In this paper, we will focus on the measurements of the linear particle depolarization ratio. Figure 1 shows a simplified diagram of the optics of the transmission system that are relevant to the measurement of depolarization. The primary optical components for the polarization of the transmitted beams are Glan laser polarizers, which have a very high polarization transmittance ratio of 2×105:1 (i.e., the light is highly linearly polarized with an extremely small fraction of cross-polarized light). The calibration of depolarization for HSRL-2 is done in a manner similar to HSRL-1 (Hair et al., 2008) for all three wavelengths. The polarization axis of the outgoing light is matched to that of the receiver with an approach similar to that outlined by Alvarez et al. (2006) using seven fixed polarization angles between ±45∘, using the half-wave calibration wave plates indicated in Fig. 1. Following the alignment, the polarization gain ratio between the cross-polarized and co-polarized channels is routinely determined in flight by rotating the transmitted polarization 45∘ relative to the receiver, so that both channels measure equal components of the co-polarized and cross-polarized backscatter returns, in a cloud-free portion of the profile; see Hair et al. (2008) for a detailed description of the calibrations and the caption accompanying Fig. 1 for more details of the HSRL-2 transmission optics.

The receiver optics relevant to depolarization measurements are shown in Fig. 2. The collimated light arrives from the telescope and is split into the three wavelengths using dichroic beam splitters. Each beam is then passed through an interference filter (1064 nm) or a combination of interference filter and etalon (355 and 532 nm) to remove background scattering. The effective full-width half-max (FWHM) bandwidths for the three channels are 0.4 nm (3.5 cm-1) at 1064 nm, 0.03 nm (1.1 cm-1) at 532, and 0.045 nm (3.6 cm-1) at 355 nm. Note that these bandwidths are narrow enough to completely exclude the rotational Raman sidebands from the receiver optics, which are found starting at ±11.9 cm-1 for N2 and ±14.4 cm-1 for O2 (Behrendt and Nakamura, 2002). The 1064 nm channel includes a half-wave plate, which can be used to correct any small polarization misalignment in the receiver system, since the 532 and 1064 nm beams are transmitted together. This half-wave plate is set during installation and is not rotated during normal operations. Next, each beam passes through polarization beam splitters (PBSs) to be separated into components that are co-polarized and cross-polarized with respect to the transmitted beam. Since the transmittance ratio of the light exiting a PBS is greater in the transmitted direction than in the reflected direction, a second cleanup PBS is included for each detector wavelength to further improve the transmittance ratio for the co-polarized light. The polarization transmittance ratio measured in the system is 300:1 for the cross-polarized light at 355 nm, 431:1 for the co-polarized light at 355 nm (with two PBSs) and greater than 1000:1 for both polarization states at 532 and 1064 nm. After exiting the polarization optics, the light in the 1064 nm channel goes directly to the avalanche photodetectors (APD). The co-polarized signal and cross-polarized signal are used to determine the volume depolarization ratio. As described by Hair et al. (2008) for HSRL-1, the co-polarized 532 nm channel is also split into a portion that is passed through an iodine cell leaving only molecular return and another portion that has both molecular and aerosol return. At 355 nm, a portion of the co-polarized light is captured for the determination of the volume depolarization ratio, while the rest of the co-polarized light is transmitted through an interferometer to produce one channel that is dominated by the aerosol return with little signal from molecular scattering and a complementary channel that is dominated by the molecular signal with much less aerosol backscatter signal. The separation of the aerosol and molecular signals is the basis of the HSRL technique for extinction and backscatter retrieval. Since it also affects the systematic uncertainty in the particle depolarization ratio, it is included in the systematic uncertainty budget discussed in Sect. 2.2, below, and more details can be found in the Appendix.

The volume (or total) linear depolarization ratio is the ratio of the signal in the cross-polarized channel to that in the co-polarized channel, normalized by the measured polarization gain ratio. δtot=GdepP⊥P∥ In Eq. (1), P⊥ and P∥ are proportional to the light measured by the photodetectors or photomultipliers in the cross-polarized channel and the co-polarized channel, respectively; Gdep is the electro-optical gain ratio between the two (for each wavelength) and δtot is the volume depolarization ratio, which is the ratio of the cross-polarized to co-polarized channel returns using the polarization gain ratio.

