Abstract

Near infrared solar spectrum observations taken on October 15, 1954 with a double-pass Nacl prism spectrometer have been analyzed for transmission coefficients for the “selective” absorption factor and for the “continuum” factor. The analysis was carried out for 59 wavelength positions between 0.872 and 2.537 μ. The monochromatic data fit well the law °nT=c1(w)12 where w is the amount of water vapor in the optical path. The coefficient c1 is given as a continuous function of the wavelength. A coefficient of extinction for the “continuum” factor is also given.

© 1960 Optical Society of America

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References

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  1. S. P. Langley, Ann. Smithsonian Inst.  1, 1 (1900).
  2. F. E. Fowle, Astrophys. J. 35, 149 (1912); Astrophys. J. 37, 359 (1913); Astrophys. J. 42, 394 (1915).
    [CrossRef]
  3. A. Adel, Astrophys. J. 90, 627 (1939); Astrophys. J. 93, 506 (1941); Astrophys. J. 96, 239 (1942).
    [CrossRef]
  4. O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).
  5. O. C. Mohler, A Table of Solar Spectrum Wavelengths (University of Michigan Press, Ann Arbor, Michigan, 1955).
  6. J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
    [CrossRef]
  7. M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.
  8. J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334 (1956).
    [CrossRef]
  9. R. P. Madden, Ph.D. Dissertation, Johns Hopkins University, 1957.
  10. W. H. Cloud, Ph.D. Dissertation, Johns Hopkins University, 1952.
  11. H. J. Kostkowski, Ph.D. Dissertation, Johns Hopkins University, 1955.
  12. A. Bemporad, Met. Z. 24, 309 (1907).
  13. R. Peyturaux, Ann. Astrophys. 15, 302 (1952).
  14. R. M. Goody, Quart. J. Roy. Met. Soc. 78, 165 (1952).
    [CrossRef]
  15. This assumes a constant distribution of the water vapor in the atmosphere although the total amount will vary.
  16. W. M. Elsasser, Harvard Meteorological Studies, No. 6 (1942).
  17. D. M. Gates, J. Meteorol. 13, 369 (1956).
    [CrossRef]
  18. From a knowledge of the distribution of the water vapor in the atmosphere one can apply the appropriate pressure correction to α.

1956 (3)

M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.

J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334 (1956).
[CrossRef]

D. M. Gates, J. Meteorol. 13, 369 (1956).
[CrossRef]

1952 (2)

R. Peyturaux, Ann. Astrophys. 15, 302 (1952).

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

1951 (1)

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

1942 (1)

W. M. Elsasser, Harvard Meteorological Studies, No. 6 (1942).

1939 (1)

A. Adel, Astrophys. J. 90, 627 (1939); Astrophys. J. 93, 506 (1941); Astrophys. J. 96, 239 (1942).
[CrossRef]

1912 (1)

F. E. Fowle, Astrophys. J. 35, 149 (1912); Astrophys. J. 37, 359 (1913); Astrophys. J. 42, 394 (1915).
[CrossRef]

1907 (1)

A. Bemporad, Met. Z. 24, 309 (1907).

1900 (1)

S. P. Langley, Ann. Smithsonian Inst.  1, 1 (1900).

Adel, A.

A. Adel, Astrophys. J. 90, 627 (1939); Astrophys. J. 93, 506 (1941); Astrophys. J. 96, 239 (1942).
[CrossRef]

Bemporad, A.

A. Bemporad, Met. Z. 24, 309 (1907).

Burch, D. E.

Chapman, R. M.

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

Cloud, W. H.

W. H. Cloud, Ph.D. Dissertation, Johns Hopkins University, 1952.

Elsasser, W. M.

W. M. Elsasser, Harvard Meteorological Studies, No. 6 (1942).

Fowle, F. E.

F. E. Fowle, Astrophys. J. 35, 149 (1912); Astrophys. J. 37, 359 (1913); Astrophys. J. 42, 394 (1915).
[CrossRef]

Gates, D. M.

D. M. Gates, J. Meteorol. 13, 369 (1956).
[CrossRef]

Goldberg, L.

O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).

Goody, R. M.

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

Howard, J. N.

J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am. 46, 186, 237, 242, 334 (1956).
[CrossRef]

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

Kostkowski, H. J.

H. J. Kostkowski, Ph.D. Dissertation, Johns Hopkins University, 1955.

Langley, S. P.

S. P. Langley, Ann. Smithsonian Inst.  1, 1 (1900).

Madden, R. P.

R. P. Madden, Ph.D. Dissertation, Johns Hopkins University, 1957.

McMath, R. R.

O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).

Migeotte, M.

M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.

Mohler, O. C.

O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).

