Effects of mixing states on the multiple-scattering properties of soot aerosols

Tianhai Cheng; Yu Wu; Xingfa Gu; Hao Chen

doi:10.1364/OE.23.010808

1.Introduction

Soot aerosols are mainly emitted from the incomplete combustion of fossil fuels and biomass burning [1, 2], which are the main sources of anthropogenic atmospheric aerosol. Soot aerosols can significantly alter the radiative budget by scattering and absorbing incoming solar radiation [3, 4]. Due to the black carbon (BC) particles in soot aerosols that are the dominant absorber of visible solar radiation, soot aerosols have become one of the most important components of global warming in terms of direct forcing [5]

The direct effects of soot aerosols on the atmospheric radiation balance of the Earth depend on their optical properties, especially the extinction coefficient (scattering + absorption), single-scattering albedo (ratio of scattering to extinction coefficient), and asymmetry parameter (ASY) [6–8]. The variation of single-scattering albedo can modify the sign of the aerosol radiative forcing (cooling/heating, depending on the planetary albedo), while the asymmetry parameter of the phase function together with aerosol loading can drive the magnitude of aerosol radiative forcing [9]. The climate impact of soot aerosols is considered to be one of the largest uncertainties in climate forcing assessments due to the lack of knowledge on their optical properties [10–12]. The optical properties of soot aerosols depend on their complex morphological properties and mixing states with other atmospheric components.

Freshly emitted black carbon (BC) particles in soot aerosols are often aggregates, mainly distinct from other aerosol particles, and are therefore mainly hydrophilic [13, 14]. During the aging process, the freshly emitted BC particles become internally mixed with other aerosols through condensation, coagulation, and/or photochemical oxidation processes in the atmosphere, in which BC particles are coated and tend to be compact. The morphology of internally mixed soot aerosols is complex, depending highly on the degree of aging, ambient temperature, and relative humidity [15–17].

The effects of mixing states on the absorption properties of soot aerosols have been widely studied [18–22]. Laboratory experiment studies show that the amplification factor reaches as high as 2 due to the mixing state of black carbon [23–25]. Ground-based measurements estimate that the internal mixing state enhanced black carbon absorption by a factor of 1.5–1.6 in the Asian outflow [26]. Aircraft measurements indicated that coatings enhance the light absorption of black carbon by at least 30% [27]. Climate models estimate an enhancement of soot aerosol forcing up to a factor of 2.9 due to the effect of internally mixed states [5, 28–30]. The absorption of soot aerosols can be significantly enhanced by internal mixing with other aerosols. However, the effects of mixing states on the scattering properties of soot aerosol have still not been completely accounted for or determined yet, especially for multiple-scattering properties [31–33]. Therefore, it is interesting to see the effects of mixing states on the multiple-scattering properties of soot aerosols.

Taking into account the critical importance of radiative forcing assessments of soot aerosols, the main goal of this study is to quantify the effects of mixing states on the multiple-scattering properties of soot aerosols. The single-scattering properties of soot aerosols with different mixing states were accurately calculated using the Multiple Sphere T-Matrix model, which uses numerically exact solution methods of Maxwell’s equations [34–36]. The numerically exact superposition T-matrix method has been increasingly extended to cases where any sphere can be located at points that are either internal or external to other spheres [34]. The effects of mixing states on the multiple-scattering properties of soot aerosols were studied using the plane-parallel polarized radiative transfer model [37], which takes into account the multiple-scattering properties of atmospheric particles based on the doubling and adding method. These findings should improve our understanding of the effects of the mixing state on the scattering properties of soot aerosols and their effects on climate.

In Section 2, the main physical properties of soot aerosols with different mixing states are briefly described. The single-scattering properties of soot aerosols with different mixing states are presented in Section 3. In Section 4, the multiple-scattering properties of soot aerosols with different mixing states are presented. Conclusions are presented in Section 5.

2. Physical properties of soot aerosols with different mixing state

Soot aerosols are composed of numerous substances which reflect the diversity of their source mechanisms and locations. Black carbon, which is the dominant absorber in soot aerosols, is co-emitted with a variety of other aerosols and aerosol precursor gases. As black carbon particles are formed and transported in the atmosphere, mixing between black carbon and other aerosol types takes place. Both internal and external mixtures exist in the soot aerosols [38–40].

