Light-absorbing organic matter, known as brown carbon
(BrC), has previously been found to significantly enhance the absorption of
solar radiation by biomass burning (BB) aerosol. Previous studies have also
proposed methods aimed at constraining the BrC contribution to the overall
aerosol absorption using the absorption Ångström exponents (AAEs)
derived from the multi-wavelength remote observations at Aerosol Robotic
Network (AERONET). However, representations of the BrC absorption in
atmospheric models remain uncertain, particularly due to the high
variability in the absorption properties of BB organic aerosol (OA). As a
result, there is a need for stronger observational constraints on these
properties. We extend the concept of the established AAE-based methods in
the framework of our Bayesian method, which combines remote optical
observations with Monte Carlo simulations of the aerosol absorption
properties. We propose that the observational constraints on the absorption
properties of BB OA can be enhanced by using the single-scattering albedo
(SSA) as part of the observation vector. The capabilities of our method were
first examined by using synthetic data, which were intended to represent the
absorption properties of BB aerosol originating from wildfires in Siberia.
We found that observations of AAEs and SSA can provide efficient constraints
not only on the BrC contribution to the total absorption but also on both
the imaginary part of the refractive index and the mass absorption
efficiency of OA. The subsequent application of our method to the original
multi-annual data from Siberian AERONET sites, along with the supplementary
analysis of possible biases in the a posteriori estimates of the inferred
absorption properties, indicates that the contribution of BrC to the overall
light absorption by BB aerosol in Siberia at the 440 nm wavelength is most
likely to range, on average, from about 15 % to 21 %, although it is highly
variable and, in some cases, can exceed 40 %. Based on the analysis of
the AERONET data, we also derived simple nonlinear parameterizations for the
absorption characteristics of BB OA in Siberia as functions of the AAE.
Introduction
Organic compounds constitute the dominant fraction of carbonaceous particles
emitted into the atmosphere from open biomass burning (Reid et al., 2005b;
Andreae, 2019). This aerosol fraction, which is also ubiquitous in other
types of carbonaceous aerosol and is conventionally termed organic aerosol
(OA), effectively scatters shortwave solar radiation, thereby providing a
considerable negative contribution to the direct radiative effect (DRE) of
atmospheric aerosol at both global and regional scales (e.g., Lin et al.,
2014; Sand et al., 2015; Hamilton et al., 2018). However, the light
scattering radiative forcing by OA is to some degree counteracted by the
light-absorbing organic compounds called brown carbon (Andreae and
Gelencsér, 2006), which is strongly absorbing in the UV and near-UV
wavelength ranges. Although the overall light absorption by brown carbon
(BrC) is typically weaker than the absorption by black carbon (BC), which is
usually the main absorbing component of carbonaceous aerosol emitted from
both biomass burning and fossil fuel combustion (Bond et al., 2013), it has
been estimated that BrC originating from all known sources provides a
considerable, albeit uncertain, positive contribution to the DRE that ranges
from 0.03 to 0.6 W m2 at the global scale (see, e.g., Wang et al., 2018,
and references therein; A. Zhang et al., 2020) and is comparable to a recent
estimate of the DRE of BC (0.18–0.42 W m-2) (Matsui et al., 2018). The
large uncertainty in the available estimates of the radiative effects of BrC
is indicative of the lack of sufficiently strong observational constraints
on the parameters quantifying the absorption properties of OA in chemistry
transport and climate models (Samset et al., 2018). As biomass burning is
known to be the major source of OA globally (Bond et al., 2013), a
significant part of the DRE and its uncertainty is likely associated with
biomass burning aerosol.
A key parameter controlling the contribution of BrC to the DRE estimated in
numerous modeling studies involving Mie theory calculations is the imaginary
refractive index (IRI) of OA (e.g., Feng et al., 2013; Lin et al., 2014;
Wang et al., 2014; Saleh et al., 2015; Wang et al., 2018; A. Zhang et al.,
2020). Some other modeling studies (Park et al., 2010; Jo et al., 2016)
have simulated the optical and radiative effects of BrC by assuming a linear
relationship between the OA emissions and BrC absorption and using
estimates of the mass absorption efficiency (MAE) of OA to quantify this
relationship. Therefore, modeling studies of BrC can benefit from stronger
observational constraints on either the IRI or the MAE of OA or both.
Reported estimates of the IRI of OA have mostly been derived from in situ or
laboratory measurements of the absorption coefficients, OA mass
concentration, and (in some cases) other parameters for carbonaceous
aerosol by using methods of varying complexity, each involving different
assumptions concerning the composition, physical and optical properties,
size distribution, and mixing state of the particles and their components
(e.g., Kirchstetter et al., 2004; Chen and Bond, 2010; Saleh et al., 2014;
Lu et al., 2015; Sumlin et al., 2018; Romonosky et al., 2019; McClure et
al., 2020). These estimates indicate, in particular, that the IRI of OA
originating from biomass burning is strongly variable, ranging from
virtually zero to almost 0.04 (at the 550 nm wavelength). Reported estimates
of the MAE of OA (e.g., Alexander et al., 2008; Favez et al., 2009;
Yang et al., 2009; Cheng et al., 2011; Chung et al., 2012a; Olson et al.,
2015) have been derived, albeit in a much simpler way, mostly from in situ
observations of the absorption coefficients and OA (or organic carbon, OC)
mass concentration and are also very diverse, differing by orders of
magnitude. Typically, such estimates involve strong assumptions about the
spectral dependence of the BC absorption.
Variations in the IRI of OA originating from different sources, including
biomass burning, were found to correlate with variations in the BC-to-OA
(BC / OA) mass ratio in aerosol particles (Saleh et al., 2014; Lu et al., 2015;
McClure et al., 2020). Furthermore, it was also demonstrated (Pokhrel et
al., 2017) that the light absorption enhancement by BrC in fresh biomass
burning aerosol is inversely dependent on the BC-to-organic carbon (OC) mass
ratio. Both findings indicate that the BC / OA ratio is one of the key
parameters controlling the absorption properties of OA. However, the BC / OA
ratio is also known to exhibit strong variations across biomass burning (BB) plumes, depending
on the type of fuel, burning conditions, and BB aerosol age (Reid et al.,
2005b; May et al., 2014; Mikhailov et al., 2017; Smith et al., 2020;
Konovalov et al., 2021). Hence, parameterizations of the BrC absorption in
atmospheric models (e.g., Wang et al., 2018; A. Zhang et al., 2020) may
strongly benefit from observational constraints on the BC / OA ratio.
The majority of the reported estimates for both the IRI and the MAE of OA are
representative of fresh aerosol. However, there is evidence that BrC
consists of unstable and chemically active compounds (Laskin et al., 2015, 2018;
Browne et al., 2019; Fleming et al., 2020). The instability of BrC is
manifested, in particular, in significant and diverse changes in BrC
absorption as a result of photochemical aging of biomass burning aerosol.
For example, based on the analysis of aircraft observations of biomass
burning plumes in North America, Forrister et al. (2015) reported rapid
bleaching of BrC on the timescale of about 10 h. Much longer (several
days) but still limited lifetimes of BrC under the UV irradiation
representative of the atmospheric conditions were observed in laboratory
experiments by Fleming et al. (2020). Both environmental chamber and
laboratory experiments have demonstrated the formation of secondary organic
chromospheres under UV irradiation (e.g., Zhong and Jang, 2014; Wong et al.,
2017, 2019; Cappa et al., 2020). Using a combination of satellite and model data,
we recently found evidence that BrC is strongly decreasing in biomass
burning plumes transported from Siberian fires into Europe, although the
absorption properties of OA are partly preserved even after several days of
atmospheric exposure (Konovalov et al., 2021). These results indicate that
the atmospheric evolution of BrC can provide a considerable contribution to
the diversity of and uncertainty in the available estimates of the absorption
properties of OA from biomass burning.
The discussion above emphasizes the need for additional observational
constraints on the BrC absorption. To address this need, multiple studies
(e.g., Arola et al., 2011; Bahadur et al., 2012; Chung et al., 2012b;
Cazorla et al., 2013; Lack and Langridge, 2013; Wang et al., 2016; Xie et
al., 2017; Chen et al., 2019; Kim et al., 2021) have employed different methods
to estimate the contribution of BrC to the total aerosol absorption using
retrievals from the Aerosol Robotic Network (AERONET), which comprises
numerous sun photometers located worldwide (Holben et al., 1998). Most of
these studies have exploited the fact that the BrC absorption rapidly decreases
with an increase in the wavelength. Specifically, Bahadur et al. (2012) and
Chung et al. (2012b) suggested that observational constraints on the BrC
absorption and DRE can be derived from the analysis of the absorption
Ångström exponents (AAEs) calculated using observations of the
absorption aerosol optical depth (AAOD) at three different wavelengths (440,
675, and 870 nm) by assuming that the contribution of BrC to the absorption
at 870 nm is negligible. A distinctive feature of their approach, which is
designed for applications at the global scale and is less suitable for
analysis of local observations, is that AAEs of BC (that is, AAEs in the
absence of BrC) are estimated through averaging over a cluster of the
observations where BrC absorption is presumably negligible. Note that there
is recent evidence that the assumption about the negligible contribution of
BrC to the absorption at 870 nm may not always be correct (Adler et al.,
2019). Wang et al. (2016) proposed a modified AAE-based method that allows
taking into account the variability in AAEs of BC and is therefore
applicable to retrievals from individual AERONET sites. The method involves
estimation of the wavelength dependence of the BC AAE for a 440–870 nm wavelength
pair as a function of the BC AAE for a 675–870 nm wavelength pair using a
Monte Carlo ensemble of Mie theory calculations and assumes that the BrC
absorption is negligible at both 675 and 870 nm wavelengths. Multiple studies have
apportioned the BrC and BC absorption using both in situ and remote
multi-wavelength observations of the aerosol absorption under the simplified
assumption that the AAE of BC is spectrally independent (e.g., Favez et al.,
2009; Yang et al., 2009; Chen et al., 2015; Olson et al., 2015; Zhao et al.,
2019; Peng et al., 2020). Note that in a general case, this assumption is
not supported by Mie theory calculations (Schuster et al., 2016; Wang et al.,
2016).
Here we substantially extend the approach proposed earlier by Wang et al. (2016) (abbreviated below as W16). Rather than using Monte Carlo
calculations only for estimating the wavelength dependence of the AAE for
BC, we directly match them to AERONET observations within a Bayesian
framework and, in this way, infer some unobserved aerosol parameters.
