#### 2.2. Method for Estimation of the EC/OC Ratio

Our estimation procedure is based on recent findings [

52] from the Fourth Fire Laboratory at Missoula Experiment (FLAME-4), which involved burning of a wide variety of biomass fuels and measuring absorption properties of the produced fresh aerosol at several wavelengths (660, 532 and 405 nm). It has been shown, specifically, that BB aerosol particle SSA (denoted in the formulations given below as

ω_{0}) can be parameterized as a linear function of the elemental to total carbon ratio:

Here and below,

${\omega}_{0}^{\lambda}$ is SSA at a given wavelength λ; [EC] and [OC] are the mass concentrations of the corresponding species; and

a^{λ} and

b^{λ} are constant positive parameters depending on the wavelength, λ. Values of

a^{λ} and

b^{λ} that have been reported [

52] for optimal fits to the FLAME-4 data are listed in

Table 2 along with their uncertainties. It is noteworthy that

a^{λ} was found to be about minus unity for all of the wavelengths considered.

The linear relationship given by Equation (2) was proven [

52] to be applicable not only to fresh and dry aerosol in a controllable laboratory environment, but also to actual aging atmospheric aerosol. Specifically, SSA values predicted for the 660-nm wavelength using Equation (2) with the parameter values fitted against the FLAME-4 data were found to be in a reasonably good agreement with observations of SSA at 637 nm made during major fires in African savanna [

18]. Moreover, the SSA predictions for 532 nm were found to be consistent with (although smaller than) corresponding observations of BB aerosol onboard aircraft intersecting forest fire plumes in North America [

70]. To further illustrate the applicability of the linear relationship given by Equation (2) to actual atmospheric aerosol, we plotted the relationship between SSA at 532 nm and the EC/(EC + OC) ratio (see

Figure 1) using the same aircraft measurements [

70] and fitted a linear regression line corresponding to Equation (2). Note that following the approach used previously [

52], the EC/(EC + OC) ratio was derived from the measurement data for the BC and PM

_{2.5} enhancement mass ratio by assuming that the OC mass fraction of the PM

_{2.5} was 39%. Evidently, the linear approximation fits the data shown in

Figure 1 quite adequately. Additionally, it is again noteworthy that the coefficient of proportionality

a^{λ} (see the fitting equation shown in

Figure 1) was found be about minus unity.

In principle, Equation (2) could be inverted and directly used to estimate the elemental to total carbon ratio as a function of SSA as follows:

However, it can be noticed that in the case of highly reflective BB aerosol (e.g., with SSA of 0.95 and higher), which is typically observed by AERONET in boreal regions [

71], such an estimate of the elemental to total carbon ratio would be very sensitive to uncertainties in

b^{λ}, especially at shorter wavelengths (as confirmed below in

Section 3). Furthermore, in the limiting case when the EC/OC ratio approaches zero and

b^{λ} is expected to approximate an observed value of SSA, BB aerosol absorption is likely to be mostly determined by BrC concentration, which has been shown to strongly decrease as BB aerosol ages [

16]. This reasoning is confirmed by the fact that the discussed parameterization fitted to the laboratory data was previously found [

52], as mentioned above, to systematically (even though not significantly) underestimate actual SSA (at 532 nm) available from the aircraft observations. Therefore, we suppose that the estimates of

b^{λ} derived for fresh BB aerosol from the FLAME-4 data may be not always representative of actual atmospheric BB aerosol that has been exposed to aging processes (unlike smoke aerosol analyzed in FLAME-4), especially at shorter wavelengths (e.g., less than 500 nm) where the absorption of BrC typically becomes quite significant.

In contrast, we assume that the estimates of

a^{λ} from the FLAME-4 study [

52] are sufficiently robust and representative of aged aerosol observed in the AERONET stations in Siberia. This assumption is upheld by the fact that the available estimates of

a^{λ} for fresh aerosol (see

Table 2), unlike the estimates for

a^{λ}, are practically independent (within their uncertainties) on the wavelength and thus on BrC absorption. Furthermore, there is no significant difference between the estimates of

a^{λ} for the 532-nm wavelength, which were derived from the FLAME-4 data (see

Table 2) and aircraft measurements of aging aerosol (see

Figure 1). Apart from variations in BrC absorption, which can change very significantly both with the wavelength (e.g., [

15]) and the BB aerosol age [

16], significant deviations of

a^{λ} from the estimates obtained for fresh and dry aerosol can potentially be caused by major morphological changes in BB aerosol particles due to aerosol aging [

57]. However, as explained above (see

Section 2.1.1), we tried to minimize the possibility that such changes affected the observations selected for our analysis.

