• Battan, L. J., 1973: Radar Observations of the Atmosphere. The University of Chicago Press, 324 pp.

  • Coppens, D., , and Z. Haddad, 2000: Effects of raindrop size distribution variations on microwave brightness temperature calculation. J. Geophys. Res, 105 , 2448324489.

    • Search Google Scholar
    • Export Citation
  • Ferrier, B., , W. Tao, , and J. Simpson, 1995: A double-moment multiple-phase four-class bulk ice scheme. Part II: Simulations of convective storms in different large-scale environments and comparisons with other bulk parametrizations. J. Atmos. Sci, 52 , 10011033.

    • Search Google Scholar
    • Export Citation
  • Goldhirsh, J., 1975: Improved error analysis in estimation of raindrop spectra, rain rate, and liquid water content using multiple wavelength radars. IEEE. Trans. Antennas Propag, 718720.

    • Search Google Scholar
    • Export Citation
  • Goldhirsh, J., , and I. Katz, 1974: Estimation of raindrop size distribution using multiple wavelength radar systems. Radio Sci, 9 , 439446.

    • Search Google Scholar
    • Export Citation
  • Haddad, Z. S., , D. A. Short, , S. L. Durden, , E. Im, , S. Hensley, , M. B. Grable, , and R. A. Black, 1997: A new parametrization of the rain drop size distribution. IEEE Trans. Geosci. Remote Sens, 35 , 532539.

    • Search Google Scholar
    • Export Citation
  • Li, F. K., , E. Im, , S. L. Durden, , and R. Girard, 2000: Cloud Profiling Radar (CPR) for the CloudSat mission. Proc. Geoscience and Remote Sensing Symp., Vol. 6, Honolulu, HI, IEEE/IGARSS, 2546–2548.

  • Marshall, J., , and W. Palmer, 1948: The distribution of rain drops with size. J. Meteor, 5 , 165166.

  • McCumber, M., , W. Tao, , J. Simpson, , R. Penc, , and S. Soong, 1991: Comparison of ice-phase microphysical parametrization schemes using numerical simulation of tropical convection. J. Appl. Meteor, 30 , 9851004.

    • Search Google Scholar
    • Export Citation
  • Meagher, J. P., 2002: Spaceborne monitoring of cloud and rain hydrometeor size distributions. Ph.D. thesis, University of California, Los Angeles, 200 pp.

  • Meneghini, R., , T. Kozu, , H. Kumagai, , and W. C. Boncyk, 1992: A study of rain estimation methods from space using dual-wavelength radar measurements at near-nadir incidence over ocean. J. Atmos. Oceanic Technol, 9 , 364382.

    • Search Google Scholar
    • Export Citation
  • Rudin, W., 1976: Principles of Mathematical Analysis. 3d ed. McGraw-Hill, 325 pp.

  • Simpson, J., 1988: TRMM—A satellite mission to measure tropical rainfall. NASA GSFC Tech. Rep. of the Science Steering Group, 94 pp.

  • Trier, S. B., , W. C. Skamarock, , M. A. LeMone, , D. B. Parsons, , and D. P. Jorgensen, 1996: Structure and evolution of the 22 February 1993 TOGA COARE squall line: Numerical simulations. J. Atmos. Sci, 53 , 28612886.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 11 11 3
PDF Downloads 4 4 3

To What Extent Can Raindrop Size Be Determined by a Multiple-Frequency Radar?

View More View Less
  • 1 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California
© Get Permissions
Restricted access

Abstract

In this paper, an analytical treatment of the atmospheric remote sensing problem of determining the raindrop size distribution (DSD) with a spaceborne multifrequency microwave nadir-looking radar system is presented. It is typically assumed that with two radar measurements at different frequencies one ought to be able to calculate two state variables of the DSD: a bulk quantity, such as the rain rate, and a distribution shape parameter. To determine if this nonlinear problem can indeed be solved, the DSD is modeled as a Γ distribution and quadratic approximations to the corresponding radar–rain relations are used to examine the invertibility of the resulting system of equations in the case of two as well as three radar frequencies. From the investigation, it is found that for regions of DSD state space multiple solutions exist for two or even three different frequency radar measurements. This should not be surprising given the nonlinear coupled nature of the problem.

Corresponding author address: Dr. Jonathan P. Meagher, 300-243, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109-8099. Email: meagher@jpl.nasa.gov

Abstract

In this paper, an analytical treatment of the atmospheric remote sensing problem of determining the raindrop size distribution (DSD) with a spaceborne multifrequency microwave nadir-looking radar system is presented. It is typically assumed that with two radar measurements at different frequencies one ought to be able to calculate two state variables of the DSD: a bulk quantity, such as the rain rate, and a distribution shape parameter. To determine if this nonlinear problem can indeed be solved, the DSD is modeled as a Γ distribution and quadratic approximations to the corresponding radar–rain relations are used to examine the invertibility of the resulting system of equations in the case of two as well as three radar frequencies. From the investigation, it is found that for regions of DSD state space multiple solutions exist for two or even three different frequency radar measurements. This should not be surprising given the nonlinear coupled nature of the problem.

Corresponding author address: Dr. Jonathan P. Meagher, 300-243, JPL, 4800 Oak Grove Drive, Pasadena, CA 91109-8099. Email: meagher@jpl.nasa.gov

Save