Abstract

The scalable theoretical model of light pollution for ground sources is presented. The model is successfully employed for simulation of angular behavior of the spectral and integral sky radiance and∕or luminance during nighttime. There is no restriction on the number of ground-based light sources or on the spatial distribution of these sources in the vicinity of the measuring point (i.e., both distances and azimuth angles of the light sources are configurable). The model is applicable for real finite-dimensional surface sources with defined spectral and angular radiating properties contrary to frequently used point-source approximations. The influence of the atmosphere on the transmitted radiation is formulated in terms of aerosol and molecular optical properties. Altitude and spectral reflectance of a cloud layer are the main factors introduced for simulation of cloudy and∕or overcast conditions. The derived equations are translated into numerically fast code, and it is possible to repeat the entire set of calculations in real time. The parametric character of the model enables its efficient usage by illuminating engineers and∕or astronomers in the study of various light-pollution situations. Some examples of numerical runs in the form of graphical results are presented.

© 2007 Optical Society of America

Full Article  |  PDF Article

Corrections

Miroslav Kocifaj, "Light pollution model for cloudy and cloudless night skies with ground-based light sources: errata," Appl. Opt. 48, 4650-4650 (2009)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-48-23-4650

References

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    [CrossRef] [PubMed]
  2. P. Cinzano and C. D. Elvidge, "Night sky brightness at sites from DMSP-OLS satellite measurements," Mon. Notes Astron. Soc. 353, 1107-1116 (2004).
    [CrossRef]
  3. P. Cinzano, "A portable spectrophotometer for light pollution measurements," Mem. Soc. Astron. Ital. Suppl. 5, 395-398 (2004).
  4. P. Cinzano, "Modelling light pollution from searchlights," Mem. Soc. Astron. Ital. 71, 239-250 (2000).
  5. K. Sokanský, "Výskum emisí svetelného rusení vyvolaného verejným osvetlením za úcelem jeho omezení v doprave mest a obcí (The study of light pollution originated from public illumination and its relation to traffic concentration in cities and villages)," Grant MMR: WB-23-05, Fakulta elektrotechniky a informatiky, VSB-TU Ostrava Czech Republic (2005-2006).
  6. P. Cinzano, F. Falchi, and C. D. Elvidge, "The first world atlas of the artificial night sky brightness," Mon. Notes Astron. Soc. 328, 689-707 (2001).
    [CrossRef]
  7. D. X. Kerola, "Modelling artificial night-sky brightness with a polarized multiple scattering radiative transfer computer code," Mon. Notes Astron. Soc. 365, 1295-1299 (2006).
    [CrossRef]
  8. J. H. Joseph, Y. J. Kaufman, and Y. Mekler, "Urban light pollution: the effect of atmospheric aerosols on astronomical observations at night," Appl. Opt. 30, 3047-3058 (2001).
    [CrossRef]
  9. M. Kocifaj and J. Lukác, "Using the multiple scattering theory for calculation of the radiation fluxes from experimental aerosol data," J. Quant. Spectrosc. Radiat. Transfer 60, 933-942 (1998).
    [CrossRef]
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  13. M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).
  14. C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
    [CrossRef]
  15. C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
    [CrossRef]
  16. O. V. Kalashnikova and I. N. Sokolik, "Modeling the radiative properties of nonspherical soil-derived mineral aerosols," J. Quant. Spectrosc. Radiat. Transfer 87, 137-166 (2004).
    [CrossRef]
  17. M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]
  23. L. M. Celnikier, "Understanding the physics of meteoritic descent," Am. J. Phys. 63, 524-535 (1995).
    [CrossRef]
  24. A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
    [CrossRef]
  25. I. N. Minin, Theory of Radiative Transfer in Planetary Atmospheres (Nauka, 1988), in Russian.
  26. R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).
  27. N. C. Hsu, "Radiative impacts from biomass burning in the presence of clouds during boreal spring in southeast Asia," Geophys. Res. Lett. 30, doi: (2003).
    [CrossRef]
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    [CrossRef]
  29. M. Kocifaj, "Scattered light in urban areas and its angular behavior influenced by complex morphology of dust-like aerosols)," Grant APVV-0112-06, Slovak Academy of Sciences, Slovak Republic (2006).