Accordingly, our analysis is based on the two main assumptions: (1) the relationship between SSA and the elemental to total carbon ratio in BB aerosol is approximately linear; and (2) the optimal estimates found in the analysis of the FLAME-4 data for the parameter

a^{λ} at the wavelengths 660 and 532 nm (

a^{660} and

a^{532}) of the relation specified in Equation (2) are sufficiently representative (given the reported uncertainty range) of actual aging BB aerosol. In addition, following previous studies (e.g., [

15]), we assume that the contribution of BrC to BB aerosol absorption at 869 nm is negligible, and so, SSA at 869 nm (

ω_{0}^{869}) should approach unity as the elemental carbon content approaches zero. Therefore, using Equation (2), we posit:

However, the value of

a^{869} is unknown. To exclude it from the analysis, we substitute Equation (4) into Equation (2) and obtain:

where,

Values of

A^{λ} and

B^{λ} can be readily estimated by fitting a linear regression to the relationship between the available observations of SSA at 675 or 440 nm and SSA at 869 nm. Then, using Equation (5), Equation (3) can be re-written as follows:

or also in another form:

Note that neither b^{λ} nor B^{λ} are used in Equations (7) and (8). In essence, we use SSA measurements at two wavelengths along with experimental estimates of the proportionality coefficient, a^{λ}, relating the elemental to total carbon ratio and SSA at a given wavelength λ, to calibrate the unknown value of a^{869}.

Our best (the “base case” or “Case 1”) estimates of the EC to OC ratio are based on using the AERONET SSA observations at 675 and 869 nm along with the estimate of

a^{675}, which was obtained from the power-law extrapolation from available values of the absolute values of

a^{660} and

a^{532} (see

Table 2). For comparison, we consider three other cases listed in

Table 3. Specifically, the Case 2 estimate is also obtained with Equation (8), but using SSA observations at 440 nm along with the corresponding estimate of

a^{440} derived by the power-law interpolation between the experimental estimates of

a^{405} and

a^{532}. The Cases 3 and 4 are based on a direct application of the available linear approximations (see Equation (3) and

Table 2) from the FLAME-4 study [

52] to the SSA values obtained correspondingly for the 660- and 405-nm wavelengths by interpolation or extrapolation from the AERONET SSA observations at the 675- and 440-nm wavelengths. In other words, Cases 3 and 4 involve not only the available estimates of

a^{λ} (as in Cases 1 and 2), but the estimates of

b^{λ}, as well. Along with the different observation-based estimates of the EC/OC ratio, we consider predictions of the EC/OC ratio from the 3D model simulations (see

Section 2.1.2). The model estimates are calculated as the ratio of the column mass densities of EC and OC in primary and secondary aerosol originating from fire emissions.

Note that all of the estimates for a^{λ}, b^{λ}, A^{λ} and B^{λ} employed in our analysis are obtained using the orthogonal distance regression (ODR). Unlike a simple linear regression model, which is based on the assumption that an explanatory variable is not affected by errors and which minimizes the distance between the dependent variable and the fitting line only in the vertical direction, the ODR method allows for observation errors in both the explanatory and dependent variables and minimizes the orthogonal distances between each data point and the regression line. Therefore, the use of the ODR method ensures that the linear fits analyzed below are sufficiently symmetric with respect to the choice of the explanatory and dependent variables, and so, the corresponding linear approximations can be inverted as suggested by Equations (3) and (7).

As noted in the Introduction, one of the main goals of our analysis was to create a robust parameterization that would allow one to estimate the EC/OC ratio in BB aerosol by using available satellite observations, such as the retrievals of the absorption AOD at 388 nm (AAOD

^{388}) from the OMI measurements [

46] and the retrievals of the extinction AOD at 550 nm (AOD

^{550}) from the MODIS measurements [

53]. To this end, we consider the ratio of AAOD

^{388} to AOD

^{550} as a function of the EC/(EC + OC) ratio estimated as described above for the Case 1. We expect that inasmuch as there is a regular relationship between the EC/(EC + OC) ratio and SSA at 440 nm, there should also be a similar relationship between the EC/(EC + OC) and AAOD

^{388}/AOD

^{550} ratios.

Indeed, SSA at 440 nm (

ω_{0}^{440}) can, by definition, be expressed through the ratio of AAOD and AOD at 440 nm (AAOD

^{440} and AOD

^{440}):

Both AAOD

^{440} and AOD

^{440} can be extrapolated to the 388-nm and 550-nm wavelengths, respectively, using the corresponding Ångström exponents, α

_{a} and α

_{e}, which, in turn, can be evaluated using the AERONET observations at two different wavelengths.

The uncertainties (confidence intervals) for any coefficients of linear regressions built in this study were evaluated using a Monte Carlo procedure based on one of the standard bootstrapping techniques [

72]. The procedure comprised 5000 iterations involving random sampling of N (20, in our case) data points from the original dataset (including the same number, N, of data points). The sampled data were then used in each of the iterations to obtain perturbed estimates of a given parameter (e.g., the slope of the linear regression in Equation (5) or the mean of the estimates for individual observations) in the same way as the original data were used to obtain a corresponding optimal estimate. The underlying assumption in this procedure is that the errors of individual SSA observations are statistically independent. Wherever an estimation involved uncertainties in input parameters (as, e.g., in the case of the estimation given by Equation (8)), such uncertainties were taken into account by randomly perturbing the corresponding parameter values (within the range of their uncertainties; see

Table 2) in each iteration of the same Monte Carlo procedure. The spread of estimates from different iterations was used to evaluate the confidence intervals for a corresponding optimal estimate. For definiteness, the confidence intervals of all estimates reported below (including estimates of regression coefficients) are given in terms of the 90th percentile.