Observations of the spectral dependence of linear particle depolarization 1 ratio of aerosols using NASA Langley airborne High Spectral Resolution 2 Lidar 3

14 Linear particle depolarization ratio is presented for three case studies from the NASA Langley 15 airborne High Spectral Resolution Lidar-2 (HSRL-2). Particle depolarization ratio from lidar is an 16 indicator of non-spherical particles and is sensitive to the fraction of non-spherical particles and 17 their size. The HSRL-2 instrument measures depolarization at three wavelengths: 355 nm, 532 18 nm, and 1064 nm. The three measurement cases presented here include two cases of dust- 19 dominated aerosol and one case of smoke aerosol. These cases have partial analogs in earlier 20 HSRL-1 depolarization measurements at 532 nm and 1064 nm and in literature, but the 21 availability of three wavelengths gives additional insight into different scenarios for non- 22 spherical particles in the atmosphere. A case of transported Saharan dust has a spectral 23 dependence with a peak of 0.30 at 532 nm with smaller particle depolarization ratios of 0.27 and 24 0.25 at 1064


Introduction 34
The impact of aerosols on climate depends on their horizontal and vertical distribution and 35 microphysical properties. Lidar is an important tool for remote sensing of aerosol, because it 36 provides vertically resolved information on aerosol abundance and aerosol type. One extremely 37 useful lidar aerosol measurement is the linear particle depolarization ratio, an indicator of non-38 spherical particles. Polarization lidar is an a large and active field, with recent contributions from 1 ground-based networks such as the European Aerosol Research Lidar Network (EARLINET;  2 Pappalardo , and will also be useful for validating 22 the EarthCARE lidar measurements. Since the airborne HSRL-2 measures particle depolarization 23 ratio at both the CALIPSO and EarthCARE wavelengths and also at 1064 nm, observations from 24 this instrument are useful for assessing how the measurements from the two satellite instruments 25 will correspond. NASA's airborne HSRL-2 is the first HSRL system making depolarization 26 measurements at three wavelengths. A ground-based Raman system operated by the Leibniz 27 Institute of Tropospheric Research has also been recently upgraded to make three-wavelength 28 depolarization measurements (Haarig et al., 2014). 29 Aerosol classification is one specific application of aerosol polarization measurements ( ratio from lidar is of key importance for the detection and assessment of dust and volcanic ash 32 since it is a clear indicator of non-spherical particles. The particle depolarization ratio is also used 33 to infer the amount of dust or ash in a mixture ( While a significant amount of study has been made of depolarization by dust and ash, smoke has 38 also been observed to produce significant depolarization of lidar light in some cases (e.g. Fiebig 39 et not in others (e.g. Müller et al., 2005). Even for cases with significant depolarization, the 41 depolarization signature for smoke is generally smaller than for dust, at the wavelengths of 532 1 nm and 1064 nm where most lidar depolarization measurements of smoke have been made. 2 We will describe two dust-dominated cases and a smoke-dominated case where depolarizing 3 aerosol was observed simultaneously at three wavelengths by the NASA Langley airborne HSRL- 4 2 instrument. We show consistency between the three HSRL-2 cases and three previously 5 published cases from the predecessor HSRL-1 instrument in which similar measurements were 6 made at 532 nm and 1064 nm, and we also discuss similarities and differences with published 7 lidar measurements globally. We find that the three cases each have a different spectral 8 dependence of the particle depolarization ratio. Accordingly, we discuss possible explanations 9 for these differences with reference to published studies. We also point out implications for future 10 space-based observations of aerosol depolarization. We begin in Section 2 with a description of 11 the NASA Langley airborne HSRL instruments and the methodology for polarization 12 measurements, including an assessment of systematic uncertainty. In Section 3 we describe and 13 discuss the dust cases and in Section 4 we describe and discuss the smoke case. We summarize 14 the discussion and conclude in Section 5. In the Appendix we give more details about the 15 estimation of systematic uncertainty. 16

Instrument Description and Measurement Methodology 17
The NASA Langley second-generation airborne High Spectral Resolution Lidar-2 (HSRL-2) uses 18 the HSRL technique (Shipley et al., 1983) to independently measure aerosol extinction and 19 backscatter at 355 and 532 nm and the standard backscatter technique (Fernald, 1984) to measure 20 aerosol backscatter at 1064 nm. It also measures linear depolarization ratio at all three 21 wavelengths. It is a follow-on to the successful airborne HSRL-1 instrument (Hair et al., 2008), 22 which has made measurements at 532 nm and 1064 nm since 2006 (Rogers et al., 2009). For 23 measurements at 532 nm and 1064 nm, HSRL-2 is essentially identical to HSRL-1. HSRL 24 measurements of extinction and backscatter at 355 nm are made using an interferometer rather 25 than an iodine filter. For 355 nm measurements of depolarization discussed here, the setup is 26 very similar to the other channels; the small differences are explained in section 2a. Data are 27 sampled at 0.5-s temporal and 30-m vertical resolutions. Aerosol backscatter and depolarization 28 products are averaged 10-s horizontally (~1 km at nominal aircraft speed) and aerosol extinction 29 products are averaged 60-s (~6 km) horizontally and 150-m vertically. Besides aerosol backscatter, 30 extinction, and depolarization ratio, products also include horizontally-and vertically-resolved 31 curtains of backscatter Ångström exponent and extinction Ångström exponent. Operational 32 retrievals also provide mixing ratio of nonspherical-to-spherical backscatter ( In this paper, we will focus on the measurements of linear particle depolarization ratio. Figure 1  2 shows a simplified diagram of the optics of the transmission system that are relevant to the 3 measurement of depolarization. The primary optical components for the polarization of the 4 transmitted beams are Glan Laser Polarizers, which