IS NEAR-SPHERICAL SHAPE “THE NEW BLACK” FOR SMOKE?

We present smoke lidar measurements from the Canadian fires of 2017. The advected smoke layers over Europe are detected at both tropospheric and stratospheric heights, with the latter presenting non-typical values of the Particle Linear Depolarization Ratio (PLDR) with strong wavelength dependence from the UV to the Near-IR. Specifically, the PLDR values are of the order of 22, 18 and 4% at 355, 532 and 1064 nm respectively. In an attempt to interpret these results, we apply the hypothesis that smoke particles have near-spherical and/or more complicated shapes. Scattering calculations with the T-matrix code support other findings in the literature ([1]- [2]), showing that the near-spherical shape (or closely similar shapes as in [2]), is the only shape that has been shown to reproduce the observed PLDR and Lidar Ratio (LR) values of the stratospheric smoke particles at the three measurement wavelengths.


INTRODUCTION
Recent studies show that the PLDR of smoke presents large variability ([3] - [7]).Since the PLDR is indicative of particle shape, this variability may be attributed to (a) smoke aerosol mixing with other aerosol types, (b) particles' aging through various atmospheric processes, (c) particle water uptake at different relative humidity conditions.These processes alter the smoke particle shape and composition.Indicatively, the typical PLDR values of aged and fresh tropospheric smoke varies from 2 to 10% at 532 and 355 nm ([3] - [5]), while this value can be larger when smoke is mixed with high depolarizing aerosol types (i.e.dust) ([6] - [7]).Lately, observational evidence of PLDR values that exceed the typical range has been reported.Burton et al. (2015) [8], showed air-borne HSRL measurements of smoke at 8 km altitude, originating from Canadian fires, revealing PLDR values of the order of 20, 9 and 1.8 % at 355, 532 and 1064 nm, respectively.These are also the first reported measurements of smoke PLDR spectral dependence.Other studies validate these high PLDR values for stratospheric smoke particles at 532 nm ([9] - [11]).In the spotlight of the large-scale Canadian fires of 2017, this unique feature of high values of PLDR with unexpected high spectral dependence for smoke particles raises once again an interesting discussion.Here, we aim to seek for an explanation on the variation of PLDR and LR from UV to Near-IR under the hypothesis that the smoke particles have a near-spherical shape.Our hypothesis and presented results are a continuation effort on previous work reported in the literature.Specifically, in Mishchenko et al. (2016) [1], the lidar measurements presented in [8] were reproduced considering near-spherical shapes for the smoke particles with an axial ratio 0.9 to 1.2.In Bi et al. 2018 [12], it was showed that the PLDR of near-spherical particles with refractive index of 1.3-1.7 + i0.001-i0.01,can take values up to 100%, depending also on the particle size parameter.However, the results of these studies are limited in terms of reproducing only the PLDR wavelength dependence.Here we make a step further, reproducing also the wavelength dependence of the LR considering near-spherical particles.Our methodology is summarized in Section 2, our results in Section 3 and we conclude in Section 4.

METHODOLOGY 2.1 The BERTHA lidar system
The lidar measurements presented in this study were conducted at the Leibniz Institute of Tropospheric Research (TROPOS), with BERTHA multi-wavelength lidar system [13].The measurements have a 7.5 m vertical resolution, while for the specific case study presented here temporal resolution was 10 sec.The capability of BERTHA to provide independent measurements of the particle extinction coefficient and PLDR at three wavelengths constitutes this lidar system unique within the EARLINET network [14].The BERTHA measurements used herein are not simultaneous for the particle extinction coefficient and PLDR at 1064 nm, since the 1064 crosspolarized channel had to be exchanged with the 1058 nm rotational Raman channel in order to measure the particle extinction at 1064 nm [15].The overall duration of this procedure was 20-30 minutes [16].This shortcoming is not expected to affect the study, since the scene analysed is very stable in terms of aerosol layering, especially in the stratosphere (Figure 1).

Scattering calculations
In order to reproduce the unique values and spectral dependence of the PLDR and LR of the stratospheric smoke from the Canadian fires, we used light scattering calculations generated with the T-matrix code 18].The T-matrix code is based on the exact numerical solution of Maxwell's equations.For the calculations we considered a wide range of refractive indices and effective radii typical for aged smoke, employing near-spherical particles but also soot fractal aggregates.

