Abstract

A new procedure is presented for determining in situ the solar calibration constant, i.e., the Sun-sky radiometer counts for a direct normal solar flux extrapolated to the top of the atmosphere. The method makes use of a modified version of the Langley plot based on the use of an inversion code of column-integrated aerosol size distribution, and it is ordinarily applied to calibrate Prede Sun-sky radiometers. To analyze how such an in situ method can work accurately, the technique has been applied to a five-month dataset obtained from measurements taken in Rome, Italy, by a Prede Sun-sky radiometer from 22 April to 5 November 2001. The precision of the in situ method has been estimated to within 1–2.5%, depending on the wavelength.

© 2004 Optical Society of America

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References

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  1. G. E. Shaw, “Error analysis of multi-wavelength sun photometry,” Pure Appl. Geophys. 114, 1–4 (1976).
    [CrossRef]
  2. B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
    [CrossRef]
  3. T. Nahajima, G. Tonna, R. Rao, P. Boi, Y. Kaufman, B. Holben, “Use of sky brightness measurements from ground for remote sensing of particulate polydispersions,” Appl. Opt. 35, 2672–2686 (1996).
    [CrossRef]
  4. M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations,” Appl. Opt. 25, 1170–1176 (1986).
    [CrossRef] [PubMed]
  5. G. E. Shaw, “Sun photometry,” Bull. Am. Meteorol. Soc. 64, 4–10 (1983).
    [CrossRef]
  6. T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
    [CrossRef]
  7. G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
    [CrossRef] [PubMed]
  8. P. Boi, G. Tonna, G. Dalu, T. Nakajima, B. Olivieri, A. Pompei, M. Campanelli, “Procedures of calibration and data elaboration in sky radiance measurements,” Appl. Opt. 38, 896–907 (1999).
    [CrossRef]
  9. H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962), pp. 78–80.

1999 (1)

1998 (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

1996 (1)

1995 (1)

1988 (1)

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[CrossRef]

1986 (1)

1983 (1)

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

1976 (1)

G. E. Shaw, “Error analysis of multi-wavelength sun photometry,” Pure Appl. Geophys. 114, 1–4 (1976).
[CrossRef]

Boi, P.

Buis, J. P.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Campanelli, M.

Dalu, G.

Eck, T. F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Holben, B.

Holben, B. N.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Jankowiak, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Kaufman, Y.

Kaufman, Y. J.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Lavenu, F.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Nahajima, T.

Nakajima, T.

P. Boi, G. Tonna, G. Dalu, T. Nakajima, B. Olivieri, A. Pompei, M. Campanelli, “Procedures of calibration and data elaboration in sky radiance measurements,” Appl. Opt. 38, 896–907 (1999).
[CrossRef]

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

G. Tonna, T. Nakajima, R. Rao, “Aerosol features retrieved from solar aureole data: a simulation study concerning a turbid atmosphere,” Appl. Opt. 34, 4486–4499 (1995).
[CrossRef] [PubMed]

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[CrossRef]

M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations,” Appl. Opt. 25, 1170–1176 (1986).
[CrossRef] [PubMed]

Olivieri, B.

Pompei, A.

Rao, R.

Reagan, J. A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Setzer, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Shaw, G. E.

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

G. E. Shaw, “Error analysis of multi-wavelength sun photometry,” Pure Appl. Geophys. 114, 1–4 (1976).
[CrossRef]

Shiobara, M.

Slutsker, I.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Smirnov, A.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Tanaka, M.

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[CrossRef]

M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations,” Appl. Opt. 25, 1170–1176 (1986).
[CrossRef] [PubMed]

Tanre, D.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Tonna, G.

Vermote, E.

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Young, H. D.

H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962), pp. 78–80.

