Abstract. The formation of black carbon fractal aggregates (BCFAs) from combustion and subsequent ageing involves several stages resulting in modifications of particle size, morphology, and composition over time. To understand and quantify how each of these modifications influences the BC radiative forcing, the optical properties of BCFAs are modelled. Owing to the high computational time involved in numerical modelling, there are some gaps in terms of data coverage and knowledge regarding how optical properties of coated BCFAs vary over the range of different factors (size, shape, and composition). This investigation bridged those gaps by following a state-of-the-art description scheme of BCFAs based on morphology, composition, and wavelength. The BCFA optical properties were investigated as a function of the radius of the primary particle (ao), fractal dimension (Df), fraction of organics (forganics), wavelength (λ), and mobility diameter (Dmob). The optical properties are calculated using the multiple-sphere T-matrix (MSTM) method. For the first time, the modelled optical properties of BC are expressed in terms of mobility diameter (Dmob), making the results more relevant and relatable for ambient and laboratory BC studies. Amongst size, morphology, and composition, all the optical properties showed the highest variability with changing size. The cross sections varied from 0.0001 to 0.1 µm2 for BCFA Dmob ranging from 24 to 810 nm. It has been shown that MACBC and single-scattering albedo (SSA) are sensitive to morphology, especially for larger particles with Dmob > 100 nm. Therefore, while using the simplified core–shell representation of BC in global models, the influence of morphology on radiative forcing estimations might not be adequately considered. The Ångström absorption exponent (AAE) varied from 1.06 up to 3.6 and increased with the fraction of organics (forganics). Measurement results of AAE ≫ 1 are often misinterpreted as biomass burning aerosol, it was observed that the AAE of purely black carbon particles can be ≫ 1 in the case of larger BC particles. The values of the absorption enhancement factor (Eλ) via coating were found to be between 1.01 and 3.28 in the visible spectrum. The Eλ was derived from Mie calculations for coated volume equivalent spheres and from MSTM for coated BCFAs. Mie-calculated enhancement factors were found to be larger by a factor of 1.1 to 1.5 than their corresponding values calculated from the MSTM method. It is shown that radiative forcings are highly sensitive to modifications in morphology and composition. The black carbon radiative forcing ΔFTOA (W m−2) decreases up to 61 % as the BCFA becomes more compact, indicating that global model calculations should account for changes in morphology. A decrease of more than 50 % in ΔFTOA was observed as the organic content of the particle increased up to 90 %. The changes in the ageing factors (composition and morphology) in tandem result in an overall decrease in the ΔFTOA. A parameterization scheme for optical properties of BC fractal aggregates was developed, which is applicable for modelling, ambient, and laboratory-based BC studies. The parameterization scheme for the cross sections (extinction, absorption, and scattering), single-scattering albedo (SSA), and asymmetry parameter (g) of pure and coated BCFAs as a function of Dmob were derived from tabulated results of the MSTM method. Spanning an extensive parameter space, the developed parameterization scheme showed promisingly high accuracy up to 98 % for the cross sections, 97 % for single-scattering albedos (SSAs), and 82 % for the asymmetry parameter (g).

Abstract. Black carbon (BC) from incomplete combustion of biomass or fossil fuels is the strongest absorbing aerosol component in the atmosphere. Optical properties of BC are essential in climate models for quantification of their impact on radiative forcing. The global climate models, however, consider BC to be spherical particles, which causes uncertainties in their optical properties. Based on this, an increasing number of model-based studies provide databases and parameterization schemes for the optical properties of BC, using more realistic fractal aggregate morphologies. In this study, the reliability of the different modelling techniques of BC was investigated by comparing them to laboratory measurements. The modelling techniques were examined for bare BC particles in the first step and for BC particles with organic material in the second step. A total of six morphological representations of BC particles were compared, three each for spherical and fractal aggregate morphologies. In general, the aggregate representation performed well for modelling the particle light absorption coefficient σabs, single-scattering albedo SSA, and mass absorption cross-section MACBC for laboratory-generated BC particles with volume mean mobility diameters dp,V larger than 100 nm. However, for modelling Ångström absorption exponent AAE, it was difficult to suggest a method due to size dependence, although the spherical assumption was in better agreement in some cases. The BC fractal aggregates are usually modelled using monodispersed particles, since their optical simulations are computationally expensive. In such studies, the modelled optical properties showed a 25 % uncertainty in using the monodisperse size method. It is shown that using the polydisperse size distribution in combination with fractal aggregate morphology reduces the uncertainty in measured σabs to 10 % for particles with dp,V between 60–160 nm. Furthermore, the sensitivities of the BC optical properties to the various model input parameters such as the real and imaginary parts of the refractive index (mre and mim), the fractal dimension (Df), and the primary particle radius (app) of an aggregate were investigated. When the BC particle is small and rather fresh, the change in the Df had relatively little effect on the optical properties. There was, however, a significant relationship between app and the particle light scattering, which increased by a factor of up to 6 with increasing total particle size. The modelled optical properties of BC are well aligned with laboratory-measured values when the following assumptions are used in the fractal aggregate representation: mre between 1.6 and 2, mim between 0.50 and 1, Df from 1.7 to 1.9, and app between 10 and 14 nm. Overall, this study provides experimental support for emphasizing the importance of an appropriate size representation (polydisperse size method) and an appropriate morphological representation for optical modelling and parameterization scheme development of BC.

