Particle size amplification of black carbon by scattering measurement due to morphology diversity

Black carbon (BC) is an important aerosol species due to its strong heating of the atmosphere accompanied by cooling of the Earth’s surface, but its radiative forcing is poorly constrained by different regional size distributions due to uncertain reproductions of a morphologically simplified model. Here, we quantify the BC morphological effect on measuring the particle size using an aggregate model. We show that the size distributions of loose BC particles could account for up to 45% underestimation by morphological simplification, leading to up to 25% differences, by relying on a simplified model to estimate radiative forcing. We find that the BC particle size is remarkably amplified for looser and larger BC aggregates by angular scattering observations. We suggest that the BC morphological diversity can be neglected in forward scattering angles (<30°), which is a useful supplement to reduce the uncertainty of radiative forcing assessment.


BC
Black carbon TEM Transmission electron microscope SP2 Single-particle soot photometer LUT Lookup

Introduction
Black carbon (BC) aerosol, also known as soot, and arising from the incomplete combustion of fossil fuels, biofuel, and biomass, is considered to be a major climate-forcing agent with a strong local heating effect to the atmosphere [1,2]. BC particles absorb solar radiation and then convert it into internal energy. However, their warming contribution to global and regional climates is still uncertain [3][4][5]. As a short-lived climate forcer, BC stays in the atmosphere for days to weeks. It has been observed by transmission electron microscopy (TEM) that freshly emitted BC particles are aggregated by hundreds of tiny monomers, and tend to be coated with other aerosol components during atmospheric aging [6]. Recent studies indicate that the radiative forcing of the BC aerosol is highly influenced by its mixing state, complex particle morphology, and particle size [7][8][9]. To reduce uncertainties in evaluating the BC radiative effect, one of the most important approaches is to quantify the BC emission size distributions and how they will change in the future [10]. As a necessary input for climate modeling, BC size distributions have been broadly measured in different regions and sources in previous studies [11][12][13].
The single-particle soot photometer (SP2) is one of the most widely used instruments for measuring the particle size of refractory BC-containing aerosols [14,15]. A two-element avalanche photo-detector is employed in the SP2 to determine the actual position of the particle in the laser beam, which allows for delay time and coating thickness analysis of refractory BC and non-refractory submicron particulate with a core-shell structure. The 1064 nm laser beam scatters light into a solid angle subtended from 13 • to 77 • and from 103 • to 167 • with respect to the laser beam axis and as set by the active area of the SP2 optical detectors. The received scattering signal will initially increase as the particle enters the laser beam, exhibiting a Gaussian-type curve dependence with time. The magnitude of this signal attains a maximum value and eventually decreases as the particle becomes smaller due to the evaporation of the non-BC substance, with the energy absorbed by the BC being dissipated as the latent heat of this non-BC material and by diffusion to the surrounding atmosphere. The initial portion of the time-dependent scattering signal is leading-edge-only fitted to a Gaussian equation, yielding an estimate of the original optical diameter of the particle [16][17][18]. All scattering amplitude results were scaled such that the theoretical results of the single core-shell sphere model matched calibrations with polystyrene-latex spheres or other calibration particles. The simulated results were used in lookup tables (LUTs) that associated a measured BC core mass and extrapolated scattering amplitude with the desired parameter [11]. However, recent studies suggests that the modeling of BC particles neglecting their fractal aggregate morphologies may lead to large errors in optical reproduction [19]. To the best of our knowledge, the impact of these assumptions regarding complex morphologies on BC particle size measurement and radiative effects is very rarely discussed within the literature.

Materials and methods
In this study, for the first time, we quantify the uncertainty of BC particle size measurement due to the morphological simplification of optical modeling. Optical simulations were performed using an aggregate model parameterized by the complex particle morphology of BC with various sizes and mixing states [20,21]. The aggregation of BC monomers is numerically constructed with the given fractal parameters for bare BC using the diffusion-limited aggregation method, and thinly coated BC was constructed by the aggregation of concentric core-shell spherical monomers. The scattering cross-sections and scattering matrices were calculated for individual BC-containing particles using the superposition T-matrix method [22].

