• Ackerman, S. A., and G. L. Stephens, 1987: The absorption of solar radiation by cloud droplets: An application of anomalous diffraction theory. J. Atmos. Sci.,44, 1574–1588.

  • Asano, S., and G. Yamamoto, 1975: Light scattering by a spheroidal particle. Appl. Opt.,14, 29–49.

  • Auer, A. H., Jr., and D. L. Veal, 1970: The dimension of ice crystals in natural clouds. J. Atmos. Sci.,27, 919–926.

  • Barber, P., and C. Yeh, 1975: Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies. Appl. Opt.,14, 2864–2872.

  • Berenger, J. P., 1994: A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys.,114, 185–200.

  • ——, 1996: Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys.,127, 363–379.

  • Dobbins, R. A., and G. S. Jizmagian, 1966: Optical scattering cross sections for polydispersions of dielectric spheres. J. Opt. Soc. Amer.,56, 1345–1350.

  • Ebert, E. E., and J. A. Curry, 1992: A parameterization of ice cloud optical properties for climate models. J. Geophys. Res.,97, 3831–3836.

  • Foot, J. S., 1988: Some observations of the optical properties of clouds. II: Cirrus. Quart. J. Roy. Meteor. Soc.,114, 145–164.

  • Francis, P. N., A. Jones, R. W. Saunders, K. P. Shine, A. Slingo, and Z. Sun, 1994: An observational and theoretical study of the radiative properties of cirrus: Some results from ICE’89. Quart. J. Roy. Meteor. Soc.,120, 809–848.

  • Fu, Q., 1996: An accurate parameterization of the solar radiative properties of cirrus clouds for climate models. J. Climate,9, 2058–2082.

  • ——, K. N. Liou, M. C. Cribb, T. P. Charlock, and A. Grossman, 1997: Multiple scattering parameterization in thermal infrared radiative transfer. J. Atmos. Sci.,54, 2799–2812.

  • ——, P. Yang, and W. B. Sun, 1998: An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models. J. Climate,11, 2223–2237.

  • Katz, D. S., E. T. Thiele, and A. Taflove, 1994: Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FDTD meshes. IEEE Microwave Guided Wave Lett.,4, 268–270.

  • Liao, Z., H. L. Wang, B. Yang, and Y. Yuan, 1984: A transmitting boundary for transient wave analyses. Sci. Sin.,27, 1063–1076.

  • Liou, K. N., and Y. Takano, 1994: Light scattering by nonspherical particles: Remote sensing and climate implications. Atmos. Res.,31, 271–298.

  • ——, Q. Fu, and T. P. Ackerman, 1988: A simple formulation of the delta-four-stream approximation for radiative transfer parameterizations. J. Atmos. Sci.,45, 1940–1947.

  • McFarquhar, G. M., and A. J. Heymsfield, 1996: Microphysical characteristics of three cirrus anvils sampled during the Central Equatorial Pacific Experiment. J. Atmos. Sci.,53, 2401–2423.

  • Mie, G., 1908: Beigrade zur Optik truber Medien, speziell kolloidaler Metallosungen. Ann. Phys.,25, 377–445.

  • Mishchenko, M. I., and L. D. Travis, 1994: Light scattering by polydisperse, rotationally symmetric nonspherical particles: Linear polarization. J. Quant. Spectros. Radiat. Transfer,51, 759–778.

  • Mitchell, D. L., 1995: How appropriate is Mie theory for predicting the radiative properties of atmospheric particles? GEWEX News,5 (1), 7–11.

  • ——, A. Macke, and Y. G. Liu, 1996: Modeling cirrus clouds. Part II: Treatment of radiative properties J. Atmos. Sci.,53, 2967–2988.

  • Mugnai, A., and W. J. Wiscombe, 1986: Scattering from nonspherical Chebyshev particles. I: Cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction. Appl. Opt.,25, 1235–1244.

  • Ono, A., 1969: The shape and riming properties of ice crystals in natural clouds. J. Atmos. Sci.,26, 138–147.

  • Rayleigh, Lord, 1918: The dispersal of light by a dielectric cylinder. Phil. Mag.,36, 365–376.

  • Spinhirne, J. D., W. D. Hart, and D. L. Hlavka, 1996: Cirrus infrared parameters and shortwave reflectance relations from observations. J. Atmos. Sci.,53, 1438–1458.

  • Stackhouse, P. W., and G. Stephens, 1991: A theoretical and observational study of the radiative properties of cirrus: Results from FIRE 1986. J. Atmos. Sci.,48, 2044–2059.

  • Sun, W. B., and Q. Fu, 1998: Anomalous diffraction theory for arbitrarily oriented hexagonal crystals. J. Quant. Spectrosc. Radiat. Transfer, in press.

  • ——, ——, and Z. Z. Chen, 1998: FDTD solution of light scattering by dielectric particles using PML ABC. Appl. Opt., in press.

  • Sun, Z., and K. P. Shine, 1995: Parameterization of ice cloud radiative properties and its application to the potential climatic importance of mixed-phase clouds. J. Climate,8, 1874–1888.