2006 (1)

D. X. Kerola, "Modelling artificial night-sky brightness with a polarized multiple scattering radiative transfer computer code," Mon. Notes Astron. Soc. 365, 1295-1299 (2006).
[CrossRef]

2004 (4)

P. Cinzano and C. D. Elvidge, "Night sky brightness at sites from DMSP-OLS satellite measurements," Mon. Notes Astron. Soc. 353, 1107-1116 (2004).
[CrossRef]

P. Cinzano, "A portable spectrophotometer for light pollution measurements," Mem. Soc. Astron. Ital. Suppl. 5, 395-398 (2004).

O. V. Kalashnikova and I. N. Sokolik, "Modeling the radiative properties of nonspherical soil-derived mineral aerosols," J. Quant. Spectrosc. Radiat. Transfer 87, 137-166 (2004).
[CrossRef]

A. Barducci, D. Guzzi, P. Marcoionni, and I. Pippi, "Algorithm for the retrieval of columnar water vapor from hyperspectral remotely sensed data," Appl. Opt. 43, 5552-5563 (2004).
[CrossRef] [PubMed]

2003 (3)

A. Barducci, P. Marcoionni, I. Pippi, and M. Poggesi, "Effects of light pollution revealed during a nocturnal aerial survey by two hyperspectral imagers," Appl. Opt. 42, 4349-4361 (2003).
[CrossRef] [PubMed]

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

N. C. Hsu, "Radiative impacts from biomass burning in the presence of clouds during boreal spring in southeast Asia," Geophys. Res. Lett. 30, doi: (2003).
[CrossRef]

2001 (4)

P. Cinzano, F. Falchi, and C. D. Elvidge, "The first world atlas of the artificial night sky brightness," Mon. Notes Astron. Soc. 328, 689-707 (2001).
[CrossRef]

J. H. Joseph, Y. J. Kaufman, and Y. Mekler, "Urban light pollution: the effect of atmospheric aerosols on astronomical observations at night," Appl. Opt. 30, 3047-3058 (2001).
[CrossRef]

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

2000 (1)

P. Cinzano, "Modelling light pollution from searchlights," Mem. Soc. Astron. Ital. 71, 239-250 (2000).

1999 (2)

W. O'Hirok and C. Gautier, "Potential biases in remotely sensed cloud properties due to the plane parallel cloud assumption employed in retrieval algorithms," in Proc. SPIE 3867, 8-16 (1999).
[CrossRef]

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

1998 (1)

M. Kocifaj and J. Lukác, "Using the multiple scattering theory for calculation of the radiation fluxes from experimental aerosol data," J. Quant. Spectrosc. Radiat. Transfer 60, 933-942 (1998).
[CrossRef]

1995 (2)

D. Lubin and P. G. Weber, "The use of cloud reflectance functions with satellite data for surface radiation budget estimation," J. Appl. Meteorol. 34, 1333-1347 (1995).
[CrossRef]

L. M. Celnikier, "Understanding the physics of meteoritic descent," Am. J. Phys. 63, 524-535 (1995).
[CrossRef]

1989 (1)

R. H. Garstang, "Night-sky brightness at observatories and sites," Astron. Soc. Pac. Pub. 101, 306-329 (1989).
[CrossRef]

1986 (1)

R. H. Garstang, "Model for artificial night-sky illumination," Astron. Soc. Pac. Pub. 98, 364-375 (1986).
[CrossRef]

Barducci, A.

Bovensmann, H.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

Braak, C. J.

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

Burrows, J. P.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

Cattani, E.

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

Celnikier, L. M.

L. M. Celnikier, "Understanding the physics of meteoritic descent," Am. J. Phys. 63, 524-535 (1995).
[CrossRef]

Cervino, M.

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

Cinzano, P.

