Abstract

The vertical distribution of the atmospheric aerosol generally differs from the vertical distribution of the molecular atmosphere. The resulting differences in the optical air masses of the aerosol and molecular constituents lead to a bias error in the solar constant inferred by the Langley method. This bias error was calculated for three characteristic aerosol height distributions, and it was found that this error becomes more significant when solar observations taken at large zenith angles are included in the Langley analysis. The bias error is not a sensitive function of wavelength or of the seasonal variation of the molecular atmosphere. Volcanic aerosol injected into the lower stratosphere can lead to large bias errors. These can be reduced significantly by using lidar to provide relatively crude measurements of the vertical distribution of the aerosol extinction coefficient.

© 1986 Optical Society of America

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References

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  1. H. G. Houghton, Physical Meteorology (MIT Press, Cambridge, 1985).
  2. F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206 (1966).
    [CrossRef]
  3. L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
    [CrossRef]
  4. S. Chapman, “The Absorption and Dissociative or Ionizing Effect of Monochromatic Radiation in an Atmosphere on a Rotating Earth: II. Grazing Incidence,” Proc. Phys. Soc. London 43, 483 (1931).
    [CrossRef]
  5. C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).
  6. A. T. Young, “Observation Technique and Data Reduction,” in Methods of Experimental Physics, Astrophysics, N. P. Carleton, Ed. (Academic, New York, 1974).
  7. G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
    [CrossRef]
  8. B. A. Herman, M. A. Box, J. A. Reagan, C M. Evans, “Alternate Approach to the Analysis of Solar Photometer Data,” Appl. Opt. 20, 2925 (1981).
    [CrossRef] [PubMed]
  9. U.S. Standard Atmosphere Supplements, prepared under sponsorship of ESSA and NASA, U.S. Air Force (1966).
  10. L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorology Ranges 2 to 13 Kilometers,” AFCRL-70-0200 (1970).
  11. J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
    [CrossRef]
  12. J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).
  13. G. E. K. Middleton, Vision Through the Atmosphere (U. Toronto, Toronto, ON, 1963).
  14. M. P. McCormick, “SAGE Aerosol Measurements,” NASA Ref. Publ. 1144 (1985).
  15. L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66–828 (1966).
  16. R. J. Szymber, W. D. Sellers, “Atmospheric Turbidity at Tucson, Arizona, 1956–83: Variations and Their Causes,” J. Clim. Appl. Meteorol. 24, 725 (1985).
    [CrossRef]

1985

M. P. McCormick, “SAGE Aerosol Measurements,” NASA Ref. Publ. 1144 (1985).

R. J. Szymber, W. D. Sellers, “Atmospheric Turbidity at Tucson, Arizona, 1956–83: Variations and Their Causes,” J. Clim. Appl. Meteorol. 24, 725 (1985).
[CrossRef]

1984

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

1983

L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
[CrossRef]

1981

1973

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
[CrossRef]

1970

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorology Ranges 2 to 13 Kilometers,” AFCRL-70-0200 (1970).

1966

L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66–828 (1966).

F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206 (1966).
[CrossRef]

1931

S. Chapman, “The Absorption and Dissociative or Ionizing Effect of Monochromatic Radiation in an Atmosphere on a Rotating Earth: II. Grazing Incidence,” Proc. Phys. Soc. London 43, 483 (1931).
[CrossRef]

1922

C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).

Abbot, C. G.

C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).

Aldrich, L. B.

C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).

Apte, M. V.

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

Box, M. A.

Bruhns, T. V.

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

Chapman, S.

S. Chapman, “The Absorption and Dissociative or Ionizing Effect of Monochromatic Radiation in an Atmosphere on a Rotating Earth: II. Grazing Incidence,” Proc. Phys. Soc. London 43, 483 (1931).
[CrossRef]

Coulson, K.

J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).

DeLuisi, J.

J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).

Derfoor, T.

J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).

Elterman, L.

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorology Ranges 2 to 13 Kilometers,” AFCRL-70-0200 (1970).

L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66–828 (1966).

Evans, C M.

Fernald, F.

J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).

Fowle, F. E.

