Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Chandrasekhar, S., 1960: Radiative Transfer. Dover, 393 pp.

  • Coakley, J., and P. Chylek, 1975: The two-stream approximation in radiative transfer: Including the angle of the incident radiation. J. Atmos. Sci., 32 , 409–418.

    • Search Google Scholar
    • Export Citation

  • Evans, K. F., and G. L. Stephens, 1991: A new polarized atmospheric radiative transfer model. J. Quant. Spectrosc. Radiat. Transfer, 46 , 413–423.

    • Search Google Scholar
    • Export Citation

  • Haferman, J. L., 2000: Microwave scattering by precipitation. Light Scattering by Nonspherical Particles: Theory, Measurements, and Geophysical Applications, M. I. Mishchenko, J. W. Hovenier, and L. D. Travis, Eds., Academic Press, 690 pp.

    • Search Google Scholar
    • Export Citation

  • Hovenier, J. W., 1969: Symmetry relationship of scattering of polarized light in a slab of randomly oriented particles. J. Atmos. Sci., 26 , 488–499.

    • Search Google Scholar
    • Export Citation

  • Kerschgens, M., U. Pilz, and E. Raschke, 1978: A modified two-stream approximation for computations of the solar radiation budget in the cloudy atmosphere. Tellus, 30 , 429–435.

    • Search Google Scholar
    • Export Citation

  • Kummerow, C., 1993: On the accuracy of the Eddington approximation for radiative transfer in the microwave frequencies. J. Geophy. Res., 98 , 2757–2765.

    • Search Google Scholar
    • Export Citation

  • Kummerow, C., and J. A. Weinman, 1988: Determining microwave brightness temperatures from precipitating horizontally finite and vertically structured clouds. J. Geophys. Res., 93 , 3720–3728.

    • Search Google Scholar
    • Export Citation

  • Kummerow, C., R. A. Mack, and I. M. Hakkarinen, 1989: A self-consistency approach to improve microwave rainfall rate estimation from space. J. Appl. Meteor., 28 , 869–884.

    • Search Google Scholar
    • Export Citation

  • Lenoble, J., 1985: Radiative Transfer in Scattering and Absorbing Atmospheres: Standard Computational Procedures. A. Deepak, 300 pp.

  • Liou, K. N., 1980: An Introduction to Atmospheric Radiation. Academic Press, 392 pp.

  • Liu, Q., and E. Ruprecht, 1996: A radiative transfer model: Matrix operator method. Appl. Opt., 35 , 4229–4237.

  • Liu, Q., and C. Simmer, 1996: Polarization and intensity in microwave radiative transfer. Contrib. Atmos. Phys., 69 , 535–545.

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

  • Petty, G., 1994: Physical retrievals of over-ocean rain rate from multichannel microwave imagery. Part I: Theoretical characteristics of normalized polarization and scattering indices. Meteor. Atmos. Phys., 54 , 79–99.

    • Search Google Scholar
    • Export Citation

  • Prigent, C., J. R. Pardo, M. I. Mishchenko, and W. B. Rossow, 2001: Microwave polarized signatures generated within cloud systems: SSM/I observations interpreted with radiative transfer simulations. J. Geophys. Res., in press.

    • Search Google Scholar
    • Export Citation

  • Schmetz, J., 1989: Operational calibration of the METEOSAT water vapor channel by calculated radiances. Appl. Opt., 28 , 3030–3038.

    • Search Google Scholar
    • Export Citation

  • Schultz, F. M., K. Stamnes, and F. Weng, 1999: An improved and generalized discrete ordinate radiative transfer model for polarized (vector) radiative transfer computations. Quant. Spectrosc. Radiat. Transfer, 61 , 105–122.

    • Search Google Scholar
    • Export Citation

  • Simmer, C., 1994: Satellitenfernerkundung hydrologischer Parameter der Atmosphaere mit Mikrowellen. Verlag Dr. Kovac, 313 pp.

  • Tsang, L., J. A. Kong, and R. T. Shin, 1985: Theory of Microwave Remote Sensing. John Wiley and Sons, 613 pp.

  • Waterman, P. C., 1981: Matrix-exponential description of radiative transfer. J. Opt. Amer., 27 , 410–422.

  • Weng, F., 1992: A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere I: Theory. J. Quant. Spec. Radiat. Transfer, 47 , 19–33.

    • Search Google Scholar
    • Export Citation

  • Weng, F., and N. C. Grody, 2000: Retrieval of ice cloud parameters using a microwave imaging radiometer. J. Atmos. Sci., 57 , 1069–1081.

    • Search Google Scholar
    • Export Citation

  • Yueh, S., 1997: Modeling of wind direction signals in polarimetric sea surface brightness temperatures. IEEE Trans. Geosci. Remote Sens., 35 , 1400–1418.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 229 41 3
PDF Downloads 104 30 2
Article Type:
Research Article

A Microwave Polarimetric Two-Stream Radiative Transfer Model

Quanhua LiuCooperative Institute of Research in the Atmosphere, Colorado State University, Fort Collins, Colorado

Search for other papers by Quanhua Liu in
Current site
Google Scholar
PubMedClose
and
Fuzhong WengNOAA/NESDIS/Office of Research and Applications, Camp Springs, Maryland

Search for other papers by Fuzhong Weng in
Current site
Google Scholar
PubMedClose
Print Publication:
01 Aug 2002
DOI:
https://doi.org/10.1175/1520-0469(2002)059<2396:AMPTSR>2.0.CO;2
Page(s):
2396–2402
Restricted access

Abstract

The assimilation of satellite microwave measurements and the retrieval of geophysical parameters require a fast and accurate radiative transfer model. In this study, a scheme is developed to solve the vector radiative transfer equation using a polarimetric two-stream approximation. In the scheme, the integration of the phase matrix over azimuth angle is derived as an analytic form that can also be directly utilized for the general radiative transfer scheme. Each Stokes radiance component is expressed as an analytical function of atmospheric and surface optical parameters. The model is applicable for spherical and randomly oriented nonspherical scatters. The differences of brightness temperatures between the polarimetric two-stream model and the matrix operator method are less than 2 K for various frequencies.

Corresponding author address: Dr. Quanhua Liu, NOAA/NESDIS, Room 601, 5200 Auth Road, Camp Springs, MD 20746. Email: quanhua.liu@noaa.gov

Abstract

The assimilation of satellite microwave measurements and the retrieval of geophysical parameters require a fast and accurate radiative transfer model. In this study, a scheme is developed to solve the vector radiative transfer equation using a polarimetric two-stream approximation. In the scheme, the integration of the phase matrix over azimuth angle is derived as an analytic form that can also be directly utilized for the general radiative transfer scheme. Each Stokes radiance component is expressed as an analytical function of atmospheric and surface optical parameters. The model is applicable for spherical and randomly oriented nonspherical scatters. The differences of brightness temperatures between the polarimetric two-stream model and the matrix operator method are less than 2 K for various frequencies.

Corresponding author address: Dr. Quanhua Liu, NOAA/NESDIS, Room 601, 5200 Auth Road, Camp Springs, MD 20746. Email: quanhua.liu@noaa.gov

Save