Mie Scattering Captures Observed Optical Properties of Ambient Biomass Burning Plumes Assuming Uniform Black, Brown, and Organic Carbon Mixtures

We use a simple model of a spherical biomass burning aerosol particle containing an internal mixture of black carbon (BC) and organic carbon (OC) with an effective refractive index calculated as a volume fraction‐weighted mean of refractive indices. Brown carbon (BrC) is considered to be an OC with an imaginary part of refractive index at the blue end of the solar spectrum higher (in absolute value) than at the red end. Mie‐scattering formalism is employed to calculate absorption Ångström exponent (AAE) as a function of single‐scattering albedo (SSA) for a set of BC refractive indices, BC volume fraction, and a set of effective refractive indices of BC and BrC mixtures. Ambient plumes are characterized by their mean SSA at 405 nm wavelength and two‐wavelength (405 and 781 nm) AAE values. Comparing observed and model‐calculated AAE and SSA values identifies the BC refractive index and its volume fraction and an effective refractive index of the BC and BrC mixture. From these values, the imaginary part of BrC refractive index is calculated. For observed southwestern ambient fires, the imaginary part of BrC refractive index is ≤0.016. In contrast, fires in the Amazon and from Africa are dominated by BC. We also use the Mie scattering model to establish the upper limit on AAE of BC (AAE ≤ 1.4) and the upper limit of the BC and OC mixture (AAE ≤ 1.7). Any AAE(405/781) > 1.7 requires the presence of BrC. We derive several relationships between AAE, SSA, BC fractions, and an imaginary part of BrC refractive index of ambient fires.


Introduction
Biomass burning produces light-absorbing aerosol containing a mixture of black carbon (BC) and organic carbon (OC). When OC absorbs more strongly at the blue end of solar spectrum than at the red end, it is called brown carbon (BrC) due to its brownish appearance. The exact configuration of BC and OC within the aerosol is highly variable over geography and time. To represent realistically the radiative properties of such composite aerosols in climate models is not an easy task. Furthermore, the amount and the chemical composition of BrC emitted is unknown and it is often inferred from measured optical properties of mixed carbonaceous aerosols.
A mixture of materials can exist as an external mixture, where there are separate particles of BC and OC, or as an internal mixture, where the BC and OC are within one aerosol particle. The internal mixture can be either quasi-homogeneous or it can have a specified heterogeneous structure. The optical properties of homogeneous internal mixtures are usually characterized by an effective refractive index. There are several prescriptions, called mixing rules (e.g., Chylek et al., 1988;Chylek & Srivastava, 1983;Videen & Chylek, 1998), that provide means to calculate the effective refractive index of the mixture given the refractive indices and volume fractions of the individual components. The simplest mixing rules use volume-fraction-weighted averages of the individual refractive indices or dielectric constants. A little more complicated are the Bruggeman (1936) and Maxwell (1904) mixing rules based on the mean field theory with different geometrical distribution of individual components. The effective refractive index is expected to transform a complex untraceable situation with many different particle shapes, compositions, and morphologies into an easily manageable case where complex structures are represented by a single complex parameter called the effective refractive index. This is an ad hoc mean state treatment rather than approximation in a mathematical sense where the accuracy can be estimate by considering contributions of neglected terms (Chylek et al., 2000).
A heterogeneous internal mixture is usually represented by a core containing BC surrounded by a shell of less absorbing material (e.g., Kanngiesser & Kahnert, 2018). Although this core-shell model seems to be in agreement with our mental picture of the aged biomass burning aerosols, its disadvantage is an increasing number of free parameters, and results which do not seem to rank this model much better than a simple homogeneous sphere model China et al., 2015;Curci et al., 2019;Kahnert et al., 2012;Lesins et al., 2002;Schuster et al., 2016). Although theoretical method to obtain scattering characteristics of nonspherical particles and particle groups are available (e.g., He et al., 2016;Mishchenko, 2014;Mishchenko et al., 1995;Videen et al., 1995Yang et al., 2019, we concentrate in the following analysis on the simple Mie scattering model. Lesins et al. (2002) compared optical properties calculated using internal mixtures where the effective refractive index was obtained using different mixing rules. The conclusion was that for the case of BC and OC, the different mixing rules have a minor effect on the derived optical properties. The results varied within 5% from each other, and the volume averaging of refractive indices was found to be a reasonable approximation. The differences between optical properties of a homogeneous sphere with an effective refractive index and the layered sphere model were within 20%. Similar results were obtained by Kahnert et al. (2012). They found that the volume averaging of refractive indices works reasonably well, only slightly worse than the Maxwell-Garnett mixing rule. In addition, Kahnert et al. found that the homogeneous sphere model provided more accurate results than the layered sphere model. Similarly, Torok et al. (2018) suggested that soot core and coating is not a good model for laboratory-produced soot. China et al. (2015) investigated soot particles transported over long distances. Particle sizes and shapes were determined using electron microscopy. They found over 70% of particles to be highly compacted with only about 25% having a core-shell geometry. The radiative forcing estimate using a simple Mie scattering calculation was within 12% (China et al., 2015) of that using the discrete dipole approximation (Draine & Flatau, 1994). Fierce et al. (2017) found that a fully mixed approximation provides an accurate estimate of the scattering coefficient, but overestimates absorption. Several investigators analyzing Brazilian biomass burning aerosols (Martins et al., 1998;Schmid et al., 2009) concluded that aerosols from the Amazon Basin are reasonably spherical with the dominating diameter between 200 and 500 nm (Rissler et al., 2006;Schmid et al., 2006;Schmid et al., 2009). Curci et al. (2019) tested several combinations of external and internal mixing. One test consisted of homogeneous mixing of all species including BC. Another test included a core-shell configuration. Although they considered the first model unrealistic and the second physically plausible, the results of those two tests were very similar. Thus, there is no clear evidence that more complicated models provide better approximations to the optical properties of biomass burning smoke than simple homogeneous particles with an effective refractive index and spherical geometry. Bahadur et al. (2012) demonstrated that BrC is an important component for absorption of solar radiation. As such, BrC can potentially alter the direct radiative forcing by aerosols. The strength of the absorption of BrC is determined by the imaginary part of its refractive index. Chakrabarty et al. (2010) found in laboratory experiments the imaginary part of BrC smoke refractive index to be 0.015 for ponderosa pine and 0.0076 for Alaskan duff. Similarly, Sumlin et al. (2018) reports imaginary part of BrC refractive index at 375 nm to be 0.014. On the other hand, Kirchstetter et al. (2004) reported an imaginary part of BrC refractive index based on an analysis of biomass burning laboratory samples to be 0.112 at 400 nm, an order of magnitude higher than Chakrabarty's values. Similarly, high values of absorption near 400 nm were found by Barnard et al. (2008). Wang et al. (2014) summarized results of several research groups reporting the range of the imaginary part of the refractive index of BrC near 400 nm to be within the range of 0.01i to 0.20i. Sengupta et al. (2018) reports even a larger span of imaginary part of refractive indices of bulk biomass burning organic aerosols at 400 nm starting around 0.002i. Thus, the imaginary part of refractive index of BrC, which determines the strength of absorption of BrC near the blue end of solar spectrum, is uncertain by several orders of magnitude. This uncertainty due to absorption strength of BrC is much higher than a potential uncertainty due to mixing rules (~10%) or due to the specific morphology of carbonaceous aerosol particles (~50%). The goal of the following analysis is to deduce the imaginary part of the BrC refractive index at the blue end of solar spectrum, especially for smoke from southwestern U.S. forest fuels, using a simple Mie scattering model.

