Reduction in MSC uncertainty when using the look-up table approach

The look-up table (Table C.1) shows the median MSC and its uncertainty for each set of values of

scatt, f/b, and az/b. The uncertainty ranges between 0.3 and 4 m²/g, with a median value of 1.6 m²/g. To compare, the distribution of MSC of all the scenarios in Table 4.2 has a variance of 4.7 m²/g. This indicates that the look-up table approach could constrain MSC by about (4.7 – 1.6)/4.7

= 66%, relative to when no method is used to constrain MSC.

The uncertainty in the MSC estimated with the look-up table also depends on the uncertainty of the inputs. For instance, if f/b, and az/b are increased from 10% to 20%, then the uncertainty in the estimated MSC increases by 30%.

The MSC estimated is also sensitive to the construction of the look-up table. Using a coarse resolution to generate plausible scenarios gives a greater uncertainty in predicted MSC. For instance, if Table 4.2 were constructed with steps of n of 0.02 instead of 0.01, 50 values of CMD instead of 200, and steps of GSD of 0.1 instead of 0.05, the table would contain 6,500 scenarios instead of 93,600. Using scatt to estimate MSC results in a value about 5% lower. However, using

f/b, the estimated MSC is about 10% lower, and the uncertainty can be about 50% higher. When using az/b, the estimated MSC is between 20% and 50% lower, and the uncertainty can be about 50% higher for az/b ratios above 6.

137 4.3.4. Scattering by a distribution of fractal aerosols

In this section I assess whether scatt, f/b, and az/b, together with Mie-Lorenz theory, can be used to estimate MSC of fractal aerosols. For modeling the scattering of fractal aerosols I used the model of Sorensen (2001), and compared with the exact T-Matrix calculations of Liu and Mishchenko (2005). The angular distribution of scattering predicted by the model of Sorensen agrees with the T-Matrix calculation within 60% on average, although at specific angles they can differ by up to a factor of two (Appendix C). In predicting MSC, the model of Sorensen reproduces the T-Matrix results within about 36%, or 1 ± 0.5 m²/g. This is sufficient for the scope of this work since I do not attempt to precisely model the scattering of a fractal but rather assess if non-spherical effects would significantly affect the conclusions of this work.

To assess the error due to the spherical assumption, I repeated the calculations of Section 4.3.3 but for fractal aerosols. Then I compared the distribution of MSC that would be estimated for spherical aerosols when using scatt as constraint, with that of fractal aerosols with the same scatt, as shown in Figure 4.6a. The blue and orange box plots show the MSC estimated for spherical or fractal aerosols, respectively, for different values of scatt. A higher or lower value of the median of a blue box plot over the orange box plot indicates that the spherical aerosol assumption leads to overestimate or underestimate the MSC of fractal aerosols, respectively. I conduct a similar analysis for f/b (Figure 4.6b) and az/b (Figure 4.6c).

138

Figure 4.6 MSC estimated for spherical (blue box plots) or fractal aerosols (orange box plots), using either (a) scatt, (b) f/b, or (c) az/b.

139

Using scatt as constraint leads to overestimating MSC of fractal aerosols by up to 80% (Figure 4.6a). Whereas the scatt of spherical aerosols is as low as 0.003, fractal aerosols are more sensitive to wavelength and the value of scatt for fractal aerosols is never smaller than 2 (blue box plots in Figure 4.6a). For instance, for m = 1.45 + 0.01i, CMD = 300 nm, and GSD = 2.2, MSC of spheres changes from 2.50 to 2.44 m²/g between  = 550 and 880 nm (equivalent to scatt of 0.03), and MSC of fractals changes from 2.6 to 0.9 m²/g (equivalent to scatt of 2.27). The high values of scatt

is consistent with the model of Sorensen (2001) being an extension of Rayleigh scattering by small aerosols. Values of scatt greater than 2 have also been reported for biomass burning aerosols. Reid et al. (1998) measured scatt between 2.4 and 2.6 for 1 = 550 and 2 = 700 nm for fresh smoke in the Amazon basin. Chand et al. (2006) found scatt = 2.0 ± 0.4 for 1 = 450 and  = 700 nm for biomass burning aerosols in the Amazon Basin. Hungershoefer et al. (2008) measured scatt

between 1.7 and 2.2 for 1 = 550 and  = 770 nm for fresh biomass burning aerosols produced in a smoke chamber.