Appl. Opt. (4)

Bull. Am. Meteorol. Soc. (1)

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

J. Quant. Spectrosc. Radiat. Transfer (1)

T. Nakajima, M. Tanaka, “Algorithms for radiative intensity calculations in moderately thick atmospheres using a truncation approximation,” J. Quant. Spectrosc. Radiat. Transfer 40, 51–69 (1988).
[CrossRef]

Pure Appl. Geophys. (1)

G. E. Shaw, “Error analysis of multi-wavelength sun photometry,” Pure Appl. Geophys. 114, 1–4 (1976).
[CrossRef]

Remote Sens. Environ. (1)

B. N. Holben, T. F. Eck, I. Slutsker, D. Tanre, J. P. Buis, A. Setzer, E. Vermote, J. A. Reagan, Y. J. Kaufman, T. Nakajima, F. Lavenu, I. Jankowiak, A. Smirnov, “AERONET-a federated instrument network and data archive for aerosol characterization,” Remote Sens. Environ. 66, 1–16 (1998).
[CrossRef]

Other (1)

H. D. Young, Statistical Treatment of Experimental Data (McGraw-Hill, New York, 1962), pp. 78–80.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram resuming two applications of the Improved Langley plot.

Fig. 2
Fig. 2

Application of the Improved Langley plot for several values of k. Notice the dependence of the slope of the straight line on the imaginary part of the refractive index.

Fig. 3
Fig. 3

F * 0 versus k at 400 nm, retrieved for all the days. The connecting line has been drawn only for five days corresponding to the following cases: the two lowest and the two highest F * 0 retrieved values (solid and dotted curves), and only one for the more frequently retrieved values (dashed curve).

Fig. 4
Fig. 4

Three cases of the dependence of the parameter ε C on k for the determination of k*.

Fig. 5
Fig. 5

Boi’s method. Temporal behavior of F 0** and F 0* for several k values, at 500 nm. Two values for each day are plotted: one for the morning, the other for the evening. To put the temporal behavior in evidence, the time scale is irregularly spaced.

Fig. 6
Fig. 6

Boi’s method. Temporal behavior of F 0** retrieved for all the wavelengths, after the quality control selection. To put the temporal behavior in evidence, the time scale is irregularly spaced.

Fig. 7
Fig. 7

Boi’s method. Temporal behavior of F 0** and F 0 obtained from the normal Langley plot, at 500 nm, before the quality control selection. For each day two values are plotted: one for the morning and one for the evening. To put the temporal behavior in evidence, the time scale is irregularly spaced.

Fig. 8
Fig. 8

Skyrad method. Temporal behavior of F 0 retrieved for all the wavelengths, after the quality control selection. To put the temporal behavior in evidence, the time scale is irregularly spaced.

Fig. 9
Fig. 9

Comparison between F 0 retrieved by Boi’s methods and the Skyrad method at 500 nm. To put the temporal behavior in evidence, the time scale is irregularly spaced.

Fig. 10
Fig. 10

F 0 retrieved by the Boi’s (top) and Skyrad (bottom) methods after the application of the 3-point moving average, for 500 and 400 nm; the regression line is plotted for the two series.

Tables (5)

Tables Icon

Table 1 Boi’s Method. Mean Percentage Dependence of F 0* on k and Its Standard Deviation after the Selection with the Chauvenet Criterion

Tables Icon

Table 2 Boi’s Method. Mean Percentage Dependence of F 0* on k and Its Standard Deviation for Three Cases of τ at 500 nm

Tables Icon

Table 3 Mean Percentage Dependence of F 0 on m, k, and ω and Its Standard Deviation after the Chauvenet Criterion

Tables Icon

Table 4 Skyrad Method. Mean Percentage Dependence of F 0 on k and Its Standard Deviation for 3 Cases of τ at 500 nm

Tables Icon

Table 5 Accuracy of the Retrieval of F 0 with the Improved Langley Method

Equations (9)

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

lnF=lnF0-τμ0,
τμ0=τ0+τμ00μ0-0=τ0+τ1μ0.
lnF=lnF0-τ1-τ0μ0.
lnFλ=lnF0λ-m0τdirextλ-m0τO3+τm,
Rλ, Θ=Lλ, ΘFλm0=Eλ, ΘΔΩλFλm0,
Rλ, Θ=ωλτλPλ, Θ+qΘ=βλ, Θ+qλ, Θ,
lnFλ+m0τO3+τm=lnF0λ-cm0τcalscλ,
lnFλ+m0τO3+τm=lnF0λ-cm0τcalextλ
εC=λ|cλ|-12Nλ1/2.

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