have a very high polarization transmittance 5 ratio of 2e5:1 (i.e. the light is highly linear polarized with an extremely small fraction of cross-6 polarized light). The calibration of depolarization for HSRL-2 is done in a manner similar to 7 HSRL-1 (Hair et al., 2008) for all three wavelengths. The polarization axis of the outgoing light is 8 matched to that of the receiver with an approach similar to that outlined by Alvarez et al. (2006) 9 using seven fixed polarization angles between 45, using the half-wave calibration wave plates 10 indicated in Figure 1. Following the alignment, the polarization gain ratio between the cross-11 polarized and co-polarized channels is routinely determined in flight by rotating the transmitted 12 polarization 45 relative to the receiver, so that both channels measure equal components of the 13 co-polarized and cross-polarized backscatter returns, in a cloud-free portion of the profile. See 14 Hair et al. (2008) for a detailed description of the calibrations. See the caption accompanying 15 Figure 1 for more details of the HSRL-2 transmission optics. 16 The receiver optics relevant to depolarization measurements are shown in Figure 2. The 17 collimated light arrives from the telescope and is split into the three wavelengths using dichroic 18 beam splitters. Each beam is then passed through an interference filter (1064 nm) or a 19 combination of interference filter and etalon (355 and 532 nm) to remove background scattering. 20 The effective full-width half-max (FWHM) bandwidths for the three channels are 0.4 nm (3.5 cm -21 1 ) at 1064 nm, 0.03 nm (1.1 cm -1 ) at 532 nm, and 0.045 nm (3.6 cm -1 ) at 355 nm. Note that these 22 bandwidths are narrow enough to completely exclude the rotational Raman sidebands from the 23 receiver optics, which are found starting at 11.9 cm -1 for N2 and 14.4 cm -1 for O2 (Behrendt and  24 Nakamura, 2002). The 1064 nm channel includes a half-wave plate which can be used to correct 25 any small polarization misalignment in the receiver system, since the 532 nm and 1064 nm beams 26 are transmitted together. This half-wave plate is set during installation and is not rotated during 27 normal operations. Next, each beam passes through Polarization Beam Splitters (PBS) to be 28 separated into components that are co-polarized and cross-polarized with respect to the 29 transmitted beam. Since the transmittance ratio of the light exiting a PBS is greater in the 30 transmitted direction than in the reflected direction, a second "clean-up" PBS is included for each 31 detector wavelength to further improve the extinction ratio for the co-polarized light. The 32 polarization transmittance ratio measured in the system is 300:1 for the cross-polarized light at 33 355 nm, 431:1 for the co-polarized light at 355 nm (with two PBS) and greater than 1000:1 for both 34 polarization states at 532 nm and 1064 nm. After exiting the polarization optics, the light in the 35 1064 nm channel goes directly to the Avalanche Photodetectors (APD). The co-polarized signal 36 and cross-polarized signal are used to determine the volume depolarization ratio. As described 37 by Hair et al. (2008) for HSRL-1, the co-polarized 532 nm channel is also split into a portion that 38 is passed through an iodine cell leaving only molecular return and a channel with both molecular 39 and aerosol return. At 355 nm, a portion of the co-polarized light is captured for the 40 determination of the volume depolarization ratio, while the rest of the co-polarized light is 41 transmitted through an interferometer to produce one channel that is dominated by the aerosol 42 return with little signal from molecular scattering and a complementary channel that is 43 5 dominated by the molecular signal with much less aerosol backscatter signal . The separation of  1  the aerosol and molecular signals is the basis of the HSRL technique for extinction and backscatter  2 retrieval. Since it also affects the systematic uncertainty in particle depolarization ratio, it is 3 included in the systematic uncertainty budget discussed in Section 2b, below, and more details 4 can be found in the Appendix. 5 The volume (or total) linear depolarization ratio is the ratio of the signal in the cross-polarized 6 channel to that in the co-polarized channel, normalized by the measured polarization gain ratio. 7 In Eq (1), P ǁ and P  are proportional to the light measured by the photodetectors or 8 photomultipliers in the co-polarized channel and the cross-polarized channel, respectively; Gdep 9 is the electro-optical gain ratio between the two (for each wavelength) and  tot is the volume 10 depolarization ratio, which is the ratio of the cross-polarized to co-polarized channel returns 11 using the polarization gain ratio. 12 The particle depolarization ratio is calculated from the volume depolarization ratio using the 13 following (Cairo et al., 1999): 14 where a indicates the particulate depolarization ratio which will be used in all of the following 15 discussion; m indicates the estimated molecular depolarization ratio; and R indicates the total 16 aerosol scattering ratio, which is the ratio of the aerosol plus molecular backscatter to the 17 molecular backscatter, including both polarization components. 18 19

b. Systematic Errors 20
Systematic error can be a concern for polarization measurements. Potential sources of systematic 21 error in volume depolarization ratio arise in the polarization optics and calibration. The retrieval 22 of particle depolarization ratio can potentially introduce additional systematic error related to the 23 total aerosol scattering ratio or uncertainty in the molecular depolarization ratio value. We will 24 provide an overview of the potential systematic errors here, including systematic uncertainty for 25 volume depolarization ratio and propagated systematic uncertainty for the particle 26 depolarization ratio. More details about these potential errors and the means of estimating the 27 systematic uncertainty are given in the Appendix. 28 The linear volume depolarization ratio, given by Eq (1), is the more basic measurement. 