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A polarized Radiative Transfer model based on successive order of scattering

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Abstract

Based on Successive Order of Scattering approach, a full Vector Radiative Transfer model (SOSVRT) for vertically inhomogeneous plane-parallel media has been developed. To overcome the computational burdens of convergence, a simple approximation technique by truncating scattering orders with a geometric series is used to reduce computational time. Analytical Fourier decomposition of phase matrix with three symmetry relationships and two mutual inverse operators have been implemented to further improve the computational efficiency. To improve the accuracy, a post-processing procedure is implemented to accurately interpolate the Stokes vector at arbitrary angles. Comparisons with the benchmarks for an atmosphere of randomly orientated oblate spheroids show excellent agreement for each Stokes parameter (within 0.1%). SOSVRT has been tested for different atmospheric condition against RT3, which is based on doubling-adding method, and the results prove that SOSVRT is accurate and much more efficient in vector radiative transfer modeling, especially for optical thin atmosphere, which is the most common case in polarized radiative transfer simulations. SOSVRT is written in Fortran 90 and the code is freely accessible by contacting the author.

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References

  • Bréon, F. M., and S. Colzy, 2000: Global distribution of cloud droplet effective radius from POLDER polarization measurements. Geophys. Res. Lett., 27(24), 4065–4068.

    Article  Google Scholar 

  • Bréon, F. M., and D. M. Boucher, 2005: A comparison of cloud droplet radii measured from space. IEEE Trans Geosc. Rem. Sens., 43, 1796–1805

    Article  Google Scholar 

  • Charles, N., and G. W. Kattawar, 1994: Effect of volume-scattering function on the errors induced when polarization is neglected in radiance calculations in an atmosphere-ocean system. Appl. Opt., 32, 4610–4617.

    Google Scholar 

  • Chowdhary, J., B. Cairns, M. Mishchenko, and L. Travis, 2001: Retrieval of aerosol properties over the ocean using multispectral and multiangle photopolarimetric measurements from the Research Scanning Polarimeter. Geophys. Res. Lett., 28, 243–246.

    Article  Google Scholar 

  • De Haan, J. F., P. B. Bosma, and J. W. Hovenier, 1987: The adding method for multiple scattering computations of polarized light. Astronomy and Astrophysics, 183, 371–391.

    Google Scholar 

  • Deuzé, J. L, P. Goloub, M. Herman, A. Marchand, G. Perry, S. Susana, and D. Tanre, 2000: Estimate of the aerosol properties over the ocean with POLDER. J. Geophys. Res., 105, 15329–15346.

    Article  Google Scholar 

  • Deuzé, J. L., and Coauthors, 2001: Remote sensing of aerosols over land surfaces from POLDER-ADEOS-1 polarized measurements. J. Geophys. Res., 106, 4913–4926.

    Article  Google Scholar 

  • Duan, M., and D. R. Lü, 2007: Simultaneously retrieving aerosol optical depth and surface albedo over land from polder’s multi-angle polarized measurements: I, theory and simulations. Chinese J. Atmos. Sci., 31, 757–765. (in Chinese)

    Google Scholar 

  • Duan, M., and D. R. Lü, 2008: Simultaneously retrieving aerosol optical depth and surface albedo over land from polder’s multi-angle polarized measurements: II, a Case Study. Chinese J. Atmos. Sci., 32, 27–35. (in Chinese)

    Google Scholar 

  • Evans, K. F., 1998: The spherical harmonic discrete ordinate method for three-dimensional atmospheric radiative transfer. J. Atmos. Sci., 55, 429–446.

    Article  Google Scholar 

  • Evans, K. F., and G. L. Stephens, 1991: A new polarized atmospheric radiative transfer model. Journal of Quantitative Spectroscopy and Radiative Transfer, 46(5), 413–423.

    Article  Google Scholar 

  • Fan, X. H., G. Philippe, J. L. Deuzé, H. Chen, W. Zhang, D. Tanré, and Z. Li, 2008: Evaluation of PARASOL aerosol retrieval over North East Asia. Remote Sensing of Environment, 112(3), 697–707.

    Article  Google Scholar 

  • Goloub, P., and O. Arino, 2000: Verification of the consistency of POLDER aerosol index over land with ATSR-2/ERS-2 fire product. Geophys. Res. Lett., 27(6), 899–902.

    Article  Google Scholar 

  • Hansen, J. E., and L. D. Travis, 1974: Light scattering in planetary atmospheres. Space Science Reviews, 16, 527–610.

    Article  Google Scholar 

  • Hansen, J. E., 1971: Multiple scattering of polarized light in planetary atmospheres. Part II. Sunlight reflected by terrestrial water clouds. J. Atmos. Sci., 28, 1400–1426.

    Article  Google Scholar 

  • Kattawar, G. W., and G. N. Plass, 1968: Radiance and polarization of multiple scattered light from haze and clouds. Appl. Opt., 7, 1519–1527.

    Article  Google Scholar 

  • Kotchenova, S. Y., E. F. Vermote, R. Matarrese, and F. J. Klemm, 2006: Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data. Part I: Path radiance. Appl. Opt., 45, 6762–6774.

    Article  Google Scholar 

  • Kuik, F., J. F. De Haan, and J. W. Hovenier, 1992: Benchmark results for single scattering by spheroids. Journal of Quantitative Spectroscopy and Radiative Transfer, 47(6), 477–489.

    Article  Google Scholar 

  • Kuščer, I., and M. Ribari 1959: Matrix formalism in the theory of diffusion of light. Opt. Acta., 6, 42–51.