Another distinction of our method from that in W16 is that we complement the
AAE values by observations of the single-scattering albedo (SSA). In other
words, we effectively combine both the absorption and the extinction
observations. As argued below, the SSA observations provide additional
information allowing us to retrieve not only the contribution of BrC to the
total absorption but also the IRI and MAE of OA. Note that our approach is
distinct from using retrievals of multiple aerosol characteristics from sun
and sky radiance measurements to estimate the aerosol chemical composition
or complex refractive indices for fine and coarse modes (see, e.g., van
Beelen et al., 2014; Xie et al., 2017; Chen et al., 2019; Choi et al., 2020; Y. Zhang
et al., 2017, 2020), since we focus on the BrC absorption and do not assign a specific value to the OA IRI.
We test our method using a multi-annual dataset from two AERONET sites in
Siberia, which is a remote boreal region where biomass burning is typically
a predominant source of aerosol during a warm season (Mikhailov et al.,
2017; Konovalov et al., 2018, 2021). The latter fact facilitates our
analysis, as it could be challenging to isolate biomass burning aerosol from
anthropogenic and dust aerosol in a general case (Bahadur et al., 2012;
Schuster et al., 2016). Even more importantly, studying the absorption
properties of biomass burning aerosol in Siberia is of interest in the
context of modeling studies aimed at better understanding the role of
atmospheric aerosol in the rapid climate change in the Arctic (Bekryaev et
al., 2010), since Siberian fires are known to be one of the major sources of
absorbing aerosol in the Arctic (Evangeliou et al., 2016). The need for
observational constraints on BrC in Siberian biomass burning aerosol is
emphasized, given evidence that OA constitutes a significant fraction (up to
40 %) of light-absorbing compounds deposited on ice and snow in the
Arctic (Doherty et al., 2010). However, there have been only a few studies
addressing BrC contained in the Siberian aerosol. In particular, Gorchakov
et al. (2016) found evidence for the presence of BrC in the Siberian aerosol
by analyzing the wavelength dependence of the AERONET retrievals of the
aerosol refractive index. Golovushkin et al. (2020) applied the W16 method
to the retrievals of the absorption aerosol optical depth at two Siberian
AERONET sites and found evidence that BrC absorption decreases as a function
of the aerosol photochemical age with an e-folding time of about 30 h.
In this study, we extend the AAE-based approach to investigate BrC in
biomass burning aerosol, arguing that when combined with measurements of
SSA, absorption measurements can provide useful constraints not only on the
BrC contribution to the total absorption but also on the IRI and MAE of OA.
By applying our method to the AERONET observations in Siberia, we infer
estimates of the aforementioned absorption parameters for aerosol emitted
from wildfires in the boreal forest and also obtain simple parameterizations
of the absorption characteristics of OA in Siberian biomass burning plumes.
MethodModeling of the optical properties of biomass burning aerosol
In this section, we describe the simulations that we used to establish the
relationships between the observed characteristics and the absorption
parameters of biomass burning (BB) aerosol. Specifically, our simulations
were designed to quantify the AAE for two pairs of wavelengths – 440–870 and
675–870 nm – as well as SSA at 440 nm. These characteristics are denoted
below as AAE440/870, AAE675/870, and SSA440, respectively,
and are referred to below to as “observed” properties of BB aerosol. In
addition, to characterize the BrC absorption, we calculated the relative
contribution of BrC to the total absorption at 440 nm (denoted below as
δBrC) and MAE of OA (MAEOA) as functions of the OA IRI (kOA) as
follows:
1δBrC=1-αakOA=0αa,2MAEOA=(αa-αakOA=0)rOA-1,
where αa (depending on kOA) and αa|kOA=0
are the mass absorption efficiencies of BB aerosol calculated with and
without taking the OA absorption into account, respectively, and
rOA is the mass fraction of organic matter in BB aerosol. The
above characteristics of the BrC absorption (δBrC, MAEOA, and
kOA) along with the BC / OA ratio are referred to below as “unobserved”
properties of BB aerosol, although it should be kept in mind that the
distinction between the observed and unobserved properties is
specific for the present study. Note that both αa and αa|kOA=0 are dependent on the BC / OA ratio. In particular, when the
BC / OA ratio approaches zero, αa|kOA=0 approaches zero too,
whereas αa is determined exclusively by the BrC absorption (and
so δBrC approaches 1). Note also that the dependencies of
αa and αa|kOA=0 on the BC / OA ratio are partly
determined by the so-called lensing effect (Fuller et al., 1999), that is,
by the enhancement of the absorption by BC as a result of the refraction of
light by weakly absorbing or non-absorbing organics.
The simulations were performed using the OPTSIM software (Stromatas et al.,
2012; Menut, 2021). It provides computer codes to simulate the absorption and scattering
efficiencies of spherical particles, including the Wiscombe Mie code
(Wiscombe, 1980) for core–shell mixtures of aerosol components, which was
used in this study. The same software along with the Wiscombe code was
employed in our recent studies (Golovushkin and Konovalov, 2020; Konovalov et al.,
2021) to simulate the optical properties of BB aerosol based on its
composition predicted by a box model and a chemistry transport model.
We assumed the particle size distribution to be bimodal and composed of the
accumulation (fine) and coarse modes, in accordance with typical
observations of BB aerosol (e.g., Eck et al., 2003). Each mode was defined
using a lognormal distribution. The mass concentrations of particle
components were distributed among 20 size sections spanning the particle
shell diameters from 10 nm to 10 µm.
Following Lu et al. (2015) and W16, we assumed that fine-mode BB aerosol
particles consist of spherical BC cores covered by a weakly absorbing
coating. We also assumed that the coating consists of organic matter,
inorganic salts, and water. The major organic and minor inorganic coating
fractions were assumed to be homogeneously mixed, and the refractive index
of the shell was calculated as a volume-weighted mean of the refractive
indices of its components.
The composition of the coarse mode of BB aerosol is poorly known but is
probably quite complex and variable. It is believed to typically include
partially combusted fuels, ash, carbon aggregates, soil mineral material,
and other components (Reid et al., 2005b; Janhäll et al., 2010). Given
the lack of corresponding experimental data, we avoid any specific
assumptions about the composition of coarse-mode particles. For definiteness
and simplicity, we assume only that these particles are spherical and
internally mixed and that their density and the refractive index are
constant and close to “climatological” values characterizing the whole
ensemble of typical BB aerosol particles in boreal forests (Reid et al.,
2005a, b). Since BC (which is the strongest absorbing component of BB
aerosol) mostly resides in the fine mode, the above assumption about the
refractive index of the coarse-mode particles is likely to result in
overestimation of the contribution of the coarse mode to the absorption by
BB aerosol, although, on the other hand, non-spherical shapes of the coarse
particles may enhance their optical effects. Note that although the
contribution of coarse particles to the BB aerosol optical properties in the
UV and most of the visible wavelength ranges is typically small (Reid et
al., 2005a), it is not necessarily negligible near the boundary between the
visible and infrared ranges and can, in particular, affect values of the AAE
(Schuster et al., 2016). Note also that to assess the impact of this
parameter on our estimates, we additionally considered a special test case
(see Sect. 4.4) in which the coarse-mode particles were assumed to be
non-absorbing.
In our simulations, we tried to address a broad spectrum of realistic
possibilities for the particle structure and composition. To this end, we
randomly varied several aerosol parameters that were expected to have a
major impact on the observed variables. In particular, following W16, we
varied the median and the standard deviation of the volume size
distributions of BC, although, unlike W16, we did not assume the relative
coating thickness to be the same across the particle size spectrum but
determined it for each size section as a function of the BC / OA mass ratio
and the size distribution of the coating components. Both the BC / OA mass
ratio and the median and standard deviation for the size distribution of the
coating components were also considered random variables. Additionally,
we varied the OA IRI at the 550 nm wavelength. Based on the analysis of the
OA absorption by Sun et al. (2007) and following Saleh et al. (2014), we
presumed that the IRI for OA at other wavelengths, kOA(λ), can be
expressed as a function of the wavelength dependence, w:
kOA(λ)=kOA(550)(550/λ)w.
Following Lu et al. (2015), we estimated the most probable value of w (denoted
below as w0) as a function of the BC / OA ratio:
w0=-0.607ln(BC/OA)-0.0251.
Note that the estimates of w according to Eq. (4) are quantitatively similar
to the estimates reported by Saleh et al. (2014). The deviation of w from
w0 was also treated as a random variable.
Water content in the fine-mode particles was calculated based on the κ-Köhler theory (Petters and Kreidenweis, 2007) as follows:
Vw=κVs(aw-1-1)-1,
where κ is the hygroscopicity parameter, which is considered one
more random variable; Vs is the dry volume of the species s in a
particle; Vw is the volume of water absorbed by this species; and
aw is the water activity (which was assumed to be equal to relative
humidity divided by 100).
Variability in the effects of the coarse mode on the BB aerosol optical
properties was taken into account by randomly sampling the mass ratio of coarse- to
accumulation-mode particles as well the median and the standard
deviation for the size distribution of the coarse-mode particles. The range
of the variations in the mass ratio of coarse- to accumulation-mode particles was
assumed based on a summary of experimental data characterizing this
parameter for BB aerosol from forest fires (Janhäll et al., 2010), while
a climatology of the optical properties of BB aerosol (Reid et al., 2005a)
was used to specify the variability in the size distribution parameters for
the coarse mode.
The aerosol parameters and the ranges of their values
assumed in the Monte Carlo runs of OPTSIM. The numbers in parentheses
provide the mean and standard deviation of the truncated Gaussian
distributions assumed as a priori PDFs for the corresponding parameters.
n: real part of the refractive index at 550 nm; k: imaginary part of the
refractive index at 550 nm; w: wavelength dependence of k for organic aerosol;
w0: the most probable value of w (see Eq. 4); GMD: geometric median
diameter; σ: standard deviation of the size distribution; κ:
hygroscopicity parameter; ρ: density.
ParameterBCOA(NH4)2SO4H2OCoarse modeGMD [µm]0.02–0.3a (0.16, 0.14)0.22–0.35b (0.28, 0.06)same as for OAsame as for OA6.0–9.0b (7.5, 1.5)σ1.4–2.2a (1.8, 0.4)1.3–1.9b (1.6, 0.3)same as for OAsame as for OA1.8–2.6b (2.2, 0.4)n (550 nm)1.95c1.55d1.52e1.33f1.50lk (550 nm)0.79c0–0.035g000.0094lw–0.5–6.0g (w0, 0.25×w0)–––κ00–0.27h0.61i–0ρ [g cm-3]1.8a1.2j1.8k1.01.3bBC / OA mass ratio [g g-1]0.011–0.071 (0.041, 0.03) –––(NH4)2SO4/ OA mass ratio [g g-1]–0.05–0.15b (0.1, 0.05) ––Coarse to fine mode mass ratio–– –0–0.35m (0.16, 0.09)
a Wang et al. (2016) and references therein. b Reid et al. (2005b). c Bond and Bergstrom (2006). d Kopke et al. (1997).
e Lide (1992). f Hale and Querry (1973). g Lu et al. (2015).
h Lambe et al. (2011). i Petters and Kreidenweis (2007).
j Turpin and Lin (2001). k Haynes (2014). l Reid et al. (2005a). m Janhäll et al. (2010).
