Abstract

The impact of multiple scattering (MS) by aerosols on satellite-borne lidar measurements is studied by Monte-Carlo radiative transfer simulations. A total of 48 aerosol scenarios are considered. We find that the frequently used MS correction factor can be parameterized as a function of aerosol size and aerosol optical depth. Its dependencies on vertical distribution and total optical depth can be treated as a random error. We illustrate the use of our parameterization by considering an episode of high sea salt concentrations over the ocean. Neglecting MS, or using a constant value of the MS correction factor, can introduce a negative bias in the computed backscattered power that exceeds the random error in our approach.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  45. E. Andersson and M. Kahnert, “Coupling aerosol optics to the MATCH (v5. 5.0) chemical transport model and the SALSA (v1) aerosol microphysics module,” Geosci. Model Dev. 9(5), 1803–1826 (2016).
    [Crossref]

2018 (1)

2016 (1)

E. Andersson and M. Kahnert, “Coupling aerosol optics to the MATCH (v5. 5.0) chemical transport model and the SALSA (v1) aerosol microphysics module,” Geosci. Model Dev. 9(5), 1803–1826 (2016).
[Crossref]

2015 (1)

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

2013 (1)

P. Liu, Y. Zhang, and S. T. Martin, “Complex refractive indices of thin films of secondary organic materials by spectroscopic ellipsometry from 220 to 1200 nm,” Environ. Sci. Technol. 47(23), 13594–13601 (2013). PMID: 24191734.
[Crossref]

2010 (2)

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

2008 (2)

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part I: Small-angle scattering using the photon variance-covariance method,” J. Atmos. Sci. 65(12), 3621–3635 (2008).
[Crossref]

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part II: Wide-angle scattering using the time-dependent two-stream approximation,” J. Atmos. Sci. 65(12), 3636–3651 (2008).
[Crossref]

2007 (2)

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

C. Andersson, J. Langner, and R. Bergström, “Interannual variation and trends in air pollution over Europe due to climate variability during 1958-2001 simulated with a regional CTM coupled to the ERA40 reanalysis,” Tellus B 59(1), 77–98 (2007).
[Crossref]

2006 (4)

H. Iwabuchi, “Efficient monte carlo methods for radiative transfer modeling,” J. Atmos. Sci. 63(9), 2324–2339 (2006).
[Crossref]

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111(D20), D20211 (2006).
[Crossref]

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

2005 (1)

2003 (2)

S. Reichardt and J. Reichardt, “Effect of multiple scattering on depolarization measurements with spaceborne lidars,” Appl. Opt. 42(18), 3620–3633 (2003).
[Crossref]

R. Scheirer and A. Macke, “Cloud inhomogeneity and broadband solar fluxes,” J. Geophys. Res.: Atmos. 108(D19), 4599 (2003).
[Crossref]

2002 (1)

2001 (1)

B. Tatarov and I. Kolev, “Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation,” Appl. Phys. B: Lasers Opt. 73(3), 261–268 (2001).
[Crossref]

2000 (1)

R. Scheirer and A. Macke, “Influence of the gaseous atmosphere on solar fluxes of inhomogeneous clouds,” Phys. Chem. Earth, Part B: Hydrol. Ocean. Atmosphere 25(2), 73–76 (2000).
[Crossref]

1998 (2)

E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37(12), 2464–2472 (1998).
[Crossref]

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

1996 (1)

1995 (2)

L. R. Bissonnette and D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34(30), 6959–6975 (1995).
[Crossref]

L. R. Bissonnette, “Miltiple scattering of narrow light beams in aerosols,” Appl. Phys. B: Lasers Opt. 60(4), 315–323 (1995).
[Crossref]

1994 (1)

1993 (1)

1990 (1)

1987 (1)

G. A. d’Almeida, “On the variability of desert aerosol radiative characteristics,” J. Geophys. Res. 92(D3), 3017–3026 (1987).
[Crossref]

1986 (1)

1977 (1)

1976 (2)

