Abstract

A general method for calibrating Sun photometers that relaxes the constraints on atmospheric conditions is described. Instead of requiring constant extinction conditions the method requires only that the relative aerosol size distribution remains constant during observations over a range of air masses during a morning or afternoon. Provided that the relative aerosol extinction component [ma(t)δ (t, λ0)] can be obtained at wavelength λ0, the calibration at wavelength channel λ can be calculated with simple least-squares techniques. A variant of the method in which a Sun photometer is used to provide [ma(t)δ(t, λ0)] is detailed and is verified with both model atmospheres and Sun-photometer data for 1988-1991 from Cape Grim, Tasmania (41° S). The method produces calibration data having sample variances more than 5 times smaller than Langley method calibration results.

© 1994 Optical Society of America

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References

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  1. M. Tanaka, T. Nakajima, M. Shiobara, “Calibration of a sunphotometer by simultaneous measurements of direct-solar circumsolar radiations,” Appl. Opt. 25, 1170–1180 (1986).
    [CrossRef] [PubMed]
  2. B. W. Forgan, “Determination of aerosol optical depth at a sea level station—investigations at Cape Grim BAPS,” CGBAPS Tech. Rep. 5 (Bureau of Meteorology, Smithton, Australia, 1987).
  3. B. W. Forgan, “Sun photometer calibration by the ratio-angley technique,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 22–26.
  4. B. W. Forgan, “A technique for calibrating Sun photometers using solar aureole measurements,” in Baseline Atmospheric Program Australia 1987, B. W. Forgan, G. P. Ayers, eds. (Bureau of Meteorology, Melbourne, Australia, 1989), pp. 15–20.
  5. V. Soufflet, C. Devaux, D. Tanré, “A modified Langley plot method for measuring the spectral aerosol opticak thickness and its daily variations,” Appl. Opt. 31, 2154–2162 (1992).
    [CrossRef] [PubMed]
  6. B. W. Forgan, “Bias in a solar constant determination by the Langley method due to structured atmospheric aerosol: comment,” Appl. Opt. 27, 2546–2548 (1988).
    [CrossRef] [PubMed]
  7. K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” Adv. Geophys. 10, 101–261 (1964).
  8. Qiu Jinhuan, “An approximate expression of the sky radiance in almucantar and its application,” Adv. Atmos. Sci. 3, 1–9 (1986).
    [CrossRef]
  9. C. Frohlich, “WRC/PMOD sunphotometer,” Report of Second WMO Expert Meeting on Turbidity Measurement (World Meteorological Organization, Geneva, 1978), pp. 8–9.
  10. P. Walford, “Data management,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 86–89.

1992

1988

1986

1964

K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” Adv. Geophys. 10, 101–261 (1964).

Bullrich, K.

K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” Adv. Geophys. 10, 101–261 (1964).

Devaux, C.

Forgan, B. W.

B. W. Forgan, “Bias in a solar constant determination by the Langley method due to structured atmospheric aerosol: comment,” Appl. Opt. 27, 2546–2548 (1988).
[CrossRef] [PubMed]

B. W. Forgan, “A technique for calibrating Sun photometers using solar aureole measurements,” in Baseline Atmospheric Program Australia 1987, B. W. Forgan, G. P. Ayers, eds. (Bureau of Meteorology, Melbourne, Australia, 1989), pp. 15–20.

B. W. Forgan, “Sun photometer calibration by the ratio-angley technique,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 22–26.

B. W. Forgan, “Determination of aerosol optical depth at a sea level station—investigations at Cape Grim BAPS,” CGBAPS Tech. Rep. 5 (Bureau of Meteorology, Smithton, Australia, 1987).

Frohlich, C.

C. Frohlich, “WRC/PMOD sunphotometer,” Report of Second WMO Expert Meeting on Turbidity Measurement (World Meteorological Organization, Geneva, 1978), pp. 8–9.

Jinhuan, Qiu

Qiu Jinhuan, “An approximate expression of the sky radiance in almucantar and its application,” Adv. Atmos. Sci. 3, 1–9 (1986).
[CrossRef]

Nakajima, T.

Shiobara, M.

Soufflet, V.

Tanaka, M.

Tanré, D.

Walford, P.

P. Walford, “Data management,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 86–89.

Adv. Atmos. Sci.

Qiu Jinhuan, “An approximate expression of the sky radiance in almucantar and its application,” Adv. Atmos. Sci. 3, 1–9 (1986).
[CrossRef]

Adv. Geophys.

K. Bullrich, “Scattered radiation in the atmosphere and the natural aerosol,” Adv. Geophys. 10, 101–261 (1964).

Appl. Opt.

Other

C. Frohlich, “WRC/PMOD sunphotometer,” Report of Second WMO Expert Meeting on Turbidity Measurement (World Meteorological Organization, Geneva, 1978), pp. 8–9.

P. Walford, “Data management,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 86–89.

B. W. Forgan, “Determination of aerosol optical depth at a sea level station—investigations at Cape Grim BAPS,” CGBAPS Tech. Rep. 5 (Bureau of Meteorology, Smithton, Australia, 1987).