  • Takano, Y., and K. N. Liou, 1989: Solar radiative transfer in cirrus clouds. Part I: Single scattering and optical properties of hexagonal ice crystals. J. Atmos. Sci.,46, 3–19.

  • ——, ——, and P. Minnis, 1992: The effects of small ice crystals on cirrus infrared radiative properties. J. Atmos. Sci.,49, 1487–1493.

  • van de Hulst, H. C., 1982: Light Scattering by Small Particles. Dover, 470 pp.

  • Wait, J. R., 1955: Scattering of a plane wave from a circular dielectric cylinder at oblique incidence. Can. J. Phys.,33, 189–195.

  • Warren, S. G., 1982: Optical properties of snow. Rev. Geophys. Space Phys.,20, 67–89.

  • Waterman, P. C., 1965: Matrix formulation of electromagnetic scattering. Proc. IEEE,53, 805–812.

  • Yang, P., and K. N. Liou, 1996a: Finite-difference time domain method for light scattering by small ice crystals in three-dimensional space. J. Opt. Soc. Amer.,13A, 2072–2085.

  • ——, and ——, 1996b: Geometric-optics-integral-equation method for light scattering by nonspherical ice crystals. Appl. Opt.,35, 6568–6584.

  • Yee, S. K., 1966: Numerical solution of initial boundary value problems involving Maxwell’s equation in isotropic media. IEEE Trans. Antennas Propag.,AP-14, 302–307.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 274 152 79
PDF Downloads 111 54 5

Modeling of Scattering and Absorption by Nonspherical Cirrus Ice Particles at Thermal Infrared Wavelengths

Qiang FuAtmospheric Science Program, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

Search for other papers by Qiang Fu in
Current site
Google Scholar
PubMed
Close
,
W. B. SunAtmospheric Science Program, Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

Search for other papers by W. B. Sun in
Current site
Google Scholar
PubMed
Close
, and
Ping YangDepartment of Atmospheric Sciences, University of California, Los Angeles, Los Angeles, California

Search for other papers by Ping Yang in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

This paper examines a number of commonly used methods for the calculation of the scattering and absorption properties of nonspherical ice crystals at thermal infrared wavelengths. It is found that, for randomly oriented nonspherical particles, Mie theory using equivalent ice spheres tends to overestimate the absorption efficiency while the anomalous diffraction theory (ADT) and the geometric optics method (GOM) tend to underestimate it. The absorption efficiency is not sensitive to the particle shape when the size parameter is large.

Herein a composite scheme is used that is valid for nonspherical particles with a wide range of size parameters. This scheme is a composite of Mie theory, GOM, and ADT to fit the single-scattering properties of hexagonal particles derived from the GOM for large size parameters and the finite-difference time domain technique for small size parameters. Applying this composite technique, errors in the broadband emissivity of cirrus clouds associated with conventional approaches are examined. It is shown that, when the projected area is preserved, Mie results overestimate the emissivity of cirrus clouds while, when the volume is preserved, Mie results underestimate the emissivity. Mie theory yields the best results when both projected area and volume are preserved (the relative errors are less than 10%). It is also shown that the ADT underestimates cirrus cloud emissivity. In some cases, the relative errors can be as large as 30%. The errors in the GOM are also significant and are largely a result of nonspherical particles with size parameters smaller than 40.

Corresponding author address: Prof. Qiang Fu, Atmospheric Science Program, Dept. of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada.

Email: qfu@atm.dal.ca

Abstract

This paper examines a number of commonly used methods for the calculation of the scattering and absorption properties of nonspherical ice crystals at thermal infrared wavelengths. It is found that, for randomly oriented nonspherical particles, Mie theory using equivalent ice spheres tends to overestimate the absorption efficiency while the anomalous diffraction theory (ADT) and the geometric optics method (GOM) tend to underestimate it. The absorption efficiency is not sensitive to the particle shape when the size parameter is large.

Herein a composite scheme is used that is valid for nonspherical particles with a wide range of size parameters. This scheme is a composite of Mie theory, GOM, and ADT to fit the single-scattering properties of hexagonal particles derived from the GOM for large size parameters and the finite-difference time domain technique for small size parameters. Applying this composite technique, errors in the broadband emissivity of cirrus clouds associated with conventional approaches are examined. It is shown that, when the projected area is preserved, Mie results overestimate the emissivity of cirrus clouds while, when the volume is preserved, Mie results underestimate the emissivity. Mie theory yields the best results when both projected area and volume are preserved (the relative errors are less than 10%). It is also shown that the ADT underestimates cirrus cloud emissivity. In some cases, the relative errors can be as large as 30%. The errors in the GOM are also significant and are largely a result of nonspherical particles with size parameters smaller than 40.

Corresponding author address: Prof. Qiang Fu, Atmospheric Science Program, Dept. of Oceanography, Dalhousie University, Halifax, NS B3H 4J1, Canada.

Email: qfu@atm.dal.ca

Save