29 Systematic errors in the volume depolarization ratio can arise from various sources, including 30 calibration errors either in the polarization angle calibration or the polarization gain ratio 31 calibration. A major concern for the measurement of depolarization is the potential for cross-talk, 32 which can arise from a number of sources, including imperfect polarization angle alignment, 33 signal impurities due to imperfections in the polarization beam splitter (particularly the reflected 1 channel), or other optics, including the aircraft window. Considering these sources, we estimate 2 the systematic uncertainty in the volume depolarization ratio measurement to be the larger of 3 4.7% (relative) or 0.001 (absolute) in the 355 nm channel, the larger of 5% (relative) or 0.007 4 (absolute) in the 532 nm channel, and the larger of 2.6% (relative) or 0.007 (absolute) in the 1064 5 nm channel. Further discussion of these estimates is given in the Appendix. 6 As can be seen in Eq. (2), the particle depolarization ratio, a, depends on the volume 7 depolarization ratio, the molecular depolarization ratio, and the total aerosol scattering ratio. 8 Therefore, an error in the assumed value of mol or any systematic error in the total aerosol 9 scattering ratio, R, can also cause systematic error in the particle depolarization ratio. Since the 10 rotational Raman scattering sidebands are completely excluded from the receiver by the narrow-11 bandwidth background filters, the molecular depolarization arises only from the central 12 Cabannes line and is very well characterized (She, 2001;Behrendt and Nakamura, 2002). More 13 critically important is any potential systematic error in the total aerosol scattering ratio, R. We 14 estimate the systematic uncertainty to be 4.1% in the 532 nm channel from an analysis of the 15 stability of the aerosol-to-molecular gain ratio; 5% in the 355 nm channel including potential 16 errors associated with gain ratio calibration transfer from the 532 nm channel; and 20% in the 17 1064 nm channel taking into account the retrieval of backscatter using an estimated lidar ratio. 18 Again, further discussion can be found in the Appendix. 19 The estimates given above are intended to be a conservative estimates of the systematic 20 uncertainty confidence limit, such that we expect a high probability that the systematic error is 21 less than this value. The systematic uncertainties on the three quantities, mol, tot, and R, are 22 combined in quadrature using standard propagation of errors for independent variables, as 23 described in the Appendix. The propagated systematic uncertainties for the case studies are 24 included in the figures and tables in Sections 3 and 4. 25

Dust 26
In this section we discuss two case studies in which HSRL-2 made three-wavelength 27 measurements of the depolarization of dust. 28 a. Case study: 13 July 2014, Dust in the residual layer in North American Midwest 29 On 13 July 2014, HSRL-2 aboard the B200 made measurements at three wavelengths on a transit 30 flight from Virginia to Colorado for the DISCOVER-AQ field mission (http://discover-31 aq.larc.nasa.gov/). The aerosol backscatter at three wavelengths and aerosol extinction at two 32 wavelengths are shown in Figure 3  Saharan origin and has undergone a very long transport period of about 14 days. Non-spherical 38 particles, such as dust, have a distinct signature in lidar particle depolarization measurements. 39 The linear particle depolarization ratio measurement curtains for all three wavelengths are shown 40 in Figure 4. Peak values of particle depolarization ratio in the 1600-2300 m altitude range are 41 approximately 0.246  0.018 (standard deviation for the sample)  (0.055 systematic), 1 0.3040.005(0.022), and 0.2700.005(0.009) at 355 nm, 532 nm, and 1064 nm, respectively. These 2 high values of the particle depolarization ratio indicate that the layer is dominated by dust 3 (approximately 90% dust using the methodology of Sugimoto and Lee (2006)). Note that the 4 particle depolarization ratio at 532 nm for this layer is larger than at either 355 nm or 1064 nm. 5 The 532 nm layer optical depth is approximately 0.1 and the total aerosol scattering ratio at 532 6 nm is 2.3. The backscatter Ångström exponent (532/1064 nm) is 0.450.03 (standard deviation) for 7 this layer. Table 1 includes these values for this sample and for the other cases discussed here. 8 Values for the particle depolarization ratios and backscatter Ångström exponents are within the 9 interquartile range we previously reported for dust-dominated aerosol measurements from  is 0.280. 16. The larger values may be consistent with large particle loss during transport, 24 discussed in more detail below. 25 The spectral dependence of the particle depolarization ratio can also be compared to 26 measurements of Saharan dust particle depolarization ratio reported by Freudenthaler et al. 27 (2009) for the SAMUM I campaign. For the four dates presented in their Figure  field campaign, HSRL-2 aboard the B200 made three-wavelength measurements of a locally 40 produced dust layer very close to the source in the U.S. Southwest. Figure 6 shows the lidar 41 curtain of the aerosol backscatter coefficient at 532 nm for a segment of approximately 280 km in 1 Arizona and New Mexico. The highest backscatter values are near the surface and are associated 2 with the dust layer. More tenuous layers are also visible between 3 and 5 km, which are probably 3 smoke. The discussion will focus primarily on the dust layer for this example. Figure 7 shows 4 particle depolarization ratio at three wavelengths for the same flight segment. 5 The maximum backscatter values occur within 400 m of the ground at about 17:08 UT (17.14 UT), 6 near the Potrillo volcanic fields in New Mexico in the Chihuahuan Desert. The layer is shallower 7 than the previous case, and the layer AOD is only about 0.02 at 532 nm, but it is very strongly 8 scattering, with 532 nm total aerosol scattering ratio of 3.1. The peak particle depolarization ratio 9 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 10 (the first uncertainty value represents standard deviation and parenthesis indicate systematic 11 uncertainty). Given that these very large depolarization ratio values occur very close to the 12 ground, we infer that this observation is close to the source region. This observed dust layer is 13 locally generated, wind driven aerosol from a bare soil surface in desert scrubland. The large 14 particle depolarization ratios provide confidence that this airmass is dominated by dust aerosol 15 rather than a mixture from distinct sources. The backscatter Ångström exponent (532/1064 nm) is 16 -0.090.04. 