Abstract

Ultraviolet light was measured at four channels (305, 311, 318, and 332 nm) with a precision filter radiometer (UV-PFR) at Arosa, Switzerland (46.78°, 9.68°, 1850 m above sea level), within the instrument trial phase of a cooperative venture of the Swiss Meteorological Institute (MeteoSwiss) and the Physikalisch-Meteorologisches Observatorium Davos/World Radiation Center. We retrieved ozone-column density data from these direct relative irradiance measurements by adapting the Dobson standard method for all possible single-difference wavelength pairs and one double-difference pair (305/311 and 305/318) under conditions of cloud-free sky and of thin clouds (cloud optical depth <2.5 at 500 nm). All UV-PFR retrievals exhibited excellent agreement with those of collocated Dobson and Brewer spectrophotometers for data obtained during two months in 1999. Combining the results of the error analysis and the findings of the validation, we propose to retrieve ozone-column density by using the 305/311 single difference pair and the double-difference pair. Furthermore, combining both retrievals by building the ratio of ozone-column density yields information that is relevant to data quality control. Estimates of the 305/311 pair agree with measurements by the Dobson and Brewer instruments within 1% for both the mean and the standard deviation of the differences. For the double pair these values are in a range up to 1.6%. However, this pair is less sensitive to model errors. The retrieval performance is also consistent with satellite-based data from the Earth Probe Total Ozone Mapping Spectrometer (EP-TOMS) and the Global Ozone Monitoring Experiment instrument (GOME).

© 2001 Optical Society of America

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2000 (2)

J. Slusser, J. Gibson, D. Bigelow, D. Kolinski, P. Disterhoft, K. Lantz, A. Beaubien, “Langley method of calibrating UV filter radiometers,” J. Geophys. Res. 105, 4841–4850 (2000).
[CrossRef]

D. S. Bigelow, J. R. Slusser, “Establishing the stability of multifilter UV rotating shadow-band radiometers,” J. Geophys. Res. 105, 4829–4832 (2000).

1999 (3)

J. Slusser, J. Gibson, D. Bigelow, D. Kolinski, W. Mou, G. Koenig, A. Beaubien, “Comparison of column ozone retrievals by use of an UV multifilter rotating shadow-band radiometer with those from Brewer and Dobson spectrophotometers,” Appl. Opt. 38, 1543–1551 (1999).
[CrossRef]

J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
[CrossRef]

S. Solomon, “Stratospheric ozone depletion: a review of concepts and history,” Rev. Geophys. 37, 275–316 (1999).
[CrossRef]

1998 (4)

J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

D. S. Bigelow, J. R. Slusser, A. F. Beaubien, J. H. Gibson, “The USDA ultraviolet radiation monitoring program,” Bull. Am. Meteorol. Soc. 79, 601–615 (1998).
[CrossRef]

B. Schmid, P. R. Spyak, S. F. Biggar, C. Wehrli, J. Sekler, T. Ingold, C. Mätzler, N. Kämpfer, “Evaluation of the applicability of solar and lamp radiometric calibrations of a precision Sun photometer operating between 300 and 1025 nm,” Appl. Opt. 37, 3923–3941 (1998).
[CrossRef]

M. Eisinger, J. P. Burrows, “Tropospheric sulfur dioxide observed by the ERS-2 GOME instrument,” Geophys. Res. Lett. 25, 4177–4180 (1998).
[CrossRef]

1997 (1)

C. Cordoba, A. Perez, I. Aguirre de Carcer, F. Jaque, D. Henriques, F. Carvalho, “Comparison of total ozone measurements from a differential optical absorption filter instrument and a Dobson spectrophotometer,” Int. J. Remote Sens. 18, 3473–3478 (1997).
[CrossRef]

1996 (2)

1995 (4)

B. Schmid, C. Wehrli, “Comparison of sun photometer calibration by Langley technique and standard lamp,” Appl. Opt. 34, 4500–4512 (1995).
[CrossRef] [PubMed]