Scattering modeling of atmospheric BC particles
The results of in situ measurements and laboratory studies have indicated that bare BC particles are aggregates of small carbon spherules (also called monomers) dominated by a loose structure, and shrink to a compact aggregate coated with the other non-BC components during atmospheric aging [23]. For a single BC particle, its complex particle morphology is generally described by the fractal law where D f is the most important parameter of the BC particle morphologies, indicating the compactness of the fractal aggregate BC particle [24,25]. Previous TEM images have shown that the values of D f vary from 1.8 to 2.8 during atmospheric aging [6], and bare BC particles are typically loose structures with small D f , whereas coated BCs are compact with large D f . The number of monomers (N s ) of a single BC particle was commonly observed to be in the range of 50-300, and may vary up to approximately 800, covering most cases of BC particles [26]. In previous field observations, the mean radius (a) of BC monomers was in the range of 10-30 nm, as reported from the suggestion of the previous review [23]. R g is the radius of gyration representing the deviation of the overall aggregate radius, and r i is the distance from the ith monomer to the center of the aggregated monomers. k 0 is the fractal prefactor of BC aggregate, assuming a constant value of 1.2 in this study. Previous measurements have suggested that the volume-equivalent diameter of pure BC (D BC ) in the BC-containing particles has a lognormal distribution from 50 to 300 nm [13,23]. D BC can be calculated by the numbers and radius of monomers in the simulations, For large BC particles with D BC in the range of 300-500 nm, figure S5 shows that different assumptions of a have a limited influence on the BC scattering properties. These parameters for BC optical simulations are shown in table S1.
The mixing states of BC particles are parameterized by F BC , indicating the fraction of the particle volume that is BC in the individual particles. For bare BC particles, F BC is without the non-BC coatings. In this study, the bare and thinly coated BC particles with F BC ranging from 0.1 to 1 are investigated, because these particles are observed after evaporation. When a BC-containing particle enters the SP2 laser beam, the particle both absorbs and scatters laser light. The absorbed energy heats the BC matter to the point of incandescence. The non-BC components are usually vaporized before incandescence. Thus, the scattering intensity (I sca ) of detected BC particles is bare and thinly coated in most cases, no longer representing the original particle. In this study, BC particles with 0.1 ⩽ F BC ⩽ 1.0 are considered, because the detected BC particles may also be thinly coated by the non-BC components in previous measurements [27]. The refractive index of a BC component is assumed to be 1.95 + 0.79i at 1064 nm, and the refractive index of the non-BC component is assumed to be 1.55 + 10 −3 i for the simulations. The sensitivity of BC scattering has limited influence from these refractive indices, as shown in figure S1.

Morphological simplification by the core-shell sphere model
The bare and thinly coated BC particles are assumed to be a single BC sphere and a core-shell sphere with a BC core and a non-BC shell, respectively. Their optical properties are calculated using the Lorenz-Mie-Debye theory, neglecting the different compactness of the detected BC particles. D BC in the individual particles is calculated by equation (3), and the volume-equivalent diameters of the entire BCcontaining particles (D P ) including BC and non-BC components, are shown as follows: where F BC of the BC-containing particles is 1 for bare BC particles.