17 Figure 8 shows line plots of the profiles of volume depolarization ratio and particle depolarization 18 ratio, plus error bars. The systematic uncertaintis are generally larger at 355 nm. This error 19 magnification at 355 nm occurs in both dust-dominated cases because of the spectral dependence 20 of the scattering and consequent small total aerosol scattering ratio at 355 nm (R = 1.2 at 355 nm). 21 However, the systematic uncertainties are small enough to clearly reveal that the wavelength 22 dependence of the particle depolarization ratio is quite different from the Saharan dust cases 23 discussed previously, both those measured by the NASA Langley HSRL-1 and HSRL- 2 24 instruments and by other researchers. In our previous observations of transported Saharan 25 aerosol, the particle depolarization ratio at 532 nm exceeds the value at 1064 nm, but this case 26 differs in that the 1064 nm particle depolarization ratio slightly exceeds the 532 nm value. The 27 difference is primarily in the 1064 nm value, since the 355 nm and 532 nm particle depolarization 28 ratios are similar to the Saharan aerosol cases. However, there was a previous observation by 29 HSRL c. Discussion of spectral dependence of particle depolarization ratio of dust-dominated aerosol 37 have particle depolarization ratios at 355 nm that are less than those at 532 nm, there is a large 3 difference at the longest wavelength, with larger 1064 nm particle depolarization ratios for the 4 local dust-dominated cases. cases of transported Saharan dust. These smaller values are an indication of larger particle sizes 8 (Sasano and Browell, 1989) (although it must be noted that the backscatter Ångström exponent is 9 also sensitive to other factors besides particle size, such as relative humidity (Su et al., 2008)). 10 Maring et al. (2003) shows measured size distributions for dust layers over the Canary Islands 11 and Puerto Rico at different stages of transport, and concluded by modeling of these distributions 12 that a combination of Stokes gravitational settling and an offset upward velocity would explain 13 these observations. According to that model, the volume mean diameter decreases only 20% after 14 10 days of atmospheric transport, but 80% of that change occurs within the first 2 days. In other 15 words, the size distributions for transported dust-dominated aerosol are similar whether 16 transported long distances or short distances, but even layers transported short distances 17 probably have already lost the largest particles to settling. This model applies to Saharan dust 18 transport, but it raises the possibility that dust-dominated aerosol size distributions immediately 19 over the source such as the North American dust cases presented here will have some proportion 20 of particles significantly larger than those found in the transported layers. 21 The spectral dependence of particle depolarization ratio is known to be related to the size of the 22 non-spherical particles (Mishchenko and Sassen, 1998). We infer that the difference in nm. This supports the connection between large particle depolarization ratios at the longer 28 wavelengths and large particles sizes. However, the long-wavelength values in the current case 29 study are not nearly as extreme, suggesting perhaps that the particle sizes are not as large. 30 Theoretical calculations to date have shown that it is difficult to quantitatively predict the spectral 31 dependence of the particle depolarization ratio for dust (Gasteiger et 3 Gasteiger and Freudenthaer (2014) perform theoretical calculations using spheroids for various 4 size parameters (single particles). These calculations show that the first peak in the spectral 5 depolarization ratio shifts to larger wavelengths as particle size increases. This result, based on 6 highly simplified modeling of dust aerosol, should be used only cautiously, but in general 7 supports the notion that the spectral particle depolarization ratio is sensitive to particle size. . Figure 11 shows a view of the smoke plume from the B200. 18 Figure 12 and Figure 13 show HSRL-2 measurements of 532 nm backscatter and three wavelength 19 linear particle depolarization ratio as time-height curtains and Figure 14 illustrates a profile at 20 19 near-field target is focused beyond the field stop, resulting in overfilling of the field stop at small 28 range from the lidar. This loss of signal is range dependent and prevents the retrieval of aerosol 29 extinction. For this reason, the layer optical depth given above is an estimate using the 30 backscatter measurements and an assumed lidar ratio of 70 sr, which is typical for smoke. Volume 31 depolarization ratio measurements and total aerosol scattering ratio measurements are ratios of 32 two channels that are equally affected and therefore have no range-dependent overlap function. 33 For this layer, the particle depolarization ratio is greatest at 355 nm, about 0.240.01(0.02) at the 34 southern end of the flight track, and about 0.17-0.22 in the more northern portions. The particle 35 depolarization ratio at 532 nm is as large as 0.090.02(0.01) at the southern end of the flight track 36 and down to about 0.06 at the northern end. Particle depolarization ratio at 1064 nm is about 37 0.0180.002(0.008) throughout the region (parenthesis indicate systematic uncertainties). Note 38 that the wavelength dependence of the particle depolarization ratio is opposite to what was 39 observed for dust on 8 February 2013, in that the smoke plume has significantly larger particle 40 depolarization ratio at the shorter wavelengths. Since this smoke layer has a very high total 41 aerosol scattering ratio, the systematic uncertainties are relatively small, and it is clear even at the 42 upper limit of the systematic uncertainty that the 355 nm particle depolarization ratio 1 significantly exceeds the 532 nm value and the 532 nm value significantly exceeds the 1064 nm 2 value. 