A. Bucholtz, “Rayleigh-scattering calculations for the terrestrial atmosphere,” Appl. Opt. 34, 2765–2773 (1995).
[CrossRef] [PubMed]

J. Stähelin, H. Schill, B. Högger, P. Viatte, G. Levrat, A. Gamma, “Total ozone observation by Sun photometry at Arosa, Switzerland,” Opt. Eng. 34, 1977–1986 (1995).
[CrossRef]

J. Malicet, D. Daumont, J. Charbonnier, C. Parisse, A. Chakir, J. Brion, “Ozone UV spectroscopy. II. Absorption cross-sections and temperature dependence,” J. Atmos. Chem. 21, 263–273 (1995).
[CrossRef]

1994 (2)

B. W. Forgan, “General method for calibrating Sun photometers,” Appl. Opt. 33, 4841–4850 (1994).
[CrossRef] [PubMed]

M. Van Roozendael, M. De Mazière, P. C. Simon, “Ground-based visible measurements at the Jungfraujoch Station since 1990,” J. Quantum Spectrosc. Radiat. Transfer 52, 231–240 (1994).
[CrossRef]

1989 (2)

F. Kasten, A. T. Young, “Revised optical air mass tables and approximation formula,” Appl. Opt. 28, 4735–4738 (1989).
[CrossRef] [PubMed]

M. Cacciani, A. Di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 at temperatures 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

1988 (1)

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “Absolute absorption cross section measurements of ozone in the wavelength region 238–335 nm and the temperature dependence,” Planet. Space Sci. 36, 395–398 (1988).
[CrossRef]

1986 (1)

L. T. Molina, M. J. Molina, “Absolute absorption cross sections of ozone in the 185- to 350-nm wavelength range,” J. Geophys. Res. 91, 14,501–14,508 (1986).
[CrossRef]

1985 (1)

J. C. Farman, G. Gardiner, J. D. Shanklin, “Large losses of total ozone in Antarctica reveal seasonal ClOx/NOx interaction,” Nature (London) 315, 207–210 (1985).
[CrossRef]

1977 (2)

R. E. Basher, W. A. Matthews, “Problems in the use of interference filters for spectrophotometric determination of total ozone,” J. Appl. Meteorol. 16, 795–802 (1977).
[CrossRef]

R. E. Basher, “The effect of bandwidth on filter instrument total ozone accuracy,” J. Appl. Meteorol. 16, 803–811 (1977).
[CrossRef]

1975 (1)

R. A. Sutherland, R. D. McPeters, G. B. Findley, A. E. S. Green, “Sun photometry and spectral radiometry at wavelengths less than 360 nm,” J. Atmos. Sci. 32, 427–436 (1975).
[CrossRef]

1974 (2)

W. A. Matthews, R. E. Basher, G. J. Fraser, “Filter ozone spectrophotometer,” Pure Appl. Geophys. 112, 931–938 (1974).
[CrossRef]

M. J. Molina, F. S. Rowland, “Stratospheric sink for chlorofluoromethanes, chlorine atom catalysed destruction of ozone,” Nature 249, 810–812 (1974).
[CrossRef]

1971 (2)

H. Johnston, “Reduction of stratospheric ozone by nitrogen oxide catalysts from supersonic transport exhaust,” Science 173, 517–522 (1971).
[CrossRef] [PubMed]

P. J. Crutzen, “Ozone production rates in an oxygen–hydrogen–nitrogen oxide atmosphere,” J. Geophys. Res. 76, 7311–7327 (1971).
[CrossRef]

1969 (2)

R. D. Bojkov, “Differences in Dobson spectrophotometer and filter ozonometer measurements of total ozone,” J. Appl. Meteorol. 8, 362–368 (1969).
[CrossRef]

J. Vanier, D. I. Wardle, “The effects of spectral resolution on total ozone measurements,” Q. J. R. Meteorol. Soc. 95, 395–399 (1969).
[CrossRef]

1965 (1)

F. Kasten, “A new table and approximation formula for relative optical air mass,” Arch. Meteorol. Geophys. Bioklimatol. Ser. B 14, 206–223 (1965).
[CrossRef]

