Abstract

Multiple-scattering correction factors for cirrus particle extinction coefficients measured with Raman and high spectral resolution lidars are calculated with a radiative-transfer model. Cirrus particle-ensemble phase functions are computed from single-crystal phase functions derived in a geometrical-optics approximation. Seven crystal types are considered. In cirrus clouds with height-independent particle extinction coefficients the general pattern of the multiple-scattering parameters has a steep onset at cloud base with values of 0.5–0.7 followed by a gradual and monotonic decrease to 0.1–0.2 at cloud top. The larger the scattering particles are, the more gradual is the rate of decrease. Multiple-scattering parameters of complex crystals and of imperfect hexagonal columns and plates can be well approximated by those of projected-area equivalent ice spheres, whereas perfect hexagonal crystals show values as much as 70% higher than those of spheres. The dependencies of the multiple-scattering parameters on cirrus particle spectrum, base height, and geometric depth and on the lidar parameters laser wavelength and receiver field of view, are discussed, and a set of multiple-scattering parameter profiles for the correction of extinction measurements in homogeneous cirrus is provided.

© 2000 Optical Society of America

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  58. C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
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  59. A. J. Heymsfield, “Ice particles in a cirriform cloud at -83 °C and implications for polar stratospheric clouds,” J. Atmos. Sci. 43, 851–855 (1986).
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  60. J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
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  61. W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
    [CrossRef]

1999 (2)

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
[CrossRef]

J. Reichardt, “Optical and geometrical properties of northern midlatitude cirrus clouds observed with a UV Raman lidar,” Phys. Chem. Earth 24, 255–260 (1999).

1998 (4)

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmospheres,” Contrib. Atmos. Phys. 71, 223–248 (1998).

U. Wandinger, “Multiple-scattering influence on extinction- and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998).
[CrossRef]

M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
[CrossRef]

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
[CrossRef]

1997 (4)

C. Zuffada, D. Crisp, “Particle scattering in the resonance regime: full-wave solution for axisymmetric particles with large aspect ratios,” J. Opt. Soc. Am. A 14, 459–474 (1997).
[CrossRef]

D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

M. I. Mishchenko, D. J. Wielaard, B. E. Carlson, “T-matrix computations of zenith-enhanced lidar backscatter from horizontally oriented ice plates,” Geophys. Res. Lett. 24, 771–774 (1997).
[CrossRef]

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
[CrossRef]

1996 (3)

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
[CrossRef]

1995 (4)

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
[CrossRef]

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
[CrossRef] [PubMed]

1994 (2)

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

1993 (1)

1992 (2)

1991 (2)

1990 (2)

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

A. Ansmann, M. Riebesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
[CrossRef] [PubMed]

1989 (5)

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

K.-D. Rockwitz, “Scattering properties of horizontally oriented ice crystal columns in cirrus clouds. Part 1,” Appl. Opt. 28, 4103–4110 (1989).
[CrossRef] [PubMed]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

S. Kinne, K. N. Liou, “The effect of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds,” Atmos. Res. 24, 273–284 (1989).
[CrossRef]

1987 (1)

1986 (2)

K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
[CrossRef]

A. J. Heymsfield, “Ice particles in a cirriform cloud at -83 °C and implications for polar stratospheric clouds,” J. Atmos. Sci. 43, 851–855 (1986).
[CrossRef]

1984 (2)

S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

1983 (1)

1981 (2)

C. M. R. Platt, A. C. Dilley, “Remote sounding of high clouds. IV. Observed temperature variations in cirrus optical properties,” J. Atmos. Sci. 38, 1069–1082 (1981).
[CrossRef]

C. M. R. Platt, “Remote sounding of high clouds. III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

1979 (2)

C. M. R. Platt, “Remote sounding of high clouds. I. Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteorol. 18, 1130–1143 (1979).
[CrossRef]

P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
[CrossRef] [PubMed]

1978 (1)

A. J. Heymsfield, “Precipitation development in stratiform ice clouds: a microphysical and dynamical study,” J. Atmos. Sci. 35, 284–295 (1978).

1976 (3)

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

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

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
[CrossRef] [PubMed]

1971 (1)

H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
[CrossRef]

1970 (1)

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Anderson, T.

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
[CrossRef]

Ansmann, A.

Arnott, W. P.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Auer, A. H.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

Bentley, W. A.

W. A. Bentley, W. J. Humphreys, Snow Crystals (Dover, New York, 1962).

Carlson, B. E.

Carswell, A. I.

Crisp, D.

