The Fire Influence on Regional and Global Environments Experiment (FIREX) 2016 study was conducted at the U.S. Forest Service's Missoula Fire Sciences Laboratory during October–November 2016 (Manfred et al., 2018; Selimovic et al., 2018). The Fire Science Laboratory contains a ∼3400 m3 indoor combustion room for controlled burns (McMeeking et al., 2009; Selimovic et al., 2018). The measurements reported here are for “room” burns, where instruments sampled well-mixed smoke from the combustion room. First, dry fuels weighing 0.24–4.4 kg were placed on a ceramic fuel bed and ignited by a heating plate to produce a small, controlled burn that lasted several minutes (Selimovic et al., 2018). The smoke became well-mixed in the combustion room within 15–20 min and persisted under steady-state, low-light conditions for 3–4 h with minimal dilution and wall loss (Stockwell et al., 2014). Fuels were representative of western US wildfires and included ponderosa pine (Pinus ponderosa), lodgepole pine (Pinus contorta), Douglas fir (Pseudotsuga menziesii), Engelmann spruce (Picea engelmannii), subalpine fir (Abies lasiocarpa), manzanita (Arctostaphylos), chamise (Adenostoma fasciculatum), juniper (Juniperus), and sage (Artemisia) (Selimovic et al., 2018). A shared aerosol inlet was connected to the combustion room, and it provided flow to a size-selected inlet and the BBCES instrument, as described below.

The optical system shown in Fig. 1a is a modified version of the two-channel instrument used previously to measure broadband aerosol extinction at 355–420 nm with two LEDs (Attwood et al., 2014; Washenfelder et al., 2015). The light source, optical filters, cavity mirrors, and spectrometer grating were replaced to measure aerosol extinction over a very broadband region, covering 360–385 and 400–720 nm.

We used a single laser-driven white-light source (EQ-99FC LDLS; Energetiq, Woburn, MA, USA), containing a continuous-wave laser at 974 nm that pumps a Xenon plasma and outputs a broad spectrum from 170–2100 nm (Islam et al., 2013). The light source was temperature-controlled to ∼20 ∘C and purged with N2 to eliminate O3 production (Washenfelder et al., 2016). The light was transmitted by fiber-optic to an off-axis parabola with a 0.36 numerical aperture (RC04SMA-F01; Thorlabs, Newton, MA, USA) for collimation and coupling into the optical cavities. Two colored glass filters (WG345 and WG320) were used to remove UV wavelengths shorter than 345 nm. A dichroic long-pass filter with a 400 nm cut point (69–897; Edmund Optics, Barrington, NJ, USA) divided the light before it was passively coupled to the two optical cavities. Additional colored glass filters and a custom interference filter (MLD Technologies LLC, Mountain View, CA, USA) eliminated out-of-band wavelengths.

The optical cavities consisted of two pairs of 2.5 cm diameter, 1 m radius of curvature plano-concave mirrors with a high-reflectivity coating covering 360–385 nm (Advanced Thin Films, Boulder, CO, USA) and 400–720 nm (MLD Technologies LLC, Mountain View, CA, USA). The broadband reflectivity of the visible mirrors was achieved with multiple layers of thin film coatings applied by ion beam sputtering to the super-polished substrate. Although the visible mirrors span a very broad range with high reflectivity (0.9993–0.9999), their losses vary strongly as a function of wavelength (Fig. S1) (He et al., 2018), due to the coating properties and possible contributions from surface roughness, interface roughness, and internal defects. The mirrors were mounted in stainless steel mounts, at either end of a 101.5 cm long aluminum flow cell (2.21 cm i.d.) with inlets for the aerosol flow and mirror purge flows. The broadband light exiting each cavity was collected by an F/3.1 lens, coupled to a bifurcated fiber-optic bundle, and imaged linearly onto the entrance slit of a grating spectrometer (IsoPlane-160; Princeton Instruments, Trenton, NJ, USA). The spectrometer contained a 300 grooves mm-1 grating with 300 nm blaze (centered at 507 nm with 290–724 nm bandwidth) and a 16-bit back-illuminated 2048 × 512 pixel charge-coupled device (CCD) detector (PIXIS 2kBUV; Princeton Instruments, Trenton, NJ, USA). During data acquisition, individual spectra were acquired with 0.3 s integration time using the physical shutter of the IsoPlane spectrometer. The CCD readout time was 0.57 s, and so a full spectrum was taken every 0.87 s. Narrow emission lines from a Hg lamp were measured multiple times each day to determine the wavelength calibration and spectral resolution (average full width at half-maximum resolution of 1.4 nm between 360–720 nm).

