Abstract

The New Zealand Meteorological Service has used a Robertson–Berger meter (RB meter) to monitor solar UV-B radiation for the past decade. The radiometric properties of the instrument have been analyzed and agree with the standard values published by Berger. A detailed theoretical treatment of the RB meter response that fully accounts for its cosine response is presented. Field measurements made with the RB meter and with a double monochromator spectral radiometer were used to validate the theoretical model and to derive a calibration for the RB meter. Only cloud-free data were considered so that the downward radiation field at the surface could be modeled as the sum of direct solar and isotropic diffuse components. The imperfect cosine responses of both instruments were modeled. A RB meter count was found to equate to 0.25 ± 0.02 Jm−2 referenced to 300-nm radiation at vertical incidence.

© 1993 Optical Society of America

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References

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  1. United Nations Environmental Program, “Environmental Effects Panel Report; pursuant to Article 6 of the Montreal Protocol on substances that deplete the ozone layer,” (United Nations Environmental Programme, Nairobi, 1989).
  2. G. W. Paltridge, I. J. Barton, “Erythemal ultraviolet radiation distribution over Australia—the calculations, detailed results and input data,” Div. Atmos. Phys. Tech. Paper 33 (CSIRO, Canberra, 1978).
  3. D. S. Berger, F. Urbach, “A climatology of sunburning ultraviolet radiation,” Photochem. Photobiol. 35, 187–192 (1982).
    [CrossRef] [PubMed]
  4. S. E. Nichol, R. E. Basher, “Analysis of three years’ measurements of erythemal ultraviolet radiation at Invercargill, New Zealand,” New Zealand Meteorological Service Scientific Rep. 21 (New Zealand Meteorological Service, P.O. Box 722, Wellington, New Zealand, 1986).
  5. J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
    [CrossRef] [PubMed]
  6. D. S. Berger, “The sunburning ultraviolet meter: design and performance,” Photochem. Photobiol. 24, 587–593 (1976).
    [CrossRef] [PubMed]
  7. B. L. Diffey, “Possible errors involved in the dosimetry of solar UV-B radiation,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 75–86.
  8. M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.
  9. A. F. McKinlay, B. L. Diffey, “A reference action spectrum for ultraviolet induced erythema in human skin,” CIE J. 6, 17–22 (1987).
  10. J. J. DeLuisi, J. M. Harris, “A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit,” Atmos. Environ. 17, 751–758 (1983).
    [CrossRef]
  11. J. J. DeLuisi, J. M. Harris, “Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson-Berger meter and a double monochromator,” NOAA Tech. Memo. ERL-ARL-99 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1981).
  12. R. L. McKenzie, P. V. Johnston, A. Bittar, J. D. Hamlin, “Solar ultraviolet spectroradiometry in New Zealand: instrumentation and sample results from 1990,” Appl. Opt. 31, 6501–6509 (1992).
    [CrossRef] [PubMed]
  13. J. V. Dave, P. M. Furukawa, “Scattered radiation in the ozone absorption bands at selected levels of a terrestrial, Rayleigh atmosphere,” Meteorol Monogr. 7 (1966).
  14. A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
    [CrossRef]
  15. A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
    [CrossRef]
  16. J. J. DeLuisi, National Oceanic and Atmospheric Administration, Boulder, Colo. 80303-3328 (personal communication).
  17. X. Zheng, R. E. Basher, “A statistical analysis of Invercargill UV-B data,” (submitted to J. Theo. Ap. Clim.).
  18. J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)
  19. “Sunscreen testing (UV.B),” CIE Tech. Commun. Rep. 90 (Commission Internationale de l’Éclairage, Paris, 1987).
  20. W. W. Coblentz, R. Stair, “Data on the spectral erythemic reaction of untanned human skin to ultraviolet radiation,” J. Res. Natl. Bur. Stand. 12, 13–14 (1934).
    [CrossRef]
  21. I. J. Barton, “The Australian WV-B monitoring network,” Div. Atmos. Phys. Tech. Paper 46, (CSIRO, Canberra, 1983).

1992 (1)

1988 (1)

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

1987 (1)

A. F. McKinlay, B. L. Diffey, “A reference action spectrum for ultraviolet induced erythema in human skin,” CIE J. 6, 17–22 (1987).

