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On the Dependence of Discrete Ordinates Models for Layer Reflectance and Transmittance on Relative Optical Depth and Solar Zenith Angle

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Abstract

We investigate the effect of layer optical depth and solar zenith angle on recently developed discrete ordinates models for the diffuse reflectance and transmittance of an optically stationary atmospheric boundary layer. We start with a mathematical formulation of the atmospheric radiative transfer problems dealt with in this article, and we consider a discrete ordinates version of the governing equations. For the sake of continuity, we give a brief account of our recently developed models, and assuming steadiness with respect to the inherent optical properties, we work on the dependence of our models on two target parameters: the relative optical depth of the boundary layer and solar zenith angle. As a result, we get optimized relations for our models in terms of the target parameters. To illustrate the relevance of such relations, we present results of computer simulations using problem sets basic to solar-atmospheric science applications such as environmental remote sensing, radiation dosimetry, and solar power plants.

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References

  1. Bennartz, R., Fischer, J.: Retrieval of columnar water vapour over land from backscattered solar radiation using the medium resolution imaging spectrometer. Remote Sens. Environ. 78, 274–283 (2001)

    Article  Google Scholar 

  2. Broesamle, H., Mannstein, H., Schillings, C., Trieb, F.: Assessment of solar electricity potentials in North Africa based on satellite data and a geographic information system. Sol. Energy 70, 1–12 (2001)

    Article  Google Scholar 

  3. Chalhoub, E.S.: Discrete-ordinates solution for radiative-transfer problems. J. Quant. Spectrosc. Radiat. Transfer 76, 193–206 (2003)

    Article  Google Scholar 

  4. Chandrasekhar, S.: Radiative Transfer. Oxford University Press, London (1950)

    MATH  Google Scholar 

  5. de Abreu, M.P., Barros, R.C., Yavuz, M., Alves Filho, H., Mello, J.A.M.: Progress in spectral nodal methods applied to discrete ordinates transport problems. Prog. Nucl. Energy 33, 117–154 (1998)

    Article  Google Scholar 

  6. de Abreu, M.P.: Mixed singular-regular boundary conditions in multislab radiation transport. J. Comput. Phys. 197, 167–185 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. de Abreu, M.P.: A two-component method for solving multislab problems in radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 85, 311–336 (2004)

    Article  Google Scholar 

  8. de Abreu, M.P.: Layer-edge conditions for multislab atmospheric radiative transfer problems. J. Quant. Spectrosc. Radiat. Transfer 94, 137–149 (2005)

    Article  Google Scholar 

  9. Durisch, W., Bulgheroni, W.: Climatological investigation for solar-power stations in the Swiss Alps. Appl. Energy 64, 411–415 (1999)

    Article  Google Scholar 

  10. Fricker, H.W.: Regenerative thermal storage in atmospheric air system solar power plants. Energy 29, 871–881 (2004)

    Article  Google Scholar 

  11. Garcia, R.D.M., Siewert, C.E.: Benchmark results in radiative transfer. Transp. Theory Stat. Phys. 14, 437–483 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  12. Horneck, G., Rettberg, P., Rabbow, E., Strauch, W., Seckmeyer, G., Facius, R., Reitz, G., Strauch, K., Schott, J.U.: Biological dosimetry of solar radiation for different simulated ozone column thicknesses. J. Photochem. Photobiol. B 32, 189–196 (1996)

    Article  Google Scholar 

  13. Krzyscin, J.W., Jaroslawski, J., Sobolewski, P.S.: Effects of clouds on the surface erythemal UV-B irradiance at northern midlatitudes: estimation from the observations taken at Belsk, Poland (1999–2001). J. Atmos. Sol.-Terr. Phys. 65, 457–467 (2003)

    Article  Google Scholar 

  14. Lewis, E.E., Miller Jr., W.F.: Computational Methods of Neutron Transport. American Nuclear Society, La Grange Park (1993)

    Google Scholar 

  15. Liou, K.N.: An Introduction to Atmospheric Radiation, 2nd edn. Academic Press, New York (2002)

    Google Scholar 

  16. Liou, K.N.: Radiation and Cloud Processes in the Atmosphere: Theory, Observation and Modeling. Oxford University Press, New York (1992)

    Google Scholar 

  17. Nair, P.R., Moorthy, K.K.: Effect of physical properties of atmospheric aerosols on path radiance. Atmos. Res. 43, 139–155 (1997)

    Article  Google Scholar 

  18. Siewert, C.E.: A concise and accurate solution to Chandrasekhar’s basic problem in radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 64, 109–130 (2000)

    Article  Google Scholar 

  19. Stamnes, K., Tsay, S., Wiscombe, W., Jayaweera, K.: Numerically stable algorithm for discrete-ordinates-method radiative transfer in multiple scattering and emitting layered media. Appl. Opt. 27, 2502–2509 (1988)

    Article  Google Scholar 

  20. Thomas, G.E., Stamnes, K.: Radiative Transfer in the Atmosphere and Ocean. Cambridge University Press, New York (1999)

    Google Scholar 

  21. Utrillas, M.P., Martinez-Lozano, J.A., Cachorro, V.E., Tena, F., Hernandez, S.: Comparison of aerosol optical thickness retrieval from spectroradiometer measurements and from two radiative transfer models. Sol. Energy 68, 197–205 (2000)

    Article  Google Scholar 

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Correspondence to Marcos Pimenta de Abreu.

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de Abreu, M.P. On the Dependence of Discrete Ordinates Models for Layer Reflectance and Transmittance on Relative Optical Depth and Solar Zenith Angle. J Sci Comput 42, 23 (2010). https://doi.org/10.1007/s10915-009-9312-2

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  • DOI: https://doi.org/10.1007/s10915-009-9312-2

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