Cross, J. D.

J. D. Cross, “Study of the surface of ice with a scanning electron microscope,” in Physics of Ice (Plenum, New York, 1968), pp. 81–94.

Dilley, A. C.

C. M. R. Platt, A. C. Dilley, “Remote sounding of high clouds. IV. Observed temperature variations in cirrus optical properties,” J. Atmos. Sci. 38, 1069–1082 (1981).
[CrossRef]

Dong, Y. Y.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

Draine, B. T.

B. T. Draine, “The discrete dipole approximation for light scattering by irregular targets,” in Light Scattering by Nonspherical Particles, M. I. Mishchenko, J. W. Hovenier, L. D. Travis, eds. (Academic, San Diego, Calif., 1999), pp. 131–145.

Eberhard, W. L.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

Eloranta, E. W.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1. Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
[CrossRef] [PubMed]

E. W. Eloranta, “Calculation of doubly scattered lidar returns,” Ph.D. dissertation (University of Wisconsin, Madison, Wisc., 1972).

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989).

Flatau, P. J.

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Hagen, D. E.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

Hallett, J.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
[CrossRef]

J. Hallett, “Faceted snow crystals,” J. Opt. Soc. Am. A 4, 581–588 (1987).
[CrossRef]

Hart, W. D.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Heintzenberg, J.

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
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Hess, M.

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
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M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
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A. J. Heymsfield, “Ice particles in a cirriform cloud at -83 °C and implications for polar stratospheric clouds,” J. Atmos. Sci. 43, 851–855 (1986).
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A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
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A. J. Heymsfield, “Precipitation development in stratiform ice clouds: a microphysical and dynamical study,” J. Atmos. Sci. 35, 284–295 (1978).

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P. V. Hobbs, Ice Physics (Oxford U. Press, Bristol, UK, 1974).

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W. A. Bentley, W. J. Humphreys, Snow Crystals (Dover, New York, 1962).

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H. Jacobowitz, “A method for computing the transfer of solar radiation through clouds of hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 11, 691–695 (1971).
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S. Kinne, K. N. Liou, “The effect of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds,” Atmos. Res. 24, 273–284 (1989).
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Koelemeijer, R. B. A.

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
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Krumbholz, S.

J. Reichardt, S. Krumbholz, C. Weitkamp, “Rotational vibrational-rotational (RVR) Raman DIAL: a novel lidar technique for atmospheric ozone measurements,” in Thirteenth ESA Symposium on European Rocket and Balloon Programmes and Related Research: Proceedings, SP-397 (European Space Research and Technology Centre, Noordwijk, The Netherlands, 1997), pp. 237–241.

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K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
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Liou, K. N.

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmospheres,” Contrib. Atmos. Phys. 71, 223–248 (1998).

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
[CrossRef]

P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
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S. Kinne, K. N. Liou, “The effect of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds,” Atmos. Res. 24, 273–284 (1989).
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K. N. Liou, “Influence of cirrus clouds on weather and climate processes: a global perspective,” Mon. Weather Rev. 114, 1167–1199 (1986).
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K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
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Macke, A.

M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
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M. I. Mishchenko, A. Macke, “Incorporation of physical optics effects and computation of the Legendre expansion for ray-tracing phase functions involving δ-function transmission,” J. Geophys. Res. 103, 1799–1805 (1998).
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D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

A. Macke, M. I. Mishchenko, K. Muinonen, B. E. Carlson, “Scattering of light by large nonspherical particles: ray-tracing approximation versus T-matrix method,” Opt. Lett. 20, 1934–1936 (1995).
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A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
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A. Macke, “Modellierung der optischen Eigenschaften von Cirruswolken,” Ph.D. dissertation, rep. GKSS 94/E/64, 1994 (Universität Hamburg, Hamburg, Germany, 1994).

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B. J. Mason, “Snow crystals, natural and man made,” Contemp. Phys. 33, 227–243 (1992).
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Melfi, S. H.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
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Michaelis, W.

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
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Mishchenko, M. I.

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A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
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Muinonen, K.

Pal, S. R.

Platt, C. M. R.

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
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A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
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C. M. R. Platt, “Remote sounding of high clouds. III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
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C. M. R. Platt, A. C. Dilley, “Remote sounding of high clouds. IV. Observed temperature variations in cirrus optical properties,” J. Atmos. Sci. 38, 1069–1082 (1981).
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C. M. R. Platt, “Remote sounding of high clouds. I. Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteorol. 18, 1130–1143 (1979).
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Poellot, M. R.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
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Poelott, M. R.