Figure 4.6b and Figure 4.6c show that assuming spherical aerosols when estimating MSC with

f/b or az/b leads to greatly overpredicting MSC if the aerosols are actually fractals. Using f/b

can lead to overestimating MSC by up to a factor of 6, and with az/b by up to a factor of 34. This is consistent with the large difference between the angular distribution of scattering by fractals and spherical aerosols, as shown in the appendix (Figure C.1).

These results indicate that using the scattering Angstrom exponent or the angular distribution of scattering to estimate MSC of fractal aerosols would lead to overpredicting their MSC, and hence

140

underpredicting the mass of BC aerosols in the flaming phase relative to OC aerosols in the smoldering phase

4.4. Conclusion

The findings presented here are relevant to the interpretation of light scattering as a proxy of aerosol mass concentration, which is done in several commercial instruments. The main uncertainty in using light scattering as a proxy of aerosol mass concentration is the assumption of a fixed MSC value. The objective of this project was to assess the use of the wavelength dependence and the angular distribution of scattered light to constrain MSC, and thus improve measurements of aerosol mass concentration, for the case of aerosols from residential biofuel combustion. Using Mie-Lorenz theory, I simulated values of MSC ranging between 0.04 and 10.8 m²/g for the range of size distributions and refractive index of biofuel burning aerosols (Table 4.2). I also evaluated how the variability of MSC within a single combustion event due to changes in combustion phase. Assuming a fixed MSC neglects changes in aerosol size with combustion phase, resulting in uncertainties in the mass apportioned to different combustion phases of up to a factor of 5 during a single combustion event, for an example where time-dependent sizes were provided.

The main contribution of this work is providing a quantitative assessment of uncertainties in MSC for aerosols emitted from biofuel combustion, since commercial instruments such as the DustTrak may be used to measure concentrations without correcting for changes in MSC. This work also evaluates the possibility of using a look-up table approach using the scattering Angstrom exponent

141

and ratios of forward-to-backward and azimuthal-to-backward scattered light to estimate MSC.

This approach could potentially reduce the uncertainty in MSC by 66% on average, if the spherical aerosol assumption is applicable. The uncertainty in the estimated MSC would increase with the uncertainty of the input parameters.

Due to the sensitivity of light scattering to aerosol morphology, the angular distribution of scattering may not be useful to estimate MSC for uncoated soot aerosols. Since efficient combustion has been correlated with non-spherical aerosols with higher BC content (Martins et al., 1998; Torvela et al., 2014; Levin et al., 2010), using f/b or az/b could overestimate MSC by up to an order of magnitude during flaming combustion. Using scatt could overestimate their MSC by up to 80%.

Assumptions in the construction of the look-up table were that each size distribution and refractive index is equally likely, and a density of 1 g/cm³ was used for biofuel burning aerosols. However, the advantage of a look-up table approach is that it can be applied to other probability distributions and aerosol densities, as well as other aerosol sources besides residential biofuel combustion. The findings presented here are important because light scattering is widely used in commercial photometers as a proxy of aerosol mass concentration.

4.5. Summary

The objective of this project was to assess ways of reducing the uncertainty in aerosol mass concentration obtained from measurements of light scattering, using parameters easily measured in field tests. The main findings are:

142

• MSC varies between 0.08 and 10.8 m²/g for the range of aerosol sizes and refractive index modeled in this study (Table 4.2).

• From a review of variations in aerosol size distribution with combustion phase, it was estimated that MSC can vary by up to an order of magnitude between start-up, flaming, and smoldering phases. Hence, assuming an average MSC for a combustion event can lead to erroneous attribution of mass to these phases, as shown in Section 4.3.2.

• A look-up table approach using scatt, f/b, and az/b can be used to constrain MSC, and hence, reduce the uncertainty in the estimated aerosol mass concentration. Using only one of the three parameters in the look-up table, i.e., either scatt, f/b, or az/b, results in an uncertainty in the estimated MSC of up to 5 m²/g. However, if the parameters are combined, the uncertainty in MSC ranges between 0.3 and 4 m²/g, with a median value of 1.6 m²/g.

• Using the look-up table with the spherical aerosol assumption for fractal aerosols would lead to overestimate MSC, and hence, underestimate their mass. Using f/b and az/b leads to overestimating MSC by up to an order of magnitude, and using scatt would overestimate MSC by up to 80%.

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