P. Cinzano, "A portable spectrophotometer for light pollution measurements," Mem. Soc. Astron. Ital. Suppl. 5, 395-398 (2004).

P. Cinzano and C. D. Elvidge, "Night sky brightness at sites from DMSP-OLS satellite measurements," Mon. Notes Astron. Soc. 353, 1107-1116 (2004).
[CrossRef]

P. Cinzano, F. Falchi, and C. D. Elvidge, "The first world atlas of the artificial night sky brightness," Mon. Notes Astron. Soc. 328, 689-707 (2001).
[CrossRef]

P. Cinzano, "Modelling light pollution from searchlights," Mem. Soc. Astron. Ital. 71, 239-250 (2000).

Coakley, J. A.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

de Haan, J. F.

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

Dlugach, J. M.

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

Elvidge, C. D.

P. Cinzano and C. D. Elvidge, "Night sky brightness at sites from DMSP-OLS satellite measurements," Mon. Notes Astron. Soc. 353, 1107-1116 (2004).
[CrossRef]

P. Cinzano, F. Falchi, and C. D. Elvidge, "The first world atlas of the artificial night sky brightness," Mon. Notes Astron. Soc. 328, 689-707 (2001).
[CrossRef]

Falchi, F.

P. Cinzano, F. Falchi, and C. D. Elvidge, "The first world atlas of the artificial night sky brightness," Mon. Notes Astron. Soc. 328, 689-707 (2001).
[CrossRef]

Garstang, R. H.

R. H. Garstang, "Night-sky brightness at observatories and sites," Astron. Soc. Pac. Pub. 101, 306-329 (1989).
[CrossRef]

R. H. Garstang, "Model for artificial night-sky illumination," Astron. Soc. Pac. Pub. 98, 364-375 (1986).
[CrossRef]

Gautier, C.

W. O'Hirok and C. Gautier, "Potential biases in remotely sensed cloud properties due to the plane parallel cloud assumption employed in retrieval algorithms," in Proc. SPIE 3867, 8-16 (1999).
[CrossRef]

Green, R. N.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

Gushchin, G. P.

G. P. Gushchin, The Methods, Instrumentation and Results of Atmospheric Spectral Measurements (Gidrometeoizdat, 1988), in Russian.

Guzzi, D.

Guzzi, R.

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

Hinton, P. O'R.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

Hovenier, J. W.

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

Hsu, N. C.

N. C. Hsu, "Radiative impacts from biomass burning in the presence of clouds during boreal spring in southeast Asia," Geophys. Res. Lett. 30, doi: (2003).
[CrossRef]

Hu, Y.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

Joseph, J. H.

Kalashnikova, O. V.

O. V. Kalashnikova and I. N. Sokolik, "Modeling the radiative properties of nonspherical soil-derived mineral aerosols," J. Quant. Spectrosc. Radiat. Transfer 87, 137-166 (2004).
[CrossRef]

Kaufman, Y. J.

Kerola, D. X.

D. X. Kerola, "Modelling artificial night-sky brightness with a polarized multiple scattering radiative transfer computer code," Mon. Notes Astron. Soc. 365, 1295-1299 (2006).
[CrossRef]

Kocifaj, M.

M. Kocifaj and J. Lukác, "Using the multiple scattering theory for calculation of the radiation fluxes from experimental aerosol data," J. Quant. Spectrosc. Radiat. Transfer 60, 933-942 (1998).
[CrossRef]

M. Kocifaj, "Scattered light in urban areas and its angular behavior influenced by complex morphology of dust-like aerosols)," Grant APVV-0112-06, Slovak Academy of Sciences, Slovak Republic (2006).

Kokhanovsky, A. A.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Levoni, C.

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

Lubin, D.

D. Lubin and P. G. Weber, "The use of cloud reflectance functions with satellite data for surface radiation budget estimation," J. Appl. Meteorol. 34, 1333-1347 (1995).
[CrossRef]

Lukác, J.