    Google Scholar 

  • Lacis, A. A., J. Chowdhary, M. I. Mishchenko, B. Cairns, 1998: Modeling errors in diffuse-sky radiation: vector versus scalar treatment. J. Geophys. Res., 25, 135–138.

    Google Scholar 

  • Levy, R. C., L. A. Remer, and Y. J. Kaufman, 2004: Effects of neglecting polarization on the MODIS aerosol retrieval over land. IEEE Geosci. Remote Sens., 42(11), 2576–2583.

    Article  Google Scholar 

  • Li, Z. Q., and Coauthors, 2009: Improvements for ground-based remote sensing of atmospheric aerosol properties by additional polarimetric measurements. Journal of Quantitative Spectroscopy and Radiative Transfer, 110, 1954–1961

    Article  Google Scholar 

  • Min, Q. L., and M. Z. Duan, 2004: A successive order of scattering model for solving vector radiative transfer in the atmosphere. Journal of Quantitative Spectroscopy and Radiative Transfer, 87, 243–259.

    Article  Google Scholar 

  • Mishchenko, M. I., 1990: The fast invariant imbedding method for polarized light: computational aspects and numerical results for rayleigh scattering. Journal of Quantitative Spectroscopy and Radiative Transfer, 43, 163–171.

    Article  Google Scholar 

  • Mishchenko, M. I., and L. D. Travis, 1997: Satellite retrieval of aerosol properties over the ocean using polarization as well as intensity of reflected sunlight. J. Geophys. Res., 102, 16989–17013.

    Article  Google Scholar 

  • Mishchenko, M. I., A. A. Lacis, L. D. Travis, 1994: Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres. Journal of Quantitative Spectroscopy and Radiative Transfer, 51, 491–510.

    Article  Google Scholar 

  • Mishchenko, M. I., and Coauthors, 2007: Accurate monitoring of terrestrial aerosols and total solar irradiance: introducing the Glory Mission. Bull. Amer. Meteorol. Soc., 88, 677–691.

    Article  Google Scholar 

  • Natraj, V., R. Spurr, H. Boesch, Y. Jiang, Y. Yung, 2007: Evaluation of errors in neglecting polarization in the forward modeling of O2 A band measurements from space, with relevance to CO2 column retrieval from polarization sensitive instruments. Journal of Quantitative Spectroscopy and Radiative Transfer, 103, 245–259.

    Article  Google Scholar 

  • Oikarinen, L., 2001: Polarization of light in UV-visible limb radiance measurements. J. Geophys. Res., 106, 1533–1544.

    Article  Google Scholar 

  • Roberti, L., and C. Kummerow, 1999: Monte Carlo calculations of polarized microwave radiation emerging from cloud structures. J. Geophy. Res., 104, 2093–2104.

    Article  Google Scholar 

  • Schulz, F. M., K. Stamnes, and F. Weng, 1999: VDISORT: An improved and generalized discrete ordinate radiative transfer model for polarized (vector) radiative transfer. Journal of Quantitative Spectroscopy and Radiative Transfer, 61(1), 105–122.

    Article  Google Scholar 

  • Siewert, C. E., 1982: On The phase matrix basic to the scattering of polarizated light. Astronomy and Astrophysics, 109, 195–200.

    Google Scholar 

  • Siewert, C. E., 2000: A discrete-ordinates solution for radiative-transfer models that include polarization effects. Journal of Quantitative Spectroscopy and Radiative Transfer, 64, 227–254.

    Article  Google Scholar 

  • Stam, D. M., and J. W. Hovenier, 2005: Errors in calculated planetary phase functions and albedos due to neglecting polarization. Astronomy and Astrophysics, 444(1), 275–286.

    Article  Google Scholar 

  • Vermeulen, A., C. Devaux, and M. Herman, 2000: Retrieval of the scattering and microphysical properties of aerosols from ground based optical measurements including polarization. 1: Method. Appl. Opt., 39, 6207–6220.

    Article  Google Scholar 

  • Wauben, W. M., J. W. Hovenier, 1992: Polarized radiation of an atmosphere containing randomly-oriented spheroids. Journal of Quantitative Spectroscopy and Radiative Transfer, 47, 491–504.

    Article  Google Scholar 

  • Weng, F., 1992: A multi-layer discrete-ordinate method for vector radiative transfer in a vertically-inhomogeneous, emitting and scattering atmosphere-I. theory. Journal of Quantitative Spectroscopy and Radiative Transfer, 47, 19–33.

    Article  Google Scholar 

  • Wu, B. Y., and D. R. Lü, 1989: Simulation of twilights after El chic eruption with the Monte-Carlo method. Chinese J. Atmos. Sci., 13, 204–213. (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Key Laboratory for Middle Atmosphere and Global Environment Observation, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    Minzheng Duan  (段民征) & Daren Lü  (吕达仁)

  2. Atmospheric Sciences Research Center, State University of New York, Albany, NY, 12203, USA

    Qilong Min

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  1. Minzheng Duan  (段民征)
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  2. Qilong Min
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  3. Daren Lü  (吕达仁)
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Correspondence to Minzheng Duan  (段民征).

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Duan, M., Min, Q. & Lü, D. A polarized Radiative Transfer model based on successive order of scattering. Adv. Atmos. Sci. 27, 891–900 (2010). https://doi.org/10.1007/s00376-009-9049-8

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  • DOI: https://doi.org/10.1007/s00376-009-9049-8

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