1957 (1)

G. M. B. Dobson, “Observers’ handbook for the ozone spectrometer,” Ann. Int. Geophys. Year 5, 90–113 (1957).

1929 (1)

A. K. Ångström, “On the atmospheric transmission of Sun radiation and on dust in the air,” Geogr. Ann. 11, 156–166 (1929).
[CrossRef]

1926 (1)

G. M. B. Dobson, D. N. Harrison, “Measurement of the amount of ozone in the Earth’s atmosphere and its relation to other geophysical conditions,” Proc. R. Soc. London Ser. A 110, 660–693 (1926).
[CrossRef]

Abreu, L. W.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Acharaya, P.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Aguirre de Carcer, I.

C. Cordoba, A. Perez, I. Aguirre de Carcer, F. Jaque, D. Henriques, F. Carvalho, “Comparison of total ozone measurements from a differential optical absorption filter instrument and a Dobson spectrophotometer,” Int. J. Remote Sens. 18, 3473–3478 (1997).
[CrossRef]

Amoruso, A.

M. Cacciani, A. Di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 at temperatures 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Anderson, G. P.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Ångström, A. K.

A. K. Ångström, “On the atmospheric transmission of Sun radiation and on dust in the air,” Geogr. Ann. 11, 156–166 (1929).
[CrossRef]

Bader, J.

J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

Basher, R. E.

R. E. Basher, W. A. Matthews, “Problems in the use of interference filters for spectrophotometric determination of total ozone,” J. Appl. Meteorol. 16, 795–802 (1977).
[CrossRef]

R. E. Basher, “The effect of bandwidth on filter instrument total ozone accuracy,” J. Appl. Meteorol. 16, 803–811 (1977).
[CrossRef]

W. A. Matthews, R. E. Basher, G. J. Fraser, “Filter ozone spectrophotometer,” Pure Appl. Geophys. 112, 931–938 (1974).
[CrossRef]

Bass, A. M.

A. M. Bass, R. J. Paur, “The ultraviolet cross-sections of ozone. Measurements in atmospheric ozone,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 606–616.

Beach, R. A.

Beaubien, A.

Beaubien, A. F.

D. S. Bigelow, J. R. Slusser, A. F. Beaubien, J. H. Gibson, “The USDA ultraviolet radiation monitoring program,” Bull. Am. Meteorol. Soc. 79, 601–615 (1998).
[CrossRef]

Berk, A.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Bernstein, L. S.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Bhartia, P. K.

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

Bigelow, D.

Bigelow, D. S.

D. S. Bigelow, J. R. Slusser, “Establishing the stability of multifilter UV rotating shadow-band radiometers,” J. Geophys. Res. 105, 4829–4832 (2000).

D. S. Bigelow, J. R. Slusser, A. F. Beaubien, J. H. Gibson, “The USDA ultraviolet radiation monitoring program,” Bull. Am. Meteorol. Soc. 79, 601–615 (1998).
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Biggar, S. F.

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R. D. Bojkov, “Differences in Dobson spectrophotometer and filter ozonometer measurements of total ozone,” J. Appl. Meteorol. 8, 362–368 (1969).
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Brion, J.

J. Malicet, D. Daumont, J. Charbonnier, C. Parisse, A. Chakir, J. Brion, “Ozone UV spectroscopy. II. Absorption cross-sections and temperature dependence,” J. Atmos. Chem. 21, 263–273 (1995).
[CrossRef]

Bucholtz, A.

Bugnion, V.

J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

Burrows, J. P.

J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
[CrossRef]

M. Eisinger, J. P. Burrows, “Tropospheric sulfur dioxide observed by the ERS-2 GOME instrument,” Geophys. Res. Lett. 25, 4177–4180 (1998).
[CrossRef]

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Byerly, W.

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

Cacciani, M.

M. Cacciani, A. Di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 at temperatures 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
[CrossRef]

Callies, J.

A. Hahne, A. Lefebvre, J. Callies, B. Christensen, “GOME—The development of a new instrument,” ESA Bull. 83 (European Space Agency Directorate for Observation of the Earth and Its Environment, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1995).