A cavity ring-down spectrometer (CRDS) at 403 nm provided an extinction measurement between the two BBCES channels at 360–385 and 400–720 nm and was used as an independent validation of the BBCES extinction. The CRDS method has been described previously (Fuchs et al., 2009) and was not modified from Washenfelder et al. (2013).

The flow to the BBCES and CRDS channels was provided by a shared aerosol inlet, shown in Fig. 1c. The shared aerosol inlet consisted of ∼30 m of 6.4 mm o.d. copper tubing connected to an inertial impactor with 50 % cut point at an aerodynamic diameter of 1.0 µm (TE296, Tisch Environmental, Cleves, OH), a silica gel dryer, an activated carbon denuder to remove NOy and O3 (Washenfelder et al., 2015), and three available thermodenuders. The 2.0 volumetric L min-1 (vlpm) flow from the burn room was evenly split between one of the thermodenuders and a bypass channel. An automated two-position valve (Hanbay Inc, Pointe-Claire, Quebec, Canada) alternately directed 1.0 vlpm of thermodenuded and 1.0 vlpm of fresh smoke to the BBCES aerosol inlet and to a mixing volume with dilution for a collection of other aerosol instruments (Manfred et al., 2018; Adler et al., 2019). The DMA, valves, MFCs, and all other components shown in Fig. 1 were controlled by custom LabVIEW software and synchronized to the timing of the two-position valve shown in Fig. 1c as part of the NOAA shared aerosol inlet.

The inlet apparatus included three separate thermodenuders to enable comparison between different temperatures, but this paper reports data from only one. This denuder consisted of an 80 cm screen tube (1.3 cm i.d.) wrapped in activated charcoal fabric to remove volatilized organic components. The first 40 cm was heated to 250 ∘C, and the remaining 40 cm served as a cool-down region. With a flow rate of 1.0 vlpm, the calculated residence time was 3.2 s and Reynolds number was 114. The denuders were similar to the design of Huffman et al. (2008), with the major difference that the heated section had charcoal fabric to absorb the volatilized species. The throughput efficiency was found to be less than unity (86 ± 4 % for particles between 100 and 300 nm) due to thermophoretic wall losses, but the analysis of the aerosol size-independent RI, which is an intrinsic property of the aerosol (Moise et al., 2015), is largely unaffected by these losses. We therefore do not make any corrections to these data.

Additional instruments sampled from the shared aerosol inlet's mixing volume, shown in Fig. 1c, and those data were used to assess the fraction of black carbon in the total aerosol mass loading of smoke from each fire. A single-particle soot photometer (SP2; Droplet Measurement Technologies, Longmont, CO, USA) measured the concentration of refractory black carbon aerosol, rBC (Schwarz et al., 2006, 2008). The rBC mass concentration was only retrieved in the mass range corresponding to particles with a volume equivalent diameter of 90–550 nm, assuming a void-free density of 1.8 g cm-3. This range typically covers 90 % or more of the accumulation-mode rBC emitted from wildfires. Refractory black carbon has been shown to be experimentally consistent with elemental carbon measured after a thermal denuder within 15 % (Kondo et al., 2011). The uncertainty of the black carbon mass at this concentration is 30 %. A compact time-of-flight aerosol mass spectrometer (c-TOF AMS; Aerodyne Research Inc., Billerica, MA, USA) measured organic aerosol (OA) mass (Bahreini et al., 2008, 2009). The uncertainty of the OA mass is typically ∼38 % due to standard uncertainties in AMS measurements (Bahreini et al., 2009) but was greater for biomass burning aerosol at the Fire Sciences Laboratory because of additional variability in aerosol volatility due to dilution of the dense smoke. Therefore, we use relative AMS masses in this analysis.

