We used the OMI AAOD retrievals provided as a part of the OMAERUV (v. 1.8.9.1) Level-2 data product that were derived by the NASA group from the OMI observations onboard of the EOS Aura satellite. OMI is a spectrally high-resolution nadir-looking spectrometer that measures the backscattered solar radiance in the ultraviolet and visible regions of the electromagnetic spectrum . The OMI measurements provide daily global coverage at a spatial resolution of 13×24 km2 at nadir. Aura is a part of NASA's A-train satellite constellation and is in a sun-synchronous ascending polar orbit with a local Equator crossing time of 13:45. The OMAERUV algorithm derives the UV aerosol index in the 354–388 nm range from radiance observations by making use of the observed departure of the spectral dependence of the near-UV upwelling radiation at the top of the atmosphere from that of a hypothetical pure molecular atmosphere. Along with the UV aerosol index, the OMAERUV data product provides AAOD, AOD, and SSA retrieved following a standard look-up table approach with assumed aerosol models, surface albedo, and aerosol layer height.

The major features of the OMAERUV retrieval algorithm that are relevant in the context of inverse modeling applications of the AAOD data are described in detail by . Briefly, they are as follows. First, the OMAERUV algorithm identifies one of the three assumed aerosol types, such as BB aerosol, desert dust, or urban/industrial aerosol, representing column aerosol load in each pixel. The selection of aerosol type is based on a scheme that uses coincident and collocated carbon monoxide (CO) observations from AIRS on Aqua and the UV aerosol index from OMI . Second, the algorithm is sensitive to assumptions about the altitude of the aerosol center mass. To address this sensitivity, the AAOD data are retrieved for a set of five different aerosol center mass locations: at the surface and 1.5, 3.0, 6.0, and 10 km above the surface. The “final” AAOD product derived by OMAERUV is referenced to the monthly climatology aerosol layer height as given by the OMI-CALIOP (Cloud-Aerosol Lidar with Orthogonal Polarization) joint dataset . Third, the major factor affecting the quality of the aerosol retrievals provided by OMAERUV is sub-pixel cloud contamination. However, compared to AOD and SSA retrievals, AAOD is less affected by cloud contamination due to the partial cancellation of errors in AOD and SSA. OMAERUV reports AOD/SSA/AAOD with the associated quality flags “0” and “1”. While all three retrievals are reliable with the quality flag “0”, only AAOD is reliable with either quality flag. Accordingly, the number of reliable AAOD retrievals is greater than the number of respective AOD and SSA retrievals.

The OMAERUV product has been validated on a global scale by comparing OMI-retrieved AOD and SSA with the corresponding data derived from ground-based measurements of the sun/sky photometers at the AERONET sites . The comparison confirmed that the OMI AOD and SSA retrievals are quite reliable. Specifically, the differences between most of the pairs of matched AOD data were found to fall into the expected uncertainty range (the greater of ±30 % or ±0.1) for the OMI AOD retrievals for all of the aerosol types, while the majority of collocated SSA retrievals for the “smoke” and “dust” aerosol were found to agree within the expected uncertainties of ±0.03 in OMI and AERONET inversions. Since AAOD can be expressed through SSA and AOD, these comparisons indicate that the OMI AAOD retrievals are also realistic.

In this study, we made use of the reliable AAOD retrievals corresponding only to the BB type of aerosol. The quality assured values of AAOD at 388 nm for the period from 1 May to 30 September 2012 were projected onto a rectangular 1∘×1∘ grid with an hourly temporal resolution. Different values falling into the same grid cell within an hourly period were averaged. We used both the AAOD datasets corresponding to the predefined altitudes of the aerosol layer and the “final” AAOD product.

As noted above, the available OMI AAOD retrievals are more abundant than the quality assured retrievals of AOD. For this reason, the OMI AOD retrievals were not used in our analysis. Instead, we employed the Collection 6 retrievals of AOD at 550 nm from the MODIS measurements onboard the Aqua satellite , which is also a part of NASA's A-train satellite constellation. The MODIS Aqua measurements are typically taken at around the same time as the OMI measurements, as Aqua overpasses the Equator daily at 13:30 (local time) in the ascending mode. The merged “dark target” and “deep blue” AOD retrievals with a nominal horizontal resolution of 10×10 km2 were obtained for the period from 1 May to 30 September 2012 as a part of the MYD04-L2 data product . Similar to the AAOD data, the quality assured AOD data for the period from 1 May to 30 September 2012 were projected onto a rectangular 1∘×1∘ grid with an hourly temporal resolution and then averaged. The expected uncertainty range of the MODIS AOD retrievals is ±(0.05+15%). A comparison of the Collection 6 MODIS AOD data with the respective AERONET retrievals has shown that this uncertainty range covers the majority (69 %) of the differences between the MODIS and AERONET collocated AOD retrievals .

The fire radiative power (FRP) data derived from the MODIS measurements onboard the Aqua and Terra satellites were used in this study to calculate BB emissions of gases and aerosols via the methods developed earlier (Konovalov et al., 2011b, 2014). The FRP data were provided at nominal 1 km spatial and 5 min temporal resolutions as a part of the MYD14/MOD14 Collection 6 MODIS fire products (Giglio and Justice, 2015a, b; Giglio et al., 2016). The Collection 6 FRP retrieval algorithm makes use of the difference between the 4 µm radiance of a pixel affected by fires compared with that of a background pixel (Wooster et al., 2012). The Collection 6 Terra MODIS fire products were validated using reference 30 m fire maps derived from high-resolution Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images (Giglio et al., 2016). The fire detection omission error was found to be less than 10 % for relatively large fires composed of 140 or more fire pixels; however, the ASTER data did not allow quantitative evaluation of the MODIS FRP retrievals which, in general, may be affected by clouds, heavy smoke, or tree crowns.

