for all aerosols are found over Southeast Asia, with the highest magnitudes over China. Sulfate direct radiative forcings are concentrated around the Northern Hemisphere (NH) midlatitudes, while black carbon is more diffuse with forcings extending further into the Arctic. High forcings for both sulfate and black carbon are also found in North America and Europe, and for black carbon, also in Africa and South America. Organic carbon forcings are much lower in magnitude, and peak in biomass burning regions in South America and Africa, Europe, and Southeast Asia.
 All aerosols reduce the amount of radiation that reaches the Earth's surface, from either trapping solar radiation in the atmosphere or scattering it out to space. The annual global mean surface forcing of sulfate is −0.98 W/m2, of black carbon is −1.33 W/m2, and of organic carbon is −0.25 W/m2. This can be compared to the small global LLGHG surface forcing of +0.4 W/m2 [Forster et al., 2007] and demonstrates how aerosol forcings dominate the anthropogenic perturbation in the surface radiation budget, with potential implications for evaporation and consequently precipitation [Ramanathan et al., 2001; Ming et al., 2010]. Note, however, that the LLGHG forcings of climatic importance derive principally from perturbations in the longwave radiation flux. The surface forcing comparison among aerosols or contrast with LLGHGs should be viewed as a diagnostic rather than leading to a simple interpretation of the surface heat and hydrologic effects. The climate process from forcing to response involves several feedbacks not captured in the formal radiative forcing definitions [Andrews et al., 2010].
3.2. Perturbed Cases
Table 1 provides global mean values for the percent change in TOA DRF and surface forcing from the presence of each physical climate perturbation factor. In addition to the control case TOA DRFs, Figure 1shows how the forcings change for cases with “clear-sky” (no clouds), “low-albedo surface” (constant 0.1 albedo) and “dry sulfate” (relative humidity fixed at 30% to suppress hygroscopic growth).Figure 2 breaks down the TOA forcings for each perturbation case into the mean aerosol DRFs for specific latitudinal bands. Figure 3displays the zonal mean change in TOA DRF from the perturbed cases (clear-sky, low-albedo surface, dry sulfate) to the control case, in order to emphasize the impact of clouds, high-albedo surfaces, and hygroscopicity on the aerosol TOA DRFs. The effect of internal mixing between sulfate and black carbon on the black carbon DRF is also addressed in this section.
Table 1. Annual and Global Mean Impact due to Presence of Clouds, High-Albedo Surfaces and High Relative Humidity on the Sulfate, Black Carbon, and Organic Carbon Direct Radiative Forcings in Terms of Percent Change From Cases With No Clouds, Low-Albedo Surfaces, and No Hygroscopic Growth, Respectively, to the “Control” Case
Clear-sky to all-sky
Low-albedo surfaces to realistic albedo
Dry sulfate to hygroscopic sulfate
 The relative location of clouds and aerosols adds a complexity to the aerosol radiative forcings [Haywood and Ramaswamy, 1998]. Clouds existing above an aerosol layer reduce the amount of solar radiation interacting with the aerosol, whereas thick clouds below an aerosol layer induce multiple scattering of radiation. Multiple scattering accounts for (1) the first pass of the radiation beam through the aerosol layer, reflection off the cloud, and subsequent pass through the aerosol layer again, (2) multiple bounces between the aerosol layer(s) and cloud layer(s), and (3) an increase in scattering in the system from radiation interacting with Rayleigh (molecular) scattering [Cess, 1983]. DRFs of scattering and absorbing aerosols have contrasting responses from the presence of low clouds; low clouds reduce the TOA forcing in the case of scattering aerosols and enhance the TOA forcing from absorbing particles. Surface forcings are reduced in the case of both scatterers and absorbers for all-sky conditions relative to clear skies.
 Although eliminating clouds does not change the sign of the aerosol DRFs, the individual magnitudes of these forcings change considerably (Figures 1, 2, and 3). The forcing sensitivities are similar for both scattering species, sulfate and organic carbon. The magnitudes of sulfate and organic carbon forcings throughout the NH midlatitudes, in particular, are considerably strengthened by the omission of clouds by at most 250%. The globally averaged annual sulfate TOA DRF doubles, from −1.12 to −2.16 W/m2 (Figure 2 and Table 1) and that of organic carbon increases by 50% from −0.27 to −0.4 W/m2. Since clouds reflect more incoming shortwave radiation than a darker underlying surface, there is more overall reflection from the scattering aerosol layer when clouds are absent, both above and below the layer. The peak strengthening in sulfate DRF from clear skies is located around 50°N, where clear skies strengthen the sulfate DRF magnitude by 4 W/m2.