Each measurement day at the Fire Sciences Laboratory included two controlled burns, with 3–4 h of sampling of each burn. The instruments and inlet components were turned on at least 1 h prior to the first burn. Each sample cycle required 30 min and began with measurements of CO2 and He to determine the BBCES mirror reflectivity, followed by measurement of the dark noise of the CCD detector with the physical shutter closed. During these BBCES calibrations, the size distribution of the aerosol sample was measured by SMPS. Next, the BBCES and CRDS measured fresh and denuded (250 ∘C) aerosol with mobility diameters (Dp) of 150, 225, 300, 375, and 450 nm for 2 min each (20 min total). The aerosol mass loading was very high in the burn room (typically ∼1 g m-3) but was reduced by a factor of ∼100 by the DMA and the dilution flows prior to measurement by the BBCES. Therefore the 2 min averaging time ensured sufficient precision in the spectra and the particle counting, particularly at the larger diameter set points. These DMA diameter set points were chosen to span the observed aerosol size distribution of the smoke. Filtered sample air was measured before and after each set of five measurements. The five mobility diameter measurements allowed RI to be retrieved once every 10 min, alternating between fresh and denuded biomass burning smoke. Between the two daily fires, NO2 additions were made to assess the spectrometer stability. The spectrometer wavelength and resolution were calibrated with the output of a Hg lamp before the first burn, between the first and second burns, and after the second burn.

After the FIREX 2016 study, the BBCES extinction measurements and complex RI retrievals were validated using standard samples of polystyrene latex spheres (PSLs; Nanosphere size standards, Thermo Fisher Scientific Inc., Waltham, MA, USA) and ammonium sulfate (Sigma Aldrich, St. Louis, MO, USA). For these measurements, the aerosols were generated using a custom-built atomizer, and dilution make-up flow was provided by scrubbed and dried air from a compressor. Five or six aerosol sizes were selected, spanning a similar range to those sampled during FIREX. The sampling scheme shown in Fig. 1a and b remained the same, but the shared inlet shown in Fig. 1c was not used. Particle-free air and mirror reflectivity measurements were performed before and after each set of aerosol sizes.

The aerosol optical extinction, α(λ), can be determined from the observed change in light intensity in the cavity according to 1αλ=dL1-R(λ)d+αRayleigh,ZA(λ)IZAλ-I(λ)I(λ), where λ is wavelength, dL is the ratio of the physical cell length to the sample cell length, R(λ) is the measured mirror reflectivity, d is the physical cell length, αRayleigh,ZA(λ) is the Rayleigh scattering of zero air, IZA(λ) is the reference intensity spectrum, and I(λ) is the measured intensity spectrum (Washenfelder et al., 2013). The extinction cross section, σ(λ), is defined as the optical extinction divided by the total number concentration of aerosol particles, N, for the given size distribution: 2σλ=α(λ)N.

The most common method for determining R(λ) in Eq. (1) is through extinction measurements of two gases with known Rayleigh scattering cross sections, typically He and N2 or zero air (Washenfelder et al., 2008). Previous BBCES applications in the UV wavelength region often used He and N2, which have substantially different cross sections (Washenfelder et al., 2013; Flores et al., 2014a; Bluvshtein et al., 2017; Zhao et al., 2017). However, Rayleigh scattering is proportional to λ-4, and more accurate characterizations of mirror reflectivity at visible wavelengths can be achieved by using a gas with a larger Rayleigh scattering cross section than N2 or O2, particularly when the mirror reflectivity is not very high. We selected CO2 as a stable, inexpensive, non-toxic gas with a large Rayleigh scattering cross section. The Rayleigh scattering cross section of CO2 has been reported (Shardanand and Rao, 1977; Sneep and Ubachs, 2005; He et al., 2018), but it is not as well-known as N2 or O2. We determined it here by introducing mixtures of CO2 in He to the BBCES instrument, measuring the extinction spectrum for each addition, and deriving the slope of the linear fit of the extinction relative to the CO2 number density.

Spectral fitting of trace gas absorbers in BBCES extinction spectra often includes a fourth-order polynomial to account for drifts in the cavity, spectrometer, and light source intensity (Platt et al., 2009; Thalman and Volkamer, 2010; Min et al., 2016). While this can be effective for trace gases with highly structured absorbing features measured using mirrors with smoothly varying reflectivity, it is not appropriate for smoothly varying aerosol extinction spectra or for cavity mirrors with reflectivity that varies strongly with wavelength (see Fig. S1). Here, we describe a new method to explicitly account for drifts in the cavity, spectrometer, and light source intensity that affected the calculated α(λ) extinction for the visible channel.