The particle depolarization ratio is calculated from the volume depolarization ratio using the following (Cairo et al., 1999): δa=Rδtotδm+1-δmδtot+1Rδm+1-δtot+1, where δa indicates the particle depolarization ratio, which will be used in all of the following discussions, δm indicates the estimated molecular depolarization ratio, and R indicates the total aerosol scattering ratio, which is the ratio of the aerosol plus molecular backscatter to the molecular backscatter, including both polarization components. R=βa+βmβm

Systematic error can be a concern for polarization measurements. Potential sources of systematic error in volume depolarization ratio arise in the polarization optics and calibration. The retrieval of the particle depolarization ratio can potentially introduce additional systematic error related to the total aerosol scattering ratio or uncertainty in the molecular depolarization ratio value. We will provide an overview of the potential systematic errors here, including systematic uncertainty for volume depolarization ratio and propagated systematic uncertainty for the particle depolarization ratio. More details about these potential errors and the means of estimating the systematic uncertainty are given in the Appendix.

The linear volume depolarization ratio, given by Eq. (1), is the more basic measurement. Systematic errors in the volume depolarization ratio can arise from various sources, including calibration errors either in the polarization angle calibration or the polarization gain ratio calibration. A major concern for the measurement of depolarization is the potential for cross talk, which can arise from a number of sources, including imperfect polarization angle alignment, signal impurities due to imperfections in the polarization beam splitter (particularly the reflected channel), or other optics, including the aircraft window. Considering these sources, we estimate the systematic uncertainty in the volume depolarization ratio measurement to be the larger of 4.7 % (relative) or 0.001 (absolute) in the 355 nm channel, the larger of 5 % (relative) or 0.007 (absolute) in the 532 nm channel, and the larger of 2.6 % (relative) or 0.007 (absolute) in the 1064 nm channel. Further discussion of these estimates is given in the Appendix.

As can be seen in Eq. (2), the particle depolarization ratio, δa, depends on the volume depolarization ratio, the molecular depolarization ratio, and the total aerosol scattering ratio. Therefore, an error in the assumed value of δmol or any systematic error in the total aerosol scattering ratio, R, can also cause systematic error in the particle depolarization ratio. Since the rotational Raman scattering sidebands are completely excluded from the receiver by the narrow-bandwidth background filters, the molecular depolarization arises only from the central Cabannes line and is very well characterized (She, 2001; Behrendt and Nakamura, 2002). More critically important is any potential systematic error in the total aerosol scattering ratio, R. We estimate the systematic uncertainty to be 4.1 % in the 532 nm channel from an analysis of the stability of the aerosol-to-molecular gain ratio; 5 % in the 355 nm channel including potential errors associated with gain ratio calibration transfer from the 532 nm channel; and 20 % in the 1064 nm channel taking into account the retrieval of backscatter using an estimated lidar ratio. Again, further discussion can be found in the Appendix.

The estimates given above are intended to be conservative estimates of the systematic uncertainty confidence limit, such that we expect a high probability that the systematic error is less than this value. The systematic uncertainties on the three quantities, δmol, δtot, and R, are combined in quadrature using standard propagation of errors for independent variables, as described in the Appendix. The propagated systematic uncertainties for the case studies are included in the figures and tables in Sects. 3 and 4.

On 13 July 2014, HSRL-2 aboard the B200 made measurements at three wavelengths on a transit flight from Virginia to Colorado for the DISCOVER-AQ field mission (http://discover-aq.larc.nasa.gov/). The aerosol backscatter at three wavelengths and aerosol extinction at two wavelengths are shown in Fig. 3 for a 180 km portion of the flight track in Missouri and Kansas, in the midwestern United States. Several aerosol layers are evident. For this case study, we will focus on a dust-dominated layer that extends from just above the boundary layer to about 3200 m a.s.l. Back trajectories derived from the NOAA Hybrid Single Particle Lagrangian Integrated Trajectory Model (HYSPLIT) tool (ready.arl.noaa.gov) indicate that this layer probably has a Saharan origin and has undergone a very long transport period of about 14 days. Non-spherical particles, such as dust, have a distinct signature in lidar particle depolarization measurements. The linear particle depolarization ratio measurement curtains for all three wavelengths are shown in Fig. 4. Peak values of the particle depolarization ratio in the 1600–2300 m altitude range are approximately 0.246 ± 0.018 (standard deviation for the sample) ± (0.055 systematic), 0.304 ± 0.005 ± (0.022), and 0.270 ± 0.005 ± (0.009) at 355, 532, and 1064 nm, respectively. These high values of the particle depolarization ratio indicate that the layer is dominated by dust (approximately 90 % dust using the methodology of Sugimoto and Lee (2006)). Note that the particle depolarization ratio at 532 nm for this layer is larger than at either 355 or 1064 nm. The 532 nm layer optical depth is approximately 0.1 and the total aerosol scattering ratio at 532 nm is 2.3. The backscatter Ångström exponent (532/1064 nm) is 0.45 ± 0.03 (standard deviation) for this layer. Table 1 includes these values for this sample and for the other cases discussed here. Values for the particle depolarization ratios and backscatter Ångström exponents are within the interquartile range we previously reported for dust-dominated aerosol measurements from HSRL-1 (Burton et al., 2013).