 On the other hand, the black carbon TOA DRF is weakened significantly in the absence of clouds, because of the lack of backscattering from cloud cover below the black carbon layer. The black carbon globally averaged annual DRF is almost halved, from +0.86 to +0.49 W/m2 when clouds are absent, with zonal mean decreases of up to 1 W/m2 in NH midlatitudes (Figure 3). In areas with high-albedo surfaces, such as the Sahara Desert, Greenland, and the Arctic Ocean, the black carbon DRF is not weakened and in some cases is strengthened by the absence of clouds. This suggests that either some clouds lie above the black carbon layer or that multiple scattering between the bright surface and aerosol layer is more efficient than that between low clouds and the aerosol layer. Nevertheless, the significance of a highly reflective underlying surface on the absorption of solar radiation by an absorber and the resultant spatial heterogeneity of the absorber forcing are evident. Black carbon forcings are thus most strongly affected by clouds in regions of lower surface albedo, such as over the oceans, because radiation is reflected back into the aerosol layer that would have otherwise been absorbed by the surface.
 Clouds therefore affect scattering and absorbing aerosols in opposing ways at the TOA, and strongly impact the magnitudes of the forcings. The global mean sulfate TOA DRF is halved when clouds are taken into consideration, the global mean organic carbon TOA DRF is reduced by a third, and the global mean black carbon TOA DRF is doubled. Clouds are therefore crucial in weakening (less negative) the sulfate and organic carbon DRFs and strengthening (more positive) the black carbon DRF, substantiating results shown in slightly different contexts in earlier studies [Haywood and Shine, 1997; Haywood and Ramaswamy, 1998; IPCC, 2001, 2007]. At the surface, cloudy conditions lead to a strong weakening (i.e., less negative) of the surface radiative forcings for all aerosol species. However, whereas the presence of clouds reduces the global mean sulfate surface forcing by almost 50% (and over 30% for organic carbon), the black carbon surface forcing is reduced by less than 25% (Table 1).
 It is important to note that this study does not make a distinction between the sensitivity to different clouds at different heights. Clouds above black carbon would be expected to reduce the DRF, however, both model and observations show a preponderance of low clouds in terms of the global cloud cover [Rossow and Schiffer, 1999]. Although globally averaged cloud cover in CM2.1 is comparable to ISCCP satellite data, regional biases exist [GFDLGAMDT, 2004]. Cloud amounts are overestimated in northern Eurasia and North America during wintertime, and underestimated over oceans between 20° and 40° in latitude. The excessive cloudiness over NH landmasses in the wintertime is attributed mostly to biases in low cloud amounts. In addition, Freidenreich and Ramaswamy  find that there is a strong correlation between the model's shortwave surface flux biases and cloud amount biases.
 Accounting for cloud biases would slightly perturb the individual forcing estimates. We have devised a simple formulation for this assessment by calculating the DRF change from clouds per low cloud amount, which measures the fractional influence of clouds on DRF for each aerosol species. We focus on black carbon and sulfate as proxies for a strong absorber and strong scatterer, respectively. In CM2.1, clouds over North America are underestimated by about 10% while clouds over Europe are overestimated by about 10% [GFDLGAMDT, 2004]. Fewer clouds would weaken the black carbon forcing and strengthen the sulfate forcing; more clouds would strengthen the black carbon forcing and weaken the sulfate forcing. Black carbon TOA DRF is greater than +1 W/m2 over North America and Europe. Increasing and decreasing the cloud amount in North America and Europe by 10%, respectively, yields a black carbon forcing perturbation of less than ±0.1 W/m2. For sulfate, whose TOA DRF is almost −2 W/m2 over North America and greater than −2 W/m2 over Europe, the forcings are perturbed by roughly ±0.5 W/m2.
