Abstract

Equations governing the radiance of the sky at a specific wavelength and distance from the sun are stated, and graphs of the Mie scattering coefficient are presented. Observations of the angular distribution of light in the aureole from 14° to 3° from the solar limb, and of the wavelength distribution from 4500 A to 8200 A were made with a special photographic sky photometer at altitudes from 5420 ft to 12450 ft above sea level. The analysis of the data shows: (1) The Mie particle density decreases exponentially with altitude. (2) Most of the light in the aureole is that which has been scattered by large particles. At 12 000 ft altitude, the radiance 2° from the center of the solar disk is six times the radiance of the Rayleigh atmosphere. (3) The relative density of large particles is greater in air masses which have been in convection over land for several days and in the air behind a warm front than in other systems. (4) An increase in the relative density of large particles seems to be encountered in the jet stream.

© 1956 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Rayleigh, Phil. Mag. 41, 107 (1871); Phil. Mag. 47, 375 (1899). Proc. Roy. Soc. (London) 84A, 25 (1911); Phil. Mag. 90A, 319 (1914).
  2. G. Mie, Ann. phys. 25, 377 (1908).
    [CrossRef]
  3. J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 568.
  4. R. Penndorf (private communication).
  5. H. Blumer, Z. Physik 32, 119 (1925); Z. Physik 38, 304 (1926); Z. Physik 38, 920 (1926); Z. Physik 39, 195 (1926).
    [CrossRef]
  6. J. W. Evans, J. Opt. Soc. Am. 38, 1038 (1948).
    [CrossRef]
  7. U. Krug-Pielsticker, Ber. Deut. Wetterd. U. S. Zone, Nr. 8.
  8. W. O. Roberts (private communication).
  9. R. Anthony, J. Meteorol. 10, 60 (1953).
    [CrossRef]
  10. F. Volz, Ber. Deut. Wetterd. U. S. Zone, Nr. 13.
  11. C. Junge, Tellus V, 1 (1953).
  12. J. S. Sawyer and B. Ilett, Meteorol. Mag. 80, 277 (1951).
  13. R. Penndorf, (1954).
  14. D. R. Barber, J. Atm. and Terrest. Phys. 7, 170 (1955).
    [CrossRef]

1955 (1)

D. R. Barber, J. Atm. and Terrest. Phys. 7, 170 (1955).
[CrossRef]

1953 (2)

R. Anthony, J. Meteorol. 10, 60 (1953).
[CrossRef]

C. Junge, Tellus V, 1 (1953).

1951 (1)

J. S. Sawyer and B. Ilett, Meteorol. Mag. 80, 277 (1951).

1948 (1)

J. W. Evans, J. Opt. Soc. Am. 38, 1038 (1948).
[CrossRef]

1925 (1)

H. Blumer, Z. Physik 32, 119 (1925); Z. Physik 38, 304 (1926); Z. Physik 38, 920 (1926); Z. Physik 39, 195 (1926).
[CrossRef]

1908 (1)

G. Mie, Ann. phys. 25, 377 (1908).
[CrossRef]

1871 (1)

Rayleigh, Phil. Mag. 41, 107 (1871); Phil. Mag. 47, 375 (1899). Proc. Roy. Soc. (London) 84A, 25 (1911); Phil. Mag. 90A, 319 (1914).

Anthony, R.

R. Anthony, J. Meteorol. 10, 60 (1953).
[CrossRef]

Barber, D. R.

D. R. Barber, J. Atm. and Terrest. Phys. 7, 170 (1955).
[CrossRef]

Blumer, H.

H. Blumer, Z. Physik 32, 119 (1925); Z. Physik 38, 304 (1926); Z. Physik 38, 920 (1926); Z. Physik 39, 195 (1926).
[CrossRef]

Evans, J. W.

J. W. Evans, J. Opt. Soc. Am. 38, 1038 (1948).
[CrossRef]

Ilett, B.

J. S. Sawyer and B. Ilett, Meteorol. Mag. 80, 277 (1951).

Junge, C.

C. Junge, Tellus V, 1 (1953).

Krug-Pielsticker, U.

U. Krug-Pielsticker, Ber. Deut. Wetterd. U. S. Zone, Nr. 8.

Mie, G.

G. Mie, Ann. phys. 25, 377 (1908).
[CrossRef]

Penndorf, R.

R. Penndorf, (1954).

R. Penndorf (private communication).

Rayleigh,

Rayleigh, Phil. Mag. 41, 107 (1871); Phil. Mag. 47, 375 (1899). Proc. Roy. Soc. (London) 84A, 25 (1911); Phil. Mag. 90A, 319 (1914).

Roberts, W. O.

W. O. Roberts (private communication).

Sawyer, J. S.

J. S. Sawyer and B. Ilett, Meteorol. Mag. 80, 277 (1951).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 568.

Volz, F.