M. Kocifaj and J. Lukác, "Using the multiple scattering theory for calculation of the radiation fluxes from experimental aerosol data," J. Quant. Spectrosc. Radiat. Transfer 60, 933-942 (1998).
[CrossRef]

Marcoionni, P.

McCartney, E. J.

E. J. McCartney, Optics of the Atmosphere (Wiley, 1977).

Mekler, Y.

Minin, I. N.

I. N. Minin, Theory of Radiative Transfer in Planetary Atmospheres (Nauka, 1988), in Russian.

Mishchenko, M. I.

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Nicolantonio, W. D.

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

O'Hirok, W.

W. O'Hirok and C. Gautier, "Potential biases in remotely sensed cloud properties due to the plane parallel cloud assumption employed in retrieval algorithms," in Proc. SPIE 3867, 8-16 (1999).
[CrossRef]

Pippi, I.

Poggesi, M.

Rozanov, V. V.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

Sokanský, K.

K. Sokanský, "Výskum emisí svetelného rusení vyvolaného verejným osvetlením za úcelem jeho omezení v doprave mest a obcí (The study of light pollution originated from public illumination and its relation to traffic concentration in cities and villages)," Grant MMR: WB-23-05, Fakulta elektrotechniky a informatiky, VSB-TU Ostrava Czech Republic (2005-2006).

Sokolik, I. N.

O. V. Kalashnikova and I. N. Sokolik, "Modeling the radiative properties of nonspherical soil-derived mineral aerosols," J. Quant. Spectrosc. Radiat. Transfer 87, 137-166 (2004).
[CrossRef]

Stowe, L. L.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

Travis, L. D.

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Van de Hulst, H. C.

H. C. Van de Hulst, Multiple Light scattering. Tables, Formulas and Applications (Academic, 1980).

Van der Mee, C. V. M.

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

Weber, P. G.

D. Lubin and P. G. Weber, "The use of cloud reflectance functions with satellite data for surface radiation budget estimation," J. Appl. Meteorol. 34, 1333-1347 (1995).
[CrossRef]

Wielicki, B. A.

R. N. Green, B. A. Wielicki, J. A. Coakley, L. L. Stowe, P. O'R. Hinton, and Y. Hu, "Clouds and the Earth's radiant energy system (CERES) algorithm theoretical basis document," CERES Inversion to Instantaneous TOA Fluxes, Release 2.2, June 2 (NASA, 1997).

Yakharova, N. T.

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

Zanovitskij, E. G.

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

Zege, E. P.

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

Am. J. Phys. (1)

L. M. Celnikier, "Understanding the physics of meteoritic descent," Am. J. Phys. 63, 524-535 (1995).
[CrossRef]

Appl. Opt. (3)

Astron. Soc. Pac. Pub. (2)

R. H. Garstang, "Model for artificial night-sky illumination," Astron. Soc. Pac. Pub. 98, 364-375 (1986).
[CrossRef]

R. H. Garstang, "Night-sky brightness at observatories and sites," Astron. Soc. Pac. Pub. 101, 306-329 (1989).
[CrossRef]

Geophys. Res. Lett. (1)

N. C. Hsu, "Radiative impacts from biomass burning in the presence of clouds during boreal spring in southeast Asia," Geophys. Res. Lett. 30, doi: (2003).
[CrossRef]

J. Appl. Meteorol. (1)

D. Lubin and P. G. Weber, "The use of cloud reflectance functions with satellite data for surface radiation budget estimation," J. Appl. Meteorol. 34, 1333-1347 (1995).
[CrossRef]

J. Geophys. Res. D (1)

A. A. Kokhanovsky, V. V. Rozanov, E. P. Zege, H. Bovensmann, and J. P. Burrows, "A semianalytical cloud retrieval algorithm using backscattered radiation in 0.4-2.4 μm spectral region," J. Geophys. Res. D 108 (D1), (2003).
[CrossRef]

J. Quant. Spectrosc. Rad. Transfer (1)

M. I. Mishchenko, J. M. Dlugach, E. G. Zanovitskij, and N. T. Yakharova, "Bidirectional reflectance of flat, optically thick particulate layers: an efficient radiative transfer solution and applications to snow and soil surfaces," J. Quant. Spectrosc. Rad. Transfer 63, 409-432 (1999).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (4)