W. P. Arnott, Y. Y. Dong, J. Hallett, M. R. Poelott, “Role of small ice crystals in radiative properties of cirrus: a case study, FIRE II, November 22, 1991,” J. Geophys. Res. 99, 1371–1381 (1994).
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W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989).

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A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
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J. Reichardt, “Optical and geometrical properties of northern midlatitude cirrus clouds observed with a UV Raman lidar,” Phys. Chem. Earth 24, 255–260 (1999).

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

J. Reichardt, S. Krumbholz, C. Weitkamp, “Rotational vibrational-rotational (RVR) Raman DIAL: a novel lidar technique for atmospheric ozone measurements,” in Thirteenth ESA Symposium on European Rocket and Balloon Programmes and Related Research: Proceedings, SP-397 (European Space Research and Technology Centre, Noordwijk, The Netherlands, 1997), pp. 237–241.

J. Reichardt, “Optische Fernmessung von Ozon in Zirruswolken,” Ph.D. dissertation, rep. GKSS 98/E/11, 1998 (Universität Hamburg, Hamburg, Germany, 1997).

J. Reichardt, C. Weitkamp, “Raman–DIAL measurements in the upper troposphere and stratosphere: the effect of high-altitude ice clouds on ozone,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 208–211.

Riebesell, M.

Rockwitz, K.-D.

Roesler, F. L.

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T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
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K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
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Schmidt, K.

T. Rother, K. Schmidt, “The discretized Mie-formalism—a novel algorithm to treat scattering on axisymmetric particles,” J. Electromagn. Waves Appl. 10, 273–297 (1996).
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J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
[CrossRef]

Serwazi, M.

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

Shipley, S. T.

Spinhirne, J. D.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

C. M. R. Platt, J. D. Spinhirne, W. D. Hart, “Optical and microphysical properties of a cold cirrus cloud: evidence for regions of small ice particles,” J. Geophys. Res. 94, 11,151–11,164 (1989).
[CrossRef]

Sroga, J. T.

Stackhouse, P. W.

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Stammes, P.

M. Hess, R. B. A. Koelemeijer, P. Stammes, “Scattering matrices of imperfect hexagonal ice crystals,” J. Quant. Spectrosc. Radiat. Transfer 60, 301–308 (1998).
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Starr, D. O’C.

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
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Stephens, G. L.

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
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Strauss, B.

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
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Ström, J.

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
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Takano, Y.

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
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Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
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W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989).

Tracy, D. H.

Trauger, J. T.

Tsay, S.

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
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S. Twomey, “Aerosols, clouds and radiation,” Atmos. Environ. 25, 2435–2442 (1991).
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H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Veal, D. L.

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
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Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989).

Wandinger, U.

Warren, S. G.

Weickmann, H. K.

Weinman, J. A.

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1. Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
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K. E. Kunkel, J. A. Weinman, “Monte Carlo analysis of multiply scattered lidar returns,” J. Atmos. Sci. 33, 1772–1781 (1976).
[CrossRef]

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

Weitkamp, C.

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

A. Ansmann, M. Riebesell, C. Weitkamp, “Measurement of atmospheric aerosol extinction profiles with a Raman lidar,” Opt. Lett. 15, 746–748 (1990).
[CrossRef] [PubMed]

J. Reichardt, C. Weitkamp, “Raman–DIAL measurements in the upper troposphere and stratosphere: the effect of high-altitude ice clouds on ozone,” in Optical Remote Sensing of the Atmosphere, Vol. 5 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997), pp. 208–211.

J. Reichardt, S. Krumbholz, C. Weitkamp, “Rotational vibrational-rotational (RVR) Raman DIAL: a novel lidar technique for atmospheric ozone measurements,” in Thirteenth ESA Symposium on European Rocket and Balloon Programmes and Related Research: Proceedings, SP-397 (European Space Research and Technology Centre, Noordwijk, The Netherlands, 1997), pp. 237–241.

Wendling, P.

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
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P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
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Wiegner, M.

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D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

M. I. Mishchenko, D. J. Wielaard, B. E. Carlson, “T-matrix computations of zenith-enhanced lidar backscatter from horizontally oriented ice plates,” Geophys. Res. Lett. 24, 771–774 (1997).
[CrossRef]

Yang, P.

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmospheres,” Contrib. Atmos. Phys. 71, 223–248 (1998).