Carvalho, F.

C. Cordoba, A. Perez, I. Aguirre de Carcer, F. Jaque, D. Henriques, F. Carvalho, “Comparison of total ozone measurements from a differential optical absorption filter instrument and a Dobson spectrophotometer,” Int. J. Remote Sens. 18, 3473–3478 (1997).
[CrossRef]

Cebula, R. P.

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

Chakir, A.

J. Malicet, D. Daumont, J. Charbonnier, C. Parisse, A. Chakir, J. Brion, “Ozone UV spectroscopy. II. Absorption cross-sections and temperature dependence,” J. Atmos. Chem. 21, 263–273 (1995).
[CrossRef]

Charbonnier, J.

J. Malicet, D. Daumont, J. Charbonnier, C. Parisse, A. Chakir, J. Brion, “Ozone UV spectroscopy. II. Absorption cross-sections and temperature dependence,” J. Atmos. Chem. 21, 263–273 (1995).
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F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Christensen, B.

A. Hahne, A. Lefebvre, J. Callies, B. Christensen, “GOME—The development of a new instrument,” ESA Bull. 83 (European Space Agency Directorate for Observation of the Earth and Its Environment, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1995).

Clough, S. A.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Cordoba, C.

C. Cordoba, A. Perez, I. Aguirre de Carcer, F. Jaque, D. Henriques, F. Carvalho, “Comparison of total ozone measurements from a differential optical absorption filter instrument and a Dobson spectrophotometer,” Int. J. Remote Sens. 18, 3473–3478 (1997).
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Daumont, D.

J. Malicet, D. Daumont, J. Charbonnier, C. Parisse, A. Chakir, J. Brion, “Ozone UV spectroscopy. II. Absorption cross-sections and temperature dependence,” J. Atmos. Chem. 21, 263–273 (1995).
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M. Van Roozendael, M. De Mazière, P. C. Simon, “Ground-based visible measurements at the Jungfraujoch Station since 1990,” J. Quantum Spectrosc. Radiat. Transfer 52, 231–240 (1994).
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Dehn, A.

J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
[CrossRef]

Deters, B.

J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
[CrossRef]

Di Sarra, A.

M. Cacciani, A. Di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 at temperatures 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
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Disterhoft, P.

J. Slusser, J. Gibson, D. Bigelow, D. Kolinski, P. Disterhoft, K. Lantz, A. Beaubien, “Langley method of calibrating UV filter radiometers,” J. Geophys. Res. 105, 4841–4850 (2000).
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G. M. B. Dobson, “Observers’ handbook for the ozone spectrometer,” Ann. Int. Geophys. Year 5, 90–113 (1957).

G. M. B. Dobson, D. N. Harrison, “Measurement of the amount of ozone in the Earth’s atmosphere and its relation to other geophysical conditions,” Proc. R. Soc. London Ser. A 110, 660–693 (1926).
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Eisinger, M.

M. Eisinger, J. P. Burrows, “Tropospheric sulfur dioxide observed by the ERS-2 GOME instrument,” Geophys. Res. Lett. 25, 4177–4180 (1998).
[CrossRef]

Elansky, N. F.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Elokhov, A. S.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Esmond, J. R.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “Absolute absorption cross section measurements of ozone in the wavelength region 238–335 nm and the temperature dependence,” Planet. Space Sci. 36, 395–398 (1988).
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J. B. Kerr, C. T. McElroy, D. I. Wardle, R. A. Olafson, W. F. Evans, “The automated Brewer spectrophotometer,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 396–401.

Farman, J. C.

J. C. Farman, G. Gardiner, J. D. Shanklin, “Large losses of total ozone in Antarctica reveal seasonal ClOx/NOx interaction,” Nature (London) 315, 207–210 (1985).
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Findley, G. B.

R. A. Sutherland, R. D. McPeters, G. B. Findley, A. E. S. Green, “Sun photometry and spectral radiometry at wavelengths less than 360 nm,” J. Atmos. Sci. 32, 427–436 (1975).
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Fiocco, G.