Figure 5 shows both the particle depolarization ratio and volume depolarization ratio measurements for all altitudes at 17:12 UT (17.2 UT). The particle depolarization ratio random and systematic uncertainties are also shown.

The predecessor of the HSRL-2, the NASA Langley HSRL-1 instrument, observed several cases of transported Saharan dust in the Caribbean in August 2010, for example the case on 18 August 2010 that is shown by Burton et al. (2012). For that case, the particle depolarization ratios at 532 and 1064 nm are 0.33 ± 0.02 (standard deviation) and 0.28 ± 0.01, slightly higher than the 13 July 2014 case but agreeing within the spread of the measurement sample. The backscatter Ångström exponent (532/1064 nm) is 0.68 ± 0.13 (Table 1). As on 13 July 2014, the particle depolarization ratios and the backscatter Ångström exponent are within the interquartile range of values for dust-dominated aerosol reported for HSRL-1. The backscatter Ångström exponents (532/1064 nm) are larger than the value reported for pure Saharan aerosol in Morocco (Tesche et al., 2009b), which is 0.28 ± 0.16. The larger values may be consistent with large particle loss during transport, discussed in more detail below.

The spectral dependence of the particle depolarization ratio can also be compared to measurements of the Saharan dust particle depolarization ratio reported by Freudenthaler et al. (2009) for the SAMUM I campaign. For the four dates presented in their Fig. 7, the minimum and maximum values for 355 nm from the portable lidar system (POLIS) were 0.21–0.31 (compare 0.25 for NASA HSRL-2 case); at 532 nm they were 0.29–0.33 from the German Aerospace Center (DLR) HSRL (compare 0.30 and 0.33 from NASA HSRL-2 and HSRL-1) and at 1064 nm they were 0.22–0.29 from the DLR HSRL (compare 0.27 and 0.28 from NASA HSRL-2 and HSRL-1). Again, the reported values at 532 nm exceed those at the other wavelengths. Indeed all three of these case studies, Saharan dust close to the source (Freudenthaler et al., 2009), transported Saharan dust observed in the Caribbean by HSRL-1, and transported Saharan dust observed by HSRL-2 in the midwestern US, have similar wavelength dependence of the particle depolarization ratio.

A less typical observation of dust-dominated aerosol was made by the HSRL-2 instrument on 8 February 2013. On a transit flight to Virginia at the conclusion of the DISCOVER-AQ California field campaign, HSRL-2 aboard the B200 made three-wavelength measurements of a locally produced dust layer very close to the source in the US Southwest. Figure 6 shows the lidar curtain of the aerosol backscatter coefficient at 532 nm for a segment of approximately 280 km in Arizona and New Mexico. The highest backscatter values are near the surface and are associated with the dust layer. More tenuous layers are also visible between 3 and 5 km, which are probably smoke. The discussion will focus primarily on the dust layer for this example. Figure 7 shows the particle depolarization ratio at three wavelengths for the same flight segment.

The maximum backscatter values occur within 400 m of the ground at about 17:08 UT (17.14 UT), near the Potrillo volcanic fields in New Mexico in the Chihuahuan Desert. The layer is shallower than the previous case, and the layer AOD is only about 0.02 at 532 nm, but it is very strongly scattering, with a 532 nm total aerosol scattering ratio of 3.1. The peak particle depolarization ratio is 0.24 ± 0.05 ± (0.05), 0.37 ± 0.01 ± (0.02), and 0.383 ± 0.006 ± (0.011) at 355, 532, and 1064 nm, respectively (the first uncertainty value represents standard deviation and the parentheses indicate systematic uncertainty). Given that these very large depolarization ratio values occur very close to the ground, we infer that this observation is close to the source region. This observed dust layer is a locally generated, wind-driven aerosol from a bare soil surface in desert scrubland. The large particle depolarization ratios provide confidence that this air mass is dominated by dust aerosol rather than a mixture from distinct sources. The backscatter Ångström exponent (532/1064 nm) is -0.09 ± 0.04.