3.2.2. Surface Albedo
 Similar to the impact from low clouds, high-albedo surfaces reflect more radiation into the aerosol layer, significantly strengthening positive DRFs by absorbing aerosols [Haywood and Ramaswamy, 1998]. High-albedo surfaces include regions with snow, ice, or deserts. Conversely, DRFs by scattering aerosols are weakened because the contrast between the high-albedo surface and the aerosol layer is weaker than with a low-albedo surface. The small near-IR absorbing effect for sulfate aerosols may account for some reduction in its negative forcing as well.
 DRFs are calculated for a case where the Earth's surface albedo is set to 0.1 globally, whereas the surface albedo in the control case ranged from 0.06 to 0.8. Comparison to the control case shows that high-albedo surfaces modify the global annual mean TOA DRF by only 8% for black carbon, and 4% for sulfate and organic carbon (Table 1). When surfaces evenly absorb 90% of incident solar radiation, as expected, the spatial pattern of TOA forcing is mostly impacted over highly reflective surfaces such as the Sahara Desert and regions in the Arctic and Antarctica. Sulfate and organic forcings are strengthened when surfaces are more absorbing, thus increasing their negativity, and the sensitivity for both scattering species is nearly identical. In fact, forcings in the Arctic and Antarctic are enhanced by over 100% when surfaces are “dark” (Figure 1). Black carbon TOA forcings are weakened such that they become less positive, with magnitudes decreased by 25 to 100%. Therefore, the presence of reflective surfaces weakens scattering aerosol forcings and strengthens absorbing aerosol forcings.
 Although the black carbon TOA DRF is significantly strengthened in the Arctic (by +0.5 W/m2) from the presence of reflective surfaces, the magnitude of sulfate DRF is weakened even more (Figure 3). If the Arctic were to experience more long-range transport from midlatitude sources, this would affect forcing magnitudes of both aerosol species, by weakening the negative “scattering” forcing and strengthening the positive “absorbing” forcing. Because forcings are much smaller for organic carbon, the zonal mean forcing curve does not change much from the low-albedo to high-albedo case (Figure 3). Forcings are, in fact, slightly enhanced for the low-albedo case, as shown regionally inFigure 2.
 Whereas sulfate and organic carbon forcings are less impacted by changing albedo in the Sahara Desert than they are in the polar regions, black carbon forcing is just as affected. The combination of high black carbon concentrations over Africa and an underlying high-albedo surface create favorable conditions for amplification of the black carbon forcing. The strong positive forcing from black carbon over northern Africa (over +2 W/m2) is due to the reflective underlying desert, because when this surface is darkened, the forcing is substantially reduced.
 Black carbon deposition on high-albedo surfaces, and thus surface albedo modification, has not been taken into consideration here for the sake of simplicity. However, since high-albedo accounts for at most an 8% strengthening in global mean black carbon TOA DRFs, it is plausible that black carbon deposited on snow or ice has a small impact on the global mean DRF. Locally, however, black carbon modification of surface albedo will contribute significantly to the forcing, providing additional warming tendencies on the climate system [Flanner et al., 2007].
3.2.3. Relative Humidity
 Relative humidity affects hygroscopic aerosols, such as ammonium sulfate, and introduces an exponential impact on the specific extinction as humidity increases and the particles swell [Haywood and Ramaswamy, 1998]. Because the scattering efficiency of a particle is determined by the size of the particle relative to the wavelength of radiation, if the particle grows from the uptake of water, it becomes more efficient at scattering solar radiation. In the CM2.1 standalone radiation code, sulfate hygroscopic growth is activated at relative humidity higher than 30%, and there is no cap on hygroscopic growth at high relative humidity. In contrast, carbonaceous aerosols are assumed to remain dry in CM2.1, and thus are not affected by relative humidity. Internal mixing of aerosol species complicates hygroscopicity, and will be discussed in section 3.2.2.
 Growth of sulfate aerosols when relative humidity exceeds 30% strengthens the globally averaged surface and TOA DRFs by 56% each (Table 1). The consequential strengthening in the sulfate forcing from hygroscopicity compensates somewhat for the weakening of the forcing from the presence of clouds. When sulfate remains dry, forcings are roughly halved, with the strongest effects taking place in the Arctic, the Indian Ocean, and parts of the Pacific Ocean (Figure 1). Regions that are typically drier—such as Australia, Southwest U.S., and the Sahara Desert—reduce forcings by less than 25% when hygroscopicity is not accounted for. Overall, however, relative humidity fairly evenly affects forcing magnitudes throughout the NH (Figure 3). There is thus a strong dependence of the sulfate TOA DRF on hygroscopic growth. Without sulfate swelling from high relative humidity, the global mean sulfate TOA DRF is −0.72 W/m2 as opposed to −1.12 W/m2 in the control case.