M. Cacciani, A. Di Sarra, G. Fiocco, A. Amoruso, “Absolute determination of the cross sections of ozone in the wavelength region 339–355 at temperatures 220–293 K,” J. Geophys. Res. 94, 8485–8490 (1989).
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Flynn, L. E.

Forgan, B. W.

Fraser, G. J.

W. A. Matthews, R. E. Basher, G. J. Fraser, “Filter ozone spectrophotometer,” Pure Appl. Geophys. 112, 931–938 (1974).
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Freeman, D. E.

K. Yoshino, D. E. Freeman, J. R. Esmond, W. H. Parkinson, “Absolute absorption cross section measurements of ozone in the wavelength region 238–335 nm and the temperature dependence,” Planet. Space Sci. 36, 395–398 (1988).
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Fröhlich, C.

R. Philipona, R. A. Heimo, C. Fröhlich, C. Marty, A. Ohmura, C. Wehrli, “The Swiss atmospheric radiation monitoring program: CHARM,” presented at International Radiation Symposium IRS96, Fairbanks, Alaska, 19–24 August 1996.

A. Heimo, R. Philipona, C. Fröhlich, C. Marty, A. Ohmura, “The Swiss atmospheric radiation monitoring network CHARM,” in Proceedings of the World Meteorological Organization Technical Conference on Meteorological and Environmental Instruments and Methods of Observation (TECO-98), Casablanca, Morocco, 13–15 May, WMO/TD-877 (World Meteorological Organization, Geneva, 1998), pp. 291–294.

Gallery, W. O.

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

Gamma, A.

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Gardiner, G.

J. C. Farman, G. Gardiner, J. D. Shanklin, “Large losses of total ozone in Antarctica reveal seasonal ClOx/NOx interaction,” Nature (London) 315, 207–210 (1985).
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Gerard, P.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Gibson, J.

Gibson, J. H.

D. S. Bigelow, J. R. Slusser, A. F. Beaubien, J. H. Gibson, “The USDA ultraviolet radiation monitoring program,” Bull. Am. Meteorol. Soc. 79, 601–615 (1998).
[CrossRef]

Giroud, M.

J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

Goody, R. M.

R. M. Goody, Y. L. Yung, Atmospheric Radiation, Theoretical Basis, 2nd ed. (Oxford U. Press, New York, 1989).

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H. H. Gränicher, Messung beendet–was nun?: Einführung und Nachschlagewerk für die Planung und Auswertung von Messungen (vdf Hochschulverlag AG an der ETH Zürich, Zürich, and Teubner, Stuttgart, 1994).

Granville, J.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Green, A. E. S.

R. A. Sutherland, R. D. McPeters, G. B. Findley, A. E. S. Green, “Sun photometry and spectral radiometry at wavelengths less than 360 nm,” J. Atmos. Sci. 32, 427–436 (1975).
[CrossRef]

Gruzdev, A. M.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Gu, X.-Y.

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

Hahne, A.

A. Hahne, A. Lefebvre, J. Callies, B. Christensen, “GOME—The development of a new instrument,” ESA Bull. 83 (European Space Agency Directorate for Observation of the Earth and Its Environment, European Space Research and Technology Centre, Noordwijk, The Netherlands, 1995).

Harrison, D. N.

G. M. B. Dobson, D. N. Harrison, “Measurement of the amount of ozone in the Earth’s atmosphere and its relation to other geophysical conditions,” Proc. R. Soc. London Ser. A 110, 660–693 (1926).
[CrossRef]

Heimo, A.

A. Heimo, R. Philipona, C. Fröhlich, C. Marty, A. Ohmura, “The Swiss atmospheric radiation monitoring network CHARM,” in Proceedings of the World Meteorological Organization Technical Conference on Meteorological and Environmental Instruments and Methods of Observation (TECO-98), Casablanca, Morocco, 13–15 May, WMO/TD-877 (World Meteorological Organization, Geneva, 1998), pp. 291–294.

Heimo, R. A.