Variations in the aerosol parameters were simulated following truncated
Gaussian distributions, except for kOA and κ, which were
specified to follow uniform distributions allowing avoiding specific
assumptions about their most probable values. The truncation was needed to
exclude physically irrelevant values and is mostly (but not always) applied
at the 1σ range (that is, about 32 % of the sampled values are
typically removed). The parameters of the probability distributions assumed
in our simulations are specified in Table 1. The assumed ranges of values of
the aerosol parameters are, in most cases, supposed to be representative of
their variability observed across different regions of the world, since
relevant measurements in Siberia are very sparse. An exception is the BC / OA
ratio, which was specified based on the long-term in situ observations
(Mikhailov et al., 2017) of elemental and organic carbon at the ZOTTO
observatory situated in a remote region in central Siberia. The literature
sources that we used to characterize typical values and the variability in
the aerosol parameters are also reported in Table 1.
In addition to the aerosol parameters listed in Table 1, we randomly varied
the relative humidity. Our previous simulations of BB plumes from major
fires that occurred in Siberia in 2012 and 2016 (Konovalov et al., 2017a,
2018, 2021) indicated that optically dense Siberian BB plumes typically
propagate in a relatively dry atmosphere. Based on these simulations (which
are further discussed below in Sect. 3), the relative humidity was assumed
to range from 25 % to 70 %, with the mean and standard deviation of the
corresponding truncated Gaussian distribution to be 50 % and 25 %,
respectively.
Some other parameters, such as the real part of the refractive
indices for all the components, the density of organic matter, or the IRI for
the coarse-mode particles, are treated as constants. Although the
ranges of probable values of any of these parameters are not necessarily
negligibly narrow according to the literature, we do not expect the
corresponding variability in most of them (except, possibly, for the coarse-mode IRI) to have a significant impact on our estimates of the absorption
properties of BB aerosol. For the same reason, we disregarded a weak
spectral dependence of the real part of the refractive indices. For
definiteness and simplicity, it was also assumed that the minor inorganic
fraction of the coating consists entirely of ammonium sulfate and that the
volume size distributions of the organic and inorganic fractions of the
coating are the same. Because of the lack of experimental data on the IRI for
the coarse-mode particles of BB aerosol, we assumed, for definiteness, this
parameter's value of 9.4×10-3, which is a typical value of
the IRI of BB aerosol particles according to Reid et al. (2005a). To assess
the impact of this parameter on our estimates, we additionally considered a
special test case (see Sect. 4.4) in which the coarse-mode particles were
assumed to be non-absorbing. Note that although we could not properly
characterize the variability in the IRI for the coarse-mode particles, the
corresponding effects on the absorption properties of BB aerosol particles
are partially taken into account by varying the mass ratio of coarse- to accumulation-mode
particles. The assigned values for the constant parameters are
also listed in Table 1.
To build a dataset (or, in other words, a look-up table) of the simulated
cases representative of the assumed variability in the aerosol parameters,
we performed 106 Monte Carlo runs of OPTSIM. The parameter values for
each run were independently sampled from the corresponding probability
distributions specified above. The look-up table is formed by the different
realizations of the aerosol parameters and the corresponding values of the
observed properties.
Bayesian inference of the aerosol parameters
Our method to retrieve the aerosol parameters is based on the Bayesian
inference of model parameters from observation data (see, e.g., Tarantola,
1987; Enting, 2002). Within the Bayesian approach, which is widely used
across the atmospheric sciences to retrieve unobserved parameters from
remote observations and to exploit observational constraints on model
parameters in data assimilation and inverse modeling studies, the model
parameters, and observational and model data are treated as random variables,
each of which is determined by a corresponding probability distribution
function (PDF). In this study, this approach is used to retrieve parameters
of BB aerosol.
The parameters that are introduced above as random variables in our Mie
theory simulations form the control vector, x, of our
inverse problem. We introduce the a priori PDF for x by
assuming that each component of the control vector is statistically
independent of other components:
papr(x)∝∏ngn(xn),
where n is the index of a component of x and gn(xn)
is the marginal PDF for xn. We consider the assumption of the
statistical independence of the a priori estimates of the components of the
control vector as the best assumption given the lack of more specific
information about the joint a priori probability distribution. This
assumption is not restrictive and therefore is unlikely to lead to any
significant biases in the inferred estimates or underestimation of
uncertainties in them. We also introduce a conditional PDF for the vectors
of the observed characteristics, zo (that
is, AAE440/870, AAE675/870, and SSA440) by assuming that both
the observation and model errors are normally distributed and that the
uncertainties in the different components of
zo are statistically independent:
Pz(zox)∝∏kexp-(zok-zmk(x))22σk2,
where zm is the modeled counterpart of
zo, k is the index of a component of
zo, and σk is the standard
deviation characterizing the combined observation and model errors in the
component k of the vectors zo and
zm.
According to the Bayes' theorem, the a posteriori conditional PDF for
x,Pp(x|zo), is defined as follows:
Pp(xzo)∝∏kexp-(zok-zmk(x))22σk2Papr(x).
In this study, we obtain the a posteriori estimate (fp) of any scalar function f(x) depending on
x as its mean value:
fp=∫-∞+∞f(x)Pp(xzo)∏ndxn.
The integration of Eq. (9) is performed numerically using a Monte Carlo
algorithm (Press et al., 1992). Monte Carlo algorithms, which have
frequently been used in the atmospheric sciences to solve optimization
problems within probabilistic frameworks (e.g., Beekmann and Derognat, 2003;
Konovalov et al., 2006; Lu et al., 2015; Kulikov et al., 2018), involve
running multiple model calculations with randomly varied parameters. In this
study, our Monte Carlo calculations included the following steps: (1) sampling of x from the corresponding a priori PDFs, (2) Mie theory simulations of zm as a function of the
given x, and (3) summation over the values of the product
of f(x) with Pp(x|zo). Similar summation over
Pp(x|zo) was
used to evaluate the confidence intervals for fp as a given percentile
(Pi%) of the a posteriori marginal PDF for |f(x)-fp|. To this end, samples of f(x) were preliminarily ordered according to their magnitude, and the following
cumulative PDF (CPDF) that indicates the probability for
f(x) to be smaller than a certain value f was then
computed:
CPDF(f)=∑forallfk(x)<fPp(xkzo),
where k is the sample index. The confidence intervals were determined
around fp as values of f, for which the CPDF of the
difference f(x)-fp was Pi%/2 and 1-Pi%/2.
Note that if both observations and simulation were perfect, then the a
posteriori PDF would collapse into the delta function, and the best
estimates of the unobserved parameters would correspond to a unique
simulation minimizing the distance between
zo and zm.
The retrieval of the aerosol parameters in such a situation could be achieved
using a standard optimization technique, similarly to, e.g., van Beelen et al. (2014)
and Xie et al. (2017). However, because of the observation error, the best
match to the observation does not necessarily ensure the best estimates of
the parameters. Furthermore, some parameters that are poorly constrained by
a given set of observations could take sporadic and physically irrelevant
values (in the absence of a priori constraints). Our Bayesian method
addresses this difficulty by “translating” the input observation data into
a range of possible physically relevant values of latent (unobserved)
parameters of the aerosol system. Our best estimates of the inferred
properties, therefore, are representative of an ensemble of the simulations
that fit the imperfect observations.
Values of x were sampled from the a priori PDFs specified
in Sect. 2.1 and Table 1. The standard deviations σk were
estimated as discussed in Sect. 3. We made sure that the sample consisting
of the 106 random combinations of the parameters allows us to obtain
sufficiently accurate a posteriori estimates and their confidence intervals.
To this end, the estimation procedure was repeated using 3×105 samples, and we found only minor differences in the retrieved
parameters and their confidence intervals compared to the base case.
AERONET data
We applied our method described above to the AERONET data that were derived
from ground-based measurements of direct sun and sky radiances in the solar
almucantar plane at several wavelengths at the ultraviolet, visible, and
infrared wavelength ranges (Holben et al., 1998). The AERONET measurements
are made with Cimel sun–sky radiometers at more than 500 sites located
across the globe and are used to derive optical and physical properties of
the atmospheric aerosol, including, in particular, aerosol optical depth
(AOD), aerosol absorption optical depth (AAOD), and SSA (Dubovik and King, 2000; Dubovik et al.,
2006). Our analysis performed in this study is based on AAOD and SSA
data that are available as part of the Level 2.0 Version 3 inversion
products. The AAOD retrievals at 440, 675, and 870 nm were used to estimate
the corresponding absorption Ångström exponents, AAE440/870 and
AAE675/870. As a source of auxiliary information, we also used the AOD
Level 2.0 data based on the Version 3 direct sun algorithm (Giles et al.,
2019). The Level 2.0 AERONET products provide quality-assured data which
undergo automatic cloud screening (Smirnov et al., 2000). Since the
uncertainty in the absorption estimates tends to be bigger for measurements
with smaller AOD, one of the criteria applied to the Level 2.0 data is that
AOD at 440 nm must be greater than 0.4 (Dubovik et al., 2000). Note that
although the measurements satisfying this and other quality-assuring
criteria applied to the Level 2.0 products are relatively scarce, we opted to
avoid using more abundant Level 1.5 data which can be more strongly affected
by uncertainties and biases (Andrews et al., 2017).
In this study, we analyzed the data that were available through the AERONET
data portal (https://aeronet.gsfc.nasa.gov/, last access: 12 October 2021) by the end of 2020 from two
AERONET sites in Siberia. One of the sites – Tomsk_22
(56.4∘ N, 84.7∘ E) – is situated in western Siberia, in
an eastern suburb of the city of Tomsk, while another site – Yakutsk
(61.7∘ N, 129.4∘ E) – is located in eastern Siberia,
about 50 km south of the city of Yakutsk. The available data records from
the Tomsk_22 and Yakutsk sites (Holben, 2021; Holben et al., 2021) go back to the years 2011 and
2004, respectively. Since this study focuses on BB aerosol, we considered
the data only for the summer months (June–August), when forest fires are the
predominant source of carbonaceous aerosol in Siberia (Mikhailov et al.,
2017; Konovalov et al., 2018). Furthermore, similarly to Konovalov et al. (2017b), we applied a criterion based on the observed AOD at 500 nm
(AOD500) to select AERONET retrievals representative of BB aerosol.