The Model
In the following, we use BC as a generic name for the soot with various degrees of carbonization reflected by specified values of the BC refractive index. The degree of carbonization depends on various factors including the material burned (chemical composition, water content, etc.), the temperature and the nature of the flame (smoldering or flaming), and on other environmental and laboratory factors. Although the absolute values of the imaginary part around 0.5 has been frequently used, some laboratory measurements (Habib & Vervisch, 1988) as well as analysis of biomass burning fires (Schmid et al., 2009) found values of an imaginary part of the refractive index of BC to be much lower (0.2 to 0.3), while others recommend much higher values up to 0.79 (Bond and Bergstrom, 2007). We consider values of the imaginary part of BC refractive index within the range between 0.1 and 0.5 as well as the value of 0.79. We find that 0.3 is the value compatible with most of the biomass burning plumes reported here. Thus, the assumption of BC refractive index of 1.5-0.3i for ambient fires can be considered a part of our model specification.
The OC is considered to have a refractive index that is a constant across the visible part of the solar spectrum. We take the real part of refractive index of OC to be n = 1.46 according to the analysis of Schmid et al. (2009). BrC is a special form of OC that absorbs sunlight with an imaginary part of the refractive index that is higher (in absolute value) at shorter blue wavelengths than at the red end of the solar spectrum. This higher absorption at blue wavelengths is responsible for the brownish appearance of some biomass burning plumes.
In creating a model of the biomass burning plumes, we keep simplicity in mind. A very complex model with many free (unknown) parameters may be less useful than a simple model with a minimum number of free parameters. A simple model may provide insights into relationship between different plume parameters that might not be apparent using a more complex model. We try to find a proper compromise between simplicity and accuracy.
Some of aerosol particles are nonspherical, especially from fresh combustion sources. However, averaging over all possible sizes, shapes, and orientations, together with biomass burning plume atmospheric aging, the spherical particle approximation is brought closer to reality. In addition, any model based on a given observed shape and composition captures just one specific configuration among many different possibilities and there is no guarantee that this one particular model will be closer to an average of all possibilities than a simple homogeneous spherical case. Considering complications by scattering and absorption by nonspherical and heterogeneous particles compared to the simplicity of the Mie scattering model, a simple model is justified among a collection of more complicated alternatives. Furthermore, these simple Mie codes are used in standard Intergovernmental Panel of Climate Change-class climate models and more complex core-shell models are usually used to evaluate sensitivities. We stress that core shell analysis is appropriate for the analysis of laboratory data such as Cross et al. (2010) where the configuration is well characterized and coating thickness and core size are systematically explored. It is also important to recognize that BC morphology and mixing is much more complex and variable with sources and regions. For example, field data in Sacramento, Fresno, and Fontana, California show a low absorption enhancement by coatings  while some others are reporting large enhancement (Liu, Scheuer, et al., 2014). Concerning the state of modelling, Cappa et al. (2019) suggest that the amount of coating is likely overestimated by models and that the mixing-induced absorption enhancement (spherical core-shell model) might be overestimated to an even greater extent. A recent paper (McClure et al., 2019) reports a negligible coating enhancement in laboratory experiments.
We therefore decided to base our parsimonious model (a compromise between simplicity and accuracy) on an internal mixture of BC and OC with an effective refractive index of a mixture obtained by volume averaging of the refractive indices of its components. The scattering characteristics are obtained using the Mie scattering formulation assuming a spherical geometry. A similar Mie scattering model was used, for example, by Feng et al. (2013), Lu et al. (2015), and Romonosky et al. (2019).
The effective refractive index, m eff , of an aerosol particle will be given by where m BC is a complex refractive index of BC, m OC is a refractive index of OC, and f is a volume fraction of BC. The OC with a stronger absorption at the blue end of the spectrum than at the red end is called the BrC, and its refractive index at the blue end of spectrum will be denoted m BrC .

