Abstract

We use the recently extended superposition T-matrix method to calculate scattering and absorption properties of micrometer-sized water droplets contaminated by black carbon. Our numerically exact results reveal that, depending on the mode of soot–water mixing, the soot specific absorption can vary by a factor exceeding 6.5. The specific absorption is maximized when the soot material is quasi-uniformly distributed throughout the droplet interior in the form of numerous small monomers. The range of mixing scenarios captured by our computations implies a wide range of remote sensing and radiation budget implications of the presence of black carbon in liquid-water clouds. We show that the popular Maxwell-Garnett effective-medium approximation can be used to calculate the optical cross sections, single-scattering albedo, and asymmetry parameter for the quasi-uniform mixing scenario, but is likely to fail in application to other mixing scenarios and in computations of the elements of the scattering matrix.

© 2014 Optical Society of America

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  1. P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
    [CrossRef]
  2. J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
    [CrossRef]
  3. Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).
  4. M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.
  5. F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
    [CrossRef]
  6. P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.
  7. M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
    [CrossRef]
  8. L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
    [CrossRef]
  9. D. W. Mackowski and M. I. Mishchenko, J. Opt. Soc. Am. A 13, 2266 (1996).
    [CrossRef]
  10. D. W. Mackowski and M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 112, 2182 (2011).
    [CrossRef]
  11. D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
    [CrossRef]
  12. M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
    [CrossRef]
  13. C. M. Sorensen, Aerosol Sci. Technol. 35, 648 (2001).
    [CrossRef]
  14. T. C. Bond and R. W. Bergstrom, Aerosol Sci. Technol. 40, 27 (2006).
    [CrossRef]
  15. K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
    [CrossRef]
  16. M. Kahnert, Aerosol Sci. Technol. 44, 453 (2010).
    [CrossRef]
  17. E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).
  18. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).
  19. M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
    [CrossRef]
  20. M. I. Mishchenko, L. Liu, and D. W. Mackowski, Opt. Lett. 39, 1701 (2014).
    [CrossRef]
  21. M. Kahnert, T. Nousiainen, and H. Lindqvist, Opt. Express 21, 7974 (2013).
    [CrossRef]

2014

D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, Opt. Lett. 39, 1701 (2014).
[CrossRef]

2013

M. Kahnert, T. Nousiainen, and H. Lindqvist, Opt. Express 21, 7974 (2013).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
[CrossRef]

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

2011

J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 112, 2182 (2011).
[CrossRef]

2010

K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

M. Kahnert, Aerosol Sci. Technol. 44, 453 (2010).
[CrossRef]

2006

T. C. Bond and R. W. Bergstrom, Aerosol Sci. Technol. 40, 27 (2006).
[CrossRef]

2004

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

2003

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

2002

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

2001

C. M. Sorensen, Aerosol Sci. Technol. 35, 648 (2001).
[CrossRef]

1997

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

1996

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Opt. Soc. Am. A 13, 2266 (1996).
[CrossRef]

Adachi, K.

K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

Bergstrom, R. W.

T. C. Bond and R. W. Bergstrom, Aerosol Sci. Technol. 40, 27 (2006).
[CrossRef]

Bond, T. C.

T. C. Bond and R. W. Bergstrom, Aerosol Sci. Technol. 40, 27 (2006).
[CrossRef]

Buseck, P. R.

K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

Chung, S. H.

K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

Chýlek, P.

J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
[CrossRef]

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

Dobbie, J. S.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

Geldart, D. J. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

Hovenier, J. W.

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.

Jing, X.

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

Kahnert, F. M.

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

Kahnert, M.

Klett, J. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Lesins, G. B.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Li, J.

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
[CrossRef]

Lindqvist, H.

Liu, L.

M. I. Mishchenko, L. Liu, and D. W. Mackowski, Opt. Lett. 39, 1701 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
[CrossRef]

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

Lu, P.

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

Macke, A.

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

Mackowski, D. W.

D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, Opt. Lett. 39, 1701 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 112, 2182 (2011).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Opt. Soc. Am. A 13, 2266 (1996).
[CrossRef]

Menon, S.

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

Mishchenko, M. I.