 As noted earlier, sulfate exists in a variety of compounds other than ammonium sulfate [Jacobson, 2001a]. However, the scattering efficiency of sulfate particles is a much stronger function of relative humidity than of the composition of sulfate [Nemesure et al., 1995]. It is the relative humidity that drastically changes the scattering efficiency (and thus forcing), and there is only a slight dependence of these features on the sulfate composition itself.
 If organic carbon is treated as hydrophilic, we can expect that the forcing sensitivity will behave somewhat more similarly to sulfate. However, sulfate is more soluble than organic carbon [Takemura et al., 2005], and therefore scaling the TOA DRF based on the sensitivity of sulfate (which would mean doubling the organic carbon TOA DRF from −0.27 to −0.54 W/m2) can be treated as an upper estimate if organic carbon had an uptake of water. In addition, the effects would be even smaller than suggested here because not all of the organic carbon would be hydrophilic. A fraction of newly emitted organic carbon would remain hydrophobic. If black carbon were treated as hydrophilic, conversely, competing processes take place. On one hand, the single scattering albedo increases because of the growth in size of the particle, which increases the chance for scattering. At the same time, the extinction coefficient increases, which increases absorption. These processes are, in some sense, offsetting, and thereby result in a complex outcome due to the interaction between black carbon and the uptake of water.
3.2.4. Aerosol Mixing State
 An important element of aerosol radiative forcing magnitudes is the strengthened role of black carbon in the context of mixing of aerosol species [Ackerman and Toon, 1981]. A more realistic, albeit more uncertain, treatment of black carbon radiative forcing could involve internal mixing with sulfate and possibly other species [Jacobson, 2000, 2001b]. However, isolating black carbon forcing in the context of internal mixing is ambiguous. Nevertheless, we explore this possibility and perform additional simulations treating black carbon as an internal mixture with sulfate, and compare with the external mixture results discussed in the control case above.
 The assumption in this section considers a homogenous mixture between sulfate, black carbon, and water [Donner et al., 2011; Bollasina et al., 2011]. We employ the traditional definition of forcing as PI to PD, which considers PI concentrations of sulfate as a reference case, and holds sulfate concentrations constant while the effect of black carbon in an altered mixture state is evaluated. The CM2.1 annual and global mean black carbon TOA DRF assuming internal mixtures is +1.28 W/m2, as compared to the externally mixed value of +0.86 W/m2. If PD sulfate concentrations are used as a reference case instead, the black carbon TOA DRF is amplified to +1.65 W/m2. This is an overestimate of the actual forcing, however, because excess sulfate is mixed with the black carbon, introducing additional water into the mixture owing to the hygroscopic growth of the sulfate component.
 The internal mixing framework in this study considers a completely homogenous mixture, pervasive globally at all heights and over all seasons. In addition, all of the sulfate is assumed to mix with black carbon. For these reasons, the internal mixing calculations can be interpreted as providing upper estimates of the forcing, since it is unlikely that all aerosols exist in internal mixtures and that, when mixed, the resulting mixtures are homogenous [Jacobson, 2000]. The CM2.1 black carbon forcing estimate will therefore be within the range of +0.86 to +1.28 W/m2 because of the consideration of the mixing state. Furthermore, Stier et al.  suggest that enhanced absorption may be compensated by a reduction in the concentration of black carbon due to enhanced wet scavenging when internally mixed with sulfate.
 The hygroscopicity of sulfate is expected to change according to the state of mixing between aerosol species. Whether hygroscopicity will increase or decrease depends on the properties of the nonsulfate species. In the case of mixing with an insoluble species such as black carbon, the hygroscopicity will be reduced and the deliquescence point will be lowered. The change in the light scattered and absorbed by such a growing particle would depend on the configuration of the particle's internal structure, which is difficult to generalize at present.