3 The pattern of larger particle depolarization ratio at 532 nm compared to 1064 nm has regularly 4 been observed for smoke with the HSRL-1 instrument; indeed the HSRL-1 aerosol classification 5 methodology (Burton et al., 2012) takes advantage of this spectral dependence. One such example 6 is the aged southwest Canadian smoke plume observed on the eastern seaboard of the U.S. on 2 7 August 2007 that was shown by Burton et al. (2012). For that prior case, the particle depolarization 8 ratios were 0.070.01 and 0.0190.005 at 532 and 1064 nm, respectively. The observation by HSRL-9 2 is the first time to our knowledge that particle depolarization ratio has been reported for pure 10 smoke at three wavelengths. Note that while the 532 nm particle depolarization ratio for the 11 smoke case is only about 25-30% of the value for pure dust, the large particle depolarization ratio 12 at 355 nm for the smoke layer is quite comparable to the 355 nm value for dust. 13 b. Discussion of particle depolarization ratio of smoke 14 Observed linear particle depolarization ratios for smoke are quite variable. Frequently the 532 nm 15 particle depolarization ratio is observed to be only a few percent at most and often discounted as obvious as local minima in the particle depolarization ratio compared to the relatively high 21 ambient values which are due to regional dusty background conditions. However, higher values pyrocumulonimbus and therefore it is inferred that strong convection lifted soil particles from 39 the surface into the smoke plume, explaining the unusually large particle depolarization ratios. 40 Lifting of soil particles is also cited as a possible explanation of the more moderate but still non- spherical particles in the observed smoke were chain aggregates of small black carbon particles, 12 and that the non-sphericity tends to increase with the black carbon ratio. Young smoke (<1 hour) 13 is composed of open clusters of high non-sphericity while aged smoke is composed of tighter 14 clusters with lesser non-sphericity. They also point out that flaming fires (high combustion 15 efficiency) tend to produce more non-spherical particles than smoldering fires. 16 Referring back to the theoretical calculations of spectral depolarization for spheroids discussed 17 in Section 3.c., the larger particle depolarization ratio at 355 nm compared to longer wavelengths 18 may indicate a smaller size for the non-spherical particles than the dust cases, although of course 19 these results may be only qualitatively applicable to more general particle shapes. use the discrete dipole method to calculate the depolarization ratio of the aggregate particle in 27 the backscatter direction at 304.0, 533.2 and 1010.1 nm. They show that the particle depolarization 28 ratio generally increases with aggregate particle radius (defined as volume-equivalent radius) 29 and with the volume fraction of LAC in the aggregate. The values also increase with decreasing 30 wavelength for aggregate volume-equivalent radii of 400 nm and smaller; but for 500 nm 31 particles, the particle depolarization ratio peaks at the middle wavelength, 533.2 nm. The 32 maximum calculated particle depolarization ratios for 7% LAC fraction by volume is 0.08-0.11 for 33 500 nm particles at 533.2 nm. This is comparable to the 532 nm measurement on 17 July 2014; 34 however, the calculated value at 304.0 nm for the same size and LAC volume fraction is 0.05-0.07, 35 much smaller than the measured value (at 355 nm) of 0.24. The largest values calculated for the 36 304.0 nm wavelength are about 0.12-0.21, occurring for the case of 400 nm particle volume-37 equivalent radius and 20% LAC volume fraction. The full set of theoretical calculations of particle 38 depolarization ratio for 20% LAC volume fraction are replotted in Figure 15 for all three 39 wavelengths to highlight the wavelength dependence. Figure 15 also indicates the HSRL-2 40 observed particle depolarization ratio in the 17 July smoke plume (at 355, 532, and 1064 nm). The 41 calculated particle depolarization ratios are roughly comparable in magnitude to the HSRL-2 42 measurements for volume-equivalent radii in the 400-500 nm range, but the wavelength 1 dependence matches better for smaller particle sizes. LAC volume fraction of 20% is quite high 2 and may be unrealistic for this smoke layer and the modeled single scattering albedos for 20% 3 LAC volume fraction, shown by Kahnert et al. (2012), are quite low (below 0.7 at 533.2 nm), 4 indicating exceptionally absorbing particles, so this model is probably not an exact match for the 5 observation in this case. Yet, it is encouraging that an estimate of particle depolarization ratio of 6 the right magnitude can be made by modeling coated soot aggregates. The model results were 7 for a constant fractal dimension of 2.6, structural prefactor of 1.2, and a monomer radius of 25 8 nm, values chosen to be consistent with the findings for soot aerosol in Mexico City (Adachi and 9 Buseck, 2008). In the HSRL-2 case study, there could be a different fractal dimension, different 10 size monomer component, different coating or a different fraction of soot per aggregate. In 11 addition, the spectral dependence of the refractive index is not well known, and this will have a 12 significant effect on the spectral dependence of the particle depolarization ratio. While the 13 current state of knowledge is not sufficient to perform a retrieval of particle size using the 14 depolarization measurements alone, it is certainly worth noting that the particle depolarization 15 ratio at three wavelengths is sensitive to and contains some information about the particle size of 16 smoke particles, information that may play a role in future microphysical retrievals. 17

Summary and Discussion 18