Specifically, based on our previous analyses (which involved AERONET,
satellite, and model data) indicating that the “background” AOD500 (or AOD550) in the absence of fires in Siberia would rarely exceed
0.2 both on average over Siberia and specifically at the
Tomsk_22 and Yakutsk sites (Konovalov et al., 2017b, 2018,
2021), we selected the Level 2.0 AERONET retrievals for which AOD500 was
larger than 0.8. As a result of this selection, we expect that the
contributions of anthropogenic, biogenic, and dust aerosol to AOD500
typically do not exceed 25 %. It should be noted, however, that our
selection procedure does not necessarily exclude possible situations where
there was a bigger contribution of anthropogenic BC to AAOD. These
situations can result in some underestimation of the relative contribution
of BrC to the overall BB aerosol absorption in our analysis but are unlikely
to lead to significant (i.e., exceeding corresponding confidence intervals)
biases in our retrievals of kOA and MAEOA.
Applying these selection criteria to the available AERONET retrievals
yielded a dataset that includes 115 data records, the majority of which (65)
come from the Yakutsk site. Different data records normally correspond to
different days, but some observations are taken on the same day. The
temporal coverage of the selected data is not uniform: the most abundant
data (40 data records) correspond to the year 2012, when a major mega-fire
event occurred in Siberia (Konovalov et al., 2014, 2017a, b, 2018; Zhuravleva
et al., 2017, 2018), while data for some other years are entirely missing.
Note that AERONET observations made at the same Siberian sites were used to
characterize BB aerosol in several previous studies. In particular,
Zhuravleva et al. (2017) used data from Tomsk_22 to identify
changes in microphysical and optical properties of Siberian aerosol due to
fire emissions. Konovalov et al. (2017b, 2018) used AERONET observations at
both the Tomsk_22 and the Yakutsk sites in 2012 to approximate
the relationship between the BC / OC ratio and AAOD. The retrievals from the
Tomsk_22 site for 2012 and 2016 were employed by Golovushkin
et al. (2020) to estimate the BrC fraction of the BB aerosol absorption
using the W16 method.
Time series of the aerosol optical properties (AOD, AAE, SSA)
derived from remote observations at the (a, c) Tomsk_22 and
(b, d) Yakutsk AERONET sites. Red circles (a, b) depict AOD500 values
corresponding to the selected retrievals of the other properties. The
threshold AOD500 value (0.8), which was used to select observations
representative of BB aerosol, is shown by the horizontal dash-dotted lines.
Also shown (a, b) are the corresponding time series of RH according to the
simulations in Konovalov et al. (2018).
Figure 1 illustrates the AERONET data selected for our analysis:
specifically, it presents values of AAE440/870, AAE675/870, and
SSA440 along with the time series of AOD500 in summer 2012.
Additionally, the same figure shows the time series of the relative humidity
(RH) and SSA at 675 nm (SSA675) for the same period. The estimates of
RH are adopted from our previous simulations (Konovalov et al., 2018) using
the CHIMERE chemistry transport model and WRF meteorological model, where
these estimates were derived as a weighted average over the BB aerosol
layer. The RH data were used in this study only to characterize the probable
range of RH variability in BB plumes observed in Siberia and were not part
of the observation vector. The retrievals of SSA675 are used below only
in auxiliary analysis.
Figure 1 indicates that there were numerous episodes of major enhancements
of AOD500 over the background fluctuations in 2012. Specifically, such
episodes were registered in Tomsk_22 in the second half of
June, in July, and at the very beginning of August. Major enhancements of
AOD500 were also observed in Yakutsk but only during a short period in
the middle of July. During all these episodes, SSA440 exceeded 0.92,
while both AAE440/870 and AAE675/870 were mostly in the range from
1 to 2. Typically, AAE440/870 exceeded AAE675/870, but in many
cases, the difference between them was rather small. Note that a positive
difference between AAE440/870 and AAE675/870 is typically
indicative of the BrC absorption (see, e.g., W16). Values of RH varied
between 25 % and 70 % in the selected episodes, thereby confirming our a
priori assumption that occurrences where RH in Siberian BB plumes exceeds 70 % are very rare.
In the analysis to follow, we consider all the selected data together,
without distinguishing between different sites and years. Note that the
relationships between AAOD and AOD retrieved from observations at the two
AERONET sites considered here were previously found (Konovalov et al., 2018)
to be consistent, on average, with the corresponding relationships based on
the AAOD and AOD retrievals from satellite observations made across Siberia,
which is indicative of the combined AERONET observations at these sites
being representative of Siberian BB aerosol, a major part of which originates
from forest fires.
The uncertainties in the standard AERONET products have been examined in
several studies and are found to depend on AOD and the solar zenith angle
among other factors (Eck et al., 1999; Dubovik et al., 2000; Mallet et al.,
2013; Torres et al., 2014). Recently, estimates of uncertainties in the
AERONET retrievals of SSA and some other variables were derived from the
analysis of 27 inversions involving different combinations of probable
biases in input data, including AOD, sky radiances, and surface reflectance
(Sinyuk et al., 2020). These uncertainty estimates are provided in terms of
the standard deviations (U27) for the corresponding retrieved variables as
part of the auxiliary data products of AERONET and are also available from
the AERONET data portal. Accordingly, we used the values of U27 for
SSA440 as estimates for the standard deviation of this input variable.
In our dataset, the values of U27 for SSA440 vary for different SSA
retrievals, ranging from 5.2×10-3 to 2.0×10-2.
The root mean square error in the SSA440 retrievals was accordingly
estimated as 1.2×10-2. For comparison, the expression
provided for the uncertainty in the AERONET SSA retrievals by van Beelen
et al. (2014; see Table 2 therein) yields an SSA uncertainty of 1.8×10-2 if AOD440 equals 1 and less if AOD440 is larger.
The previous analyses, however, did not provide a sufficient quantitative
basis for the estimation of the uncertainties in the absorption
Ångström exponents. These uncertainties – according to the AAE
definition – depend on the errors in the AAOD retrievals in a strongly
nonlinear manner, and the errors in the AAOD retrievals at the different
wavelengths can covary to an unknown extent. Given this difficulty, we
derived a robust estimate of the uncertainties in both AAE440/870
(σ1) and AAE675/870 (σ2) from the variance of
the differences between AAE440/870 and AAE675/870:
σ1,22≈12(N-1)σ32σ32‾-1∑iAAE440/870i-AAE675/870i-AAE440/870‾+AAE675/870‾2,
where the upper horizontal bars indicate the average of the N data records
considered and σ3 denotes values of U27 for SSA440. This
estimation assumes that (1) there are two types of errors in the AAOD
retrievals – specifically, the errors that are similar across the
wavelength spectrum and the entirely random errors that differ at different
wavelengths; (2) the errors in AAOD of the first type tend to cancel each
other out when the AAE is calculated and so a value of the expression in the
parentheses is determined predominantly by random errors in AAE440/870 and
AAE675/870; and (3) the uncertainty in the AAE is likely larger for
retrievals where the uncertainty in SSA is larger (since the uncertainties
in SSA are determined mostly by uncertainties in the AAOD retrievals). Since
part of the observed variability in the differences between AAE440/870
and AAE675/870 reflects the real wavelength dependence of the AAE, Eq. (11)
is expected to provide an upper limit for the uncertainty in the absorption
Ångström exponents. As a result of the application of Eq. (11) to
our dataset, we estimated the root mean square error in both AAE440/870
and AAE675/870 as 0.12. Note that a probable overestimation of the
uncertainties in AAEs can result in some biases of the a posteriori
estimates of the retrieved properties toward the a priori ones. However, as
argued in Sect. 4.3, such biases are unlikely to be significant in our case.
Note also that since possible uncertainties in our a posteriori estimates
due to uncertainties in our simulations are addressed through the random
variations in the model parameters, the part of the model uncertainties
contributing to σ1-3 is assumed to be negligible in comparison
with the observation error.
Simulated relationships between several characteristics of BB
aerosol: (a)δBrC as a function of the difference between
AAE440/870 and AAE675/870, (b)δBrC as a function of
AAE440/870, (c) AAE440/870 as a function of AAE675/870, and
(d) the BC / OA ratio as a function of SSA440. Different computations
were performed with different values of kOA (reported in the figure
legends for the 550 nm wavelength) and the BC / OA ratio, which are denoted by
different symbols and colors, respectively.
ResultsAnalysis of observational constraints for the unobserved properties
As an initial step in our investigation, we numerically analyzed the
relationships between the observed optical properties of BB aerosol
(such as the AAE and SSA) and its unobserved characteristics (such as
δBrC, kOA, and the BC / OA ratio) to learn whether there is a
physical basis for expecting that the observed properties can provide strong
constraints to the unobserved characteristics at least in the ideal
situation in which the observation errors are absent. Implications of this
analysis for inference of the absorption characteristic from imperfect
observations are briefly discussed at the end of this section. The
relationships were obtained as a result of Mie theory calculations performed
with different values of kOA and the BC / OA ratio and are presented in
Fig. 2. The parameters varied within the a priori assumed ranges (see Table 1). All other parameters that were treated in our Bayesian analysis as
random variables were assigned with the median values from the corresponding
ranges given in Table 1.
Specifically, Fig. 2a shows the relationship between δBrC (which is
the relative contribution of BrC to the overall absorption at 440 nm) and
the difference between the two absorption Ångström exponents
calculated for the different pairs of wavelengths (440–870 and 675–870 nm).
Analysis of this difference between the absorption Ångström
exponents for these or slightly different wavelengths has been a basis for
estimation of δBrC in previous studies (e.g., Bahadur et al., 2012;
Chung et al., 2012b; W16; Saturno et al., 2018): since the BrC absorption
increases for smaller wavelengths, a larger difference between
AAE440/870 and AAE675/870 is indicative of a larger δBrC
(as confirmed by our simulations shown in Fig. 2a). Of special interest in
the context of this study are the following features of our simulations.
First, δBrC is not unambiguously determined by the AAE440/870
and AAE675/870 difference, also being dependent on both kOA and the
BC / OA ratio. In other words, the difference in the absorption
Ångström exponents does not necessarily provide an unambiguous
observational constraint on δBrC. Note that because a smaller BC / OA
ratio corresponds to a thicker organic coating of a BC core, a decrease in
the BC / OA ratio is associated with an increase in δBrC (albeit only
when OA is absorbing). Second, the same value of the difference between
AAE440/870 and AAE675/870 can correspond to quite different values
of kOA and the BC / OA ratio, indicating that observations of AAEs, if
taken alone, can hardly be useful as constraints on these parameters.