Our processing of the available FRP data was the same as described in Konovalov et al. (2014). Briefly, we first estimated the FRP density on a 0.2∘×0.1∘ grid covering the northern Eurasian region considered in this study as the ratio of the total FRP in a given grid cell to the observed area of that grid cell. The estimation was done for any Aqua and Terra orbit overpassing a given grid cell during a given day, and a maximum FRP density value for each grid cell and day in the period from 1 May to 30 September 2012 was selected. Persistent FRP pixels (which may be due to gas flaring) were filtered out. We then estimated the daily mean FRP density by scaling the maximum FRP density with the assumed diurnal cycle of FRP. The diurnal cycle of FRP was estimated using the method proposed by Konovalov et al. (2014) which involved fitting a Gaussian function approximating the diurnal cycle to the selected FRP daily maxima corresponding to different hours of the day. The daily mean gridded FRP densities were then used to calculate BB emissions as described in Sect. .

To characterize the optical properties of BB aerosol in Siberia, we used (along with the satellite retrievals) the aerosol data derived from ground-based measurements of the spectral diffuse sky and direct sun radiation by photometers at the sites of the AErosol RObotic NETwork (AERONET) (Holben et al., 1998). Specifically, we used AAOD and SSA retrievals at 440 and 675 nm and AOD observations at 500 and 675 nm. The AAOD and SSA data were obtained from the version 2, level-2 (cloud screened and quality assured) aerosol inversion product (Dubovik and King, 2000), while the AOD data were provided from the version 2, level-2 direct sun AERONET observations. The uncertainty of the AOD measurements has been estimated to be within ±0.01 in the visible region and ±0.02 at near-UV wavelengths, and the uncertainty in retrieved SSA has been estimated to be within ±0.03 when AOD at 440 nm is larger than 0.4 (Dubovik et al., 2000). Note that AOD at 440 nm is greater than 0.4 for all retrievals provided in the level-2 AERONET inversion product (since inversions corresponding to smaller AOD values are considered to be less accurate). Following Konovalov et al. (2017b), in this study we analyze the AERONET data from sites situated in Siberia. The direct sun measurements and inversions for the fire season of 2012 were only available from two Siberian sites: Tomsk-22 (56.4∘ N, 84.7∘ E) situated in western Siberia and Yakutsk (61.7∘ N, 129.4∘ E) situated in eastern Siberia.

To evaluate the simulated concentrations of EC and OC, we used the data collected at the Zotino Tall Tower Observatory (ZOTTO) established at a remote location (about 600 km from the nearest city, Krasnoyarsk) in the boreal forest of central Siberia (Heimann et al., 2014). The geographic coordinates of the observatory are 60.8∘ N and 89.4∘ E. Due to the background character of its environment, ZOTTO is suitable for studying natural sources of aerosol and gases in the boreal forest (Chi et al., 2013). The observatory includes a 300 m tall mast that enables probing of the atmospheric composition within the planetary boundary layer and the capture of the regional concentration signal (Gloor et al., 2001).

Continuous long-term measurements of the ambient aerosol carbonaceous fraction (including those of elemental and organic carbon) have been carried out at ZOTTO since 2010 (Mikhailov et al., 2015, 2017). The ambient aerosol was sampled from the top of the tower through a stainless steel inlet pipe and collected on quartz fiber filters. The sampling period varied from 10 to 480 h, depending on the air pollution level. Concentrations of EC and OC were measured by a thermal–optical carbon analyzer from Sunset Laboratory (OR, USA). The uncertainties of the EC and OC measurements consist of a constant part of 0.2 µgCcm-2 and a multiplicative part of 5 %. Further details regarding the techniques and protocols used for the EC and OC measurements at ZOTTO can be found elsewhere (Mikhailov et al., 2017).

Aircraft measurements spanning large areas and wide altitude ranges are an indispensable source of the observational data for evaluation in chemistry transport models. Here we use the data collected over eastern and western Siberia onboard the Optik Tu-134 aircraft laboratory in the framework of the Airborne Extensive Regional Observations in SIBeria (YAK-AEROSIB) experiments (Paris et al., 2008, 2009a). In summer 2012, the YAK-AEROSIB measurement campaign was carried out on 31 July and 1 August (Antokhin et al., 2018). On 31 July, the aircraft departed from Novosibirsk (54.9∘ N, 85.2∘ E) and arrived in Yakutsk (61.9∘ N, 128.5∘ E), with an intermediate landing in Tomsk (56.2∘ N, 84.7∘ E). On 1 August, the aircraft departed (return flight) from Yakutsk and landed in Novosibirsk. During the flights, the aircraft performed several ascents and descents within the altitude range from about 1 to 8 km and crossed several major smoke plumes originating from fires in Siberia. Further information regarding the tracks of flights carried out in the framework of the YAK-AEROSIB campaign from July to August 2012 can be found elsewhere (Antokhin et al., 2018).

In this study, we considered the YAK-AEROSIB observations of mass concentrations of equivalent black carbon (eBC) and fine fraction of aerosol (PM2.5) along with the mixing ratio of carbon monoxide (CO). The measurement techniques have been described previously (Paris et al., 2008; 2009a, b). Briefly, eBC was measured using an Aethalometer (Panchenko et al., 2000, 2012), which detects diffuse light attenuation by particles collected on a filter. The measurements considered in this study were performed at a wavelength of 640 nm. The sensitivity of the Aethalometer is estimated to be 0.01 µgm-3. The eBC measurements were calibrated against gravimetric measurements of BC mass concentration, using BC particles produced by a pyrolysis generator. It should be noted that the accuracy of Aethalometer measurements may be affected by several factors, including the SSA of ambient aerosol particles, particle size, composition, and filter loading (see, e.g., Liousse et al., 1993; Sharma et al., 2002; Lack et al., 2014). In particular, the eBC concentration may be strongly overestimated due to greater light scattering by ambient aerosol particles compared to scattering by the soot particles used in the calibration procedure, although this effect can be counterbalanced by lower attenuation for larger filter loadings (see, e.g., Weingartner et al., 2003). Furthermore, the eBC concentration can be different from the EC concentration in the same aerosol sample, simply because eBC and EC measurements represent fundamentally different physical properties of the aerosol (Andreae and Gelencsér, 2006; Bond et al., 2013). Parallel field measurements of eBC (with a standard Aethalometer) and EC (using a thermal technique) at an Arctic station (Sharma et al., 2017) revealed that eBC was systematically larger (by about 30 %) than EC in winter and spring (when the aerosol was predominantly anthropogenic) but almost 50 % smaller in summer (when the contribution of BB aerosol might be significant). Whilst the eBC observations that are widely used for characterizing radiative properties of aerosol in remote regions can not provide a strong constraint on BC emissions (especially when the BC emissions are interpreted as those of EC), the analysis of the eBC observations performed during the YAK-AEROSIB campaign is useful as it allows us to get an idea of the consistency of different types of BB BC measurements in Siberia.

