Abstract

Two methods of determining instrumental scattering for correcting aureolegraph measurements of particulate solar scattering are presented. One involves subtracting measurements made with and without an external occluding ball and the other is a modification of the Langley Plot method and involves extrapolating aureolegraph measurements collected through a large range of solar zenith angles. Examples of internal scattering correction determinations using the latter method show similar power-law dependencies on scattering, but vary by roughly a factor of 8 and suggest that changing aerosol conditions during the determinations render this method problematic. Examples of corrections of scattering profiles using the former method are presented for a range of atmospheric particulate layers from aerosols to cumulus and cirrus clouds.

© 2012 Optical Society of America

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References

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  1. F. Vilas and B. A. Smith, “Coronagraph for astronomical imaging and spectrophotometry,” Appl. Opt. 26, 664–668 (1987).
    [CrossRef]
  2. J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
    [CrossRef]
  3. M. B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580 (1939).
  4. N. T. O’Neill and J. R. Miller, “Combined solar aureole and solar beam extinction measurements. 1: calibration considerations,” Appl. Opt. 23, 3691–3696 (1984).
    [CrossRef]
  5. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
    [CrossRef]
  6. A. Ångström, “Apparent solar constant variations and their relation to the variability of atmospheric transmission,” Tellus 22, 205–218 (1970).
    [CrossRef]
  7. K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).
  8. M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
    [CrossRef]
  9. J. V. Dave, “Importance of higher order scattering in a molecular atmosphere,” J. Opt. Soc. Am. 54, 307–315 (1964).
    [CrossRef]
  10. A. Marshak and A. B. Davis, “Numerical methods,” in 3D Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis, eds. (Springer, 2005), pp 243–281.
  11. I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).
  12. D. Hestroffer and C. Magnan, “Wavelength dependency of the solar limb darkening,” Astron. Astrophys. 333, 338–342 (1984).
  13. M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).
  14. T. Nakajima, G. Tonna, R. Rao, P. Boi, Y. Kaufman, and B. Holben, “Use of sky brightness measurements from ground for remote sensing of particulate polydispersions,” Appl. Opt. 35, 2672–2686 (1996).
    [CrossRef]
  15. O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20,673–20,696 (2000).
    [CrossRef]
  16. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).
  17. J. G. DeVore, “Improved normalization of the size distribution of atmospheric particles retrieved from aureole measurements using the diffraction approximation,” J. Atmos. Ocean. Technol. 28, 1019–1027 (2011).
    [CrossRef]
  18. P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
    [CrossRef]
  19. S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

2011

J. G. DeVore, “Improved normalization of the size distribution of atmospheric particles retrieved from aureole measurements using the diffraction approximation,” J. Atmos. Ocean. Technol. 28, 1019–1027 (2011).
[CrossRef]

2009

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

2003

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

2000

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20,673–20,696 (2000).
[CrossRef]

1998

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

1996

1987

1984

N. T. O’Neill and J. R. Miller, “Combined solar aureole and solar beam extinction measurements. 1: calibration considerations,” Appl. Opt. 23, 3691–3696 (1984).
[CrossRef]

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

D. Hestroffer and C. Magnan, “Wavelength dependency of the solar limb darkening,” Astron. Astrophys. 333, 338–342 (1984).

1970

A. Ångström, “Apparent solar constant variations and their relation to the variability of atmospheric transmission,” Tellus 22, 205–218 (1970).
[CrossRef]

1964

1939

M. B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580 (1939).

Ackerman, S.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Ångström, A.

A. Ångström, “Apparent solar constant variations and their relation to the variability of atmospheric transmission,” Tellus 22, 205–218 (1970).
[CrossRef]

Atkinson, J.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Baum, B. A.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Boi, P.

Born, M.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Dave, J. V.

Davis, A. B.

A. Marshak and A. B. Davis, “Numerical methods,” in 3D Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis, eds. (Springer, 2005), pp 243–281.

DeVore, J.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

DeVore, J. G.

J. G. DeVore, “Improved normalization of the size distribution of atmospheric particles retrieved from aureole measurements using the diffraction approximation,” J. Atmos. Ocean. Technol. 28, 1019–1027 (2011).
[CrossRef]

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Dubovik, O.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20,673–20,696 (2000).
[CrossRef]

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).

Gueymard, C.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

Hestroffer, D.

D. Hestroffer and C. Magnan, “Wavelength dependency of the solar limb darkening,” Astron. Astrophys. 333, 338–342 (1984).

Heymsfield, A. J.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Holben, B.

Holben, B. N.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Hu, H.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Huang, H.-L.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Jankowiak, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Joss, P. C.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Kaufman, Y.