Absorption Ångström Exponent
The absorption Ångström exponent (AAE) has been generally used to characterize the wavelength dependence of the slowly changing aerosol absorption. AAEs have been found useful in the classification of aerosols according to their origin, to distinguish between urban aerosol, biomass burning aerosols, or desert dust (e.g., Russell et al., 2010). We approximate the AAE between the two wavelengths λ 1 and λ 2 by where λ 1 and λ 2 are the two wavelengths at which the AAE is calculated and the b absλ1 and b absλ2 are the absorption coefficients at the selected wavelengths λ 1 and λ 2 . In this report, we will be working with the wavelengths at 405 and 781 nm determined by instruments we use (Gomez et al., 2018;Romonosky et al., 2019). Our phase space is defined by two variables: the AAE and a single-scattering albedo (SSA) at the wavelength 405 nm given by where b scat and b ext are the scattering and extinction coefficients.
Whenever we use the SSA or AAE without designating specifically which wavelengths are being used, it should be understood that we mean 405 nm for SSA and 405 nm and 781 nm for AAE.
From equation (2), it follows that which is approximately satisfied for small particles within the Rayleigh scattering regime where absorption varies with wavelength approximately as 1/λ and wherever else by chance equation (5) is satisfied. Thus, some of the earlier statements (e.g., Kirchstetter et al., 2004;Lack et al., 2008;Lack & Landridge, 2013;Lewis et al., 2008;Liu et al., 2015;Moosmuller et al., 2009;Russell et al., 2010) that AAE = 1 for BC or BC and OC mixture are generally not exact (Liu et al., 2018).
The definition of AAE by equation (2) allows us to derive an interesting relationship between AAE at some value babsλ 1 babsλ 2 and twice its value, . Following the definition of the AAE (equation (2)), we can write for the case when absorption is doubled at the wavelength λ 1 If we select the wavelengths in such a way that their ratio λ 1 /λ 2 = 1/2, for example 400 and 800 nm, we get and 10.1029/2019JD031224

Journal of Geophysical Research: Atmospheres
Thus, in the case when absorption of aerosol particle at the shorter wavelength is doubled, and when the ratio of the wavelengths is exactly equal to 2, each doubling of absorption at the blue end increases the AAE value by one unit.
This (equation (7)) is an important new relationship derived just from the basic definition of the AAE approximation given by equation (2). For practical application, consider the case when, for example, AAE~6 is observed. Using equation (7), we can immediately deduce that the absorption of aerosol particle at the blue end is approximately 2 6 times stronger that absorption at the red end. In general, the derived relations (6-8) can be used to estimate the rate of absorption increase at the blue end of the spectrum from a measured value of AAE.
In our case, the wavelength ratio is not exactly 2, but 781/405 = 1.93. The increase of AAE with each doubling of the blue end absorption is then Sometimes, a different set of wavelengths are used to calculate AAE ( Figure 1). The relationship between AAE at different sets of wavelengths can be written as