K. E. Kunkel and J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33(9), 1772–1781 (1976).
[Crossref]

J. A. Weinman, “Effects of multiple scattering on light pulses reflected by turbid atmospheres,” J. Atmos. Sci. 33(9), 1763–1771 (1976).
[Crossref]

1973 (1)

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30(6), 1191–1204 (1973).
[Crossref]

1972 (1)

J. A. Weinman, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77(36), 7123–7128 (1972).
[Crossref]

1971 (2)

K. Liou and R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28(5), 772–784 (1971).
[Crossref]

G. N. Plass and G. W. Kattawar, “Reflection of light pulses from clouds,” Appl. Opt. 10(10), 2304–2310 (1971).
[Crossref]

1904 (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc., A 203(359-371), 385–420 (1904).
[Crossref]

a. Teukolsky, S.

W. H. Press, S. a. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: the Art of Scientific Computing. Second Edition, vol. 1 (Cambridge University Press, 1996).

Ackerman, T. P.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Allan, R. P.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Allen, R. J.

Althausen, D.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Andersson, C.

C. Andersson, J. Langner, and R. Bergström, “Interannual variation and trends in air pollution over Europe due to climate variability during 1958-2001 simulated with a regional CTM coupled to the ERA40 reanalysis,” Tellus B 59(1), 77–98 (2007).
[Crossref]

Andersson, E.

E. Andersson and M. Kahnert, “Coupling aerosol optics to the MATCH (v5. 5.0) chemical transport model and the SALSA (v1) aerosol microphysics module,” Geosci. Model Dev. 9(5), 1803–1826 (2016).
[Crossref]

Ansmann, A.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Barnard, J. C.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Battaglia, A.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

Benker, N.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Bergstrom, R. W.

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111(D20), D20211 (2006).
[Crossref]

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

Bergström, R.

C. Andersson, J. Langner, and R. Bergström, “Interannual variation and trends in air pollution over Europe due to climate variability during 1958-2001 simulated with a regional CTM coupled to the ERA40 reanalysis,” Tellus B 59(1), 77–98 (2007).
[Crossref]

Bissonnette, L. R.

Bond, T. C.

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
[Crossref]

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111(D20), D20211 (2006).
[Crossref]

Bundke, U.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Cheong, H. D.

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Cober, S. G.

Cuevas, E.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

d’Almeida, G. A.

G. A. d’Almeida, “On the variability of desert aerosol radiative characteristics,” J. Geophys. Res. 92(D3), 3017–3026 (1987).
[Crossref]

Dewitte, S.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Dubuisson, P.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

Dukhyeon, K.

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Durand, L.

Ebert, M.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Echle, G.

Eloranta, E. W.

Flannery, B. P.

W. H. Press, S. a. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: the Art of Scientific Computing. Second Edition, vol. 1 (Cambridge University Press, 1996).

Garnier, A.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

Habib, G.

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111(D20), D20211 (2006).
[Crossref]

Harries, J. E.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Hess, M.

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Hogan, R. J.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part I: Small-angle scattering using the photon variance-covariance method,” J. Atmos. Sci. 65(12), 3621–3635 (2008).
[Crossref]

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part II: Wide-angle scattering using the time-dependent two-stream approximation,” J. Atmos. Sci. 65(12), 3636–3651 (2008).
[Crossref]

Hutt, D. L.

Isaac, G. A.

Ishimoto, H.

Iwabuchi, H.

H. Iwabuchi, “Efficient monte carlo methods for radiative transfer modeling,” J. Atmos. Sci. 63(9), 2324–2339 (2006).
[Crossref]

Kahnert, M.

E. Andersson and M. Kahnert, “Coupling aerosol optics to the MATCH (v5. 5.0) chemical transport model and the SALSA (v1) aerosol microphysics module,” Geosci. Model Dev. 9(5), 1803–1826 (2016).
[Crossref]

Kandler, K.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Kassianov, E. I.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Kattawar, G. W.

Kim, Y.