C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).

Herman, B. A.

Herman, B. M.

L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
[CrossRef]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
[CrossRef]

Houghton, H. G.

H. G. Houghton, Physical Meteorology (MIT Press, Cambridge, 1985).

Kasten, F.

F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206 (1966).
[CrossRef]

McCormick, M. P.

M. P. McCormick, “SAGE Aerosol Measurements,” NASA Ref. Publ. 1144 (1985).

Middleton, G. E. K.

G. E. K. Middleton, Vision Through the Atmosphere (U. Toronto, Toronto, ON, 1963).

Reagan, J. A.

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
[CrossRef]

B. A. Herman, M. A. Box, J. A. Reagan, C M. Evans, “Alternate Approach to the Analysis of Solar Photometer Data,” Appl. Opt. 20, 2925 (1981).
[CrossRef] [PubMed]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
[CrossRef]

Sellers, W. D.

R. J. Szymber, W. D. Sellers, “Atmospheric Turbidity at Tucson, Arizona, 1956–83: Variations and Their Causes,” J. Clim. Appl. Meteorol. 24, 725 (1985).
[CrossRef]

Shaw, G. E.

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
[CrossRef]

Szymber, R. J.

R. J. Szymber, W. D. Sellers, “Atmospheric Turbidity at Tucson, Arizona, 1956–83: Variations and Their Causes,” J. Clim. Appl. Meteorol. 24, 725 (1985).
[CrossRef]

Thomason, L. W.

L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
[CrossRef]

Young, A. T.

A. T. Young, “Observation Technique and Data Reduction,” in Methods of Experimental Physics, Astrophysics, N. P. Carleton, Ed. (Academic, New York, 1974).

Youngbluth, O.

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

Aerosol Sci. Technol.

J. A. Reagan, M. V. Apte, T. V. Bruhns, O. Youngbluth, “Lidar and Balloons—Some Cascade Impactor Measurements of Aerosols: A Case Study,” Aerosol Sci. Technol. 3, 259 (1984).
[CrossRef]

AFCRL-66–828

L. Elterman, “An Atlas of Aerosol Attenuation and Extinction Profiles for the Troposphere and Stratosphere,” AFCRL-66–828 (1966).

AFCRL-70-0200

L. Elterman, “Vertical Attenuation Model with Eight Surface Meteorology Ranges 2 to 13 Kilometers,” AFCRL-70-0200 (1970).

Am. Astrophys. Obs. Smithson. Inst.

C. G. Abbot, F. E. Fowle, L. B. Aldrich, “New Evidence on the Intensity of Solar Radiation Outside the Atmosphere,” Am. Astrophys. Obs. Smithson. Inst. 4, 323 (1922).

Appl. Opt.

Arch. Meteorol. Geophys. Bioklimatol. Ser. B

F. Kasten, “A New Table and Approximation Formula for the Relative Optical Air Mass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206 (1966).
[CrossRef]

J. Appl. Meteorol.

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigations of Atmospheric Extinction Using Direct Solar Radiation Measurements Made with a Multiple Wavelength Radiometer,” J. Appl. Meteorol. 12, 374 (1973).
[CrossRef]

J. Atmos. Sci.

L. W. Thomason, B. M. Herman, J. A. Reagan, “The Effect of Atmospheric Attenuators with Structured Vertical Distributions on Air Mass Determinations and Langley Plot Analysis,” J. Atmos. Sci. 40, 1851 (1983).
[CrossRef]

J. Clim. Appl. Meteorol.

R. J. Szymber, W. D. Sellers, “Atmospheric Turbidity at Tucson, Arizona, 1956–83: Variations and Their Causes,” J. Clim. Appl. Meteorol. 24, 725 (1985).
[CrossRef]

NASA Ref. Publ. 1144

M. P. McCormick, “SAGE Aerosol Measurements,” NASA Ref. Publ. 1144 (1985).

Proc. Phys. Soc. London

S. Chapman, “The Absorption and Dissociative or Ionizing Effect of Monochromatic Radiation in an Atmosphere on a Rotating Earth: II. Grazing Incidence,” Proc. Phys. Soc. London 43, 483 (1931).
[CrossRef]

Other

A. T. Young, “Observation Technique and Data Reduction,” in Methods of Experimental Physics, Astrophysics, N. P. Carleton, Ed. (Academic, New York, 1974).