BC and AAE
One of the fundamental properties of BC (soot) is its refractive index. Since BC is produced by burning organic material, it is understandable that the refractive index of BC depends on how the BC was  (8)).
produced. It depends on the material being burned as well as on the process and environmental conditions during the burning. Thus, a wide range of values have been reported in the published literature. Although the BC refractive index m = 1.5-0.3i has been defined as a part of our Mie scattering model, we will consider BC refractive indices with the real part of 1.5 and imaginary parts between 0.1i and 0.5i. In addition, we also use the BC refractive index of 1.95-0.79i as recommended by Bond and Bergstrom (2007) and used in climate models.
The SSA at a given wavelength of a spherical homogeneous particle depends on the refractive index and on particle size. Extensive discussions of this have been recently given by Sorensen et al. (2019) and by Sorensen (2018a, 2018b). Figure 2a shows SSA at 405 nm for several refractive indices of BC with diameters of the spherical particle from 10 to 500 nm. Figure 2b shows AAE(405/781) as a function of SSA(405) for the same BC particles.
In general, AAE = 1 for small particles within the Rayleigh limit, where absorption varies with wavelength as 1/λ. Thus, AAE = 1 is a good approximation for small BC particles regardless of their refractive index and morphology. For particle sizes outside of the Rayleigh limit, AAE increases with increasing particle size ( Figure 2b) until it reaches a constant or slowly varying value of SSA ( Figure 2a). Then, AAE falls sharply (Figure 2b), passing through the value of AAE = 1 again at a specific size, which is different for each refractive index value. At this point, the ratio of absorption at the two considered wavelengths is equal to the reciprocal of the wavelength ratio. We note that for the considered range of refractive indices, AAE(405/781) for BC never reaches values over 1.4.
Thus, we set the upper limit on AAE(405/781) of BC to be Our upper limit of BC AAE is the same as that that of Lack and Landridge (2013) of 1.1 ± 0.3. However, the lower AAE limit is a sensitive function of the refractive index and can be as low as zero (Figure 2b) for particle diameter ≤500 nm.
Given a real part of refractive index of BC, for each value of the imaginary part, there is a maximum value of SSA which a small spherical particle of that BC can reach. This provides an opportunity to estimate the imaginary part of the refractive index (assuming that the real part is known) of BC from the maximum SSA value (Figure 2b). For example, the samples used in laboratory measurements by Romonosky et al. (2019) and shown in their Figures 3 and 4, suggest by comparison with our Figure 2, the imaginary part of the refractive index close to 0.5i for BC, and close to 0.2i for nigrosin.
We also note that SSA and AAE properties of spherical particle with the refractive index of 1.95-0.79i are close to a particle with the index 1.5-0.3i ( Figure 2). Consequently, only the SSA and AAE values for BC may not be able to distinguish between these pairs of refractive indices.
Several published papers suggested that the AAE = 1 for "pure" BC. It has been shown that this assumption may produce a considerable uncertainty in produced results (Lack & Landridge, 2013). Others proposed the AAE of BC to be <1 (e.g., Zhang et al., 2018). The larger BC particles (or aggregates of small particles) may have indeed the AAE values <1 depending on their diameter and refractive index ( Figure 2b). Thus, both past claims are valid within specified particle size regions. Of course, as with each AAE value, the two wavelengths used need to be specified (405 and 781 nm in our case).

BC-OC in Internal Mixture
We now consider a mixture of BC with OC or water. We define OC as a material that does not absorb visible and near ultraviolet solar radiation. The goal is to determine the region of AAE(405/781) and SSA(405) phase space that can be occupied by this BC and OC mixture. In Figure 3, we show cases of several refractive indices of BC to explore across the range of possible AAE/SSA values. The first two points on each curve ( Figure 3) are values of AAE and SSA for a diameter of a spherical particle of 10 and 50 nm. After that, the diameter increases in 50 nm steps up to 500 nm. The advantage of showing individual points is to retain the size related information, which would be lost if only smooth curves were presented.
A small amount of BC (1%) mixed in water (m = 1.33) or OC (m = 1.46) is characterized by a high value of the SSA(405) and by an AAE that approaches 1.4 for water ( Figure 3a) and slightly over 1.6 for OC ( Figure 3b).
With an increasing concentration of BC, both the SSA and the AAE decrease. We note that the AAE, in the case of a mixture of BC and spectrally flat OC materials, never increases above about 1.63. This remains true even if we change the real part of refractive index of BC to 1.7 (Figure 3c) or change the imaginary part to 0.3 (Figure 3d), or if we adopt the refractive index of 1.95-0.79i. Thus, in agreement with earlier publications (Lack & Cappa, 2010;Romonosky et al., 2019;Zhang et al., 2018), and rounding to the higher one decimal place number, we conclude that the AAE(405/781) of a mixture of BC and spectrally flat organic material is limited by The same limit was deduced by Lack and Cappa (2010) using an aerosol particle model of a layered sphere with a BC core and a spherical shell of nonabsorbing or slightly absorbing material. In our work, this limit is a result of a simple Mie scattering by a homogeneous spherical particle and does not require a coreshell model.
In our model of internal mixture of BC and OC with spectrally flat refractive indices, the AAE values >1.7 cannot be reached. To explain AAE values larger than 1.7 with BC and organic material only (excluding mineral dust and other inorganic material), we need at least one of the materials present to have a higher imaginary part of the refractive index at the blue end of the solar spectrum than at the red end. An organic material with a higher imaginary part of the refractive index at the blue end of the spectrum is known as BrC. Thus, for AAE values >1.7, BrC is a required component of the material mixture.
AAE generally increases with increasing diameter (Figure 3). Larger than some characteristic diameters, SSA changes only slightly or remains constant with increasing diameter, and the AAE value falls sharply. The value of the SSA at this downward turn characterizes a maximum value of the SSA which the corresponding mixture of BC and OC can achieve. Thus, each mixture of BC and OC can be characterized by a maximum value of the SSA it can reach. Therefore, the maximum SSA of a mixture can be used to estimate the percent of BC involved in the mixture (Figure 3), assuming the refractive index of BC is known.