PM2.5 mass concentrations were obtained using the GRIMM 1.109 optical particle counter (GRIMM Aerosol Technik GmbH & Co. KG, Germany) which measures particle number concentration in 31 size channels in the range from 0.25 to 32 µm. Following Burkart et al. (2010), the conversion of number concentration to mass concentration was performed by applying the instrument-specific factor (equal to 1.65) and an additional correction factor, the C factor, which is dependent on the bulk density of the sampled aerosol. Burkart et al. (2010) found that the C factor can be estimated as the ratio of the instrument-specific factor to the aerosol density. Accordingly, assuming that the typical density of BB aerosol is about 1.3 gcm-3 (Reid et al., 2005b), we estimated the C factor for our case to be 1.27.

Measurements of the CO mixing ratio were made using a modified commercial gas analyzer Thermo 48C (Thermo Environmental Instruments, USA; see Nedelec et al., 2003; Paris et al., 2008). Note that the measurements of the CO mixing ratio were only used in this study for the selection of aerosol measurements representative of BB plumes (as explained in Sect. 3.4). The eBC, PM2.5, and CO observations were matched in time by first averaging the PM2.5 concentrations (which were nominally available each second) over a variable period (4–16 s) between two consecutive eBC observations and then selecting the closest CO observation (among the data that were nominally available every 4 s).

The simulations considered in this paper were performed with the 2017 version of the CHIMERE model (Mailler et al., 2017), which is an off-line chemistry transport model designed to produce forecasts and simulations of air pollution over a range of spatial scales, from urban to hemispheric. We used the model to simulate mass concentration, composition, and optical depth of BB aerosol as well aerosol optical properties (AOD and AAOD) in the absence of fires. Earlier versions of the CHIMERE model have been successfully used in a number of studies of BB aerosol and related atmospheric processes (see, e.g., Hodzic et al., 2007, 2010; Konovalov et al., 2012; Péré et al., 2014; Turquety et al., 2014). The codes of the 2017 version of the CHIMERE model (CHIMERE-2017) have evolved significantly with respect to the codes of the previous versions; the most significant changes are associated with the realization of parallel computations and the representation of the optical effects of aerosols and clouds. However, these changes do not cause major differences in the simulations of the concentration and composition of BB aerosol. A detailed description of the CHIMERE-2017 model and a list of the recommended model settings (most of which were adopted in our simulations) can be found elsewhere (CHIMERE-2017, 2018; Mailler et al., 2017); hence, we only describe the main features of our computations in the following.

We took BB emissions of aerosol and reactive gases along with their other anthropogenic and biogenic sources into account, including non-BB sources of dust and sea-salt aerosol. The BB emissions were calculated using the MODIS FRP data as explained in Sect. . The anthropogenic emissions were specified by applying the CHIMERE standard emission interface to the monthly emission data from the global Hemispheric Transport of Air Pollution (HTAP) v2 emission inventory (Janssens-Maenhout at al., 2015). Since HTAP data for the year 2012 were unavailable, we used the corresponding data for the year 2010; the differences between the annual anthropogenic emissions in 2010 and 2012 are unlikely to exceed a few percent in the region considered. Note that the HTAP inventory does not consider emissions from gas flaring; however, these emissions likely only provide a very minor contribution (less than 2 %) to the BC emissions (Winiger et al., 2017) in Siberia in summer 2012. Other sources of aerosol and gases were taken into account using the standard CHIMERE procedures described in Mailler et al. (2017).

Aerosol particles of all types were distributed among 10 size bins covering the particle diameters from 10 nm to 40 µm following a lognormal size distribution. Based on an empirical BB particle emission model by Reid et al. (2005b), the emissions of BC and OC from fires were distributed among a range of particle sizes using a lognormal particle size distribution with a mass mean diameter of 0.3 µm and a geometric standard deviation of 1.6. A minor fraction of BB emissions, which comprises coarse particles with a typical mean diameter of about 5 µm, was disregarded in our simulations. Note that these coarse particles are not likely to provide a significant contribution to aerosol optical properties in the visible and UV regions of the spectrum (Reid et al., 2005a). The parameters of the distributions for other aerosol types were specified using the standard settings described in the CHIMERE technical documentation (CHIMERE-2017, 2018).

Aerosol evolution in the atmosphere was simulated with the standard parameterizations implemented in CHIMERE-2017 (Mailler et al., 2017) by taking secondary organic aerosol (SOA) formation as well coagulation and dry and wet deposition into account, except that the wet deposition of BB aerosol (which was assumed to be hydrophobic) due to in-cloud scavenging was effectively disregarded by setting the empirical uptake coefficient to be zero. Specifically, the SOA formation was represented by the scheme proposed and evaluated by Bessagnet et al. (2008). Note that, as shown by Konovalov et al. (2015, 2017a), the atmospheric evolution of aerosol originating from Russian boreal fires may be much more strongly affected by aerosol aging processes involving both primary and secondary semi-volatile organic compounds than represented in the CHIMERE simulations using the standard SOA scheme. Note also that, although experimental findings (Hand et al., 2010) suggest that fresh BB aerosol particles originating from forest fires are composed of predominantly hydrophobic material, aerosol aging processes are likely to increase the hygroscopicity of aerosol particles containing BC and to accelerate their removal from the atmosphere by precipitation through in-cloud scavenging (Stier et al., 2006; Oshima et al., 2012; Paramonov et al., 2013). However, these shortcomings of our simulations are not likely to lead to any significant biases in our estimates of BC emissions, as evidenced by the sensitivity tests discussed in Sect. .