P. Yang, K. N. Liou, “Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models,” J. Opt. Soc. Am. A 12, 162–176 (1995).
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Appl. Opt. (11)

S. T. Shipley, D. H. Tracy, E. W. Eloranta, J. T. Trauger, J. T. Sroga, F. L. Roesler, J. A. Weinman, “High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1. Theory and instrumentation,” Appl. Opt. 22, 3716–3724 (1983).
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D. J. Wielaard, M. I. Mishchenko, A. Macke, B. E. Carlson, “Improved T-matrix computations for large, nonabsorbing and weakly absorbing nonspherical particles and comparison with geometrical-optics approximation,” Appl. Opt. 36, 4305–4313 (1997).
[CrossRef] [PubMed]

P. Wendling, R. Wendling, H. K. Weickmann, “Scattering of solar radiation by hexagonal ice crystals,” Appl. Opt. 18, 2663–2671 (1979).
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K.-D. Rockwitz, “Scattering properties of horizontally oriented ice crystal columns in cirrus clouds. Part 1,” Appl. Opt. 28, 4103–4110 (1989).
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U. Wandinger, “Multiple-scattering influence on extinction- and backscatter-coefficient measurements with Raman and high-spectral-resolution lidars,” Appl. Opt. 37, 417–427 (1998).
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A. Macke, “Scattering of light by polyhedral ice crystals,” Appl. Opt. 32, 2780–2788 (1993).
[CrossRef] [PubMed]

M. Hess, M. Wiegner, “COP: a data library of optical properties of hexagonal ice crystals,” Appl. Opt. 33, 7740–7746 (1994).
[CrossRef] [PubMed]

A. Ansmann, U. Wandinger, M. Riebesell, C. Weitkamp, W. Michaelis, “Independent measurement of extinction and backscatter profiles in cirrus clouds by using a combined Raman elastic-backscatter lidar,” Appl. Opt. 31, 7113–7131 (1992).
[CrossRef] [PubMed]

S. R. Pal, A. I. Carswell, “Multiple scattering in atmospheric clouds: lidar observations,” Appl. Opt. 15, 1990–1995 (1976).
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M. I. Mishchenko, A. Macke, “How big should hexagonal ice crystals be to produce halos?” Appl. Opt. 38, 1626–1629 (1999).
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S. G. Warren, “Optical constants of ice from the ultraviolet to the microwave,” Appl. Opt. 23, 1206–1225 (1984).
[CrossRef] [PubMed]

Atmos. Environ. (1)

S. Twomey, “Aerosols, clouds and radiation,” Atmos. Environ. 25, 2435–2442 (1991).
[CrossRef]

Atmos. Res. (1)

S. Kinne, K. N. Liou, “The effect of the nonsphericity and size distribution of ice crystals on the radiative properties of cirrus clouds,” Atmos. Res. 24, 273–284 (1989).
[CrossRef]

Contemp. Phys. (1)

B. J. Mason, “Snow crystals, natural and man made,” Contemp. Phys. 33, 227–243 (1992).
[CrossRef]

Contrib. Atmos. Phys. (1)

P. Yang, K. N. Liou, “Single-scattering properties of complex ice crystals in terrestrial atmospheres,” Contrib. Atmos. Phys. 71, 223–248 (1998).

Geophys. Res. Lett. (2)

M. I. Mishchenko, D. J. Wielaard, B. E. Carlson, “T-matrix computations of zenith-enhanced lidar backscatter from horizontally oriented ice plates,” Geophys. Res. Lett. 24, 771–774 (1997).
[CrossRef]

J. Reichardt, A. Ansmann, M. Serwazi, C. Weitkamp, W. Michaelis, “Unexpectedly low ozone concentration in midlatitude tropospheric ice clouds: a case study,” Geophys. Res. Lett. 23, 1929–1932 (1996).
[CrossRef]

J. Appl. Meteorol. (1)

C. M. R. Platt, “Remote sounding of high clouds. I. Calculation of visible and infrared optical properties from lidar and radiometer measurements,” J. Appl. Meteorol. 18, 1130–1143 (1979).
[CrossRef]

J. Atmos. Sci. (15)

C. M. R. Platt, “Remote sounding of high clouds. III. Monte Carlo calculations of multiple-scattered lidar returns,” J. Atmos. Sci. 38, 156–167 (1981).
[CrossRef]

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

C. M. R. Platt, A. C. Dilley, “Remote sounding of high clouds. IV. Observed temperature variations in cirrus optical properties,” J. Atmos. Sci. 38, 1069–1082 (1981).
[CrossRef]