BC-BrC Mixture
In   Chakrabarty et al., 2010;Liu, Scheuer, et al., 2014;Romonosky et al., 2019). These values AAE >1.7 cannot be explained without BrC. Here, we refer to BrC as an OC which has absorption at the blue end of the spectrum (in our case, at 405 nm) higher than the absorption at the red end (at 781 nm).
AAE(405/781) values for cases of BC refractive indices 1.5-0.5i, 1.5-0.3i, and 1.5-0.1i in 1% and 5% mixture with BrC are shown in Figure 4. The increasing BrC absorption is simulated by an increasing imaginary part of an effective refractive index at 405 nm. The right-hand column in each panel shows the chosen imaginary part of an effective refractive index of the mixture at 405 nm. The lowest imaginary part of an effective refractive index in each panel is given by the internal mixture of BC and OC only. After that, the imaginary part of an effective refractive index is doubled as the absorption of the organics at 405 nm is increased. With each doubling of the imaginary part of an effective refractive index, the AAE(405/781) increases by 1.05 (equation (8)). At the same time, the SSA at the short wavelength decreases. This decrease of the SSA is faster with higher BC fraction and with the higher absolute value of the imaginary part of effective refractive index (Figure 4).
The observed AAE(405/781) values of around 6 together with a SSA(405) of over 0.9 require special consideration. With the BC refractive index of 1.5-0.5i, when we reach AAE around 6, the SSA has already decreased to well below 0.55 (Figure 4a the top curve). It is clear that this BC refractive index (1.5-0.5i) cannot explain the observed high values of AAE (AAE > 6), and at the same time, the high values of SSA (SSA > 0.9). In this case, we need BC with a much smaller imaginary part of refractive index. Figure 4c shows the case of 1% BC with a refractive index of n = 1.5-0.1i. A high value of AAE~6 is reached while the SSA remains around 0.9. Thus, the observed high values of AAE > 6 require, within the range of refractive indices considered, a small amount of BC (≤1%) with a small imaginary part of BC refractive index, not larger than 0.1.
In general, the pair of values of the SSA(405) and the AAE(405/781) (Figure 4) determines the imaginary part of the effective refractive index of an internal mixture of BC and BrC (right hand column in each panel of Figure 4). Using the deduced imaginary part of an effective refractive index and the mixing rule (equation (1)), the imaginary part of the refractive index of BrC can be calculated. When there are more than one possible solutions for a given pair of the SSA and the AAE (e.g., Figures 4a and 4f), they lead to the same (or very close to each other) values of the imaginary part of refractive index of BrC (Table 1).