3.3. Comparison With Earlier Studies
 In this section, we compare our control case results (and perturbed cases when possible) with previous estimates in the literature, with the objective of examining the degree to which physical climate factors affect the negativity and positivity of scattering and absorbing aerosol TOA DRFs, respectively. The main purpose of this comparison is not to adjudicate one estimate versus another. Furthermore, considerable uncertainties exist when quantifying and examining DRF estimates, since individual forcings cannot be directly measured. Sources of divergence among literature estimates include differing emissions inventories, horizontal and vertical distributions of aerosols based on transport and removal parameterizations, optical and physical/chemical state assumptions (e.g., particle size distribution, aerosol composition, refractive indices, etc.), and mixing states [Forster et al., 2007]. These factors inhibit consistency and a fair comparison of the numerical estimates in the literature. Even more acute are insufficient comparisons reported of the aerosol forcings among the very climate models that actually simulate the climate responses and are used, for example, in detection-attribution analyses of climate change.
 It is important to note the criticality of cloud cover and relative humidity in determining the global radiative forcings, as presented quantitatively in this study. In addition, the vertical distribution of clouds, cloud biases, and treatment of mixtures can significantly alter forcings [Jacobson, 2000, 2001b]. Different parameterizations of clouds and relative humidity in the GCMs used to calculate radiative forcings could substantially alter the magnitudes of forcing. Since it is difficult to determine the effects of clouds and relative humidity in other studies in view of the relevant data inaccessibility, our estimates of clear-sky and dry sulfate DRFs can be considered to provide a maximal uncertainty range in the context of the present model assuming external mixtures. For sulfate, the range considering both clouds and relative humidity is −2.16 W/m2(“wet” and clear-sky) to −0.72 W/m2(“dry” and all-sky). For black carbon, this range, due to clouds, is +0.49 to +0.86 W/m2. For organic carbon, this range, due to clouds, is −0.4 to −0.27 W/m2.
Haywood and Ramaswamy  accounted for excess black carbon at high elevations by performing loading and vertical profile sensitivity tests, and scaled their forcing down from +1.06 W/m2 to +0.4 W/m2. They calculated radiative forcings for cases where black carbon concentrations were confined to below 1, 2.5, and 5 km, and considered loading changes from 0.05 to 0.3 Tg. Following their approach, the scaling factors computed by Haywood and Ramaswamy  are applied to calculate how forcings in this study would change if black carbon concentrations were restricted to these elevations. A 15% reduction in black carbon loading due to a possible overestimation of the emissions inventory used in this study [Bond et al., 1998; Jacobson, 2000] is also accounted for. The black carbon TOA DRF is reduced from +0.86 to +0.57 W/m2. The sensitivity test provided by Haywood and Ramaswamy  lowers the magnitude of black carbon forcing by 0.66 W/m2 (compared to our lowering of 0.29 W/m2) because the forcing is averaged over an extreme range in black carbon loading (0.05 to 0.3 Tg). A significantly lower loading subsequently lowers the forcing. For the sensitivity test here, the loading is only reduced by 15%, which scales the CM2.1 black carbon loading of 0.29 Tg down to 0.25 Tg.
 Assuming internal mixtures increases the black carbon TOA DRF to +1.28 W/m2. This value is slightly higher than calculations by Sato et al.  and Ramanathan and Carmichael . Sato et al.  calculated global mean black carbon TOA DRF of +0.91 W/m2 and +1.05 W/m2, using two different models with AERONET-derived black carbon absorption.Ramanathan and Carmichael  used satellites to observationally constrain aerosol loadings and account for internal mixtures, and estimated a forcing of +0.9 W/m2 for black carbon. Therefore, the range in the black carbon forcing here (+0.86 to +1.28 W/m2) is fairly comparable to estimates in the literature that consider an internal mixing framework.
Ginoux et al.  indicate that sulfate optical depths in CM2.1—especially in the northern midlatitudes—are amplified when compared to previous modeling studies, most likely due excessive hygroscopic growth in the model. The frequency of relative humidities over 99% may be too high in CM2.1, allowing particles to exponentially swell unrealistically. When relative humidity is capped at 97% in our model, the annual and global mean forcing is scaled down from −1.12 W/m2 to −1.05 W/m2.
 Biases in the downward shortwave surface flux in the CM2.1 model have been identified by Freidenreich and Ramaswamy . Underestimates in the surface flux in North American, European and Asian locations are hypothesized to be results of the overestimation of sulfate aerosol optical depth that is due to excessive hygroscopic growth at high relative humidity. Dry sulfate simulations are shown by Freidenreich and Ramaswamy  to yield a reduction in the flux bias. Thus, relative humidity strongly enhances the DRF of sulfate in the climate model. On the other hand, Haywood et al.  hypothesize that global climate models considerably underestimate DRF from sulfate in areas of high relative humidity, although different models are cited there.