Finally, consistent with the analysis in W16, our computations indicate that
BB aerosol with a non-absorbing or weakly absorbing shell can yield a
negative difference between AAE440/870 and AAE675/870,
thereby indicating that using observations of AAEs as constraints on BrC
requires careful consideration of the wavelength dependence of the BC
absorption.
Figure 2b shows how δBrC relates directly to the absorption
Ångström exponent for the 440–870 nm wavelengths. Our computations
indicate that the relationship between δBrC and AAE440/870 is
relatively unambiguous, and so AAE440/870 can (at least, theoretically)
provide a rather strong constraint on δBrC even when neither
kOA nor the BC / OA ratio is known. However, Fig. 2b also indicates that
the same value of AAE440/870 can correspond to very different values
of kOA and the BC / OA ratio since AAE440/870 is a growing function of kOA and a decreasing function of the BC / OA ratio. Hence, we can
conclude that these parameters cannot be inferred only from observations of
AAE440/870.
The relationship between AAE440/870 and AAE675/870 is
illustrated in Fig. 2c. The calculations indicate that BrC affects not only
AAE440/870 but also AAE675/870. Specifically, AAE675/870
increases by more than 50 % (from ∼1.5 to 2.3) when
kOA at 550 nm increases from 0 to 10-2, although the effect of
BrC on AAE675/870 is relatively weak when kOA is in the
lowest range of it values. Variations in the BC / OA ratio can strongly affect
AAE675/870 too. It is also noteworthy that the relative difference
between AAE440/870 and AAE675/870 is small (does not
exceed 10 %) across the cases addressed in Fig. 2c.
Figure 2d examines the relationship between SSA440 and the BC / OA ratio.
According to our calculations, SSA440 strongly (and almost linearly)
increases with a decrease in BC / OA. Taking into account that the mass
fraction of BC in BB aerosol is much less than unity in all our
calculations, this result is consistent with the experimental analysis by
Pokhrel et al. (2016), in which SSA was found to be linearly dependent on
the BC-to-(BC + OC) ratio. While the results presented in Fig. 2a–c indicate
that the AAE-based estimation of the absorption properties of BB aerosol can
benefit from constraints on the BC / OA ratio, Fig. 2d shows evidence that
such constraints can be provided by observations of SSA. It should be noted,
however, that SSA440 itself depends not only on BC / OA but also on
kOA.
Taken together, the calculations shown in Fig. 2 suggest that in an ideal
situation, in which all parameters except for kOA and the BC / OA ratio
are fixed, these unobserved parameters can be constrained by simultaneously
applying observations of at least one of the absorption Ångström
exponents and SSA. It should be kept in mind, however, that in the real
situation, the relationships illustrated in Fig. 2 can be affected by
variations in other aerosol parameters. Even more importantly, the values of
the observed properties are inevitably uncertain. In particular, as we
estimated above (see Eq. 11), the uncertainty in AAE440/870 and
AAE675/870 derived from the AERONET observations can be characterized
by a standard deviation of 0.12. Under the aerosol parameter values assumed
in our computations, this uncertainty essentially devaluates the difference
in AAEs as a potential observational constraint on δBrC (see Fig. 2a). However, according to the calculations shown in Fig. 2b, application of
the same uncertainty to AAE440/870 would not result in considerable
changes in δBrC (on a scale of 1). Furthermore, since the
variations in AAE440/870 and AAE675/870 due to variations in
kOA and the BC / OA ratio are closely related (see Fig. 2c), the use of
AAE675/870 as part of the observation vector can be expected to reduce
the effect of the uncertainty in AAE440/870 (assuming that the errors
in AAE440/870 and AAE675/870 are statistically independent). A
relatively small uncertainty in SSA (of 0.012) is also not likely to
preclude inferring reasonable estimates of BC / OA from SSA440 (when
kOA is known). We strive to take possible variations in the aerosol
parameters and the observation errors into account in our Monte Carlo
analysis presented in the next sections.
Validation of the retrieval algorithm
Next, we examine the capability of our method to retrieve δBrC,
kOA, MAEOA, and the BC / OA ratio from perfectly accurate (ideal)
observations of AAEs and SSA by using the corresponding perfect calculations
which take into account random variations in several aerosol parameters as
discussed in Sect. 2.1. To this end, we test our algorithm using synthetic
data which are intended to best represent the properties of real BB aerosol
in Siberia.
The synthetic dataset was formed from our simulations included in the
look-up table described in Sect. 2.1. For each data point from our AERONET
dataset, we selected a simulation that minimized the mismatch, εf, between the observations and simulations. The mismatch was defined
as follows:
εf2=zo-zmTzo-zm.
An additional criterion was that the absolute difference between any
component k of zo and
zm could not exceed the corresponding
standard deviation σk (see Sect. 3). We presumed that
observations that do not satisfy this criterion are not sufficiently
represented in our simulations. As a result, the set of our synthetic
observations includes 96 data points (of 115 data points in the original
AERONET dataset). These data points were excluded from the look-up table
and were then used to obtain the a posteriori estimates of the
unobserved parameters following Eq. (9).
The retrievals that can be obtained using Eqs. (6)–(9) depend on the
standard deviations σk, which, as noted above, represent both
the observation and model errors. Therefore, if the observations are perfect
(as we assume), σk is determined entirely by the model error.
Even though our simulations are also assumed to be perfectly accurate, the
model error is not zero even in the presumed ideal situation. This is
because the complex and nonlinear relationships between the physical
parameters and optical properties of BB aerosol are approximated by a finite
(albeit very big) set of Monte Carlo calculations. It should also be noted
that this “approximation” error is not directly related to the observation
errors discussed in Sect. 3. Taking these considerations into account, we
estimated the standard deviations representative of the approximation error
as follows. First, we replaced the variable values of σ1-3
(estimated as discussed in Sect. 3) with the corresponding constant root mean
square errors (also reported in Sect. 3), presuming that the difference
between the root mean square errors for the AAE and SSA partly reflects the
distinction between the natural factors contributing to the variability in
these parameters in both the observations and the simulations. Second, we scaled
these estimates of σ1-3 with a constant factor (fs), which
was optimized by minimizing the mean square difference between the “true”
values of kOA from the synthetic dataset and the corresponding
retrievals of kOA. The optimal value of fs was found to be equal to
0.20. Then the error inherent to our Bayesian algorithm (with a look-up
table consisting of 106 simulations) can roughly be estimated as a
fifth part of the observation uncertainty. Note that the dependence of the
errors in our retrievals of kOA and other parameters on fs is found
to be rather weak. Note also that, since we optimized only one parameter
(fs) and our test dataset is relatively large, the performance
statistics for our retrieval algorithm could hardly change significantly if
our test dataset were split into optimization and validation subsets (as
would probably be necessary if a larger number of parameters of the
retrieval algorithm were optimized using the same data).
Relationships between the observed optical properties of BB
aerosol (AAE440/870, AAE675/870, and SSA440) from the set of
synthetic test data and their retrieved counterparts.
Figure 3 demonstrates the relationships between the values of the observed
properties of BB aerosol (AAE440/870, AAE675/870, and SSA440)
from the set of synthetic data and the corresponding retrieved values. The
agreement between the true and “retrieved” data is nearly perfect,
indicating that the approximation error is rather small. (But note that it
would be larger if the Monte Carlo simulations were less numerous.)
An example of the cumulative probability distributions (CPDFs) for
several properties – (a)δBrC, (b) the IRI of OA (kOA), (c) the MAE of
OA, and (d) the BC / OA ratio – inferred from the synthetic data. Values of
δBrC, kOA, and MAEOA correspond to the 440 nm wavelength.
The CPDFs were computed according to Eq. (10) using three different
combinations of the observational constraints: the two AAEs and SSA440
(“standard constraints”), only two AAEs, and AAE440/870 combined with
SSA440. The unconstrained (a priori) CPDFs are also shown. Note that
CPDFs for kOA and MAEOA for the unconstrained case are depicted
against the upper axes of abscissas. The true values of the inferred
parameters are indicated with the vertical dash-dotted lines with arrows. The
error bars show the confidence intervals in terms of the 90th percentile of the underlying probability distributions for the inferred
properties.
Results of the application of the retrieval algorithm to the
synthetic test data: the relationships between the test (true) and
predicted values of (a)δBrC, (b)kOA, (c) MAEOA, and (d) the BC / OA ratio. Values of δBrC, kOA, and MAEOA are shown
for the 440 nm wavelength. Vertical bars depict the confidence intervals in
terms of the 90th percentile of the corresponding a posteriori probability
distributions. The legends report the averages of the test and predicted
values, the coefficient of determination (R2), and the mean square
error (MSE).
The capability of our method to retrieve the unobserved properties of BB
aerosol (δBrC, kOA, MAEOA, and the BC / OC ratio) from the
perfect observations of AAE440/870, AAE675/870, and SSA440 is
demonstrated in Figs. 4 and 5. Specifically, Fig. 4 shows examples of CPDFs
calculated for the four parameters inferred from one point of the synthetic
dataset. The synthetic data point originally corresponds to the AERONET
observations performed on 26 July 2014. The CPDFs were computed according to
Eq. (10) using three different combinations of the constraining observed
properties, such as (i) the two AAEs and SSA440 (standard
constraints), (ii) only two AAEs, and (iii) AAE440/870 combined with
SSA440. The CPDFs calculated from a priori assumptions without using
any observational constraints are also shown in Fig. 4. Our calculations
indicate that the use of any of the three combinations of the components of
the observation vector results in major transformations of the a priori
CPDFs (and thus underlying PDFs), leading to steeper a posteriori CPDFs
which are underlain by more narrow PDFs. The standard constraints result in
the steepest CPDFs and, accordingly, in the least uncertain estimates of all
of the inferred parameters. At the same time, the use of only two AAEs as
the observational constraints results in the largest uncertainties in three
of the four inferred parameters (kOA, MAEOA, and the BC / OC ratio).
Note that the fact that the confidence intervals determined by the CPDFs
cover the true estimates of the parameters is indicative of the adequacy
of our sampling procedure.
Figure 5 compares the test (true) and predicted values of the BB aerosol
properties inferred from the synthetic data using the standard constraints.
All these properties can be retrieved fairly well (although, as expected,
not perfectly), with the coefficient of determination, R2, equal to or
exceeding 0.8 and the relative bias being smaller than 8 % in all four
cases. The differences between the true and predicted values (that is, the
retrieval errors) are typically within the confidence intervals. Note that
the confidence intervals shown in Fig. 5 quantify the uncertainties in terms
of the 90th percentile, so they are not expected to always cover the
retrieval errors. Note also that the confidence intervals for
kOA, and the BC / OC ratio are, on average, several times smaller
than the ranges of the a priori estimates for these parameters. The
retrieval errors stem mainly from the fact that the observed properties
depend not only on kOA and the BC / OC ratio but also on other
parameters (see Table 1) that were varied in our Monte Carlo calculations.