B. W. Forgan, “Sun photometer calibration by the ratio-angley technique,” in Baseline Atmospheric Program Australia 1986, B. W. Forgan, P. J. Fraser, eds. (Bureau of Meteorology, Melbourne, Australia, 1988), pp. 22–26.

B. W. Forgan, “A technique for calibrating Sun photometers using solar aureole measurements,” in Baseline Atmospheric Program Australia 1987, B. W. Forgan, G. P. Ayers, eds. (Bureau of Meteorology, Melbourne, Australia, 1989), pp. 15–20.

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Figures (4)

Fig. 1
Fig. 1

Langley calibration data for the CGBAPS 868-nm channel for the period January 1988–June 1991. The solid curve is the assumed representation of the 868-nm calibration for the general method.

Fig. 2
Fig. 2

General method results for wavelength channels of 368, 500, and 778 nm for the period January 1988–June 1991. The data have been scaled so that the mean calibration for the period is unity. The solid curves represent the reference calibrations produced with the ratio–Langley method.

Fig. 3
Fig. 3

Percentage deviations from the reference 778-nm calibration curve for the (upper) general and (lower) Langley method results for the same data series between January 1988–June 1991.

Fig. 4
Fig. 4

Percentage deviations from the reference 500-nm calibration curve for the (upper) general and (lower) Langley method results for the same data series between January 1988–June 1991.

Tables (6)

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Table 1 General Method Results Expressed as Deviation from the Correct Calibrationa

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Table 2 Langley Method Results Expressed as a Deviation from the Correct Calibrationa

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Table 3 Comparison of Calibration Biases (ΔV0i) and Estimates of the Standard Deviation (σ) from the 154 Samples of Langley and General Method Results for the Period January 1989-June 1991 with the CGBAPS Sun Photometer

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Table 4 Summary Statistics for the 92 Sample Series of α01 Derived for Each Wavelength Paira

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Table 5 Mean Aerosol Optical Depth Derived from a Combination of the General and the Ratio–Langley Results for the January 1989–June 1991 Period at CGBAPS

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Table 6 Extinction Model Parameters for the 29 Cases Used in the Testing of the General and the Langley Methods

Equations (23)

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N ( t ) / ln r = A ( t ) f ( r ) ,
δ ( t , λ ) = π A ( t ) Q ext ( r , λ ) r 2 f ( r ) d ln r ,
δ ( t , λ ) = δ ( t 0 , λ ) A ( t ) / A ( t 0 ) .
δ ( t , λ 1 ) = δ ( t 0 , λ 1 ) A ( t ) / A ( t 0 ) ,
δ ( t , λ 0 ) = δ ( t 0 , λ 0 ) A ( t ) / A ( t 0 ) ,
δ ( t , λ 1 ) / δ ( t 0 , λ 1 ) = δ ( t , λ 0 ) / δ ( t 0 , λ 0 ) = A ( t ) / A ( t 0 )
δ ( t , λ 1 ) / δ ( t 0 , λ 0 ) = δ ( t 0 , λ 1 ) / δ ( t 0 , λ 0 ) = constant = Ψ 01 .
m a ( t ) δ ( t , λ i ) = ln V 0 i [ ln V i ( t ) + m m ( t ) δ m ( t , λ i ) + m g ( t ) δ g ( t , λ i ) ] ,
Ψ 01 [ m a ( t ) δ ( t , λ 0 ) ] ln V 01 = [ ln V 1 ( t ) + m m ( t ) δ m ( t , λ 1 ) + m g ( t ) δ g ( t , λ 1 ) ] .
A x ( t ) + B = y ( t ) ,
δ ( t , λ i ) = β 01 t λ i α 01
Ψ 01 = ( λ 0 / λ 1 ) α 01 .
( d Ω P a ϖ ) m a ( t ) δ ( t , λ 0 ) = [ d Ω m m ( t ) P m δ m ] + L 0 ( t ) / V 0 ( t ) ,
[ d Ω m m ( t ) P m δ m ] L 0 ( t ) / V 0 ( t ) ,
A = Ψ 01 [ d Ω P a ( λ 0 ) ϖ ] 1 ,
A = [ d Ω P a ( λ 0 ) ϖ ] 1 .
Ψ 01 ɛ .
[ m a ( t ) δ ( t , λ 0 ) ] versus [ ln V 1 ( t ) + m m ( t ) δ m ( t , λ 1 ) + m g ( t ) δ g ( t , λ 1 ) ]
Δ δ m ( λ 1 ) m a ( t 1 ) m a ( t n ) [ δ ( t n , λ 0 ) δ ( t 1 , λ 0 ) ] / [ m a ( t n ) δ ( t n , λ 0 ) m a ( t 1 ) δ ( t 1 , λ 0 ) ] ,
δ ( t , λ i ) = β ( t ) ( λ i / 1000 ) α ( t ) ,
δ i = m 1
δ ( t , λ ) = β ( t ) ( λ / 1000 ) α ( t ) ,
t = T / 450 ,

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