Abstract

We present a methodology for correcting the global UV spectral measurements of a Brewer MKIII spectroradiometer for the error introduced by the deviation of the angular response of the instrument from the ideal response. This methodology is applicable also to other Brewer spectroradiometers that are currently in operation. The various stages of the methodology are described in detail, together with the uncertainties involved in each stage. Finally global spectral UV measurements with and without the application of the correction are compared with collocated measurements of another spectroradiometer and with model calculations, demonstrating the efficiency of the method. Depending on wavelength and on the aerosol loading, the cosine correction factors range from 2% to 7%. The uncertainties involved in the calculation of these correction factors were found to be relatively small, ranging from ∼0.2% to ∼2%.

© 1998 Optical Society of America

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References

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  1. G. Seckmeyer, G. Bernhard, “Cosine error correction of spectral UV irradiances,” in Atmospheric Radiation, K. H. Stamnes, ed., Proc. SPIE2049, 140–151 (1993).
    [CrossRef]
  2. U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
    [CrossRef]
  3. A. F. Bais, “Spectrometers: operational errors and uncertainties,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 163–173.
  4. M. Blumthaler, A. F. Bais, “Cosine corrections of global sky measurements,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana October 1996. Final Report, B. Kjeldstad, B. Johnsen, T. Koskela, eds. (Finnish Meteorological Institute, Helsinki, 1997), pp. 161–172.
  5. K. Leszczynski, “Material and methods,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana from 24 October to 5 November 1993. Final Report, T. Koskela, ed. (Finnish Meteorological Institute, Helsinki, 1994), pp. 27–49.
  6. B. G. Gardiner, “Spectroradiometer calibration methods and techniques,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 119–132.
    [CrossRef]
  7. M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
    [CrossRef]
  8. K. H. Stamnes, S. C. Tsay, W. Wiscombe, K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media,” Appl. Opt. 27, 2502–2509 (1988).
    [CrossRef] [PubMed]
  9. A. F. Bais, “Absolute spectral measurements of direct solar ultraviolet irradiance with a Brewer spectrophotometer,” Appl. Opt. 21, 5199–5204 (1997).
    [CrossRef]
  10. S. Madronich, “UV radiation in the natural and perturbed atmosphere,” in Environmental Effects of Ultraviolet Radiation, M. Tevini, ed. (Lewis, Boca Raton, Fla., 1993), pp. 17–69.
  11. D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.
  12. J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
    [CrossRef]

1997 (2)

U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
[CrossRef]

A. F. Bais, “Absolute spectral measurements of direct solar ultraviolet irradiance with a Brewer spectrophotometer,” Appl. Opt. 21, 5199–5204 (1997).
[CrossRef]

1996 (2)

J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
[CrossRef]

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

1988 (1)

Ambach, W.

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
[CrossRef]

Bais, A. F.

A. F. Bais, “Absolute spectral measurements of direct solar ultraviolet irradiance with a Brewer spectrophotometer,” Appl. Opt. 21, 5199–5204 (1997).
[CrossRef]

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

A. F. Bais, “Spectrometers: operational errors and uncertainties,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 163–173.

M. Blumthaler, A. F. Bais, “Cosine corrections of global sky measurements,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana October 1996. Final Report, B. Kjeldstad, B. Johnsen, T. Koskela, eds. (Finnish Meteorological Institute, Helsinki, 1997), pp. 161–172.

Balis, D. S.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

Bernhard, G.

G. Seckmeyer, G. Bernhard, “Cosine error correction of spectral UV irradiances,” in Atmospheric Radiation, K. H. Stamnes, ed., Proc. SPIE2049, 140–151 (1993).
[CrossRef]

Blumthaler, M.

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
[CrossRef]

M. Blumthaler, A. F. Bais, “Cosine corrections of global sky measurements,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana October 1996. Final Report, B. Kjeldstad, B. Johnsen, T. Koskela, eds. (Finnish Meteorological Institute, Helsinki, 1997), pp. 161–172.

Feister, U.

U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
[CrossRef]

Gardiner, B. G.

B. G. Gardiner, “Spectroradiometer calibration methods and techniques,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 119–132.
[CrossRef]

Gericke, K.

U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
[CrossRef]

Grewe, R.

U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
[CrossRef]

Groebner, J.

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
[CrossRef]

Huber, M.

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

Jayaweera, K.

Leszczynski, K.

K. Leszczynski, “Material and methods,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana from 24 October to 5 November 1993. Final Report, T. Koskela, ed. (Finnish Meteorological Institute, Helsinki, 1994), pp. 27–49.

