Abstract

Series of measurements of the distribution of radiance over a clear sky made from locations at approximately 1000, 6000, and 14 000 ft elevation are reported. A theoretical relation is shown to correctly predict the observed variation in radiance with elevation angle in the 2–40 μ wavelength region, where radiation from the sky is mainly due to thermal emission by the atmosphere. In the 0.6–2 μ region where the radiation is mainly scattered sunlight the distribution is related to that which was observed simultaneously in the visible but forward scattering is relatively more important in the near infrared and the relative intensities in the two regions are not constant.

© 1960 Optical Society of America

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References

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  1. A summary of the work prior to 1951 is given by O. Lönnqvist, Tellus 3, 148 (1951).
    [CrossRef]
  2. J. Strong, J. Franklin Inst. 232, 1 (1941).
    [CrossRef]
  3. F. A. Brooks, J. Meteorol. 9, 41 (1952).
    [CrossRef]
  4. Sloan, Shaw, and Williams, J. Opt. Soc. Am. 46, 543 (1956).
    [CrossRef]
  5. Bennett, Bennett, and Nagel, (September, 1959).
  6. Sloan, Shaw, and Williams, J. Opt. Soc. Am. 45, 455 (1955).
    [CrossRef]
  7. D. E. Burch and J. H. Shaw, J. Opt. Soc. Am. 47, 227 (1957).
    [CrossRef]
  8. R. A. Oetjen and E. E. Bell, , ARDC Project No. 5-(4-4056) (1955).
  9. R. W. Astheimer and E. M. Wormser, J. Opt. Soc. Am. 49, 179 (1959).
    [CrossRef]
  10. A. LaRocca and G. Zissis, Rev. Sci. Instr. 30, 200 (1959).
    [CrossRef]
  11. R. N. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
    [CrossRef]
  12. Howard, Burch, and Williams, J. Opt. Soc. Am. 46, 334 (1956).
    [CrossRef]
  13. W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University, Blue Hill Meteorological Observatory, Milton, Massachusetts, 1942), p. 93.
  14. D. Brunt, Quart. J. Roy. Meteorol. Soc. 58, 389 (1932).
    [CrossRef]
  15. J. R. Goss and F. A. Brooks, J. Meteorol. 13, 482 (1956).
    [CrossRef]
  16. See reference 13, p. 42.
  17. W. H. Dines and L. H. G. Dines, Mem. Roy. Meteorol. Soc. 2, 1 (1927).
  18. A. Adel, Phys. Rev. 76, 446 (1949).
    [CrossRef]
  19. H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 422.
  20. H. P. Gush and A. V. Jones, J. Atmos. Terrestrial Phys. 7, 285 (1955).
    [CrossRef]
  21. E. O. Hulburt, J. Opt. Soc. Am. 31, 467 (1941).
    [CrossRef]
  22. E. V. Ashburn, (August, 1954).

1959 (2)

R. W. Astheimer and E. M. Wormser, J. Opt. Soc. Am. 49, 179 (1959).
[CrossRef]

A. LaRocca and G. Zissis, Rev. Sci. Instr. 30, 200 (1959).
[CrossRef]

1957 (1)

1956 (3)

1955 (2)

H. P. Gush and A. V. Jones, J. Atmos. Terrestrial Phys. 7, 285 (1955).
[CrossRef]

Sloan, Shaw, and Williams, J. Opt. Soc. Am. 45, 455 (1955).
[CrossRef]

1952 (2)

F. A. Brooks, J. Meteorol. 9, 41 (1952).
[CrossRef]

R. N. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

1951 (1)

A summary of the work prior to 1951 is given by O. Lönnqvist, Tellus 3, 148 (1951).
[CrossRef]

1949 (1)

A. Adel, Phys. Rev. 76, 446 (1949).
[CrossRef]

1941 (2)

E. O. Hulburt, J. Opt. Soc. Am. 31, 467 (1941).
[CrossRef]

J. Strong, J. Franklin Inst. 232, 1 (1941).
[CrossRef]

1932 (1)

D. Brunt, Quart. J. Roy. Meteorol. Soc. 58, 389 (1932).
[CrossRef]

1927 (1)

W. H. Dines and L. H. G. Dines, Mem. Roy. Meteorol. Soc. 2, 1 (1927).

Adel, A.