We determined that each measured spectrum may be affected by drift in the light source intensity, drift in the spectrometer dark current background counts, and a wavelength shift incurred by the temperature-dependent drifts in the spectrometer optics and that these can each be represented by a scalar parameter. Using a nonlinear Levenberg–Marquardt least-squares fitting algorithm, the scalar parameters for these different types of drift were fitted and the drifts removed. The fitting algorithm was tested successfully on spectra of zero air and found to remove nearly all the structure due to intensity and spectrometer drift. This correction was subsequently used on all extinction spectra. Further details for this correction can be found in the Supplement and in Fig. S2.

The aerosol optical extinction derived in Eq. (1) depends on wavelength, aerosol size distribution, and the RI. Measurements of aerosol optical extinction for different size selections can be used to retrieve n(λ) and k(λ) (Washenfelder et al., 2013; Flores et al., 2014a; He et al., 2018) with assumptions that the aerosol population is internally and externally well-mixed and that the refractive index does not vary systematically with size. For PSL and ammonium sulfate aerosol, this approach was used as described previously (Washenfelder et al., 2013; Flores et al., 2014a). Each 2 min group of spectra for a single aerosol population was averaged to determine I(λ). The aerosol extinction cross section, σ(λ), was then calculated using Eqs. (1) and (2), with values of IZA(λ) and R(λ) linearly interpolated from the nearest measurements. The set of aerosol extinction cross section spectra (σDp=150nm(λ), σDp=225nm(λ), … ) and the average aerosol size distribution N(Dp) for each time interval can then be used to retrieve the complex refractive index, n(λ)+ki(λ) using a scattering theory.

We use a retrieval algorithm that calculates the expected extinction cross section for a given wavelength, a given RI, and the measured N(Dp) and compares it to the measured extinction cross section. Since the RI consists of both n and k, at least two extinction measurements are required to retrieve these two parameters (Bluvshtein et al., 2012). We use five diameter set points to increase the accuracy of the retrieval. A least-squares minimization fit is used to identify the n and k values that minimize χ2 for each wavelength: 3χ2λ=∑DpN=5σcalculatedn,k,λ,Dp-σmeasured(λ,Dp)σmeasured(λ,Dp)2, where σ represents the extinction cross section from Eq. (2).

Previous work has assumed spherical aerosol populations that are well-represented by Mie theory and have easily measured size distributions (Washenfelder et al., 2013; Flores et al., 2014a; He et al., 2018). The biomass burning aerosol produced from some of the fires at the Fire Sciences Laboratory was fractal and strongly absorbing. This required two improvements to the retrieval algorithms, described further below: (1) the incorporation of two methods for size distribution measurements (the OPC and the SMPS) to better characterize N(Dp) and (2) the incorporation of two scattering theories, Mie and Rayleigh–Debye–Gans (RDG), to represent both spherical and fractal aerosol.

The accuracy of the measured aerosol extinction, λ, was determined by propagating the known uncertainties of the measurement. The precision in the I(λ) spectrum is shot noise limited at the CCD. Figure S1b demonstrates that error from this photon counting is negligible compared to the other uncertainties. The majority of the error is attributed to uncertainty in the Rayleigh scattering cross sections of zero air (±2 %) and CO2 (±2 %) as well as uncertainty in the measured temperature (±0.5 %) and pressure (±0.5 %) and flow rates (±0.3 %) (Washenfelder et al., 2013). Summed in quadrature, the total calculated uncertainty in α(λ) is approximately ±3 %, with some wavelength dependence. The uncertainty in the extinction cross section, σ(λ) as shown in Eq. (2), is derived from summing in quadrature the error in α(λ) and the error in N. The error in the particle counting, N, by the CPC is due to the uncertainty in the flow rate and the variability in the number of particles entering the CPC. The last factor is highest for the largest diameter set points due to the low number of particles, and thus the uncertainty in N typically lay between ±5 and ±10 % and was highest at the largest aerosol diameter set points. The standard deviations for all measurements are indicated in the figures by shaded error bars. The derived lower detection limit as a function of wavelength is shown in Fig. S1b and spans 1 × 10-8–7 × 10-8 cm-1. Extinction values measured during FIREX 2016 were generally greater than 1 × 10-7 cm-1 and therefore within the measurable range of the BBCES.