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Knippertz, P.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Kobayashi, S.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

Koepke, P.

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Kolev, I.

B. Tatarov and I. Kolev, “Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation,” Appl. Phys. B: Lasers Opt. 73(3), 261–268 (2001).
[Crossref]

Kuehn, R.

S. A. Young, D. M. Winker, M. A. Vaughan, K. A. Powell, and R. Kuehn, “Treatment of multiple-scattering effects in extinction retrievals in complex atmospheric scenes probed by CALIPSO,” in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (Nara, Japan, 2006).

Kunkel, K. E.

K. E. Kunkel and J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33(9), 1772–1781 (1976).
[Crossref]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, absorption, and emission of light by small particles (Cambridge University Press, Cambridge, 2002).

Langner, J.

C. Andersson, J. Langner, and R. Bergström, “Interannual variation and trends in air pollution over Europe due to climate variability during 1958-2001 simulated with a regional CTM coupled to the ERA40 reanalysis,” Tellus B 59(1), 77–98 (2007).
[Crossref]

Lee, J.

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Lee, Y.-H.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Lin, H.-C.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Liou, K.

K. Liou and R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28(5), 772–784 (1971).
[Crossref]

Liu, P.

P. Liu, Y. Zhang, and S. T. Martin, “Complex refractive indices of thin films of secondary organic materials by spectroscopic ellipsometry from 220 to 1200 nm,” Environ. Sci. Technol. 47(23), 13594–13601 (2013). PMID: 24191734.
[Crossref]

Liu, Q.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Liu, Z.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Macke, A.

R. Scheirer and A. Macke, “Cloud inhomogeneity and broadband solar fluxes,” J. Geophys. Res.: Atmos. 108(D19), 4599 (2003).
[Crossref]

R. Scheirer and A. Macke, “Influence of the gaseous atmosphere on solar fluxes of inhomogeneous clouds,” Phys. Chem. Earth, Part B: Hydrol. Ocean. Atmosphere 25(2), 73–76 (2000).
[Crossref]

Martin, S. T.

P. Liu, Y. Zhang, and S. T. Martin, “Complex refractive indices of thin films of secondary organic materials by spectroscopic ellipsometry from 220 to 1200 nm,” Environ. Sci. Technol. 47(23), 13594–13601 (2013). PMID: 24191734.
[Crossref]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc., A 203(359-371), 385–420 (1904).
[Crossref]

McFarlane, S. A.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Miller, M. A.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, absorption, and emission of light by small particles (Cambridge University Press, Cambridge, 2002).

Müller, D.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Okamoto, H.

Pelon, J.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

Petrilla, R. L.

Plass, G. N.

Platt, C. M. R.

R. J. Allen and C. M. R. Platt, “Lidar for multiple backscattering and depolarization observations,” Appl. Opt. 16(12), 3193–3199 (1977).
[Crossref]

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30(6), 1191–1204 (1973).
[Crossref]

Powell, K. A.

S. A. Young, D. M. Winker, M. A. Vaughan, K. A. Powell, and R. Kuehn, “Treatment of multiple-scattering effects in extinction retrievals in complex atmospheric scenes probed by CALIPSO,” in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (Nara, Japan, 2006).

Poytier, L.

Press, W. H.

W. H. Press, S. a. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: the Art of Scientific Computing. Second Edition, vol. 1 (Cambridge University Press, 1996).

Reichardt, J.

Reichardt, S.

Robinson, G. J.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Rodríguez, S.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Roy, G.

Roy, N.

Russell, J. E.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Sassen, K.

Sato, K.

Scheirer, R.

R. Scheirer and A. Macke, “Cloud inhomogeneity and broadband solar fluxes,” J. Geophys. Res.: Atmos. 108(D19), 4599 (2003).
[Crossref]

R. Scheirer and A. Macke, “Influence of the gaseous atmosphere on solar fluxes of inhomogeneous clouds,” Phys. Chem. Earth, Part B: Hydrol. Ocean. Atmosphere 25(2), 73–76 (2000).
[Crossref]

Schotland, R. M.