Figure 8 shows line plots of the volume depolarization ratio and the particle depolarization ratio profiles, plus error bars. The systematic uncertainties are generally larger at 355 nm. This error magnification at 355 nm occurs in both dust-dominated cases because of the spectral dependence of the scattering and consequent small total aerosol scattering ratio at 355 nm (R = 1.2 at 355 nm). However, the systematic uncertainties are small enough to clearly reveal that the wavelength dependence of the particle depolarization ratio is quite different from the Saharan dust cases discussed previously, both those measured by the NASA Langley HSRL-1 and HSRL-2 instruments and by other researchers. In our observations of transported Saharan aerosol, including the case discussed in Sect. 3.1, the particle depolarization ratio at 532 nm exceeds the value at 1064 nm, but this case differs in that the 1064 nm particle depolarization ratio slightly exceeds the 532 nm value. The difference is primarily in the 1064 nm value, since the 355 and 532 nm particle depolarization ratios are similar to the Saharan aerosol cases. However, there was a previous observation by HSRL-1 of windblown North American dust on the slope of the Pico de Orizaba near Veracruz, Mexico, on 12 March 2006 (Burton et al., 2014; de Foy et al., 2011), which provides an analogous case for comparison. In this case the particle depolarization ratios are 0.33 ± 0.02 (standard deviation) and 0.40 ± 0.01 at 532 and 1064 nm, respectively, similar to the Chihuahuan Desert aerosol on 8 February 2013, and the backscatter Ångström exponent (532/1064 nm) is -0.9 ± 0.4. Note that these backscatter Ångström exponents are significantly smaller than the transported Saharan dust-dominated aerosol cases discussed in Sect. 3.1.

Figure 9 shows the linear particle depolarization ratio at all three wavelengths for the four HSRL-1 and HSRL-2 cases discussed so far. The HSRL-2 observations of transported Saharan aerosol have spectral dependence consistent with the elevated Saharan dust-dominated aerosol reported by Freudenthaler et al. (2009) for the DLR airborne HSRL and ground-based lidar. However, the NASA HSRL-1 and HSRL-2 observations of North American dust at low altitude close to the source appear to fall into a different category. Although all of the observations discussed here from the NASA HSRL-2 and those of Saharan desert aerosol in Africa (Freudenthaler et al., 2009) have particle depolarization ratios at 355 nm that are less than those at 532 nm, there is a large difference at the longest wavelength, with larger 1064 nm particle depolarization ratios for the local dust-dominated cases.

Furthermore, the backscatter Ångström exponents in the Chihuahuan Desert observation on 8 February 2013 and on Pico de Orizaba on 12 March 2006 are much smaller compared to 0.45–0.68 for the cases of transported Saharan dust. These smaller values are an indication of larger particle sizes (Sasano and Browell, 1989) (although it must be noted that the backscatter Ångström exponent is also sensitive to other factors besides particle size, such as relative humidity (Su et al., 2008)). Maring et al. (2003) shows measured size distributions for dust layers over the Canary Islands and Puerto Rico at different stages of transport, and concluded by modeling of these distributions that a combination of Stokes gravitational settling and an offset upward velocity would explain these observations. According to that model, the volume mean diameter decreases only 20 % after 10 days of atmospheric transport, but 80 % of that change occurs within the first 2 days. In other words, the size distributions for transported dust-dominated aerosol are similar whether transported long distances or short distances, but even layers transported short distances probably have already lost the largest particles to settling. This model applies to Saharan dust transport, but it raises the possibility that dust-dominated aerosol size distributions immediately over the source, such as the North American dust cases presented here, will have some proportion of particles significantly larger than those found in the transported layers.