 The global mean organic carbon TOA DRF calculated by CM2.1 (−0.27 W/m2) is similar to the estimates provided by other studies, such as that of Koch  that calculates −0.3 W/m2 and Takemura et al.  that calculates −0.27 W/m2. Spatial distributions are also consistent with the work of Koch . As addressed by Ginoux et al. , the concentrations of organic carbon in CM2.1 may be underestimated by a factor of almost two owing to conversion discrepancies between organic matter and organic carbon. Further sources of error also include underestimates in emissions in West Africa and underestimates of optical depths in biomass burning regions, the latter of which arise because of specific extinction assumptions in the model. Improving the organic carbon aerosol DRFs also requires considerations involving different kinds of organic matter and the inclusion of the respective hydrophilic and absorbing properties. Accounting for these collective uncertainties, we can scale our organic carbon global mean DRF (−0.27 W/m2) using the uncertainty range in the work of Forster et al.  of a factor of two. The CM2.1 organic carbon TOA DRF would fall within the range of −0.14 W/m2 to −0.54 W/m2. While including hygroscopicity would further increase the magnitude of the forcing as discussed in section 3.2.3, accounting for possible absorbing properties would weaken the forcing and perhaps even change its sign. The optical properties of organic carbon likely fall in between the two extremes of sulfate and black carbon, and therefore estimates in its forcing are bound by that of sulfate and black carbon for similar spatial distributions.
 Comparisons of CM2.1 surface forcings to past publications, on the other hand, are difficult, because very few studies have published surface forcings. For those values that are available, our estimates are higher than that of Takemura et al. , comparable to Ramanathan and Carmichael , and higher than Jacobson [2001a] for sulfate, and comparable for black carbon. Although all of these studies to an extent assumed internal mixtures, the total extinction of radiation from an internal mixture of black carbon and sulfate would be virtually identical to that in an external mixture [Seinfeld and Pandis, 1998]. This is because the decrease in the scattering coefficient would compensate to some extent for the increase in the absorption coefficient. Therefore, it is probable that surface forcings are relatively little affected by the type of mixture. Our results yield larger values of the radiative forcing at the surface than found in previous studies due to the same reasons cited for the overestimates in TOA forcing. It would be gainful to compare this variable among the different IPCC-class models since there now exists accurate surface-based measurements of aerosol optical depths and surface solar fluxes for model evaluation purposes [e.g.,Ginoux et al., 2006; Freidenreich and Ramaswamy, 2011].
 An additional comparison can be drawn from Chýlek and Wong's  analytical expression for DRF at the TOA for scattering and absorbing aerosols. Inserting appropriate global mean values into this expression yields forcings comparable but slightly lower than our model results (sulfate: −0.93 W/m2; black carbon +0.74 W/m2; organic carbon −0.1 W/m2). For comparison of the perturbed cases with previous literature, we examine scalings and sensitivity tests. Although few recent studies provide clear-sky estimates of radiative forcing,Koch  and Takemura et al. show scalings of all-sky values that are twice as high as clear-sky forcing for black carbon and half the clear-sky forcing for sulfate, both of which match the results presented here. For organic carbon, comparison with the work ofKoch  shows that the forcing increases by the same percentage (47/48%) when clouds are removed from the system. However, Takemura et al.  shows that organic carbon TOA DRFs double when clouds are absent. Schulz et al. provides clear-sky estimates for the net aerosol forcing, and reach similar conclusions regarding strengthened negative forcings and weakened positive forcings. Relative humidity sensitivity tests are provided byHaywood and Ramaswamy  and Jacobson [2001a]. Rough comparisons reveal amplifications of global mean sulfate DRFs from hygroscopic growth that are similar to this study, and perhaps slightly higher for that of Haywood and Ramaswamy .
 Aerosols are widely recognized to produce a net negative TOA direct radiative forcing that acts to partly offset the positive forcing from LLGHGs. However, not all aerosols contribute to the negative radiative forcing, and absorbing and scattering aerosols often exhibit opposite behaviors. This study considers how different physical climate factors (e.g., clouds, surface albedo, and relative humidity) independently contribute to the sign and magnitude of scattering (sulfate and organic carbon) and absorbing (black carbon) aerosol TOA direct radiative forcings, respectively.
