The Aethalometer model has been used widely for estimating the contributions
of fossil fuel emissions and biomass burning to equivalent black carbon
(eBC). The calculation is based on measured absorption Ångström
exponents (

Incomplete combustion of organic fuels results in emission of
light-absorbing carbon (LAC) particles that contain both black carbon (BC)
and brown carbon (BrC). BrC is light-absorbing organic matter in atmospheric
aerosols of various origins, e.g., soil humics, humic-like substances
(HULIS), tarry materials from combustion, and bioaerosols (Andreae and
Gelenscer, 2006; Laskin et al., 2015). BrC can significantly absorb solar
radiation in the ultraviolet–visible (UV–Vis) wavelength range (

The absorption coefficient

One of the instruments used for measuring black carbon concentrations is the
Aethalometer that collects aerosol on a filter tape, measures changes in
light attenuation in the wavelength range of 370–950 nm, and calculates the equivalent black carbon (eBC) concentrations. The data are used also to
calculate

The interpretation of

The aim of this study is to estimate uncertainties of the
Aethalometer-model-derived fractions of absorption by eBC from fossil fuel
and biomass burning when spherical BC cores are coated by some non-absorbing
material. To state this more clearly, it is assumed that there is only one
type of BC particles that can be called fossil fuel BC in the Aethalometer
model terminology. Consequently, any deviations from biomass-burning
fraction of BB %

The BC cores were assumed to be coated with an ammonium sulfate shell by
using two approaches. It was assumed (1) that the shell thickness is the same
for all particles in a size distribution (Fig. 1a) and (2) that the core
volume fraction is the same for all particles in a size distribution (Fig. 1b). The core volume fraction was calculated from

Examples of particles and size distributions used in the
simulations:

Lognormal size distributions

Absorption coefficients were calculated from

Nomenclature.

For the absorption due to particles from wood burning or biomass burning,
Zotter et al. (2017) give the equation

The absorption Ångström exponent

Absorption Ångström exponent (

The first approach (Fig. 2a, c, and e) shows that when

The visualization of

The visualization also shows that the

For single particles

Unimodal particle size distributions with a size-independent shell
thickness (

The results are first shown as a function of

Both for single particles and size distributions the first maximum of

Size distribution dependence of the first maximum of

Examples of the growth of a non-size-dependent scattering shell on
BC core size distributions with

This approach is further followed by plotting the parameters as a function
of shell thickness for three different BC core diameters, 50, 70, and
90 nm of single particles and core size distributions with the geometric
standard deviations of

The number-weighted

The referenced studies show that the

After reaching the first maximum,

As

Figure 5 can also be considered a proxy for a time series of the
development of

The second approach is to assume that the BC core fraction – or
equivalently the shell volume fraction – is the same for all sizes, which
means that the shell thickness increases with size as was visualized in Fig. 1b. This can be considered to be a result of aging of BC by not only
condensational growth but also by cloud processing. The latter would lead to
thick shells on particles activated into cloud droplets that would absorb
for instance SO

Unimodal particle size distributions with size-independent shell
volume fractions

In this approach the geometric standard deviations of the whole size
distributions were set to

Several observations can be made from Fig. 6. One of them is that the
isoline of

Size-dependent sensitivity of

The last observation leads to calculations of size-dependent sensitivities
of

Another step for visualizing the sensitivities was taken by calculating
size-dependent average sensitivities of

According to Eq. (2) the

Bimodal particle size distributions with size-independent shell
volume fractions

Finally, bimodal size distributions are examined briefly. The size
distributions consist of two externally mixed modes that have different
shell volume fractions. In both modes the shell volume fractions are
size-independent as in Fig. 1b. Mode 1 is an Aitken mode with the geometric
mean diameter

The results show that

The purpose of this study is not to claim that all Aethalometer model results are wrong but that they have higher uncertainties than have been discussed in the literature. It is clear that there are BrC particles that have absorption Ångström exponents clearly larger than 1, as shown in a very large number of publications. However, the size of light-absorbing particles and their coating even by purely scattering material clearly affect the wavelength dependence of absorption and thus have the potential to affect the Aethalometer model results. Since the wavelength dependency is used for source apportionment, these effects have the potential to result in contributions of wood-burning or fossil fuel emissions that are tens of percent too high or low.

There are some important results. In the modeling,

The goal of the paper was not to find out whether some pair of

There are obvious limitations in this study. A core–shell Mie model was used only so the work is limited to spherical particles. Fresh BC particles are usually agglomerates. There are studies that show that during aging processes these agglomerate may collapse and become closer to spherical particles, so Mie modeling probably agrees better for aged than fresh BC particles. Further, even if particles were spherical, how well can they be modeled with a Mie code when they are collected on filters? Or does light absorption then follow the spectral absorbance of the bulk materials?

This question could in principle be answered by generating spherical BC
particles, coating them in an aging chamber with some non-absorbing
material – for instance ammonium sulfate, and measuring both light absorption
at multiple wavelengths with an Aethalometer and BC core size distributions
and shell thicknesses with an SP2. If

On the other hand, if none of these effects were observed and the absorption
Ångström exponents of the collected particles were

The code is described in Voshchinnikov and Mathis (1999) and it is available in

The data can be generated as described in Sect. 2. No real data were used in this paper.

The supplement related to this article is available online at:

The author declares that there is no conflict of interest.

This article is part of the special issue “Satellite and ground-based remote sensing of aerosol optical, physical, and chemical properties over China”. It is not associated with a conference.

This research has been supported by the Academy of Finland via the projects NABCEA (grant no. 296302) and ACFA (grant no. 335845) and by Business Finland via project BC Footprint (grant no. 528/31/2019).

This paper was edited by Linlu Mei and reviewed by two anonymous referees.