Abstract

A new approach based on a neural-network technique for reduction in the computation time of radiative-transfer models is presented. This approach gives high spectral resolution without significant loss of accuracy. A rigorous radiative-transfer model is used to calculate radiation values at a few selected wavelengths, and a neural-network algorithm replenishes them to a complete spectrum with radiation values at a high spectral resolution. This method is used for the UV and visible spectral ranges. The results document the ability of a neural network to learn this specific task. More than 20,000 UV-index values for all kinds of atmosphere are calculated by both the rigorous radiative-transfer model alone and the model in combination with the neural-network algorithm. The agreement between both approaches is generally of the order of ±1%; the computation time is reduced by a factor of more than 20. The new algorithm can be used for all kinds of high-quality radiative-transfer model to speed up computation time.

© 2001 Optical Society of America

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  1. P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
    [CrossRef] [PubMed]
  2. A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
    [CrossRef]
  3. 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]
  4. M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).
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  6. P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).
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    [CrossRef] [PubMed]
  8. M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
    [CrossRef]
  9. R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).
  10. U. Köhler, W. Vandersee, P. Winkler, “Spektrale und integrale Messungen der UV-B-Strahlung im Vergleich zu Ozonmessungen,” (Deutscher Wetterdienst, Meteorologisches Observatorium, Hohenpeissenberg, Germany, 1995).
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  14. L. J. Landau, J. G. Taylor, eds., Concepts for Neural Networks: a Survey (Springer-Verlag, New York, 1998).
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  15. M. Riedmiller, H. Braun, “A direct adaptive method for faster backpropagation learning: the RPROP algorithm,” ICNN-93, in IEEE International Conference on Neural Networks, San Francisco, Calif., 1993 (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 586–591.
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2000 (1)

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

1998 (2)

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[CrossRef]

1994 (1)

A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
[CrossRef]

1989 (1)

K. M. Hornik, R. W. Stincombe, “Multilayer feed-forward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

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]

1983 (1)

P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).

1980 (1)

Backer, H. D.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Bais, A.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Balis, D.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Blumthaler, M.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Bowker, D. E.

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

Braun, H.

M. Riedmiller, H. Braun, “A direct adaptive method for faster backpropagation learning: the RPROP algorithm,” ICNN-93, in IEEE International Conference on Neural Networks, San Francisco, Calif., 1993 (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 586–591.

Brogniez, C.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Buchwitz, M.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Cabo, X. D.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Chýlek, P.

P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).

Davis, R. E.

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

den Outer, P.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Dlugi, R.

A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
[CrossRef]

Doda, D. D.

Eckert, P.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Engelsen, O.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Erikson, P.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Fenn, R. W.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

Garing, J. S.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

Gillotay, D.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Green, A. E. S.

Heikkilä, A.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Hess, M.

M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[CrossRef]

Hornik, K. M.

K. M. Hornik, R. W. Stincombe, “Multilayer feed-forward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Jones, W. T.

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

Koepke, P.

M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[CrossRef]

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Köhler, U.

U. Köhler, W. Vandersee, P. Winkler, “Spektrale und integrale Messungen der UV-B-Strahlung im Vergleich zu Ozonmessungen,” (Deutscher Wetterdienst, Meteorologisches Observatorium, Hohenpeissenberg, Germany, 1995).

Koskela, T.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Lapeta, B.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Lenoble, J.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Littynska, Z.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Lorente, J.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Martin, T.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Mayer, B.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

McClatchey, R. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

Murray, A. F.

A. F. Murray, Applications of Neural Networks (Kluwer Academic, Boston, Mass., 1995).
[CrossRef]

Myrick, D. L.

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

Nakajima, T.

A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
[CrossRef]

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]

Pfister, G.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Ramaswamy, V.

P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).

Renaud, A.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Riedmiller, M.

M. Riedmiller, H. Braun, “A direct adaptive method for faster backpropagation learning: the RPROP algorithm,” ICNN-93, in IEEE International Conference on Neural Networks, San Francisco, Calif., 1993 (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 586–591.

Ruggaber, A.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
[CrossRef]

Schauberger, G.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Schmalwieser, A.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Schult, I.

M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[CrossRef]

Schwander, H.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Seckmeyer, G.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Seifert, P.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Selby, J. E. A.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

Srivastava, V.

P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).

Stacy, K.

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

Stincombe, R. W.

K. M. Hornik, R. W. Stincombe, “Multilayer feed-forward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[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]

van Hoosier, M.

M. van Hoosier, Naval Research Laboratory Washington, D.C. (personal communication, 1996). The solar spectrum is available at ftp from ftp://susim.nrl.navy.mil/pub/atlas3 .

Van Weele, M.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Vandersee, W.

U. Köhler, W. Vandersee, P. Winkler, “Spektrale und integrale Messungen der UV-B-Strahlung im Vergleich zu Ozonmessungen,” (Deutscher Wetterdienst, Meteorologisches Observatorium, Hohenpeissenberg, Germany, 1995).