Calculations of the optical properties of soot aerosols are usually performed by computing single-particle optical properties based on the physical and chemical properties of the particles, followed by performing an ensemble average over morphologies, sizes, and compositions. To quantify and study the impact of mixing states on the multi-scattering properties of soot aerosols, models of the radiative properties of soot aerosols were simply assumed to be either external mixture only or internal mixture only and composed of two components (black carbon particles and sulfate). For external mixtures, black carbon particles are physically separated from sulfate aerosol, while for internal mixtures, black carbon particles are incorporated within sulfate aerosol.

Based on in situ measurements and laboratory studies [41], black carbon particles consist of small spherical primary particles combined into branched aggregates. The construction and morphology of black carbon particles can be described by the well-known statistical scaling law:

N s = k 0 {(\frac{R g}{a})}^{D f}

R_{g}^{2} = \frac{1}{N_{s}} \sum_{i = 1}^{N_{s}} r_{i}^{2}

in which the fractal dimension ( $D_{f}$ ), fractal prefactor ( $k_{0}$ ), number of the monomers in the black carbon ( $N_{s}$ ), and mean radius of the monomer ( $a$ ) are used to reconstruct the morphology of the black carbon particles. $R g$ is the radius of gyration, which represents the deviation of the overall aggregate radius in a cluster, $r_{i}$ is the distance from the ith monomer to the center of the cluster. The radius of sulfate particle $R_{s}$ is used to reconstruct the morphology of sulfate particles. The shell/core diameter ratio ( $S / C$ ) was used to demonstrate the degree of the internal mixing state of the soot aerosols.

In this study, the morphology of external mixture (black carbon and spherical sulfate) and internal mixture (black carbon embedded into spherical sulfate) models are modeled using the parallel diffusion limited aggregation (DLA) algorithm [42]. Figure 1. shows the schematic image of external mixture and internal mixture soot aerosol in the atmosphere. Following the studies by Sorensen and Roberts [43], and Bond and Bergstrom [44], in this study, we assume $S / C = 2.0$ , $N s = 100$ , $D_{f} = 2.4$ , $k_{0} = 1.2$ and $a = 0.02 u m$ .

Fig. 1 Schematic image of the two mixing states of soot aerosols: (Left) external mixture soot aerosol models, (right) internal mixture aerosol models. Only two aerosol components are taken into account. Black is the black carbon, and gray is the sulfate.

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The wavelength-dependent refractive indices of black carbon particles employ the values reported by Change and Charalampopulos [45], while the refractive indices of sulfate are taken from the OPAC database [46].

3. Single-scattering properties of soot aerosols with different mixing state

Modeling the multiple-scattering properties of soot aerosols requires the following aerosol optical properties: aerosol optical depth (the integral of the product of particle number concentration and particle extinction cross-section along a path length through the atmosphere); phase function (angular dependence of light scattering), and the single-scattering albedo (ratio of scattering to scattering + absorption).

The single-scattering properties of the individual soot aerosol model with different mixing states (external mixture and internal mixture) were calculated using the Multiple Sphere T-Matrix model. The ensemble optical properties of soot aerosols for external mixtures are constructed by black carbon particles and sulfate particles as shown in Eq. (3) and Eq. (4); $a$ is the radius of the size distribution:

〈 F (Θ) 〉 = \frac{\int_{0}^{\infty} F_{B C} (Θ) σ_{B C, s c a} (a) n (a) d a + \int_{0}^{\infty} F_{S u l f a t e} (Θ) σ_{S u l f a t e, s c a} (b) N (b) d b}{\int_{0}^{\infty} σ_{B C, s c a} (a) n (a) d a + \int_{0}^{\infty} σ_{S u l f a t e, s c a} (b) N (b) d b}

〈 ω 〉 = \frac{\int_{0}^{\infty} σ_{B C, s c a} (a) n (a) d a + \int_{0}^{\infty} σ_{S u l f a t e, s c a} (b) N (b) d b}{\int_{0}^{\infty} σ_{B C, e x t} (a) n (a) d a + \int_{0}^{\infty} σ_{S u l f a t e, e x t} (b) N (b) d b}

where

〈 F (Θ) 〉

is the ensemble averaged phase function for the whole size range.