K. Liou and R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28(5), 772–784 (1971).
[Crossref]

Schult, I.

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Schütz, L.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Schwartz, C. S.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Seifert, P.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Simmer, C.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

Slingo, A.

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Tanelli, S.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

Tatarov, B.

B. Tatarov and I. Kolev, “Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation,” Appl. Phys. B: Lasers Opt. 73(3), 261–268 (2001).
[Crossref]

Tesche, M.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, absorption, and emission of light by small particles (Cambridge University Press, Cambridge, 2002).

Trepte, C. R.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

Vaughan, M. A.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

S. A. Young, D. M. Winker, M. A. Vaughan, K. A. Powell, and R. Kuehn, “Treatment of multiple-scattering effects in extinction retrievals in complex atmospheric scenes probed by CALIPSO,” in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (Nara, Japan, 2006).

Vetterling, W. T.

W. H. Press, S. a. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: the Art of Scientific Computing. Second Edition, vol. 1 (Cambridge University Press, 1996).

Volkov, S.

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Wandinger, U.

U. Wandinger, M. Tesche, P. Seifert, A. Ansmann, D. Müller, and D. Althausen, “Size matters: Influence of multiple scattering on CALIPSO light-extinction profiling in desert dust,” Geophys. Res. Lett.37(10), (2010).
[Crossref]

Wang, T.

Z. Liu, Q. Liu, H.-C. Lin, C. S. Schwartz, Y.-H. Lee, and T. Wang, “Three-dimensional variational assimilation of modis aerosol optical depth: Implementation and application to a dust storm over east asia,” J. Geophys. Res.116(D23), (2011).
[Crossref]

Weinbruch, S.

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Weinman, J. A.

K. E. Kunkel and J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33(9), 1772–1781 (1976).
[Crossref]

J. A. Weinman, “Effects of multiple scattering on light pulses reflected by turbid atmospheres,” J. Atmos. Sci. 33(9), 1763–1771 (1976).
[Crossref]

J. A. Weinman, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77(36), 7123–7128 (1972).
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Wiegner, M.

Winker, D.

D. Winker, “Accounting for multiple scattering in retrievals from space lidar,” in 12th International Workshop on Lidar Multiple Scattering Experiments, C. Werner, U. G. Oppel, and T. Rother, eds. (SPIE, 2003), pp. 128–139.

Winker, D. M.

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

S. A. Young, D. M. Winker, M. A. Vaughan, K. A. Powell, and R. Kuehn, “Treatment of multiple-scattering effects in extinction retrievals in complex atmospheric scenes probed by CALIPSO,” in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (Nara, Japan, 2006).

Young, S. A.

S. A. Young, D. M. Winker, M. A. Vaughan, K. A. Powell, and R. Kuehn, “Treatment of multiple-scattering effects in extinction retrievals in complex atmospheric scenes probed by CALIPSO,” in Reviewed and Revised Papers Presented at the 23rd International Laser Radar Conference, C. Nagasawa and N. Sugimoto, eds. (Nara, Japan, 2006).

Zhang, Y.

P. Liu, Y. Zhang, and S. T. Martin, “Complex refractive indices of thin films of secondary organic materials by spectroscopic ellipsometry from 220 to 1200 nm,” Environ. Sci. Technol. 47(23), 13594–13601 (2013). PMID: 24191734.
[Crossref]

Zrnic, D.