C. J. Braak, J. F. de Haan, C. V. M. Van der Mee, J. W. Hovenier, and L. D. Travis, "Parameterized scattering matrices for small particles in planetary atmospheres," J. Quant. Spectrosc. Radiat. Transfer 69, 585-604 (2001).
[CrossRef]

C. Levoni, E. Cattani, M. Cervino, R. Guzzi, and W. D. Nicolantonio, "Effectiveness of the MS-method for computation of the intensity field reflected by a multi-layer plane parallel atmosphere," J. Quant. Spectrosc. Radiat. Transfer 69, 635-650 (2001).
[CrossRef]

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M. Kocifaj and J. Lukác, "Using the multiple scattering theory for calculation of the radiation fluxes from experimental aerosol data," J. Quant. Spectrosc. Radiat. Transfer 60, 933-942 (1998).
[CrossRef]

Mem. Soc. Astron. Ital. (1)

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P. Cinzano, "A portable spectrophotometer for light pollution measurements," Mem. Soc. Astron. Ital. Suppl. 5, 395-398 (2004).

Mon. Notes Astron. Soc. (3)

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[CrossRef]

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Other (9)

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Figures (6)

Fig. 1
Fig. 1

Geometrical setup of the light-pollution model.

Fig. 2
Fig. 2

Distribution of integral radiances under cloudless conditions. The angle along the circle represents azimuth of the sky element. The zenith angle of the element is measured from the center to the margin of the polar graph. (a) L 1 = 5   km , (b) L 1 = L 2 = 5   km , I 0 , 2 = 2 I 0 , 1 , (c) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 1   km , (d) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 3   km , (e) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 5   km .

Fig. 3
Fig. 3

Distribution of integral radiances in the case of overcast sky ( H = 1   km , ρ ¯ = 0.4 ) . The angle along the circle represents azimuth of the sky element. The zenith angle of the element is measured from the center to the margin of the polar graph. (a) L 1 = 5   km , (b) L 1 = L 2 = 5   km , I 0 , 2 = 2 I 0 , 1 , (c) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 1   km , (d) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 3   km , (e) I 0 , 2 = I 0 , 1 , L 1 = 5   km , L 2 = 5   km .

Fig. 4
Fig. 4

Distribution of integral radiances under overcast conditions ( H = 1   km , ρ ¯ = 0.7 ) . The rest description of the figure is the same as in Fig. 3.

Fig. 5
Fig. 5

Distribution of integral radiances under overcast conditions ( H = 3   km , ρ ¯ = 0.4 ) . The rest description of the figure is the same as in Fig. 3.

Fig. 6
Fig. 6

Distribution of integral radiances under overcast conditions ( H = 3   km , ρ ¯ = 0.7 ) . The rest description of the figure is the same as in Fig. 3.

Equations (38)