It can be noted that the retrieved values tend to be overestimated when the
true values are the smallest and underestimated when the true values are the
largest. This is an expected result of averaging over multiple realizations
of the parameter functions in accordance with Eq. (9) and is also partly due
to a priori constraints. On the whole, this analysis demonstrates that
perfect observations of AAE440/870, AAE675/870, and SSA440 can
provide strong constraints on the two major parameters of BB aerosol, such
as the IRI of its organic fraction and the BC / OC ratio, and will also allow
deriving reasonable estimates of the BrC absorption (δBrC) and the
mass absorption efficiency of OA (MAEOA).
The same as in Fig. 5 but without using the SSA data as a
component of the observation vector. The confidence intervals for
kOA, MAEOA, and the BC / OA ratio are not shown as they frequently
exceed the axis limits.
A key distinction of our method from the other AAE-based methods aimed at
estimation of the BrC absorption is that we suggest complementing the AAE
data by SSA observations. To examine the usefulness of SSA as an additional
constraint on the BrC absorption parameters, we repeated the analysis
presented in Fig. 5 without using SSA as a component of the observation
vector zo. The results of this test (see
Fig. 6) are rather unsurprising, given the above discussion (see Sect. 4.1).
Although a pair of the absorption Ångström exponents still allows
estimating δBrC, it provides only very weak constraints on the other
three aerosol characteristics considered here. Specifically, the mean square
errors of the retrievals of kOA, MAEOA, and BC / OA increased by 2.9,
2.7, and 3.9 times, respectively, compared to the base case. The much larger
errors in the retrievals of kOA and MAEOA are a result
of the uncertainty in the BC / OA ratio. This ratio cannot be constrained with
the absorption Ångström exponents: indeed, the coefficient of
determination calculated for the retrievals of the BC / OA ratio dropped from
0.86 (in the case of estimation involving SSA) to virtually zero (in the
case of estimation without SSA). Therefore, the results presented in Fig. 6
confirm the significant benefits of using SSA observations as a constraint
on the BrC absorption in addition to the absorption Ångström
exponents.
In addition, we also examined the feasibility to use only AAE440/870
and SSA440 as observational constraints (see Supplement Fig. S1). The
inferred estimates are found to be more uncertain than with the standard
constraints (see Fig. 5) but still reasonably accurate (R2 is larger
than 0.7 and the bias does not exceed 15 % for all the four parameters
considered). Therefore, consistently with the analysis discussed in Sect. 4.1 (see Fig. 2b and d), these results indicate that the BB OA
absorption parameters can be efficiently constrained with only the
observations of AAE440/870 and SSA440.
Finally, it is useful to note that an important source of the uncertainty in
the inferred estimates kOA, MAEOA, and BC / OA is associated with the
wavelength dependence of the OA IRI, w (see Eq. 3). Our supplementary
analysis indicated (see Supplement Fig. S2) that this parameter cannot be
well constrained by the three observational properties considered above,
although the predicted values of w, when constrained with both AAEs and
SSA440, can nonetheless capture the major part of the observed
variability in this parameter (R2>0.5) and are not
affected by a significant bias.
The same as in Fig. 3 but in the case of application of the
Bayesian algorithm to the original AERONET data. The solid lines show the
best linear fits through the origin.
Application to the AERONET data
In this section, we discuss the application of our method to the original
AERONET data. Figure 7 shows a comparison of the original values of the
observed properties of BB aerosol with the corresponding calculations
processed with Eq. (9). First of all, it should be noted that these
calculations tacitly assume that the observations can be closely reproduced
by some (or, ideally many) samples of the model data from the generated
look-up table (see Sect. 2.1). However, this proves to be not always
possible (due to, e.g., unusual composition of the observed aerosol). To
exclude such situations, we used a criterion similar to one applied to the
synthetic data. Namely, we required that the absolute difference between any
component k of the observation vector (zo)
and its model counterpart (zm) should not
exceed the corresponding standard deviation σk (estimated as
discussed in Sect. 3) at least for one sample of the model data.
Consequently, our algorithm provided a posteriori estimates for 100 data
points (of 115) from our dataset of the AERONET observations. Figure 7
looks similar to Fig. 3, but the agreement between the observations and the
calculations has visibly deteriorated in Fig. 7 due to uncertainties (σk) assumed for the AERONET data a factor of 5 larger than for the
synthetic data (see Sects. 3 and 4.2). It is important, however, that the
biases in the calculated values remain small (much less than 5 %) even in
the case with the original data: large biases in the calculations of the
observed properties would be indicative of probable significant biases in
the retrievals of the unobserved properties.
Results of the application of the retrieval algorithm to the
AERONET data: inferred values of (a)δBrC, (b)kOA, and (c) MAEOA at the 440 nm wavelength as a function of the observed values of
AAE440/870, along with (d) the BC / OA ratio as a function of the
observed SSA440. Values of δBrC, kOA, and MAEOA are
shown for the 440 nm wavelength. Vertical bars depict the confidence
intervals in terms of the 68.3th percentile of the corresponding a posteriori
probability distributions. Also shown are (a) the contribution of the BrC
absorption to AAE440/870 (ΔAAE440/870), (a–c) nonlinear approximations of the relationships between the retrieved and
observed absorption characteristics, and (d) a linear fit to the
relationship between the BC / OA ratio and SSA440.
Retrievals of the unobserved properties from the AERONET observations are
presented in Fig. 8. Specifically, it shows δBrC, kOA, and
MAEOA as a function of the observed values of AAE440/870 and also
demonstrates the BC / OA ratio as a function of the observed values of
SSA440. Additionally, Fig. 8a shows the retrieved (calculated)
contribution of BrC to AAE440/870:
ΔAAE440/870=AAE440/870-AAE440/870BC,
where AAE440/870BC is the absorption Ångström
exponents calculated with kOA=0.
Figure 8 also presents several approximations explained below. In
particular, using the common assumption that the BrC absorption at 870 nm is
negligible, ΔAAE440/870 determines δBrC as follows:
δBrC=1-(440/870)ΔAAE440/870.
The dependence of the calculated values of ΔAAE440/870 on the
observed values of AAE440/870 can be approximated by a quadratic
function as follows (see dashed green curve in Fig. 8a):
ΔAAE440/870≅0.79×(AAE440/870)2-1.78AAE440/870+1.13.
Using this approximation and taking Eq. (14) into account, we can
approximate our retrievals of δBrC as follows:
δBrC≅1.33×(1-[440/870]ΔAAE440/870),
where ΔAAE440/870 is approximated as suggested by Eq. (15) and the scaling factor of 1.33 is determined from the condition that the
averages of the approximated and retrieved values of δBrC should be
equal. Note that because the dependence given by Eq. (14) is essentially
nonlinear, it does not necessarily apply directly to values of δBrC
and ΔAAE440/870 obtained as a result of integration using Eq. (9).
Based on the idea that the dependence of δBrC on AAE440/870 is
underlain by a similar dependence of the OA IRI (kOA), we approximated
kOA at 440 nm as a function of AAE440/870 as follows:
kOA≅1.15×10-2×([870/440]ΔAAE440/870-1),
where the scaling factor of 1.15×10-2 was determined by
requiring that the averages of the approximated and retrieved values of
kOA are equal. A similar approximation can be suggested for MAEOA:
MAEOA≅0.42×([870/440]ΔAAE440/870-1).
The approximations by Eqs. (16)–(18) are shown in Fig. 8a–c by blue symbols.
Consistent with the analysis by Pokhrel et al. (2016), the dependence of the
BC / OA ratio on SSA can be approximated by a linear function shown in
Fig. 8d.
The retrievals shown in Fig. 8 indicate that OA is a minor absorbing
component in typical Siberian BB plumes. Specifically, BrC contributes, on
average, only about 21 % to the absorption at 440 nm, although there were
several occasions when the BrC contribution exceeded 40 % (Fig. 8a). The
BrC absorption may be relatively weak as a result of the rapid bleaching of
OA under solar UV radiation. Indeed, on the one hand, based on aircraft
observations in North America, Forrister et al. (2015) found that BrC almost
totally disappears from BB plumes after about 15 h of aging under
illuminated conditions. On the other hand, our model analysis of the 2012
fires in Siberia (Konovalov et al., 2018) indicated that the
Tomsk_22 and Yakutsk AERONET sites typically detect aged BB
aerosol, with a median photochemical age of about 25 h. It should be noted,
however, that the findings reported by Forrister et al. (2015) may not be
fully applicable to BrC in smoke plumes from Siberian fires, as there is
also an indication that Siberian BB aerosol contains a sizable BrC fraction
even after much longer photochemical aging, partly due to formation of
absorbing secondary organic aerosol (SOA) (Konovalov et al., 2021). Note
also that the BrC absorption can be much stronger at shorter wavelengths,
depending on the wavelength dependence of kOA, w, which, as noted above,
cannot be well constrained by only the observations considered here.
According to our estimates, the IRI at 440 nm varies from about 7×10-4 to 8×10-3 (see Fig. 8b). These values are within
the lowest part of the range of kOA values reported by Lu et al. (2015)
for the 550 nm wavelength. Our estimates of MAEOA (also at 440 nm)
range from 0.03 to 0.3 m2 g-1 (see Fig. 8c). This range
intersects with the broad range of 0.05–1.5 m2 g-1, which was
derived in W16 from AERONET observations for the mean values of MAEOA
(at 440 nm) across four different big regions of the world (such as East
Asia, Europe, North America, and the Southern Hemisphere). Similarly to our
estimates of δBrC, the estimates of both kOA and MAEOA are
also likely to reflect losses of BrC as a result of photobleaching and
photooxidation.
The BC / OA ratio is found to range from 0.013 to 0.040, with a mean value of
0.019 (see Fig. 8d). Assuming an OA / OC ratio of 1.8 (Mikhailov et al., 2017),
the retrieved mean value of the BC / OA ratio corresponds to a BC / OC ratio of
0.034, which is very close to our previous estimate (Konovalov et al.,
2017b) of this characteristic of 0.036 (±0.009), derived from the
AERONET observations of BB plumes in Siberia in 2012.
The approximations given by Eqs. (16)–(18) are in fairly good agreement
with our retrievals of δBrC, kOA, and MAEOA. Specifically,
in all three cases, the mean square error of the approximations is at least
a factor of 3 smaller than the corresponding mean values. These results
suggest that Eqs. (16)–(18) can be used to parameterize the BrC absorption
in models, given observations of the absorption Ångström exponent.