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
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Aerosol Sci. Technol. (1)

T. C. Bond and R. W. Bergstrom, “Light absorption by carbonaceous particles: An investigative review,” Aerosol Sci. Technol. 40(1), 27–67 (2006).
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Appl. Opt. (12)

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E. W. Eloranta, “Practical model for the calculation of multiply scattered lidar returns,” Appl. Opt. 37(12), 2464–2472 (1998).
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G. N. Plass and G. W. Kattawar, “Reflection of light pulses from clouds,” Appl. Opt. 10(10), 2304–2310 (1971).
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R. J. Allen and C. M. R. Platt, “Lidar for multiple backscattering and depolarization observations,” Appl. Opt. 16(12), 3193–3199 (1977).
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K. Sassen and R. L. Petrilla, “Lidar depolarization from multiple scattering in marine stratus clouds,” Appl. Opt. 25(9), 1450–1459 (1986).
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L. R. Bissonnette and D. L. Hutt, “Multiple scattering lidar,” Appl. Opt. 29(34), 5045–5046 (1990).
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D. L. Hutt, L. R. Bissonnette, and L. Durand, “Multiple field of view lidar returns from atmospheric aerosols,” Appl. Opt. 33(12), 2338–2348 (1994).
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L. R. Bissonnette and D. L. Hutt, “Multiply scattered aerosol lidar returns: inversion method and comparison with in situ measurements,” Appl. Opt. 34(30), 6959–6975 (1995).
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L. R. Bissonnette, G. Roy, and N. Roy, “Multiple-scattering-based lidar retrieval: method and results of cloud probings,” Appl. Opt. 44(26), 5565–5581 (2005).
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L. R. Bissonnette, “Multiple-scattering lidar equation,” Appl. Opt. 35(33), 6449–6465 (1996).
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L. R. Bissonnette, G. Roy, L. Poytier, S. G. Cober, and G. A. Isaac, “Multiple-scattering lidar retrieval method: tests on Monte Carlo simulations and comparisons with in situ measurements,” Appl. Opt. 41(30), 6307–6324 (2002).
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S. Reichardt and J. Reichardt, “Effect of multiple scattering on depolarization measurements with spaceborne lidars,” Appl. Opt. 42(18), 3620–3633 (2003).
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Appl. Phys. B: Lasers Opt. (2)

B. Tatarov and I. Kolev, “Experimental determination of the multiple-scattering effect on the lidar-signal polarization characteristics during liquid- and solid-phase precipitation,” Appl. Phys. B: Lasers Opt. 73(3), 261–268 (2001).
[Crossref]

L. R. Bissonnette, “Miltiple scattering of narrow light beams in aerosols,” Appl. Phys. B: Lasers Opt. 60(4), 315–323 (1995).
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Atmos. Environ. (1)

K. Kandler, N. Benker, U. Bundke, E. Cuevas, M. Ebert, P. Knippertz, S. Rodríguez, L. Schütz, and S. Weinbruch, “Chemical composition and complex refractive index of saharan mineral dust at Izaña, Tenerife (Spain) derived by electron microscopy,” Atmos. Environ. 41(37), 8058–8074 (2007).
[Crossref]

Atmos. Meas. Tech. (1)

A. Garnier, J. Pelon, M. A. Vaughan, D. M. Winker, C. R. Trepte, and P. Dubuisson, “Lidar multiple scattering factors inferred from CALIPSO lidar and IIR retrievals of semi-transparent cirrus cloud optical depths over oceans,” Atmos. Meas. Tech. 8(7), 2759–2774 (2015).
[Crossref]

Bull. Am. Meteorol. Soc. (1)

M. Hess, P. Koepke, and I. Schult, “Optical properties of aerosols and clouds: The software package OPAC,” Bull. Am. Meteorol. Soc. 79(5), 831–844 (1998).
[Crossref]

Environ. Sci. Technol. (1)

P. Liu, Y. Zhang, and S. T. Martin, “Complex refractive indices of thin films of secondary organic materials by spectroscopic ellipsometry from 220 to 1200 nm,” Environ. Sci. Technol. 47(23), 13594–13601 (2013). PMID: 24191734.
[Crossref]

Geophys. Res. Lett. (1)

A. Slingo, T. P. Ackerman, R. P. Allan, E. I. Kassianov, S. A. McFarlane, G. J. Robinson, J. C. Barnard, M. A. Miller, J. E. Harries, J. E. Russell, and S. Dewitte, “Observations of the impact of a major saharan dust storm on the atmospheric radiation balance,” Geophys. Res. Lett. 33(24), L24817 (2006).
[Crossref]