Figure 1 presents the observations from Leipzig, on 22
August 2017, with the 3+3+3 polarization/Raman lidar BERTHA.As it can be seen from the Range Corrected Signal (RCS) at 1064 nm, the stratospheric smoke layer lies between 15 and 16 km, while there is also a smoke layer in the troposphere at 5-6 km.For deriving the smoke optical properties, lidar signals were averaged over a time window of 2.5 hours (20:45 -23:15 UTC) to achieve satisfying signal to noise ratio (SNR), even at high altitudes.For deriving the PLDR at 1064 nm a time window of 40 min was used (23:50 -00:30 UTC). Figure 2 shows the mean PLDR and LR of the stratospheric smoke layers.The LR values are found to be typical for aged smoke particles (40 ± 16) sr at 355 nm, (66 ± 12) sr at 532 nm, which are consistent with what is reported in the literature (i.e.[3] - [7], [19] - [20]), and (92 ± 27) sr at 1064 nm.No significant difference has been detected for the LR values between the tropospheric and stratospheric layers (for the first one LR is not presented here), while this does not hold true for the PLDR values.In the case of stratospheric smoke the PLDR values are 22.5, 18.5 and 4% at 355, 532 and 1064 nm, respectively, while in the troposphere they are no higher than 3% at all wavelenghts.
Building on the previous studies of [1] and [12] we used near-spherical smoke particles to reproduce the measured PLDR and LR at 355, 532 and 1064 nm in the stratosphere.T-matrix simulations were conducted for a range of refractive index values: m = 1.4 -1.65 (with step of 0.05) + i0.005 -0.04 (with step of 0.005), effective radius: reff = 0.25 -0.45 μm (with step of 0.05) and axial ratio: a/b = 0.7 -1.2 (with step of 0.05).Figure 3 presents the best fit of the measured PLDR and LR at 355, 532 and 1064 nm, calculated for near-spherical smoke particles with a/b = 1.11, m = 1.42 + i0.02 and reff = 0.55 μm (Figure 4).Table 1 summarizes the results of our simulations for near-spherical particles, in comparison with the Leipzig observations.The T-matrix-calculated PLDR values were found to be 20.8, 16.6 and 1.15 % at 355, 532 and 1064 nm respectively, while the LR values were 47.4, 59.5 and 131 sr at 355, 532 and 1064 nm.A slight deviation from the measured mean values is found at all wavelengths, with maximum for the LR value at 1064 nm.However, it has to be noted here that the retrieval of the LR at 1064 nm from BERTHA measurements had an uncertainty of the order of 50% [16].This uncertainty comes from the fact that the 1058 nm signal Raman returns were too weak from the stratospheric height of 15-16 km to derive the particle extinction coefficient at 1064 nm.To compensate this, a least-squares linear regression method has applied with a vertical smoothing window of 2500 m in the stratosphere.This treatment yielded to LR values in the range of 65 to 119 sr at 1064 nm.The methodology is described in detail in [16].In an attempt to more-precisely reproduce the observed measurements, we also performed scattering calculations with the Superposition T-Matrix Method (STMM) [21] for highly irregular smoke particles with a simple chain-like fractal morphology (Figure 5).Specifically, we considered a soot fractal aggregate with a fractal geometry provided by a diffusionlimited cluster-aggregation (DLCA) model [22].
Here, the complex refractive index is 1.42 + i0.02 and the fractal morphology of the particle is characterized by the fractal pre-factor   = 1.3 , the fractal dimension   = 1.8 , the number of monomers  = 90 , and the volume-equivalent radius   = 0.55 µ.The calculated LPDR of the fractal soot aggregate at 355, 532 and 1064 nm are presented in Table 2.Although the use of this simple fractal geometry provides significantly large PLDR, it does not reproduce the measured values of both PLDR and LR, as it can also be seen in Fig. 9 and 10 in [2].In order to reproduce the measurements for aged smoke particles the fractals need to be coated by other material, producing a shape that closely resembles the near-spherical shape, as shapes for Type-B, size 11, Vr = 20, found in [2], Fig. 4.

CONCLUSIONS
Near-spherical assumption explains at a large extent the exceptional PLDR values observed at stratospheric smoke layers over Leipzig, Germany, originated by Canadian wildfires.This hypothesis also reproduce the high PLDR spectral dependence found, when the aspect ratio is very close to unity for typical refractive index, and size of smoke particles.The assumption of soot particles with more complicated morphology used here, is not reproducing the observations.The next step is to extend our analysis of monodispersed nearspherical smoke particles, to the retrieval of the microphysical properties of pollydispersed nearspherical smoke particles in the stratosphere.

Fig. 5
Fig. 5 Model morphology of soot fractal aggregate used in STMM simulations.