Biomass Burning Ambient Fires
There have been many laboratory measurements and field data analysis leading to the estimate of an imaginary part of refractive index of BrC. The deduced range spans from 0.01 to about 0.2 at short wavelength (Kirchstetter et al., 2004;Alexander et al., 2008;Wang et al., 2014;Saleh et al., 2013Saleh et al., , 2014 Table 1. To deduce the parameters of internal mixtures from their mean values of AAE(405/781) and SSA(405), we divide the mixtures into different bands according to the AAE values. We already know that for AAE <1.7, we do not need any BrC to obtain an agreement between the observations and model results. Let us consider first the AAE band between 2.7 and 3.7. There is only one biomass burning plume (Whitewater Baldy; WWB) that has a mean value of the AAE within this band (Table 1). To approximate the maximum value of SSA for each curve in Figure 4, we average SSAs for particle diameter 300 ≤ d ≤ 500 nm (the last five points on each curve in Figure 4). The same procedure is followed for AAE values between 1.7 and 2.7.
The model estimated maximum SSA for a selected set of BC refractive indices (1.5-0.5i, 1.5-0.3i, and 1.5-0.1i) and selected set of BC volume fractions (1, 3, and 5%) is shown in Figure 5. The observed mean SSA of the considered ambient biomass burning fire can be matched with one of the modeled SSA. This determines the effective refractive index of the aerosol particles (the second row of panels in Figure 5). Using the mixing rule (equation (1)), the imaginary part of refractive index of BrC is now obtained (the third line of panels in Figure 5).
A large portion of biomass burning fires are smoldering fires. Thus, the imaginary part of refractive index of BC is expected to be relatively low. We use the BC refractive index of 1.5-0.3i for the following analysis of ambient biomass burning fires. This relatively low imaginary part is close to the imaginary part of the BC refractive index of 0.2i deduced from observation of Amazonian plumes (Schmid et al., 2009) or laboratory-produced methane soot with an imaginary part of refractive index of 0.3i (Habib & Vervisch, 1988).
There is not a unique value of the BC refractive index that should be used for all biomass burning fires. The power of BC to absorb solar radiation, characterized by the imaginary part of its refractive index, depends on the material being burned and on the form of burning. When carbonization is not complete, the imaginary part of refractive index of BC is lower than the value expected for fully carbonized BC.
The AAE(405/781) and SSA(405) values of several southwestern fires (Las Conchas, WWB, Buzzard, Ute Park, and San Antonio) are shown in Figure 6. Details concerning these fires can be found in Romonosky et al. (2019). The Las Conchas fire data were divided into two groups according to a high or low AAE value. In addition to biomass burning fires, we consider the results of two major Department of Energy (DOE) Atmospheric Radiation Measurements Climate Research Facility field programs, namely GOAmazon (Martin et al., 2017) and the LASIC (Zuidema et al., 2018). GOAmazon data were collected at ARM's field site in Manacapuru, Amazon, during the 2014 dry biomass burning season. The LASIC data sampled African biomass burning plumes that have aged over a timescale of a few weeks. The southwestern plumes were observed within a few hours after the smoke emission.
The mean values of the SSA of the southwestern fires are clustered near SSA(405) = 0.9 ± 0.1. However, their AAE(405/781) varies significantly with mean values between 1.4 and 3.3, indicating different amounts or different properties of BrC present.
The two field programs (GOAmazon and LASIC) show lower SSAs than the U.S. southwestern fires. The lowest value of the SSA = 0.79 is observed for the LASIC campaign. Here the African biomass burning smoke is analyzed a few weeks after emission in the middle of southern Atlantic at Ascension Island (Zuidema et al., 2018). During the transport, aging, and modification, the OC (including BrC) can be removed, which leads to a higher fraction of BC, lower SSA, and lower AAE values ( Figure 6). The three plumes with mean AAE >1.7 (San Antonio, Las Conchas 1, and WWB) indicate the presence of the BrC. Following the procedure described, we estimate a fraction of BC in the mixture using the observed range of the AAE(405/781) and the mean value of the SSA(405). This is followed by determination of the imaginary part of an effective refractive index of a mixture and calculation of an imaginary part of a complex refractive index of BrC. The results are summarized in the last column of Table 1. The LASIC data taken in the middle of south Atlantic might contain some sea salt with much different chemical composition and radiative properties (Ma et al., 2008;Winter & Chylek, 1997). However, most of the sea salt was likely eliminated by considering aerosol particles below 1 μm diameter. The three datasets (Ute Park, Buzzard and Las Conchas 2) do not require any BrC to explain their SSA and AAE values. This does not, however, preclude the presence of some BrC. To estimate an absorbance of a potentially present BrC, we have increased the imaginary part of an effective refractive index of internal mixture, Im (m eff ), by 30% to estimate an imaginary part of refractive index of potentially present BrC (last column in Table 1).
The deduced imaginary part of the refractive index of BrC in ambient biomass burning fires (Table 1) is at the lower end of previously reported data (e.g., Wang et al., 2014). However it is consistent with results reported by Chakrabarty et al. (2010), Lack et al. (2012), Feng et al. (2013), and Cappa et al. (2019). The imaginary part of an effective refractive index of aerosol particle, Im (meff) in Table 1, from 0.015 to 0.022, is also comparable to the range of the imaginary part of aerosol particle refractive indices, from 0.010 to 0.021, derived from AERONET data for biomass burning regions of Africa and South America (Dubovik et al., 2002).
After finishing our analysis using BC refractive index of 1.5-0.3i, we repeated the whole process now using the refractive index of 1.95-0.79i. The final results, the imaginary part of refractive index of BrC, was found to be almost identical to those deduced using the BC index of 1.5-0.3i (Table 1). This can be understood from the equation for the imaginary part of BrC refractive index The volume fraction of BC, f, is in our cases usually <<1. Therefore, for a given m eff , as long as the product fIm(m BC ) remains about a constant, the Im(m BrC ) will change very little with changing imaginary part of refractive index of BC. It is only the total strength of BC absorption characterized by the product of the imaginary part of refractive index and volume fraction of BC which enters equation (12). As long as this product remains constant, the Im(m BrC ) will change very little. To determine the imaginary part of BC refractive index, we would need an independent measurement of the BC fraction present in biomass burning aerosol particles.

Journal of Geophysical Research: Atmospheres
Our result for the BrC refractive index assumes that all the organic mass is the BrC. This is similar to work of Lu et al. (2015). On the other hand, Feng et al. (2013) assumes that only 66% of the total OC mass is BrC. To compare our results with those of Feng et al., our imaginary part of refractive index of BrC has to be divided by 0.66.
A new DOE climate model, Exascale Earth System Model (E3SM), not yet perfectly tuned (Golaz et al., 2019;Rasch et al., 2019), was recently modified for major aerosol species production and transport including BC, primary organic aerosol (POA), and secondary organic aerosol (SOA). The ratios of vertical profiles of BC to OA (sum of POA and SOA) from the Amazon (September), LASIC (August-September), and southwestern fires in New Mexico (May-June) are provided in Figure 7. E3SM sensitivity simulations were conducted varying multigenerational chemistry of SOA precursors emitted from urban and biomass-burning sources. FRAG75 (75% fragmentation) and FRAG50 (50% fragmentation) represent simulations varying the fragmentation to functionalization branching ratio during aging of SOA precursors, as described in Shrivastava et al. (2015). POA to SOA represent a simplified treatment of POA that is converted to SOA assuming a 1-day aging timescale.

Relations Between Ambient Fires Parameters
Till now, we have considered each of the ambient fire individually without any relation to other fires. Now we look for similarities between all the considered biomass burning fires. Most of the fires considered were smoldering fires. Figure 8a shows a relationship between the SSA(405) and the percent of BC in