The spectral dependence of the particle depolarization ratio is known to be related to the size of the non-spherical particles (Mishchenko and Sassen, 1998). We infer that the difference in depolarization spectral dependence, and in particular the 1064 nm values, are due to larger particles in the observations of windblown dust close to the surface. Ground-based lidar observations by Ansmann et al. (2009) of convective plumes of dust and sand being lifted from the surface in Morocco included extremely large particle depolarization ratios of 0.50–1.0 at 710 nm. This supports the connection between large particle depolarization ratios at the longer wavelengths and large particles sizes. However, the long-wavelength values in the current case study are not nearly as extreme, suggesting perhaps that the particle sizes are not as large.

Theoretical calculations to date have shown that it is difficult to quantitatively predict the spectral dependence of the particle depolarization ratio for dust (Gasteiger et al., 2011; Wiegner et al., 2009; Gasteiger and Freudenthaler, 2014), due in part to the need for parameterizing the shape of the dust aerosols as spheroids or other simplified shapes.

In a theoretical treatment of a particular measurement case, Gasteiger et al. (2011) modeled the particle depolarization ratio at multiple wavelengths using size distributions and refractive indices appropriate for SAMUM measurements, using mixtures of various irregular shapes to represent the dust particles. For their reference distribution, the modeled particle depolarization ratio reflects a spectral dependence with a peak in the middle of the wavelength range. Calculated values at 355, 532, 710, and 1064 nm were 0.275, 0.306, 0.311, 0.298, respectively, consistent with the measurements we report for the Saharan dust-dominated cases from the NASA HSRL-1 and HSRL-2. However, for the dust-dominated cases in the immediate vicinity of North American sources, the measured maximum shifts to longer wavelengths, and there is no longer agreement with the modeled values at 1064 nm.

Gasteiger et al. (2011) do not show results for size distributions with different size particles, but Gasteiger and Freudenthaler (2014) perform theoretical calculations using spheroids for various size parameters (single particles). These calculations show that the first peak in the spectral depolarization ratio shifts to larger wavelengths as particle size increases. This result, based on highly simplified modeling of dust aerosol, should be used only cautiously, but in general supports the notion that the spectral particle depolarization ratio is sensitive to particle size.

Our third three-wavelength case study is an observation of a smoke plume with large particle depolarization ratios measured during the Colorado deployment of the DISCOVER-AQ field mission on 17 July 2014 at about 8 km altitude. At this time, wildfire smoke from fires in the Pacific Northwest of the United States blanketed much of the region, visible in a composited Moderate Resolution Imaging Spectroradiometer (MODIS) true color image in Fig. 10. (The smoke situation on that day is also discussed in University of Maryland Baltimore County's US Air Quality Smog Blog; see http://alg.umbc.edu/usaq/archives/2014_07.html). Figure 11 shows a view of the smoke plume from the B200.

Figures 12 and 13 show HSRL-2 measurements of 532 nm backscatter and three-wavelength linear particle depolarization ratios as time-height curtains and Fig. 14 illustrates a profile at 19:18 UT (19.3 UT) as a line plot with random and systematic uncertainty error bars. The pictured flight segment began near the Boulder Atmospheric Observatory tall tower north of downtown Denver and proceeded south for about 70 km to Chatfield State Park, then turned north again on a parallel track for 135 km to Fort Collins. The layer optical thickness is about 0.05 at 532 nm and the total aerosol scattering ratio is 2.9. This layer was at high altitude near the aircraft, in the overlap region, where there is a range dependence of the detected backscattered light (Hair et al., 2008). While backscattered light from a distant target is fully imaged in the detector, light from a near-field target is focused beyond the field stop, resulting in overfilling of the field stop at small range from the lidar. This loss of signal is range dependent and prevents the retrieval of aerosol extinction. For this reason, the layer optical depth given above is an estimate using the backscatter measurements and an assumed lidar ratio of 70 sr, which is typical for smoke. Volume depolarization ratio measurements and total aerosol scattering ratio measurements are ratios of two channels that are equally affected and therefore have no range-dependent overlap function. For this layer, the particle depolarization ratio is greatest at 355 nm, about 0.24 ± 0.01 ± (0.02) at the southern end of the flight track, and about 0.17–0.22 in the more northern portions. The particle depolarization ratio at 532 nm is as large as 0.09 ± 0.02 ± (0.01) at the southern end of the flight track and down to about 0.06 at the northern end. The particle depolarization ratio at 1064 nm is about 0.018 ± 0.002 ± (0.008) throughout the region (parenthesis indicate systematic uncertainties). Note that the wavelength dependence of the particle depolarization ratio is opposite to what was observed for dust on 8 February 2013, in that the smoke plume has a significantly larger particle depolarization ratio at the shorter wavelengths. Since this smoke layer has a very high total aerosol scattering ratio, the systematic uncertainties are relatively small, and it is clear even at the upper limit of the systematic uncertainty that the 355 nm particle depolarization ratio significantly exceeds the 532 nm value and the 532 nm value significantly exceeds the 1064 nm value.