The chemical evolution of gaseous air pollutants was represented using the MELCHIOR2 chemical mechanism. Following Konovalov et al. (2017a, b), we introduced two additional trace species that allowed us to estimate the photochemical age of the BB aerosol. One of the tracers (T1) is chemically passive, while the second tracer (T2) reacts with OH (without consuming it) with a constant rate (kOH) of 9×10-12 s-1cm3. This rate constant is chosen to give the reactive tracer a lifetime of about 6 h, given a typical OH concentration in BB plumes of 5×106 cm-3 (Akagi et al., 2012). The emissions of both tracers were the same as the BB emissions of OC. The photochemical age (ta) of BB aerosol was evaluated in each grid cell and hour as follows: ta=-(kOH[OH])-1ln⁡[T2]/[T1], where [T1] and [T2] are column densities of the tracers, and [OH] is the column-average OH concentration within the BB aerosol layer.

As explained in Mailler et al. (2017), the 2017 version of CHIMERE includes the Fast-JX module that computes photolysis rates and some additional diagnostics, including aerosol optical depth. The module first calculates aerosol Mie scattering and absorption for each aerosol species and bin, assuming sphericity of the aerosol particles and using a set of refractive indexes provided with the model. It then computes the radiative transfer in the model atmospheric column and evaluates the actinic fluxes at each model level. Note that the Fast-JX module was slightly modified in this study to enable simulations of AAOD along with AOD. The calculations of AOD and AAOD are performed for five wavelengths (200, 300, 400, 600, and 1000 nm). To evaluate AOD and AAOD at any other wavelength considered in our study, we used a power-law interpolation (assuming a constant Ångström exponent within a given wavelength interval) between the nearest wavelengths from the model's output. As noted in the introduction, the AAOD values computed in the CHIMERE runs taking BB emissions into account were not used in this study because of the high uncertainty of the imaginary part of the refractive index for organic carbon. Instead, we calculated the BB fraction of AAOD using an empirical parameterization (see Sect.  below) involving the CHIMERE simulations of the BC and OC column amounts and AOD. However, we used AAOD values directly simulated with CHIMERE to characterize the background atmospheric conditions (in the absence of fires).

To enable better consistency between the OMI-derived and simulated AAOD, the simulated vertical profiles of the BB fraction in PM2.5 were used to evaluate the altitude of the center of mass of the BB aerosol layer. The OMI-derived AAOD values corresponding to different assumed altitudes of the BB aerosol center of mass were linearly interpolated to the peak height derived from the simulations. The same approach was employed earlier by Zhang et al. (2015). Considering that the aerosol distribution was represented in the AAOD retrieval procedure by a Gaussian profile (Torres et al., 1998), each simulated PM2.5 profile was approximated by a Gaussian function and its maximum was considered as the aerosol center of mass.

Following Konovalov et al. (2014, 2017a, b), the simulations in this study were performed on a 1∘×1∘ model grid covering a large region in northern Eurasia (35.5–136.5∘ E; 38.5–75.5∘ N), including Siberia and parts of eastern Europe and the “Far East”. In addition, to simulate the aerosol concentrations at the ZOTTO site, the model was run with a higher resolution of 0.2∘×0.1∘ in a nested domain covering a part of central Siberia (86.2–92.4∘ E; 57.6–63.9∘ N). In the vertical, the model meshes include 12 non-equidistant layers extending from the surface up to the 200 hPa pressure level. The meteorological fields were obtained using the WRF (Weather Research and Forecasting; version 3.9) model (Skamarock et al., 2008), which was run with a spatial resolution of 50×50 km2 and driven with the FNL reanalysis data (NCEP, 2017). Boundary and initial conditions were specified using climatological monthly concentrations of aerosols and gases from the LMDZ-INCA chemistry transport model.

The model runs were carried out for the period from 18 April to 30 September 2012 both with and without BB emissions of aerosols and gases in the main model domain. Using the results of these model runs, we specified two main modeling scenarios. The first (base) scenario was assumed to represent the real atmosphere – the modeled data corresponding to this scenario were obtained by including all contributions to aerosol from BB and other sources. The simulations corresponding to the base scenario were performed both with the optimized (as explained in Sect. ) and unoptimized BB emissions. The simulation using the optimized emissions is labeled below as “base-opt”, and the simulation using the initial guesses for the parameters involved in our computation of the BB emissions (see Sect. ) is labeled as “base-ini”. The second scenario was designed to represent aerosol concentrations and optical properties under “background” conditions (in the absence of fires) – the data corresponding to this scenario were obtained from a model run (labeled as “bgr”) performed without BB emissions in the model domain. The first 13 days (18–30 April) of the runs were considered as the model spin-up period and were excluded from the subsequent analysis.

Following a number of previous studies (e.g., Sofiev et al., 2009; Konovalov et al., 2011a, b; Kaiser et al., 2012; Huijnen et al., 2016), we calculated BB emissions by assuming a direct instantaneous relationship between the FRP and the emission rate at a time t: Es(t)=Φd∑lαρlβlshl(t)Fms, where Es (gs-1m-2) is the emission rate for a species s, Φd (Wm-2) is the daily mean FRP density (see Sect. ), α (g[drybiomass]s-1W-1) is the empirical factor relating FRP to the rate of biomass burning, ρl is a fraction of a given type, l, of the land cover, βls (g[model species] g-1[dry biomass]) are the emission factors and hl(t) is the diurnal variation of the FRP density. The relationship in Eq. () also involves the correction factors, Fms, which are introduced here to enable the optimization of the BB emissions for BC and OC in a given month, m.