To ascertain the uncertainty in the retrieved RI, we retrieve values three times: once for the best estimate of σ(λ), and once for the upper and lower bounds of σ(λ). This is likely a conservative estimate of the total uncertainty and is shown as shaded error bars in the figures. The RI was retrieved with a resolution of 0.01 in both n and k, so if the upper or lower bound of the retrieved RI was within 0.01 of the best estimate, those error bars appear to be zero. In that case, the error should be interpreted as being no more than 0.01.

Figure 2 shows the measured CO2 Rayleigh scattering extinction spectra, determined from six fractional concentrations of CO2 in He that evenly span 0–1. The mirror reflectivity, R(λ), was determined here using pure He and zero air standards. The CO2 extinction spectrum, α(λ), at each concentration was determined using Eq. (1), with He replacing zero air as the reference gas. Spectral peaks attributed to absorption by O2 near 688 nm (Greenblatt et al., 1990) and the O4 oxygen dimer near 477, 577, and 630 nm (Hermans, 2011) were fitted and removed prior to further analysis. At each wavelength, the measured extinction (units of cm-1) was plotted against the number density of CO2 (units of cm-3), and the slope of the linear fit is the Rayleigh scattering cross section (units of cm2).

The CO2 Rayleigh scattering cross section determined for the two BBCES channels and CRDS channel agree well, as shown in Fig. 2. A power law fit to the BBCES data from 360–720 nm is parameterized as σRayleigh,CO2=1.43 × 10-15×λ-4.036. Three literature values for the CO2 Rayleigh scattering cross section are also plotted in Fig. 2. These were experimentally determined using a scattering chamber (Shardanand and Rao, 1977), CRDS (Sneep and Ubachs, 2005), and BBCES (He et al., 2018). Our power law fit is consistent with all prior measurements within 10 % at all wavelengths and is within 5 % of the two more recent studies at lower wavelengths where the Rayleigh scattering is greater. We use the power law parameterization of CO2 Rayleigh scattering cross section for the retrievals described below.

To assess the long-term stability of the instrument, we introduced concentrations of NO2 during each of the 16 measurement days at the Fire Sciences Laboratory, using the flow system shown in Fig. 1b. Each set of additions included four NO2 concentrations from 0 to 72 ppbv. Measured NO2 number densities were retrieved by fitting the NO2 absorption cross section (Vandaele et al., 1998) to the extinction, α(λ), with shift and stretch of the literature spectrum to account for discrepancies in the BBCES wavelength calibration (Min et al., 2016). A small amount of HONO was observed in the UV channel, but it has distinct spectral peaks and did not interfere with the NO2 fits. The measured NO2 concentrations are compared to the nominal concentrations determined by the flow rates and shown in Fig. S3. The r2 values are greater than 0.99 and the slopes vary from 0.8–1, with a slight downward drift in both parameters over time. This could be due to conversion of NO2, as the BBCES is designed to minimize particle losses, not NO2 conversion on surfaces. It is also possible that the NO2 calibration tank concentration changes over time, as the output of these tanks is known to deviate significantly from the manufacturer's specified concentration (Chilton et al., 2005). The two fires examined in this paper – Fires A and B – occurred on 31 October and 1 November 2016, and Fig. S3 shows agreement of ±7 % with the nominal NO2 concentration on those 2 d.

We atomized five aqueous solutions of monodisperse PSL with diameters from 150 to 400 nm and passed the resulting aerosol flow through a DMA to remove any clumped particles or small spheres of surfactant (Miles et al., 2010; Thalman and Volkamer, 2010). The size-selected aerosol was monitored by a UHSAS OPC and found to be consistent within uncertainty with the manufacturer-specified mode diameter and Gaussian distribution. SMPS-derived size distributions of PSL were not measured, due to their narrow diameter distribution. The intensity spectra and size distributions were averaged for approximately 90 s at each diameter set point, and extinction cross sections were derived using Eqs. (1) and (2), as described in Sect. 4.1 and 4.2. To minimize errors due to changes in the light source and optical stability, we measured the mirror reflectivity before and after each PSL diameter set point, in addition to using the fitting algorithm described in Sects. 3.2 and S1.