H. G. Houghton, Physical Meteorology (MIT Press, Cambridge, 1985).

U.S. Standard Atmosphere Supplements, prepared under sponsorship of ESSA and NASA, U.S. Air Force (1966).

J. DeLuisi, T. Derfoor, K. Coulson, F. Fernald, “Lidar Observations of Stratospheric Aerosol over Mauna Loa Observatory: 1982–1983,” NOAA Data Report ERL ARL-5 (1985).

G. E. K. Middleton, Vision Through the Atmosphere (U. Toronto, Toronto, ON, 1963).

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Figures (6)

Fig. 1
Fig. 1

Ray refraction in a spherical atmosphere.

Fig. 2
Fig. 2

Tropospheric aerosol extinction models. Model 1, solid line, represents an exponential form with scale height of 1 km. Model 2, dashed line, represents constant extinction to height of 3 km, then an exponential decrease with a scale height of 0.3 km.

Fig. 3
Fig. 3

Volcanic aerosol extinction model 3. El Chichon volcano dust (data11 taken from Mauna Loa observatory on 30 Mar. 1983 using λ = 0.694-μm lidar system).

Fig. 4
Fig. 4

Zenith angle sensitivity of bias error in solar constant determination. (Molecular model July 30°N. Aerosol model 2, δH = 3 km, ZH = 0.3 km. Wavelength 0.45 μm. Instrument located at ground.)

Fig. 5
Fig. 5

Aerosol model sensitivity of bias error at different wavelength.

Fig. 6
Fig. 6

Bias error in solar constant due to stratospheric volcanic aerosol based on El Chichon data (Fig. 3) for τa = 0.067. Data scaled from extinction coefficient to other aerosol optical depths.

Tables (3)

Tables Icon

Table I Optical Air Mass Calculationsa

Tables Icon

Table II Seasonal Effect on Bias Errora

Tables Icon

Table III Bias Error Correction by Lidar Measurementa

Equations (17)

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

F λ 0 ( θ 0 ) = F λ T exp - z 0 σ ( z ) d z [ 1 - ( n 0 z 0 n z sin θ 0 ) 2 ] 1 / 2 .
σ ( z ) = σ m ( z ) + 1 N σ i ( z ) ,
1 N σ i ( z )
m i = 1 τ i z 0 σ i ( z ) d z [ 1 - ( n 0 z 0 n z sin θ 0 ) 2 ] 1 / 2 ,
τ = z 0 σ ( z ) d z = z 0 σ m ( z ) d z + z 0 σ a ( z ) d z τ m + τ a .
F λ 0 = F λ T exp - ( τ m m m + τ a m a )
F λ 0 = F λ T exp - ( τ m e ) ,
m e = m m + τ a / τ m · m a 1 + τ a / τ m
ln F λ 0 = ln F λ T - τ m e .
ln F λ 0 = ln F λ T * - τ m m * ,
F λ 0 1 = F λ T exp - ( - τ m m m 1 + τ a m a 1 ) , F λ 0 2 = F λ T exp - ( - τ m m m 2 + τ a m a 2 ) .
F λ 0 1 = F λ T * exp - ( τ * m m 1 ) , F λ 0 2 = F λ T * exp - ( τ * m m 2 ) .
ln F λ T * F λ T = τ a ( m m 1 m a 2 - m m 2 m a 1 m m 2 - m m 1 ) ,
τ a * = τ a ( m a 2 - m a 1 m m 2 - m m 1 ) .
ln F λ T * F λ T F λ T * F λ T - 1 , F λ T - F λ T * F λ T - τ a ( m m 1 m a 2 - m m 2 m a 1 m m 2 - m m 1 ) .
τ a - τ a * τ a = 1 - m a 2 - m a 1 m m 2 - m m 1 .
σ a λ ( z ) = σ a λ ( z 0 ) exp - [ z - z 0 ) Z H ] ;

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