Abstract

<p>A model of a clear atmosphere is presented based upon two assumptions: (1) the point-function equilibrium radiance for a given path of sight does not change with altitude; (2) there is no absorption. As a result of these assumptions, the equation of transfer can be integrated. The path radiance for any slant path becomes a function of the equilibrium radiance and the beam transmittance of that path. In addition, the equilibrium radiance is a function of the scalar irradiance from the sun, sky, and earth and the proportional directional scattering coefficient for ground level. Sky radiances, and path radiances through the atmosphere for both upward and downward paths are determined by four parameters; the proportional directional scattering function for ground level, the total vertical beam transmittance of the atmosphere, the scalar albedo, and the solar zenith angle.</p><p>There is evidence that the real atmosphere does on some days conform to the above two assumptions to a useful extent for the visible portion of the spectrum.</p>

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  1. S. Q. Duntley, J. Opt. Soc. Am. 38, 181 (1948).
  2. S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage. Summary Tech. Rept. of Div. 16, NDRC (Columbia University Press, New York, 1946), Vol. 2, p. 20.
  3. W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Canada, 1952), p. 64–68.
  4. S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957), Eq. (10).
  5. The path radiance for the upward path between altitude zt and z is found from the experimental data by use of the relation Nr* (z,θ,ø) = N* (z,θ,ø) -N* (zt,θ,ø)Tr (z,θ). For upward-looking paths of sight N* (z,θ,ø) is the sky radiance at altitude z.
  6. E. O. Hulburt, J. Opt. Soc. Am. 31, 474 (1941).
  7. G. I. Pokrowski, Z. Physik 34, 49, 496 (1925); 53, 67 (1926); Z. Physik. 30, 697 (1929).
  8. R. W. Kittler, in Proceedings of the CIE International Conference on Sunlighting, April 1965 at Newcastle-upon-Tyne (Bouwcentrum, Rotterdam, 1967).
  9. R. Anthony, 3. Meteorol. 10, 60 (1953).
  10. F. E. Volz and K. Bullrich, J. Meteorol. 18, 306 (1961).
  11. R. W. Fenn, Beitr. Physik Atmosphäre 37, 71 (1964).
  12. R. Tousey and E. O. Hulburt, J. Opt. Soc. Am. 37, 78 (1947).
  13. S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950).
  14. L. Goldberg, in The Earth as a Planet, G. P. Kuiper, Ed. (University of Chicago Press, Chicago, 1954), Ch. 5.

Anthony, R.

R. Anthony, 3. Meteorol. 10, 60 (1953).

Boileau, A. R.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957), Eq. (10).

Bullrich, K.

F. E. Volz and K. Bullrich, J. Meteorol. 18, 306 (1961).

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950).

Duntley, S. Q.

S. Q. Duntley, J. Opt. Soc. Am. 38, 181 (1948).

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage. Summary Tech. Rept. of Div. 16, NDRC (Columbia University Press, New York, 1946), Vol. 2, p. 20.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957), Eq. (10).

Fenn, R. W.

R. W. Fenn, Beitr. Physik Atmosphäre 37, 71 (1964).

Goldberg, L.

L. Goldberg, in The Earth as a Planet, G. P. Kuiper, Ed. (University of Chicago Press, Chicago, 1954), Ch. 5.

Hulburt, E. O.

R. Tousey and E. O. Hulburt, J. Opt. Soc. Am. 37, 78 (1947).

E. O. Hulburt, J. Opt. Soc. Am. 31, 474 (1941).

Kittler, R. W.

R. W. Kittler, in Proceedings of the CIE International Conference on Sunlighting, April 1965 at Newcastle-upon-Tyne (Bouwcentrum, Rotterdam, 1967).

Middleton, W. E. K.

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Canada, 1952), p. 64–68.

Pokrowski, G. I.

G. I. Pokrowski, Z. Physik 34, 49, 496 (1925); 53, 67 (1926); Z. Physik. 30, 697 (1929).

Preisendorfer, R. W.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957), Eq. (10).

Tousey, R.

R. Tousey and E. O. Hulburt, J. Opt. Soc. Am. 37, 78 (1947).

Volz, F. E.

F. E. Volz and K. Bullrich, J. Meteorol. 18, 306 (1961).

Other (14)

S. Q. Duntley, J. Opt. Soc. Am. 38, 181 (1948).

S. Q. Duntley, Visibility Studies and Some Applications in the Field of Camouflage. Summary Tech. Rept. of Div. 16, NDRC (Columbia University Press, New York, 1946), Vol. 2, p. 20.

W. E. K. Middleton, Vision Through the Atmosphere (University of Toronto Press, Canada, 1952), p. 64–68.

S. Q. Duntley, A. R. Boileau, and R. W. Preisendorfer, J. Opt. Soc. Am. 47, 501 (1957), Eq. (10).

The path radiance for the upward path between altitude zt and z is found from the experimental data by use of the relation Nr* (z,θ,ø) = N* (z,θ,ø) -N* (zt,θ,ø)Tr (z,θ). For upward-looking paths of sight N* (z,θ,ø) is the sky radiance at altitude z.

E. O. Hulburt, J. Opt. Soc. Am. 31, 474 (1941).

G. I. Pokrowski, Z. Physik 34, 49, 496 (1925); 53, 67 (1926); Z. Physik. 30, 697 (1929).

R. W. Kittler, in Proceedings of the CIE International Conference on Sunlighting, April 1965 at Newcastle-upon-Tyne (Bouwcentrum, Rotterdam, 1967).

R. Anthony, 3. Meteorol. 10, 60 (1953).

F. E. Volz and K. Bullrich, J. Meteorol. 18, 306 (1961).

R. W. Fenn, Beitr. Physik Atmosphäre 37, 71 (1964).

R. Tousey and E. O. Hulburt, J. Opt. Soc. Am. 37, 78 (1947).

S. Chandrasekhar, Radiative Transfer (Clarendon Press, Oxford, England, 1950).

L. Goldberg, in The Earth as a Planet, G. P. Kuiper, Ed. (University of Chicago Press, Chicago, 1954), Ch. 5.

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