Geosci. Model Dev. (1)

E. Andersson and M. Kahnert, “Coupling aerosol optics to the MATCH (v5. 5.0) chemical transport model and the SALSA (v1) aerosol microphysics module,” Geosci. Model Dev. 9(5), 1803–1826 (2016).
[Crossref]

J. Atmos. Sci. (7)

H. Iwabuchi, “Efficient monte carlo methods for radiative transfer modeling,” J. Atmos. Sci. 63(9), 2324–2339 (2006).
[Crossref]

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part I: Small-angle scattering using the photon variance-covariance method,” J. Atmos. Sci. 65(12), 3621–3635 (2008).
[Crossref]

R. J. Hogan, “Fast lidar and radar multiple-scattering models. Part II: Wide-angle scattering using the time-dependent two-stream approximation,” J. Atmos. Sci. 65(12), 3636–3651 (2008).
[Crossref]

K. E. Kunkel and J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33(9), 1772–1781 (1976).
[Crossref]

J. A. Weinman, “Effects of multiple scattering on light pulses reflected by turbid atmospheres,” J. Atmos. Sci. 33(9), 1763–1771 (1976).
[Crossref]

C. M. R. Platt, “Lidar and radiometric observations of cirrus clouds,” J. Atmos. Sci. 30(6), 1191–1204 (1973).
[Crossref]

K. Liou and R. M. Schotland, “Multiple backscattering and depolarization from water clouds for a pulsed lidar system,” J. Atmos. Sci. 28(5), 772–784 (1971).
[Crossref]

J. Geophys. Res. (3)

J. A. Weinman, “Effects of multiple scattering on laser pulses transmitted through clouds,” J. Geophys. Res. 77(36), 7123–7128 (1972).
[Crossref]

T. C. Bond, G. Habib, and R. W. Bergstrom, “Limitations in the enhancement of visible light absorption due to mixing state,” J. Geophys. Res. 111(D20), D20211 (2006).
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G. A. d’Almeida, “On the variability of desert aerosol radiative characteristics,” J. Geophys. Res. 92(D3), 3017–3026 (1987).
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J. Geophys. Res.: Atmos. (1)

R. Scheirer and A. Macke, “Cloud inhomogeneity and broadband solar fluxes,” J. Geophys. Res.: Atmos. 108(D19), 4599 (2003).
[Crossref]

J. Quant. Spectrosc. Radiat. Transfer (1)

A. Battaglia, S. Tanelli, S. Kobayashi, D. Zrnic, R. J. Hogan, and C. Simmer, “Multiple-scattering in radar systems: A review,” J. Quant. Spectrosc. Radiat. Transfer 111(6), 917–947 (2010).
[Crossref]

Opt. Express (1)

Opt. Rev. (1)

K. Dukhyeon, H. D. Cheong, Y. Kim, S. Volkov, and J. Lee, “Optical depth and multiple scattering depolarization in liquid clouds,” Opt. Rev. 17(6), 507–512 (2010).
[Crossref]

Philos. Trans. R. Soc., A (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc., A 203(359-371), 385–420 (1904).
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Phys. Chem. Earth, Part B: Hydrol. Ocean. Atmosphere (1)

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Figures (6)