Considering the experimental analysis by Wooster et al. (2005), we assumed α to be 3.68×10-4 gs-1W-1. The vegetation land cover fractions, ρl, were evaluated with the initial resolution of 0.2∘×0.1∘ using the NCAR USGS land use dataset (Homer et al., 2004), which was also used to specify the land use data in the CHIMERE model. Consistent with the land use categories defined in CHIMERE, our BB emission model given by Eq. () formally takes five vegetation cover types (needleleaf forest, broadleaf forest, shrubs, grassland, and agricultural land) into account, although no practical distinction was made in this study between BB emissions from needleleaf and broadleaf forest, as well as between BB emissions from shrubs and grassland. The emission factor values for BC and OC (see Table ) were chosen to be the same as those in the GFED4 inventory; this choice simplifies the comparison of the results of our analysis with the GFED4 data. The emissions of OC were converted into the emission of particulate organic matter (POM) using a constant OC-to-POM conversion factor (denoted below as η) of 1.8. This value has been found to provide reasonable agreement between the measurements of PM10 in central Siberia during the period of major fires in summer 2012 and the mass concentration of the total carbonaceous matter derived from the corresponding EC and OC measurements (Mikhailov et al., 2017; see Fig.  therein). The emission factor values for gaseous species were taken to be the same as in Konovalov et al. (2015, 2017a); they were specified using Andreae and Merlet (2001) and subsequent updates (Meinrat O. Andreae, unpublished data, 2014). The diurnal profile of BB emissions, hl(t), was derived directly from the FRP measurements and approximated by Gaussian functions as described in Konovalov et al. (2014, 2015). The correction factors for BC and OC (FmBC and FmOC) were estimated as described in Sect. ; their initial guess values (corresponding to the “base-ini” simulation scenario) were equal to unity. The correction factors for other species were set to be equal to 1.3, based on the results of the optimization of CO emissions from Siberian fires in Konovalov et al. (2017a). The fire emissions were first calculated using Eq. () with a spatial resolution of 0.2∘×0.1∘ and then projected onto a coarser model grid of 1∘×1∘.

Figures  and illustrate the FRP data used in our analysis and characterize the spatial structure and temporal evolution of the corresponding fires. Specifically, Fig.  shows the spatial distributions (within the region covered by the CHIMERE domain) of the daily mean FRP densities, Φd, integrated over the study period from 1 May to 30 September 2012 and scaled with the area fraction, ρl, of a given land cover type; in other words, it shows the integral fire radiation energy per unit area corresponding to a given type of land cover. The fire radiation energy distributions are shown in Fig.  for the two aggregated types of vegetation land cover, one of which includes needleleaf and broadleaf forest and the other comprises all other types of vegetation land cover. Note that the emission estimates are derived in this study for the Siberian region that is depicted in Fig.  by red rectangles and referred to below as the study region. These definitions of the study region and model domain allowed us to focus our analysis on the Siberian fires, and at the same time, to take the effects of grassland fires in Kazakhstan and large anthropogenic emissions in the European part of Russia into account. The same study region and model domain were specified in Konovalov et al. (2014); however, in the study from Konovalov et al. (2014) BC emissions were not estimated and older versions of the MODIS FRP and AOD data were used. Figure 3 shows the monthly variations of the FRP densities integrated both in time (over a given month) and space (over the study region). Evidently (see Fig. ), the FRP data are indicative of the major fires that occurred in the study region in 2012 both in western Siberia (north of Tomsk) and in eastern Siberia (east of Yakutsk). The largest fires occurred in the forested areas; the contribution of other (predominantly agricultural and grass) fires to the monthly- and regionally-integrated FRP was only comparable to that of the forest fires in May (see Fig. ). The fires were, on average, most intense in July and least intense in September. The fire radiative energy released from Siberian fires in May, June, and August was nearly the same.

Similar to Konovalov et al. (2014, 2017a, b), the injection height of BB emissions was evaluated using the parameterization proposed by Sofiev et al. (2012) as a function of the observed FRP, the boundary layer height, and the Brunt–Väisälä frequency. However, in this study, we used the advanced (two-step) version of the same parameterization (Sofiev et al., 2012), which allows the underestimation of the heights of BB plumes injected above the atmospheric boundary layer into the free troposphere to be avoided. Both the boundary layer height and the Brunt–Väisälä frequency were derived from the same WRF output data that were used for the simulations with the CHIMERE model. The BB emissions given by Eq. () for each model grid cell were distributed among the model layers proportionally to the weighted number of pixels which yields the injection height that corresponds to the altitude of a given layer; the weight of each pixel was defined proportionally to the corresponding FRP value. The FRP values in any pixel were assumed to have the same diurnal variation as the BB emissions in Eq. ().

The method used in this study to evaluate AAOD as a function of the modeled BB aerosol composition and AOD was introduced in Konovalov et al. (2017b). The main assumption underlying our method is that the dependence of the SSA on the ratio of elemental to total carbon, EC/(EC+OC), in the aerosol can be approximated by a linear function. This assumption is based on the results of the fourth Fire Laboratory at Missoula Experiment (FLAME-4) (Pokhrel et al., 2016), where an almost linear relationship between SSA and EC/(EC+OC) was found for fresh BB aerosol from a wide variety of biomass fuels. Furthermore, this assumption has been corroborated by the analysis of aircraft observations of aging BB aerosol (Pokhrel et al., 2016; Konovalov et al., 2017b). Accordingly, based on this assumption, we evaluate EC/(EC+OC) in the atmospheric BB aerosol column using the following empirical relationship: [EC][EC]+[OC]≅(ω0λ-bλ)(aλ)-1, where [EC] and [OC] are the column densities of EC and OC, ω0λ is the columnar SSA (at wavelength λ) of dry BB aerosol particles, and aλ and bλ are empirical fitting parameters. Note that aλ is a negative number. Estimates of aλ and bλ for several wavelengths (405, 532, and 660 nm), which are rather close to minus and plus unity, respectively, have been reported by Pokhrel et al. (2016). In particular, a660 and b660 have been estimated to be -1.11 (±0.04) and 0.99 (±0.004), respectively, using the orthogonal distance regression (ODR) method. These values and Eq. () indicate, for instance, that SSA is very close to one (at 660 nm) for pure OC aerosol without absorbing EC.