10.1029/2019JD031224
Journal of Geophysical Research: Atmospheres biomass burning aerosol particles. As expected, we observe that with increasing fraction of highly absorbing BC, the SSA decreases. The decrease is approximately linear with the relation between the SSA and BC given by where BC is a volume fraction of BC in percent. A similar linear relationship between the BC and SSA has been reported earlier by Pokhrel et al. (2016) by analysis of laboratory FLAME-4 measurements with quantitatively similar coefficients (0.91 instead of 0.942 and 0.0087 instead of 0.009).
Next we look for a relationship between the AAE(405/781) and the volume fraction of BC ( Figure 8b). All the points representing the observed fires form a curve approximated by the equation where again the BC stands for a BC volume fraction in percent.
Equations (13) and (14) provide "rather surprising but useful results" (Pokhrel et al., 2016), suggesting that the knowledge of the fraction of BC in the mixture allows us to estimate the SSA and the AAE. In our case, we have derived appropriate relations (13 and 14) from the ambient plumes fire observations while Pokhrel et al. (2016) derived similar relations from analysis of laboratory data.
The relation between the imaginary part of the BrC refractive index and the observed mean AAE(405/781) of the ambient fire data is given by Thus, the imaginary part of BrC refractive index increases approximately linearly with the observed AAE and decreases linearly with increasing fraction of BC. In another words, the imaginary part of BrC refractive index is anticorrelated to the volume fraction of BC present. This supports the idea that both the BC and BrC are produced by the same biomass burning mechanism with the BrC turning to the BC with increasing temperature of the flame, as suggested by Saleh et al. (2014Saleh et al. ( , 2018. The fact that these relations (equations (13) to (16)) were derived in our case from the SSA and AAE assigned to individual ambient fires based on a simple Mie scattering model suggests that the model works as expected describing correctly, even though approximately, the basic relationship between the individual smoke variables. AAE can be useful to estimate the fraction of BC in aerosol particle (Figure 8b). SSA can be useful for estimating fractions of BC ( Figure 8a). Both AAE and BC fractions can be used to estimate the imaginary part of BrC refractive index in ambient biomass burning fires (Figures 8c and 8d).

Laboratory Measurements
In our laboratory experiment, we performed 21 individual burns of Russian olive wood using the approach described by Romonosky et al. (2019). The absorption and scattering coefficients were measured with a photoacoustic soot spectrometer (Droplet Measurement Technologies PASS-3). Absorption and scattering data are reported at 1-min resolution, represented by individual data points in Figure 8 a. Each burn includes 20-40 min of data; individual burns are coded by different colors. Fuel for the burns was about 0.50 g of dried Russian olive branches ground with an electric coffee blade grinder and was comprised of pieces ranging from fine dust to 2-cm long "sticks" approximately 1-3 mm diameter. Burns were ignited with an electric resistance heater held over the fuel for 10 s. Aerosols emitted from the burns were sampled through a cyclone (URG-2000-30EHB) which removes aerosols greater than 1 micron in diameter.
Although the controlled conditions were the same for all the burns, the AAE/SSA data are scattered across a wide range of these two variables. This suggests that the conditions of burning not controlled in the experiments varied significantly, as discussed in detail by Romonosky et (2019). For example, at low ignition temperatures, the fire can start as smoldering and upon heating transition to flaming at the end. At the other limit at high ignition temperatures, the fire can start of as flaming and then transition to smoldering as it runs out of fuel. We are unable to control these environmental variables or the airflow rate. Our data does sample the complete SSA and AAE spectrum as shown in Figure 9a. From the 21 burns, 10 had mean AAE below 1.7 and 11 had AAE above 1.7. Thus, about 50% of experiments produced plume that contained BrC, while in the other 50%, the BC and OC were sufficient to explain the observed values.
The curves of ambient plumes and laboratory biomass burnings in the AAE/SSA space are not identical (Figure 9b) for laboratory data. While additive and multiplicative coefficients are not too different, it is the exponent of 0.12 and 0.43 that makes the difference between the ambient and laboratory samples.
In general, the ambient plumes' AAE is shifted towards the higher values of SSA compared to laboratory experiment. A shift in the direction of a higher SSA means less absorption. Since the BC is not removed from the aerosol particles, possible causes of lower absorption include the BC particles that grow by coagulation and collapse to larger sizes with lower specific absorption per gram and/or aging mixes BC with organics in the plume and other constituents in the ambient air. In the case of our laboratory burning experiments, there is a short time for coagulation and collapse and photochemical oxidation, while in the case of ambient fires, there are hours to days available for these processes to take place.
Furthermore, in laboratory experiments, the measurements are done within a few minutes after the burning. The structure of BC is likely highly nonspherical, and more complex models of optical properties of composite particles will be required.