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d ϕ λ , 0 = A 0 I λ ( z 0 , φ 0 ) cos z 0 d ω 0 ,
d ϕ λ , 0 ( h ) = d ϕ λ , 0 t λ ( h , z 0 ) = A 0 I λ ( z 0 ) cos z 0 d σ 0 r 0 2 t λ ( h , z 0 ) .
p λ ( ω 0 , ω ) = 1 4 π P λ ( ω 0 , ω ) ω ,
d 2 ϕ λ * ( h , z , φ ) = d ϕ λ , 0 ( h ) p λ ( ω 0 , ω ) k s c a , λ ( h ) d r 0 ,
d 2 ϕ λ ( h , z , φ ) = A 0 I λ ( z 0 ) cos z 0 t λ ( h , z 0 ) t λ ( h , z ) r 0 2 × d r k s c a , λ ( h ) [ A 4 π P λ ( ω 0 , ω ) ] d ω .
τ λ ( h 1 , h 2 ) = h 1 h 2 k e x t , λ ( h ) d h ,
k e x t , λ ( h ) = k e x t , λ ( M ) ( h ) + k e x t , λ ( A ) ( h ) .
τ λ ( M ) ( 0 , h ) = 0 h k e x t , λ ( M ) ( h ) d h ,
τ λ ( A ) ( 0 , h ) = 0 h k e x t , λ ( A ) ( h ) d h .
t λ ( h , z 0 ) = exp { M λ ( M ) ( z 0 ) τ λ ( M ) ( 0 , h ) M λ ( A ) ( z 0 ) τ λ ( A ) ( 0 , h ) } ,
t λ ( h , z ) = exp { M λ ( M ) ( z ) τ λ ( M ) ( 0 , h ) M λ ( A ) ( z ) τ λ ( A ) ( 0 , h ) } ,
cos z 0 ( h , z , φ ) = { ( 1 + t g 2 z ) + L h × [ L h 2 t g z cos ( φ φ C ) ] } 1 / 2 .
T λ ( h , z , φ ) = t λ ( h , z ) t λ ( h , z 0 , h ) .
d 2 ϕ λ ( h , z , φ ) = A 0 I λ ( z 0 , h ) cos 3 z 0 , h T λ ( h , z , φ ) h 2 d h cos z × [ A 4 π k s c a , λ ( h ) P λ ( ω 0 , ω ) ] d ω .
k s c a , λ ( h ) P λ ( ω 0 , ω ) = k s c a , λ ( M ) ( h ) P λ ( M ) ( ω 0 , ω ) + k s c a , λ ( A ) ( h ) P λ ( A ) ( ω 0 , ω ) ,
P λ ( M ) ( ω 0 , ω ) P λ ( M ) ( ϑ ) = 3 4 ( 1 + cos 2 ϑ ) ,
P λ ( A ) ( ω 0 , ω ) P λ ( A ) ( ϑ ) = ( 1 g λ 2 ) ( 1 + g λ 2 2 g λ 2 cos ϑ ) 3 / 2
cos ϑ h = 1 2 ( L 2 h 2 cos z cos z 0 , h cos z 0 , h cos z cos z cos z 0 , h )
d 2 ϕ λ ( h , z , φ ) = A 0 A I λ ( z 0 , h ) cos 3 z 0 , h T λ ( h , z , φ ) h 2 × Γ λ ( h , z , φ ) d h cos z d ω ,
Γ λ ( h , z , φ ) = 1 4 π [ k s c a , λ ( M ) ( h ) P λ ( M ) ( ω 0 , ω ) + k s c a , λ ( A ) ( h ) P λ ( A ) ( ω 0 , ω ) ] = 1 4 π [ Ω λ ( M ) k e x t , λ ( M ) ( h ) P h ( M ) ( ω 0 , ω ) + Ω λ ( A ) k e x t , λ ( A ) ( h ) P λ ( A ) ( ω 0 , ω ) ]
d ϕ λ , 1 * ( H ) = d ϕ λ , 0 ( H ) cos z 0 , H ρ λ ( z 0 , H , z , ϑ H ) = A 0 I λ ( z 0 , H ) ρ λ ( z 0 , H , z , ϑ H ) cos 4 z 0 , H d σ 0 H 2 × t λ ( H , z 0 , H ) ,
d ϕ λ , 0 ( H , z , φ ) = A 0 I λ ( z 0 , H ) cos 4 z 0 , H cos z d σ 0 H 2 × T λ ( H , z , φ ) A ρ λ ( z 0 , H , z , ϑ H ) π r 2 ,
d ω = cos z d σ 0 cos z 0 , H r 2 ,