A. Adel, Phys. Rev. 76, 446 (1949).
[CrossRef]

Ashburn, E. V.

E. V. Ashburn, (August, 1954).

Astheimer, R. W.

Bell, E. E.

R. A. Oetjen and E. E. Bell, , ARDC Project No. 5-(4-4056) (1955).

Bennett,

Bennett, Bennett, and Nagel, (September, 1959).

Bennett, Bennett, and Nagel, (September, 1959).

Brooks, F. A.

J. R. Goss and F. A. Brooks, J. Meteorol. 13, 482 (1956).
[CrossRef]

F. A. Brooks, J. Meteorol. 9, 41 (1952).
[CrossRef]

Brunt, D.

D. Brunt, Quart. J. Roy. Meteorol. Soc. 58, 389 (1932).
[CrossRef]

Burch,

Burch, D. E.

Dines, L. H. G.

W. H. Dines and L. H. G. Dines, Mem. Roy. Meteorol. Soc. 2, 1 (1927).

Dines, W. H.

W. H. Dines and L. H. G. Dines, Mem. Roy. Meteorol. Soc. 2, 1 (1927).

Elsasser, W. M.

W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University, Blue Hill Meteorological Observatory, Milton, Massachusetts, 1942), p. 93.

Goody, R. N.

R. N. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

Goss, J. R.

J. R. Goss and F. A. Brooks, J. Meteorol. 13, 482 (1956).
[CrossRef]

Gush, H. P.

H. P. Gush and A. V. Jones, J. Atmos. Terrestrial Phys. 7, 285 (1955).
[CrossRef]

Howard,

Hulburt, E. O.

Jones, A. V.

H. P. Gush and A. V. Jones, J. Atmos. Terrestrial Phys. 7, 285 (1955).
[CrossRef]

LaRocca, A.

A. LaRocca and G. Zissis, Rev. Sci. Instr. 30, 200 (1959).
[CrossRef]

Lönnqvist, O.

A summary of the work prior to 1951 is given by O. Lönnqvist, Tellus 3, 148 (1951).
[CrossRef]

Nagel,

Bennett, Bennett, and Nagel, (September, 1959).

Oetjen, R. A.

R. A. Oetjen and E. E. Bell, , ARDC Project No. 5-(4-4056) (1955).

Shaw,

Shaw, J. H.

Sloan,

Strong, J.

J. Strong, J. Franklin Inst. 232, 1 (1941).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 422.

Williams,

Wormser, E. M.

Zissis, G.

A. LaRocca and G. Zissis, Rev. Sci. Instr. 30, 200 (1959).
[CrossRef]

J. Atmos. Terrestrial Phys. (1)

H. P. Gush and A. V. Jones, J. Atmos. Terrestrial Phys. 7, 285 (1955).
[CrossRef]

J. Franklin Inst. (1)

J. Strong, J. Franklin Inst. 232, 1 (1941).
[CrossRef]

J. Meteorol. (2)

F. A. Brooks, J. Meteorol. 9, 41 (1952).
[CrossRef]

J. R. Goss and F. A. Brooks, J. Meteorol. 13, 482 (1956).
[CrossRef]

J. Opt. Soc. Am. (6)

Mem. Roy. Meteorol. Soc. (1)

W. H. Dines and L. H. G. Dines, Mem. Roy. Meteorol. Soc. 2, 1 (1927).

Phys. Rev. (1)

A. Adel, Phys. Rev. 76, 446 (1949).
[CrossRef]

Quart. J. Roy. Meteorol. Soc. (2)