Kaufman, Y. J.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

King, M. D.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20,673–20,696 (2000).
[CrossRef]

Lavenu, F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

LePage, A.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Liou, K. N.

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

Lyot, M. B.

M. B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580 (1939).

Magnan, C.

D. Hestroffer and C. Magnan, “Wavelength dependency of the solar limb darkening,” Astron. Astrophys. 333, 338–342 (1984).

Marshak, A.

A. Marshak and A. B. Davis, “Numerical methods,” in 3D Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis, eds. (Springer, 2005), pp 243–281.

McClatchey, R. A.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Miller, J. R.

Nakajima, T.

Nakamima, T.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Nicolet, M.

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

O’Neill, N. T.

Pitz-Paal, R.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).

Rall, D.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Rao, R.

Rappaport, S. A.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Reagan, J. A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Reinhardt, B.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

Röger, M.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

Setzer, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Slutsker, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Smith, B. A.

Sobol, I. M.

I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).

Stair, A. T.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Tanré, D.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).

Tonna, G.

Tsay, S.-C.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).

Vilas, F.

Villanucci, D.

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

Wilbert, S.

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).

Yang, P.

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Appl. Opt.

Astron. Astrophys.

D. Hestroffer and C. Magnan, “Wavelength dependency of the solar limb darkening,” Astron. Astrophys. 333, 338–342 (1984).

J. Atmos. Ocean. Technol.

J. G. DeVore, “Improved normalization of the size distribution of atmospheric particles retrieved from aureole measurements using the diffraction approximation,” J. Atmos. Ocean. Technol. 28, 1019–1027 (2011).
[CrossRef]

J. G. DeVore, A. T. Stair, A. LePage, D. Rall, J. Atkinson, D. Villanucci, S. A. Rappaport, P. C. Joss, and R. A. McClatchey, “Retrieving properties of thin clouds from solar aureole measurements,” J. Atmos. Ocean. Technol. 26, 2531–2548 (2009).
[CrossRef]

J. Geophys. Res.

O. Dubovik and M. D. King, “A flexible inversion algorithm for retrieval of aerosol optical properties from Sun and sky radiance measurements,” J. Geophys. Res. 105, 20,673–20,696 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Quant. Spectrosc. Radiat. Transfer

P. Yang, B. A. Baum, A. J. Heymsfield, H. Hu, H.-L. Huang, S.-C. Tsay, and S. Ackerman, “Single-scattering properties of droxtals,” J. Quant. Spectrosc. Radiat. Transfer 79, 1159–1169 (2003).
[CrossRef]

Mon. Not. R. Astron. Soc.

M. B. Lyot, “A study of the solar corona and prominences without eclipses,” Mon. Not. R. Astron. Soc. 99, 580 (1939).

Planet. Space Sci.

M. Nicolet, “On the molecular scattering in the terrestrial atmosphere: an empirical formula for its calculation in the homosphere,” Planet. Space Sci. 32, 1467–1468 (1984).
[CrossRef]

Remote Sens. Environ.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanré, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakamima, F. Lavenu, I. Jankowiak, and A. Smirnov, “AERONET—a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Tellus

A. Ångström, “Apparent solar constant variations and their relation to the variability of atmospheric transmission,” Tellus 22, 205–218 (1970).
[CrossRef]

Other

K. N. Liou, An Introduction to Atmospheric Radiation, 2nd ed. (Academic, 2002).

A. Marshak and A. B. Davis, “Numerical methods,” in 3D Radiative Transfer in Cloudy Atmospheres, A. Marshak and A. B. Davis, eds. (Springer, 2005), pp 243–281.

I. M. Sobol, A Primer for the Monte Carlo Method (CRC Press, 1994).

S. Wilbert, B. Reinhardt, J. DeVore, M. Röger, R. Pitz-Paal, and C. Gueymard, “Measurement of solar radiance profiles with the Sun and Aureole Measurement System (SAM),” in Proceedings of the International SolarPACES Conference (SolarPACES, 2011).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, The Art of Scientific Computing, 2nd ed. (Cambridge, 1992).

M. Born and E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Pergamon, 1959).

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Figures (15)

Fig. 1.
Fig. 1.

Plot comparing Pray(θ) and an example of ϖPpar(θ) from the AERONET inversion at the ARM SGP site at 18.636 UT on10 January 2008, for λ=0.67μm.

Fig. 2.
Fig. 2.

Multiplicative factor to correct single-scattering radiance to multiple-scattering for Rayleigh scattering for 0.6°θ8.0° and aerosol scattering for θ=0.6°, 8.0°.

Fig. 3.
Fig. 3.