The resulting extinction cross sections for the five PSL diameters are shown in Fig. 3a. Calculated extinction cross sections from the measured OPC size distribution and the RI reported by Nikolov and Ivanov (2000) are also shown, and these agree with our measured extinction cross sections within the instrument uncertainty. The largest error bars appear in the Dp=400 nm extinction cross section. It was difficult to produce PSL solutions with sufficiently high concentrations at the larger diameters, and the extinction cross section, which is the total extinction divided by the total particle counts, is therefore highly sensitive to the accuracy of the particle counting. To reduce error in the RI retrieval, we exclude the 400 nm spectrum from the RI retrieval.

The retrieved RI is shown in Fig. 3b. We find that n varies from 1.65 to 1.57 between 360 and 700 nm, while k=0 throughout, as expected for purely scattering particles. We empirically fit n to a third-order polynomial function of wavelength as n=2.30-0.0035×λ+(6.05×10-6)×λ2-(3.62×10-6)×λ3 across the measured spectral range. Nikolov and Ivanov (2000) measured the RI of PSL spheres using a direct scattering photodetector and found a gradual decrease from 1.62+0.00i to 1.59+0.00i over the wavelength region 450 to 700 nm, as shown in Fig. 3b. Several other recent experimental studies (Garvey and Pinnick, 1983; Abo Riziq et al., 2007; Dinar et al., 2008; Washenfelder et al., 2013) at 390 and 532 nm are also shown and agree well with our results.

Figure 4 shows the retrieved RI for ammonium sulfate aerosol, using the two different size distribution methods. Ammonium sulfate particles were atomized from a 6.0 g L-1 aqueous solution of ammonium sulfate in distilled water and then dried to less than 5 % RH to minimize the water content. Extinction cross sections were determined at diameter set points from 150–450 in 75 nm increments. The aerosol size distribution was measured continuously after the DMA by a UHSAS OPC, which was independently calibrated for ammonium sulfate particles prior to the experiment (Kupc et al., 2018). Additionally, SMPS scans were taken before and after each set of aerosol diameter set points, and an inversion algorithm was used to derive the full size distribution of the atomized aerosol entering the DMA. Spurious peaks in the size distribution at diameters greater than 750 nm were removed. Section S2 describes this correction further. The DMA transfer function was then used to determine the aerosol size distribution at each diameter set point.

The RI values in Fig. 4 range from 1.55+0.00i at 360 nm to 1.40+0.01i at 720 nm, though the error bars for the imaginary component span 0i and thus cannot be distinguished from a non-absorbing aerosol. The results from the two size distribution methods agree well, indicating that the SMPS size distribution is an accurate assessment of the aerosol population. We empirically fit the n derived by OPC as a third-order polynomial function of wavelength as n=0.69+0.0052×λ-(9.85×10-6)×λ2+(5.51×10-6)×λ3 across the entire spectral range. Recent literature values measured by CRDS at 355, 390, 405, and 532 nm are shown and summarized in Washenfelder et al. (2013). Few measurements of ammonium sulfate RI have been reported at wavelengths greater than 532 nm. The calculated uncertainty is higher at longer wavelengths due to increased uncertainty in the Rayleigh scattering at those wavelengths.

Fire A (no. 086) was a lodgepole pine (Pinus contorta) fire, with a mixture of small logs, litter duff, and canopy branches with low moisture content, intended to be representative of wildfire fuel composition. The smoke was dominated by BrC with a small contribution from fractal soot-like particles, as shown by the large decrease in number and mode volume when the aerosol was thermodenuded (Manfred et al., 2018). This implies that the majority of the particles consisted of volatile organic matter that was efficiently vaporized in the thermodenuder. We assume that the volatile organic matter has spherical or near-spherical morphology that can be represented using Mie theory.

The retrieved RI values for undenuded aerosol measured 1 h after fire ignition are shown in Fig. 5a for one 10 min measurement cycle. Both SMPS and OPC size distributions were available for this set of extinction cross sections, and two diameters are displayed in Fig. 5b. However, there are some differences between the two size distribution measurements. First, as in the ammonium sulfate retrieval in Sect. 4.4, the SMPS inverted full size distribution has some spurious values at diameters above 550 nm which are not observed in the OPC and which skew the size distributions to higher diameters. Therefore, we again apply an upper diameter threshold, above which the SMPS size distributions are set to zero. Second, the OPC size distribution for every diameter set point shows a small peak near 100 nm. That these small particles passed through the DMA at larger diameter set points suggests that they are small fractal particles, which were selected by the DMA due to their relatively large aerodynamic diameter. Scanning electron microscopy images from the denuded channel for this fire confirm the presence of small fractal particles (Manfred et al., 2018). These particles are quite small and therefore do not contribute much to the total aerosol extinction, but for the larger diameter set points they comprise a significant percentage of the total number of particles. Therefore, we must explicitly include these small particles as part of the size distribution.