R. N. Goody, Quart. J. Roy. Meteorol. Soc. 78, 165 (1952).
[CrossRef]

D. Brunt, Quart. J. Roy. Meteorol. Soc. 58, 389 (1932).
[CrossRef]

Rev. Sci. Instr. (1)

A. LaRocca and G. Zissis, Rev. Sci. Instr. 30, 200 (1959).
[CrossRef]

Tellus (1)

A summary of the work prior to 1951 is given by O. Lönnqvist, Tellus 3, 148 (1951).
[CrossRef]

Other (6)

W. M. Elsasser, Heat Transfer by Infrared Radiation in the Atmosphere (Harvard University, Blue Hill Meteorological Observatory, Milton, Massachusetts, 1942), p. 93.

H. C. van de Hulst, Light Scattering by Small Particles (John Wiley & Sons, Inc., New York, 1957), p. 422.

See reference 13, p. 42.

R. A. Oetjen and E. E. Bell, , ARDC Project No. 5-(4-4056) (1955).

Bennett, Bennett, and Nagel, (September, 1959).

E. V. Ashburn, (August, 1954).

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Figures (7)

Fig. 1
Fig. 1

Experimental records of brightness in the visible in lamberts and radiance in the infrared in w/m2-sterad at 53° elevation, 0°–180° azimuth, 11:14 a.m., September 11 at Peterson Field. Sun position was 53.5° elev., 0° az.

Fig. 2
Fig. 2

Sky maps showing lines of constant radiance in w/m2-sterad in the 2–40 μ wavelength region at Pikes Peak. The data in map A were taken at 7:23 p.m., September 14 after sunset and those in map B at 3:47 p.m., September 15, with a sun elev. of 27°.

Fig. 3
Fig. 3

Experimental values of log(B/BS) plotted versus csc 1 2 θ with θ the elevation angle measured from the horizon, S the radiance observed from the sky, and B the radiance from a blackbody at ambient temperature. Graph A shows data taken at Peterson Field at 5:06 a.m., September 11; graph B data taken at Pikes Peak at 5:16 a.m., September 15.

Fig. 4
Fig. 4

Zenith emissivity in the 2–40 μ wavelength region as a function of absolute humidity at the point of observation. Measurements at Pikes Peak are represented by triangles, at Peterson Field by squares and at Wright Field by circles. The solid line shows calculated values of the zenith emissivity and the dotted line the average results of Sloan et al. for the 4–15 μ wavelength region.

Fig. 5
Fig. 5

Sky maps showing lines of constant radiance in w/m2-sterad in the 0.6–2 μ wavelength region at Pikes Peak, September 15. The data were taken at: A, 12:05 p.m., sun elev. 54°; B, 2:06 p.m., sun elev. 43°; C, 3:47 p.m., sun elev. 27°; and D, 6:05 p.m., sun elev. 0°.

Fig. 6
Fig. 6

Sky maps at Peterson Field at 11:14 a.m., September 11, with sun elev. 53.5°. Map A shows lines of constant brightness in the visible expressed in lamberts and map B lines of constant radiance in the 0.6–2 μ infrared region expressed in w/m2-sterad.

Fig. 7
Fig. 7

Sky maps at Wright Field at 3:25 p.m., June 27, with sun elev. 53°. Map A shows lines of constant brightness in the visible expressed in lamberts and map B lines of constant radiance in the 0.6–2 μ infrared region expressed in w/m2-sterad.

Equations (7)

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T = exp [ - m σ α δ [ α 2 + ( m σ α / π ) ] 1 2 ] .
E = 1 - exp [ - c 1 m 0 1 2 csc 1 2 θ ]
log B B - S = c 2 m 0 1 2 csc 1 2 θ ,
E Av ( R / σ T 4 ) = a + b e 1 2 .
E Av = 1 - exp [ - α ( 1.66 t ) 1 2 ] ,
E z = 1 - exp ( - α t 1 2 )
log ( 1 - E z ) = 0.776 log ( 1 - E Av ) ,