Illustration of instrument setup for ball-and-stick measurements.

Fig. 4.
Fig. 4.

Particulate optical depth measured by SAM #300 at the ARM SGP site on 8 January 2010.

Fig. 5.
Fig. 5.

Solar disk and aureole radiance profiles collected around 16.8 UT on 8 January 2010 at the ARM SGP site by SAM #300 with and without an occluding ball.

Fig. 6.
Fig. 6.

Internal scattering function calculated using Eq. (9) and the data shown in Fig. 5.

Fig. 7.
Fig. 7.

Examples of uncorrected (gray) and corrected (black) particulate scattering profiles Lpar(θ) for 8 January 2009 at 15.881 and 21.776 UT, both for τpar/μs0.15.

Fig. 8.
Fig. 8.

Plot of ϖPpar(θ) versus time for 0°θ10.63° based on the AERONET retrievals of ϖ and Ppar(θ) at the ARM SGP site on 8 January 2010 for λ=0.67μm.

Fig. 9.
Fig. 9.

Plots of SAM radiance Lsam normalized by the solar irradiance at the aureolegraph aperture Isunexp(τtot/μs) as a function of corrected column optical depth τcor for θ=1.72°, 3.94°, and 6.16° and corresponding best fits.

Fig. 10.
Fig. 10.

Plot of β(θ) as a function of θ found using the MLP method.

Fig. 11.
Fig. 11.

Internal scattering functions calculated using Eq. (14) (black diamonds, MLP method) and Eq. (9) (gray dots, BAS Method) for the 8 June 2010 ARM SGP SAM dataset.

Fig. 12.
Fig. 12.

Examples of Sint(θ) calculated using the MLP method over a period of nearly half a year at the ARM SGP site.

Fig. 13.
Fig. 13.

Examples of uncorrected (gray) and corrected (black) particulate scattering profiles Lpar(θ) for 12 February 2010 at the ARM SGP site, when aerosols were the dominant particulate.

Fig. 14.
Fig. 14.

Examples of uncorrected (gray) and corrected (black) particulate scattering profiles Lpar(θ) for 26 May 2010, at the ARM SGP site. Three thin cumulus cases (τpar/μs=1.20, 0.80, and 0.21) are compared with an aerosol case (τpar/μs=0.19).

Fig. 15.
Fig. 15.

Examples of uncorrected (gray) and corrected (black) particulate scattering profiles Lpar(θ) for 20 January 2010 at the ARM SGP site. Four thin cirrus cases are shown.

Equations (17)

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Lsam(θ,μs)=Lsca(θ,μs)+Lint(θ,μs),
Lsingle-scatter(θ,μs)=Isun(λ)exp(τtot/μs)[τparμsϖPpar(θ)4π+τrayμsPray(θ)4π],
ρray(τrayμs)1.281+0.8641(τrayμs)+0.2264(τrayμs)2.
Lsca(θ,μs)Isun(λ)exp(τtot/μs)[τparμsϖPpar(θ)4π+ρray(τray/μs)τrayμsPray(θ)4π].
Ldir(θ,μs)=Isun(λ)exp(τtot/μs)δ(θ)4π,
Lint(θ,μs)Isun(λ)exp(τtot/μs)Sint(θ),
Lsca(θ,μs)=Lsam(θ,μs)Isun(λ)exp(τtot/μs)Sint(θ),
Lpar(θ,μs)=Lsam(θ,μs)Isun(λ)exp(τtot/μs)[Sint(θ)+ρray(τray/μs)τrayμsPray(θ)4π].
Sint(θ)=Lsam(θ,μs)Locc(θ,μs)Isun(λ)exp(τtot/μs),
Lsam(θ,μs)Isun(λ)exp(τtot/μs)=[τparμsϖPpar(θ)4π+ρ(τray/μs)τrayμsPray(θ)4π]+Sint(θ).
Ssam(θ,μs)Lsam(θ,μs)Isun(λ)exp(τtot/μs)ρ(τray/μs)τrayμsPray(θ)4π.
Ssam(θ,μs)=τparμsϖPpar(θ)4π+Sint(θ),
ϖPpar(θ)ϖ0P0(θ)[1+β(θ)(tt0)],
Ssam(θ,μs)=ϖ0P0(θ)4π[1+β(θ)(tt0)](τpar(t)μs(t))+Sint(θ).
τcor(t)τpar(t)[1+β(θ)(tt0)]μs(t).
Ssam(θ,μs)=ϖ0P0(θ)4πτcor(t)+Sint(θ).
n(a)=4θ6μseτlosIsunλ3dLpar(θ)dθ,

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