Similarly, the BC / OA ratio can be parameterized as a function of SSA using
the linear equation reported in Fig. 8d. Note, however, that the suggested
parameterizations reflect statistical relationships specific to Siberian BB
aerosol and are not necessarily directly applicable to constraining BrC in BB
aerosol in other regions of the world. Furthermore, the derived
parameterizations can also be affected by systematic uncertainties in the
inferred parameters (see Sect. 4.4). Note also that the required AAE and
SSA values can be derived not only from the remote measurements of AERONET
or other sun–sky radiometer networks but also from in situ measurements of
aerosol absorption and scattering with an aethalometer and nephelometer
(e.g., Chiliński et al., 2019). The aethalometer observations proved to
be especially useful in remote regions such as the Arctic (Schmeisser et
al., 2018). Tentative data on the wavelength-dependent BB OA absorption are
becoming available from satellite observations (Junghenn Noyes et al.,
2020).
Comparison of (a)δBrC and (b) the BC / OA ratio inferred
from AERONET observations using the method proposed in this study with
corresponding estimates derived from the same observations following Wang et
al. (2016) and Pokhrel et al. (2016), respectively. The confidence intervals
are shown in terms of the 68.3th percentile, except that the confidence
intervals for the estimates based on Wang et al. (2016) represent only the
uncertainty associated with the wavelength dependence of the AAE for BC.
Our estimates discussed above can further be compared with estimates based
on alternative methods. Specifically, Fig. 9 shows our estimates of
δBrC and the BC / OA ratio in comparison with the corresponding
estimates based on W16 and Pokhrel et al. (2016), respectively. As mentioned
above, W16 suggested deriving δBrC from the difference between
AAE440/870 and AAE675/870 by taking into account the wavelength
dependence of the AAE for BC as a function of AAE675/870 from Mie theory
calculations. Pokhrel et al. (2016) derived the empirical linear
relationships between SSA and the EC / (EC + OC) ratio from data of the
laboratory measurements of fresh BB aerosol from a range of fuels from North
America. Here we applied the original relationship provided by Pokhrel et
al. (2016) for SSA at 660 nm to the SSA observations at 675 nm from our set
of the AERONET data (see Sect. 3 and Fig. 1), disregarding a minor
discrepancy in the wavelengths.
It can be seen that there are big differences between the different
estimates of δBrC for individual observations (see Fig. 9a). In most
cases, these differences can be explained by uncertainties in both kinds of
estimates, but there are also systematic differences. Specifically, the mean
value of δBrC according to our estimates is almost a factor of 2
larger than that based on W16, which is probably mainly due to disregarding
the contribution of BrC to the absorption at the 675 and 870 nm wavelengths
as well as the effects of the coarse-mode absorption in W16. Furthermore,
while a sizable fraction of δBrC estimates based on W16 are less
than 0.05, our algorithm predicts that the corresponding values of δBrC are greater than 0.08. This difference can partly be an effect of the a
priori constraints on the IRI in our estimation: because of the observation
error, the a posteriori estimates tend to be biased (either positively or
negatively) toward the mean of the a priori estimates. There would be no
such biases if the observations were perfect, as evidenced by our tests with
synthetic data (see Fig. 5). Note that the average of the δBrC
values (0.171) obtained by directly matching our simulations to the AERONET
observations (see Fig. 4a) is only 18 % lower than the average of the
corresponding a posteriori estimates (0.209) inferred from the same
observations using the Bayesian algorithm (see Fig. 8a), and the similar
differences for kOA, MAEOA, and the BC / OA ratio are also rather
small (compared to the confidence intervals). These facts indicate that the
biases in our a posteriori estimates of the unobserved characteristics due
to random uncertainties in the AERONET data are not very significant.
Our estimates of the BC / OA ratio are, in most cases, also higher than the
alternative estimates (see Fig. 9b), which can be because the relationships
by Pokhrel et al. (2016) are obtained for fresh aerosol and can therefore
underestimate SSA for aged aerosol (with the same BC / OA ratio) if the aging
results in BrC losses. Nonetheless, there is a rather high correlation
(r>0.68) between the two kinds of estimates, indicating that the
variability in both kinds of estimates is driven by the same factors.
Overall, we find the different estimates of δBrC and BC / OA to be in
reasonable agreement and consider this comparison as evidence for the
robustness of our estimates. Note that both alternative methods show
inferior performances when applied to the synthetic dataset used above in
comparison with our algorithm.
Relationships between retrievals of BB aerosol characteristics
from AERONET observations: (a)δBrC vs. kOA, (b)δBrC
vs. the BC / OA ratio, and (c)kOA vs. the BC / OA ratio. The solid lines
and shading show the best linear fits to the data and the corresponding 68.3 % confidence intervals.
Finally, we examined some relationships between the variables retrieved with
our method (see Fig. 10). Specifically, Fig. 10a reveals a close
relationship between the OA IRI (kOA) and δBrC. Similarly to the
dependence of δBrC on AAE440/870 (see Fig. 8a), this
relationship indicates that variations in the OA IRI are a key factor
determining the variability in the BrC absorption of Siberian BB aerosol.
Not surprisingly, δBrC is also affected by variations in the BC / OA
ratio, depending inversely on it (see Fig. 10b): consistent with the
definition of δBrC (see Eq. 1), a stronger BC absorption is
associated with a smaller relative contribution of BrC to the overall
absorption (see also Sect. 4.1 and Fig. 2). Pokhrel et al. (2017) reported a
similar inverse relationship between the light absorption enhancement by BrC
and the BC / OC mass ratio. However, the derived inverse relationship between
δBrC and the BC / OA ratio is rather weak, apparently reflecting the
effects of variations in kOA (as evidenced by Fig. 10a) and other
aerosol parameters on δBrC. In turn, the OA IRI does not manifest
any significant statistical relationship with the BC / OA ratio (see Fig. 10c). This is not quite an expected result. Indeed, based on the findings of
previous studies (Saleh et al., 2014; Lu et al., 2015), it could be expected
that kOA is typically larger in BB aerosol samples which feature a
larger BC / OA ratio: as argued by Saleh et al. (2014), a larger BC content is
associated with a larger fraction of strongly absorbing organic compounds of
extremely low volatility. It seems reasonable to suggest that a positive
association between kOA and the BC / OA ratio is lacking in our case
because of the effect of aging of BB aerosol on the BrC content. In
particular, according to our previous analysis (Konovalov et al., 2021),
strongly aged Siberian BB aerosol is likely to feature a higher BC / OA ratio
than relatively fresh aerosol (because of evaporation and fragmentation of
organic compounds) but a lower BrC absorption (because of photodegradation
and photooxidation of BrC). On the other hand, an aerosol aged 10–30 h
may feature, in some situations, a relatively low BC / OA ratio and high BrC
absorption as a result of the formation of absorbing SOA (Saleh et al.,
2013; Konovalov et al., 2021). Note that the estimates of kOA and BC / OA
reported by Saleh et al. (2014) and Lu et al. (2015) are representative
mostly of relatively fresh BB aerosol.
Sensitivity test cases
In this section, we examine how our estimates of the BB OA absorption
properties can be affected by several factors that could not be formally
addressed in the framework of our Bayesian algorithm as part of the
observation errors or the a priori uncertainty in the aerosol parameters. To
this end, we considered three sensitivity test cases described below. The
results from these test cases are presented in the Supplement (Figs. S3–S8)
and are summarized in Table 2. The inferred estimates reported in the
previous section are referred to below as the base case estimates.
Estimates of the mean values of the inferred
characteristics of Siberian BB aerosol according to several estimation cases
described in Sect. 4.4.
Estimation caseKey featuresδBrCkOAMAEOA [m2 g-1]BC / OA [g g-1]Base caseThe configuration of the estimation procedure described in Sect. 20.212.3×10-38.5×10-21.9×10-2Test case 1The same as the base case but with non-absorbing coarse-mode particles0.161.6×10-36.1×10-22.3×10-2Test case 2The same as the base case but assuming internally mixed aerosol having the same composition for all particle sizes0.151.7×10-35.6×10-21.7×10-2Test case 3The same as the base case but the wavelength dependence of the IRI of OA follows McClure et al. (2020)0.171.9×10-37.1×10-21.9×10-2A priori (unconstrained) estimatesThe same as the base case but assuming infinitely large errors in all components of the observation vector (see also Fig. 3)0.642.7×10-28.9×10-14.1×10-2
The first test case (hereinafter, test case 1) addresses a possible
systematic uncertainty in our estimates due to our assumption regarding the
IRI of the coarse-mode aerosol particles (see Sect. 2.1). To assess this
uncertainty, we assumed, for test case 1, that the IRI of the coarse-mode
particles is zero. As explained above, the value of this parameter has been
chosen as a typical (climatological) value of the IRI characterizing BB
plumes in boreal forests. However, we also noted that assuming this value
would likely result in an overestimation of the absorption by real coarse-mode particles since BC (which is known as the major absorbing component of
BB aerosol) is likely to reside mostly in fine-mode particles (e.g., May et
al., 2014; Morgan et al., 2020). Taking this consideration into account, we
expect the most representative values of the IRI of the coarse-mode
particles to lie in the range between the value assumed for the base case
and zero.
The OA absorption parameter estimates inferred in test case 1 are, on
average, up to 30 % lower and the BC / OA ratio is about 20 % higher than
those in the base case (cf. Figs. 8 and S3). The decrease in the estimated
values of the absorption parameters can be explained as a result of smaller
values of the AAEs in the base case due to a contribution of the coarse-mode
particles to the absorption at the 870 nm wavelength since the smaller values of
the computed AAEs would require larger values of the OA IRI to match the
observed AAEs. Although seemingly considerable, the differences between the
estimates for the two cases fall into the 68.3 percentile confidence
intervals for the base case estimates (see Fig. S4). Furthermore, these
differences are small in comparison with the a priori estimates of the
unobserved properties and their uncertainty (see Table 2 and Fig. 4).
Therefore, although test case 1 confirms the previous analysis (Schuster et
al., 2016) that the coarse-mode particles can have a significant impact on
the AAEs and, hence, on the deduced BrC absorption, it also indicates that
our estimates are sufficiently robust against the backdrop of the huge
uncertainty in the a priori estimates.
Test case 2 was designed to give an idea about possible systematic
uncertainties in our estimates that result from the fact that the AERONET
retrievals of the different components of the observational vector are
related through a common retrieval algorithm and therefore may be affected
by error covariances. Taking into account that the AERONET algorithm is very
flexible, with aerosol column concentrations being optimized almost
independently for many size sections (Dubovik and King, 2000), we presume that
any significant error covariances may arise mostly because AERONET
retrievals are based on an aerosol model featuring the same refractive index
for all sizes of internally mixed aerosol particles. To assess the effect of
these possible error covariances on our estimates, we modified our aerosol
model described in Sect. 2.1 by assuming that (1) the BC size distribution
is the same as that of OA, (2) the aerosol components are internally
(homogeneously) mixed, and (3) all particles from both fine and coarse modes
have the same composition (and, hence, the same refractive index) dependent
on the BC / OA ratio and relative humidity similarly to fine particles in the
base case. Our idea behind these modifications was that the use of such
modified computations in our estimation algorithm could compensate for the
effect of the error covariances in the AERONET retrievals on our estimates.