In this study, we applied Eq. () to the AERONET observations at 675 nm. The empirical coefficients a675 and b675 were evaluated using the power-law extrapolation from the absolute values reported by Pokhrel et al. (2016) at 532 and 660 nm and were found to be -1.12 (±0.04) and 0.99 (±0.004), respectively. Note that using a more sophisticated analysis, Konovalov et al. (2017b) derived EC/(EC+OC) from the AERONET observations at 870 nm. However, we found that the impact of the differences between the EC/(EC+OC) estimates corresponding to the two wavelengths on the empirical parameterization discussed below was negligible, and so we opted for a simpler and more transparent approach in this study.

The estimates of EC/(EC+OC) derived from the AERONET observations using Eq. () were then related to the ratio of AAOD at 388 nm (AAOD388) and AOD at 550 nm (AOD550). As noted in Sect.  and , we considered the ratio of the AAOD and AOD observations at the different wavelengths rather than direct SSA retrievals because the number of reliable OMI AAOD retrievals is much greater than the number of reliable SSA retrievals. The AAOD388 and AOD550 values were obtained by extrapolating AAOD and AOD observations at 440 nm to the 388 and 550 nm wavelengths, respectively, using the corresponding Ångström exponents, which were evaluated using the AERONET observations at pairs of different wavelengths: 440 and 675 nm for AAOD and 440 and 500 nm for AOD. The relationship between the AAOD388/AOD550 ratio and the EC/(EC+OC) ratio was approximated by a linear regression fitted to the data using the ODR method: AAOD388AOD550=κ1[EC][EC]+[OC]+κ2, where κ1 and κ2 are the regression coefficients, which were estimated in Konovalov et al. (2017b) to be 2.05 (±0.86) and 0.014 (±0.028) (the confidence intervals are given in terms of the 90th percentile). Note that unlike the standard least-squares method which disregards errors in a predictor variable, the ODR method takes random errors in both variables into account.

In this study, the analysis involving Eqs. () and () was performed using the same AERONET data (see Sect. ) as in Konovalov et al. (2017b) but with relaxed selection criteria. Specifically, instead of requiring that AOD at 500 nm should exceed the fixed value of 0.5, we demanded that AOD550 derived from the AERONET measurements should be at least a factor of 2 larger than the corresponding “background” AOD550 values predicted by CHIMERE (see Sect. ). We also did not put any restrictions on the photochemical age of BB aerosol (whereas Konovalov et al., 2017b, required that the photochemical age must not exceed 30 h). While the restriction on the photochemical age diminishes the risk that the relationship between SSA and the EC/(EC+OC) can be affected by morphological changes in aged BB aerosol particles, it also strongly reduces the amount of data available for the analysis and greatly increases the statistical uncertainty of the regression coefficients κ1 and κ2. We assume that the effects of aging processes are manifested as deviations of the data points from the linear relationship given by Eq. (); thus, this can be taken into account in the confidence intervals of the optimal estimates of κ1 and κ2. Furthermore, unlike Konovalov et al. (2017b), we did not assume that the selected SSA observations are fully representative of BB aerosol (in other words, we did not assume that the impact of the background fraction of aerosol on the observed SSA can be disregarded). Instead, we derived SSA for BB aerosol particles from the AERONET retrievals of AAOD and AOD using the background AAOD and AOD values predicted in the CHIMERE simulation without BB emissions. That is, we evaluated ω0λ as follows: ω0λ≅1-AAODoλ-AAODbλAODoλ-AODbλ, where the subscripts “o” and “b” denote the observations and the simulations for the “bgr” scenario (without BB emissions), respectively.

As the validity of Eq. () has only been demonstrated for dry aerosol, any AERONET observations corresponding to an average relative humidity in the aerosol column (RHC) greater than 60 % were disregarded – similar to Konovalov et al., 2017b). The values of RHC were derived from the CHIMERE simulations.

Figure  demonstrates the linear relationship between the AAOD388/AOD550 and the EC/(EC+OC) ratios (see Eq. ) that was obtained in this study. In spite of a considerable scatter of the data points, the relationship is rather well constrained because of the large number (equal 66) of selected observations. The regression coefficients, κ1 and κ2, are estimated to be 2.31 (±0.24) and 0.012 (±0.008), respectively. Note that a non–zero intercept (κ2) is indicative of a contribution of brown carbon to the imaginary part of the BB aerosol refractive index; however, it should also be noted that the brown carbon content in aerosol particles can, in principle, correlate or anti-correlate with the BC content. The confidence intervals were evaluated using the bootstrapping method in terms of the 68.3 percentile (1-σ) and both random uncertainties in the EC/(EC+OC) and AAOD388/AOD550 ratios and the uncertainty in the empirical coefficients a675 and b675 were taken into account. It is noteworthy that, when considering the uncertainty ranges, these estimates are entirely consistent with the corresponding estimates (see above) obtained earlier (Konovalov et al., 2017b) using a much smaller number (20) of selected data points.

To evaluate the impact of the possible biases in the simulated data involved in Eq. () on our estimates of κ1 and κ2, we performed several sensitivity tests (see the Supplement, Sect. S1), in which AAODbλ and AODbλ were scaled with constant factors. The test results indicate (see Figs. S1–S3 in the Supplement) that our optimal estimates of the regression coefficients κ1 and κ2 are sufficiently robust with respect to possible biases in AAODbλ and AODbλ.