K. Sassen, D. O’C. Starr, G. G. Mace, M. R. Poellot, S. H. Melfi, W. L. Eberhard, J. D. Spinhirne, E. W. Eloranta, D. E. Hagen, J. Hallett, “The 5–6 December 1991 FIRE IFO II jet stream cirrus case study: possible influences of volcanic aerosols,” J. Atmos. Sci. 52, 97–123 (1995).
[CrossRef]

A. Macke, J. Mueller, E. Raschke, “Single scattering properties of atmospheric ice crystals,” J. Atmos. Sci. 53, 2813–2825 (1996).
[CrossRef]

A. J. Heymsfield, “Precipitation development in stratiform ice clouds: a microphysical and dynamical study,” J. Atmos. Sci. 35, 284–295 (1978).

A. J. Heymsfield, “Ice particles in a cirriform cloud at -83 °C and implications for polar stratospheric clouds,” J. Atmos. Sci. 43, 851–855 (1986).
[CrossRef]

J. Ström, B. Strauss, T. Anderson, F. Schröder, J. Heintzenberg, P. Wendling, “In situ observations of the microphysical properties of young cirrus clouds,” J. Atmos. Sci. 54, 2542–2553 (1997).
[CrossRef]

A. J. Heymsfield, C. M. R. Platt, “A parameterization of the particle size spectrum of ice clouds in terms of the ambient temperature and the ice water content,” J. Atmos. Sci. 41, 846–855 (1984).
[CrossRef]

A. H. Auer, D. L. Veal, “The dimension of ice crystals in natural clouds,” J. Atmos. Sci. 27, 919–926 (1970).
[CrossRef]

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

G. L. Stephens, S. Tsay, P. W. Stackhouse, P. J. Flatau, “The relevance of the microphysical and radiative properties of cirrus clouds to climate and climate feedback,” J. Atmos. Sci. 47, 1742–1753 (1990).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part I: Single-scattering and optical properties of hexagonal ice crystals,” J. Atmos. Sci. 46, 3–19 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Solar radiative transfer in cirrus clouds. Part II: Theory and computation of multiple scattering in an anisotropic medium,” J. Atmos. Sci. 46, 20–36 (1989).
[CrossRef]

Y. Takano, K. N. Liou, “Radiative transfer in cirrus clouds. Part III: Light scattering by irregular ice crystals,” J. Atmos. Sci. 52, 818–837 (1995).
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Figures (10)

Fig. 1
Fig. 1

Geometric cross sections (symbols) of the crystals used for the calculation of the single-crystal phase functions. Application ranges of the single-crystal phase functions are illustrated by the histograms.

Fig. 2
Fig. 2

Composite phase function p (solid curve), fitted phase function p fit (dashed curve), and relative difference between p and p fit (dotted curve) of an ensemble of truncated plates. The particle size distribution is D 5, with d min = 20 µm and d max = 200 µm. The laser wavelength is 355 nm.

Fig. 3
Fig. 3

Multiple-scattering parameters F VR of crystals (curves with symbols) and projected-area equivalent ice spheres (solid curves), and ratios of corresponding F VR (bottom, right) in warm cirrus clouds. Q is plotted as error bars. The crystal particle size spectrum ranges from 20- to 200-µm maximum dimension. The cloud base height and geometrical depth are 7 km and 2000 m, respectively. The laser wavelength is 355 nm, and the RFOV is 0.6 mrad.

Fig. 4
Fig. 4

Same as Fig. 3 but for cold cirrus clouds.

Fig. 5
Fig. 5

Multiple-scattering parameters F VR of crystals in warm cirrus (curves with symbols) and cold cirrus (solid curves), and ratios of corresponding F VR (bottom, right). Particle spectrum, cloud parameters, laser wavelength, and RFOV are the same as in Figs. 3 and 4.

Fig. 6
Fig. 6

Multiple-scattering parameters F VR of crystals in cold cirrus clouds obtained with 308-nm (curves with symbols) and 355-nm (solid curves) laser wavelengths, and corresponding F VR ratios (bottom, right). The crystal size spectrum, the cloud geometric parameters, and the RFOV are the same as in Fig. 3.

Fig. 7
Fig. 7

Multiple-scattering parameters F VR of crystals in cold cirrus clouds obtained with 1.0-mrad (curves with symbols) and 0.6-mrad (solid curves) RFOV, and corresponding F VR ratios (bottom, right). The crystal size spectrum, the cloud geometric parameters, and the laser wavelength are the same as in Fig. 3.