F. Volz, Ber. Deut. Wetterd. U. S. Zone, Nr. 13.

Ann. phys. (1)

G. Mie, Ann. phys. 25, 377 (1908).
[CrossRef]

J. Atm. and Terrest. Phys. (1)

D. R. Barber, J. Atm. and Terrest. Phys. 7, 170 (1955).
[CrossRef]

J. Meteorol. (1)

R. Anthony, J. Meteorol. 10, 60 (1953).
[CrossRef]

J. Opt. Soc. Am. (1)

J. W. Evans, J. Opt. Soc. Am. 38, 1038 (1948).
[CrossRef]

Meteorol. Mag. (1)

J. S. Sawyer and B. Ilett, Meteorol. Mag. 80, 277 (1951).

Phil. Mag. (1)

Rayleigh, Phil. Mag. 41, 107 (1871); Phil. Mag. 47, 375 (1899). Proc. Roy. Soc. (London) 84A, 25 (1911); Phil. Mag. 90A, 319 (1914).

Tellus (1)

C. Junge, Tellus V, 1 (1953).

Z. Physik (1)

H. Blumer, Z. Physik 32, 119 (1925); Z. Physik 38, 304 (1926); Z. Physik 38, 920 (1926); Z. Physik 39, 195 (1926).
[CrossRef]

Other (6)

J. A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, Inc., New York, 1941), p. 568.

R. Penndorf (private communication).

U. Krug-Pielsticker, Ber. Deut. Wetterd. U. S. Zone, Nr. 8.

W. O. Roberts (private communication).

F. Volz, Ber. Deut. Wetterd. U. S. Zone, Nr. 13.

R. Penndorf, (1954).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (16)

Fig. 1
Fig. 1

Geometrical situation for atmospheric scattering.

Fig. 2
Fig. 2

Wavelength distribution of light scattered at γ=178° by single water drop of radius r.

Fig. 3
Fig. 3

Angular distribution of light scattered by water droplets.

Fig. 4
Fig. 4

Comparison of scattered intensity at γ=175° for spherical drops of ice and water.

Fig. 5
Fig. 5

Schematic diagram of photographic sky photometer (from drawing by Yü of High Altitude Observatory).

Fig. 6
Fig. 6

Relative spectral sensitivities for filter-emulsion combinations.

Fig. 7
Fig. 7

Wavelength dependence of radiance for a uniform particle size atmosphere observed at γ=178° through filters.

Fig. 8
Fig. 8

Wavelength dependence of radiance for a uniform particle size atmosphere observed at γ=178° through filters.

Fig. 9
Fig. 9

A sample frame from the photographic sky photometer and a microdensitometer tracing of the frame. Note the occulting disk and the photometric standard in the sky photograph.

Fig. 10
Fig. 10

Observed scattering diagrams under various sky conditions (λ=4500 A) (corrected to 10 000 ft altitude).

Fig. 11
Fig. 11

Aureole radiance (φ=120′, λ=4500 A) vs altitude above sea level.

Fig. 12
Fig. 12

Aureole gradient (λ=4500 A) vs altitude above sea level.

Fig. 13
Fig. 13

Distribution of radiance with wavelength—observed and calculated.

Fig. 14
Fig. 14

Aureole gradient vs radiance (φ=120′, λ=4500 A).

Fig. 15
Fig. 15

Angular radiance distributions—observed and calculated.

Fig. 16
Fig. 16

Daily variation of gradient and radiance (φ=120′, λ=4500 A).

Tables (2)

Tables Icon

Table I Radiance correction factors for opal-wedge system at different wavelengths.

Tables Icon

Table II Data on observing sites (all stations are in Colorado).

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

d E λ ( Z , φ , x ) = F λ f λ ( φ , x ) d s
F λ = F λ e - τ λ ( x ) sec Z ,
E λ ( Z , φ ) = e - τ λ ( h ) sec Z sec Z h F λ f λ ( φ , x ) d x .
B λ ( Z , φ ) B λ ( 0 ) = d ω 0 sec Z f λ ( φ , x ) d x ,
f λ ( φ ) = 2 π 2 n λ 4 ( μ λ - 1 ) 2 ( 1 + cos 2 φ ) ,
8.0 × 10 5 cm atmospheric pressure at h atmospheric pressure at sea level .
f λ , m ( γ , α ) = λ 2 8 π 2 { i 1 ( γ , m , α ) + i 2 ( γ , m , α ) } N ( α , m ) ,
radiation from around occulting disk radiation from center of solar disk
B ( opal ) B ( sun ) = 20 × 10 - 6 ± 2 % .
f ¯ ( α , γ , filter ) = λ 1 λ 2 f λ ( α , γ ) t λ d λ λ 1 λ 2 t λ d λ ,
Γ = log B λ ( Z , φ = 10 0 ) B λ ( 0 ) - log B λ ( Z , φ = 18 0 ) B λ ( 0 )
d N ( r ) d ( log r ) = constant r δ ,
f λ ( φ = 12 0 ) = 1 N r = 0.01 μ 2.0 μ f λ ( φ = 12 0 , r ) d N ( r ) ,
N = r = 0.01 μ 2.0 μ d N ( r ) .
0.01 r < 0.1 δ = 0 , 0.1 r 2.0 δ = 3.
f λ = 4500 A ( φ ) = 1 N r = 0.01 μ 2.0 μ f λ = 4500 A ( φ , r ) d N ( r )