Abstract

Optical depth retrieval by means of Langley regression is complicated by cloud transits and other time-varying interferences. An algorithm is described that objectively selects data points from a continuous time series and performs the required regression. The performance of this algorithm is compared by a double-blind test with an analysis done subjectively. The limits to accuracy imposed by time-averaged data are discussed, and an additional iterative postprocessing algorithm is described that improves the accuracy of optical depth inferences made from data with time-averaging periods longer than 5 min. Such routine algorithms are required to provide intercomparable retrievals of optical depths from widely varying historical data sets and to support large networks of instruments such as the multifilter rotating shadow-band radiometer.

© 1994 Optical Society of America

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  1. C. G. Abbott, F. E. Fowle, Annals of the Astrophysical Observatory of the Smithsonian Institution (U.S. Government Printing Office, Washington, D.C., 1908), Vol. II, Part 1, pp. 13–64. Langley died on 27 February 1906, and his research was published posthumously by the Institution. Langley’s method was known commonly throughout the early years of the century as the Long Method (no doubt describing the tediousness of the necessary calculations in the precomputational era). Langley developed it subsequent to his famous Mount Whitney expedition of 1881; however, early errors of misapplication resulted in an estimate of the solar constant that was nearly a factor of 2 too large.
  2. E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
    [CrossRef]
  3. G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
    [CrossRef]
  4. G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–10 (1983).
    [CrossRef]
  5. R. Guzzi, G. C. Maracci, R. Rizzi, A. Sicardi, “Spectroradiometer for ground-based measurements related to remote sensing in the visible from a satellite,” Appl. Opt. 24, 2859–2863 (1985).
    [CrossRef] [PubMed]
  6. F. E. Voltz, “Some results of turbidity networks,” Tellus 21, 625–630 (1969).
    [CrossRef]
  7. L. Harrison, J. J. Michalsky, J. Berndt, “Automated multifilter rotation shadow-band radiometer: an instrument for optical depth and radiation measurements,” Appl. Opt. 33, (1994).
    [CrossRef] [PubMed]
  8. R. M. Goody, Atmospheric Radiation: I. Theoretical Basis (Oxford U. Press, London, 1964).
  9. J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
    [CrossRef]
  10. R. M. Schotland, T. K. Lea, “Bias in a solar constant determination by the Langley method due to a structured atmospheric aerosol,” Appl. Opt. 25, 2486–2491 (1986).
    [CrossRef] [PubMed]
  11. L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
    [CrossRef]
  12. J. J. Michalsky, “The astronomical almanac’s algorithm for approximate solar position,” Sol. Energy 40, 227–235 (1988).
    [CrossRef]
  13. F. Kasten, “A new table and approximate formula for relative airmass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206–223 (1966).
    [CrossRef]
  14. P. Foukal, J. Lean, “An empirical model of total solar irradiance variation between 1874 and 1988,” Science 247, 556–558 (1990).
    [CrossRef] [PubMed]
  15. LiCor Terrestrial Radiation Sensors, type SZ instruction manual (LiCor Inc., Lincoln, Neb., 1986).
  16. Commission Internationale de l’Eclairage, “Recommended practice for the calculation of daylight availability,” IES J. 13, 381–392 (1984).
  17. H. Neckel, D. Labs, “Improved data of solar spectral irradiance from 0.33 to 1.25 micrometers,” Solar Physics. 74, 231–249 (1981).
    [CrossRef]

1994 (1)

L. Harrison, J. J. Michalsky, J. Berndt, “Automated multifilter rotation shadow-band radiometer: an instrument for optical depth and radiation measurements,” Appl. Opt. 33, (1994).
[CrossRef] [PubMed]

1990 (1)

P. Foukal, J. Lean, “An empirical model of total solar irradiance variation between 1874 and 1988,” Science 247, 556–558 (1990).
[CrossRef] [PubMed]

1988 (1)

J. J. Michalsky, “The astronomical almanac’s algorithm for approximate solar position,” Sol. Energy 40, 227–235 (1988).
[CrossRef]

1986 (2)

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

R. M. Schotland, T. K. Lea, “Bias in a solar constant determination by the Langley method due to a structured atmospheric aerosol,” Appl. Opt. 25, 2486–2491 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

Commission Internationale de l’Eclairage, “Recommended practice for the calculation of daylight availability,” IES J. 13, 381–392 (1984).