F_{B C} (Θ)

is the phase function of the individual BC particle,

σ_{B C, s c a} (a)

is the scattering cross section of the individual BC particle.

F_{S u l f a t e} (Θ)

is the phase function of the individual sulfate particles, and

σ_{S u l f a t e, s c a} (a)

is the scattering cross section of the individual sulfate particle.

n (a)

is the size distribution of BC particles.

N (b)

is the size distribution of sulfate particles. The ensemble averaged single-scattering albedo

〈 ω 〉

can be obtained using scattering and extinction coefficients for the integration of the scattering and extinction cross sections of the single particles of BC and sulfate particles.

The ensemble optical properties of soot aerosols for the internal mixture state are constructed by internal mixture aerosol models as shown in Eq. (5) and Eq. (6),

〈 F (Θ) 〉 = \frac{\int_{0}^{\infty} F_{I n t e r n a l (B C + S u l f a t e)} (Θ) σ_{I n t e r n a l (BC+Sulfate), s c a} (c) m (c) d c}{\int_{0}^{\infty} σ_{I n t e r n a l (B C + S u l f a t e), s c a} (c) m (c) d c}

〈 ω 〉 = \frac{\int_{0}^{\infty} σ_{I n t e r n a l (B C + S u l f a t e), s c a} (c) m (c) d c}{\int_{0}^{\infty} σ_{I n t e r n a l (B C + S u l f a t e), e x t} (c) m (c) d c}

where

F_{I n t e r n a l (B C + S u l f a t e)} (Θ)

is the phase function of the individual internal mixture aerosol particle,

σ_{I n t e r n a l (B C + S u l f a t e), s c a} (a)

is the scattering cross section of the individual internal mixture aerosol particle, and

m (c)

is the size distribution of internal mixture aerosol particles.

〈 ω 〉

can be obtained using scattering and extinction coefficients for the integration of the scattering and extinction cross sections of individual internal mixture aerosol particles.

To investigate and quantify the effects of mixing on the multiple-scattering properties of soot aerosols, we set aside the variation of the morphology and number of BC and sulfate particles, which are at any rate poorly characterized. The morphologies and size of black carbon particles are simply assumed to be equal, and the morphology of sulfate particles is simplified and assumed to be homogeneous spheres of equal size. The number of BC and sulfate particles is assumed to be equal, and the number of internal mixture aerosol models is also equal to the number of BC particles. The volume of BC particles and sulfate particles are same for the external and internal mixtures. Further detailed work should include variation of the morphology and the number of BC and sulfate particles. The ensemble optical properties of soot aerosols with different mixing states were calculated at four wavelengths, namely, 440 nm, 670 nm, 870 nm, and 1020 nm.

The scattering matrices of external mixture soot aerosols and internal mixture soot aerosols at 440 nm and 870 nm are shown in Fig. 2. and Fig. 3., respectively. The phase function ( $F_{11}$ ) describes how much light is scattered in each direction. As shown in Fig. 2, the phase function depends on the mixing state of soot aerosols. The phase function of different mixing states varies significantly as a function of the scattering angle at backscattering directions. From Fig. 2. we can see that the effects of mixing on the degree of linear polarization (DLP), which is equivalent to $- F_{12} / F_{11}$ ,cannot be ignored, especially in the backscattering directions. Figure 3. shows that the effect of the mixing state of soot aerosols on the scattering matrices weakened as the incident wavelength increased.

Fig. 2 Effects of soot aerosol mixing state on the Mueller matrix elements at 440 nm.

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Fig. 3 Effects of soot aerosol mixing state on the Mueller matrix elements at 870 nm.

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The effect of mixing states on the extinction cross section and single-scattering albedo is presented in Fig. 4. It is evident from Fig. 4 that extinction properties and the single-scattering albedo of the external mixtures soot aerosol model differ from those calculated for the internal mixture aerosol model. The extinction cross section of the internal mixture aerosol model is higher than those of the external mixture aerosol model.