M. I. Mishchenko, L. Liu, and D. W. Mackowski, Opt. Lett. 39, 1701 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 112, 2182 (2011).
[CrossRef]

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

D. W. Mackowski and M. I. Mishchenko, J. Opt. Soc. Am. A 13, 2266 (1996).
[CrossRef]

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

Mlawer, E.

J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
[CrossRef]

Ngo, D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Nousiainen, T.

Pinnick, R. G.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Sorensen, C. M.

C. M. Sorensen, Aerosol Sci. Technol. 35, 648 (2001).
[CrossRef]

Travis, L. D.

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.

Tso, H. C. W.

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

Videen, G.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

Wang, Z.

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

Wiscombe, W. J.

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.

Wong, J. G. D.

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

Yanovitskij, E. G.

E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).

Zhang, H.

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

Aerosol Sci. Technol.

C. M. Sorensen, Aerosol Sci. Technol. 35, 648 (2001).
[CrossRef]

T. C. Bond and R. W. Bergstrom, Aerosol Sci. Technol. 40, 27 (2006).
[CrossRef]

M. Kahnert, Aerosol Sci. Technol. 44, 453 (2010).
[CrossRef]

J. Geophys. Res.

K. Adachi, S. H. Chung, and P. R. Buseck, J. Geophys. Res. 115, D15206 (2010).
[CrossRef]

P. Chýlek, G. B. Lesins, G. Videen, J. G. D. Wong, R. G. Pinnick, D. Ngo, and J. D. Klett, J. Geophys. Res. 101, 23365 (1996).
[CrossRef]

J. Li, E. Mlawer, and P. Chýlek, J. Geophys. Res. 116, D23212 (2011).
[CrossRef]

Z. Wang, H. Zhang, J. Li, X. Jing, and P. Lu, J. Geophys. Res. 118, 3662 (2013).

J. Opt. Soc. Am. A

J. Quant. Spectrosc. Radiat. Transfer

D. W. Mackowski and M. I. Mishchenko, J. Quant. Spectrosc. Radiat. Transfer 112, 2182 (2011).
[CrossRef]

D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 133, 264 (2014).
[CrossRef]

M. I. Mishchenko, L. Liu, L. D. Travis, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 88, 139 (2004).
[CrossRef]

F. M. Kahnert, J. Quant. Spectrosc. Radiat. Transfer 79–80, 775 (2003).
[CrossRef]

M. I. Mishchenko and A. Macke, J. Quant. Spectrosc. Radiat. Transfer 57, 767 (1997).
[CrossRef]

L. Liu, M. I. Mishchenko, S. Menon, A. Macke, and A. A. Lacis, J. Quant. Spectrosc. Radiat. Transfer 74, 195 (2002).
[CrossRef]

M. I. Mishchenko, L. Liu, and D. W. Mackowski, J. Quant. Spectrosc. Radiat. Transfer 123, 135 (2013).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. Chýlek, G. Videen, D. J. W. Geldart, J. S. Dobbie, and H. C. W. Tso, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 273–308.

M. I. Mishchenko, J. W. Hovenier, W. J. Wiscombe, and L. D. Travis, in Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, eds. (Academic, 2000), pp. 29–60.

E. G. Yanovitskij, Light Scattering in Inhomogeneous Atmospheres (Springer, 1997).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge University, 2002).

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Figures (3)

Fig. 1.
Fig. 1.

Models of soot-contaminated water droplets.

Fig. 2.
Fig. 2.

Absorption cross section versus 2πd/λ for Models A–C.

Fig. 3.
Fig. 3.

(a) The ratio a2(Θ)/a1(Θ) for Models A, C, D, G, and J. The elements of the normalized scattering matrix are averaged over orientations and, for Models A and C, over the applicable ranges of d. (b), (c) STMM and MGA results for a water droplet filled quasi-uniformly with N small black carbon inclusions. (d), (e) MGA errors as functions of the droplet size parameter or the number of black carbon inclusions.

Tables (1)

Tables Icon

Table 1. Integral Radiative Characteristics of Water Droplets Mixed with Black Carbon

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

F˜(Θ)=[a1(Θ)b1(Θ)00b1(Θ)a2(Θ)0000a3(Θ)b2(Θ)00b2(Θ)a4(Θ)],
120πdΘsinΘa1(Θ)=1.
a2(Θ)/a1(Θ)1anda3(Θ)/a4(Θ)1.

Metrics