Based on the empirical parameterization given by Eq. (), we could predict AAOD388 for the BB aerosol in a given model grid cell using the model output data as follows: AAOD388≅AOD550κ1[BC][BC]+[POM]η-1+κ2, where [BC] and [POM] are the BC and POM column densities that were simulated with AOD550 using the CHIMERE model by only taking the BB emissions of aerosol into account(see Sect. ), and η is the OC-to-POM conversion factor of 1.8 (see Sect. ).

We inferred optimal BB emissions of BC and OC following an inverse modeling approach (Enting, 2002) which generally suggests that the emissions specified in an atmospheric model can be constrained by analyzing the differences between observations and corresponding simulations of the atmospheric composition. Our inverse modeling analysis was aimed at optimizing the correction factors, FmBC and FmOC (see Eq. ), for the emissions of BC and OC in each month, m, of the study period (May–September 2012). Accordingly, the monthly values of the correction factors constitute the components of the state vectors, FBC and FOC of our inverse modeling problem. The same value of a correction factor for a given species and a given month applies to each grid cell in the model domain. We require that the optimal estimates of FBC and FOC enable the elimination of the relative differences between the mean values of both AOD and AAOD simulated with optimized BB emissions and their preselected matchups derived from satellite measurements for a given month: Vco-VcsVco<o, where Vco are the daily AOD (when c equals 1) or AAOD (when c equals 2) values derived from satellite observations, Vcs are the simulated counterpart of Vco, the angular brackets denote averaging over the available data (preselected as explained below) for the study region in a given month, and o is an arbitrarily small number, which, for definiteness, was set to be 3×10-2 in this study both when c equals 1 and 2. Note that the value of o approximately characterizes the relative numerical error (imprecision) of the correction factor estimates. The values of Vcs are dependent on FBC and FOC, which were optimized independently for each month by assuming that the simulated values of AAOD and AOD in a given month are independent of the BB emissions in any other months. To better isolate different months in the estimation procedure, we established a “buffer” between the two neighboring months, comprising 5 days that were excluded from the analysis. Note that BB BC and OC transported into the study region from outside of the model domain are regarded as a part of background concentrations of these species.

The optimization of FBC and FOC in accordance with Eq. () is equivalent to establishing a simple balance between spatially- and temporally-averaged AAOD (or AOD) retrievals and their simulated matchups on a monthly basis. Note that the criterion given by Eq. () would not be sufficient if we were interested not only in constraining total monthly emissions but also in improving their spatial structure. A more general approach to the estimation of BB emissions using satellite observations involves minimization of the least-square differences between the observations and simulations (see, e.g., Konovalov et al., 2014, 2016; Heymann et al., 2017). However, it was shown (Konovalov et al., 2011a) that the application of the least-square method may result in an underestimation of BB emissions in the presence of multiplicative model errors (which may be due to random uncertainties in the spatial structure and temporal evolution of BB emissions); in accordance with the analysis from Konovalov et al. (2011a), some negative biases (10 %–15 %) in simulated AOD values were found in Konovalov et al. (2014, 2017b) after the optimization of BB emissions in Siberia. Such biases are “automatically” avoided in the optimization method used in this study. Note also that improving the spatial structure of the emissions would require much larger computational resources than were available for this study or more sophisticated computational tools, such as an adjoint model, which was not available for CHIMERE-2017. Furthermore, the findings from a previous study of BB emissions in Siberia (Konovalov et al., 2014) indicate that increasing the dimension of the state vector would result in a very large uncertainty of the optimal estimates of its components, at least when no a priori constraints (in the Bayesian sense) and explicit quantitative assumptions about the magnitudes of model and measurement errors are used. Conversely, fixing the spatial structure of the emissions unavoidably results in an aggregation error of the top-down emission estimates (Kaminski et al., 2001). This is because the actual emission fields can be substantially different from those specified in the simulations due to the crude representation of spatial and temporal variability of the factors involved in our emission model (see Eq. ) as well as due to uncertainties in the FRP observations. However, the aggregation error is unlikely to be considerable in our case, as the satellite observations are expected to be representative of all areas in the study region where BB emissions were important; therefore, the contributions of random errors in the emission values for different grid cells to the uncertainty of our total monthly emission estimates are likely to compensate each other. Possible uncertainties associated with the optimization criterion given by Eq. () are discussed in more detail in Sect. S2 (see the Supplement).

The data selected for our optimization procedure satisfied the following two criteria. First, taking the limitations of the empirical parameterization given by Eq. () into account, we disregarded any data points (on an hourly basis) corresponding to RHC (see Sect. ) greater than 60 %. The remaining hourly data matching the corresponding hourly data from the satellite observations were averaged on a daily basis. Note that we did not require the AAOD observations to overlap with the AOD observations in space and time, as the estimates of FBC and FOC are supposed to be representative of BB emissions in the whole study region. Second, we tried to ensure that the selected data contained a sufficiently strong “signal” from BB aerosol, so that the emission estimates would not be strongly affected by possible biases in the simulated background AOD or AAOD values. Specifically, we required AOD-AODbAODb-1>γ, where AOD includes both the background and BB components, AODb represents the background component of AOD, and γ is a constant. This criterion, which is aimed at removing any data points for which the contribution of fire emissions to AOD is small, was applied in each grid cell to the daily AOD data from both observations and simulations. As a base case option, we made γ equal to unity; other values were considered in sensitivity tests described in Sect. . To enable validation of our simulations against an independent subset of the OMI-derived AAOD and MODIS-derived AOD data, one-third of the daily data points satisfying the above criteria were randomly withheld from the estimation procedure to constitute a validation subset of the satellite data.