1983 (2)

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–10 (1983).
[CrossRef]

L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
[CrossRef]

1981 (1)

H. Neckel, D. Labs, “Improved data of solar spectral irradiance from 0.33 to 1.25 micrometers,” Solar Physics. 74, 231–249 (1981).
[CrossRef]

1973 (1)

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
[CrossRef]

1969 (2)

E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
[CrossRef]

F. E. Voltz, “Some results of turbidity networks,” Tellus 21, 625–630 (1969).
[CrossRef]

1966 (1)

F. Kasten, “A new table and approximate formula for relative airmass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206–223 (1966).
[CrossRef]

Abbott, C. G.

C. G. Abbott, F. E. Fowle, Annals of the Astrophysical Observatory of the Smithsonian Institution (U.S. Government Printing Office, Washington, D.C., 1908), Vol. II, Part 1, pp. 13–64. Langley died on 27 February 1906, and his research was published posthumously by the Institution. Langley’s method was known commonly throughout the early years of the century as the Long Method (no doubt describing the tediousness of the necessary calculations in the precomputational era). Langley developed it subsequent to his famous Mount Whitney expedition of 1881; however, early errors of misapplication resulted in an estimate of the solar constant that was nearly a factor of 2 too large.

Berndt, J.

L. Harrison, J. J. Michalsky, J. Berndt, “Automated multifilter rotation shadow-band radiometer: an instrument for optical depth and radiation measurements,” Appl. Opt. 33, (1994).
[CrossRef] [PubMed]

Flowers, E. C.

E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
[CrossRef]

Foukal, P.

P. Foukal, J. Lean, “An empirical model of total solar irradiance variation between 1874 and 1988,” Science 247, 556–558 (1990).
[CrossRef] [PubMed]

Fowle, F. E.

C. G. Abbott, F. E. Fowle, Annals of the Astrophysical Observatory of the Smithsonian Institution (U.S. Government Printing Office, Washington, D.C., 1908), Vol. II, Part 1, pp. 13–64. Langley died on 27 February 1906, and his research was published posthumously by the Institution. Langley’s method was known commonly throughout the early years of the century as the Long Method (no doubt describing the tediousness of the necessary calculations in the precomputational era). Langley developed it subsequent to his famous Mount Whitney expedition of 1881; however, early errors of misapplication resulted in an estimate of the solar constant that was nearly a factor of 2 too large.

Goody, R. M.

R. M. Goody, Atmospheric Radiation: I. Theoretical Basis (Oxford U. Press, London, 1964).

Guzzi, R.

Harrison, L.

L. Harrison, J. J. Michalsky, J. Berndt, “Automated multifilter rotation shadow-band radiometer: an instrument for optical depth and radiation measurements,” Appl. Opt. 33, (1994).
[CrossRef] [PubMed]

Herman, B. M.

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
[CrossRef]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
[CrossRef]

Kasten, F.

F. Kasten, “A new table and approximate formula for relative airmass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206–223 (1966).
[CrossRef]

Kurfis, K. R.

E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
[CrossRef]

Labs, D.

H. Neckel, D. Labs, “Improved data of solar spectral irradiance from 0.33 to 1.25 micrometers,” Solar Physics. 74, 231–249 (1981).
[CrossRef]

Lea, T. K.

Lean, J.

P. Foukal, J. Lean, “An empirical model of total solar irradiance variation between 1874 and 1988,” Science 247, 556–558 (1990).
[CrossRef] [PubMed]

Maracci, G. C.

McCormick, R. A.

E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
[CrossRef]

Michalsky, J. J.

L. Harrison, J. J. Michalsky, J. Berndt, “Automated multifilter rotation shadow-band radiometer: an instrument for optical depth and radiation measurements,” Appl. Opt. 33, (1994).
[CrossRef] [PubMed]

J. J. Michalsky, “The astronomical almanac’s algorithm for approximate solar position,” Sol. Energy 40, 227–235 (1988).
[CrossRef]

Neckel, H.

H. Neckel, D. Labs, “Improved data of solar spectral irradiance from 0.33 to 1.25 micrometers,” Solar Physics. 74, 231–249 (1981).
[CrossRef]

Palmer, J. M.

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

Reagan, J. A.

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
[CrossRef]

Regan, J. A.

L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
[CrossRef]

Rizzi, R.

Schotland, R. M.

Shaw, G. E.

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–10 (1983).
[CrossRef]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
[CrossRef]

Sicardi, A.

Thomason, L. W.

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
[CrossRef]

Voltz, F. E.