 Global and regional TOA and surface radiative forcings for preindustrial to present-day conditions are calculated in this study using the GFDL CM2.1 model. The model is forced by aerosol concentrations based on standard emissions data, and model-simulated cloud coverage, surface albedo, and relative humidity distributions. Perturbation calculations are performed to assess how the DRF magnitudes are strengthened or weakened by clouds, high-albedo surfaces, and hygroscopic growth.
 Although the forcings calculated by GFDL CM2.1 tend to be at the higher end of the range of estimates when compared to previous studies (most likely due to high emissions and excess vertical transport of black carbon, and excess hygroscopic growth by sulfate), this bias does not affect the sensitivities of the scattering and absorbing aerosols to physical climate factors. Cloud cover and high-albedo surfaces strengthen global mean black carbon TOA forcings by ∼80% and ∼8%, respectively, and weaken global mean sulfate TOA forcings by ∼50% and ∼4%, respectively. In areas of year-round high-albedo surfaces, the presence of clouds weakens the black carbon TOA DRF. The sensitivities of organic carbon forcings—of which forcings are much smaller in magnitude than that of black carbon or sulfate—are similar to sulfate because of its treatment as a nonabsorbing particle. If organic carbon were treated as partially absorbing, the forcing magnitude would further decrease. Hygroscopic growth strengthens the global mean sulfate forcing by ∼60%, compensating for the weakening of the forcing by clouds. If organic carbon were treated as hygroscopic, this would increase the negativity of the forcing because a larger particle would scatter more radiation. If sulfate and black carbon are treated as internally mixed, the global mean black carbon forcing is amplified by 50%.
 The aerosol TOA DRFs can be further perturbed by a number of variables, such as changes in the geographical emissions patterns. Aerosols also affect water cloud properties [Charlson et al., 1992; Chýlek et al., 1984; Hansen et al., 2005; IPCC, 2007], convection [e.g., Erlick et al., 2006; Ramanathan and Carmichael, 2008], ice cloud properties [Lohmann, 2002], and surface albedo from deposition on snow and ice [IPCC, 2007]. Aerosols that serve as cloud condensation nuclei (CCN) exert indirect radiative forcings (IRFs) on the climate system by “brightening” liquid clouds by increasing their albedo [Twomey, 1977] and/or lengthening cloud lifetimes [Albrecht, 1989]. As both processes tend to enhance shortwave cloud reflection, it is predictable that IRFs would tilt the total aerosol forcing toward being more negative. Nonetheless, it is worth noting that IRFs still suffer from the largest uncertainty among all radiative forcings quantified by the IPCC , with some of the uncertainty factors only qualitatively understood at best; estimates of the aerosol IRF vary over a large range, from as low as −0.2 W/m2 to as high as −2.3 W/m2. The IRF is substantially sensitive to several factors, with global atmospheric general circulation characteristics, sea surface temperatures, and cloud processes such as formation, maintenance and dissipation playing major but complicated roles. Because of gaps in the knowledge on clouds—particularly cloud frequency of occurrence, areal extent, and morphology—the meteorological factors and their regional intricacies pose a severe limitation in the analysis of sensitivities compared to analysis of factors that principally govern DRF sensitivities as discussed in this paper.
 In conclusion, this study reiterates that the negativity and positivity of sulfate and black carbon DRFs, respectively, are highly sensitive to cloud cover, due to the weakened sulfate forcing (decreased by a factor of two) and strengthened black carbon forcing (increased by a factor of two) relative to the respective clear-sky conditions. Sulfate's growth, however, from absorption of water in the atmosphere, almost doubles its forcing on average. High-albedo surfaces are shown to have a small impact on the global mean DRFs (less than 10% change), however, effects are large in areas with persistent reflective surfaces. Organic carbon—coemitted with black carbon and treated as a scattering particle—exhibits similar sensitivities to that of sulfate. However, the organic carbon forcings are much smaller in magnitude than for sulfate and black carbon.
 We thank Stuart Freidenreich for reviewing our manuscript and providing useful comments. Ilissa B. Ocko is supported by the National Science Foundation Graduate Research Fellowship under grant DGE 0646086.