• Andsager, K., K. V. Beard, and N. F. Laird, 1999: Laboratory measurements of axis ratios for large raindrops. J. Atmos. Sci.,56, 2673–2683.

  • Arfken, G., 1970: Mathematical Methods for Physicists. 2d ed. Academic Press, 815 pp.

  • Aydin, K., and Y.-M. Lure, 1991: Millimeter wave scattering and propagation in rain: A computational study at 94 and 140 GHz for oblate spheroidal and spherical raindrops. IEEE Trans. Geosci. Remote Sens.,29, 593–601.

  • Beard, K. V., and C. Chuang, 1987: A new model for the equilibrium shape of raindrops. J. Atmos. Sci.,44, 1509–1524.

  • ——, and R. J. Kubesh, 1991: Laboratory measurements of small raindrop distortion. Part II: Oscillation frequencies and modes. J. Atmos. Sci.,48, 2245–2264.

  • ——, H. T. Ochs III, and R. J. Kubesh, 1989: Natural oscillations of small raindrops. Nature,342, 408–410.

  • Bohren, C. F., and D. R. Huffman, 1983: Absorption and Scattering of Light by Small Particles. John Wiley & Sons, 530 pp.

  • Cataneo, R., and G. E. Stout, 1968: Raindrop-size distributions in humid continental climates, and associated rainfall rate-radar reflectivity relationships. J. Appl. Meteor.,7, 901–907.

  • Chandrasekar, V., W. A. Cooper, and V. N. Bringi, 1988: Axis ratios and oscillations of raindrops. J. Atmos. Sci.,45, 1323–1333.

  • Chuang, C. C., and K. V. Beard, 1990: A numerical model for the equilibrium shape of electrified raindrops. J. Atmos. Sci.,47, 1374–1389.

  • Feingold, G., and Z. Levin, 1986: The lognormal fit to raindrop spectra from frontal convective clouds in Israel. J. Climate Appl. Meteor.,25, 1346–1363.

  • Glantschnig, W. J., and S.-H. Chen, 1981: Light scattering from water droplets in the geometrical optics approximation. Appl. Opt.,20, 2499–2509.

  • Johnson, D. B., and K. V. Beard, 1984: Oscillation energies of colliding raindrops. J. Atmos. Sci.,41, 1235–1241.

  • Joss, J., and E. G. Gori, 1978: Shapes of raindrop size distributions. J. Appl. Meteor.,17, 1054–1061.

  • Kubesh, R. J., and K. V. Beard, 1993: Laboratory measurements of spontaneous oscillations for moderate-size raindrops. J. Atmos. Sci.,50, 1089–1098.

  • Macke, A., and M. Großklaus, 1998: Light scattering by nonspherical raindrops: Implications for lidar remote sensing of rainrates. J. Quant. Spectrosc. Radiat. Transfer,60, 355–363.

  • Marshall, J. S., and W. McK. Palmer, 1948: The distribution of raindrops with size. J. Meteor.,5, 165–166.

  • Muinonen, K., 1996: Light scattering by Gaussian random particles. Earth, Moon, and Planets,72, 339–342.

  • ——, T. Nousiainen, P. Fast, K. Lumme, and J. I. Peltoniemi, 1996:Light scattering by Gaussian random particles: Ray optics approximation. J. Quant. Spectrosc. Radiat. Transfer,55, 577–601.

  • Nousiainen, T., and K. Muinonen, 1999: Light scattering by Gaussian, randomly oscillating raindrops. J. Quant. Spectrosc. Radiat. Transfer,63, 643–666.

  • Sauvageot, H., and J.-P. Lacaux, 1995: The shape of averaged drop size distributions. J. Atmos. Sci.,52, 1070–1083.

  • Stow, C. D., S. G. Bradley, K. Paulson, and L. Couper, 1991: The simultaneous measurement of rainfall intensity, drop-size distribution, and the scattering of visible light. J. Appl. Meteor.,30, 1422–1435.

  • Tokay, A., and K. V. Beard, 1996: A field study of raindrop oscillations. Part I: Observation of size spectra and evaluation of oscillation causes. J. Appl. Meteor.,35, 1671–1687.

  • Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor.,22, 1764–1775.

  • Willis, P. T., 1984: Functional fits to some observed drop size distributions and parameterization of rain. J. Atmos. Sci.,41, 1648–1661.

  • ——, and P. Tattelman, 1989: Drop-size distributions associated with intense rainfall. J. Appl. Meteor.,28, 3–15.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 295 69 4
PDF Downloads 182 58 3

Scattering of Light by Raindrops with Single-Mode Oscillations

Timo NousiainenDepartment of Meteorology, University of Helsinki, Helsinki, Finland

Search for other papers by Timo Nousiainen in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

Light scattering by oscillating raindrops is studied theoretically in the ray optics approximation. The effects of oscillation mode, amplitude, time dependence, drop size, and size distribution on the light scattering are studied. The oscillations are modeled as individual spherical harmonics modes with sinusoidal time dependence, and an example size-dependent oscillation scheme is created for size distribution simulations. Marshall–Palmer (M–P) and gamma size distributions are used to represent continuous frontal rain and convective showers, respectively. Lognormal distribution is used in studying the effect of the width of the distribution on light scattering. It is shown that the introduction of studied oscillation modes (2, 0), (2, 1), and (3, 1) change the scattering properties of equilibrium raindrops differently and are thus, in principle, recognizable by light-scattering measurements. Further, individual oscillation modes introduce new features in the scattering pattern, unlike the Gaussian random oscillations that tend to smooth it. Even a population of differently oscillating drops causes relatively little smoothing as long as each drop has only one oscillation mode. The M–P and gamma size distributions, although remarkably different, smooth the scattering patterns in a very similar manner, making the derivation of raindrop size distribution as an inverse light-scattering problem very difficult. The time dependence of scattering is found to be quite strong. The location of the so-called 90° rainbow depends strongly on the drop size. As a result, realistic M–P and gamma size distributions effectively smooth away the bow, whereas it is clearly seen in narrow lognormal distributions with drop size centered around d = 2.0 mm. As instantaneous size distributions are observed to be more monodisperse than the averaged distributions, it is thus possible that in some rare conditions this novel feature could be seen in nature.

Corresponding author address: Dr. Timo Nousiainen, Department of Meteorology, University of Helsinki, P.O. Box 4 (Yliopistonkatu 3), SF-00014 Helsinki, Finland.

Email: timo.nousiainen@helsinki.fi

Abstract

Light scattering by oscillating raindrops is studied theoretically in the ray optics approximation. The effects of oscillation mode, amplitude, time dependence, drop size, and size distribution on the light scattering are studied. The oscillations are modeled as individual spherical harmonics modes with sinusoidal time dependence, and an example size-dependent oscillation scheme is created for size distribution simulations. Marshall–Palmer (M–P) and gamma size distributions are used to represent continuous frontal rain and convective showers, respectively. Lognormal distribution is used in studying the effect of the width of the distribution on light scattering. It is shown that the introduction of studied oscillation modes (2, 0), (2, 1), and (3, 1) change the scattering properties of equilibrium raindrops differently and are thus, in principle, recognizable by light-scattering measurements. Further, individual oscillation modes introduce new features in the scattering pattern, unlike the Gaussian random oscillations that tend to smooth it. Even a population of differently oscillating drops causes relatively little smoothing as long as each drop has only one oscillation mode. The M–P and gamma size distributions, although remarkably different, smooth the scattering patterns in a very similar manner, making the derivation of raindrop size distribution as an inverse light-scattering problem very difficult. The time dependence of scattering is found to be quite strong. The location of the so-called 90° rainbow depends strongly on the drop size. As a result, realistic M–P and gamma size distributions effectively smooth away the bow, whereas it is clearly seen in narrow lognormal distributions with drop size centered around d = 2.0 mm. As instantaneous size distributions are observed to be more monodisperse than the averaged distributions, it is thus possible that in some rare conditions this novel feature could be seen in nature.

Corresponding author address: Dr. Timo Nousiainen, Department of Meteorology, University of Helsinki, P.O. Box 4 (Yliopistonkatu 3), SF-00014 Helsinki, Finland.

Email: timo.nousiainen@helsinki.fi

Save