Direct Radiative Forcing by Biomass Burning Aerosols
The aerosol direct radiative forcing by absorbing aerosols can be estimated from the expression derived by Chylek and Wong from a thin atmosphere limit of a radiative transfer equation Chylek & Coakley, 1974;Chylek & Wong, 1995;Coakley & Chylek, 1975;Hobbs et al., 1997) or from its later slight modification (Bond & Bergstrom, 2007). Here, ΔF is a change of radiative flux at the top of the atmosphere, S o is a solar constant, T atm is an average atmospheric transmission for solar radiation, N is the mean cloudiness, a is the surface albedo, and β is the upward scattering fraction. The τ sc and τ abs are the scattering and absorption optical depths.
As long as the direct radiative forcing will be negative and aerosol will cool the atmosphere. Within the Mie scattering model, the ratio of optical depths τabs = τsc can be calculated for a given BC refractive index, BC volume fraction, and an observed AAE value of the biomass burning plume. Figure 10 shows the K values (defined by equation (20)) as a function of the surface albedo. The up-scattering fraction is taken as β = 0.20 (Chylek & Wong, 1995). The ratio τabs = τsc is calculated for three AAE bands, for AAE < 1.7, 1.7 < AAE < 2.7, and 2.7 < AAE < 3.7, and averaged over the aerosol particle diameter between 300 and 500 nm. The warming occurs to the right of the solid black curve. As can be seen (Figure 10), the aerosols without BrC (AAE < 1.7) will warm the atmosphere over surface albedo a > 0.6, which is limited to surfaces covered by ice and snow. The biomass burning plumes with the 1.7 < AAE <2.7 will warm over the surface with albedo a > 0.45, and plumes with 2.7 < AAE < 3.7 will warm the atmosphere over the surface with albedo a > 0.25. Thus, to get a warming effect over a significant part of Earth surface, we need biomass burning plumes with AAE > 2.7, which are values not observed frequently in ambient fires. These limits on the surface albedo will change slightly when the up-scattering fraction β is changed between the estimated values of 0.16-0.26 (Bond & Bergstrom, 2007;Chakrabarty et al., 2016;Chylek & Wong, 1995;Hobbs et al., 1997). A similar discussion showing the dependence of the warming/cooling on the surface albedo was presented in Chylek and Coakley (1974).
Considering that the biomass burning ambient plumes observed with AAE > 2.7 are infrequent even within a few hours after the emission, and relatively short BrC lifetime (of the order of less than a day), the global long-term effect of BrC from large fire plumes with properties similar to those we have analyzed on climate is expected to be rather limited. In addition, our radiative forcing estimate is at the 405-nm wavelength, which represents the maximum forcing compared to other wavelengths of solar spectrum. At the longer wavelengths, the effect of BrC will be weaker and will diminish towards the red end of solar spectrum.
The BrC effect may have some direct radiative climate-related significance in geographically limited regions where the biomass burning is steady, like in regions where wooden stoves are used daily for cooking or heating purposes (Ahmed et al., 2018;Feng et al., 2013). The cooling/warming regime may also change by considering the semidirect and indirect aerosol effects (e.g., Jacobson, 2014), which are not considered in this study. The global direct biomass burning climate effects might also become significant in the case of disastrous continent-wide fires.

Conclusion and Summary
We used a simple model of biomass burning aerosol consisting of homogeneous spherical particles and volume mixing of refractive indices. This avoids introducing additional parameters needed for more complicated models that are often difficult to measure. This also simplifies climate model parameterizations of biomass burning aerosols.
We have shown that several known limits on the AAE values follow directly from the Mie scattering by spherical particles without any requirement of a more complicated structure, like a core-shell model. The mixture of BC and OC is limited by AAE ≤ 1.7. Any value of AAE above this limit requires the presence of BrC. Figure 10. A direct brown carbon radiative forcing causing a cooling or a warming of the atmosphere depending on the surface albedo and on the absorption Ångström exponent (AAE) of the biomass burning plume. The calculation shown is for the blue end of the solar spectrum at the wavelength of 405 nm, average for particle diameters from 300 to 500 nm, for the BC refractive index of 1.5-0.3i and the BC volume fraction of 5%. K stands for expression defined by equation (20). Other choices of parameters will change the K-curve only slightly. The warming occurs on the right hand side of the K curve, and cooling on the left-hand side. The colored dash lines represent the AAE smaller than 1.7 (red), between 1.7 and 2.7 (blue), and between 2.7 and 3.7 (black). Although plumes with the AAE > 2.7 will cause warming over surfaces with a > 0.25, such plumes are rare.
Similarly, we find that AAE limit for pure BC is AAE ≤ 1.4. The frequently used assumption of AAE = 1 is generally valid for small aerosol particles in Rayleigh scattering limit.
We have derived quantitative relations (equations (13)-(16)) between the values of the AAE, BC fraction, and the imaginary part of refractive index of BrC, using ambient plumes field observations. In the case when the ratio of the two wavelengths used in an approximation of AAE (equation (2)) is equal to 2, the AAE increases by one unit with each doubling of the imaginary part of an effective refractive index of a particle (equation (7)).
The current spread of reported values of the imaginary part of BrC refractive index ranges from 0.01 to about 0.20. The values we obtain using Mie scattering model are close to the lower edge of published range consistent with studies of BrC effects by Chakrabarty et al. (2010), Lack et al. (2012), Feng et al. (2013), and Cappa et al. (2019). We also show that aged ambient plumes have larger SSA for a given value of AAE than laboratory experiments (Figure 9).
Finally, our study reduces the range of potential global direct radiative forcing by BrC from large fire episodes and shifts it to lower impacts. Based on our results, positive climate forcing due to BrC is rather limited due to its low imaginary part of refractive index, short lifetime, and infrequent occurrence. A globally significant radiative forcing by BrC would require persistent large-scale biomass fires along with high AAE values and sufficiently high surface albedo. More probable, BrC significance may be relegated to local and regional effects due to limited lifetime, typically lower AAE values in real plumes, and the episodic nature of wildland fire. The BrC may be responsible for a local and regional climate modification. The indirect aerosol effects (aerosol cloud interaction) are clearly much more complicated and uncertain (Jacobson, 2014). The OC that is much more abundant than BC is likely to play an important role.