F. E. Voltz, “Some results of turbidity networks,” Tellus 21, 625–630 (1969).
[CrossRef]

Appl. Opt. (3)

Arch. Meteorol. Geophys. Bioklimatol. Ser. B (1)

F. Kasten, “A new table and approximate formula for relative airmass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206–223 (1966).
[CrossRef]

Bull. Am. Meteorol. Soc. (1)

G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–10 (1983).
[CrossRef]

IEEE Trans. Geosci. Remote Sensing (1)

J. A. Reagan, L. W. Thomason, B. M. Herman, J. M. Palmer, “Assessment of atmospheric limitations on the determination of the solar spectral constant from ground based spectroradiometer measurements,” IEEE Trans. Geosci. Remote Sensing GRS-24, 258–266 (1986).
[CrossRef]

IES J. (1)

Commission Internationale de l’Eclairage, “Recommended practice for the calculation of daylight availability,” IES J. 13, 381–392 (1984).

J. Appl. Meterol. (2)

E. C. Flowers, R. A. McCormick, K. R. Kurfis, “Atmospheric turbidity over the United States, 1961–1966,” J. Appl. Meterol. 8, 955–962 (1969).
[CrossRef]

G. E. Shaw, J. A. Reagan, B. M. Herman, “Investigation of atmospheric extinction using direct solar radiation measurements made with a multiple wavelength radiometer,” J. Appl. Meterol. 12, 374–380 (1973).
[CrossRef]

J. Atmos. Sci. (1)

L. W. Thomason, B. M. Herman, J. A. Regan, “The effect of atmospheric attenuators with structured vertical distributions on air-mass determinations and Langley plot analysis,” J. Atmos. Sci. 40, 1851–1858 (1983).
[CrossRef]

Science (1)

P. Foukal, J. Lean, “An empirical model of total solar irradiance variation between 1874 and 1988,” Science 247, 556–558 (1990).
[CrossRef] [PubMed]

Sol. Energy (1)

J. J. Michalsky, “The astronomical almanac’s algorithm for approximate solar position,” Sol. Energy 40, 227–235 (1988).
[CrossRef]

Solar Physics. (1)

H. Neckel, D. Labs, “Improved data of solar spectral irradiance from 0.33 to 1.25 micrometers,” Solar Physics. 74, 231–249 (1981).
[CrossRef]

Tellus (1)

F. E. Voltz, “Some results of turbidity networks,” Tellus 21, 625–630 (1969).
[CrossRef]

Other (3)

R. M. Goody, Atmospheric Radiation: I. Theoretical Basis (Oxford U. Press, London, 1964).

C. G. Abbott, F. E. Fowle, Annals of the Astrophysical Observatory of the Smithsonian Institution (U.S. Government Printing Office, Washington, D.C., 1908), Vol. II, Part 1, pp. 13–64. Langley died on 27 February 1906, and his research was published posthumously by the Institution. Langley’s method was known commonly throughout the early years of the century as the Long Method (no doubt describing the tediousness of the necessary calculations in the precomputational era). Langley developed it subsequent to his famous Mount Whitney expedition of 1881; however, early errors of misapplication resulted in an estimate of the solar constant that was nearly a factor of 2 too large.

LiCor Terrestrial Radiation Sensors, type SZ instruction manual (LiCor Inc., Lincoln, Neb., 1986).

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Figures (4)

Fig. 1
Fig. 1

(a) Time series of observed irradiance components for an example case (the irradiance scale is uncalibrated). (b) Objective optical depth retrieval for the morning shown in (a); the ordinate is ln(uncalibrated direct-normal irradiance).

Fig. 2
Fig. 2

Comparison of total optical depths retrieved by the two analyses.

Fig. 3
Fig. 3

Comparison of the extrapolated zero-air-mass irradiance retrieved by the two analyses (uncalibrated).

Fig. 4
Fig. 4

Histogram of retrieved E 0 that uses a laboratory calibration for the irradiance scale.

Equations (5)

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L ( x ) L ( 0 ) = exp ( - τ x ) .
ln E ( A n ) - ln E ( 0 ) = - τ A n ,
1 t 2 - t 1 t 1 t 2 exp [ - τ A ( t ) ] d t = exp ( - τ A * ) .
1 A 2 - A 1 A 1 A 2 exp ( - τ A ) d A = exp ( - τ A * ) ,
1 - τ ( A 2 - A 1 ) [ exp ( - τ A 2 ) - exp ( - τ A 1 ) ] = exp ( - τ A * ) .

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