The optimization problem defined by Eq. () was solved iteratively. In each iteration (i), Vcs was computed using the corresponding estimates of the correction factors, FOC(i) and FBC(i), and the improved estimates, FOC(i+1) and FBC(i+1), were obtained as follows: FOC(i+1)=V1o-V1sbV1s-V1sbFOC(i),FBC(i+1)=V2o-V2sbV2s-V2sbFBC(i), where V1s and V2s are calculated using the values of FOC(i) and FBC(i), and V1sb and V2sb are the simulated background values of AOD and AAOD. Note that the optimization problem considered is not strictly linear, particularly because the results of the application of the second criterion (see Eq. ) to the AOD simulated with different OC emissions can be different. Nonetheless, the nonlinearities are relatively weak, and the convergence of the simple iteration procedure given by Eqs. () and () is ensured as long as the BC contribution to AOD is small compared to that of OC. In this study, the initial guesses for FOC and FBC (corresponding to the “base-ini” case) were equal to unity, and the convergence criterion given by Eq. () was satisfied after four iterations.

The uncertainty in the optimal estimates of FOC and FBC was evaluated by means of a bootstrapping technique (Efron and Tibshirani, 1993) using Eqs. () and () which were applied to the optimized estimates of the correction factors and corresponding simulations. Specifically, the AOD and AAOD data involved in Eqs. () and () were randomly sampled (with replacements) 3000 times, and the spread of the correction factor values from the left-hand part of Eqs. () and () was used to evaluate the confidence intervals for the optimal estimates of FBC and FOC. To take possible spatial and temporal covariances of the model and/or measurement errors into account, we ensured that the size of any sampled dataset is not larger than the number of the available (in the optimization subset) data points, for which the distances between them (both in space and time) are larger than the corresponding de-correlation length/time scales (which were evaluated separately both for AAOD and AOD). As a result of this limitation, the size of any sampled monthly dataset was several times smaller than the size of the original optimization dataset for a given month. In each iteration of the bootstrapping procedure, we randomly changed the parameters of the AAOD parameterization given by Eq. () by sampling them from a Gaussian distribution with the standard deviations evaluated above (see Sect. ).

Furthermore, we took into account that the AOD simulated by CHIMERE may be biased and/or not sufficiently representative of the variability in the mass extinction efficiency (αe) of the actual BB aerosol in Siberia. Based on BB aerosol properties summarized by Reid et al. (2005a), we assumed that the regional scale variability of αe for BB aerosol can be characterized by means of the confidence intervals (in terms of the 90th percentile) of 0.7 m2g-1. Accordingly, we considered the uncertainty of αe by sampling its value in each iteration of the bootstrapping procedure from a Gaussian distribution with a standard deviation of 0.43 m2g-1. Note that the average value of αe for BB aerosol in our simulations is found to be 4.92 m2g-1, which is rather close to the likely value of 4.7 m2g-1 suggested by Reid et al. (2005a).

Finally, we considered that the estimates of both FBC and FOC could be affected by the uncertainty of the assumed value of the OC-to-POM conversion factor (η) (see Sect.  and Eq. () in Sect. ): larger values of η would yield smaller values of the correction factors. The BB aerosol composition measurements performed in different regions of the world and summarized by Reid et al. (2005b) suggest that the POM/OC ratio is likely to range from 1.4 to 1.8. Conversely, Turpin and Lim (2001) indicated that the POM/OC ratio in non-urban aged aerosol affected by wood smoke could be as large as 2.6. However, we believe that the reported extreme values of the POM/OC ratio do not characterize the range of the uncertainty of the assumed value of η (equal 1.8), as this estimate is supposed to represent the average properties of BB aerosol of different origin and age in the vast region considered in this study. For definiteness, we characterized the uncertainty of η by means of a Gaussian distribution with a standard deviation of 0.2. This value corresponds to an uncertainty range of η from about 1.5 to 2.1 in terms of the 90th percentile confidence intervals.

Note that the mean POM/OC ratio representative of the ensemble of aerosol observations considered in this study can actually be different from that representative of BB aerosol emissions; this is in contrast to our assumption that η has the same value both for the observed aerosol and the fresh emissions. The variability of the POM/OC ratio in ambient (aging) aerosol may partly be due to the formation of SOA from the oxidation of semi-volatile organic compounds (SVOCs) and other processes involving SVOCs. These processes, which have been shown to significantly affect BB aerosol evolution in Siberia and to have the potential to cause strong biases in OC emission estimates inferred from AOD measurements (Konovalov et al., 2017a), are not taken into account in the simulations performed in this study. To get some idea about the impact of this omission on our BC emission estimates, it is useful to transform Eq. () by taking into account that (i) POM constitutes the major component of BB aerosol, typically accounting for about 80 % of its mass, and (ii) the BC mass fraction is about 10 times smaller than that of OC in BB aerosol in temperate/boreal forest (Reid et al., 2005b). Accordingly, by assuming that AOD is only determined by POM and disregarding the contribution of BC to total carbon concentration, Eq. () can be approximated as follows: AAOD388≈αe(κ1η[BC]+κ2[POM]), where αe is the mass extinction efficiency discussed above. According to Eq. (), AAOD may be underestimated in our simulations in cases with fresh aerosol (where η and [POM] are likely underestimated) but overestimated in cases with aged aerosol. However, it seems reasonable to expect that such biases in AAOD can not cause a significant bias in our optimal estimates of FBC and BC emissions as long as the assumed value of the factor η is representative of the average value of this factor over the ensemble of the all (both fresh and aged) plumes observed from the satellites and as long as the simulated AOD values (and, accordingly, POM columns) are, on average, consistent with the AOD observations. Furthermore, considering that the term proportional to κ2 in Eq. () is typically much smaller than that proportional to κ1 (see Fig. ), the possible biases in AAOD due to BB aerosol aging are effectively included in our confidence intervals for BC emission estimates by considering the uncertainties in η and αe as noted above. Any uncertainty of our estimates of FBC and BC emissions due to model errors in the spatial and temporal distributions of the POM columns and AOD is also taken into account in the respective confidence intervals as explained above. The robustness of our BC emission estimates with respect to the treatment of SOA formation processes in our model is confirmed by a sensitivity test reported in Sect. .