d ϕ λ , 0 ( H , z , φ ) = A 0 A ρ λ ( z 0 , H , z , ϑ H ) π H 2 I λ ( z 0 , H ) cos 5 z 0 , H × T λ ( H , z , φ ) d ω .
I λ ( z , φ ) = d ϕ λ , 0 ( H , z , φ ) A d ω + 1 A d ω 0 H d 2 ϕ λ ( h , z , φ ) ,
I λ ( z , φ ) = A 0 ρ λ ( z 0 , H , z , ϑ H ) π H 2 I λ ( z 0 , H ) cos 5 z 0 , H × T λ ( H , z , φ ) + A 0 cos z 0 H I λ ( z 0 , h ) cos 3 z 0 , h × T λ ( h , z , φ ) h 2 Γ λ ( h , z , φ ) d h .
I λ with   M L ( z , φ ) = I λ ( z , φ ) + I λ M L cos z 0 H Γ λ M L ( h , z , φ ) × [ t λ ( , ξ 0 ) t λ ( h , ξ 0 ) ] t λ ( h , z ) d h ,
cos ϑ M L = cos ξ 0 cos z + sin ξ 0 sin z cos α 0 .
I λ ( z , φ ) = I λ , 0 A 0 ρ λ ( z 0 , H , z , ϑ H ) π H 2 cos 4 z 0 , H B ( Q , q , z 0 , H ) × T λ ( H , z , φ ) + A 0 I λ , 0 cos z 0 H B ( Q , q , z 0 , h ) cos 2 z 0 , h × T λ ( h , z , φ ) h 2 Γ λ ( h , z , φ ) d h .
J λ ( z , φ ) = i = 1 N I λ , i ( z , φ ) .
J ( z , φ ) = i = 1 N λ 1 λ 2 I λ , i ( z , φ ) d λ .
J V ( z , φ ) = i = 1 N λ 1 λ 2 V λ I λ , i ( z , φ ) d λ .
I λ , i ( z , φ ) = I λ , 0 , i π H 2 R = 0 R i ( φ 0 ) φ 0 = 0 2 π ρ λ ( z 0 , H , i , z , ϑ H , i ) cos 4 z 0 , H , i × B ( Q i , q i , z 0 , H , i ) T λ ( H , z , φ ) sin φ 0 d φ 0 d R + I λ , 0 , i cos z 0 R i ( φ 0 ) φ 0 = 0 2 π 0 H B ( Q i , q i , z 0 , h , i ) × cos 2 z 0 , h , i T λ ( h , z , φ ) h 2 × Γ λ ( h , z , φ ) d h sin φ 0 d φ 0 d R ,
J V , i ( z , φ ) = 1 π H 2 R = 0 R i ( φ 0 ) φ 0 = 0 2 π cos 4 z 0 , H , i B ( Q i , q i , z 0 , H , i ) × { λ 1 λ 2 ρ λ ( z 0 , H , i , z , ϑ H , i ) I λ , 0 , i V λ × T λ ( H , z , φ ) d λ } sin φ 0 d φ 0 d R + 1 cos z × R = 0 R i ( φ 0 ) φ 0 = 0 2 π 0 H B ( Q i , q i , z 0 , h , i ) cos 2 z 0 , h , i h 2 × { λ 1 λ 2 I λ , 0 , i V λ T λ ( h , z , φ ) Γ λ ( h , z , φ ) d λ } × d h sin φ 0 d φ 0 d R .
t g 2 z 0 , h , i ( h , z , φ ) = t g 2 z + R 2 + L i 2 + 2 R L i cos φ 0 h 2 2 t g z h [ ( L i + R cos φ 0 ) cos ( φ φ C , i ) + R sin ( φ φ C , i ) sin φ 0 ] ,
τ λ ( A ) ( 0 , h ) = τ λ , 0 ( A ) [ 1 e γ h ] ,
T λ ( h , z , φ ) = exp { [ 1 cos z 0 , h + 1 cos z ] [ τ λ , 0 ( M ) ( e h / h 0 1 ) + τ λ , 0 ( A ) ( e γ h 1 ) ] } ,
Γ λ ( h , z , φ ) = 1 4 π [ Ω λ ( M ) P λ ( M ) ( ϑ ) τ λ , 0 ( M ) h 0 e h / h 0 + Ω λ ( A ) P λ ( A ) ( ϑ ) γ τ λ , 0 ( A ) e γ h ] .

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