Partially Coherent Backscatter in Radar Observations of Precipitation

A. R. Jameson RJH Scientific, Inc., El Cajon, California

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A. B. Kostinski Michigan Technological University, Houghton, Michigan

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Abstract

Classical radar theory only considers incoherent backscatter from precipitation. Can precipitation generate coherent scatter as well? Until now, the accepted answer has been no, because hydrometeors are distributed sparsely in space (relative to radar wavelength) so that the continuum assumption used to explain coherent scatter in clear air and clouds does not hold.

In this work, a theory for a different mechanism is presented. The apparent existence of the proposed mechanism is then illustrated in both rain and snow. A new power spectrum Z( f ), the Fourier transform of the time series of the radar backscattered reflectivities, reveals statistically significant frequencies f of periodic components that cannot be ascribed to incoherent scatter. It is shown that removing those significant fs from Z( f ) at lower frequencies greatly reduces the temporal coherency. These lower frequencies, then, are associated with the increased temporal coherency. It is also shown that these fs are also directly linked to the Doppler spectral peaks through integer multiples of one-half the radar wavelength, characteristic of Bragg scatter. Thus, the enhanced temporal coherency is directly related to the presence of coherent scatter in agreement with theory.

Moreover, the normalized backscattered power spectrum Z( f ) permits the estimation of the fractional coherent power contribution to the total power, even for an incoherent radar. Analyses of approximately 26 000 one-second Z( f ) in both rain and snow reveal that the coherent scatter is pervasive in these data. These findings present a challenge to the usual assumption that the scatter of radar waves from precipitation is always incoherent and to interpretations of backscattered power based on this assumption.

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. Email: arjatrjhsci@verizon.net

Abstract

Classical radar theory only considers incoherent backscatter from precipitation. Can precipitation generate coherent scatter as well? Until now, the accepted answer has been no, because hydrometeors are distributed sparsely in space (relative to radar wavelength) so that the continuum assumption used to explain coherent scatter in clear air and clouds does not hold.

In this work, a theory for a different mechanism is presented. The apparent existence of the proposed mechanism is then illustrated in both rain and snow. A new power spectrum Z( f ), the Fourier transform of the time series of the radar backscattered reflectivities, reveals statistically significant frequencies f of periodic components that cannot be ascribed to incoherent scatter. It is shown that removing those significant fs from Z( f ) at lower frequencies greatly reduces the temporal coherency. These lower frequencies, then, are associated with the increased temporal coherency. It is also shown that these fs are also directly linked to the Doppler spectral peaks through integer multiples of one-half the radar wavelength, characteristic of Bragg scatter. Thus, the enhanced temporal coherency is directly related to the presence of coherent scatter in agreement with theory.

Moreover, the normalized backscattered power spectrum Z( f ) permits the estimation of the fractional coherent power contribution to the total power, even for an incoherent radar. Analyses of approximately 26 000 one-second Z( f ) in both rain and snow reveal that the coherent scatter is pervasive in these data. These findings present a challenge to the usual assumption that the scatter of radar waves from precipitation is always incoherent and to interpretations of backscattered power based on this assumption.

Corresponding author address: A. R. Jameson, 5625 N. 32nd St., Arlington, VA 22207-1560. Email: arjatrjhsci@verizon.net

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  • Atlas, D., 1964: Advances in radar meteorology. Adv. Geophys., 10 , 317478.

  • Battan, L. J., 1973: Radar Observation of the Atmosphere. Techbooks, 324 pp.

  • Civil Aviation Authority of New Zealand, 2008: Wake turbulence. Civil Aviation Authority of New Zealand Rep., 16 pp. [Available online at www.caa.govt.nz/safety_info/gaps/wake_turbulence.pdf].

    • Search Google Scholar
    • Export Citation
  • Erkelens, J. S., V. K. C. Venema, H. W. J. Russchenberg, and L. P. Ligthart, 2001: Coherent scattering of microwaves by particles: Evidence from clouds and smoke. J. Atmos. Sci., 58 , 10911102.

    • Search Google Scholar
    • Export Citation
  • Evans, M., N. Hastings, and B. Peacock, 1993: Statistical Distributions. 2nd ed. John Wiley and Sons, 170 pp.

  • Gossard, E. E., and R. G. Strauch, 1983: Radar Observations of Clear Air and Clouds. Elsevier, 280 pp.

  • Ishimaru, A., 1997: Wave Propagation and Scattering in Random Media. IEEE Press, 600 pp.

  • Jameson, A. R., and A. B. Kostinski, 1996: Non-Rayleigh signal statistics caused by relative motion during measurement. J. Appl. Meteor., 35 , 18461859.

    • Search Google Scholar
    • Export Citation
  • Kelly, A. J., and M. Handelsman, 1974: Electromagnetic effects of aircraft wake-active feuillet interaction. IEEE Trans. Aerosp. Electron. Syst., 10 , 136143.

    • Search Google Scholar
    • Export Citation
  • Knight, C. A., and L. J. Miller, 1993: First radar echoes from cumulus clouds. Bull. Amer. Meteor. Soc., 74 , 179188.

  • Kolmogorov, A. N., 1941a: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers (in Russian). Dokl. Akad. Nauk SSSR, 30 , 299303.

    • Search Google Scholar
    • Export Citation
  • Kolmogorov, A. N., 1941b: Dissipation of energy in locally isotropic turbulence (in Russian). Dokl. Akad. Nauk SSSR, 32 , 1618.

  • Kostinski, A. B., and A. R. Jameson, 2000: On the spatial distribution of cloud particles. J. Atmos. Sci., 57 , 901915.

  • Lhermitte, R. M., and E. Kessler, 1966: Estimation of the average intensity of precipitation targets. Proc. 12th Conf. on Radar Meteorology, Norman, OK, Amer. Meteor. Soc., 23–27.

    • Search Google Scholar
    • Export Citation
  • Marshall, J. S., and W. Hitschfeld, 1953: Interpretation of the fluctuating echo from randomly distributed scatterers. Part I. Can. J. Phys., 31 , 962994.

    • Search Google Scholar
    • Export Citation
  • Myers, T. J., W. A. Scales, and R. E. Marshall, 1999: Determination of aircraft wake vortex radar cross section due to coherent Bragg scatter from mixed atmospheric water vapor. Radio Sci., 34 , 103111.

    • Search Google Scholar
    • Export Citation
  • Rayleigh, J. W. S., 1945: The Theory of Sound. 2nd ed. Dover, 480 pp.

  • Rice, S. O., 1945: Mathematical analysis of random noise. Bell Syst. Tech. J., 24 , 46156.

  • Rogers, R. R., and W. O. J. Brown, 1997: Radar observations of a major industrial fire. Bull. Amer. Meteor. Soc., 78 , 803814.

  • Rughaven, S., 2003: Radar Meteorology. Springer, 564 pp.

  • Siegert, A. J. F., and H. Goldstein, 1990: Coherent and incoherent scattering from assemblies of scatterers. Propagation of Short Radio Waves, IEE Electromagnetic Wave Series, Vol. 24, Institution of Electrical Engineers, 699–706.

    • Search Google Scholar
    • Export Citation
  • Squires, K. D., and J. K. Eaton, 1991: Preferential concentration of particles by turbulence. Phys. Fluids, 3 , 11691178.

  • Tatarskii, V. I., 1961: Wave Propagation in a Turbulent Medium. McGraw-Hill, 285 pp.

  • Wolf, E., 2007: Introduction to the Theory of Coherence and Polarization of Light. Cambridge University Press, 236 pp.

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