Fig. 8
Fig. 8

Multiple-scattering parameters F VR of crystals in warm cirrus clouds with particle size spectra of 100–1000 µm (curves with symbols) and 50–1000 µm (solid curves), and ratios of corresponding F VR (extreme right, top and bottom). The cloud base height and geometrical depth are 7 km and 2000 m, respectively. The laser wavelength is 355 nm, and the RFOV is 0.6 mrad. F VR of truncated plates and of convolved plates and columns have been multiplied by 2/3 to fit into the display range.

Fig. 9
Fig. 9

Multiple-scattering parameters F VR of (left to right) truncated, convolved, and imperfect hexagonal columns (curves with symbols) and projected-area equivalent ice spheres (solid curves) in cold cirrus clouds. The crystal particle size spectrum maximum dimension ranges from 6 to 80 µm (top row), 10 to 80 µm (middle row), and 20 to 80 µm (bottom row). In the rightmost figures, ratios of F VR obtained with a 20-µm minimum-diameter particle spectrum to F VR obtained with a 6-µm minimum-diameter particle spectrum (top), to F VR obtained with a 10-µm minimum-diameter particle spectrum (middle), and to F VR of projected-area equivalent ice spheres (bottom) are plotted. The cloud base height and geometrical depth are 7 km and 2000 m, respectively. The laser wavelength is 355 nm, and the RFOV is 0.6 mrad. FVR20 µm/FVR6 µm curves have been multiplied by 3/4 to fit into the display range.

Fig. 10
Fig. 10

Multiple-scattering parameters F VR of (left to right) truncated, convolved, and imperfect hexagonal columns in cold cirrus clouds obtained with different cloud base heights (top row) and geometrical depths (bottom row) and (rightmost figures) ratios of corresponding F VR. The crystal particle size spectrum ranges from 10- to 80-µm maximum dimension. The laser wavelength is 355 nm, and the RFOV is 0.6 mrad. FVR4000 m/FVR2000 m curves have been enlarged twofold to fit into the display range. Rescaling of ξ causes F VR of different cloud base heights and F VR of different cloud geometrical depths to overlap completely; the two traces are therefore hard to distinguish.

Tables (3)

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Table 1 Parameters of the Particle Size Distributionsa

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Table 2 Maximum Dimensions d c and Application Ranges of Single-Crystal Phase Functions

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Table 3 Fit Coefficients e 0 to e 4 of the Standard F VR Profilesa

Equations (26)

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N1λVR, z=KλL, λVROzz2 βλL, λVR, z×exp-0zαλL, ζ+αλVR, ζdζ,
αλ, z=αparscaλ, z+αparabsλ, z+αmolscaλ, z+αO3absλ, z+j αgas,jabsλ, z.
αλ, z=αparscaλ, zαparλ, z.
αparz=-12ddz ln N1λVR, z.
NtotλVR, z=N1λVR, z+NMSλVR, z=N1λVR, z+N2λVR, z+N3λVR, z+,
αpareffz=1-FVRzαparz,  FVRz0, 1.
NtotλVR, z=N1λVR, z×exp0zFVRζαparλL, ζ+αparλVR, ζdζ,
FVRz=12αparzddz lnNtotλVR, zN1λVR, z.
FVRz=12αparzddzNMSλVR, zN1λVR, z-NMSλVR, zN1λVR, zddzNMSλVR, zN1λVR, z.
pφ, ϑ=pϑ.
02π0πpϑsin ϑdϑdφ=1.
pϑ=12-l pdifϑ+1-12-lpGOϑ.
pikϑ=j=1jmaxipi,jϑmaxdmin, dminjmindmax, dmaxjCiscaδDkδdδ×dmindmaxCiscaδDkδdδ-1,
D1kd=A1kd/100B1k,  D2kd=A2kd/1000B2k,  Dkd=minD1kd, D2kd;
pϑ=j=15ajπθj2 exp-ϑ/θj2,
FVR,iz=14k FVR,ikz
Qiz=4314k |FVR,ikz-FVR,iz|/FVR,iz.
ξ=z-zbzt-zb,
ξ=zb,2zb,1-1ξ,
ξ=Δz2Δz1 ξ,
ξδ2δ1-1.25ξ,
ξλL,2λL,11.35ξ,
zbz αpareffζdζ=ηz-zbzbz αparζdζ.
1-FVRz=ηz-zb+z-zbddz ηz-zb.
ηz-zb=c0+c1z-zb,
FVRz=1+c0-2ηz-zb.

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