Estimations of BC size distributions by scattering properties
The normalized Stokes scattering matrix P(Θ) has the well-known 4 × 4 structure with six independent elements that depend on the scattering angle: where Θ∈[0, 180] is the scattering angle, and the phase function P 11 (Θ) characterizes the angular intensity proportion of incident light in all directions after being scattered, and satisfies the normalization formulation with scattering angle For spherical particles, P 11 (Θ) = P 22 (Θ) and P 33 (Θ) = P 44 (Θ).
The current BC particle size measurement is based on the LUT of I sca simulated as equation (7) using the single core-shell sphere model, which is simplified by fractal aggregate morphologies of BC particles in the real atmosphere.
where R is the distance between the particle and detector, and I sca is the incident intensity. These two parameters are constant for the simulations with different models. As shown in figure S2, w(Θ) is the weight function for different scattering angles. The phase function P 11 (Θ) for different scattering angles and cross-sections of BC particles are calculated using both the core-shell sphere model and the more realistic aggregate model. Figure S4 shows the simulated phase function and corresponding I sca by the different models.
To estimate D BC , the LUT of this study is composed of varying input parameters as shown in table S1 (e.g. D f , F BC , and D BC ) and their calculated results of I sca . Bare and thinly coated BC particles are assumed to be a single BC sphere and a core-shell sphere with a BC core and a non-BC shell, respectively. Their optical properties are calculated using the Lorenz-Mie-Debye theory, neglecting the compactness of BC monomers. The simulations of the BC scattering cross-sections show a satisfactory agreement with previous measurements [24,25], as shown in figure S3. BC mixing states are measured by the time delay of incandescence peaks of SP2, which is convincing due to the volume estimations of nonrefractory aerosol components. Thus, the volume fraction of the BC component is constant for the calculations using both the core-shell sphere model and the more realistic aggregate model, and varied BC D f are simulated for the aggregate model representing different BC morphology cases.
Previous studies of the SP2 indicate that the detectors receiving scattered signals are 45 • ± 32 • and 135 ± 32 • ; thus, the detected I sca is integrated by these angle ranges, as shown in figure S2. For the same measured I sca , the volume-equivalent diameters of BC particles are estimated by the aggregate model with different compactness and their spherical assumptions neglecting particle compactness. The D BC is inversely estimated by the optimized results of I sca , assuming the other input parameters are constant. The linear interpolation of the nearest values from LUT is applied for the D BC estimation. To estimate D BC considering the BC complex particle morphology, I sca calculated by the core-shell sphere model is matched for the simulated results using the aggregate model with different D f . Furthermore, the BC size distribution is constructed by the numbers of the BC-containing particles with a fixed D BC . The number distribution (N(D BC )) of a BC aerosol ensemble is as follows: where σ m is the standard deviation and D m is the peak volume-equivalent diameter of the pure BC component in the BC aerosol ensembles. Some typical values of σ m and D m are shown in table S2 from previous observations [11-13, 18, 27-30], covering the major conditions in different regions and emission sources, as shown in table S2.

Calculations of BC direct radiative forcing at top of the atmosphere (TOA)
Direct radiative forcing at the TOA is modeled using the Libradtran package with the DISORT radiative transfer equation solver [31]. The standard atmospheric profiles for mid-latitude summer and a constant day (the day of the year is 160) are assumed, and the air density, pressure, water vapor, and ozone were assumed to be the default values. The spectral range was assumed to be 0.2-4 µm, and the band parameterization REPTRAN was used for the spectral calculations of molecular absorption. The Lambertian surface was assumed constant for all wavelengths, and the albedo is simulated from 0 to 0.6 for the majority of cases, whereas the results are integrated by the solar zenith angles from 10 • to 80 • . BC aerosols were assumed to be distributed in the homogeneous layer of 0-10 km, and the values of aerosol optical depth (AOD) ranged from 0.1 to 5. The altitude of the TOA was assumed to be 120 km, and the radiative forcing of the BC aerosol (RF TOA ) was defined as the subtraction of upward irradiance in clear conditions without aerosols and in polluted conditions with aerosols. The optical properties of aerosols were calculated using the corresponding models for ten wavelengths in the spectral range of 0.
where F clear and F aerosol are the irradiance of clear-sky conditions without aerosols and polluted conditions with BC aerosols, respectively. The relative deviations of BC TOA radiative forcing due to morphological simplifications are further investigated between the single core-shell sphere model and the more realistic aggregate model.