We have presented three case studies of depolarizing aerosol observed at three wavelengths (355 19 nm, 532 nm and 1064 nm) by the NASA airborne HSRL-2 instrument. These three aerosol layers, 20 two dust-dominated layers and a smoke layer, each have a different spectral dependence of linear 21 particle depolarization ratio, but in each case, the 532 nm and 1064 nm values agree well with 22 prior analogs in the long record of observations by the predecessor instrument, HSRL-1, and with 23 comparable measurements in literature. The first case, transported Saharan desert aerosol, has a 24 peak in the spectral dependence of the particle depolarization ratio at 532 nm. This is in 25 accordance with prior measurements of Saharan desert aerosol aloft both close to the source and 26 transported to the Caribbean Sea. The second case, also a dust-dominated measurement, but near 27 the surface and very close to the source, has a spectral dependence increasing monotonically with 28 wavelength, differing from the previous case primarily at the longest wavelength, 1064 nm. We 29 infer the cause of this difference to be a greater fraction of very large particles due to proximity 30 to the source region; we believe that the largest particles have settled out of the observed Saharan 31 layers but not the locally produced North American dust plumes in this case and a prior HSRL-1 32 case. Our third case study is of an elevated, transported smoke layer and has spectral 33 depolarization ratio decreasing monotonically with wavelength. Again we infer that the 34 difference in spectral dependence is due to the size of the non-spherical particles, and specifically, 35 that the depolarization is probably due to smoke aerosols and may be explained by soot 36 aggregates. 37 Microphysical retrievals (Müller et al., 2014) were not available for these HSRL-2 measurement 38 cases, because the current state of these retrievals is limited to spherical particles. However, as 39 suggested by Gasteiger and Freudenthaler (2014) for dust and ash, these observations suggest the 40 possibility that the particle depolarization ratio measurements may aid in retrievals of particle 1 size of non-spherical dust and smoke particles in the future. 2 More immediately, since the upcoming EarthCARE satellite mission will include a lidar 3 instrument that measures particle depolarization ratio and lidar ratio at 355 nm only, it is valuable 4 to have measurements of the spectral dependence of depolarization ratio for depolarizing aerosol 5 types. These data will help to build the basis for comparing observations from EarthCARE to 6 existing measurements at 532 nm from the CALIPSO satellite. Studying such correspondence is 7 particularly motivated by the desire to identify different aerosol types observed by the 8 EarthCARE satellite. Particle depolarization ratio is hoped to be particularly useful for However, as illustrated by the case studies presented here, there is not a single consistent spectral 12 dependence of particle depolarization ratio. On the positive side (from the perspective of 13 corresponding CALIPSO and EarthCARE measurements), for aerosols dominated by dust the 355 14 nm and 532 nm particle depolarization ratios appear to be fairly consistent even for different 15 particle sizes and may be relatively easily converted. Variation in the 532 nm and 355 nm particle 16 depolarization ratio for dusty aerosols has been primarily linked to the fraction of dust particles may not be done with 355 nm measurements. However, in the case of dust-dominated aerosol, 20 the 355 nm signal consistently is significantly both smaller and more difficult to measure 21 accurately than the 532 nm signal, and so the signature of dust may be harder to detect from space 22 at 355 nm than at 532 nm for dilute dust mixtures. 23 On the other hand, the third case study presented here showed that smoke particle depolarization 24 ratio can be significantly larger at 355 nm than at 532 nm, and in fact the particle depolarization 25 ratio at 355 nm for this smoke case was quite comparable to the dust-dominated cases. If this is 26 not an isolated case, and this signature proves typical for some subsets of smoke aerosol in 27 particular conditions, the EarthCARE satellite may observe significant particle depolarization in 28 some types of smoke as well as in dust-dominated aerosol. If this is the case, global observations 29 of smoke depolarization will present an exciting opportunity for improving our understanding 30 of the optical properties of smoke and how they change with age and processing; however, it will 31 also present a challenge. That is, a significant particle depolarization ratio signature at the single 32 wavelength of 532 nm has been sufficient for distinguishing dust-dominated aerosol from smoke 33 aerosol, but at 355 nm this signature by itself is more ambiguous, if the smoke case presented here 34 is not an isolated case. . EarthCARE will also measure lidar ratio at 355 nm; this is related to 35 absorption but has significant variability for smoke (Groß et al., 2014). EarthCARE will not have 36 backscatter or extinction measurements at a second wavelength to give an indicator of particle 37 size. Therefore, for any cases where particle depolarization ratio is ambiguous, smoke and dust 38 may not be easily separable. 39

Appendix: Systematic Uncertainties 40
In Section 2.b. we provided systematic uncertainties in the linear volume depolarization ratio of 1 the larger of 4.7% (relative) or 0.001 (absolute) in the 355 nm channel, the larger of 5% (relative) 2 or 0.007 (absolute) in the 532 nm channel, and the larger of 2.6% (relative)or 0.007 (absolute) in 3 the 1064 nm channel. For R (total aerosol scattering ratio) we estimate the systematic uncertainty 4 to be 4.1% for the 532 nm channel, 5% for the 355 channel, and 20% for the 1064 nm channels. The 5 systematic uncertainties are estimated conservatively as confidence limits, such that we expect a 6 high probability that the true systematic error is within this uncertainty. Here in the Appendix, 7 we discuss the error sources and estimates of the uncertainties in more detail. 8 For the linear volume depolarization ratio, potential sources of systematic error include an error 9 in the polarization gain ratio calibration or cross-talk between the co-polarized and cross-10 polarized signals. The polarization gain ratio calibration generally occurs once or twice per flight 11 as described above in Section 2.a. Since gain ratios can potentially change during a flight, due to 12 temperature changes for example, our best estimate of uncertainty in the gain ratio during a flight 13 is obtained by examining the change in the gain ratio between successive calibrations in the same 14 flight. Conservatively choosing the mean difference plus two standard deviations (calculated 15 for all flights with at least two calibrations per flight in the most recent field campaign) as a 16 realistic limit on the probable polarization gain ratio systematic error yields 4.7% uncertainty for 17 the 355 nm channel, 5.0% for the 532 nm channel, and 2.6% for the 1064 nm channel. The relative 18 systematic uncertainty from the polarization gain ratio propagates directly to the volume 19 depolarization ratio, since the volume depolarization ratio is linearly related to the polarization 20 gain ratio. 