Optics of water microdroplets with soot inclusions: Exact versus approximate results

We use the recently generalized version of the multi-sphere superposition T-matrix method (STMM) to compute the scattering and absorption properties of microscopic water droplets contaminated by black carbon. The soot material is assumed to be randomly distributed throughout the droplet interior in the form of numerous small spherical inclusions. Our numerically-exact STMM results are compared with approximate ones obtained using the Maxwell-Garnett effective-medium approximation (MGA) and the Monte Carlo ray-tracing approximation (MCRTA). We show that the popular MGA can be used to calculate the droplet optical cross sections, single-scattering albedo, and asymmetry parameter provided that the soot inclusions are quasi-uniformly distributed throughout the droplet interior, but can fail in computations of the elements of the scattering matrix depending on the volume fraction of soot inclusions. The integral radiative characteristics computed with the MCRTA can deviate more significantly from their exact STMM counterparts, while accurate MCRTA computations of the phase function require droplet size parameters substantially exceeding 60.

[1]  F.Michael Kahnert,et al.  Numerical methods in electromagnetic scattering theory , 2003 .

[2]  P. Chylek,et al.  Black carbon and absorption of solar radiation by clouds , 1996 .

[3]  M. Kajino,et al.  Mixing state of regionally transported soot particles and the coating effect on their size and shape at a mountain site in Japan , 2014 .

[4]  M. Mishchenko.  Electromagnetic Scattering by Particles and Particle Groups: An Introduction , 2014 .

[5]  M. Mishchenko,et al.  Asymmetry parameters of the phase function for isolated and densely packed spherical particles with multiple internal inclusions in the geometric optics limit , 1997 .

[6]  A. Lacis,et al.  Multiple Scattering of Light by Particles: Radiative Transfer and Coherent Backscattering , 2006 .

[7]  P. Chylek,et al.  Effective Medium approximations for Heterogeneous Particles , 2000 .

[8]  Radiative forcing and climate response due to the presence of black carbon in cloud droplets , 2013 .

[9]  J. Kong,et al.  Theory of microwave remote sensing , 1985 .

[10]  Andrew A. Lacis,et al.  Scattering, Absorption, and Emission of Light by Small Particles , 2002 .

[11]  R. Hitzenberger,et al.  CCN activation of pure and coated carbon black particles. , 2006, Environmental science & technology.

[12]  Adrian Doicu,et al.  Light Scattering by Systems of Particles: Null-Field Method with Discrete Sources: Theory and Programs , 2014 .

[13]  A. Macke,et al.  Scattering of light by polyhedral ice crystals. , 1993, Applied optics.

[14]  Brian Cairns,et al.  First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media. , 2016, Physics reports.

[15]  Michael Kahnert,et al.  Modelling radiometric properties of inhomogeneous mineral dust particles: Applicability and limitations of effective medium theories , 2015 .

[16]  Patrick Minnis,et al.  Effect of the inhomogeneity of ice crystals on retrieving ice cloud optical thickness and effective particle size , 2009 .

[17]  P. Palmer,et al.  Size-dependent wet removal of black carbon in Canadian biomass burning plumes , 2014 .

[18]  Andrew A. Lacis,et al.  Scattering and radiative properties of semi-external versus external mixtures of different aerosol types , 2004 .

[19]  Rosalba Saija,et al.  Scattering from Model Nonspherical Particles: Theory and Applications to Environmental Physics , 2003 .

[20]  N. Takegawa,et al.  Critical condensed mass for activation of black carbon as cloud condensation nuclei , 2009 .

[21]  A. Lacis,et al.  The effect of black carbon on scattering and absorption of solar radiation by cloud droplets , 2002 .

[22]  A. Macke,et al.  Polarized light scattering by inhomogeneous hexagonal monocrystals: Validation with ADEOS-POLDER measurements , 2001 .

[23]  T. Bond,et al.  Light Absorption by Carbonaceous Particles: An Investigative Review , 2006 .

[24]  Thomas Wriedt,et al.  Comprehensive Thematic T-matrix Reference Database: a 2013-2014 Update , 2014 .

[25]  D. Mackowski,et al.  A general superposition solution for electromagnetic scattering by multiple spherical domains of optically active media , 2014 .

[26]  S. Warren,et al.  Light-Absorbing Material Extracted From Cloud Droplets and Its Effect on Cloud Albedo , 1989 .

[27]  A. Macke,et al.  Single Scattering Properties of Atmospheric Ice Crystals , 1996 .

[28]  M. Mishchenko,et al.  COHERENT BACKSCATTERING VERIFIED NUMERICALLY FOR A FINITE VOLUME OF SPHERICAL PARTICLES , 2012 .

[29]  P. Forster,et al.  Global cloud condensation nuclei influenced by carbonaceous combustion aerosol , 2011 .

[30]  Yangang Liu,et al.  Relationship of refractive index to mass density and self-consistency of mixing rules for multicomponent mixtures like ambient aerosols , 2008 .

[31]  J. Hudson,et al.  Maritime-Continental Drizzle Contrasts in Small Cumuli , 2001 .

[32]  J. Hovenier,et al.  Overview of Scattering by Nonspherical Particles , 2000 .

[33]  M. Chin,et al.  Evaluation of black carbon estimations in global aerosol models , 2009 .

[34]  Michael I. Mishchenko,et al.  Applicability of the effective-medium approximation to heterogeneous aerosol particles , 2016 .

[35]  A. Bertram,et al.  Size-resolved observations of refractory black carbon particles in cloud droplets at a marine boundary layer site , 2014 .

[36]  M. Mishchenko,et al.  The influence of inclusions on light scattering by large ice particles , 1996 .

[37]  P. Chylek,et al.  Parameterization of cloud optical properties for semidirect radiative forcing , 2011 .

[38]  A. Macke.  Monte Carlo calculations of light scattering by large particles with multiple internal inclusions , 2000 .

[39]  A. Kasper-Giebl,et al.  Black carbon (BC) in alpine aerosols and cloud water—concentrations and scavenging efficiencies , 2001 .

[40]  P. Chylek,et al.  Black carbon: Atmospheric concentrations and cloud water content measurements over southern Nova Scotia , 1996 .

[41]  M. Mishchenko,et al.  T-matrix theory of electromagnetic scattering by particles and its applications: a comprehensive reference database , 2004 .

[42]  J. Hansen,et al.  Light scattering in planetary atmospheres , 1974 .

[43]  Adrian Doicu,et al.  Acoustic and Electromagnetic Scattering Analysis Using Discrete Sources , 2000 .

[44]  P. Waterman,et al.  SYMMETRY, UNITARITY, AND GEOMETRY IN ELECTROMAGNETIC SCATTERING. , 1971 .

[45]  E. Clothiaux,et al.  Cloud Droplet Size Distributions in Low-Level Stratiform Clouds , 2000 .

[46]  Larry D. Travis,et al.  Light scattering by nonspherical particles : theory, measurements, and applications , 1998 .

[47]  Michael Kahnert,et al.  Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review , 2016 .

[48]  Ping Yang,et al.  Inhomogeneity structure and the applicability of effective medium approximations in calculating light scattering by inhomogeneous particles , 2014 .

[49]  Brian Cairns,et al.  Optics of water cloud droplets mixed with black-carbon aerosols. , 2014, Optics letters.

[50]  Nadezhda T. Zakharova,et al.  Direct demonstration of the concept of unrestricted effective-medium approximation. , 2014, Optics letters.