Fig. 4 Effects of soot aerosol mixing state on the extinction cross section and single-scattering albedo, units of extinction cross section is μm.

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The different mixing states of soot aerosols resulted in dramatic changes in single-scattering albedo. External mixtures led to stronger scattering properties. The single-scattering albedo was enlarged from 0.72 to 0.83 at 440 nm, which corresponds to an enhancement of a factor of 1.15. The internal mixing of BC with sulfate amplifies absorption cross sections because of the lens effect.

4. Multiple-scattering properties of soot aerosols with different mixing states

The incident solar spectral radiative field can be modified due to scattering or absorption by soot aerosol particles. To investigate and quantify the effects of the mixing state on the multiple scattering of soot aerosols, the angular dependence of multiple-scattering effects with the top-of-the-atmosphere (TOA) upward radiances and polarized radiances were simulated using the multi-layered plane-parallel atmosphere vector radiative transfer model. The multiple-scattering properties due to soot aerosols with different mixing states are fully considered by using the vector radiative transfer model. Meanwhile, the multiple-scattering effects with the upwelling hemispheric flux were also simulated using the atmosphere vector radiative transfer model. The different atmospheric scenarios with variable soot aerosol loadings for clear and haze scenarios were considered to evaluate the effects of the mixing state on the multiple-scattering of soot aerosols.

The doubling and adding technique is used to solve the plane-parallel radiative transfer equation. Each input layer is divided into a number of homogeneous sublayers with each sublayer being thin enough for the finite difference initialization to be accurate. Infinitesimal generator initialization is used to relate the scattering matrix to the reflection and transmission matrices. The sublayers are integrated with the doubling algorithm. For each desired output level, the transmission, reflection, and source of the layers above and below the level are combined with the adding algorithm. The internal radiances are computed from the properties of the layers above and below and the incident radiance from the boundaries.

The aerosol optical depth ( $τ$ ) was used to represent the soot aerosol loading, which is defined as the integrated extinction coefficient over a vertical column of unit cross section. With the assumption that BC and sulfate particles are uniformed distributed with equal number, and the number of internal mixture aerosol models is also equal to the number of BC particles, the soot aerosol optical depth ratio of the external and internal mixtures is equal to the ratio of the respective extinction coefficients ( $τ_{ext} / τ_{int} = C e_{ext} / C e_{int}$ ). The solar irradiance at TOA is taken from studies by Thuillier et al. (2003). Specifically, the surface is assumed to be Lambertian with albedo, and the atmosphere is assumed to be plane-parallel and cloud-free.

4.1 Effects of soot aerosols mixing states on the TOA radiances/polarization

To investigate the effects of mixing on the multiple-scattering of soot aerosols, the angular dependence of multiple-scattering effects with TOA upward radiances and polarization were studied.

Figure 5 and Fig. 6 show the relative differences in TOA multi-angular upward radiance $(| R_{E x t e r n a l} - R_{I n t e r n a l} | / R_{E x t e r n a l} \times 100 %)$ for a simple cloud-free atmosphere composed of different mixing state soot aerosols particles with a variable Lambertian surface albedo.

Fig. 5 Polar plot (radius: view zenith angle; angle: relative azimuthal angle) of relative differences of TOA upward radiance simulated for different mixing state soot aerosol particles with variable soot aerosol loadings for clear (left) and haze scenarios (right) at a wavelength of 0.670μm. The external mixed aerosol optical depth is 0.129 for clear scenarios and 0.645 for haze scenarios. The solar zenith angle is 45°, and the Lambertian surface albedo is 0.02.

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Fig. 6 Same as Fig. 5, but for the Lambertian surface albedo is 0.5.

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The results shown in Fig. 5 and Fig. 6 illustrate that the patterns of TOA radiance under soot aerosols with different mixing states are quite different. The relative difference of TOA multi-angular upward radiance can reach 16%. The effects of mixing on the multiple-scattering properties of soot aerosols increase with increasing soot aerosol loadings (aerosol optical depth), which is caused by increasing path lengths or particle concentration or both.