Fig. 1.
Fig. 1. Optical paths for (a) single scattering events, (b) regular multiple scattering, and (c) irregular multiple scattering. The physical length of all three optical paths is $2R\pm \Delta R$, where the resolution of the instrument $\Delta R$ is indicated by the shaded area.
Fig. 2.
Fig. 2. Backscattered energy as a function of altitude (top row), fraction of regular (second row) and irregular multiple scattering (third row), and multiple scattering correction factor $\eta$ as a function of aerosol optical depth $\tau _a$. The columns pertain to three different aerosol scenarios as indicated in the column heading.
Fig. 3.
Fig. 3. Fit of the multiple scattering correction factor $\eta$ as a function of effective radius $r_{\mathrm {eff}}$ and aerosol optical depth $\tau _a$ according to Eq. (15). The bottom panel shows the full 3D plot, while the upper four panels show cross sections for fixed values of $r_{\mathrm {eff}}$. The least-square fitting result is represented by the black lines (upper four panels) and by the surface plot (bottom panel).
Fig. 4.
Fig. 4. Multiple scattering correction factor $\eta$ as a function of $r_{\mathrm {eff}}$ and $\tau _a$ according to Eq. (15) (left), and standard deviation $\Delta \eta$ (right).
Fig. 5.
Fig. 5. Effective radius 750 m above the ground (left) and aerosol optical depth (right) obtained with the MATCH model on June 13 2006, 1800 UTC. The ’X’ in the Nordic Sea marks the location selected for the test case shown in Fig. 6.
Fig. 6.
Fig. 6. Attenuated backscattering coefficient $\beta _{\mathrm {att}}$ simulated with the MATCH observation operator (left). The results have been obtained by (i) modelling $\eta$ according to Eq. (15) (black, uncertainty indicated by shaded region), (ii) by setting $\eta =$0.93 (green), and (iii) by setting $\eta =$1.00 (red). The right diagram shows the magnitude of the relative biases of cases (ii) and (iii), and the relative random error in case (i).

Tables (1)

Tables Icon

Table 1. Mean radius $r_0$, geometric standard deviation $\sigma _g$, and effective radius $r_{\mathrm {eff}}$ for the lognormal size distributions considered in our aerosol scenarios.

Equations (21)

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β a t t ( x ; R ) = [ β m + β a ( x ) ] T 2 ( x ; R ) .
T 2 ( x ; R ) = exp ( 2 τ ( x ; R ) ) ,
T m s 2 ( x ; R ) = exp ( 2 η ( x ) τ ( x ; R ) ) .
τ d = l n ( )
n ( r ) = 1 2 2 π r ln σ g exp [ 1 2 ( ln ( r / r 0 ) ln σ g ) 2 ] ,
r e f f = 0 n ( r ) r π r 2 d r 0 n ( r ) π r 2 d r ,
E ( x ; R ) = E 0 A Δ R 2 R 2 [ β a ( x ; R ) + β m ( R ) ] T 2 ( x ; R ) ,
τ ( x ; R ) = 0 R k e x t ( x ; R ) d R .
k e x t ( x ; R ) = k e x t , m ( R ) + k e x t , a ( x ; R ) .
τ a ( x ; R ) = 0 R k e x t , a ( x ; R ) d R ,
E ( x ; R ) = E s s ( x ; R ) + E m s , r e g ( x ; R ) + E m s , i r r ( x ; R ) .
E ( x ; R ) E ss ( x ; R ) = T ms 2 ( x ; R ) T 2 ( x ; R ) = exp [ 2 η ( x ; R ) τ ( x ; R ) ] exp [ 2 τ ( x ; R ) ] ,
η ( x ; R ) = 1 + 1 2 τ ( x ; R ) ln E ss ( x ; R ) E ( x ; R ) .
η ( τ a ) = A B exp ( C τ a ) + D exp ( E τ a ) .
η ( τ a , r e f f ) = A + r e f f [ B exp ( C τ a ) + D exp ( E τ a ) ] ,
A = 0.933 ± 0.004 B = 0.075 ± 0.003 C = 0.15 ± 0.02 D = 0.080 ± 0.002 E = 8.0 ± 0.5.
Δ η = 1 N i = 1 N ( η i η i MC ) 2 .
Δ η = { 0.21 : r e f f > 5 μ m , τ a < 0.5 0.07 : o t h e r w i s e .
lim r e f f 0 η = A = 0.93
lim τ a 0 η = A + r e f f ( D B ) = 0.93 + 0.005 r e f f 0.93.
T m s 2 ( x ; R ) = exp ( 2 η a ( x ) τ a ( x ; R ) ) exp ( 2 η m τ m ( R ) ) ,

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