1983 (1)

J. J. DeLuisi, J. M. Harris, “A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit,” Atmos. Environ. 17, 751–758 (1983).
[CrossRef]

1982 (1)

D. S. Berger, F. Urbach, “A climatology of sunburning ultraviolet radiation,” Photochem. Photobiol. 35, 187–192 (1982).
[CrossRef] [PubMed]

1980 (1)

A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
[CrossRef]

1977 (1)

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

1976 (1)

D. S. Berger, “The sunburning ultraviolet meter: design and performance,” Photochem. Photobiol. 24, 587–593 (1976).
[CrossRef] [PubMed]

1974 (1)

A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
[CrossRef]

1966 (1)

J. V. Dave, P. M. Furukawa, “Scattered radiation in the ozone absorption bands at selected levels of a terrestrial, Rayleigh atmosphere,” Meteorol Monogr. 7 (1966).

1934 (1)

W. W. Coblentz, R. Stair, “Data on the spectral erythemic reaction of untanned human skin to ultraviolet radiation,” J. Res. Natl. Bur. Stand. 12, 13–14 (1934).
[CrossRef]

Barton, I. J.

G. W. Paltridge, I. J. Barton, “Erythemal ultraviolet radiation distribution over Australia—the calculations, detailed results and input data,” Div. Atmos. Phys. Tech. Paper 33 (CSIRO, Canberra, 1978).

I. J. Barton, “The Australian WV-B monitoring network,” Div. Atmos. Phys. Tech. Paper 46, (CSIRO, Canberra, 1983).

Basher, R. E.

X. Zheng, R. E. Basher, “A statistical analysis of Invercargill UV-B data,” (submitted to J. Theo. Ap. Clim.).

S. E. Nichol, R. E. Basher, “Analysis of three years’ measurements of erythemal ultraviolet radiation at Invercargill, New Zealand,” New Zealand Meteorological Service Scientific Rep. 21 (New Zealand Meteorological Service, P.O. Box 722, Wellington, New Zealand, 1986).

Berger, D.

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

Berger, D. S.

D. S. Berger, F. Urbach, “A climatology of sunburning ultraviolet radiation,” Photochem. Photobiol. 35, 187–192 (1982).
[CrossRef] [PubMed]

D. S. Berger, “The sunburning ultraviolet meter: design and performance,” Photochem. Photobiol. 24, 587–593 (1976).
[CrossRef] [PubMed]

Bittar, A.

Borkowski, J.

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

Caldwell, M. M.

M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.

Camp, L. B.

M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.

Chai, A.

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

Coblentz, W. W.

W. W. Coblentz, R. Stair, “Data on the spectral erythemic reaction of untanned human skin to ultraviolet radiation,” J. Res. Natl. Bur. Stand. 12, 13–14 (1934).
[CrossRef]

Cotton, G.

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

Cross, K. R.

A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
[CrossRef]

Dave, J. V.

J. V. Dave, P. M. Furukawa, “Scattered radiation in the ozone absorption bands at selected levels of a terrestrial, Rayleigh atmosphere,” Meteorol Monogr. 7 (1966).

DeLuisi, J. J.

J. J. DeLuisi, J. M. Harris, “A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit,” Atmos. Environ. 17, 751–758 (1983).
[CrossRef]

J. J. DeLuisi, J. M. Harris, “Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson-Berger meter and a double monochromator,” NOAA Tech. Memo. ERL-ARL-99 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1981).

J. J. DeLuisi, National Oceanic and Atmospheric Administration, Boulder, Colo. 80303-3328 (personal communication).

Diffey, B. L.

A. F. McKinlay, B. L. Diffey, “A reference action spectrum for ultraviolet induced erythema in human skin,” CIE J. 6, 17–22 (1987).

B. L. Diffey, “Possible errors involved in the dosimetry of solar UV-B radiation,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 75–86.

Fears, T.

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

Flint, S. D.

M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.

Furukawa, P. M.

J. V. Dave, P. M. Furukawa, “Scattered radiation in the ozone absorption bands at selected levels of a terrestrial, Rayleigh atmosphere,” Meteorol Monogr. 7 (1966).

Green, A. E. S.

A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
[CrossRef]

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
[CrossRef]

Hamlin, J. D.

Harris, J. M.

J. J. DeLuisi, J. M. Harris, “A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit,” Atmos. Environ. 17, 751–758 (1983).
[CrossRef]

J. J. DeLuisi, J. M. Harris, “Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson-Berger meter and a double monochromator,” NOAA Tech. Memo. ERL-ARL-99 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1981).

Johnston, P. V.

McKenzie, R. L.

McKinlay, A. F.

A. F. McKinlay, B. L. Diffey, “A reference action spectrum for ultraviolet induced erythema in human skin,” CIE J. 6, 17–22 (1987).

Mo, T.

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

Nichol, S. E.