The pattern of larger particle depolarization ratios at 532 nm compared to 1064 nm has regularly been observed for smoke with the HSRL-1 instrument; indeed the HSRL-1 aerosol classification methodology (Burton et al., 2012) takes advantage of this spectral dependence. One such example is the aged southwest Canadian smoke plume observed on the eastern seaboard of the US on 2 August 2007 that was shown by Burton et al. (2012). For that prior case, the particle depolarization ratios were 0.07 ± 0.01 and 0.019 ± 0.005 at 532 and 1064 nm, respectively.

The observations by HSRL-2 in Figs. 12 and 13 are, to our knowledge, the first reported three-wavelength measurements of linear particle depolarization ratio from pure smoke. Note that while the 532 nm particle depolarization ratio for the smoke case is only about 25–30 % of the value for pure dust, the large particle depolarization ratio at 355 nm for the smoke layer is quite comparable to the 355 nm value for dust.

Observed linear particle depolarization ratios for smoke are quite variable. Frequently, the 532 nm particle depolarization ratio is observed to be only a few percent at most and often discounted as negligibly close to zero (e.g., Mattis et al., 2003; Müller et al., 2005). For example, small values of about 2–3 % at 532 nm were observed by HSRL-1 in smoke plumes in Mexico City during the Megacity Initiative: Local and Global Research Observations (MILAGRO) field mission described by de Foy et al. (2011). In the published images of HSRL-1 measurements, the smoke plumes are obvious as local minima in the particle depolarization ratio compared to the relatively high ambient values, which are due to regional dusty background conditions. However, higher values of the particle depolarization ratio at 532 nm of 0.05–0.11 have sometimes been observed in aged smoke layers, e.g., 0.07 observed by HSRL-1 on 2 August 2007 noted above (Burton et al., 2012), 0.06–0.11 for transported Canadian smoke reported in Lindenberg, Germany, during the Lindenberg Aerosol Characterization Experiment (LACE) 1998 by Fiebig et al. (2002), 0.06 to 0.08 for 3–4 day old smoke from North America observed over Germany in 2011 by Dahlkötter et al. (2014), 0.06 for transported Siberian smoke observed in Tokyo in 2003 by Murayama et al. (2004), and 0.05 for Alaskan forest fire smoke observed by Sassen and Khvorostyanov (2008) in 2004. Sugimoto et al. (2010) discuss a case in which much higher 532 nm particle depolarization ratios were observed for smoke from a Mongolian forest fire transported to Japan in 2007. The particle depolarization ratios measured for this smoke were 0.12, 0.14, and 0.15 for layers at two different altitudes observed at Nagasaki and Tsukuba. Nisantzi et al. (2014) observe values of 0.09 to 0.18 at 532 nm for aerosol from Turkish fires observed in Cyprus after 1 to 4 days of transport.

The causes of depolarization by smoke are not well understood. Two possible explanations are frequently cited in literature: lifting and entrainment of surface soil into the smoke plume and asymmetry of smoke particles themselves.

For example, the smoke observed by Sugimoto et al. (2010) was associated with pyrocumulonimbus and therefore it is inferred that strong convection lifted soil particles from the surface into the smoke plume, explaining the unusually large particle depolarization ratios. Lifting of soil particles is also cited as a possible explanation of the more moderate but still non-negligible particle depolarization ratios reported by Fiebig et al. (2002), since chemical composition analysis of this plume reveals the presence of aluminosilicates and iron oxides/hydroxides. Nisantzi et al. (2014) assume that the depolarization is due to fine-mode dust and infer the mass fraction of dust mixed in the smoke plumes using lab measurements of fine and coarse dust by Sakai et al. (2010). However, this explanation is not sufficient in every case. Murayama et al. (2004) discount soil lifting for their observations of depolarizing smoke, since no signature of mineral dust is found in a chemical analysis of this plume. Instead, they cite non-sphericity of smoke particle aggregates as the probable cause. Martins et al. (1998) discuss the non-sphericity of smoke particles observed by scanning electron microscope images and an electro-optical aerosol asymmetry analyzer for a variety of smoke types during the Smoke, Clouds, and Radiation – Brazil (SCAR-B) project in 1995. They concluded that most of the non-spherical particles in the observed smoke were chain aggregates of small black carbon particles, and that the non-sphericity tends to increase with the black carbon ratio. Young smoke (< 1 h) is composed of open clusters of high non-sphericity while aged smoke is composed of tighter clusters with lesser non-sphericity. They also point out that flaming fires (high combustion efficiency) tend to produce more non-spherical particles than smoldering fires.