R. Philipona, R. A. Heimo, C. Fröhlich, C. Marty, A. Ohmura, C. Wehrli, “The Swiss atmospheric radiation monitoring program: CHARM,” presented at International Radiation Symposium IRS96, Fairbanks, Alaska, 19–24 August 1996.

Henriques, D.

C. Cordoba, A. Perez, I. Aguirre de Carcer, F. Jaque, D. Henriques, F. Carvalho, “Comparison of total ozone measurements from a differential optical absorption filter instrument and a Dobson spectrophotometer,” Int. J. Remote Sens. 18, 3473–3478 (1997).
[CrossRef]

Herman, J. R.

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

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J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
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J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

J. Stähelin, H. Schill, B. Högger, P. Viatte, G. Levrat, A. Gamma, “Total ozone observation by Sun photometry at Arosa, Switzerland,” Opt. Eng. 34, 1977–1986 (1995).
[CrossRef]

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Ionov, D. V.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

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R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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R. Philipona, R. A. Heimo, C. Fröhlich, C. Marty, A. Ohmura, C. Wehrli, “The Swiss atmospheric radiation monitoring program: CHARM,” presented at International Radiation Symposium IRS96, Fairbanks, Alaska, 19–24 August 1996.

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J. B. Kerr, C. T. McElroy, D. I. Wardle, R. A. Olafson, W. F. Evans, “The automated Brewer spectrophotometer,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 396–401.

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A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

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A. Heimo, R. Philipona, C. Fröhlich, C. Marty, A. Ohmura, “The Swiss atmospheric radiation monitoring network CHARM,” in Proceedings of the World Meteorological Organization Technical Conference on Meteorological and Environmental Instruments and Methods of Observation (TECO-98), Casablanca, Morocco, 13–15 May, WMO/TD-877 (World Meteorological Organization, Geneva, 1998), pp. 291–294.

R. Philipona, R. A. Heimo, C. Fröhlich, C. Marty, A. Ohmura, C. Wehrli, “The Swiss atmospheric radiation monitoring program: CHARM,” presented at International Radiation Symposium IRS96, Fairbanks, Alaska, 19–24 August 1996.

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J. B. Kerr, C. T. McElroy, D. I. Wardle, R. A. Olafson, W. F. Evans, “The automated Brewer spectrophotometer,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 396–401.

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J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

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J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

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A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

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R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

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J. Stähelin, A. Renaud, J. Bader, R. McPeters, P. Viatte, B. Högger, V. Bugnion, M. Giroud, H. Schill, “Total ozone series at Arosa (Switzerland): homogenization and data comparison,” J. Geophys. Res. 34, 1977–1986 (1998).

J. Stähelin, H. Schill, B. Högger, P. Viatte, G. Levrat, A. Gamma, “Total ozone observation by Sun photometry at Arosa, Switzerland,” Opt. Eng. 34, 1977–1986 (1995).
[CrossRef]

Voigt, S.

J. P. Burrows, A. Richter, A. Dehn, B. Deters, S. Himmelmann, S. Voigt, J. Orphal, “Atmospheric remote-sensing reference data from GOME. 2. Temperature-dependent absorption cross sections of O3 in the 231–794 nm range,” J. Quant. Spectrosc. Radiat. Transfer 61, 509–517 (1999).
[CrossRef]

von Bergen, A.

A. von Bergen, W. Thomas, “GOME Data Processor Update Report for GDP 0-to-1 Version 2.0 and GDP 1-to-2 Version 2.7,” (Deutsches Zentrum für Luft- und Raumfahrt e.V., Deutsches Fernerkundungsdatenzentrum, Oberpfaffenhofen, Germany, 1999).

Wagner, T.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Wardle, D. I.

J. Vanier, D. I. Wardle, “The effects of spectral resolution on total ozone measurements,” Q. J. R. Meteorol. Soc. 95, 395–399 (1969).
[CrossRef]

J. B. Kerr, C. T. McElroy, D. I. Wardle, R. A. Olafson, W. F. Evans, “The automated Brewer spectrophotometer,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 396–401.