Results and discussion
3.1. Scattering diversity in particle size measurement We carry out model experiments to quantify the importance of resolving the BC complex particle morphology by comparing the scattering simulations using the single core-shell sphere model to the more realistic aggregate model (table S1). The observed I sca of the input particle is matched with the simulations using the single core-shell sphere model to estimate its particle size. Figure 1 demonstrates that the angular I sca of BC particles is significantly influenced by their morphological simplification, especially for those with looser structures and larger sizes. As shown in figure 1(a), the angular diversities of the BC I sca were more than 60% between the single core-shell sphere model and the more realistic aggregate model in the scattering angle range from 60 • to 300 • . For particles with a small BC volume-equivalent diameter (D BC < 100 nm), the relative deviations of I sca are less than 25% for all the scattering angles. Previous studies suggest that the optimal range of SP2 for the size of the BC cores is 90-300 nm volume-equivalent diameter [11,14]; thus, the morphological effect can hardly be neglected when measuring the BC particle sizes. It is worth noting that the scattering simulations of the major BC-containing particles are not significantly influenced by the morphological simplification in the proper observing angle range of ±30 • to the incident light. Thus, it is suggested that increasing the optical detectors positioned in this angle range would be a reasonable solution to improve the applicability of BC particle size measurement caused by simplified morphologies. Figures 1(b) and (c) show that the compactness of the BC aggregate plays an important role in the reproduction of angular I sca . For loose BC particles, the relative deviations of the simulated BC I sca may reach up to ∼80% between the core-shell sphere model and the more realistic aggregate model. In comparison, those of compact BC particles are less than 30% in most cases. During atmospheric aging, the freshly emitted BC particles tend to be more compact by coating non-BC components, and this diversity due to particle morphology is largely weakened for heavily coated BC particles. Previous studies of SP2 observations indicate that the uncertainty of BC sizing is 10%-25% [14,28]. However, potential errors may exist in BC particles with very loose structures significantly influencing the angular scattering observations. The scattering signal of the SP2 was commonly calibrated using dry polystyrene sphere latex particles (size standard particles, JSR Corporation, Japan) with known sizes. Previous measurements indicated that the SP2 would underestimate the total number concentration of lightscattering particles in ambient conditions because particles that are smaller than ∼170 nm may not be counted [12,18]. It is, therefore, necessary to compare estimations of BC size distributions by various complex morphologies. Figure 2 indicates that the BC volume-equivalent diameters may be underestimated by the morphological simplification, and looser BC particles may lead to larger size estimation errors. For particles with a BC volume-equivalent diameter larger than 200 nm, the size of loose BC particles may be underestimated by ∼30%-45% by the core-shell sphere model, as shown in the left upper subfigure of figure 2. For compact BC particles, this morphological simplification has a limited influence (<10%) on their size estimations. Previous simulations also show that the diversity of BC scattering properties between the aggregate and morphologically simplified models may become larger for looser BC with bare and thinly coated states [32,33]. Our results show that the morphological effect of size estimations can be neglected (<5%) for those particles with small BC cores (D BC < 100 nm) because of fewer aggregated monomers. With the increase in BC core size in the BC-containing particles, the errors in BC size estimations are increased. This can be attributed to the multiple scattering effects of monomers in a single aggregate, which are enhanced for larger BC particles, leading to larger deviations due to morphological simplifications.

Size distributions estimated by different morphologies
As shown in figure 3, this underestimation of BC volume-equivalent diameters due to morphological simplification may produce a 'spring effect' in measuring BC size distributions, indicating a particle diameter amplification for looser BC. A typical BC size distribution averaged by previous observations (table  S2) is corrected by assuming both loose and compact structures of BC particles, respectively. It can be seen from the size distributions that the larger volumeequivalent diameter and smaller D f of the fractal aggregated BC core in the single particles tend to be more remarkably underestimated by current measurements. Particles with a BC volume-equivalent diameter equal to ∼180 nm may be measured to be ∼150 nm using the single core-shell sphere model. In comparison, the BC particles with D BC = ∼350 nm are largely underestimated to be ∼260 nm. It is also found that the estimated BC size distributions are highly sensitive to the compactness of their fractal aggregate morphologies. This morphological effect is intensified for the looser BC aggregates rather than those with compact structures. For the measured BC particles with ∼260 nm by the core-shell sphere model, the actual D BC of these BC particles may be ∼280 nm if compact aggregated with D f = 2.8, while D BC can reach up to ∼350 nm for loose BC with D f = 1.8. The relative deviations due to BC D f are increased with the augmentation of BC particle sizes, in the main range of BC size distributions.
The uncertainty in BC size distributions caused by unknown complex morphologies may introduce difficulty in the parameterizations of aerosol ensembles in different regions and conditions. Previous studies have indicated that the calibration material choice is important for achieving accurate BC measurement using the SP2 [14,27]. It is suggested that the BC particles can be accurately measured only if the calibration particles show similar physical and chemical properties. The exact D f of the observed BC particles and the calibration particles may reduce the uncertainty of the size measurement for different BC types. Moreover, it is shown that BC particles from wood burning and diesel exhaust are observed differently by the SP2, due to the incomplete removal of non-BC coatings before mass selection of the wood burning BC [27]. A possible reason is that the BC particles emitted from diesel exhaust generally exhibit a loose structure, and those from wood burning are more compact due to the thick organic coating. In particular, previous measurements have suggested that D BC conforms to a lognormal distribution [18,34], while the dN/dlogD BC can be described by D m and σ m . For example, the D m of the BC size distributions measured in biomass burning is obviously larger than that observed in urban emissions [11]. Quantitative diversity between these two emission sources needs further evaluation using the aggregate model with exact BC fractal parameters in the future, which would be an important factor for the assessment of regional radiative forcing.