21 Residual cross-talk is known to occur in polarization lidars, and must be carefully characterized 22 and eliminated as much as possible. A well-known potential source of cross talk occurs in the 23 reflected channel from a polarization beam splitter. Therefore, this system has been designed 24 with extra polarization beam splitters to eliminate that potential concern, as described in Section 25 2.a and illustrated in Figure 2. Clear-air studies have found a small residual cross-talk, which 26 appears as a value of the "clear air" volume depolarization ratio that exceeds the theoretical 27 (molecular only) value. As described in Section 2.a., the narrow bandwidths in the system 28 completely eliminate the rotational Raman scattering sidebands, and so the molecular 29 depolarization ratio is temperature independent and is calculated to be 0.0036 using N2 and O2 30 molecules (ignoring a negligible wavelength dependence due to non-linear molecules like CO2) 31 (Behrendt and Nakamura, 2002 the 532 nm channel, which we attribute to a small remaining ellipticity in the optics or stress 35 birefringence in the aircraft window. Cross talk due to ellipticity in the transmission system can 36 be modeled, as follows. 37 We start with the polarization Stokes vector (Born and Wolf, 1999) 38 where the angles  and  represent the ellipticity angle and polarization offset angle, plus the 1 Mueller matrix for a partially depolarizing backward scattering process (Mishchenko and  2 Hovenier, 1995; Gimmestad, 2008 Assuming there is apolarization offset angle (rotation) or ellipticity in the transmission, we derive 4 the correction to the measured depolarization ratio to be 5 The subscript 'meas' indicates the measured depolarization ratio and 'corr' represents the 7 corrected depolarization ratio, assuming the measurement to be affected by cross-talk, caused by 8 ellipticity or an angle offset, or both. Eqs (6) and (7) make no distinction between the ellipticity 9 and polarization offset angles  and . Therefore, we can model cross talk due to either source 10 using the same correction, although noting that an offset angle would additionally affect the 11 polarization gain ratio, treated separately. Equation (6) represents a fairly constant shift in the 12 volume depolarization ratio approximately equal to the offset between the measured clear air 13 value and the molecular-only depolarization ratio. An ellipticity angle of 5.8 (=0.980) would 14 explain the error in the depolarization ratio at 532 nm where the error is largest. A partial 15 correction for the cross-talk was implemented in the archived HSRL-2 data (A full correction as 16 in Eq (6) will be included in the next version of processed HSRL-2 data). Taking the partial 17 correction into account, we include a component of 0.007 (absolute) due to cross-talk in the 18 estimated volume depolarization ratio error for the 532 nm and 1064 nm channels and 0.001 19 (absolute) for the 355 nm channel. 20 We believe that the polarization angle error is much smaller than the inferred angle of 5.8.The 21 angle calibration procedure has been carefully designed and used successfully on both the HSRL- during the latest field mission), which is a good indicator of the systematic uncertainty in the 30 polarization angle for measurements between calibrations. Since the polarization angle 31 calibration error is much smaller than the inferred ellipticity (0.4 compared to 6), we do not 1 include polarization angle calibration directly in the systematic uncertainty budget. 2 Note that not only the volume depolarization ratio measurement itself but also the polarization 3 gain ratio calibration depend on the correct alignment of the calibration waveplates in Figure 1. 4 The polarization gain ratio assessment depends on a polarization alignment of 45 during 5 calibration. This effect on the measured gain will be reflected in the error of the gain ratio, and 6 so is already included in the polarization gain ratio systematic uncertainty discussed above. 7 The calculated particle depolarization ratio, a, is additionally affected by any errors in the total 8 aerosol scattering ratio, R, in Eq (2). For 532 nm, the only significant potential systematic error in 9 R is an error in the gain ratio between the aerosol and molecular channels. The uncertainty of the 10 aerosol-to-molecular gain ratio was assessed in a similar manner to the offset angle and 11 polarization gain ratios given above, by examining the change in the gain ratio on flights where 12 multiple aerosol-to-molecular gain calibrations occurred during a flight. The uncertainty in the 13 532 nm aerosol-to-molecular gain ratio is estimated to be 4.1%. A systematic uncertainty of 4.1% 14 in the aerosol-to-molecular gain ratio propagates directly to a 4.1% uncertainty in R for the 532 15 nm channel, since the aerosol-to-molecular gain ratio and the total aerosol scattering ratio are 16 linearly related. 17 The 355 nm and 1064 nm channels are somewhat more complicated, because it is not possible to 18 calibrate them directly in the same way as 532 nm. The iodine filter for the 532 nm HSRL channel 19 allows for essentially complete separation of the aerosol signal from the total (aerosol plus 20 molecular) signal, but this is not the case for the interferometer used at 355 nm, and the 1064 nm 21 channel has only one total channel with no separation. So for these channels, the calibration is 22 transferred from 532 nm in a cloud-free region in the free troposphere, as described by Hair et al. 23 (2008). In the calibration transfer region, we do not assume that there is no aerosol, but do look 24 for regions where the aerosol backscatter ratio is small and can be inferred from the value at 532 25 nm assuming a constant backscatter Ångström exponent. By using a range of reasonable 26 backscatter Ångström exponents, we conservatively estimate an uncertainty of 3% in total aerosol 27 scattering ratio for the 355 nm channel. The 1064 nm aerosol backscatter ratio is also affected by 28 the assumption of the lidar ratio to use for separating the aerosol and molecular part; this 29 sensitivity is relatively small for backscatter at 1064 nm, compared to shorter wavelengths or 30 compared to the sensitivity of extinction. Taking these sources into account, we conservatively 31 use 20% as the uncertainty in total aerosol scattering ratio, R, at 1064 nm. 32 For the 355 nm channel, the system implements an interferometer to spectrally separate the 33 aerosol and molecular scattering components. The ratio of the aerosol signal in the aerosol-34 dominated channel to the aerosol signal in the molecular-dominated channel is referred to as the 35 contrast ratio, which needs to be determined to accurately derive the total aerosol scattering ratio. 