Wehrli, C.

Wellemeyer, C. G.

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, C. G. Wellemeyer, C. J. Seftor, G. Jaross, O. Torres, L. Moy, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Tech. Publ. 1998-206895 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

Wenig, M.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

Wittrock, F.

J.-C. Lambert, P. Peeters, A. Richter, N. A. J. Schutgens, Y. M. Timofeyev, T. Wagner, J. P. Burrows, N. F. Elansky, A. S. Elokhov, P. Gerard, J. Granville, A. M. Gruzdev, D. V. Ionov, V. V. Ionov, R. B. A. Koelemeijer, A. Ladstätter-Weissenmayer, C. Leue, D. Loyola, U. Platt, O. V. Postylyakov, A. M. Shalamiansky, P. C. Simon, P. Stammes, W. Thomas, M. Van Roozendael, M. Wenig, F. Wittrock, “ERS-2 GOME Data Products Delta Characterisation Report 1999: Validation Report for GOME Data Processor Upgrade: Level-0-to-1 Version 2.0 and Level-1-to-2 Version 2.7,” J.-C. Lambert, P. Skarlas, eds. (ESA/ESRIN, Frascati, Italy, 1999).

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J. B. Kerr, C. T. McElroy, D. I. Wardle, R. A. Olafson, W. F. Evans, “The automated Brewer spectrophotometer,” in Atmospheric Ozone, Proceedings of the Quadrennial Ozone Symposium, Halkidiki, Greece, C. S. Zerefos, A. Ghazi, eds. (Reidel, Hingham, Mass., 1985), pp. 396–401.

R. Spurr, “GOME Level 1-to-2 Algorithms Description,” ER-TN-DLR-GO-0025, Iss./Rev. 2/A (Deutsches Zentrum für Luft- und Raumfahrt e.V., Deutsches Fernerkundungsdatenzentrum, Oberpfaffenhofen, Germany, 1996).

A. von Bergen, W. Thomas, “GOME Data Processor Update Report for GDP 0-to-1 Version 2.0 and GDP 1-to-2 Version 2.7,” (Deutsches Zentrum für Luft- und Raumfahrt e.V., Deutsches Fernerkundungsdatenzentrum, Oberpfaffenhofen, Germany, 1999).

F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharaya, L. S. Rothmann, J. E. A. Selby, W. O. Gallery, S. A. Clough, “The Modtran 2/3 report and LOWTRAN 7 model,” (Phillips Laboratory, Hanscom Air Force Base, Mass., 1996).

R. D. McPeters, P. K. Bhartia, A. J. Krueger, J. R. Herman, B. M. Schlesinger, C. G. Wellemeyer, C. J. Seftor, G. Jaross, S. L. Taylor, T. Swissler, O. Torres, G. Labow, W. Byerly, R. P. Cebula, “Nimbus7 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1384 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1996).

J. R. Herman, P. K. Bhartia, A. J. Krueger, R. D. McPeters, C. G. Wellemeyer, C. J. Seftor, G. Jaross, B. M. Schlesinger, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, X.-Y. Gu, “Meteor3 Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publication 1393 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Maryland, 1996).

A. J. Krueger, P. K. Bhartia, R. D. McPeters, J. R. Herman, C. G. Wellemeyer, G. Jaross, C. J. Seftor, O. Torres, G. Labow, W. Byerly, S. L. Taylor, T. Swissler, R. P. Cebula, “ADEOS Total Ozone Mapping Spectrometer (TOMS) data products user’s guide,” NASA Ref. Publ. 1998-206857 (Goddard Space Flight Center, National Aeronautics and Space Administration, Greenbelt, Md., 1998).

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Figures (9)

Fig. 1
Fig. 1

Zenith transmittance of ozone absorption in the UV through the MLS (Ω = 331.7 DU) computed with modtran 3.7. Resolution is set to 5 cm-1 (≈0.05 nm, depending on wavelength). Superimposed are the spectral responses of the four UV-PFR channels.