O. C. Mohler, A Table of Solar Spectrum Wavelengths (University of Michigan Press, Ann Arbor, Michigan, 1955).

Neven, L.

M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.

Oxholm, M. L.

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

Peyturaux, R.

R. Peyturaux, Ann. Astrophys. 15, 302 (1952).

Pierce, A. K.

O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).

Sevenson, J.

M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.

Shaw, J. H.

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

Williams, D.

Ann. Astrophys. (1)

R. Peyturaux, Ann. Astrophys. 15, 302 (1952).

Ann. Smithsonian Inst (1)

S. P. Langley, Ann. Smithsonian Inst.  1, 1 (1900).

Astrophys. J. (3)

F. E. Fowle, Astrophys. J. 35, 149 (1912); Astrophys. J. 37, 359 (1913); Astrophys. J. 42, 394 (1915).
[CrossRef]

A. Adel, Astrophys. J. 90, 627 (1939); Astrophys. J. 93, 506 (1941); Astrophys. J. 96, 239 (1942).
[CrossRef]

J. H. Shaw, R. M. Chapman, J. N. Howard, and M. L. Oxholm, Astrophys. J. 113, 268 (1951).
[CrossRef]

Harvard Meteorological Studies, No. 6 (1)

W. M. Elsasser, Harvard Meteorological Studies, No. 6 (1942).

J. Meteorol. (1)

D. M. Gates, J. Meteorol. 13, 369 (1956).
[CrossRef]

J. Opt. Soc. Am. (1)

Mém. soc. roy. sci. Liége (1)

M. Migeotte, L. Neven, and J. Sevenson, Mém. soc. roy. sci. Liége, Special Volume No.  1 (1956), Part I; Mém. soc. roy. sci. Liége Special Volume No.  2(1957), Part II.

Met. Z. (1)

A. Bemporad, Met. Z. 24, 309 (1907).

Quart. J. Roy. Met. Soc. (1)

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

Other (7)

This assumes a constant distribution of the water vapor in the atmosphere although the total amount will vary.

From a knowledge of the distribution of the water vapor in the atmosphere one can apply the appropriate pressure correction to α.

R. P. Madden, Ph.D. Dissertation, Johns Hopkins University, 1957.

W. H. Cloud, Ph.D. Dissertation, Johns Hopkins University, 1952.

H. J. Kostkowski, Ph.D. Dissertation, Johns Hopkins University, 1955.

O. C. Mohler, A. K. Pierce, R. R. McMath, and L. Goldberg, Photometric Atlas of the Near Infrared Solar Spectrumλ8465 toλ25 242 A (University of Michigan Press, Ann Arbor, Micigan, 1950).

O. C. Mohler, A Table of Solar Spectrum Wavelengths (University of Michigan Press, Ann Arbor, Michigan, 1955).

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Figures (4)

Fig. 1
Fig. 1

Near infrared solar spectrum from 0.85 to 2.70 μ as recorded with a double pass infrared spectrometer with NaCl prism. Identifications of the absorption bands are given above the spectrum. The ordinate represents the deflection of the recorder.

Fig. 2
Fig. 2

“Selective” transmission plots for solar radiation through the atmosphere, illustrating the goodness of fit to straight lines through the origin for the “square root” law behavior at various wavelengths.

Fig. 3
Fig. 3

Transmission coefficient of the “selective” absorption factor for solar radiation through the earth’s atmosphere. The coefficient is defined by the “square root” law ln T = c 1 ( w ) 1 2 where T is the transmission and w is the amount of precipitable water vapor in the optical path in millimeters of liquid water.

Fig. 4
Fig. 4

Transmission coefficient of the “continuum” absorption factor for solar radiation through the earth’s atmosphere. The coefficient is defined by the law lnT=cm, where T is the transmission and m is the amount of attenuating material in the optical path. The upper curve is given in terms of the water vapor content of the atmosphere in millimeters of precipitable water and the lower curve is given in terms of air mass.

Equations (9)

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e λ = J λ s 1 l 1 A f 2 Δ λ · T ,
T ¯ ( α , m ) = exp ( - k m 2 π δ ( 1 + k m π α ) 1 2 ) ,
ln T ¯ ( k α 4 π δ 2 ) 1 2 m 1 2 = c 1 m 1 2 .
ln T ¯ k ( 2 δ ) 1 2 m = c 2 m
ln T ¯ k m δ ( 1 - 1 2 k m π α ) = c 3 m - c 4 m 2 .
T ¯ = - 1 2 + 1 2 exp [ - k m δ sinh 2 π α / δ cosh 2 π α / δ - cos ν / δ ] d ν δ .
T ¯ 1 - erf [ π α δ ( k m π α ) 1 2 ]
1 - 2 ( α k m ) 1 2 δ .
ln T = c m ,