36 For the HSRL-2 system, fairly high contrast ratios of 15-20 are routinely achieved. Our estimate 37 of the error in the contrast ratio definition is usually a few percent but can be up to 20%. A 20% 38 error in the contrast ratio for the smoke case presented here would produce an error in the total 39 aerosol scattering ratio of less than 4%. Adding the contrast ratio uncertainty, 4%, and the 40 calibration transfer uncertainty, 3%, in quadrature yields an uncertainty of 5% for the 355 nm total 41 aerosol scattering ratio. 42 The uncertainties given above are intended to be an upper bound on the probable systematic 1 errors. The systematic errors on the three quantities, mol, tot, and R, are independent and, since 2 their actual values within these uncertainty estimates are unknown, they should be treated 3 statistically. We therefore combine the three sources of systematic uncertainty in quadrature to 4 assess the systematic uncertainty in the particle depolarization ratio, a. The propagation is 5 described by the following equation: 6 (   Here, the  symbol indicates the systematic uncertainty associated with the various quantities 7 and the propagation factors Fx are defined like this: 8 The partial derivatives are calculated easily from Eq. (2) which relates the particle depolarization 9 ratio to the factors R,  ,and  . From Eq. (8), the propagation factors, Fx, are the factors by 10 which the relative uncertainty in the particle depolarization ratio is magnified with respect to the 11 relative uncertainty in the component variables. 12 These factors vary with total aerosol scattering ratio and volume depolarization ratio but do not 13 depend on the systematic uncertainties. To illustrate the behavior of the particle depolarization 14 ratio systematic uncertainty, Table 2 gives the value of particle depolarization ratio and its 15 propagated systematic uncertainty (as a percent error) for benchmark values of the total aerosol 16 scattering ratio and the volume and molecular depolarization ratios, plus their estimated 17 systematic uncertainties. It also gives the propagation factors, Fx. From Table 2, it is clear that 18 the propagation factor for the uncertainty in the molecular depolarization ratio is always small, 19 the propagation factor for the volume depolarization ratio uncertainty is typically 1-2, and the 20 propagation factor for uncertainty in the total aerosol scattering ratio, FR, varies significantly with 21 the total aerosol scattering ratio. FR is comparable to Ftot except when the total aerosol scattering 22 ratio is fairly small; in the case of small scattering, it is significantly larger. 23  Table 1. Measured properties for specific dust and smoke samples. To obtain these values, samples were taken at 2 specific times and altitudes comprising 400-4500 distinct measurement points. For the dust cases, values were 3 chosen near the peak value of the 532 nm particle depolarization ratio, where it can be inferred that the aerosol is 4 nearly pure dust. The values are reported as meanstandard deviation for the sample. Systematic uncertainties for 5 particle depolarization ratio from HSRL-2 are indicated in parentheses. 6 Layer AOD (532 nm) Linear particle depolarization ratio (1064 nm) Linear particle depolarization ratio (532 nm)  Table 2. Illustrates the systematic uncertainty in linear particle depolarization ratio propagated from the systematic 1 uncertainties in total aerosol scattering ratio, linear volume depolarization ratio, and linear molecular 2 depolarization ratio. Benchmark values of R (total aerosol scattering ratio), tot (the volume depolarization ratio) 3 and mol (the molecular depolarization ratio) and typical systematic uncertainties are given in the first three columns.

4
Columns 4-6 give the propagation factors, as described in the text. Column 7 gives the resulting particle 5 depolarization ratio and systematic uncertainty for each benchmark set. Note: percentages given in this    fraction. Dots indicate five realizations with randomly generated geometries, per aggregate 20 volume-equivalent particle radius, and the colored lines connect the averages of the five for 21 each wavelength. The legend shows the aggregate volume-equivalent particle radii at which the 22 calculation was performed. The thick black line indicates the particle depolarization ratios 23 measured by airborne HSRL-2 within a smoke plume observed on 17 July 2014 at 355, 532, and 24 1064 nm. 25   Figure 5. Line plots illustrating the volume and aerosol linear depolarization ratio profile for the HSRL-2 measurements at 17.2 UT (17:12 UT) on 13 July 2014. The volume depolarization ratio is shown as a thin black line. The error bars on the volume depolarization ratio represent random error (most are small and mostly obscured except 1064 nm). The particle depolarization ratio is shown as a thick colored line. Colored error bars indicate random error (most are small enough to be obscured by the line) while gray error bars indicate systematic uncertainty, estimated as described in the text. Systematic uncertaintyis not shown for the volume depolarization ratio but see text for estimate. The vertical resolution of these measurements is 30 m and the horizontal resolution is 10 s for all wavelengths.    , for 20% LAC volume fraction. Dots indicate five realizations with randomly generated geometries, per aggregate volume-equivalent particle radius, and the colored lines connect the averages of the five for each wavelength. The legend shows the aggregate volume-equivalent particle radii at which the calculation was performed. The thick black line indicates the particle depolarization ratios measured by airborne HSRL-2 within a smoke plume observed on 17 July 2014 at 355, 532, and 1064 nm. Error bars represent systematic uncertainty in HSRL-2 particle depolarization ratio, estimated as described in the text.