Finally, it can be seen in Fig. 5b that the main mode diameter for each set point is approximately 5 % higher in the OPC than the intended set point, as indicated by the mode diameter in the SMPS. The LAS OPC is calibrated for ammonium sulfate particles, assuming an RI of 1.52+0.00i. If these brown carbon particles scatter light more effectively than ammonium sulfate particles, then the OPC will interpret this increased light scattering as a larger particle. This also holds true for the small ∼100 nm peaks, which likely consist of BC particles with an RI very different from that of ammonium sulfate. Therefore, the sizing of these particles by the OPC may be somewhat incorrect.

Despite these caveats, we use the LAS size distribution without further modification for the RI retrieval in Fig. 5a. We find that the real component of the retrieved RI varies from 1.55 to 1.60, while the imaginary component steadily increases from ∼0i to 0.25i as the wavelength decreases from 550–360 nm. This is highly characteristic of BrC aerosol and consistent with previous estimates of the complex refractive index of fresh biomass burning aerosol summarized in Bluvshtein et al. (2017). Furthermore, these observations differ significantly from the measured RI of ∼1.8+0.01i for spherical BC described as tar balls by Chakrabarty et al. (2010), indicating that the aerosol population measured here does not have a significant contribution from tar balls. At the OPC laser wavelength of 663 nm, the retrieved RI is (1.61 ± 0.14) + (0.00 ± 0.06)i. Particles with this RI will scatter light slightly more efficiently than ammonium sulfate particles, and therefore the LAS will attribute this scattered light to a slightly larger particle. Therefore, this result is consistent with our finding that the LAS mode diameters are slightly higher than the diameter set point. However, we do not attempt to correct the LAS diameters further, as that analysis is complicated by the small number of fractal particles also observed. Manfred et al. (2018) assumed a typical RI for brown carbon (Dinar et al., 2008), shown as filled squares at 375 and 405 nm, to model the measured phase function from this fire, with good results. We find good agreement with those assumed RIs within instrumental uncertainty.

Fire B (no. 085) was a sage (Artemisia) fire that produced smoke with a high BC content, as evidenced by the minimal change in particle counts and volume between the fresh and thermodenuded smoke (Manfred et al., 2018). Furthermore, Manfred et al. (2018) demonstrated that the measured phase function for this aerosol population could not be accurately fit assuming Mie theory and a typical BrC RI. Instead, they used Rayleigh–Debye–Gans theory, along with two different parameterizations of the fractal particles, to fit the measurement. As described in Sect. 3.3.2, RDG theory treats fractal particles as an aggregate of many smaller monomers, and the input parameters describe the number of monomers, their configuration in the aggregate, and the extinction properties of each monomer.

Unfortunately, neither size distribution method used here can accurately constrain these parameters well. The SMPS size distributions are inaccurate because fractal particles have mobility diameters that differ significantly from their geometric diameters. The OPC size distributions yield more useful information because they measure scattered light within a certain solid angle range, which is later attributed to a certain particle diameter. Only purely scattering and very slightly absorbing particles display monotonically increasing scattering as a function of increasing particle diameter. Highly or moderately absorbing particles tend to side-scatter significantly less than scattering particles to the angles the LAS is most sensitive to, and the scattering often non-monotonically increases as particle size increases (Szymanski et al., 2009). Therefore, a large diameter range of absorbing particles has similar scattering properties and cannot be distinguished, as illustrated in Fig. S5. However, we can make an adjustment to the measured OPC size distributions. As described in Sect. 3.3.2, we use RDG theory to predict the side scatter into the OPC collection optics for particles as a function of the number of monomers, Np, while holding the other parameters in Eq. (4) constant. This allows us to treat the nominal OPC size distribution as a distribution of monomers in the fractal particle. We can then use the same RDG parameters to estimate the extinction cross section and compare it to the measured spectra. Because the RI retrieval is so sensitive to an accurate representation of the particle size, we do not attempt to fit any of the RDG parameters. Instead, we show the expected cross sections for two plausible RDG parameterizations of BC particles.