S. E. Nichol, R. E. Basher, “Analysis of three years’ measurements of erythemal ultraviolet radiation at Invercargill, New Zealand,” New Zealand Meteorological Service Scientific Rep. 21 (New Zealand Meteorological Service, P.O. Box 722, Wellington, New Zealand, 1986).

Paltridge, G. W.

G. W. Paltridge, I. J. Barton, “Erythemal ultraviolet radiation distribution over Australia—the calculations, detailed results and input data,” Div. Atmos. Phys. Tech. Paper 33 (CSIRO, Canberra, 1978).

Sawada, T.

A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
[CrossRef]

Scotto, J.

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

Shettle, E. P.

A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
[CrossRef]

Smith, L. A.

A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
[CrossRef]

Stair, R.

W. W. Coblentz, R. Stair, “Data on the spectral erythemic reaction of untanned human skin to ultraviolet radiation,” J. Res. Natl. Bur. Stand. 12, 13–14 (1934).
[CrossRef]

Urbach, F.

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

D. S. Berger, F. Urbach, “A climatology of sunburning ultraviolet radiation,” Photochem. Photobiol. 35, 187–192 (1982).
[CrossRef] [PubMed]

Warner, C. W.

M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.

Zheng, X.

X. Zheng, R. E. Basher, “A statistical analysis of Invercargill UV-B data,” (submitted to J. Theo. Ap. Clim.).

Acta Geophys. Pol. (1)

J. Borkowski, A. Chai, T. Mo, A. E. S. Green, “Cloud effects on middle ultraviolet global radiation,” Acta Geophys. Pol. 25, 287–301 (1977)

Appl. Opt. (1)

Atmos. Environ. (1)

J. J. DeLuisi, J. M. Harris, “A determination of the absolute radiant energy of a Robertson–Berger meter sunburn unit,” Atmos. Environ. 17, 751–758 (1983).
[CrossRef]

CIE J. (1)

A. F. McKinlay, B. L. Diffey, “A reference action spectrum for ultraviolet induced erythema in human skin,” CIE J. 6, 17–22 (1987).

J. Res. Natl. Bur. Stand. (1)

W. W. Coblentz, R. Stair, “Data on the spectral erythemic reaction of untanned human skin to ultraviolet radiation,” J. Res. Natl. Bur. Stand. 12, 13–14 (1934).
[CrossRef]

Meteorol Monogr. (1)

J. V. Dave, P. M. Furukawa, “Scattered radiation in the ozone absorption bands at selected levels of a terrestrial, Rayleigh atmosphere,” Meteorol Monogr. 7 (1966).

Photochem. Photobiol. (4)

A. E. S. Green, T. Sawada, E. P. Shettle, “The middle ultraviolet reaching the ground,” Photochem. Photobiol. 19, 251–259 (1974).
[CrossRef]

A. E. S. Green, K. R. Cross, L. A. Smith, “Improved analytic characterization of ultraviolet skylight,” Photochem. Photobiol. 31, 59–65 (1980).
[CrossRef]

D. S. Berger, “The sunburning ultraviolet meter: design and performance,” Photochem. Photobiol. 24, 587–593 (1976).
[CrossRef] [PubMed]

D. S. Berger, F. Urbach, “A climatology of sunburning ultraviolet radiation,” Photochem. Photobiol. 35, 187–192 (1982).
[CrossRef] [PubMed]

Science (1)

J. Scotto, G. Cotton, F. Urbach, D. Berger, T. Fears, “Biologically effective ultraviolet radiation: surface measurements in the United States, 1974 to 1985,” Science 239, 762–764 (1988).
[CrossRef] [PubMed]

Other (10)

B. L. Diffey, “Possible errors involved in the dosimetry of solar UV-B radiation,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 75–86.

M. M. Caldwell, L. B. Camp, C. W. Warner, S. D. Flint, “Action spectra and their role in assessing biological consequences of solar UV-B radiation change,” in Stratospheric Ozone Reduction, Solar Ultraviolet Radiation and Plant Life, R. C. Worrest, M. M. Caldwell, eds., Vol. G8 of the NATO Advanced Science Institutes Series (Springer-Verlag, Berlin, 1983), pp. 87–111.

S. E. Nichol, R. E. Basher, “Analysis of three years’ measurements of erythemal ultraviolet radiation at Invercargill, New Zealand,” New Zealand Meteorological Service Scientific Rep. 21 (New Zealand Meteorological Service, P.O. Box 722, Wellington, New Zealand, 1986).