Referring back to the theoretical calculations of spectral depolarization for spheroids discussed in Sect. 3.3., the larger particle depolarization ratio at 355 nm compared to longer wavelengths may indicate a smaller size for the non-spherical particles than the dust cases, although of course these results may be only qualitatively applicable to more general particle shapes.

Theoretical calculations of the linear particle depolarization ratio by aggregates of soot are given by, e.g., Sorensen (2001), Bescond et al. (2013), and Kahnert et al. (2012). Calculations for bare carbon aggregates (Sorensen, 2001; Bescond et al., 2013) tend to produce small values of the particle depolarization ratio, much smaller than what was measured in the HSRL-2 case study. However, Kahnert et al. (2012) modeled the scattering properties of a more realistic particle morphology, light absorbing carbon (LAC) aggregates embedded in a sulfate shell, and obtain larger values. They use the discrete dipole method to calculate the depolarization ratio of the aggregate particle in the backscatter direction at 304.0, 533.2, and 1010.1 nm. They show that the particle depolarization ratio generally increases with aggregate particle radius (defined as volume-equivalent radius) and with the volume fraction of LAC in the aggregate. The values also increase with decreasing wavelength for aggregate volume-equivalent radii of 400 nm and smaller; conversely, for 500 nm particles, the particle depolarization ratio peaks at the middle wavelength, 533.2 nm. The maximum calculated particle depolarization ratios for 7 % LAC fraction by volume is 0.08–0.11 for 500 nm particles at 533.2 nm. This is comparable to the 532 nm measurement on 17 July 2014; however, the calculated value at 304.0 nm for the same size and LAC volume fraction is 0.05–0.07, much smaller than the measured value (at 355 nm) of 0.24. The largest values calculated for the 304.0 nm wavelength are about 0.12–0.21, occurring for the case of 400 nm particle volume-equivalent radius and 20 % LAC volume fraction. The full set of theoretical calculations of the particle depolarization ratio for 20 % LAC volume fraction are replotted in Fig. 15 for all three wavelengths to highlight the wavelength dependence. Figure 15 also indicates the HSRL-2 observed particle depolarization ratio in the 17 July smoke plume (at 355, 532, and 1064 nm). The calculated particle depolarization ratios are roughly comparable in magnitude to the HSRL-2 measurements for volume-equivalent radii in the 400–500 nm range, but the wavelength dependence matches better for smaller particle sizes. A LAC volume fraction of 20 % is quite high and may be unrealistic for this smoke layer and the modeled single scattering albedos for a 20 % LAC volume fraction, shown by Kahnert et al. (2012), are quite low (below 0.7 at 533.2 nm), indicating exceptionally absorbing particles; therefore, this model is probably not an exact match for the observation in this case. Yet, it is encouraging that an estimate of the particle depolarization ratio of the right magnitude can be made by modeling coated soot aggregates. The model results were for a constant fractal dimension of 2.6, structural prefactor of 1.2, and a monomer radius of 25 nm, values chosen to be consistent with the findings for soot aerosol in Mexico City (Adachi and Buseck, 2008). In the HSRL-2 case study, there could be a different fractal dimension, different size monomer component, different coating, or a different fraction of soot per aggregate. In addition, the spectral dependence of the refractive index is not well-known, and this will have a significant effect on the spectral dependence of the particle depolarization ratio. While the current state of knowledge is not sufficient to perform a retrieval of particle size using the depolarization measurements alone, it is certainly worth noting that the particle depolarization ratio at three wavelengths is sensitive to and contains some information about the particle size of smoke particles, information that may play a role in future microphysical retrievals.