Fig. 2
Fig. 2

Scatterplot of ozone-column density retrievals of the UV-PFR 305/311 and the Brewer72, as measured in Arosa (1850 m asl) from mid-July 1999 to mid-September 1999. UV-PFR data were averaged over 20-min intervals.

Fig. 3
Fig. 3

Mean (top) and standard deviation (bottom) of ozone-column density difference, UV-PFR minus Dobson or Brewer. Results for each UV-PFR pair are averaged and are given for all data and for a reduced data set when no clouds obscured the Sun.

Fig. 4
Fig. 4

Variation of daily means of ozone-column density as measured at Arosa (1850 m asl) with the Dobson101 spectrometer and the UV-PFR with the single-difference pair 305/311 and the double-difference pair. In addition, satellite-based EP-TOMS and GOME overpass data are plotted for the selected dates.

Fig. 5
Fig. 5

Time series of ozone-column density (top) and nonmolecular zenith optical depth (NMOD) at 500 nm (bottom) measured at Arosa (1850 m asl) for 18 July 1999. The ozone data were derived from the UV-PFR instrument (305/311, 318/332, and double pair), the Brewer72 spectrometer, and the Dobson101 spectrometer. Until 11:00 UT clear sky (no clouds) was observed; i.e., NMOD equals the aerosol optical depth.

Fig. 6
Fig. 6

Relative variation of the ozone-column density above Arosa from temperature and ozone profile weighted absorption coefficients for modtran simulations from radiosonde data. Negative data yield an underestimation of ozone-column density if the fixed MLS absorption coefficients are used.

Fig. 7
Fig. 7

modtran simulation of the aerosol term in the ozone retrievals for the single-difference pair and the double-difference pair, from different built-in aerosol profiles along a vertical path to space (0° SZA). Neglecting the aerosol term leads to an overestimation (underestimation) for the single pairs (double pair).

Fig. 8
Fig. 8

Distribution of aerosol optical depth measured at 500 nm for Arosa during the period from mid-July to mid-September 1999. The AOD values of the modtran simulations for the tropospheric case (×) and the rural case with visibility of 23 km (+) are superimposed. stdev, Standard deviation.

Fig. 9
Fig. 9

Uncertainty p of Ω that is due to errors in V 0 for the single-difference and the double-difference retrieval of the UV-PFR versus air mass.

Tables (4)

Tables Icon

Table 1 Manufacturer Specifications of Central Wavelength and Bandwidth for the Nominal UV-PFR Channels of the Instrument Installed at Arosa

Tables Icon

Table 2 Error Contribution of Ozone Retrievals in the UVa for Ω = 300 DU and SZA = 25° for Cloud-Free Sky and Cirrus Clouds with a Climatological Mean for NO 2 b

Tables Icon

Table 3 Total Ozone Statistics of Measurements Performed at Arosa (1850 m asl) of UV-PFR, Dobson, and Brewer Data from Mid-July 1999 to Mid-September 1999a

Tables Icon

Table 4 Total Ozone Statistics of Measurements from UV-PFR Data Obtained at Arosa (1850 m asl) and Satellite Overpass Data for Arosaa

Equations (10)

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

Vλi=R-2V0λiexp-m1α1λiΩ-mRτRλi-maτaλi-m2τ2λi-m3τ3λi, i=1,  , 4,
α1λ=-logT1λΩMLS,
m1=r0+hr0+h2-r0+r2 sin2 θ1/2,
Ω=N-τ˜RmR-τ˜2m2-τ˜3m3-τ˜amaα˜m1,
N=lnV0/V0-lnV/V,
α˜=α1-α1,  τ˜R=τR-τR,  τ˜2=τ2-τ2, τ˜3=τ3-τ3,  τ˜a=τa-τa,
Ω=NA-NBm1α˜A-α˜B-mRτR˜,A-τR˜,Bm1α˜A-α˜B-maτã,A-τã,Bm1α˜A-α˜B,
X=Ω305311Ωdp,
ΔΩi=-Xiαi-αimiα1-α1m1-Xiαi-αiα1-α1,
ΔΩ=pj2+qj2.

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