The effects of the mixing state on the multiple-scattering properties of soot aerosols show angular dependence. When surface contribution can be neglected (Lambertian surface albedo is 0.02), the relative difference in TOA multi-angular upward radiance in backscattering directions is ~10% smaller than that in the forward directions. On the contrary, when taken into account the surface contribution (Lambertian surface albedo is 0.5), the relative difference in TOA multi-angular upward reflectance in backscattering directions is ~3-5%larger than that in the forward directions.

Figure 7 and Fig. 8 show the relative differences in TOA multi-angular upward polarization for a simple cloud-free atmosphere composed of different mixing state soot aerosols particles with a variable Lambertian surface albedo.

Fig. 7 As in Fig. 5, but relative differences in TOA upward polarization simulated for different mixing state of soot aerosol particles with variable soot aerosol loadings for a clear atmosphere.

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Fig. 8 As in Fig. 7, but for a Lambertian surface albedo of 0.5.

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The results shown in Fig. 7 and Fig. 8 illustrate that the relative differences in TOA multi-angular upward polarization for a simple cloud-free atmosphere due to the different mixing states are 40-60%, and the largest relative difference can reach 200%. TOA polarization is more sensitive to variations in the mixing states of soot aerosols than to variations in TOA radiance.

For TOA polarization, the effects of mixing on the multiple-scattering properties of soot aerosols decrease with increasing soot aerosol loading (aerosol optical depth), which is contrary to the magnitude of the angular variations of the radiance. The reason for this is that multiple scattering tends to diminish the polarization feature of the reflected light while enhancing the intensity of the backscattering. The surface contributions enhance the effects of mixing on the TOA polarized reflectance. The explanation is that surface contributions tend to enhance the polarization of the backscattering.

4.2 Effects of soot aerosol mixing on the upwelling hemispheric flux

To investigate the effects of soot aerosol mixing states on climate modeling applications, upwelling hemispheric flux was studied using the atmosphere vector radiative transfer model.

Figure 9 and Fig. 10 show effects of the soot aerosol mixing states on the upwelling hemispheric flux for different solar zenith angles with variable soot aerosol loadings and a variable Lambertian surface albedo at a wavelength of 0.670μm.

Fig. 9 Effects of the soot aerosol mixing state on the upwelling hemispheric flux for different solar zenith angles with variable soot aerosol loadings for clear (left) and haze scenarios (right) at a wavelength of 0.670μm. The external mixed aerosol optical depth is 0.129 for clear scenarios and 0.645 for haze scenarios. The Lambertian surface albedo is 0.02. The units of flux is W/ (m*m)/ μm.

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Fig. 10 As in Fig. 9, but with a Lambertian surface albedo of 0.5. The units of flux is W/ (m*m)/ μm.

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The results shown in Fig. 9 and Fig. 10 illustrate that the effects of the soot aerosol mixing state on upwelling hemispheric flux are smaller than on TOA bidirectional radiance and polarization, and their relative deviations on upwelling hemispheric flux increase with increasing solar zenith angle. In the case of low albedo and high aerosol loading the upwelling flux relative difference is ~10% (at 45 degrees) while the upward radiance differences are maximally 16% (with strong azimuthal variation) and the upward polarization state differences are ~40-60%, without strong angular dependence. The explanation is that integration averages out the contrasting effects of soot aerosol mixing on radiance at various scattering angles of reflectance. The relative difference in upwelling hemispheric flux due to the different soot aerosol mixing states can reach 18% when the solar zenith angle is 75°.

The dependence of the effects of the soot aerosol mixing state on solar zenith angle is weakened due to the surface contribution. When the surface contribution can be neglected (Lambertian surface albedo is 0.02), the effects of the soot aerosol mixing state on upwelling hemispheric flux changes from 0% to 18% when the solar zenith angle changes from 0° to 75°. When considering the surface contribution (Lambertian surface albedo is 0.5), the SZA-dependence of the effects of the soot aerosol mixing state on solar zenith angle for high aerosol loading can reach to 8%.