United Nations Environmental Program, “Environmental Effects Panel Report; pursuant to Article 6 of the Montreal Protocol on substances that deplete the ozone layer,” (United Nations Environmental Programme, Nairobi, 1989).

G. W. Paltridge, I. J. Barton, “Erythemal ultraviolet radiation distribution over Australia—the calculations, detailed results and input data,” Div. Atmos. Phys. Tech. Paper 33 (CSIRO, Canberra, 1978).

J. J. DeLuisi, National Oceanic and Atmospheric Administration, Boulder, Colo. 80303-3328 (personal communication).

X. Zheng, R. E. Basher, “A statistical analysis of Invercargill UV-B data,” (submitted to J. Theo. Ap. Clim.).

J. J. DeLuisi, J. M. Harris, “Characteristics of ultraviolet radiation in the human erythema band measured with a Robertson-Berger meter and a double monochromator,” NOAA Tech. Memo. ERL-ARL-99 (National Oceanic and Atmospheric Administration, Boulder, Colo., 1981).

“Sunscreen testing (UV.B),” CIE Tech. Commun. Rep. 90 (Commission Internationale de l’Éclairage, Paris, 1987).

I. J. Barton, “The Australian WV-B monitoring network,” Div. Atmos. Phys. Tech. Paper 46, (CSIRO, Canberra, 1983).

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Figures (7)

Fig. 1
Fig. 1

(a) Global solar spectral irradiance measured on 1 December 1990 at Lauder, New Zealand. The measurement was made with the spectral radiometer, discussed later in the text, for cloud-free conditions when the solar zenith angle was 23.4°. The dotted curve shows the CIE curve representing the relative erythemal response normalized to unity at 300 nm. (b) The convolution of the solar spectral irradiance and the erythemal response.

Fig. 2
Fig. 2

Relative spectral response of the New Zealand Meteorological Science (NZMS) Invercargill RB meter compared with the RB meter response published by Berger and the CIE erythemal curve (all curves normalized to unity at 300 nm).

Fig. 3
Fig. 3

Cosine response of the NZMS Invercargill RB meter compared with the RB meter cosine response published by Berger.

Fig. 4
Fig. 4

Ratio of the direct to diffuse insolation measured by the RB meter as a function of angle.

Fig. 5
Fig. 5

RB meter data recorded at Lauder, New Zealand, 19–27 March 1991. The day numbers are marked at 0000 h New Zealand standard time (NZST).

Fig. 6
Fig. 6

Cloud-free integrated spectral radiometer data weighted by the RB meter response and cosine-corrected versus RB meter counts interpolated to the time of spectral measurement.

Fig. 7
Fig. 7

Integrated spectral radiometer data weighted by the RB meter response versus RB meter counts interpolated to the time of spectral measurement. The radiation field has been assumed isotropic for all the study data.

Tables (1)

Tables Icon

Table 1 Atmospheric Parameters Monitored during the Experimenta

Equations (11)

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Q ery = T 1 T 2 λ 1 λ 2 E ( λ , T ) ɛ ( λ ) d λ d T .
C ( θ ) = A ( θ ) cos θ ,
D = 1 π 0 2 π 0 π / 2 C ( θ ) cos θ sin θ d θ d ϕ ,
N = λ 1 λ 2 0 2 π 0 π / 2 R ( λ , θ , ϕ ) L ( λ , θ , ϕ ) sin θ d θ d ϕ d λ ,
R ( λ , θ , ϕ ) = K A ( θ ) r ( λ ) ,
N = K λ 1 λ 2 r ( λ ) 0 2 π 0 π / 2 C ( θ ) L ( λ , θ , ϕ ) × cos θ sin θ d θ d ϕ d λ .
N = K λ 1 λ 2 r ( λ ) 0 2 π 0 π / 2 C ( θ ) × [ L dif ( λ , θ , ϕ ) + L dir ( λ , θ , ϕ ) ] cos θ sin θ d θ d ϕ d λ ,
L dir ( λ , θ , ϕ ) = π L dir ( λ , θ , ϕ ) δ ( θ - θ 0 ) δ ( ϕ - ϕ 0 )
N = K [ D λ 1 λ 2 r ( λ ) E dif ( λ ) d λ + C ( θ 0 ) × cos θ 0 λ 1 λ 2 r ( λ ) E dir ( λ ) d λ ] ,
value in MED = ( 1.0 - 0.00095 θ 0 - 0.00011 θ 0 2 ) × value in SU ,
MED enregy per SU = 355 ( 1.0 + 0.0041 θ 0 - 0.00015 θ 0 2 ) J m - 2 .

Metrics