Madronich, S.

S. Madronich, “UV radiation in the natural and perturbed atmosphere,” in Environmental Effects of Ultraviolet Radiation, M. Tevini, ed. (Lewis, Boca Raton, Fla., 1993), pp. 17–69.

Marenco, F.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

Papayannis, A.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

Santacesaria, V.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

Seckmeyer, G.

G. Seckmeyer, G. Bernhard, “Cosine error correction of spectral UV irradiances,” in Atmospheric Radiation, K. H. Stamnes, ed., Proc. SPIE2049, 140–151 (1993).
[CrossRef]

Stamnes, K. H.

Tsay, S. C.

Wiscombe, W.

Zerefos, C. S.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

Appl. Opt. (2)

Geophys. Res. Lett. (2)

M. Blumthaler, J. Groebner, M. Huber, W. Ambach, “Measuring spectral and spatial variations of UVB and UVA sky radiance,” Geophys. Res. Lett. 23, 547–550 (1996).
[CrossRef]

J. Groebner, M. Blumthaler, W. Ambach, “Experimental investigation of spectral global irradiance measurement errors due to a non ideal cosine response,” Geophys. Res. Lett. 23, 2493–2496 (1996).
[CrossRef]

Solar Energy (1)

U. Feister, R. Grewe, K. Gericke, “A method for correction of cosine errors in measurements of spectral UV irradiance,” Solar Energy 60, 313–332 (1997).
[CrossRef]

Other (7)

A. F. Bais, “Spectrometers: operational errors and uncertainties,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 163–173.

M. Blumthaler, A. F. Bais, “Cosine corrections of global sky measurements,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana October 1996. Final Report, B. Kjeldstad, B. Johnsen, T. Koskela, eds. (Finnish Meteorological Institute, Helsinki, 1997), pp. 161–172.

K. Leszczynski, “Material and methods,” in The Nordic Intercomparison of Ultraviolet and Total Ozone Instruments at Izana from 24 October to 5 November 1993. Final Report, T. Koskela, ed. (Finnish Meteorological Institute, Helsinki, 1994), pp. 27–49.

B. G. Gardiner, “Spectroradiometer calibration methods and techniques,” in Solar Ultraviolet Radiation Modeling, Measurements and Effects, C. S. Zerefos, A. F. Bais, eds., Vol. 52 of NATO ASI Series I, Global Environmental Change (Springer-Verlag, Berlin, 1997), pp. 119–132.
[CrossRef]

S. Madronich, “UV radiation in the natural and perturbed atmosphere,” in Environmental Effects of Ultraviolet Radiation, M. Tevini, ed. (Lewis, Boca Raton, Fla., 1993), pp. 17–69.

D. S. Balis, A. F. Bais, A. Papayannis, F. Marenco, V. Santacesaria, C. S. Zerefos, “Comparison of model calculations with spectral solar UV measurements,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, R. D. Bojkov, G. Visconti, eds. (Edigralital F.P.A., Italy, 1997), pp. 837–840.

G. Seckmeyer, G. Bernhard, “Cosine error correction of spectral UV irradiances,” in Atmospheric Radiation, K. H. Stamnes, ed., Proc. SPIE2049, 140–151 (1993).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Cosine error of the Brewer MKIII 086 spectroradiometer as measured in the laboratory. The error bars represent the uncertainty of repeatable measurements.

Fig. 2
Fig. 2

Spectral ratios of direct-to-global solar irradiance for various SZA’s and aerosol optical depths. The measurements were obtained by the Brewer spectroradiometer at Thessaloniki and Tenerife.

Fig. 3
Fig. 3

Spectral ratio of direct-to-global solar irradiance as measured by the Brewer spectroradiometer at various SZA’s at a site with low aerosol content. Dashed curves correspond to polynomial fits of the data taken in steps of 10 nm.

Fig. 4
Fig. 4

Diurnal variation of the ratio between global solar UV irradiances measured by the Brewer spectroradiometer at 330 nm and calculated by the model before and after the application of the angular response correction.

Fig. 5
Fig. 5

Diurnal variation of the ratio between global solar UV irradiances measured by the Brewer spectroradiometer at 330 nm and calculated by the model before and after the application of the angular response correction.

Equations (5)

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

f g = F g / F g = F d + F b / F g ,
f d = F d / F d ,     f b = F b / F b ,
f g = F d f d + F b f b / F g .
f g = 1 - f bg f d + f bg f b .
fd =   I d θ ,   φ f b   cos   θ   sin   θ   d θ d φ   I d θ ,   φ cos   θ   sin   θ   d θ d φ ,

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