In other words, our expectation was that the difference between the test and
base cases would manifest possible systematic uncertainties in our estimates
associated with the mentioned feature of the AERONET algorithm.
The results of test case 2 (see Fig. S5) turned out to be rather similar to
those of test case 1, except that the BC / OA ratio decreased rather than
increased compared to the base case. The differences between the estimates
for the base case and test case 2 (see Fig. S6) are also covered by the
confidence intervals for the base case estimates. So, following the same
reasoning as in the above discussion of the results of test case 1, we
consider the results of test case 2 as strong evidence that possible error
covariances in the AERONET retrievals cannot devalue the inferred estimates.
Note that the estimates obtained for test case 2 are not necessarily more
accurate than those for the base case because the simplified aerosol model
assumed for this test can hardly provide sufficiently accurate relationships
between the observed properties and the BB OA absorption parameters, even if
it is expected to compensate for some errors in the AERONET retrievals.
Physically, the differences between the estimates for the base case and test
case 2 can be caused by several complex factors but are likely predominantly
due to the significant effects of the different mixing states on the
absorption properties of carbonaceous aerosol particles (e.g., Jacobson,
2001). A more detailed analysis of these factors goes beyond the scope of
this study.
Finally, in test case 3, we assessed the sensitivity of our estimates to
potential systematic uncertainties in the wavelength dependence of the OA
IRI, w. As explained in Sect. 2.1, the a priori estimates of w are based on
the parameterization by Lu et al. (2015), which is quantitatively consistent
with the estimates that were reported earlier by Saleh et al. (2014).
However, according to a more recent laboratory study by McClure et al. (2020), values of w for fresh BB aerosol in the range of BC / OA ratios
relevant for Siberian BB aerosol are typically larger (up to a factor of 2)
than those reported by Saleh et al. (2014) and Lu et al. (2015). Taking into
account that the estimates of w reported by Lu et al. (2015) were derived
from a variety of laboratory and in situ measurements, we presumed they are more
representative of the observations analyzed here than the laboratory data by
McClure et al. (2020). Nonetheless, the discussed differences are indicative
of the possibility that our a priori values of w may be biased. Therefore, to
examine the effects of this potential bias on the a posteriori estimates, we
repeated all our computations described in Sect. 2 by using the estimates of
w by McClure et al. (2020). Specifically, the dependence of w0 (see Eq. 4) on the BC / OA ratio was parameterized as follows (Crystal D. McClure, personal
communication, 2021):
w0=0.29+7.951.+6.06×(BC/OA)0.43.
Similarly to the previous test cases, test case 3 yields somewhat lower
estimates of the OA absorption properties (δBrC, kOA, and
MACOA), but the difference with respect to the base case is, on
average, smaller (less than 20 % for any of the properties) than for the
other test cases. Smaller values of the absorption parameters in this test
case (see Figs. S7 and S8) are an expected result, since stronger wavelength
dependence in our computations leads to larger AAE values, and so less
absorbing OA is needed to provide agreement between the observed and
computed AAEs.
Overall, the results for the three test cases indicate that the
inferred estimates of the OA absorption parameters and the BC / OA ratio are
sufficiently robust with respect to possible systematic errors in our
estimates. By the robustness of our estimates, we understand, specifically,
that possible biases in them are small compared to the a priori uncertainty
in the estimated parameters and are probably not inconsistent with the
reported confidence intervals. At the same time, the test case results
suggest that our base case estimates of the absorption parameters are likely
at the upper edge of the most probable values of these parameters,
particularly in view of the likely overestimation of the IRI of the coarse-mode particles and possible systematic uncertainties in the AERONET data.
Conclusions
We developed a Bayesian method to infer parameters characterizing the
absorption of solar light by BrC contained in particles of BB aerosol. The
method involves Monte Carlo calculations of the aerosol optical properties
using Mie theory. As a result of a probabilistic combination of the
calculation and observations of optical properties of BB aerosol with a
priori estimates of the aerosol parameters, we inferred a posteriori
estimates of the parameters characterizing BrC absorption and estimated
their confidence intervals. In this study, we applied our method to the AAE and
SSA derived from ground-based measurements of solar and sky radiances at two
AERONET sites (Tomsk_22 and Yakutsk) in Siberia. The
available observation data were screened to select only observations of
optically dense BB plumes. In our baseline calculations, we assumed a
core–shell structure of fine-mode aerosol particles and randomly varied
parameters of both the core (consisting of BC) and shell (consisting of
organic carbon, inorganic salts, and water) within a wide range of observed
values. Possible effects of coarse-mode particles on the observed absorption
properties of BB aerosol were also taken into account, albeit in a highly
simplified manner.
We first evaluated our method using synthetic (perfect) data, which were
obtained by fitting our calculations to the AERONET retrievals. Consistent
with previous studies, we found that two AAEs calculated for the 440–870 and
675–870 nm wavelength pairs provide a strong constraint on the relative
contribution of BrC to aerosol absorption (δBrC). However, the use
of only AAEs was found to be insufficient to constrain the IRI of OA (kOA) and
the MAE of OA (MAEOA). We argued that this is because the same δBrC can correspond to different combinations of values of kOA and the
BC / OA ratio. We argued also that the ambiguity associated with the
estimation of kOA and the BC / OA ratio can be resolved using SSA as an
additional observational constraint. We demonstrated that, when the AAE data
are complemented with SSA observations, our method can provide reasonably
accurate estimates of kOA, MAEOA, and the BC / OA ratio. The
remaining uncertainties in the a posteriori estimates of these parameters
are mostly due to the variability in other aerosol parameters and are
reflected in the corresponding confidence intervals.
The application of our method to the original AAE and SSA data derived from
the AERONET observations indicated that the absorption characteristics
mentioned above (δBrC, kOA, and MAEOA) are highly variable,
but, on the whole, the OA in BB plumes in Siberia is weakly absorbing.
Specifically, the mean values of δBrC, kOA, and MAEOA are
found to be about 0.21, 2.3×10-3, and 0.08 m2 g-1,
which are at the lower end of the ranges of values derived for these
characteristics in earlier studies from laboratory and in situ data.
Furthermore, supplementary analysis aimed at examining possible systematic
uncertainties in our estimates, which could be properly assessed directly in
the framework of our Bayesian algorithm, indicates that the above-baseline
values are likely at the upper edge of the most probable values of the
corresponding parameters. However, these low values are consistent with the
previously reported degradation of atmospheric BrC under UV irradiation.
The OA absorption characteristics were found to closely correlate with the
AAE for the 440–870 nm wavelengths (AAE440/870). Based on the analysis
of the retrieved contributions of BrC and BC to AAE440/870, we
suggested nonlinear approximations for the dependences of δBrC,
kOA, and MAEOA on AAE440/870. We also derived a simple linear
approximation for the dependence of the BC / OA ratio on SSA440. These
approximations can be used to parameterize the BB aerosol absorption in
atmospheric models, although it is necessary to keep in mind that the
parameterizations suggested in this paper are directly applicable only to
Siberian BB aerosol.
Finally, we considered the relationships between our retrievals of the
different aerosol properties. We found, in particular, that δBrC
strongly (and positively) correlates with kOA and inversely (but weakly)
depends on the BC / OA ratio. No statistically significant dependence of
kOA on the BC / OA ratio was found. The lack of such a dependence
(which was reported in previous studies) in our case is probably another
manifestation of the atmospheric aging of BB aerosol.
Overall, we proposed major development of the AAE-based methods suggested
earlier and demonstrated that it is beneficial to constrain the BB aerosol
parameters determining the BrC absorption by using both AAE and SSA data,
which are presently available from both ground-based measurements (in
particular, conducted with aethalometers and nephelometers) and satellite
observations. The application of our method to the AERONET observations
allowed us to obtain useful quantitative insights into the absorption
properties of Siberian BB aerosol, which plays a major role in the radiative
processes in northern Eurasia and the Arctic but has been poorly investigated. It
should be noted, however, that the current application is limited by
observations of dense BB plumes (having AOD at 550 nm larger than 0.8), and
so our estimates may not be representative of BB aerosol in highly diluted
(and strongly aged) plumes. Overcoming this limitation is challenging and
would require good knowledge of the optical properties of the background
aerosol as well as the use of the potentially less accurate Level 1.5
AERONET data instead of the quality-assured Level 2.0 data (which are not
representative of low-AOD conditions). Future developments of our method may
also include (1) an enhancement of the number of the observed
characteristics considered the components of the observation vector in
the Bayesian analysis, (2) accounting for a possibility of external mixing
of BC and OA within the Mie theory calculations, and (3) improving the
representation of the absorption properties of coarse particles. The
potential of the suggested Bayesian approach to the investigation of BrC
absorption should be explored further using observations in other regions of
the world.
Code availability
OPTSIM software is available at https://www.lmd.polytechnique.fr/optsim/
(last access: 6 May 2021, Menut, 2021).
Data availability
The AERONET data for the Tomsk_22 site are available from https://aeronet.gsfc.nasa.gov/cgi-bin/data_display_inv_v3?site=Tomsk_22 (Holben, 2021). The AERONET data for the Yakutsk site are available from https://aeronet.gsfc.nasa.gov/cgi-bin/data_display_inv_v3?site=Yakutsk (Holben et al., 2021).
The supplement related to this article is available online at: https://doi.org/10.5194/amt-14-6647-2021-supplement.
Author contributions
IBK designed the study and the method to analyze optical observations,
contributed to the analysis of AERONET data, and prepared the paper. NAG
developed computer codes for the Bayesian analysis and conducted simulations
with the OPTSIM software. MVP contributed to the preparation of the AERONET
dataset. MB and MOA contributed to the discussion of the results and the
preparation of the paper.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests.
Disclaimer
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
The
authors acknowledge the free use of the AERONET data available from
https://aeronet.gsfc.nasa.gov.
Financial support
The development of the BrC estimation
method was supported by the Russian Science Foundation (grant
no. 19-77-20109). The analysis of the retrieved optical
properties of BB aerosol was supported by the CNRS International
Emerging Actions program no. 304365 (project MERSI) and the Russian Foundation for Basic Research (project no. 21-55-15009).
Review statement
This paper was edited by Alexander Kokhanovsky and reviewed by two anonymous referees.
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