Figure 6 shows the measured extinction cross sections for the five diameter set points. These spectra were taken 1 h after the fire was ignited and represent the aerosol that passed through the thermodenuder. Therefore, the majority of organic coatings that might complicate the analysis are removed prior to measurement. Following Manfred et al. (2018), we use two parameterizations. Both assume an RI for BC of 1.95+0.8i (Bond and Bergstrom, 2006) and an individual monomer diameter of 50 nm. The first is meant to represent fractal particles from fossil fuel combustion. It assumes a prefactor of 1.2 and a fractal dimension of 1.75 (Sorensen, 2001). The second represents sage biomass burning and consists of a prefactor of 2.56 and a fractal dimension of 1.79 (Chakrabarty et al., 2006). The two parameterizations are shown in Fig. 6a and b. The fossil fuel parameterization yields the closer approximation of the measured data, but the measurement lies in between the two parameterizations. This is consistent with the results of Manfred et al. (2018), in which the measured phase function for thermodenuded smoke from Fire B lay in between the two parameterizations.

We place the Fire A and B retrievals in the context of the other FIREX measurements by analyzing the quality of the RI retrieval method assuming Mie theory and relating these values to the fraction of aerosol that is black carbon. The BC / (BC + OA) fraction was calculated relative to the largest BC fraction for 13 fires for which the data were available from the average SP2 black carbon mass and the relative AMS organic aerosol mass, and the error bars were derived from propagating the two instrument uncertainties. Only aerosol that bypassed the thermodenuder was used in this analysis, in order to quantify fresh non-denuded smoke. We elected to evaluate the RI retrieval as a function of the BC / (BC + OA) ratio instead of the mass combustion efficiency, as BC / (BC + OA) has been shown to more strongly correlate with single scattering albedo and the Ångström absorption coefficient (Pokhrel et al., 2016). The RI retrievals were performed using the SMPS size distributions, as the LAS data were often not available. Therefore, this analysis is also a function of how well the SMPS size distributions characterize the aerosol geometric diameter. Figure S6 shows the retrieved wavelength-dependent RI for each fire across the entire 360–720 nm wavelength range. To demonstrate the effectiveness of the retrieval method, we report the χ2 of the RI retrieval in Fig. 7 at a single wavelength, 475 nm, where the BBCES instrument had high mirror reflectivity and therefore good precision. The reported χ2 for each fire is from a single set of measurements through the bypass channel, approximately 1 h after the fire start, and therefore represents well-mixed smoke. The derived real part of the RI for the low-BC fires ranged from 1.54 to 1.69 at 475 nm with an average value of 1.635 ± 0.056, and the imaginary part ranged from 0.00i to 0.23i with an average value of 0.06i ± 0.12. At 365 nm, the average value of the real part was 1.605 ± 0.041 and the imaginary part was 0.038i ± 0.074. We note that the average k value is slightly greater at 475 nm than at 365 nm, but the two values are consistent within the error bars of the averaged measurements of aerosol from different fuel types and fire conditions.

Figure 7 shows a correlation between the relative fraction of BC in the total aerosol mass and the quality of the RI retrieval assuming Mie theory and spherical particles well-characterized by the SMPS. Fire B has the highest relative BC fraction, defined here as 1, and is poorly described by Mie theory, with a χ2 of 1.3. This finding is consistent with Smith and Grainger (2014), who found that there is no refractive index that suitably describes fractal BC if those particles are treated as spheres with Mie theory. Fire A has a lower relative BC fraction and is better described by Mie theory, consistent with Sect. 4.5 and 4.6. Most of the other 11 fires analyzed here have a smaller BC fraction than Fire A and a correspondingly lower χ2 value. This indicates that the majority of smoke sampled during FIREX had relatively low BC and could reasonably be analyzed using Mie theory. However, we note that this freshly emitted smoke was from small-scale burns under controlled conditions and may not represent the full range of smoke aerosol types in ambient aerosol, including dust and biological fragments. Additionally, further downwind of the fire, coagulation and fractal aggregate collapse can alter the particle morphology. Furthermore, the poor fit quality of the high-BC fire (Fire B) shows that Mie theory is not appropriate for all smoke, especially smoke with a high BC fraction. Since BC fraction is not a metric that is easily quantified with remote sensing, further work is still needed to link this parameterization to remote-sensing measurements to predict when Mie theory representation of wildfire smoke is appropriate.