Vanicek, K.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Volz, F. E.

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

Walraven, B.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Weber, M.

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Weihs, P.

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

Winkler, P.

U. Köhler, W. Vandersee, P. Winkler, “Spektrale und integrale Messungen der UV-B-Strahlung im Vergleich zu Ozonmessungen,” (Deutscher Wetterdienst, Meteorologisches Observatorium, Hohenpeissenberg, Germany, 1995).

Zurada, J. M.

J. M. Zurada, Introduction to Artificial Neural Network Systems (West Publishing, St. Paul, Minn., 1992).

Appl. Opt. (1)

Bull. Am. Meteorol. Soc. (1)

M. Hess, P. Koepke, I. Schult, “Optical properties of aerosols and clouds: the software package OPAC,” Bull. Am. Meteorol. Soc. 79, 831–844 (1998).
[CrossRef]

J. Atmos. Chem. (1)

A. Ruggaber, R. Dlugi, T. Nakajima, “Modeling radiation quantities and photolysis frequencies in the troposphere,” J. Atmos. Chem. 18, 171–210 (1994).
[CrossRef]

J. Geophys. Res (1)

P. Chýlek, V. Ramaswamy, V. Srivastava, “Albedo of soot-comtaminated snow,” J. Geophys. Res. 88, C15, 10,837–10,843 (1983).

J. Geophys. Res. (1)

M. Van Weele, M. Blumthaler, C. Brogniez, O. Engelsen, D. Gillotay, J. Lenoble, T. Martin, P. den Outer, G. Pfister, A. Ruggaber, B. Walraven, P. Weihs, “1999: From model intercomparison toward benchmark UV spectra for real atmospheric cases,” J. Geophys. Res. 105, D4, 4915–4925 (2000).

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]

Neural Networks (1)

K. M. Hornik, R. W. Stincombe, “Multilayer feed-forward networks are universal approximators,” Neural Networks 2, 359–366 (1989).
[CrossRef]

Photochem. Photobiol. (1)

P. Koepke, A. Bais, D. Balis, M. Buchwitz, H. D. Backer, X. D. Cabo, P. Eckert, P. Erikson, D. Gillotay, A. Heikkilä, T. Koskela, B. Lapeta, Z. Littynska, J. Lorente, B. Mayer, A. Renaud, A. Ruggaber, G. Schauberger, G. Seckmeyer, P. Seifert, A. Schmalwieser, H. Schwander, K. Vanicek, M. Weber, “Comparison of models used for UV index calculations,” Photochem. Photobiol. 67, 657–662 (1998).
[CrossRef] [PubMed]

Other (9)

D. E. Bowker, R. E. Davis, D. L. Myrick, K. Stacy, W. T. Jones, “Spectral reflectances of natural targets for use in remote sensing studies,” (NASA, Hampton, Va., 1985).

L. J. Landau, J. G. Taylor, eds., Concepts for Neural Networks: a Survey (Springer-Verlag, New York, 1998).
[CrossRef]

M. Riedmiller, H. Braun, “A direct adaptive method for faster backpropagation learning: the RPROP algorithm,” ICNN-93, in IEEE International Conference on Neural Networks, San Francisco, Calif., 1993 (Institute of Electrical and Electronic Engineers, New York, 1993), pp. 586–591.

M. van Hoosier, Naval Research Laboratory Washington, D.C. (personal communication, 1996). The solar spectrum is available at ftp from ftp://susim.nrl.navy.mil/pub/atlas3 .

World Meteorological Organisation (WMO), Report of the WMO–WHO Meeting of Experts on Standardization of UV Indices and their Dissemination to the Public, (Les Diablerets, Switzerland, 1997).

R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, “Optical properties of the atmosphere,” Environmental Research Paper 441, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).

U. Köhler, W. Vandersee, P. Winkler, “Spektrale und integrale Messungen der UV-B-Strahlung im Vergleich zu Ozonmessungen,” (Deutscher Wetterdienst, Meteorologisches Observatorium, Hohenpeissenberg, Germany, 1995).

J. M. Zurada, Introduction to Artificial Neural Network Systems (West Publishing, St. Paul, Minn., 1992).

A. F. Murray, Applications of Neural Networks (Kluwer Academic, Boston, Mass., 1995).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Schematic structure of a neural network used for spectral radiative-transfer modeling.

Fig. 2
Fig. 2

Ratio (|$$̂= percentage deviation) between the calculated UV index with and without use of the neural-network algorithm for (a) the training data set and (b) the test data.

Tables (2)

Tables Icon

Table 1 Atmospheric Conditions for 20,394 Spectra of the Training and 20,394 Spectra of the Test Data Set, Aerosol Types Specified According to OPAC Nomenclature

Tables Icon

Table 2 Errors in Percent within Specific Wavelength Intervals of the Developed Algorithm for the Training and Test Data Set

Metrics