Radiative forcing influenced by BC complex morphologies
The observed size distributions neglecting complex particle morphologies have important implications for the climate modeling of BC aerosols. Previous studies show that aerosol radiative forcing is largely influenced by the multiple components and mixing states [9,35,36], but few models have attempted to investigate the effect of BC complex particle morphologies. Figure 4 shows that the size distributions estimated by different morphological assumptions of loose BC aggregates may lead to ∼25% diversity in the assessment of BC radiative forcing. This diversity of compact BC aggregates is limited to ∼12% because of the smaller errors in the size distribution estimations of compact BC aggregates. Due to the multiple scattering of aerosols in the atmosphere, this relative diversity of radiative forcing due to morphological simplification is weakened for larger BC AODs ranging from 0.1 to 5. The global MERRA-2 data show that in most cases the BC AOD is less than 1 [37]. Therefore, the BC particle morphological simplification may introduce ∼15%-25% and ∼5%-12% differences in radiative forcing for loose and compact morphologies, respectively.
Loose BC particles are most often found in diesel exhaust and urban emissions, while compact BC particles commonly exist in biomass burning. The smaller BC size distribution leads to larger radiative forcing, which is consistent with the previous modeling [10]. This diversity of BC radiative forcing varied by particle morphology is essential but often neglected in the current parameterization of climate assessment. These findings suggest that accurate particle morphologies, mixing states, and corresponding scattering properties of BC aerosols are necessary for their estimations of size distributions, which play an important role in their source identification and warming assessment.

Climate implication
BC particles are fractal aggregates in the atmosphere, but their optical properties are simulated using the same morphologically simplified model as other sphere-like particles, leading to possible uncertainty in their size measurements. In the widely used SP2 instrument, the BC particle size is measured by matching the I sca observed at fixed angle ranges and the LUT estimated by the core-shell sphere model using the Mie scattering method. However, this morphologically simplified model fails to reproduce the optical properties of single BC particles with various fractal parameters, such as the loose BC commonly emitted from diesel exhaust and the compact BC from wood burning. On the one hand, the observed I sca can be corrected by the synchronous observations of TEM and SP2 with clearer morphological and chemical parameters [15,38]. On the other hand, the observation errors of BC aerosols with complex morphologies may be reduced by positioning more detectors at the fixed angular range influenced insignificantly by the BC modeling with the particle morphological simplification. The accuracy and stability of the single particle size measurement of BC aerosols with fractal aggregate morphologies would be effectively improved for different regions and conditions.
In climate models, BC size distribution is one of the most important factors in evaluating aerosol radiative forcing. The mass absorption cross-sections and absorption enhancement of BC particles with fixed particle size, mixing states, and morphologies have been investigated in previous studies [19,39]. The optical properties of BC particles with various volume-equivalent diameters are integrated for atmospheric aerosol ensembles, providing the necessary input for further calculations of global and regional models. Therefore, BC amounts distributed in different regions and conditions have become an urgent problem in reducing the uncertainty of radiative forcing assessment [3][4][5]. In climate models, accurate size measurements may support the temporal and spatial parameterizations of BC aerosols, providing a feasible tool to track progress in reducing emissions and to develop and implement mitigation policies.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).