The effects of mixing on the upwelling hemispheric flux depends on soot aerosol loadings (aerosol optical depth). When the soot aerosol loading increases, the multiple scattering of soot aerosols is enhanced by increasing path lengths or particle concentration or both. Due to the surface contribution, the dependence of the effects of soot aerosol mixing state on soot aerosol loading is enhanced.

5. Summary and Conclusions

The incident solar spectral radiative field can be modified due to scattering or absorption by soot aerosol particles. The radiative properties of soot aerosols are highly sensitive to the mixing states of black carbon particles and other aerosol components. To investigate and quantify the effects of mixing states on the multiple scattering of soot aerosols, the angular dependence of multiple-scattering effects with the top-of-the-atmosphere upward radiances/polarization and upwelling hemispheric flux are studied with variable soot aerosol loadings for clear and haze scenarios.

The single-scattering properties of soot aerosols with different mixing states were accurately calculated using the Multiple Sphere T-Matrix model, which used the numerically exact solution methods of Maxwell’s equations. The multiple-scattering properties due to soot aerosols with different mixing states are considered by using the vector radiative transfer model. Specifically, the surface is assumed to be Lambertian with albedo, and the atmosphere is assumed to be plane-parallel and cloud-free.

The extinction properties and single-scattering albedo of the external mixture soot aerosol model differ from those calculated for the internal mixture aerosol model. The extinction cross-section of internal mixture aerosol model is higher than that of the external mixture aerosol model. The different mixing states of soot aerosols resulted in dramatic changes in single-scattering albedo. The single-scattering albedo was enlarged from 0.72 to 0.83 at 440 nm, which corresponds to an enhancement factor of 1.15.

The patterns of upward radiance/polarization under soot aerosols with different mixing states are quite different. The relative difference in upward radiance due to different mixing states can reach 16%, while the relative difference of upward polarization can reach 200%. The effects of the mixing state on the multiple-scattering properties of soot aerosols show angular dependence. The angular dependence of the effects of the mixing state on polarization is quite different from that of the effects of the mixing state on radiance.

The effects of soot aerosol mixing on upward polarization decrease with increasing soot aerosol loading (aerosol optical depth), which is contrary to the magnitude of the angular variations of the radiance. The reason is that multiple scattering tends to diminish the polarization feature of the reflected light while enhancing the intensity of the backscattering.

The effects of the soot aerosol mixing state on upwelling hemispheric flux are much smaller than on TOA bidirectional radiance and polarization, which increase with increasing solar zenith angle. The relative difference in upwelling hemispheric flux can reach 18% when the solar zenith angle is 75° due to the different soot aerosol mixing state. The dependence of the effects of soot aerosol mixing state on the solar zenith angle is weakened due to surface contribution. The effects of the mixing state on the upwelling hemispheric flux depend on soot aerosol loading. When the soot aerosol loading increases, the multiple scattering of soot aerosols is enhanced by an increase in path lengths or particle concentration or both. The dependence of the effects of soot aerosol mixing state on soot aerosol loading is enhanced due to surface contribution.

Our studies indicate that the mixing states of soot aerosols must be explicitly considered in aerosol remote sensing and climate radiation balance studies. These findings should improve our understanding of the effects of mixing states on the multiple-scattering properties of soot aerosols and their effects on climate.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant No: 41371015, 41001207), the National Basic Research Program of China (973 Program) (Grant No: 2010CB950800), the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant No: KZCX2-EW-QN311). We would like to acknowledge the authors of superposition T-matrix: Daniel Mackowski, Kirk Fuller, and Michael Mishchenko. The code of MSTM version 3.0 was downloaded from http://www.eng.auburn.edu/users/dmckwski/scatcodes/.

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Effects of mixing states on the multiple-scattering properties of soot aerosols

Abstract

1.Introduction

2. Physical properties of soot aerosols with different mixing state

3. Single-scattering properties of soot aerosols with different mixing state

4. Multiple-scattering properties of soot aerosols with different mixing states

4.1 Effects of soot aerosols mixing states on the TOA radiances/polarization

4.2 Effects of soot aerosol mixing on the upwelling hemispheric flux

5. Summary and Conclusions

Acknowledgments

References and links

Cited By

Figures (10)

Equations (6)

Optics Express