Abstract. The formation of black carbon fractal aggregates (BCFAs) from combustion and subsequent aging involves several stages resulting in modifications of particle size, morphology, and composition over time. To understand and quantify how each of these modifications influences the BC radiative forcing, the radiative properties of BCFAs are modelled. Owing to the high computational time involved in numerical modelling, there are some gaps in terms of data coverage and knowledge regarding how radiative properties of coated BCFAs vary over the range of different factors (size, shape, and composition). This investigation bridged those gaps by following a state-of-the-art description scheme of BCFAs based on morphology, composition, and wavelength. The BCFAs radiative properties were investigated as a function of the radius of the primary particle (ao), fractal dimension (Df), fraction of organics (forganics), wavelength (λ), and mobility diameter (Dmob). The radiative properties are calculated using the multiple sphere T-matrix (MSTM) method. Amongst size, morphology, and composition, all the radiative properties showed the highest variability with changing size. The cross-sections varied from 0.0001 μm2 to 0.1 μm2 for BCFA Dmob ranging from 24 nm to 810 nm. After size or Dmob, the absorption cross-section (Cabs) and BC mass absorption cross-section (MACBC) showed the highest sensitivity towards composition or forganics, whereas the asymmetry parameter (g) showed higher dependence on morphology, which is represented by Df. The Ångstrom absorption exponent varied from 1.06 up to 3.6 and increases with the fraction of organics (forganics). The values of the absorption enhancement factor (Eλ) were found between 1.01 and 3.28 in the visible spectrum. The Eλ was derived from Mie calculations for coated volume equivalent spheres, and from MSTM for coated BCFAs. Mie calculated enhancement factors were found to be larger by a factor of 1.1 to 1.5 than their corresponding values calculated from the MSTM method. It is shown that radiative forcings are highly sensitive towards modifications in morphology and composition. The black carbon radiative forcing ΔFTOA (Wm−2) decreases up to 61 % as the BCFA becomes more compact in morphology. Whereas, there is a decrease of > 50 % in ΔFTOA as the organic content of the particle increase up to 90 %. Based on our results, which showed a significant effect of coating and morphology on the BC radiative properties, a parametrization scheme for radiative properties of BC fractal aggregates was developed, which is applicable for modelling, ambient, and laboratory-based BC studies. The parameterization scheme for the cross-sections (extinction, absorption, and scattering), single scattering albedo (SSA), and asymmetry parameter (g) of pure and coated BCFAs as a function of Dmob were derived from tabulated results of the MSTM method. Spanning over an extensive parameter space, the developed parametrization scheme showed promisingly high accuracy up to 98 % for the cross-sections, 97 % for single scattering albedos (SSA), and 82 % for asymmetry parameter (g).

Abstract. Black carbon (BC) from incomplete combustion of biomass or fossil fuels is the strongest absorbing aerosol component in the atmosphere. Optical properties of BC are essential in climate models for quantification of their impact on radiative forcing. The global climate models, however, consider BC to be spherical particles which causes uncertainties in their optical properties. Based on this, an increasing number of model-based studies provide databases and parametrization schemes for the optical properties of BC using more realistic fractal aggregate morphologies. In this study, the reliability of the different modelling techniques of BC was investigated by comparing them to laboratory measurements. In the first step, the modeling techniques were examined for bare BC particles, and in the second step, for BC particles with organic material. A total of six morphological representations of BC particles were compared, three each for spherical and fractal aggregate morphologies. The BC fractal aggregate is usually modelled using monodispersed particles since their optical simulations are computationally expensive. In such studies, the modelled optical properties showed a 25 % uncertainty in using the monodisperse size method. It is shown that using the polydisperse size distribution in combination with fractal aggregate morphology reduces the discrepancy between modelled and measured particle light absorption coefficient σabs to 10 %, for particles with volume mean mobility diameters between 60–160 nm. However, for particles larger than 100 nm, the Absorption Ångström Exponent (AAE) calculated by using a spherical morphology was more consistent with the measured value. Furthermore, the sensitivities of the BC optical properties to the various model input parameters such as the real and imaginary parts of the refractive index (mre and mim), the fractal dimension (Df), and the primary particle radius (app) of an aggregate were investigated. The modelled optical properties of BC are well aligned with laboratory-measured values when the following assumptions are used in the fractal aggregate representation: mre between 1.6 to 2; mim between 0.50 to 1; Df from 1.7 to 1.9, and app between 10 to 14 nm. Overall, this study provides experimental support for emphasizing the use of an appropriate size representation (polydisperse size method) and an appropriate morphological representation (aggregate morphology) for optical modelling and parametrization scheme development of BC.

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